initial commit of ebook 35092HEADmain

90 files changed, 51298 insertions, 0 deletions

diff --git a/.gitattributes b/.gitattributes
new file mode 100644
index 0000000..6833f05
--- /dev/null
+++ b/.gitattributes
@@ -0,0 +1,3 @@
+* text=auto
+*.txt text
+*.md text
diff --git a/35092-8.txt b/35092-8.txt
new file mode 100644
index 0000000..37fbc7b
--- /dev/null
+++ b/35092-8.txt
@@ -0,0 +1,16330 @@
+The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
+Volume 9, Slice 2, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2
+       "Ehud" to "Electroscope"
+
+Author: Various
+
+Release Date: January 27, 2011 [EBook #35092]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 9 SL 2 ***
+
+
+
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+
+
+
+
+
+
+
+Transcriber's notes:
+
+(1) Numbers following letters (without space) like C2 were originally
+      printed in subscript. Letter subscripts are preceded by an
+      underscore, like C_n.
+
+(2) Characters following a carat (^) were printed in superscript.
+
+(3) Side-notes were relocated to function as titles of their respective
+      paragraphs.
+
+(4) Macrons and breves above letters and dots below letters were not
+      inserted.
+
+(5) dP stands for the partial-derivative symbol, or curled 'd'.
+
+(6) [oo] stands for the infinity symbol, and [int] for the integral
+      symbol.
+
+(7) The following typographical errors have been corrected:
+
+    ARTICLE EKATERINOSLAV: "Nearly 40,000 persons find occupation in
+      factories, the most important being iron-works and agricultural
+      machinery works, though there are also tobacco ... " 'important'
+      amended from 'imporant'.
+
+    ARTICLE ELASTICITY: "The limits of perfect elasticity as regards
+      change of shape, on the other hand, are very low, if they exist at
+      all, for glasses and other hard, brittle solids; but a class of
+      metals including copper, brass, steel, and platinum are very
+      perfectly elastic as regards distortion, provided that the
+      distortion is not too great." Missing 'and' after 'steel'.
+
+    ARTICLE ELASTICITY: "The parts of the radii vectors within the
+     sphere ..." 'vectors' amended from 'vectores'.
+
+    ARTICLE ELBE: "Its total length is 725 m., of which 190 are in
+      Bohemia, 77 in the kingdom of Saxony, and 350 in Prussia, the
+      remaining 108 being in Hamburg and other states of Germany." 'Its'
+      amended from 'it'.
+
+    ARTICLE ELBE: "Finally, in 1870, 1,000,000 thalers were paid to
+      Mecklenburg and 85,000 thalers to Anhalt, which thereupon abandoned
+      all claims to levy tolls upon the Elbe shipping, and thus
+      navigation on the river became at last entirely free. 'Anhalt'
+      amended from 'Anhal'.
+
+    ARTICLE ELBE: "... after driving back at Lobositz the Austrian
+      forces which were hastening to their assistance; but only nine
+      months later he lost his reputation for "invincibility" by his
+      crushing defeat at Kolin ..." 'assistance' amended from
+      'asistance'.
+
+    ARTICLE ELECTRICITY: "De la Rive reviews the subject in his large
+      Treatise on Electricity and Magnetism, vol. ii. ch. iii. The writer
+      made a contribution to the discussion in 1874 ..." 'Magnetism'
+      amended from 'Magnestism'.
+
+    ARTICLE ELECTRICITY SUPPLY: "... or by means of overhead wires
+      within restricted areas, but the limitations proved uneconomical
+      and the installations were for the most part merged into larger
+      undertakings sanctioned by parliamentary powers." 'limitations'
+      amended from 'limitatons'.
+
+    ARTICLE ELECTROKINETICS: "A vector can most conveniently be
+      represented by a symbol such as a + ib, where a stands for any
+      length of a units measured horizontally and b for a length b units
+      measured vertically, and the symbol i is a sign of perpendicularity
+      ..." 'symbol' amended from 'smybol'.
+
+    ARTICLE ELECTROSCOPE: "The collapse of the gold-leaf is observed
+      through an aperture in the case by a microscope, and the time taken
+      by the gold-leaf to fall over a certain distance is proportional to
+      the ionizing current, that is, to the intensity of the
+      radioactivity of the substance. 'microscope' amended from
+      'miscroscope'.
+
+
+
+
+          ENCYCLOPAEDIA BRITANNICA
+
+  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
+           AND GENERAL INFORMATION
+
+              ELEVENTH EDITION
+
+
+            VOLUME IX, SLICE II
+
+           Ehud to Electroscope
+
+
+
+
+ARTICLES IN THIS SLICE:
+
+
+  EHUD                                ELBERFELD
+  EIBENSTOCK                          ELBEUF
+  EICHBERG, JULIUS                    ELBING
+  EICHENDORFF, JOSEPH, FREIHERR VON   ELBOW
+  EICHHORN, JOHANN GOTTFRIED          ELBURZ
+  EICHHORN, KARL FRIEDRICH            ELCHE
+  EICHSTÄTT                           ELCHINGEN
+  EICHWALD, KARL EDUARD VON           ELDAD BEN MA[H.]LI
+  EIDER (river of Prussia)            ELDER (ruler or officer)
+  EIDER (duck)                        ELDER (shrubs and trees)
+  EIFEL                               ELDON, JOHN SCOTT
+  EIFFEL TOWER                        EL DORADO
+  EILDON HILLS                        ELDUAYEN, JOSÉ DE
+  EILENBURG                           ELEANOR OF AQUITAINE
+  EINBECK                             ELEATIC SCHOOL
+  EINDHOVEN                           ELECAMPANE
+  EINHARD                             ELECTION (politics)
+  EINHORN, DAVID                      ELECTION (English law choice)
+  EINSIEDELN                          ELECTORAL COMMISSION
+  EISENACH                            ELECTORS
+  EISENBERG                           ELECTRA
+  EISENERZ                            ELECTRICAL MACHINE
+  EISLEBEN                            ELECTRIC EEL
+  EISTEDDFOD                          ELECTRICITY
+  EJECTMENT                           ELECTRICITY SUPPLY
+  EKATERINBURG                        ELECTRIC WAVES
+  EKATERINODAR                        ELECTROCHEMISTRY
+  EKATERINOSLAV (Russian government)  ELECTROCUTION
+  EKATERINOSLAV (Russian town)        ELECTROKINETICS
+  EKHOF, KONRAD                       ELECTROLIER
+  EKRON                               ELECTROLYSIS
+  ELABUGA                             ELECTROMAGNETISM
+  ELAM                                ELECTROMETALLURGY
+  ELAND                               ELECTROMETER
+  ELASTICITY                          ELECTRON
+  ELATERITE                           ELECTROPHORUS
+  ELATERIUM                           ELECTROPLATING
+  ELBA                                ELECTROSCOPE
+  ELBE
+
+
+
+EHUD, in the Bible, a "judge" who delivered Israel from the Moabites
+(Judg. iii. 12-30). He was sent from Ephraim to bear tribute to Eglon
+king of Moab, who had crossed over the Jordan and seized the district
+around Jericho. Being, like the Benjamites, left-handed (cf. xx. 16), he
+was able to conceal a dagger and strike down the king before his
+intentions were suspected. He locked Eglon in his chamber and escaped.
+The men from Mt Ephraim collected under his leadership and by seizing
+the fords of the Jordan were able to cut off the Moabites. He is called
+the son of Gera a Benjamite, but since both Ehud and Gera are tribal
+names (2 Sam. xvi. 5, 1 Chron. viii. 3, 5 sq.) it has been thought that
+this notice is not genuine. The tribe of Benjamin rarely appears in the
+old history of the Hebrews before the time of Saul. See further
+BENJAMIN; JUDGES.
+
+
+
+
+EIBENSTOCK, a town of Germany, in the kingdom of Saxony, near the Mulde,
+on the borders of Bohemia, 17 m. by rail S.S.E. of Zwickau. Pop. (1905)
+7460. It is a principal seat of the tambour embroidery which was
+introduced in 1775 by Clara Angermann. It possesses chemical and tobacco
+manufactories, and tin and iron works. It has also a large cattle
+market. Eibenstock, together with Schwarzenberg, was acquired by
+purchase in 1533 by Saxony and was granted municipal rights in the
+following year.
+
+
+
+
+EICHBERG, JULIUS (1824-1893), German musical composer, was born at
+Düsseldorf on the 13th of June 1824. When he was nineteen he entered the
+Brussels Conservatoire, where he took first prizes for violin-playing
+and composition. For eleven years he occupied the post of professor in
+the Conservatoire of Geneva. In 1857 he went to the United States,
+staying two years in New York and then proceeding to Boston, where he
+became director of the orchestra at the Boston Museum. In 1867 he
+founded the Boston Conservatory of Music. Eichberg published several
+educational works on music; and his four operettas, _The Doctor of
+Alcantara_, _The Rose of Tyrol_, _The Two Cadis_ and _A Night in Rome_,
+were highly popular. He died in Boston on the 18th of January 1893.
+
+
+
+
+EICHENDORFF, JOSEPH, FREIHERR VON (1788-1857), German poet and
+romance-writer, was born at Lubowitz, near Ratibor, in Silesia, on the
+10th of March 1788. He studied law at Halle and Heidelberg from 1805 to
+1808. After a visit to Paris he went to Vienna, where he resided until
+1813, when he joined the Prussian army as a volunteer in the famous
+Lützow corps. When peace was concluded in 1815, he left the army, and in
+the following year he was appointed to a judicial office at Breslau. He
+subsequently held similar offices at Danzig, Königsberg and Berlin.
+Retiring from public service in 1844, he lived successively in Danzig,
+Vienna, Dresden and Berlin. He died at Neisse on the 26th of November
+1857. Eichendorff was one of the most distinguished of the later members
+of the German romantic school. His genius was essentially lyrical. Thus
+he is most successful in his shorter romances and dramas, where
+constructive power is least called for. His first work, written in 1811,
+was a romance, _Ahnung und Gegenwart_ (1815). This was followed at short
+intervals by several others, among which the foremost place is by
+general consent assigned to _Aus dem Leben eines Taugenichts_ (1826),
+which has often been reprinted. Of his dramas may be mentioned _Ezzelin
+von Romano_ (1828); and _Der letzte Held von Marienburg_ (1830), both
+tragedies; and a comedy, _Die Freier_ (1833). He also translated several
+of Calderon's religious dramas (_Geistliche Schauspiele_, 1846). It is,
+however, through his lyrics (_Gedichte_, first collected 1837) that
+Eichendorff is best known; he is the greatest lyric poet of the romantic
+movement. No one has given more beautiful expression than he to the
+poetry of a wandering life; often, again, his lyrics are exquisite word
+pictures interpreting the mystic meaning of the moods of nature, as in
+_Nachts_, or the old-time mystery which yet haunts the twilight forests
+and feudal castles of Germany, as in the dramatic lyric _Waldesgespräch_
+or _Auf einer Burg_. Their language is simple and musical, which makes
+them very suitable for singing, and they have been often set, notably by
+Schubert and Schumann.
+
+In the later years of his life Eichendorff published several works on
+subjects in literary history and criticism such as _Über die ethische
+und religiöse Bedeutung der neuen romantischen Poesie in Deutschland_
+(1847), _Der deutsche Roman des 18. Jahrhunderts in seinem Verhältniss
+zum Christenthum_ (1851), and _Geschichte der poetischen Litteratur
+Deutschlands_ (1856), but the value of these works is impaired by the
+author's reactionary standpoint. An edition of his collected works in
+six volumes, appeared at Leipzig in 1870.
+
+  Eichendorff's _Sämtliche Werke_ appeared in 6 vols., 1864 (reprinted
+  1869-1870); his _Sämtliche poetische Werke_ in 4 vols. (1883). The
+  latest edition is that edited by R. von Gottschall in 4 vols. (1901).
+  A good selection edited by M. Kaoch will be found in vol. 145 of
+  Kürschner's _Deutsche Nationalliteratur_ (1893). Eichendorff's
+  critical writings were collected in 1866 under the title _Vermischte
+  Schriften_ (5 vols.). Cp. H. von Eichendorff's biographical
+  introduction to the _Sämtliche Werke_; also H. Keiter, _Joseph von
+  Eichendorff_ (Cologne, 1887); H.A. Krüger, _Der junge Eichendorff_
+  (Oppeln, 1898).
+
+
+
+
+EICHHORN, JOHANN GOTTFRIED (1752-1827), German theologian, was born at
+Dörrenzimmern, in the principality of Hohenlohe-Oehringen, on the 16th
+of October 1752. He was educated at the state school in Weikersheim,
+where his father was superintendent, at the gymnasium at Heilbronn and
+at the university of Göttingen (1770-1774), studying under J.D.
+Michaelis. In 1774 he received the rectorship of the gymnasium at
+Ohrdruf, in the duchy of Gotha, and in the following year was made
+professor of Oriental languages at Jena. On the death of Michaelis in
+1788 he was elected professor _ordinarius_ at Göttingen, where he
+lectured not only on Oriental languages and on the exegesis of the Old
+and New Testaments, but also on political history. His health was
+shattered in 1825, but he continued his lectures until attacked by fever
+on the 14th of June 1827. He died on the 27th of that month. Eichhorn
+has been called "the founder of modern Old Testament criticism." He
+first properly recognized its scope and problems, and began many of its
+most important discussions. "My greatest trouble," he says in the
+preface to the second edition of his _Einleitung_, "I had to bestow on a
+hitherto unworked field--on the investigation of the inner nature of the
+Old Testament with the help of the Higher Criticism (not a new name to
+any humanist)." His investigations led him to the conclusion that "most
+of the writings of the Hebrews have passed through several hands." He
+took for granted that all the so-called supernatural facts relating to
+the Old and New Testaments were explicable on natural principles. He
+sought to judge them from the standpoint of the ancient world, and to
+account for them by the superstitious beliefs which were then generally
+in vogue. He did not perceive in the biblical books any religious ideas
+of much importance for modern times; they interested him merely
+historically and for the light they cast upon antiquity. He regarded
+many books of the Old Testament as spurious, questioned the genuineness
+of _2 Peter_ and _Jude_, denied the Pauline authorship of _Timothy_ and
+_Titus_, and suggested that the canonical gospels were based upon
+various translations and editions of a primary Aramaic gospel. He did
+not appreciate as sufficiently as David Strauss and the Tübingen critics
+the difficulties which a natural theory has to surmount, nor did he
+support his conclusions by such elaborate discussions as they deemed
+necessary.
+
+  His principal works were--_Geschichte des Ostindischen Handels vor
+  Mohammed_ (Gotha, 1775); _Allgemeine Bibliothek der biblischen
+  Literatur_ (10 vols., Leipzig, 1787-1801); _Einleitung in das Alte
+  Testament_ (3 vols., Leipzig, 1780-1783); _Einleitung in das Neue
+  Testament_ (1804-1812); _Einleitung in die apokryphischen Bücher des
+  Alten Testaments_ (Gött., 1795); _Commentarius in apocalypsin Joannis_
+  (2 vols., Gött., 1791); _Die Hebr. Propheten_ (3 vols., Gött.,
+  1816-1819); _Allgemeine Geschichte der Cultur und Literatur des neuern
+  Europa_ (2 vols., Gött., 1796-1799); _Literärgeschichte_ (1st vol.,
+  Gött., 1799, 2nd ed. 1813, 2nd vol. 1814); _Geschichte der Literatur
+  von ihrem Anfange bis auf die neuesten Zeiten_ (5 vols., Gött.,
+  1805-1812); _Übersicht der Französischen Revolution_ (2 vols., Gött.,
+  1797); _Weltgeschichte_ (3rd ed., 5 vols., Gött., 1819-1820);
+  _Geschichte der drei letzten Jahrhunderte_ (3rd ed., 6 vols., Hanover,
+  1817-1818); _Urgeschichte des erlauchten Hauses der Welfen_ (Hanover,
+  1817).
+
+  See R.W. Mackay, _The Tübingen School and its Antecedents_ (1863), pp.
+  103 ff.; Otto Pfleiderer, _Development of Theology_ (1890), p. 209;
+  T.K. Cheyne, _Founders of Old Testament Criticism_ (1893), pp. 13 ff.
+
+
+
+
+EICHHORN, KARL FRIEDRICH (1781-1854), German jurist, son of the
+preceding, was born at Jena on the 20th of November 1781. He entered the
+university of Göttingen in 1797. In 1805 he obtained the professorship
+of law at Frankfort-on-Oder, holding it till 1811, when he accepted the
+same chair at Berlin. On the call to arms in 1813 he became a captain of
+horse, and received at the end of the war the decoration of the Iron
+Cross. In 1817 he was offered the chair of law at Göttingen, and,
+preferring it to the Berlin professorship, taught there with great
+success till ill-health compelled him to resign in 1828. His successor
+in the Berlin chair having died in 1832, he again entered on its duties,
+but resigned two years afterwards. In 1832 he also received an
+appointment in the ministry of foreign affairs, which, with his labours
+on many state committees and his legal researches and writings, occupied
+him till his death at Cologne on the 4th of July 1854. Eichhorn is
+regarded as one of the principal authorities on German constitutional
+law. His chief work is _Deutsche Staats- und Rechtsgeschichte_
+(Göttingen, 1808-1823, 5th ed. 1843-1844). In company with Savigny and
+J.F.L. Göschen he founded the _Zeitschrift für geschichtliche
+Rechtswissenschaft_. He was the author besides of _Einleitung in das
+deutsche Privatrecht mit Einschluss des Lehnrechts_ (Gött., 1823) and
+the _Grundsätze des Kirchenrechts der Katholischen und der Evangelischen
+Religionspartei in Deutschland_, 2 Bde. (ib., 1831-1833).
+
+  See Schulte, _Karl Friedrich Eichhorn, sein Leben und Wirken_ (1884).
+
+
+
+
+EICHSTÄTT, a town and episcopal see of Germany, in the kingdom of
+Bavaria, in the deep and romantic valley of the Altmühl, 35 m. S. of
+Nuremberg, on the railway to Ingolstadt and Munich. Pop. (1905) 7701.
+The town, with its numerous spires and remains of medieval
+fortifications, is very picturesque. It has an Evangelical and seven
+Roman Catholic churches, among the latter the cathedral of St Wilibald
+(first bishop of Eichstätt),--with the tomb of the saint and numerous
+pictures and relics,--the church of St Walpurgis, sister of Wilibald,
+whose remains rest in the choir, and the Capuchin church, a copy of the
+Holy Sepulchre. Of its secular buildings the most noticeable are the
+town hall and the Leuchtenberg palace, once the residence of the prince
+bishops and later of the dukes of Leuchtenberg (now occupied by the
+court of justice of the district), with beautiful grounds. The
+Wilibaldsburg, built on a neighbouring hill in the 14th century by
+Bishop Bertold of Hohenzollern, was long the residence of the prince
+bishops of Eichstätt, and now contains an historical museum. There are
+an episcopal lyceum, a clerical seminary, a classical and a modern
+school, and numerous religious houses. The industries of the town
+include bootmaking, brewing and the production of lithographic stones.
+
+Eichstätt (Lat. _Aureatum_ or _Rubilocus_) was originally a Roman
+station which, after the foundation of the bishopric by Boniface in 745,
+developed into a considerable town, which was surrounded with walls in
+908. The bishops of Eichstätt were princes of the Empire, subject to the
+spiritual jurisdiction of the archbishops of Mainz, and ruled over
+considerable territories in the Circle of Franconia. In 1802 the see was
+secularized and incorporated in Bavaria. In 1817 it was given, with the
+duchy of Leuchtenberg, as a mediatized domain under the Bavarian crown,
+by the king of Bavaria to his son-in-law Eugène de Beauharnais,
+ex-viceroy of Italy, henceforth styled duke of Leuchtenberg. In 1855 it
+reverted to the Bavarian crown.
+
+
+
+
+EICHWALD, KARL EDUARD VON (1795-1876), Russian geologist and physician,
+was born at Mitau in Courland on the 4th of July 1795. He became doctor
+of medicine and professor of zoology in Kazañ in 1823; four years later
+professor of zoology and comparative anatomy at Vilna; in 1838 professor
+of zoology, mineralogy and medicine at St Petersburg; and finally
+professor of palaeontology in the institute of mines in that city. He
+travelled much in the Russian empire, and was a keen observer of its
+natural history and geology. He died at St Petersburg on the 10th of
+November 1876. His published works include _Reise auf dem Caspischen
+Meere und in den Caucasus_, 2 vols. (Stuttgart and Tübingen, 1834-1838);
+_Die Urwelt Russlands_ (St Petersburg, 1840-1845); _Lethaea Rossica, ou
+paléontologie de la Russie_, 3 vols. (Stuttgart, 1852-1868), with
+Atlases.
+
+
+
+
+EIDER, a river of Prussia, in the province of Schleswig-Holstein. It
+rises to the south of Kiel, in Lake Redder, flows first north, then west
+(with wide-sweeping curves), and after a course of 117 m. enters the
+North Sea at Tönning. It is navigable up to Rendsburg, and is embanked
+through the marshes across which it runs in its lower course. Since the
+reign of Charlemagne, the Eider (originally _Ägyr Dör_--Neptune's gate)
+was known as _Romani terminus imperii_ and was recognized as the
+boundary of the Empire in 1027 by the emperor Conrad II., the founder of
+the Salian dynasty. In the controversy arising out of the
+Schleswig-Holstein Question, which culminated in the war of Austria and
+Prussia against Denmark in 1864, the Eider gave its name to the "Eider
+Danes," the _intransigeant_ Danish party which maintained that Schleswig
+(Sonderjylland, South Jutland) was by nature and historical tradition an
+integral part of Denmark. The Eider Canal (_Eider-Kanal_), which was
+constructed between 1777 and 1784, leaves the Eider at the point where
+the river turns to the west and enters the Bay of Kiel at Holtenau. It
+was hampered by six sluices, but was used annually by some 4000 vessels,
+and until its conversion in 1887-1895 into the Kaiser Wilhelm Canal
+afforded the only direct connexion between the North Sea and the Baltic.
+
+
+
+
+EIDER (Icelandic, _Ædur_), a large marine duck, the _Somateria
+mollissima_ of ornithologists, famous for its down, which, from its
+extreme lightness and elasticity, is in great request for filling
+bed-coverlets. This bird generally frequents low rocky islets near the
+coast, and in Iceland and Norway has long been afforded every
+encouragement and protection, a fine being inflicted for killing it
+during the breeding-season, or even for firing a gun near its haunts,
+while artificial nesting-places are in many localities contrived for its
+further accommodation. From the care thus taken of it in those countries
+it has become exceedingly tame at its chief resorts, which are strictly
+regarded as property, and the taking of eggs or down from them, except
+by authorized persons, is severely punished by law. In appearance the
+eider is somewhat clumsy, though it flies fast and dives admirably. The
+female is of a dark reddish-brown colour barred with brownish-black. The
+adult male in spring is conspicuous by his pied plumage of velvet-black
+beneath, and white above: a patch of shining sea-green on his head is
+only seen on close inspection. This plumage he is considered not to
+acquire until his third year, being when young almost exactly like the
+female, and it is certain that the birds which have not attained their
+full dress remain in flocks by themselves without going to the
+breeding-stations. The nest is generally in some convenient corner among
+large stones, hollowed in the soil, and furnished with a few bits of dry
+grass, seaweed or heather. By the time that the full number of eggs
+(which rarely if ever exceeds five) is laid the down is added. Generally
+the eggs and down are taken at intervals of a few days by the owners of
+the "eider-fold," and the birds are thus kept depositing both during the
+whole season; but some experience is needed to ensure the greatest
+profit from each commodity. Every duck is ultimately allowed to hatch an
+egg or two to keep up the stock, and the down of the last nest is
+gathered after the birds have left the spot. The story of the drake's
+furnishing down, after the duck's supply is exhausted is a fiction. He
+never goes near the nest. The eggs have a strong flavour, but are much
+relished by both Icelanders and Norwegians. In the Old World the eider
+breeds in suitable localities from Spitsbergen to the Farne Islands off
+the coast of Northumberland--where it is known as St Cuthbert's duck.
+Its food consists of marine animals (molluscs and crustaceans), and
+hence the young are not easily reared in captivity. The eider of the New
+World differs somewhat, and has been described as a distinct species
+(_S. dresseri_). Though much diminished in numbers by persecution, it is
+still abundant on the coast of Newfoundland and thence northward. In
+Greenland also eiders are very plentiful, and it is supposed that
+three-fourths of the supply of down sent to Copenhagen comes from that
+country. The limits of the eider's northern range are not known, but the
+Arctic expedition of 1875 did not meet with it after leaving the Danish
+settlements, and its place was taken by an allied species, the king-duck
+(_S. spectabilis_), a very beautiful bird which sometimes appears on the
+British coast. The female greatly resembles that of the eider, but the
+male has a black chevron on his chin and a bright orange prominence on
+his forehead, which last seems to have given the species its English
+name. On the west coast of North America the eider is represented by a
+species (_S. v-nigrum_) with a like chevron, but otherwise resembling
+the Atlantic bird. In the same waters two other fine species are also
+found (_S. fischeri_ and _S. stelleri_), one of which (the latter) also
+inhabits the Arctic coast of Russia and East Finmark and has twice
+reached England. The Labrador duck (_S. labradoria_), now extinct, also
+belongs to this group.     (A. N.)
+
+
+
+
+EIFEL, a district of Germany, in the Prussian Rhine Province, between
+the Rhine, the Moselle and the frontier of the grand duchy of Luxemburg.
+It is a hilly region, most elevated in the eastern part (Hohe Eifel),
+where there are several points from 2000 up to 2410 ft. above sea-level.
+In the west is the Schneifels or Schnee-Eifel; and the southern part,
+where the most picturesque scenery and chief geological interest is
+found, is called the Vorder Eifel.
+
+The Eifel is an ancient massif of folded Devonian rocks upon the margins
+of which, near Hillesheim and towards Bitburg and Trier, rest
+unconformably the nearly undisturbed sandstones, marls and limestones of
+the Trias. On the southern border, at Wittlich, the terrestrial deposits
+of the Permian Rothliegende are also met with. The slates and sandstones
+of the Lower Devonian form by far the greater part of the region; but
+folded amongst these, in a series of troughs running from south-west to
+north-east lie the fossiliferous limestones of the Middle Devonian, and
+occasionally, as for example near Büdesheim, a few small patches of the
+Upper Devonian. Upon the ancient floor of folded Devonian strata stand
+numerous small volcanic cones, many of which, though long extinct, are
+still very perfect in form. The precise age of the eruptions is
+uncertain. The only sign of any remaining volcanic activity is the
+emission in many places of carbon dioxide and of heated waters. There is
+no historic or legendary record of any eruption, but nevertheless the
+eruptions must have continued to a very recent geological period. The
+lavas of Papenkaule are clearly posterior to the excavation of the
+valley of the Kyll, and an outflow of basalt has forced the Uess to seek
+a new course. The volcanic rocks occur both as tuffs and as lava-flows.
+They are chiefly leucite and nepheline rocks, such as leucitite,
+leucitophyre and nephelinite, but basalt and trachyte also occur. The
+leucite lavas of Niedermendig contain haüyne in abundance. The most
+extensive and continuous area of volcanic rocks is that surrounding the
+Laacher See and extending eastwards to Neuwied and Coblenz and even
+beyond the Rhine.
+
+The numerous so-called crater-lakes or _maare_ of the Eifel present
+several features of interest. They do not, as a rule, lie in true
+craters at the summit of volcanic cones, but rather in hollows which
+have been formed by explosions. The most remarkable group is that of
+Daun, where the three depressions of Gemünd, Weinfeld and Schalkenmehren
+have been hollowed out in the Lower Devonian strata. The first of these
+shows no sign of either lavas or scoriae, but volcanic rocks occur on
+the margins of the other two. The two largest lakes in the Eifel region,
+however, are the Laacher See in the hills west of Andernach on the
+Rhine, and the Pulvermaar S.E. of the Daun group, with its shores of
+peculiar volcanic sand, which also appears in its waters as a black
+powder (_pulver_).
+
+
+
+
+EIFFEL TOWER. Erected for the exposition of 1889, the Eiffel Tower, in
+the Champ de Mars, Paris, is by far the highest artificial structure in
+the world, and its height of 300 metres (984 ft.) surpasses that of the
+obelisk at Washington by 429 ft., and that of St Paul's cathedral by 580
+ft. Its framework is composed essentially of four uprights, which rise
+from the corners of a square measuring 100 metres on the side; thus the
+area it covers at its base is nearly 2½ acres. These uprights are
+supported on huge piers of masonry and concrete, the foundations for
+which were carried down, by the aid of iron caissons and compressed air,
+to a depth of about 15 metres on the side next the Seine, and about 9
+metres on the other side. At first they curve upwards at an angle of
+54°; then they gradually become straighter, until they unite in a single
+shaft rather more than half-way up. The first platform, at a height of
+57 metres, has an area of 5860 sq. yds., and is reached either by
+staircases or lifts. The next, accessible by lifts only, is 115 metres
+up, and has an area of 32 sq. yds; while the third, at 276, supports a
+pavilion capable of holding 800 persons. Nearly 25 metres higher up
+still is the lantern, with a gallery 5 metres in diameter. The work of
+building this structure, which is mainly composed of iron lattice-work,
+was begun on the 28th of January 1887, and the full height was reached
+on the 13th of March 1889. Besides being one of the sights of Paris, to
+which visitors resort in order to enjoy the extensive view that can be
+had from its higher galleries on a clear day, the tower is used to some
+extent for scientific and semi-scientific purposes; thus meteorological
+observations are carried on. The engineer under whose direction the
+tower was constructed was Alexandre Gustave Eiffel (born at Dijon on the
+15th of December 1832), who had already had a wide experience in the
+construction of large metal bridges, and who designed the huge sluices
+for the Panama Canal, when it was under the French company.
+
+
+
+
+EILDON HILLS, a group of three conical hills, of volcanic origin, in
+Roxburghshire, Scotland, 1 m. S. by E. of Melrose, about equidistant
+from Melrose and St Boswells stations on the North British railway. They
+were once known as Eldune--the _Eldunum_ of Simeon of Durham (fl.
+1130)--probably derived from the Gaelic _aill_, "rock," and _dun_,
+"hill"; but the name is also said to be a corruption of the Cymric
+_moeldun_, "bald hill." The northern peak is 1327 ft. high, the central
+1385 ft. and the southern 1216 ft. Whether or not the Roman station of
+_Trimontium_ was situated here is matter of controversy. According to
+General William Roy (1726-1790) Trimontium--so called, according to this
+theory, from the triple Eildon heights--was Old Melrose; other
+authorities incline to place the station on the northern shore of the
+Solway Firth. The Eildons have been the subject of much legendary lore.
+Michael Scot (1175-1234), acting as a confederate of the Evil One (so
+the fable runs) cleft Eildon Hill, then a single cone, into the three
+existing peaks. Another legend states that Arthur and his knights sleep
+in a vault beneath the Eildons. A third legend centres in Thomas of
+Erceldoune. The Eildon Tree Stone, a large moss-covered boulder, lying
+on the high road as it bends towards the west within 2 m. of Melrose,
+marks the spot where the Fairy Queen led him into her realms in the
+heart of the hills. Other places associated with this legend may still
+be identified. Huntly Banks, where "true Thomas" lay and watched the
+queen's approach, is half a mile west of the Eildon Tree Stone, and on
+the west side of the hills is Bogle Burn, a streamlet that feeds the
+Tweed and probably derives its name from his ghostly visitor. Here, too,
+is Rhymer's glen, although the name was invented by Sir Walter Scott,
+who added the dell to his Abbotsford estate. Bowden, to the south of the
+hills, was the birthplace of the poets Thomas Aird (1802-1876) and James
+Thomson, and its parish church contains the burial-place of the dukes of
+Roxburghe. Eildon Hall is a seat of the duke of Buccleuch.
+
+
+
+
+EILENBURG, a town of Germany, in the Prussian province of Saxony, on an
+island formed by the Mulde, 31 m. E. from Halle, at the junction of the
+railways Halle-Cottbus and Leipzig-Eilenburg. Pop. (1905) 15,145. There
+are three churches, two Evangelical and one Roman Catholic. The
+industries of the town include the manufacture of chemicals, cloth,
+quilting, calico, cigars and agricultural implements, bleaching, dyeing,
+basket-making, carriage-building and trade in cattle. In the
+neighbourhood is the iron foundry of Erwinhof. Opposite the town, on the
+steep left bank of the Mulde, is the castle from which it derives its
+name, the original seat of the noble family of Eulenburg. This castle
+(Ilburg) is mentioned in records of the reigns of Henry the Fowler as an
+important outpost against the Sorbs and Wends. The town itself,
+originally called Mildenau, is of great antiquity. It is first mentioned
+as a town in 981, when it belonged to the house of Wettin and was the
+chief town of the East Mark. In 1386 it was incorporated in the
+margraviate of Meissen. In 1815 it passed to Prussia.
+
+  See Gundermann, _Chronik der Stadt Eilenburg_ (Eilenburg, 1879).
+
+
+
+
+EINBECK, or EIMBECK, a town of Germany, in the Prussian province of
+Hanover, on the Ilm, 50 m. by rail S. of Hanover. Pop. (1905) 8709. It
+is an old-fashioned town with many quaint wooden houses, notable among
+them the "Northeimhaus," a beautiful specimen of medieval architecture.
+There are several churches, among them the Alexanderkirche, containing
+the tombs of the princes of Grubenhagen, and a synagogue. The schools
+include a _Realgymnasium_ (i.e. predominantly for "modern" subjects),
+technical schools for the advanced study of machine-making, for weaving
+and for the textile industries, a preparatory training-college and a
+police school. The industries include brewing, weaving and the
+manufacture of cloth, carpets, tobacco, sugar, leather-grease, toys and
+roofing-felt.
+
+Einbeck grew up originally round the monastery of St Alexander (founded
+1080), famous for its relic of the True Blood. It is first recorded as a
+town in 1274, and in the 14th century was the seat of the princes of
+Grubenhagen, a branch of the ducal house of Brunswick. The town
+subsequently joined the Hanseatic League. In the 15th century it became
+famous for its beer ("Eimbecker," whence the familiar "Bock"). In 1540
+the Reformation was introduced by Duke Philip of
+Brunswick-Saltzderhelden (d. 1551), with the death of whose son Philip
+II. (1596) the Grubenhagen line became extinct. In 1626, during the
+Thirty Years' War, Einbeck was taken by Pappenheim and in October 1641
+by Piccolomini. In 1643 it was evacuated by the Imperialists. In 1761
+its walls were razed by the French.
+
+  See H.L. Harland, _Gesch. der Stadt Einbeck_, 2 Bde. (Einbeck,
+  1854-1859; abridgment, ib. 1881).
+
+
+
+
+EINDHOVEN, a town in the province of North Brabant, Holland, and a
+railway junction 8 m. by rail W. by S. of Helmond. Pop. (1900) 4730.
+Like Tilburg and Helmond it has developed in modern times into a
+flourishing industrial centre, having linen, woollen, cotton, tobacco
+and cigar, matches, &c., factories and several breweries.
+
+
+
+
+EINHARD (c. 770-840), the friend and biographer of Charlemagne; he is
+also called Einhartus, Ainhardus or Heinhardus, in some of the early
+manuscripts. About the 10th century the name was altered into Agenardus,
+and then to Eginhardus, or Eginhartus, but, although these variations
+were largely used in the English and French languages, the form
+Einhardus, or Einhartus, is unquestionably the right one.
+
+According to the statement of Walafrid Strabo, Einhard was born in the
+district which is watered by the river Main, and his birth has been
+fixed at about 770. His parents were of noble birth, and were probably
+named Einhart and Engilfrit; and their son was educated in the monastery
+of Fulda, where he was certainly residing in 788 and in 791. Owing to
+his intelligence and ability he was transferred, not later than 796,
+from Fulda to the palace of Charlemagne by abbot Baugulf; and he soon
+became very intimate with the king and his family, and undertook various
+important duties, one writer calling him _domesticus palatii regalis_.
+He was a member of the group of scholars who gathered around Charlemagne
+and was entrusted with the charge of the public buildings, receiving,
+according to a fashion then prevalent, the scriptural name of Bezaleel
+(Exodus xxxi. 2 and xxxv. 30-35) owing to his artistic skill. It has
+been supposed that he was responsible for the erection of the basilica
+at Aix-la-Chapelle, where he resided with the emperor, and the other
+buildings mentioned in chapter xvii. of his _Vita Karoli Magni_, but
+there is no express statement to this effect. In 806 Charlemagne sent
+him to Rome to obtain the signature of Pope Leo III. to a will which he
+had made concerning the division of his empire; and it was possibly
+owing to Einhard's influence that in 813, after the death of his two
+elder sons, the emperor made his remaining son, Louis, a partner with
+himself in the imperial dignity. When Louis became sole emperor in 814
+he retained his father's minister in his former position; then in 817
+made him tutor to his son, Lothair, afterwards the emperor Lothair I.;
+and showed him many other marks of favour. Einhard married Emma, or
+Imma, a sister of Bernharius, bishop of Worms, and a tradition of the
+12th century represented this lady as a daughter of Charlemagne, and
+invented a romantic story with regard to the courtship which deserves to
+be noticed as it frequently appears in literature. Einhard is said to
+have visited the emperor's daughter regularly and secretly, and on one
+occasion a fall of snow made it impossible for him to walk away without
+leaving footprints, which would lead to his detection. This risk,
+however, was obviated by the foresight of Emma, who carried her lover
+across the courtyard of the palace; a scene which was witnessed by
+Charlemagne, who next morning narrated the occurrence to his
+counsellors, and asked for their advice. Very severe punishments were
+suggested for the clandestine lover, but the emperor rewarded the
+devotion of the pair by consenting to their marriage. This story is, of
+course, improbable, and is further discredited by the fact that Einhard
+does not mention Emma among the number of Charlemagne's children.
+Moreover, a similar story has been told of a daughter of the emperor
+Henry III. It is uncertain whether Einhard had any children. He
+addressed a letter to a person named Vussin, whom he calls _fili_ and
+_mi nate_, but, as Vussin is not mentioned in documents in which his
+interests as Einhard's son would have been concerned, it is possible
+that he was only a young man in whom he took a special interest. In
+January 815 the emperor Louis I. bestowed on Einhard and his wife the
+domains of Michelstadt and Mulinheim in the Odenwald, and in the charter
+conveying these lands he is called simply Einhardus, but, in a document
+dated the 2nd of June of the same year, he is referred to as abbot.
+After this time he is mentioned as head of several monasteries: St
+Peter, Mount Blandin and St Bavon at Ghent, St Servais at Maastricht, St
+Cloud near Paris, and Fontenelle near Rouen, and he also had charge of
+the church of St John the Baptist at Pavia.
+
+During the quarrels which took place between Louis I. and his sons, in
+consequence of the emperor's second marriage, Einhard's efforts were
+directed to making peace, but after a time he grew tired of the troubles
+and intrigues of court life. In 818 he had given his estate at
+Michelstadt to the abbey of Lorsch, but he retained Mulinheim, where
+about 827 he founded an abbey and erected a church, to which he
+transported some relics of St Peter and St Marcellinus, which he had
+procured from Rome. To Mulinheim, which was afterwards called
+Seligenstadt, he finally retired in 830. His wife, who had been his
+constant helper, and whom he had not put away on becoming an abbot, died
+in 836, and after receiving a visit from the emperor, Einhard died on
+the 14th of March 840. He was buried at Seligenstadt, and his epitaph
+was written by Hrabanus Maurus. Einhard was a man of very short
+stature, a feature on which Alcuin wrote an epigram. Consequently he was
+called _Nardulus_, a diminutive form of Einhardus, and his great
+industry and activity caused him to be likened to an ant. He was also a
+man of learning and culture. Reaping the benefits of the revival of
+learning brought about by Charlemagne, he was on intimate terms with
+Alcuin, was well versed in Latin literature, and knew some Greek. His
+most famous work is his _Vita Karoli Magni_, to which a prologue was
+added by Walafrid Strabo. Written in imitation of the _De vitis
+Caesarum_ of Suetonius, this is the best contemporary account of the
+life of Charlemagne, and could only have been written by one who was
+very intimate with the emperor and his court. It is, moreover, a work of
+some artistic merit, although not free from inaccuracies. It was written
+before 821, and having been very popular during the middle ages, was
+first printed at Cologne in 1521. G.H. Pertz collated more than sixty
+manuscripts for his edition of 1829, and others have since come to
+light. Other works by Einhard are: _Epistolae_, which are of
+considerable importance for the history of the times; _Historia
+translationis beatorum Christi martyrum Marcellini et Petri_, which
+gives a curious account of how the bones of these martyrs were stolen
+and conveyed to Seligenstadt, and what miracles they wrought; and _De
+adoranda cruce_, a treatise which has only recently come to light, and
+which has been published by E. Dümmler in the _Neues Archiv der
+Gesellschaft für ältere deutsche Geschichtskunde_, Band xi. (Hanover,
+1886). It has been asserted that Einhard was the author of some of the
+Frankish annals, and especially of part of the annals of Lorsch
+(_Annales Laurissenses majores_), and part of the annals of Fulda
+(_Annales Fuldenses_). Much discussion has taken place on this question,
+and several of the most eminent of German historians, Ranke among them,
+have taken part therein, but no certain decision has been reached.
+
+  The literature on Einhard is very extensive, as nearly all those who
+  deal with Charlemagne, early German and early French literature, treat
+  of him. Editions of his works are by A. Teulet, _Einhardi omnia quae
+  extant opera_ (Paris, 1840-1843), with a French translation; P. Jaffé,
+  in the _Bibliotheca rerum Germanicarum_, Band iv. (Berlin, 1867); G.H.
+  Pertz in the _Monumenta Germaniae historica_, Bände i. and ii.
+  (Hanover, 1826-1829), and J.P. Migne in the _Patrologia Latina_, tomes
+  97 and 104 (Paris, 1866). The _Vita Karoli Magni_, edited by G.H.
+  Pertz and G. Waitz, has been published separately (Hanover, 1880).
+  Among the various translations of the _Vita_ may be mentioned an
+  English one by W. Glaister (London, 1877) and a German one by O. Abel
+  (Leipzig, 1893). For a complete bibliography of Einhard, see A.
+  Potthast, _Bibliotheca historica_, pp. 394-397 (Berlin, 1896), and W.
+  Wattenbach, _Deutschlands Geschichtsquellen_, Band i. (Berlin, 1904).
+       (A. W. H.*)
+
+
+
+
+EINHORN, DAVID (1809-1879), leader of the Jewish reform movement in the
+United States of America, was born in Bavaria. He was a supporter of the
+principles of Abraham Geiger (q.v.), and while still in Germany
+advocated the introduction of prayers in the vernacular, the exclusion
+of nationalistic hopes from the synagogue service, and other ritual
+modifications. In 1855 he migrated to America, where he became the
+acknowledged leader of reform, and laid the foundation of the régime
+under which the mass of American Jews (excepting the newly arrived
+Russians) now worship. In 1858 he published his revised prayer book,
+which has formed the model for all subsequent revisions. In 1861 he
+strongly supported the anti-slavery party, and was forced to leave
+Baltimore where he then ministered. He continued his work first in
+Philadelphia and later in New York.     (I. A.)
+
+
+
+
+EINSIEDELN, the most populous town in the Swiss canton of Schwyz. It is
+built on the right bank of the Alpbach (an affluent of the Sihl), at a
+height of 2908 ft. above the sea-level on a rather bare moorland, and by
+rail is 25 m. S.E. of Zürich, or by a round-about railway route about 38
+m. north of Schwyz, with which it communicates directly over the Hacken
+Pass (4649 ft.) or the Holzegg Pass (4616 ft.). In 1900 the population
+was 8496, all (save 75) Romanists and all (save 111) German-speaking.
+The town is entirely dependent on the great Benedictine abbey that rises
+slightly above it to the east. Close to its present site Meinrad, a
+hermit, was murdered in 861 by two robbers, whose crime was made known
+by Meinrad's two pet ravens. Early in the 10th century Benno, a hermit,
+rebuilt the holy man's cell, but the abbey proper was not founded till
+about 934, the church having been consecrated (it is said by Christ
+Himself) in 948. In 1274 the dignity of a prince of the Holy Roman
+Empire was confirmed by the emperor to the reigning abbot. Originally
+under the protection of the counts of Rapperswil (to which town on the
+lake of Zürich the old pilgrims' way still leads over the Etzel Pass,
+3146 ft., with its chapel and inn), this position passed by marriage
+with their heiress in 1295 to the Laufenburg or cadet line of the
+Habsburgs, but from 1386 was permanently occupied by Schwyz. A black
+wooden image of the Virgin and the fame of St Meinrad caused the throngs
+of pilgrims to resort to Einsiedeln in the middle ages, and even now it
+is much frequented, particularly about the 14th of September. The
+existing buildings date from the 18th century only, while the treasury
+and the library still contain many precious objects, despite the sack by
+the French in 1798. There are now about 100 fully professed monks, who
+direct several educational institutions. The Black Virgin has a special
+chapel in the stately church. Zwingli was the parish priest of
+Einsiedeln 1516-1518 (before he became a Protestant), while near the
+town Paracelsus (1493-1541), the celebrated philosopher, was born.
+
+  See Father O. Ringholz, _Geschichte d. fürstl. Benediktinerstiftes
+  Einsiedeln_, vol. i. (to 1526), (Einsiedeln, 1904).     (W. A. B. C.)
+
+
+
+
+EISENACH, a town of Germany, second capital of the grand-duchy of
+Saxe-Weimar-Eisenach, lies at the north-west foot of the Thuringian
+forest, at the confluence of the Nesse and Hörsel, 32 m. by rail W. from
+Erfurt. Pop. (1905) 35,123. The town mainly consists of a long street,
+running from east to west. Off this are the market square, containing
+the grand-ducal palace, built in 1742, where the duchess Hélène of
+Orleans long resided, the town-hall, and the late Gothic St
+Georgenkirche; and the square on which stands the Nikolaikirche, a fine
+Romanesque building, built about 1150 and restored in 1887. Noteworthy
+are also the Klemda, a small castle dating from 1260; the Lutherhaus, in
+which the reformer stayed with the Cotta family in 1498; the house in
+which Sebastian Bach was born, and that (now a museum) in which Fritz
+Reuter lived (1863-1874). There are monuments to the two former in the
+town, while the resting-place of the latter in the cemetery is marked by
+a less pretentious memorial. Eisenach has a school of forestry, a school
+of design, a classical school (_Gymnasium_) and modern school
+(_Realgymnasium_), a deaf and dumb school, a teachers' seminary, a
+theatre and a Wagner museum. The most important industries of the town
+are worsted-spinning, carriage and wagon building, and the making of
+colours and pottery. Among others are the manufacture of cigars, cement
+pipes, iron-ware and machines, alabaster ware, shoes, leather, &c.,
+cabinet-making, brewing, granite quarrying and working, tile-making, and
+saw- and corn-milling.
+
+The natural beauty of its surroundings and the extensive forests of the
+district have of late years attracted many summer residents.
+Magnificently situated on a precipitous hill, 600 ft. above the town to
+the south, is the historic Wartburg (q.v.), the ancient castle of the
+landgraves of Thuringia, famous as the scene of the contest of
+Minnesingers immortalized in Wagner's Tannhäuser, and as the place where
+Luther, on his return from the diet of Worms in 1521, was kept in hiding
+and made his translation of the Bible. On a high rock adjacent to the
+Wartburg are the ruins of the castle of Mädelstein.
+
+Eisenach (_Isenacum_) was founded in 1070 by Louis II. the Springer,
+landgrave of Thuringia, and its history during the middle ages was
+closely bound up with that of the Wartburg, the seat of the landgraves.
+The Klemda, mentioned above, was built by Sophia (d. 1284), daughter of
+the landgrave Louis IV., and wife of Duke Henry II. of Brabant, to
+defend the town against Henry III., margrave of Meissen, during the
+succession contest that followed the extinction of the male line of the
+Thuringian landgraves in 1247. The principality of Eisenach fell to the
+Saxon house of Wettin in 1440, and in the partition of 1485 formed part
+of the territories given to the Ernestine line. It was a separate Saxon
+duchy from 1596 to 1638, from 1640 to 1644, and again from 1662 to
+1741, when it finally fell to Saxe-Weimar. The town of Eisenach, by
+reason of its associations, has been a favourite centre for the
+religious propaganda of Evangelical Germany, and since 1852 it has been
+the scene of the annual conference of the German Evangelical Church,
+known as the Eisenach conference.
+
+  See Trinius, _Eisenach und Umgebung_ (Minden, 1900); and H.A. Daniel,
+  _Deutschland_ (Leipzig, 1895), and further references in U. Chevalier,
+  "Répertoire des sources," &c., _Topo-bibliogr._ (Montbéliard,
+  1894-1899), s.v.
+
+
+
+
+EISENBERG (_Isenberg_), a town of Germany, in the duchy of
+Saxe-Altenburg, on a plateau between the rivers Saale and Elster, 20 m.
+S.W. from Zeitz, and connected with the railway Leipzig-Gera by a branch
+to Crossen. Pop. (1905) 8824. It possesses an old castle, several
+churches and monuments to Duke Christian of Saxe-Eisenberg (d. 1707),
+Bismarck, and the philosopher Karl Christian Friedrich Krause (q.v.).
+Its principal industries are weaving, and the manufacture of machines,
+ovens, furniture, pianos, porcelain and sausages.
+
+  See Back, _Chronik der Sladt und des Amtes Eisenberg_ (Eisenb., 1843).
+
+
+
+
+EISENERZ ("Iron ore"), a market-place and old mining town in Styria,
+Austria, 68 m. N.W. of Graz by rail. Pop. (1900) 6494. It is situated in
+a deep valley, dominated on the east by the Pfaffenstein (6140 ft.), on
+the west by the Kaiserschild (6830 ft.), and on the south by the Erzberg
+(5030 ft.). It has an interesting example of a medieval fortified
+church, a Gothic edifice founded by Rudolph of Habsburg in the 13th
+century and rebuilt in the 16th. The Erzberg or Ore Mountain furnishes
+such rich ore that it is quarried in the open air like stone, in the
+summer months. There is documentary evidence of the mines having been
+worked as far back as the 12th century. They afford employment to two or
+three thousand hands in summer and about half as many in winter, and
+yield some 800,000 tons of iron per annum. Eisenerz is connected with
+the mines by the Erzberg railway, a bold piece of engineering work, 14
+m. long, constructed on the Abt's rack-and-pinion system. It passes
+through some beautiful scenery, and descends to Vordernberg (pop. 3111),
+an important centre of the iron trade situated on the south side of the
+Erzberg. Eisenerz possesses, in addition, twenty-five furnaces, which
+produce iron, and particularly steel, of exceptional excellence. A few
+miles to the N.W. of Eisenerz lies the castle of Leopoldstein, and near
+it the beautiful Leopoldsteiner Lake. This lake, with its dark-green
+water, situated at an altitude of 2028 ft., and surrounded on all sides
+by high peaks, is not big, but is very deep, having a depth of 520 ft.
+
+
+
+
+EISLEBEN (Lat. _Islebia_), a town of Germany, in the Prussian province
+of Saxony, 24 m. W. by N. from Halle, on the railway to Nordhausen and
+Cassel. Pop. (1905) 23,898. It is divided into an old and a new town
+(Altstadt and Neustadt). Among its principal buildings are the church of
+St Andrew (Andreaskirche), which contains numerous monuments of the
+counts of Mansfeld; the church of St Peter and St Paul
+(Peter-Paulkirche), containing the font in which Luther was baptized;
+the royal gymnasium (classical school), founded by Luther shortly before
+his death in 1546; and the hospital. Eisleben is celebrated as the place
+where Luther was born and died. The house in which he was born was
+burned in 1689, but was rebuilt in 1693 as a free school for orphans.
+This school fell into decay under the régime of the kingdom of
+Westphalia, but was restored in 1817 by King Frederick William III. of
+Prussia, who, in 1819, transferred it to a new building behind the old
+house. The house in which Luther died was restored towards the end of
+the 19th century, and his death chamber is still preserved. A bronze
+statue of Luther by Rudolf Siemering (1835-1905) was unveiled in 1883.
+Eisleben has long been the centre of an important mining district
+(Luther was a miner's son), the principal products being silver and
+copper. It possesses smelting works and a school of mining.
+
+The earliest record of Eisleben is dated 974. In 1045, at which time it
+belonged to the counts of Mansfeld, it received the right to hold
+markets, coin money, and levy tolls. From 1531 to 1710 it was the seat
+of the cadet line of the counts of Mansfeld-Eisleben. After the
+extinction of the main line of the counts of Mansfeld, Eisleben fell to
+Saxony, and, in the partition of Saxony by the congress of Vienna in
+1815, was assigned to Prussia.
+
+  See G. Grössler, _Urkundliche Gesch. Eislebens bis zum Ende des 12.
+  Jahrhunderts_ (Halle, 1875); _Chronicon Islebiense; Eisleben
+  Stadtchronik aus den Jahren_ 1520-1738, edited from the original, with
+  notes by Grössler and Sommer (Eisleben, 1882).
+
+
+
+
+EISTEDDFOD (plural Eisteddfodau), the national bardic congress of Wales,
+the objects of which are to encourage bardism and music and the general
+literature of the Welsh, to maintain the Welsh language and customs of
+the country, and to foster and cultivate a patriotic spirit amongst the
+people. This institution, so peculiar to Wales, is of very ancient
+origin.[1] The term _Eisteddfod_, however, which means "a session" or
+"sitting," was probably not applied to bardic congresses before the 12th
+century.
+
+The Eisteddfod in its present character appears to have originated in
+the time of Owain ap Maxen Wledig, who at the close of the 4th century
+was elected to the chief sovereignty of the Britons on the departure of
+the Romans. It was at this time, or soon afterwards, that the laws and
+usages of the Gorsedd were codified and remodelled, and its motto of "Y
+gwir yn erbyn y byd" (The truth against the world) given to it. "Chairs"
+(with which the Eisteddfod as a national institution is now inseparably
+connected) were also established, or rather perhaps resuscitated, about
+the same time. The chair was a kind of convention where disciples were
+trained, and bardic matters discussed preparatory to the great Gorsedd,
+each chair having a distinctive motto. There are now existing four
+chairs in Wales,--namely, the "royal" chair of Powys, whose motto is "A
+laddo a leddir" (He that slayeth shall be slain); that of Gwent and
+Glamorgan, whose motto is "Duw a phob daioni" (God and all goodness);
+that of Dyfed, whose motto is "Calon wrth galon" (Heart with heart); and
+that of Gwynedd, or North Wales, whose motto is "Iesu," or "O Iesu! na'd
+gamwaith" (Jesus, or Oh Jesus! suffer not iniquity).
+
+The first Eisteddfod of which any account seems to have descended to us
+was one held on the banks of the Conway in the 6th century, under the
+auspices of Maelgwn Gwynedd, prince of North Wales. Maelgwn on this
+occasion, in order to prove the superiority of vocal song over
+instrumental music, is recorded to have offered a reward to such bards
+and minstrels as should swim over the Conway. There were several
+competitors, but on their arrival on the opposite shore the harpers
+found themselves unable to play owing to the injury their harps had
+sustained from the water, while the bards were in as good tune as ever.
+King Cadwaladr also presided at an Eisteddfod about the middle of the
+7th century.
+
+Griffith ap Cynan, prince of North Wales, who had been born in Ireland,
+brought with him from that country many Irish musicians, who greatly
+improved the music of Wales. During his long reign of 56 years he
+offered great encouragement to bards, harpers and minstrels, and framed
+a code of laws for their better regulation. He held an Eisteddfod about
+the beginning of the 12th century at Caerwys in Flintshire, "to which
+there repaired all the musicians of Wales, and some also from England
+and Scotland." For many years afterwards the Eisteddfod appears to have
+been held triennially, and to have enforced the rigid observance of the
+enactments of Griffith ap Cynan. The places at which it was generally
+held were Aberffraw, formerly the royal seat of the princes of North
+Wales; Dynevor, the royal castle of the princes of South Wales; and
+Mathrafal, the royal palace of the princes of Powys: and in later times
+Caerwys in Flintshire received that honourable distinction, it having
+been the princely residence of Llewelyn the Last. Some of these
+Eisteddfodau were conducted in a style of great magnificence, under the
+patronage of the native princes. At Christmas 1107 Cadwgan, the son of
+Bleddyn ap Cynfyn, prince of Powys, held an Eisteddfod in Cardigan
+Castle, to which he invited the bards, harpers and minstrels, "the best
+to be found in all Wales"; and "he gave them chairs and subjects of
+emulation according to the custom of the feasts of King Arthur." In 1176
+Rhys ab Gruffydd, prince of South Wales, held an Eisteddfod in the same
+castle on a scale of still greater magnificence, it having been
+proclaimed, we are told, a year before it took place, "over Wales,
+England, Scotland, Ireland and many other countries."
+
+On the annexation of Wales to England, Edward I. deemed it politic to
+sanction the bardic Eisteddfod by his famous statute of Rhuddlan. In the
+reign of Edward III. Ifor Hael, a South Wales chieftain, held one at his
+mansion. Another was held in 1451, with the permission of the king, by
+Griffith ab Nicholas at Carmarthen, in princely style, where Dafydd ab
+Edmund, an eminent poet, signalized himself by his wonderful powers of
+versification in the Welsh metres, and whence "he carried home on his
+shoulders the silver chair" which he had fairly won. Several
+Eisteddfodau, were held, one at least by royal mandate, in the reign of
+Henry VII. In 1523 one was held at Caerwys before the chamberlain of
+North Wales and others, by virtue of a commission issued by Henry VIII.
+In the course of time, through relaxation of bardic discipline, the
+profession was assumed by unqualified persons, to the great detriment of
+the regular bards. Accordingly in 1567 Queen Elizabeth issued a
+commission for holding an Eisteddfod at Caerwys in the following year,
+which was duly held, when degrees were conferred on 55 candidates,
+including 20 harpers. From the terms of the royal proclamation we find
+that it was then customary to bestow "a silver harp" on the chief of the
+faculty of musicians, as it had been usual to reward the chief bard with
+"a silver chair." This was the last Eisteddfod appointed by royal
+commission, but several others of some importance were held during the
+16th and 17th centuries, under the patronage of the earl of Pembroke,
+Sir Richard Neville, and other influential persons. Amongst these the
+last of any particular note was one held in Bewper Castle, Glamorgan, by
+Sir Richard Basset in 1681.
+
+During the succeeding 130 years Welsh nationality was at its lowest ebb,
+and no general Eisteddfod on a large scale appears to have been held
+until 1819, though several small ones were held under the auspices of
+the Gwyneddigion Society, established in 1771,--the most important being
+those at Corwen (1789), St Asaph (1790) and Caerwys (1798).
+
+At the close of the Napoleonic wars, however, there was a general
+revival of Welsh nationality, and numerous Welsh literary societies were
+established throughout Wales, and in the principal English towns. A
+large Eisteddfod was held under distinguished patronage at Carmarthen in
+1819, and from that time to the present they have been held (together
+with numerous local Eisteddfodau), almost without intermission,
+annually. The Eisteddfod at Llangollen in 1858 is memorable for its
+archaic character, and the attempts then made to revive the ancient
+ceremonies, and restore the ancient vestments of druids, bards and
+ovates.
+
+To constitute a provincial Eisteddfod it is necessary that it should be
+proclaimed by a graduated bard of a Gorsedd a year and a day before it
+takes place. A local one may be held without such a proclamation. A
+provincial Eisteddfod generally lasts three, sometimes four days. A
+president and a conductor are appointed for each day. The proceedings
+commence with a Gorsedd meeting, opened with sound of trumpet and other
+ceremonies, at which candidates come forward and receive bardic degrees
+after satisfying the presiding bard as to their fitness. At the
+subsequent meetings the president gives a brief address; the bards
+follow with poetical addresses; adjudications are made, and prizes and
+medals with suitable devices are given to the successful competitors for
+poetical, musical and prose compositions, for the best choral and solo
+singing, and singing with the harp or "Pennillion singing"[2] as it is
+called, for the best playing on the harp or stringed or wind
+instruments, as well as occasionally for the best specimens of
+handicraft and art. In the evening of each day a concert is given,
+generally attended by very large numbers. The great day of the
+Eisteddfod is the "chair" day--usually the third or last day--the grand
+event of the Eisteddfod being the adjudication on the chair subject, and
+the chairing and investiture of the fortunate winner. This is the
+highest object of a Welsh bard's ambition. The ceremony is an imposing
+one, and is performed with sound of trumpet. (See also the articles
+BARD, CELT: _Celtic Literature_, and WALES.)     (R. W.*)
+
+
+FOOTNOTE:
+
+  [1] According to the Welsh Triads and other historical records, the
+    _Gorsedd_ or assembly (an essential part of the modern Eisteddfod,
+    from which indeed the latter sprung) is as old at least as the time
+    of Prydain the son of Ædd the Great, who lived many centuries before
+    the Christian era. Upon the destruction of the political ascendancy
+    of the Druids, the Gorsedd lost its political importance, though it
+    seems to have long afterwards retained its institutional character as
+    the medium for preserving the laws, doctrines and traditions of
+    bardism.
+
+  [2] According to Jones's _Bardic Remains_, "To sing 'Pennillion' with
+    a Welsh harp is not so easily accomplished as may be imagined. The
+    singer is obliged to follow the harper, who may change the tune, or
+    perform variations _ad libitum_, whilst the vocalist must keep time,
+    and end precisely with the strain. The singer does not commence with
+    the harper, but takes the strain up at the second, third or fourth
+    bar, as best suits the 'pennill' he intends to sing.... Those are
+    considered the best singers who can adapt stanzas of various metres
+    to one melody, and who are acquainted with the twenty-four measures
+    according to the bardic laws and rules of composition."
+
+
+
+
+EJECTMENT (Lat. e, out, and _jacere_, to throw), in English law, an
+action for the recovery of the possession of land, together with damages
+for the wrongful withholding thereof. In the old classifications of
+actions, as real or personal, this was known as a mixed action, because
+its object was twofold, viz. to recover both the realty and personal
+damages. It should be noted that the term "ejectment" applies in law to
+distinct classes of proceedings--ejectments as between rival claimants
+to land, and ejectments as between those who hold, or have held, the
+relation of landlord and tenant. Under the Rules of the Supreme Court,
+actions in England for the recovery of land are commenced and proceed in
+the same manner as ordinary actions. But the historical interest
+attaching to the action of ejectment is so great as to render some
+account of it necessary.
+
+The form of the action as it prevailed in the English courts down to the
+Common Law Procedure Act 1852 was a series of fictions, among the most
+remarkable to be found in the entire body of English law. A, the person
+claiming title to land, delivered to B, the person in possession, a
+declaration in ejectment in which C and D, fictitious persons, were
+plaintiff and defendant. C stated that A had devised the land to him for
+a term of years, and that he had been ousted by D. A notice signed by D
+informed B of the proceedings, and advised him to apply to be made
+defendant in D's place, as he, D, having no title, did not intend to
+defend the suit. If B did not so apply, judgment was given against D,
+and possession of the lands was given to A. But if B did apply, the
+Court allowed him to defend the action only on condition that he
+admitted the three fictitious averments--the lease, the entry and the
+ouster--which, together with title, were the four things necessary to
+maintain an action of ejectment. This having been arranged the action
+proceeded, B being made defendant instead of D. The names used for the
+fictitious parties were John Doe, plaintiff, and Richard Roe, defendant,
+who was called "the casual ejector." The explanation of these mysterious
+fictions is this. The writ _de ejectione firmae_ was invented about the
+beginning of the reign of Edward III. as a remedy to a lessee for years
+who had been ousted of his term. It was a writ of trespass, and carried
+damages, but in the time of Henry VII., if not before that date, the
+courts of common law added thereto a species of remedy neither warranted
+by the original writ nor demanded by the declaration, viz. a judgment to
+recover so much of the term as was still to run, and a writ of
+possession thereupon. The next step was to extend the remedy--limited
+originally to leaseholds--to cases of disputed title to freeholds. This
+was done indirectly by the claimant entering on the land and there
+making a lease for a term of years to another person; for it was only a
+term that could be recovered by the action, and to create a term
+required actual possession in the granter. The lessee remained on the
+land, and the next person who entered even by chance was accounted an
+ejector of the lessee, who then served upon him a writ of trespass and
+ejectment. The case then went to trial as on a common action of
+trespass; and the claimant's title, being the real foundation of the
+lessee's right, was thus indirectly determined. These proceedings might
+take place without the knowledge of the person really in possession; and
+to prevent the abuse of the action a rule was laid down that the
+plaintiff in ejectment must give notice to the party in possession, who
+might then come in and defend the action. When the action came into
+general use as a mode of trying the title to freeholds, the actual
+entry, lease and ouster which were necessary to found the action were
+attended with much inconvenience, and accordingly Lord Chief Justice
+Rolle during the Protectorate (c. 1657) substituted for them the
+fictitious averments already described. The action of ejectment is now
+only a curiosity of legal history. Its fictitious suitors were swept
+away by the Common Law Procedure Act of 1852. A form of writ was
+prescribed, in which the person in possession of the disputed premises
+by name and all persons entitled to defend the possession were informed
+that the plaintiff claimed to be entitled to possession, and required to
+appear in court to defend the possession of the property or such part of
+it as they should think fit. In the form of the writ and in some other
+respects ejectment still differed from other actions. But, as already
+mentioned, it has now been assimilated (under the name of action for the
+recovery of lands) to ordinary actions by the Rules of the Supreme
+Court. It is commenced by writ of summons, and--subject to the rules as
+to summary judgments (_v. inf._)--proceeds along the usual course of
+pleadings and trial to judgment; but is subject to one special rule,
+viz: that except by leave of the Court or a judge the only claims which
+may be joined with one for recovery of land are claims in respect of
+arrears of rent or double value for holding over, or mesne profits (i.e.
+the value of the land during the period of illegal possession), or
+damages for breach of a contract under which the premises are held or
+for any wrong or injury to the premises claimed (R.S.C., O. xviii. r.
+2). These claims were formerly recoverable by an independent action.
+
+With regard to actions for the recovery of land--apart from the
+relationship of landlord and tenant--the only point that need be noted
+is the presumption of law in favour of the actual possessor of the land
+in dispute. Where the action is brought by a landlord against his
+tenant, there is of course no presumption against the landlord's title
+arising from the tenant's possession. By the Common Law Procedure Act
+1852 (ss. 210-212) special provision was made for the prompt recovery of
+demised premises where half a year's rent was in arrear and the landlord
+was entitled to re-enter for non-payment. These provisions are still in
+force, but advantage is now more generally taken of the summary judgment
+procedure introduced by the Rules of the Supreme Court (Order 3, r. 6.).
+This procedure may be adopted when (a) the tenant's term has expired,
+(b) or has been duly determined by notice to quit, or (c) has become
+liable to forfeiture for non-payment of rent, and applies not only to
+the tenant but to persons claiming under him. The writ is specially
+endorsed with the plaintiff's claim to recover the land with or without
+rent or mesne profits, and summary judgment obtained if no substantial
+defence is disclosed. Where an action to recover land is brought against
+the tenant by a person claiming adversely to the landlord, the tenant is
+bound, under penalty of forfeiting the value of three years' improved or
+rack rent of the premises, to give notice to the landlord in order that
+he may appear and defend his title. Actions for the recovery of land,
+other than land belonging to spiritual corporations and to the crown,
+are barred in 12 years (Real Property Limitation Acts 1833 (s. 29) and
+1874 (s. 1). A landlord can recover possession in the county court (i.)
+by an action for the recovery of possession, where neither the value of
+the premises nor the rent exceeds £100 a year, and the tenant is holding
+over (County Courts Acts of 1888, s. 138, and 1903, s. 3); (ii.) by "an
+action of ejectment," where (a) the value or rent of the premises does
+not exceed £100, (b) half a year's rent is in arrear, and (c) no
+sufficient distress (see RENT) is to be found on the premises (Act of
+1888, s. 139; Act of 1903, s. 3; County Court Rules 1903, Ord. v. rule
+3). Where a tenant at a rent not exceeding £20 a year of premises at
+will, or for a term not exceeding 7 years, refuses nor neglects, on the
+determination or expiration of his interest, to deliver up possession,
+such possession may be recovered by proceedings before justices under
+the Small Tenements Recovery Act 1838, an enactment which has been
+extended to the recovery of allotments. Under the Distress for Rent Act
+1737, and the Deserted Tenements Act 1817, a landlord can have himself
+put by the order of two justices into premises deserted by the tenant
+where half a year's rent is owing and no sufficient distress can be
+found.
+
+In _Ireland_, the practice with regard to the recovery of land is
+regulated by the Rules of the Supreme Court 1891, made under the
+Judicature (Ireland) Act 1877; and resembles that of England. Possession
+may be recovered summarily by a special indorsement of the writ, as in
+England; and there are analogous provisions with regard to the recovery
+of small tenements (see Land Act, 1860 ss. 84 and 89). The law with
+regard to the ejectment or eviction of tenants is consolidated by the
+Land Act 1860. (See ss. 52-66, 68-71, and further under LANDLORD AND
+TENANT.)
+
+In _Scotland_, the recovery of land is effected by an action of
+"removing" or summary ejection. In the case of a tenant "warning" is
+necessary unless he is bound by his lease to remove without warning. In
+the case of possessors without title, or a title merely precarious, no
+warning is needed. A summary process of removing from small holdings is
+provided for by Sheriff Courts (Scotland) Acts of 1838 and 1851.
+
+In the United States, the old English action of ejectment was adopted to
+a very limited extent, and where it was so adopted has often been
+superseded, as in Connecticut, by a single action for all cases of
+ouster, disseisin or ejectment. In this action, known as an action of
+disseisin or ejectment, both possession of the land and damages may be
+recovered. In some of the states a tenant against whom an action of
+ejectment is brought by a stranger is bound under a penalty, as in
+England, to give notice of the claim to the landlord in order that he
+may appear and defend his title.
+
+In _French law_ the landlord's claim for rent is fairly secured by the
+hypothec, and by summary powers which exist for the seizure of the
+effects of defaulting tenants. Eviction or annulment of a lease can only
+be obtained through the judicial tribunals. The Civil Code deals with
+the position of a tenant in case of the sale of the property leased. If
+the lease is by authentic act (_acte authentique_) or has an ascertained
+date, the purchaser cannot evict the tenant unless a right to do so was
+reserved on the lease (art. 1743), and then only on payment of an
+indemnity (arts. 1744-1747). If the lease is not by authentic act, or
+has not an ascertained date, the purchaser is not liable for indemnity
+(art. 1750). The tenant of rural lands is bound to give the landlord
+notice of acts of usurpation (art. 1768). There are analogous provisions
+in the Civil Codes of Belgium (arts. 1743 et seq.), Holland (arts. 1613,
+1614), Portugal (art. 1572); and see the German Civil Code (arts. 535 et
+seq.). In many of the colonies there are statutory provisions for the
+recovery of land or premises on the lines of English law (cf. Ontario,
+Rev. Stats. 1897, c. 170. ss. 19 et seq.; Manitoba, Rev. Stats. 1902, c.
+1903). In others (e.g. New Zealand, Act. No. 55 of 1893, ss. 175-187;
+British Columbia, Revised Statutes, 1897, c. 182: Cyprus, Ord. 15 of
+1895) there has been legislation similar to the Small Tenements Recovery
+Act 1838.
+
+  AUTHORITIES.--_English Law_: Cole on _Ejectment_; Digby, _History of
+  Real Property_ (3rd ed., London, 1884); Pollock and Maitland, _History
+  of English Law_ (Cambridge, 1895); Foa, _Landlord and Tenant_ (4th
+  ed., London, 1907); Fawcett, _Landlord and Tenant_ (London, 1905).
+  _Irish Law_: Nolan and Kane's _Statutes relating to the Law of
+  Landlord and Tenant_ (5th ed., Dublin, 1898); Wylie's _Judicature
+  Acts_ (Dublin, 1900). _Scots Law_: Hunter on _Landlord and Tenant_
+  (4th ed., Edin., 1878); Erskine's _Principles_ (20th ed., Edin.,
+  1903). _American Law: Two Centuries' Growth of American Law_ (New York
+  and London, 1901); Bouvier's _Law Dictionary_ (Boston and London,
+  1897); Stimson, _American Statute Law_ (Boston, 1886).     (A. W. R.)
+
+
+
+
+EKATERINBURG, a town of Russia, in the government of Perm, 311 m. by
+rail S.E. of the town of Perm, on the Iset river, near the E. foot of
+the Ural Mountains, in 56° 49' N. and 60° 35' E., at an altitude of 870
+ft. above sea-level. It is the most important town of the Urals. Pop.
+(1860) 19,830; (1897) 55,488. The streets are broad and regular, and
+several of the houses of palatial proportions. In 1834 Ekaterinburg was
+made the see of a suffragan bishop of the Orthodox Greek Church. There
+are two cathedrals--St Catherine's, founded in 1758, and that of the
+Epiphany, in 1774--and a museum of natural history, opened in 1853.
+Ekaterinburg is the seat of the central mining administration of the
+Ural region, and has a chemical laboratory for the assay of gold, a
+mining school, the Ural Society of Naturalists, and a magnetic and
+meteorological observatory. Besides the government mint for copper
+coinage, which dates from 1735, the government engineering works, and
+the imperial factory for the cutting and polishing of malachite, jasper,
+marble, porphyry and other ornamental stones, the industrial
+establishments comprise candle, paper, soap and machinery works, flour
+and woollen mills, and tanneries. There is a lively trade in cattle,
+cereals, iron, woollen and silk goods, and colonial products; and two
+important fairs are held annually. Nearly forty gold and platinum mines,
+over thirty iron-works, and numerous other factories are scattered over
+the district, while wheels, travelling boxes, hardware, boots and so
+forth are extensively made in the villages. Ekaterinburg took its origin
+from the mining establishments founded by Peter the Great in 1721, and
+received its name in honour of his wife, Catherine I. Its development
+was greatly promoted in 1763 by the diversion of the Siberian highway
+from Verkhoturye to this place.
+
+
+
+
+EKATERINODAR, a town of South Russia, chief town of the province of
+Kubañ, on the right bank of the river Kubañ, 85 m. E.N.E. of
+Novo-rossiysk on the railway to Rostov-on-Don, and in 45° 3' N. and 38°
+50' E. It is badly built, on a swampy site exposed to the inundations of
+the river; and its houses, with few exceptions, are slight structures of
+wood and plaster. Founded by Catherine II. in 1794 on the site of an old
+town called Tmutarakan, as a small fort and Cossack settlement, its
+population grew from 9620 in 1860 to 65,697 in 1897. It has various
+technical schools, an experimental fruit-farm, a military hospital, and
+a natural history museum. A considerable trade is carried on, especially
+in cereals.
+
+
+
+
+EKATERINOSLAV, a government of south Russia, having the governments of
+Poltava and Kharkov on the N., the territory of the Don Cossacks on the
+E., the Sea of Azov and Taurida on the S., and Kherson on the W. Area,
+24,478 sq. m. Its surface is undulating steppe, sloping gently south and
+north, with a few hills reaching 1200 ft. in the N.E., where a slight
+swelling (the Don Hills) compels the Don to make a great curve
+eastwards. Another chain of hills, to which the eastward bend of the
+Dnieper is due, rises in the west. These hills have a crystalline core
+(granites, syenites and diorites), while the surface strata belong to
+the Carboniferous, Permian, Cretaceous and Tertiary formations. The
+government is rich in minerals, especially in coal--the mines lie in the
+middle of the Donets coalfield--iron ores, fireclay and rock-salt, and
+every year the mining output increases in quantity, especially of coal
+and iron. Granite, limestone, grindstone, slate, with graphite,
+manganese and mercury are found. The government is drained by the
+Dnieper, the Don and their tributaries (e.g. the Donets and Volchya) and
+by several affluents (e.g. the Kalmius) of the Sea of Azov. The soil is
+the fertile black earth, but the crops occasionally suffer from drought,
+the average annual rainfall being only 15 in. Forests are scarce. Pop.
+(1860) 1,138,750; (1897) 2,118,946, chiefly Little Russians, with Great
+Russians, Greeks (48,740), Germans (80,979), Rumanians and a few
+gypsies. Jews constitute 4.7% of the population. The estimated
+population in 1906 was 2,708,700.
+
+Wheat and other cereals are extensively grown; other noteworthy crops
+are potatoes, tobacco and grapes. Nearly 40,000 persons find occupation
+in factories, the most important being iron-works and agricultural
+machinery works, though there are also tobacco, glass, soap and candle
+factories, potteries, tanneries and breweries. In the districts of
+Mariupol the making of agricultural implements and machinery is carried
+on extensively as a domestic industry in the villages. Bees are kept in
+very considerable numbers. Fishing employs many persons in the Don and
+the Dnieper. Cereals are exported in large quantities via the Dnieper,
+the Sevastopol railway, and the port of Mariupol. The chief towns of the
+eight districts, with their populations in 1897, are Ekaterinoslav
+(135,552 inhabitants in 1900), Alexandrovsk (28,434), Bakhmut (30,585),
+Mariupol (31,772), Novomoskovsk (12,862), Pavlograd (17,188),
+Slavyanoserbsk (3120), and Verkhne-dnyeprovsk (11,607).
+
+
+
+
+EKATERINOSLAV, a town of Russia, capital of the government of the same
+name, on the right bank of the Dnieper above the rapids, 673 m. by rail
+S.S.W. of Moscow, in 48° 21' N. and 35° 4' E., at an altitude of 210 ft.
+Pop. (1861) 18,881, without suburbs; (1900) 135,552. If the suburb of
+Novyikoindak be included, the town extends for upwards of 4 m. along the
+river. The oldest part lies very low and is much exposed to floods.
+Contiguous to the towns on the N.W. is the royal village of Novyimaidani
+or the New Factories. The bishop's palace, mining academy,
+archaeological museum and library are the principal public buildings.
+The house now occupied by the Nobles Club was formerly inhabited by the
+author and statesman Potemkin. Ekaterinoslav is a rapidly growing city,
+with a number of technical schools, and is an important depot for timber
+floated down the Dnieper, and also for cereals. Its iron-works,
+flour-mills and agricultural machinery works give occupation to over
+5000 persons. In fact since 1895 the city has become the centre of
+numerous Franco-Belgian industrial undertakings. In addition to the
+branches just mentioned, there are tobacco factories and breweries.
+Considerable trade is carried on in cattle, cereals, horses and wool,
+there being three annual fairs. On the site of the city there formerly
+stood the Polish castle of Koindak, built in 1635, and destroyed by the
+Cossacks. The existing city was founded by Potemkin in 1786, and in the
+following year Catherine II. laid the foundation-stone of the cathedral,
+though it was not actually built until 1830-1835. On the south side of
+it is a bronze statue of the empress, put up in 1846. Paul I. changed
+the name of the city to Novo-rossiysk, but the original name was
+restored in 1802.
+
+
+
+
+EKHOF, KONRAD (1720-1778), German actor, was born in Hamburg on the 12th
+of August 1720. In 1739 he became a member of Johann Friedrich
+Schönemann's (1704-1782) company in Lüneburg, and made his first
+appearance there on the 15th of January 1740 as Xiphares in Racine's
+_Mithridate_. From 1751 the Schönemann company performed mainly in
+Hamburg and at Schwerin, where Duke Christian Louis II. of
+Mecklenburg-Schwerin made them comedians to the court. During this
+period Ekhof founded a theatrical academy, which, though short-lived,
+was of great importance in helping to raise the standard of German
+acting and the status of German actors. In 1757 Ekhof left Schönemann to
+join Franz Schuch's company at Danzig; but he soon returned to Hamburg,
+where, in conjunction with two other actors, he succeeded Schönemann in
+the direction of the company. He resigned this position, however, in
+favour of H.G. Koch, with whom he acted until 1764, when he joined K.E.
+Ackermann's company. In 1767 was founded the National Theatre at
+Hamburg, made famous by Lessing's _Hamburgische Dramaturgie_, and Ekhof
+was the leading member of the company. After the failure of the
+enterprise Ekhof was for a time in Weimar, and ultimately became
+co-director of the new court theatre at Gotha. This, the first
+permanently established theatre in Germany, was opened on the 2nd of
+October 1775. Ekhof's reputation was now at its height; Goethe called
+him the only German tragic actor; and in 1777 he acted with Goethe and
+Duke Charles Augustus at a private performance at Weimar, dining
+afterwards with the poet at the ducal table. He died on the 16th of June
+1778. His versatility may be judged from the fact that in the comedies
+of Goldoni and Molière he was no less successful than in the tragedies
+of Lessing and Shakespeare. He was regarded by his contemporaries as an
+unsurpassed exponent of naturalness on the stage; and in this respect he
+has been not unfairly compared with Garrick. His fame, however, was
+rapidly eclipsed by that of Friedrich U.L. Schröder. His literary
+efforts were chiefly confined to translations from French authors.
+
+  See H. Uhde, biography of Ekhof in vol. iv. of _Der neue Plutarch_
+  (1876), and J. Rüschner, _K. Ekhofs Leben und Wirken_ (1872). Also H.
+  Devrient, _J.F. Schönemann und seine Schauspielergesellschaft_ (1895).
+
+
+
+
+EKRON (better, as in the Septuagint and Josephus, ACCARON, [Greek:
+Akkarôn]), a royal city of the Philistines commonly identified with the
+modern Syrian village of `Akir, 5 m. from Ramleh, on the southern slope
+of a low ridge separating the plain of Philistia from Sharon. It lay
+inland and off the main line of traffic. Though included by the
+Israelites within the limits of the tribe of Judah, and mentioned in
+Judges xix. as one of the cities of Dan, it was in Philistine possession
+in the days of Samuel, and apparently maintained its independence.
+According to the narrative of the Hebrew text, here differing from the
+Greek text and Josephus (which read Askelon), it was the last town to
+which the ark was transferred before its restoration to the Israelites.
+Its maintenance of a sanctuary of Baal Zebub is mentioned in 2 Kings i.
+From Assyrian inscriptions it has been gathered that Padi, king of
+Ekron, was for a time the vassal of Hezekiah of Judah, but regained his
+independence when the latter was hard pressed by Sennacherib. A notice
+of its history in 147 B.C. is found in 1 Macc. x. 89; after the fall of
+Jerusalem A.D. 70 it was settled by Jews. At the time of the crusades it
+was still a large village. Recently a Jewish agricultural colony has
+been settled there. The houses are built of mud, and in the absence of
+visible remains of antiquity, the identification of the site is
+questionable. The neighbourhood is fertile.     (R. A. S. M.)
+
+
+
+
+ELABUGA, a town of Russia, in the government of Vyatka, on the Kama
+river, 201 m. by steamboat down the Volga from Kazan and then up the
+Kama. It has flour-mills, and carries on a brisk trade in exporting
+corn. Pop. (1897) 9776.
+
+The famous _Ananiynskiy Mogilnik_ (burial-place) is on the right bank of
+the Kama, 3 m. above the town. It was discovered in 1858, was excavated
+by Alabin, Lerch and Nevostruyev, and has since supplied extremely
+valuable collections belonging to the Stone, Bronze and Iron Ages. It
+consisted of a mound, about 500 ft. in circumference, adorned with
+decorated stones (which have disappeared), and contained an inner wall,
+65 ft. in circumference, made of uncemented stone flags. Nearly fifty
+skeletons were discovered, mostly lying upon charred logs, surrounded
+with cinerary urns filled with partially burned bones. A great variety
+of bronze decorations and glazed clay pearls were strewn round the
+skeletons. The knives, daggers and arrowpoints are of slate, bronze and
+iron, the last two being very rough imitations of stone implements. One
+of the flags bore the image of a man, without moustaches or beard,
+dressed in a costume and helmet recalling those of the Circassians.
+
+
+
+
+ELAM, the name given in the Bible to the province of Persia called
+Susiana by the classical geographers, from Susa or Shushan its capital.
+In one passage, however (Ezra iv. 9), it is confined to Elymais, the
+north-western part of the province, and its inhabitants distinguished
+from those of Shushan, which elsewhere (Dan. viii. 2) is placed in Elam.
+Strabo (xv. 3. 12, &c.) makes Susiana a part of Persia proper, but a
+comparison of his account with those of Ptolemy (vi. 3. 1, &c.) and
+other writers would limit it to the mountainous district to the east of
+Babylonia, lying between the Oroatis and the Tigris, and stretching from
+India to the Persian Gulf. Along with this mountainous district went a
+fertile low tract of country on the western side, which also included
+the marshes at the mouths of the Euphrates and Tigris and the
+north-eastern coast land of the Gulf. This low tract, though producing
+large quantities of grain, was intensely hot in summer; the high
+regions, however, were cool and well watered.
+
+The whole country was occupied by a variety of tribes, speaking
+agglutinative dialects for the most part, though the western districts
+were occupied by Semites. Strabo (xi. 13. 3, 6), quoting from Nearchus,
+seems to include the Susians under the Elymaeans, whom he associates
+with the Uxii, and places on the frontiers of Persia and Susa; but
+Pliny more correctly makes the Eulaeus the boundary between Susiana and
+Elymais (_N.H._ vi. 29-31). The Uxii are described as a robber tribe in
+the mountains adjacent to Media, and their name is apparently to be
+identified with the title given to the whole of Susiana in the Persian
+cuneiform inscriptions, _Uwaja_, i.e. "Aborigines." Uwaja is probably
+the origin of the modern Khuzistan, though Mordtmann would derive the
+latter from [Arab script] "a sugar-reed." Immediately bordering on the
+Persians were the Amardians or Mardians, as well as the people of
+Khapirti (Khatamti, according to Scheil), the name given to Susiana in
+the Neo-Susian texts. Khapirti appears as Apir in the inscriptions of
+Mal-Amir, which fix the locality of the district. Passing over the
+Messabatae, who inhabited a valley which may perhaps be the modern
+Mah-Sabadan, as well as the level district of Yamutbal or Yatbur which
+separated Elam from Babylonia, and the smaller districts of Characene,
+Cabandene, Corbiana and Gabiene mentioned by classical authors, we come
+to the fourth principal tribe of Susiana, the Cissii (Aesch. _Pers._ 16;
+Strabo xv. 3. 2) or Cossaei (Strabo xi. 5. 6, xvi. 11. 17; Arr. _Ind._
+40; Polyb. v. 54, &c.), the Kassi of the cuneiform inscriptions. So
+important were they, that the whole of Susiana was sometimes called
+Cissia after them, as by Herodotus (iii. 91, v. 49, &c.). In fact
+Susiana was only a late name for the country, dating from the time when
+Susa had been made a capital of the Persian empire. In the Sumerian
+texts of Babylonia it was called Numma, "the Highlands," of which Elamtu
+or Elamu, "Elam," was the Semitic translation. Apart from Susa, the most
+important part of the country was Anzan (Anshan, contracted Assan),
+where the native population maintained itself unaffected by Semitic
+intrusion. The exact position of Anzan is still disputed, but it
+probably included originally the site of Susa and was distinguished from
+it only when Susa became the seat of a Semitic government. In the
+lexical tablets Anzan is given as the equivalent of Elamtu, and the
+native kings entitle themselves kings of "Anzan and Susa," as well as
+"princes of the Khapirti."
+
+The principal mountains of Elam were on the north, called Charbanus and
+Cambalidus by Pliny (vi. 27, 31), and belonging to the Parachoathras
+chain. There were numerous rivers flowing into either the Tigris or the
+Persian Gulf. The most important were the Ulai or Eulaeus (_Kuran_) with
+its tributary the Pasitigris, the Choaspes (_Kerkhah_), the Coprates
+(river of _Diz_ called Itite in the inscriptions), the Hedyphon or
+Hedypnus (_Jerrahi_), and the Croatis (_Hindyan_), besides the
+monumental Surappi and Ukni, perhaps to be identified with the Hedyphon
+and Oroatis, which fell into the sea in the marshy region at the mouth
+of the Tigris. Shushan or Susa, the capital now marked by the mounds of
+_Shush_, stood near the junction of the Choaspes and Eulaeus (see SUSA);
+and Badaca, Madaktu in the inscriptions, lay between the _Shapur_ and
+the river of _Diz_. Among the other chief cities mentioned in the
+inscriptions may be named Naditu, Khaltemas, Din-sar, Bubilu, Bit-imbi,
+Khidalu and Nagitu on the sea-coast. Here, in fact, lay some of the
+oldest and wealthiest towns, the sites of which have, however, been
+removed inland by the silting up of the shore. J. de Morgan's
+excavations at Susa have thrown a flood of light on the early history of
+Elam and its relations to Babylon. The earliest settlement there goes
+back to neolithic times, but it was already a fortified city when Elam
+was conquered by Sargon of Akkad (3800 B.C.) and Susa became the seat of
+a Babylonian viceroy. From this time onward for many centuries it
+continued under Semitic suzerainty, its high-priests, also called "Chief
+Envoys of Elam, Sippara and Susa," bearing sometimes Semitic, sometimes
+native "Anzanite" names. One of the kings of the dynasty of Ur built at
+Susa. Before the rise of the First Dynasty of Babylon, however, Elam had
+recovered its independence, and in 2280 B.C. the Elamite king
+Kutur-Nakhkhunte made a raid in Babylonia and carried away from Erech
+the image of the goddess Nana. The monuments of many of his successors
+have been discovered by de Morgan and their inscriptions deciphered by
+v. Scheil. One of them was defeated by Ammi-zadoq of Babylonia (c. 2100
+B.C.); another would have been the Chedor-laomer (Kutur-Lagamar) of
+Genesis xiv. One of the greatest builders among them was Untas-GAL (the
+pronunciation of the second element in the name is uncertain). About
+1330 B.C. Khurba-tila was captured by Kuri-galzu III., the Kassite king
+of Babylonia, but a later prince Kidin-Khutrutas avenged his defeat, and
+Sutruk-Nakhkhunte (1220 B.C.) carried fire and sword through Babylonia,
+slew its king Zamama-sum-iddin and carried away a stela of Naram-Sin and
+the famous code of laws of Khammurabi from Sippara, as well as a stela
+of Manistusu from Akkuttum or Akkad. He also conquered the land of
+Asnunnak and carried off from Padan a stela belonging to a refugee from
+Malatia. He was succeeded by his son who was followed on the throne by
+his brother, one of the great builders of Elam. In 750 B.C. Umbadara was
+king of Elam; Khumban-igas was his successor in 742 B.C. In 720 B.C. the
+latter prince met the Assyrians under Sargon at Dur-ili in Yamutbal, and
+though Sargon claims a victory the result was that Babylonia recovered
+its independence under Merodach-baladan and the Assyrian forces were
+driven north. From this time forward it was against Assyria instead of
+Babylonia that Elam found itself compelled to exert its strength, and
+Elamite policy was directed towards fomenting revolt in Babylonia and
+assisting the Babylonians in their struggle with Assyria. In 716 B.C.
+Khumban-igas died and was followed by his nephew, Sutruk-Nakhkhunte. He
+failed to make head against the Assyrians; the frontier cities were
+taken by Sargon and Merodach-baladan was left to his fate. A few years
+later (704 B.C.) the combined forces of Elam and Babylonia were
+overthrown at Kis, and in the following year the Kassites were reduced
+to subjection. The Elamite king was dethroned and imprisoned in 700 B.C.
+by his brother Khallusu, who six years later marched into Babylonia,
+captured the son of Sennacherib, whom his father had placed there as
+king, and raised a nominee of his own, Nergal-yusezib, to the throne.
+Khallusu was murdered in 694 B.C., after seeing the maritime part of his
+dominions invaded by the Assyrians. His successor Kudur-Nakhkhunte
+invaded Babylonia; he was repulsed, however, by Sennacherib, 34 of his
+cities were destroyed, and he himself fled from Madaktu to Khidalu. The
+result was a revolt in which he was killed after a reign of ten months.
+His brother Umman-menan at once collected allies and prepared for
+resistance to the Assyrians. But the terrible defeat at Khalule broke
+his power; he was attacked by paralysis shortly afterwards, and
+Khumba-Khaldas II. followed him on the throne (689 B.C.). The new king
+endeavoured to gain Assyrian favour by putting to death the son of
+Merodach-baladan, but was himself murdered by his brothers Urtaki and
+Teumman (681 B.C.), the first of whom seized the crown. On his death
+Teumman succeeded and almost immediately provoked a quarrel with
+Assur-bani-pal by demanding the surrender of his nephews who had taken
+refuge at the Assyrian court. The Assyrians pursued the Elamite army to
+Susa, where a battle was fought on the banks of the Eulaeus, in which
+the Elamites were defeated, Teumman captured and slain, and Umman-igas,
+the son of Urtaki, made king, his younger brother Tammaritu being given
+the district of Khidalu. Umman-igas afterwards assisted in the revolt of
+Babylonia under Samas-sum-yukin, but his nephew, a second Tammaritu,
+raised a rebellion against him, defeated him in battle, cut off his head
+and seized the crown. Tammaritu marched to Babylonia; while there, his
+officer Inda-bigas made himself master of Susa and drove Tammaritu to
+the coast whence he fled to Assur-bani-pal. Inda-bigas was himself
+overthrown and slain by a new pretender, Khumba-Khaldas III., who was
+opposed, however, by three other rivals, two of whom maintained
+themselves in the mountains until the Assyrian conquest of the country,
+when Tammaritu was first restored and then imprisoned, Elam being
+utterly devastated. The return of Khumba-Khaldas led to a fresh Assyrian
+invasion; the Elamite king fled from Madaktu to Dur-undasi; Susa and
+other cities were taken, and the Elamite army almost exterminated on the
+banks of the Itite. The whole country was reduced to a desert, Susa was
+plundered and razed to the ground, the royal sepulchres were desecrated,
+and the images of the gods and of 32 kings "in silver, gold, bronze and
+alabaster," were carried away. All this must have happened about 640
+B.C. After the fall of the Assyrian empire Elam was occupied by the
+Persian Teispes, the forefather of Cyrus, who, accordingly, like his
+immediate successors, is called in the inscriptions "king of Anzan."
+Susa once more became a capital, and on the establishment of the Persian
+empire remained one of the three seats of government, its language, the
+Neo-Susian, ranking with the Persian of Persepolis and the Semitic of
+Babylon as an official tongue. In the reign of Darius, however, the
+Susianians attempted to revolt, first under Assina or Atrina, the son of
+Umbadara, and later under Martiya, the son of Issainsakria, who called
+himself Immanes; but they gradually became completely Aryanized, and
+their agglutinative dialects were supplanted by the Aryan Persian from
+the south-east.
+
+Elam, "the land of the cedar-forest," with its enchanted trees, figured
+largely in Babylonian mythology, and one of the adventures of the hero
+Gilgamesh was the destruction of the tyrant Khumbaba who dwelt in the
+midst of it. A list of the Elamite deities is given by Assur-bani-pal;
+at the head of them was In-Susinak, "the lord of the Susians,"--a title
+which went back to the age of Babylonian suzerainty,--whose image and
+oracle were hidden from the eyes of the profane. Nakhkhunte, according
+to Scheil, was the Sun-goddess, and Lagamar, whose name enters into that
+of Chedor-laomer, was borrowed from Semitic Babylonia.
+
+  See W.K. Loftus, _Chaldaea and Susiana_ (1857); A. Billerbeck, _Susa_
+  (1893); J. de Morgan, _Mémoires de la Délégation en Perse_ (9 vols.,
+  1899-1906).     (A. H. S.)
+
+
+
+
+ELAND (= elk), the Dutch name for the largest of the South African
+antelopes (_Taurotragus oryx_), a species near akin to the kudu, but
+with horns present in both sexes, and their spiral much closer, being in
+fact screw-like instead of corkscrew-like. There is also a large dewlap,
+while old bulls have a thick forelock. In the typical southern form the
+body-colour is wholly pale fawn, but north of the Orange river the body
+is marked by narrow vertical white lines, this race being known as _T.
+oryx livingstonei_. In Senegambia the genus is represented by _T.
+derbianus_, a much larger animal, with a dark neck; while in the
+Bahr-el-Ghazal district there is a gigantic local race of this species
+(_T. derbianus giganteus_).     (R. L.*)
+
+
+
+
+ELASTICITY. 1. Elasticity is the property of recovery of an original
+size or shape. A body of which the size, or shape, or both size and
+shape, have been altered by the application of forces may, and generally
+does, tend to return to its previous size and shape when the forces
+cease to act. Bodies which exhibit this tendency are said to be
+_elastic_ (from Greek, [Greek: elaunein], to drive). All bodies are more
+or less elastic as regards size; and all solid bodies are more or less
+elastic as regards shape. For example: gas contained in a vessel, which
+is closed by a piston, can be compressed by additional pressure applied
+to the piston; but, when the additional pressure is removed, the gas
+expands and drives the piston outwards. For a second example: a steel
+bar hanging vertically, and loaded with one ton for each square inch of
+its sectional area, will have its length increased by about seven
+one-hundred-thousandths of itself, and its sectional area diminished by
+about half as much; and it will spring back to its original length and
+sectional area when the load is gradually removed. Such changes of size
+and shape in bodies subjected to forces, and the recovery of the
+original size and shape when the forces cease to act, become conspicuous
+when the bodies have the forms of thin wires or planks; and these
+properties of bodies in such forms are utilized in the construction of
+spring balances, carriage springs, buffers and so on.
+
+It is a familiar fact that the hair-spring of a watch can be coiled and
+uncoiled millions of times a year for several years without losing its
+elasticity; yet the same spring can have its shape permanently altered
+by forces which are much greater than those to which it is subjected in
+the motion of the watch. The incompleteness of the recovery from the
+effects of great forces is as important a fact as the practical
+completeness of the recovery from the effects of comparatively small
+forces. The fact is referred to in the distinction between "perfect"
+and "imperfect" elasticity; and the limitation which must be imposed
+upon the forces in order that the elasticity may be perfect leads to the
+investigation of "limits of elasticity" (see §§ 31, 32 below). Steel
+pianoforte wire is perfectly elastic within rather wide limits, glass
+within rather narrow limits; building stone, cement and cast iron appear
+not to be perfectly elastic within any limits, however narrow. When the
+limits of elasticity are not exceeded no injury is done to a material or
+structure by the action of the forces. The strength or weakness of a
+material, and the safety or insecurity of a structure, are thus closely
+related to the elasticity of the material and to the change of size or
+shape of the structure when subjected to forces. The "science of
+elasticity" is occupied with the more abstract side of this relation,
+viz. with the effects that are produced in a body of definite size,
+shape and constitution by definite forces; the "science of the strength
+of materials" is occupied with the more concrete side, viz. with the
+application of the results obtained in the science of elasticity to
+practical questions of strength and safety (see STRENGTH OF MATERIALS).
+
+2. _Stress._--Every body that we know anything about is always under the
+action of forces. Every body upon which we can experiment is subject to
+the force of gravity, and must, for the purpose of experiment, be
+supported by other forces. Such forces are usually applied by way of
+pressure upon a portion of the surface of the body; and such pressure is
+exerted by another body in contact with the first. The supported body
+exerts an equal and opposite pressure upon the supporting body across
+the portion of surface which is common to the two. The same thing is
+true of two portions of the same body. If, for example, we consider the
+two portions into which a body is divided by a (geometrical) horizontal
+plane, we conclude that the lower portion supports the upper portion by
+pressure across the plane, and the upper portion presses downwards upon
+the lower portion with an equal pressure. The pressure is still exerted
+when the plane is not horizontal, and its direction may be obliquely
+inclined to, or tangential to, the plane. A more precise meaning is
+given to "pressure" below. It is important to distinguish between the
+two classes of forces: forces such as the force of gravity, which act
+all through a body, and forces such as pressure applied over a surface.
+The former are named "body forces" or "volume forces," and the latter
+"surface tractions." The action between two portions of a body separated
+by a geometrical surface is of the nature of surface traction. Body
+forces are ultimately, when the volumes upon which they act are small
+enough, proportional to the volumes; surface tractions, on the other
+hand, are ultimately, when the surfaces across which they act are small
+enough, proportional to these surfaces. Surface tractions are always
+exerted by one body upon another, or by one part of a body upon another
+part, across a surface of contact; and a surface traction is always to
+be regarded as one aspect of a "stress," that is to say of a pair of
+equal and opposite forces; for an equal traction is always exerted by
+the second body, or part, upon the first across the surface.
+
+3. The proper method of estimating and specifying stress is a matter of
+importance, and its character is necessarily mathematical. The
+magnitudes of the surface tractions which compose a stress are estimated
+as so much force (in dynes or tons) per unit of area (per sq. cm. or per
+sq. in.). The traction across an assigned plane at an assigned point is
+measured by the mathematical limit of the fraction F/S, where F denotes
+the numerical measure of the force exerted across a small portion of the
+plane containing the point, and S denotes the numerical measure of the
+area of this portion, and the limit is taken by diminishing S
+indefinitely. The traction may act as "tension," as it does in the case
+of a horizontal section of a bar supported at its upper end and hanging
+vertically, or as "pressure," as it does in the case of a horizontal
+section of a block resting on a horizontal plane, or again it may act
+obliquely or even tangentially to the separating plane. Normal tractions
+are reckoned as positive when they are tensions, negative when they are
+pressures. Tangential tractions are often called "shears" (see § 7
+below). Oblique tractions can always be resolved, by the vector law,
+into normal and tangential tractions. In a fluid at rest the traction
+across any plane at any point is normal to the plane, and acts as
+pressure. For the complete specification of the "state of stress" at any
+point of a body, we should require to know the normal and tangential
+components of the traction across every plane drawn through the point.
+Fortunately this requirement can be very much simplified (see §§ 6, 7
+below).
+
+  4. In general let [nu] denote the direction of the normal drawn in a
+  specified sense to a plane drawn through a point O of a body; and let
+  T{[nu]} denote the traction exerted across the plane, at the point O,
+  by the portion of the body towards which [nu] is drawn upon the
+  remaining portion. Then T{[nu]} is a vector quantity, which has a
+  definite magnitude (estimated as above by the limit of a fraction of
+  the form F/S) and a definite direction. It can be specified completely
+  by its components X{[nu]}, Y{[nu]}, Z{[nu]}, referred to fixed
+  rectangular axes of x, y, z. When the direction of [nu] is that of the
+  axis of x, in the positive sense, the components are denoted by X_x,
+  Y_x, Z_x; and a similar notation is used when the direction of [nu] is
+  that of y or z, the suffix x being replaced by y or z.
+
+5. Every body about which we know anything is always in a state of
+stress, that is to say there are always internal forces acting between
+the parts of the body, and these forces are exerted as surface tractions
+across geometrical surfaces drawn in the body. The body, and each part
+of the body, moves under the action of all the forces (body forces and
+surface tractions) which are exerted upon it; or remains at rest if
+these forces are in equilibrium. This result is expressed analytically
+by means of certain equations--the "equations of motion" or "equations
+of equilibrium" of the body.
+
+  Let [rho] denote the density of the body at any point, X, Y, Z, the
+  components parallel to the axes of x, y, z of the body forces,
+  estimated as so much force per unit of mass; further let f_x, f_y, f_z
+  denote the components, parallel to the same axes, of the acceleration
+  of the particle which is momentarily at the point (x, y, z). The
+  equations of motion express the result that the rates of change of the
+  momentum, and of the moment of momentum, of any portion of the body
+  are those due to the action of all the forces exerted upon the portion
+  by other bodies, or by other portions of the same body. For the
+  changes of momentum, we have three equations of the type
+      _ _ _                 _ _            _ _ _
+     / / /                 / /            / / /
+     | | |[rho]Xdx dy dz + | |X_[nu] dS = | | |[rho]f_x dx dy dz,  (1)
+    _/_/_/                _/_/           _/_/_/
+
+  in which the volume integrations are taken through the volume of the
+  portion of the body, the surface integration is taken over its
+  surface, and the notation X_[nu] is that of § 4, the direction of [nu]
+  being that of the normal to this surface drawn outwards. For the
+  changes of moment of momentum, we have three equations of the type
+      _ _ _                         _ _
+     / / /                         / /
+     | | |[rho](yZ - zY)dx dy dz + | |(yZ_[nu] - zY_[nu])dS =
+    _/_/_/                        _/_/
+         _ _ _
+        / / /
+        | | |[rho](yf_z - zf_y)dx dy dz. (2)
+       _/_/_/
+
+  The equations (1) and (2) are the equations of motion of any kind of
+  body. The equations of equilibrium are obtained by replacing the
+  right-hand members of these equations by zero.
+
+  6. These equations can be used to obtain relations between the values
+  of X_[nu], Y_[nu], ... for different directions [nu]. When the
+  equations are applied to a very small volume, it appears that the
+  terms expressed by surface integrals would, unless they tend to zero
+  limits in a higher order than the areas of the surfaces, be very great
+  compared with the terms expressed by volume integrals. We conclude
+  that the surface tractions on the portion of the body which is bounded
+  by any very small closed surface, are ultimately in equilibrium. When
+  this result is interpreted for a small portion in the shape of a
+  tetrahedron, having three of its faces at right angles to the
+  co-ordinate axes, it leads to three equations of the type
+
+    X_[nu] = X_x cos(x, [nu]) + X_y cos(y, [nu]) + X_z cos(z, [nu]), (1)
+
+  where [nu] is the direction of the normal (drawn outwards) to the
+  remaining face of the tetrahedron, and (x, [nu]) ... denote the angles
+  which this normal makes with the axes. Hence X_[nu], ... for any
+  direction [nu] are expressed in terms of X_x,.... When the above
+  result is interpreted for a very small portion in the shape of a cube,
+  having its edges parallel to the co-ordinate axes, it leads to the
+  equations
+
+    Y_z = Z_y,   Z_x = X_z,   X_y = Y_x.  (2)
+
+  When we substitute in the general equations the particular results
+  which are thus obtained, we find that the equations of motion take
+  such forms as
+
+             dPX_x   dPX_y   dPZ_x
+    [rho]X + ----- + ----- + ----- = [rho] f_x,  (3)
+              dPx     dPy     dPz
+
+  and the equations of moments are satisfied identically. The equations
+  of equilibrium are obtained by replacing the right-hand members by
+  zero.
+
+7. A state of stress in which the traction across any plane of a set of
+parallel planes is normal to the plane, and that across any
+perpendicular plane vanishes, is described as a state of "simple
+tension" ("simple pressure" if the traction is negative). A state of
+stress in which the traction across any plane is normal to the plane,
+and the traction is the same for all planes passing through any point,
+is described as a state of "uniform tension" ("uniform pressure" if the
+traction is negative). Sometimes the phrases "isotropic tension" and
+"hydrostatic pressure" are used instead of "uniform" tension or
+pressure. The distinction between the two states, simple tension and
+uniform tension, is illustrated in fig. 1.
+
+[Illustration: FIG. 1.]
+
+A state of stress in which there is purely tangential traction on a
+plane, and no normal traction on any perpendicular plane, is described
+as a state of "shearing stress." The result (2) of § 6 shows that
+tangential tractions occur in pairs. If, at any point, there is
+tangential traction, in any direction, on a plane parallel to this
+direction, and if we draw through the point a plane at right angles to
+the direction of this traction, and therefore containing the normal to
+the first plane, then there is equal tangential traction on this second
+plane in the direction of the normal to the first plane. The result is
+illustrated in fig. 2, where a rectangular block is subjected on two
+opposite faces to opposing tangential tractions, and is held in
+equilibrium by equal tangential tractions applied to two other faces.
+
+[Illustration: FIG. 2.]
+
+Through any point there always pass three planes, at right angles to
+each other, across which there is no tangential traction. These planes
+are called the "principal planes of stress," and the (normal) tractions
+across them the "principal stresses." Lines, usually curved, which have
+at every point the direction of a principal stress at the point, are
+called "lines of stress."
+
+8. It appears that the stress at any point of a body is completely
+specified by six quantities, which can be taken to be the X_x, Y_y, Z_z
+and Y_z, Z_x, X_y of § 6. The first three are tensions (pressures if
+they are negative) across three planes parallel to fixed rectangular
+directions, and the remaining three are tangential tractions across the
+same three planes. These six quantities are called the "components of
+stress." It appears also that the components of stress are connected
+with each other, and with the body forces and accelerations, by the
+three partial differential equations of the type (3) of § 6. These
+equations are available for the purpose of determining the state of
+stress which exists in a body of definite form subjected to definite
+forces, but they are not sufficient for the purpose (see § 38 below). In
+order to effect the determination it is necessary to have information
+concerning the constitution of the body, and to introduce subsidiary
+relations founded upon this information.
+
+9. The definite mathematical relations which have been found to connect
+the components of stress with each other, and with other quantities,
+result necessarily from the formation of a clear conception of the
+nature of stress. They do not admit of experimental verification,
+because the stress within a body does not admit of direct measurement.
+Results which are deduced by the aid of these relations can be compared
+with experimental results. If any discrepancy were observed it would not
+be interpreted as requiring a modification of the concept of stress, but
+as affecting some one or other of the subsidiary relations which must
+be introduced for the purpose of obtaining the theoretical result.
+
+10. _Strain._--For the specification of the changes of size and shape
+which are produced in a body by any forces, we begin by defining the
+"average extension" of any linear element or "filament" of the body. Let
+l0 be the length of the filament before the forces are applied, l its
+length when the body is subjected to the forces. The average extension
+of the filament is measured by the fraction (l - l0)/l0. If this
+fraction is negative there is "contraction." The "extension at a point"
+of a body in any assigned direction is the mathematical limit of this
+fraction when one end of the filament is at the point, the filament has
+the assigned direction, and its length is diminished indefinitely. It is
+clear that all the changes of size and shape of the body are known when
+the extension at every point in every direction is known.
+
+  The relations between the extensions in different directions around
+  the same point are most simply expressed by introducing the extensions
+  in the directions of the co-ordinate axes and the angles between
+  filaments of the body which are initially parallel to these axes. Let
+  e_(xx), e_(yy), e_(zz) denote the extensions parallel to the axes of
+  x, y, z, and let e_(yz), e_(zx), e_(xy) denote the cosines of the
+  angles between the pairs of filaments which are initially parallel to
+  the axes of y and z, z and x, x and y. Also let e denote the extension
+  in the direction of a line the direction cosines of which are l, m, n.
+  Then, if the changes of size and shape are slight, we have the
+  relation
+
+    e = e_(xx)l² + e_(yy)m² + e_(zz)n² + e_(yz)mn + e_(zx)nl + e_(xy)lm.
+
+The body which undergoes the change of size or shape is said to be
+"strained," and the "strain" is determined when the quantities e_(xx),
+e_(yy), e_(zz) and e_(yz), e_(zx), e_(xy) defined above are known at
+every point of it. These quantities are called "components of strain."
+The three of the type e_(xx) are extensions, and the three of the type
+e_(yz) are called "shearing strains" (see § 12 below).
+
+11. All the changes of relative position of particles of the body are
+known when the strain is known, and conversely the strain can be
+determined when the changes of relative position are given. These
+changes can be expressed most simply by the introduction of a vector
+quantity to represent the displacement of any particle.
+
+  When the body is deformed by the action of any forces its particles
+  pass from the positions which they occupied before the action of the
+  forces into new positions. If x, y, z are the co-ordinates of the
+  position of a particle in the first state, its co-ordinates in the
+  second state may be denoted by x + u, y + v, z + w. The quantities, u,
+  v, w are the "components of displacement." When these quantities are
+  small, the strain is connected with them by the equations
+
+    e_(xx) = dPu/dPx,  e_(yy) = dPv/dPy,  e_(zz) = dPw/dPz,        \
+                                                                   |
+             dPw   dPv            dPu   dPw            dPv   dPu    >(1)
+    e_(yz) = --- + ---,  e_(zx) = --- + ---,  e_(xy) = --- + --- . |
+             dPy   dPz            dPz   dPx            dPx   dPy   /
+
+12. These equations enable us to determine more exactly the nature of
+the "shearing strains" such as e_(xy). Let u, for example, be of the
+form sy, where s is constant, and let v and w vanish. Then e_(xy) = s,
+and the remaining components of strain vanish. The nature of the strain
+(called "simple shear") is simply appreciated by imagining the body to
+consist of a series of thin sheets, like the leaves of a book, which lie
+one over another and are all parallel to a plane (that of x, z); and the
+displacement is seen to consist in the shifting of each sheet relative
+to the sheet below in a direction (that of x) which is the same for all
+the sheets. The displacement of any sheet is proportional to its
+distance y from a particular sheet, which remains undisplaced. The
+shearing strain has the effect of distorting the shape of any portion of
+the body without altering its volume. This is shown in fig. 3, where a
+square ABCD is distorted by simple shear (each point moving parallel to
+the line marked xx) into a rhombus A'B'C'D', as if by an extension of
+the diagonal BD and a contraction of the diagonal AC, which extension
+and contraction are adjusted so as to leave the area unaltered. In the
+general case, where u is not of the form sy and v and w do not vanish,
+the shearing strains such as e_(xy) result from the composition of pairs
+of simple shears of the type which has just been explained.
+
+  13. Besides enabling us to express the extension in any direction and
+  the changes of relative direction of any filaments of the body, the
+  components of strain also express the changes of size of volumes and
+  areas. In particular, the "cubical dilatation," that is to say, the
+  increase of volume per unit of volume, is expressed by the quantity
+
+                                dPu   dPv   dPw
+    e_(xx) + e_(yy) + e_(zz) or --- + --- + ---.
+                                dPx   dPy   dPz
+
+  When this quantity is negative there is "compression."
+
+[Illustration: FIG. 3.]
+
+14. It is important to distinguish between two types of strain: the
+"rotational" type and the "irrotational" type. The distinction is
+illustrated in fig. 3, where the figure A"B"C"D" is obtained from the
+figure ABCD by contraction parallel to AC and extension parallel to BD,
+and the figure A'B'C'D' can be obtained from ABCD by the same
+contraction and extension followed by a rotation through the angle
+A"OA'. In strains of the irrotational type there are at any point three
+filaments at right angles to each other, which are such that the
+particles which lie in them before strain continue to lie in them after
+strain. A small spherical element of the body with its centre at the
+point becomes a small ellipsoid with its axes in the directions of these
+three filaments. In the case illustrated in the figure, the lines of the
+filaments in question, when the figure ABCD is strained into the figure
+A"B"C"D", are OA, OB and a line through O at right angles to their
+plane. In strains of the rotational type, on the other hand, the single
+existing set of three filaments (issuing from a point) which cut each
+other at right angles both before and after strain do not retain their
+directions after strain, though one of them may do so in certain cases.
+In the figure, the lines of the filaments in question, when the figure
+ABCD is strained into A'B'C'D', are OA, OB and a line at right angles to
+their plane before strain, and after strain they are OA', OB', and the
+same third line. A rotational strain can always be analysed into an
+irrotational strain (or "pure" strain) followed by a rotation.
+
+  Analytically, a strain is irrotational if the three quantities
+
+    dPw   dPv    dPu   dPw    dPv   dPu
+    --- - ---,   --- - ---,   --- - ---.
+    dPy   dPz    dPz   dPx    dPx   dPy
+
+  vanish, rotational if any one of them is different from zero. The
+  halves of these three quantities are the components of a vector
+  quantity called the "rotation."
+
+  15. Whether the strain is rotational or not, there is always one set
+  of three linear elements issuing from any point which cut each other
+  at right angles both before and after strain. If these directions are
+  chosen as axes of x, y, z, the shearing strains e_(yz), e_(zx), e_(xy)
+  vanish at this point. These directions are called the "principal axes
+  of strain," and the extensions in the directions of these axes the
+  "principal extensions."
+
+16. It is very important to observe that the relations between
+components of strain and components of displacement imply relations
+between the components of strain themselves. If by any process of
+reasoning we arrive at the conclusion that the state of strain in a body
+is such and such a state, we have a test of the possibility or
+impossibility of our conclusion. The test is that, if the state of
+strain is a possible one, then there must be a displacement which can
+be associated with it in accordance with the equations (1) of § 11.
+
+  We may eliminate u, v, w from these equations. When this is done we
+  find that the quantities e_(xx), ... e_(yz) are connected by the two
+  sets of equations
+
+    dP²e_(yy)   dP²e_(zz)   dP²e_(yz)   \
+    --------- + --------- = ---------   |
+       dPz²       dPy²       dPydPz     |
+                                        |
+    dP²e_(zz)   dP²e_(xx)   dP²e_(zx)   |
+    --------- + --------- = ---------    > (1)
+       dPx²       dPz²       dPzdPx     |
+                                        |
+    dP²e_(xx)   dP²e_(yy)   dP²e_(xy)   |
+    --------- + --------- = ---------   |
+       dPy²       dPx²       dPxdPy     /
+
+  and
+
+      dP²e_(xx)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   \
+    2 --------- = --- ( - -------- + -------- + -------- )  |
+       dPydPz     dPx  \    dPx        dPy        dPz   /   |
+                                                            |
+      dP²e_(yy)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   |
+    2 --------- = --- (   -------- - -------- + -------- )   > (2)
+       dPzdPx     dPy  \    dPx        dPy        dPz   /   |
+                                                            |
+      dP²e_(zz)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   |
+    2 --------- = --- (   -------- + -------- - -------- )  |
+       dPxdPy     dPz  \    dPx        dPy        dPz   /   /
+
+These equations are known as the _conditions of compatibility of
+strain-components_. The components of strain which specify any possible
+strain satisfy them. Quantities arrived at in any way, and intended to
+be components of strain, if they fail to satisfy these equations, are
+not the components of any possible strain; and the theory or speculation
+by which they are reached must be modified or abandoned.
+
+  When the components of strain have been found in accordance with these
+  and other necessary equations, the displacement is to be found by
+  solving the equations (1) of § 11, considered as differential
+  equations to determine u, v, w. The most general possible solution
+  will differ from any other solution by terms which contain arbitrary
+  constants, and these terms represent a possible displacement. This
+  "complementary displacement" involves no strain, and would be a
+  possible displacement of an ideal perfectly rigid body.
+
+17. The relations which connect the strains with each other and with the
+displacement are geometrical relations resulting from the definitions of
+the quantities and not requiring any experimental verification. They do
+not admit of such verification, because the strain within a body cannot
+be measured. The quantities (belonging to the same category) which can
+be measured are displacements of points on the surface of a body. For
+example, on the surface of a bar subjected to tension we may make two
+fine transverse scratches, and measure the distance between them before
+and after the bar is stretched. For such measurements very refined
+instruments are required. Instruments for this purpose are called
+barbarously "extensometers," and many different kinds have been devised.
+From measurements of displacement by an extensometer we may deduce the
+average extension of a filament of the bar terminated by the two
+scratches. In general, when we attempt to measure a strain, we really
+measure some displacements, and deduce the values, not of the strain at
+a point, but of the average extensions of some particular linear
+filaments of a body containing the point; and these filaments are, from
+the nature of the case, nearly always superficial filaments.
+
+18. In the case of transparent materials such as glass there is
+available a method of studying experimentally the state of strain within
+a body. This method is founded upon the result that a piece of glass
+when strained becomes doubly refracting, with its optical principal axes
+at any point in the directions of the principal axes of strain (§ 15) at
+the point. When the piece has two parallel plane faces, and two of the
+principal axes of strain at any point are parallel to these faces,
+polarized light transmitted through the piece in a direction normal to
+the faces can be used to determine the directions of the principal axes
+of the strain at any point. If the directions of these axes are known
+theoretically the comparison of the experimental and theoretical results
+yields a test of the theory.
+
+19. _Relations between Stresses and Strains._--The problem of the
+extension of a bar subjected to tension is the one which has been most
+studied experimentally, and as a result of this study it is found that
+for most materials, including all metals except cast metals, the
+measurable extension is proportional to the applied tension, provided
+that this tension is not too great. In interpreting this result it is
+assumed that the tension is uniform over the cross-section of the bar,
+and that the extension of longitudinal filaments is uniform throughout
+the bar; and then the result takes the form of a law of proportionality
+connecting stress and strain: The tension is proportional to the
+extension. Similar results are found for the same materials when other
+methods of experimenting are adopted, for example, when a bar is
+supported at the ends and bent by an attached load and the deflexion is
+measured, or when a bar is twisted by an axial couple and the relative
+angular displacement of two sections is measured. We have thus very
+numerous experimental verifications of the famous law first enunciated
+by Robert Hooke in 1678 in the words "_Ut Tensio sic vis_"; that is,
+"the Power of any spring is in the same proportion as the Tension
+(--stretching) thereof." The most general statement of Hooke's Law in
+modern language would be:--_Each of the six components of stress at any
+point of a body is a linear function of the six components of strain at
+the point._ It is evident from what has been said above as to the nature
+of the measurement of stresses and strains that this law in all its
+generality does not admit of complete experimental verification, and
+that the evidence for it consists largely in the agreement of the
+results which are deduced from it in a theoretical fashion with the
+results of experiments. Of such results one of a general character may
+be noted here. If the law is assumed to be true, and the equations of
+motion of the body (§ 5) are transformed by means of it into
+differential equations for determining the components of displacement,
+these differential equations admit of solutions which represent periodic
+vibratory displacements (see § 85 below). The fact that solid bodies can
+be thrown into states of isochronous vibration has been emphasized by
+G.G. Stokes as a peremptory proof of the truth of Hooke's Law.
+
+20. According to the statement of the generalized Hooke's Law the
+stress-components vanish when the strain-components vanish. The
+strain-components contemplated in experiments upon which the law is
+founded are measured from a zero of reckoning which corresponds to the
+state of the body subjected to experiment before the experiment is made,
+and the stress-components referred to in the statement of the law are
+those which are called into action by the forces applied to the body in
+the course of the experiment. No account is taken of the stress which
+must already exist in the body owing to the force of gravity and the
+forces by which the body is supported. When it is desired to take
+account of this stress it is usual to suppose that the strains which
+would be produced in the body if it could be freed from the action of
+gravity and from the pressures of supports are so small that the strains
+produced by the forces which are applied in the course of the experiment
+can be compounded with them by simple superposition. This supposition
+comes to the same thing as measuring the strain in the body, not from
+the state in which it was before the experiment, but from an ideal state
+(the "unstressed" state) in which it would be entirely free from
+internal stress, and allowing for the strain which would be produced by
+gravity and the supporting forces if these forces were applied to the
+body when free from stress. In most practical cases the initial strain
+to be allowed for is unimportant (see §§ 91-93 below).
+
+21. Hooke's law of proportionality of stress and strain leads to the
+introduction of important physical constants: the _moduluses of
+elasticity_ of a body. Let a bar of uniform section (of area [omega]) be
+stretched with tension T, which is distributed uniformly over the
+section, so that the stretching force is Tw[omega], and let the bar be
+unsupported at the sides. The bar will undergo a longitudinal extension
+of magnitude T/E, where E is a constant quantity depending upon the
+material. This constant is called _Young's modulus_ after Thomas Young,
+who introduced it into the science in 1807. The quantity E is of the
+same nature as a traction, that is to say, it is measured as a force
+estimated per unit of area. For steel it is about 2.04×10^12 dynes per
+square centimetre, or about 13,000 tons per sq. in.
+
+22. The longitudinal extension of the bar under tension is not the only
+strain in the bar. It is accompanied by a lateral contraction by which
+all the transverse filaments of the bar are shortened. The amount of
+this contraction is [sigma]T/E, where [sigma] is a certain number called
+_Poisson's ratio_, because its importance was at first noted by S.D.
+Poisson in 1828. Poisson arrived at the existence of this contraction,
+and the corresponding number [sigma], from theoretical considerations,
+and his theory led him to assign to [sigma] the value ¼. Many
+experiments have been made with the view of determining [sigma], with
+the result that it has been found to be different for different
+materials, although for very many it does not differ much from ¼. For
+steel the best value (Amagat's) is 0.268. Poisson's theory admits of
+being modified so as to agree with the results of experiment.
+
+23. The behaviour of an elastic solid body, strained within the limits
+of its elasticity, is entirely determined by the constants E and [sigma]
+if the body is _isotropic_, that is to say, if it has the same quality
+in all directions around any point. Nevertheless it is convenient to
+introduce other constants which are related to the action of particular
+sorts of forces. The most important of these are the "modulus of
+compression" (or "bulk modulus") and the "rigidity" (or "modulus of
+shear"). To define the _modulus of compression_, we suppose that a solid
+body of any form is subjected to uniform hydrostatic pressure of amount
+p. The state of stress within it will be one of uniform pressure, the
+same at all points, and the same in all directions round any point.
+There will be compression, the same at all points, and proportional to
+the pressure; and the amount of the compression can be expressed as p/k.
+The quantity k is the modulus of compression. In this case the linear
+contraction in any direction is p/3k; but in general the linear
+extension (or contraction) is not one-third of the cubical dilatation
+(or compression).
+
+24. To define the _rigidity_, we suppose that a solid body is subjected
+to forces in such a way that there is shearing stress within it. For
+example, a cubical block may be subjected to opposing tractions on
+opposite faces acting in directions which are parallel to an edge of the
+cube and to both the faces. Let S be the amount of the traction, and let
+it be uniformly distributed over the faces. As we have seen (§ 7), equal
+tractions must act upon two other faces in suitable directions in order
+to maintain equilibrium (see fig. 2 of § 7). The two directions involved
+may be chosen as axes of x, y as in that figure. Then the state of
+stress will be one in which the stress-component denoted by X_y is equal
+to S, and the remaining stress-components vanish; and the strain
+produced in the body is shearing strain of the type denoted by e _(xy).
+The amount of the shearing strain is S/µ, and the quantity µ is the
+"rigidity."
+
+25. The modulus of compression and the rigidity are quantities of the
+same kind as Young's modulus. The modulus of compression of steel is
+about 1.43 × 10^12 dynes per square centimetre, the rigidity is about
+8.19 × 10^11 dynes per square centimetre. It must be understood that the
+values for different specimens of nominally the same material may differ
+considerably.
+
+  The modulus of compression k and the rigidity µ of an isotropic
+  material are connected with the Young's modulus E and Poisson's ratio
+  [sigma] of the material by the equations
+
+    k = E/3(1 - 2[sigma]),   µ = E/2(1 + [sigma]).
+
+  26. Whatever the forces acting upon an isotropic solid body may be,
+  provided that the body is strained within its limits of elasticity,
+  the strain-components are expressed in terms of the stress-components
+  by the equations
+
+    e_(xx) = (X_x - [sigma]Y_y - [sigma]Z_z)/E,  e_(yz) = Y_z/µ, \
+    e_(yy) = (Y_y - [sigma]Z_z - [sigma]X_x)/E,  e_(zx) = Z_x/µ,  > (1)
+    e_(zz) = (Z_z - [sigma]X_x - [sigma]Y_y)/E,  e_(xy) = X_y/µ. /
+
+  If we introduce a quantity [lambda], of the same nature as E or µ, by
+  the equation
+
+    [lambda] = E[sigma]/(1 + [sigma])(1 - 2[sigma]),  (2)
+
+  we may express the stress-components in terms of the strain-components
+  by the equations
+
+    X_x = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2µe_(xx), Y_z = µe_(yz), \
+    Y_y = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2µe_(yy), Z_x = µe_(zx),  > (3)
+    Z_z = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2µe_(zz), X_y = µe_(xy); /
+
+  and then the behaviour of the body under the action of any forces
+  depends upon the two constants [lambda] and µ. These two constants
+  were introduced by G. Lamé in his treatise of 1852. The importance of
+  the quantity µ had been previously emphasized by L.J. Vicat and G.G.
+  Stokes.
+
+  27. The potential energy per unit of volume (often called the
+  "resilience") stored up in the body by the strain is equal to
+
+    ½([lambda] + 2µ)(e_(xx) + e_(yy) + e_(zz))² + ½µ[e²_(yz) + e²_(zx) +
+      e²_(xy) - 4e_(yy)e_(zz) - 4e_(zz)e_(xx) - 4e_(xx)e_(yy)],
+
+  or the equivalent expression
+
+    ½[(X²_x + Y²_y + Z²_z) - 2[sigma](Y_yZ_z + Z_zX_x + X_xY_y) +
+      2(1 + [sigma])(Y²_z + Z²_x + X²_y)]/E.
+
+  The former of these expressions is called the
+  "strain-energy-function."
+
+28. The Young's modulus E of a material is often determined
+experimentally by the direct method of the extensometer (§ 17), but more
+frequently it is determined indirectly by means of a result obtained in
+the theory of the flexure of a bar (see §§ 47, 53 below). The rigidity µ
+is usually determined indirectly by means of results obtained in the
+theory of the torsion of a bar (see §§ 41, 42 below). The modulus of
+compression k may be determined directly by means of the piezometer, as
+was done by E.H. Amagat, or it may be determined indirectly by means of
+a result obtained in the theory of a tube under pressure, as was done by
+A. Mallock (see § 78 below). The value of Poisson's ratio [sigma] is
+generally inferred from the relation connecting it with E and µ or with
+E and k, but it may also be determined indirectly by means of a result
+obtained in the theory of the flexure of a bar (§ 47 below), as was done
+by M.A. Cornu and A. Mallock, or directly by a modification of the
+extensometer method, as has been done recently by J. Morrow.
+
+29. The _elasticity of a fluid_ is always expressed by means of a single
+quantity of the same kind as the _modulus of compression_ of a solid
+body. To any increment of pressure, which is not too great, there
+corresponds a proportional cubical compression, and the amount of this
+compression for an increment [delta]p of pressure can be expressed as
+[delta]p/k. The quantity that is usually tabulated is the reciprocal of
+k, and it is called the _coefficient of compressibility_. It is the
+amount of compression per unit increase of pressure. As a physical
+quantity it is of the same dimensions as the reciprocal of a pressure
+(or of a force per unit of area). The pressures concerned are usually
+measured in atmospheres (1 atmosphere = 1.014 × 10^6 dynes per sq. cm.).
+For water the coefficient of compressibility, or the compression per
+atmosphere, is about 4.5 × 10^-5. This gives for k the value 2.22 ×
+10^10 dynes per sq. cm. The Young's modulus and the rigidity of a fluid
+are always zero.
+
+30. The relations between stress and strain in a material which is not
+isotropic are much more complicated. In such a material the Young's
+modulus depends upon the direction of the tension, and its variations
+about a point are expressed by means of a surface of the fourth degree.
+The Poisson's ratio depends upon the direction of the contracted lateral
+filaments as well as upon that of the longitudinal extended ones. The
+rigidity depends upon both the directions involved in the specification
+of the shearing stress. In general there is no simple relation between
+the Young's moduluses and Poisson's ratios and rigidities for assigned
+directions and the modulus of compression. Many materials in common use,
+all fibrous woods for example, are actually _aeolotropic_ (that is to
+say, are not isotropic), but the materials which are aeolotropic in the
+most regular fashion are natural crystals. The elastic behaviour of
+crystals has been studied exhaustively by many physicists, and in
+particular by W. Voigt. The strain-energy-function is a homogeneous
+quadratic function of the six strain-components, and this function may
+have as many as 21 independent coefficients, taking the place in the
+general case of the 2 coefficients [lambda], µ which occur when the
+material is isotropic--a result first obtained by George Green in 1837.
+The best experimental determinations of the coefficients have been made
+indirectly by Voigt by means of results obtained in the theories of the
+torsion and flexure of aeolotropic bars.
+
+31. _Limits of Elasticity._--A solid body which has been strained by
+considerable forces does not in general recover its original size and
+shape completely after the forces cease to act. The strain that is left
+is called _set_. If set occurs the elasticity is said to be
+"imperfect," and the greatest strain (or the greatest load) of any
+specified type, for which no set occurs, defines the "limit of perfect
+elasticity" corresponding to the specified type of strain, or of stress.
+All fluids and many solid bodies, such as glasses and crystals, as well
+as some metals (copper, lead, silver) appear to be perfectly elastic as
+regards change of volume within wide limits; but malleable metals and
+alloys can have their densities permanently increased by considerable
+pressures. The limits of perfect elasticity as regards change of shape,
+on the other hand, are very low, if they exist at all, for glasses and
+other hard, brittle solids; but a class of metals including copper,
+brass, steel, and platinum are very perfectly elastic as regards
+distortion, provided that the distortion is not too great. The question
+can be tested by observation of the torsional elasticity of thin fibres
+or wires. The limits of perfect elasticity are somewhat ill-defined,
+because an experiment cannot warrant us in asserting that there is no
+set, but only that, if there is any set, it is too small to be observed.
+
+32. A different meaning may be, and often is, attached to the phrase
+"limits of elasticity" in consequence of the following experimental
+result:--Let a bar be held stretched under a moderate tension, and let
+the extension be measured; let the tension be slightly increased and the
+extension again measured; let this process be continued, the tension
+being increased by equal increments. It is found that when the tension
+is not too great the extension increases by equal increments (as nearly
+as experiment can decide), but that, as the tension increases, a stage
+is reached in which the extension increases faster than it would do if
+it continued to be proportional to the tension. The beginning of this
+stage is tolerably well marked. Some time before this stage is reached
+the limit of perfect elasticity is passed; that is to say, if the load
+is removed it is found that there is some permanent set. The limiting
+tension beyond which the above law of proportionality fails is often
+called the "limit of _linear_ elasticity." It is higher than the limit
+of perfect elasticity. For steel bars of various qualities J.
+Bauschinger found for this limit values varying from 10 to 17 tons per
+square inch. The result indicates that, when forces which produce any
+kind of strain are applied to a solid body and are gradually increased,
+the strain at any instant increases proportionally to the forces up to a
+stage beyond that at which, if the forces were removed, the body would
+completely recover its original size and shape, but that the increase of
+strain ceases to be proportional to the increase of load when the load
+surpasses a certain limit. There would thus be, for any type of strain,
+a _limit of linear elasticity_, which exceeds the limit of perfect
+elasticity.
+
+33. A body which has been strained beyond the limit of linear elasticity
+is often said to have suffered an "over-strain." When the load is
+removed, the _set_ which can be observed is not entirely permanent; but
+it gradually diminishes with lapse of time. This phenomenon is named
+"elastic after-working." If, on the other hand, the load is maintained
+constant, the strain is gradually increased. This effect indicates a
+gradual flowing of solid bodies under great stress; and a similar effect
+was observed in the experiments of H. Tresca on the punching and
+crushing of metals. It appears that all solid bodies under sufficiently
+great loads become "plastic," that is to say, they take a set which
+gradually increases with the lapse of time. No plasticity is observed
+when the limit of linear elasticity is not exceeded.
+
+34. The values of the elastic limits are affected by overstrain. If the
+load is maintained for some time, and then removed, the limit of linear
+elasticity is found to be higher than before. If the load is not
+maintained, but is removed and then reapplied, the limit is found to be
+lower than before. During a period of rest a test piece recovers its
+elasticity after overstrain.
+
+35. The effects of repeated loading have been studied by A. Wöhler, J.
+Bauschinger, O. Reynolds and others. It has been found that, after many
+repetitions of rather rapidly alternating stress, pieces are fractured
+by loads which they have many times withstood. It is not certain whether
+the fracture is in every case caused by the gradual growth of minute
+flaws from the beginning of the series of tests, or whether the elastic
+quality of the material suffers deterioration apart from such flaws. It
+appears, however, to be an ascertained result that, so long as the limit
+of linear elasticity is not exceeded, repeated loads and rapidly
+alternating loads do not produce failure of the material.
+
+36. The question of the conditions of safety, or of the conditions in
+which rupture is produced, is one upon which there has been much
+speculation, but no completely satisfactory result has been obtained. It
+has been variously held that rupture occurs when the numerically
+greatest principal stress exceeds a certain limit, or when this stress
+is tension and exceeds a certain limit, or when the greatest difference
+of two principal stresses (called the "stress-difference") exceeds a
+certain limit, or when the greatest extension or the greatest shearing
+strain or the greatest strain of any type exceeds a certain limit. Some
+of these hypotheses appear to have been disproved. It was held by G.F.
+Fitzgerald (_Nature_, Nov. 5, 1896) that rupture is not produced by
+pressure symmetrically applied all round a body, and this opinion has
+been confirmed by the recent experiments of A. Föppl. This result
+disposes of the greatest stress hypothesis and also of the greatest
+strain hypothesis. The fact that short pillars can be crushed by
+longitudinal pressure disposes of the greatest tension hypothesis, for
+there is no tension in the pillar. The greatest extension hypothesis
+failed to satisfy some tests imposed by H. Wehage, who experimented with
+blocks of wrought iron subjected to equal pressures in two directions at
+right angles to each other. The greatest stress-difference hypothesis
+and the greatest shearing strain hypothesis would lead to practically
+identical results, and these results have been held by J.J. Guest to
+accord well with his experiments on metal tubes subjected to various
+systems of combined stress; but these experiments and Guest's conclusion
+have been criticized adversely by O. Mohr, and the question cannot be
+regarded as settled. The fact seems to be that the conditions of rupture
+depend largely upon the nature of the test (tensional, torsional,
+flexural, or whatever it may be) that is applied to a specimen, and that
+no general formula holds for all kinds of tests. The best modern
+technical writings emphasize the importance of the limits of linear
+elasticity and of tests of dynamical resistance (§ 87 below) as well as
+of statical resistance.
+
+37. The question of the conditions of rupture belongs rather to the
+science of the strength of materials than to the science of elasticity
+(§ 1); but it has been necessary to refer to it briefly here, because
+there is no method except the methods of the theory of elasticity for
+determining the state of stress or strain in a body subjected to forces.
+Whatever view may ultimately be adopted as to the relation between the
+conditions of safety of a structure and the state of stress or strain in
+it, the calculation of this state by means of the theory or by
+experimental means (as in § 18) cannot be dispensed with.
+
+  38. _Methods of determining the Stress in a Body subjected to given
+  Forces._--To determine the state of stress, or the state of strain, in
+  an isotropic solid body strained within its limits of elasticity by
+  given forces, we have to use (i.) the equations of equilibrium, (ii.)
+  the conditions which hold at the bounding surface, (iii.) the
+  relations between stress-components and strain-components, (iv.) the
+  relations between strain-components and displacement. The equations of
+  equilibrium are (with notation already used) three partial
+  differential equations of the type
+
+    dPX_x   dPX_y   dPZ_z
+    ----- + ----- + ----- + [rho]X = 0.  (1)
+     dPx     dPy     dPz
+
+  The conditions which hold at the bounding surface are three equations
+  of the type
+
+    X_x cos(x, [nu]) + X_y cos(y, [nu]) + Z_x cos(z, [nu]) = X`_[nu], (2)
+
+  where [nu] denotes the direction of the outward-drawn normal to the
+  bounding surface, and X`_[nu] denotes the x-component of the applied
+  surface traction. The relations between stress-components and
+  strain-components are expressed by either of the sets of equations (1)
+  or (3) of § 26. The relations between strain-components and
+  displacement are the equations (1) of § 11, or the equivalent
+  conditions of compatibility expressed in equations (1) and (2) of §
+  16.
+
+  39. We may proceed by either of two methods. In one method we
+  eliminate the stress-components and the strain-components and retain
+  only the components of displacement. This method leads (with notation
+  already used) to three partial differential equations of the type
+
+                   dP   /dPu   dPv   dPw\      /dP²u   dP²u   dP²u\
+    ([lambda] + µ) --- ( --- + --- + --- ) + µ( ---- + ---- + ---- ) + [rho]X = 0, (3)
+                   dPx  \dPx   dPy   dPz/      \dPx²   dPy²   dPz²/
+
+  and three boundary conditions of the type
+                                                  _
+                          /dPu   dPv   dPw\      |               dPu
+    [lambda] cos(x, [nu])( --- + --- + --- ) + µ | 2 cos(x, [nu])---
+                          \dPx   dPy   dPz/      |_              dPx
+                                                             _
+                     /dPv   dPu\                 /dPu   dPw\  |
+      + cos(y, [nu])( -- + --   ) + cos(z, [nu])( -- + --   ) | = X`_[nu], (4)
+                     \dPx   dPy/                 \dPz   dPx/ _|
+
+  In the alternative method we eliminate the strain-components and the
+  displacements. This method leads to a system of partial differential
+  equations to be satisfied by the stress-components. In this system
+  there are three equations of the type
+
+    dPX_x   dPX_y   dPX_z
+    ----- + ----- + ----- + [rho]X = 0,  (1 _bis_)
+     dPx     dPy     dPz
+
+  three of the type
+
+    dP²X_x   dP²X_x   dP²X_x        1      dP²
+    ------ + ------ + ------ + ----------- --- (X_x + Y_y + Z_z) =
+     dPx²     dPy²     dPz²    1 + [sigma] dPx²
+
+          [sigma]       /dPX   dPY   dPZ\           dPX
+      -  ---------[rho]( --- + --- + --- ) - 2[rho] ---,  (5)
+         1-[sigma]      \dPx   dPy   dPz/           dPx
+
+  and three of the type
+
+    dP²Y_z   dP²Y_z   dP²Y_z        1       dP²
+    ------ + ------ + ------ + ----------- ------ (X_x + Y_y + Z_z) =
+     dPx²     dPy²     dPz²    1 + [sigma] dPydPz
+
+              /dPZ   dPY\
+      - [rho]( --- + --- ), (6)
+              \dPy   dPz/
+
+  the equations of the two latter types being necessitated by the
+  conditions of compatibility of strain-components. The solutions of
+  these equations have to be adjusted so that the boundary conditions of
+  the type (2) may be satisfied.
+
+  40. It is evident that whichever method is adopted the mathematical
+  problem is in general very complicated. It is also evident that, if we
+  attempt to proceed by help of some intuition as to the nature of the
+  stress or strain, our intuition ought to satisfy the tests provided by
+  the above systems of equations. Neglect of this precaution has led to
+  many errors. Another source of frequent error lies in the neglect of
+  the conditions in which the above systems of equations are correct.
+  They are obtained by help of the supposition that the relative
+  displacements of the parts of the strained body are small. The
+  solutions of them must therefore satisfy the test of smallness of the
+  relative displacements.
+
+41. Torsion.--As a first example of the application of the theory we
+take the problem of the torsion of prisms. This problem, considered
+first by C.A. Coulomb in 1784, was finally solved by B. de Saint-Venant
+in 1855. The problem is this:--A cylindrical or prismatic bar is held
+twisted by terminal couples; it is required to determine the state of
+stress and strain in the interior. When the bar is a circular cylinder
+the problem is easy. Any section is displaced by rotation about the
+central-line through a small angle, which is proportional to the
+distance z of the section from a fixed plane at right angles to this
+line. This plane is a terminal section if one of the two terminal
+sections is not displaced. The angle through which the section z rotates
+is [tau]z, where [tau] is a constant, called the amount of the twist;
+and this constant [tau] is equal to G/µI, where G is the twisting
+couple, and I is the moment of inertia of the cross-section about the
+central-line. This result is often called "Coulomb's law." The stress
+within the bar is shearing stress, consisting, as it must, of two sets
+of equal tangential tractions on two sets of planes which are at right
+angles to each other. These planes are the cross-sections and the axial
+planes of the bar. The tangential traction at any point of the
+cross-section is directed at right angles to the axial plane through the
+point, and the tangential traction on the axial plane is directed
+parallel to the length of the bar. The amount of either at a distance r
+from the axis is µ[tau]r or Gr/I. The result that G = µ[tau]I can be
+used to determine µ experimentally, for [tau] may be measured and G and
+I are known.
+
+42. When the cross-section of the bar is not circular it is clear that
+this solution fails; for the existence of tangential traction, near the
+prismatic bounding surface, on any plane which does not cut this surface
+at right angles, implies the existence of traction applied to this
+surface. We may attempt to modify the theory by retaining the
+supposition that the stress consists of shearing stress, involving
+tangential traction distributed in some way over the cross-sections.
+Such traction is obviously a necessary constituent of any stress-system
+which could be produced by terminal couples around the axis. We should
+then know that there must be equal tangential traction directed along
+the length of the bar, and exerted across some planes or other which are
+parallel to this direction. We should also know that, at the bounding
+surface, these planes must cut this surface at right angles. The
+corresponding strain would be shearing strain which could involve (i.) a
+sliding of elements of one cross-section relative to another, (ii.) a
+relative sliding of elements of the above mentioned planes in the
+direction of the length of the bar. We could conclude that there may be
+a longitudinal displacement of the elements of the cross-sections. We
+should then attempt to satisfy the conditions of the problem by
+supposing that this is the character of the strain, and that the
+corresponding displacement consists of (i.) a rotation of the
+cross-sections in their planes such as we found in the case of the
+circle, (ii.) a distortion of the cross-sections into curved surfaces by
+a displacement (w) which is directed normally to their planes and varies
+in some manner from point to point of these planes. We could show that
+all the conditions of the problem are satisfied by this assumption,
+provided that the longitudinal displacement (w), considered as a
+function of the position of a point (x, y) in the cross-section,
+satisfies the equation
+
+  dP²w   dP²w
+  ---- + ---- = 0,  (1)
+  dPx²   dPy²
+
+and the boundary condition
+
+   / dPw         \                  / dPw         \
+  (  --- - [tau]y ) cos(x, [nu]) + (  --- + [tau]x ) cos(y, [nu]) = 0, (2)
+   \ dPx         /                  \ dPy         /
+
+where [tau] denotes the amount of the twist, and [nu] the direction of
+the normal to the boundary. The solution is known for a great many forms
+of section. (In the particular case of a circular section w vanishes.)
+The tangential traction at any point of the cross-section is directed
+along the tangent to that curve of the family [psi] = const. which
+passes through the point, [psi] being the function determined by the
+equations
+
+  dPw         /dP[psi]    \    dPw           /dP[psi]    \
+  --- = [tau]( ------- + y ),  --- = - [tau]( ------- + x ).
+  dPx         \  dPy      /    dPy           \  dPx      /
+
+The amount of the twist [tau] produced by terminal couples of magnitude
+G is G/C, where C is a constant, called the "torsional rigidity" of the
+prism, and expressed by the formula
+         _  _  _                         _
+        /  /  |  /dP[psi]\²    /dP[psi]\² |
+  C = µ |  |  | ( ------- ) + ( ------- ) | dxdy,
+       _/ _/  |_ \  dPx  /     \  dPy  / _|
+
+the integration being taken over the cross-section. When the coefficient
+of µ in the expression for C is known for any section, µ can be
+determined by experiment with a bar of that form of section.
+
+43. The distortion of the cross-sections into curved surfaces is shown
+graphically by drawing the contour lines (w = const.). In general the
+section is divided into a number of compartments, and the portions that
+lie within two adjacent compartments are respectively concave and
+convex. This result is illustrated in the accompanying figures (fig. 4
+for the ellipse, given by x²/b² + y²/c² = 1; fig. 5 for the equilateral
+triangle, given by (x + (1/3)a) [x² - 3y² - (4/3)ax + (4/9)a²] = 0; fig.
+6 for the square).
+
+[Illustration: FIG. 4.]
+
+44. The distribution of the shearing stress over the cross-section is
+determined by the function [psi], already introduced. If we draw the
+curves [psi] = const., corresponding to any form of section, for
+equidifferent values of the constant, the tangential traction at any
+point on the cross-section is directed along the tangent to that curve
+of the family which passes through the point, and the magnitude of it is
+inversely proportional to the distance between consecutive curves of the
+family. Fig. 7 illustrates the result in the case of the _equilateral_
+triangle. The boundary is, of course, one of the lines. The "lines of
+shearing stress" which can thus be drawn are in every case identical
+with the lines of flow of frictionless liquid filling a cylindrical
+vessel of the same cross-section as the bar, when the liquid circulates
+in the plane of the section with uniform spin. They are also the same as
+the contour lines of a flexible and slightly extensible membrane, of
+which the edge has the same form as the bounding curve of the
+cross-section of the bar, when the membrane is fixed at the edge and
+slightly deformed by uniform pressure.
+
+[Illustration: FIG. 5.]
+
+[Illustration: FIG. 6.]
+
+[Illustration: FIG. 7.]
+
+45. Saint-Venant's theory shows that the true torsional rigidity is in
+general less than that which would be obtained by extending Coulomb's
+law (G = µ[tau]I) to sections which are not circular. For an elliptic
+cylinder of sectional area [omega] and moment of inertia I about its
+central-line the torsional rigidity is µ[omega]^4/4[pi]²I, and this
+formula is not far from being correct for a very large number of
+sections. For a bar of square section of side a centimetres, the
+torsional rigidity in C.G.S. units is (0.1406)µa^4 approximately, µ
+being expressed in dynes per square centimetre. How great the defect of
+the true value from that given by extending Coulomb's law may be in the
+case of sections with projecting corners is shown by the diagrams (fig.
+8 especially no. 4). In these diagrams the upper of the two numbers
+under each figure indicates the fraction which the true torsional
+rigidity corresponding to the section is of that value which would be
+obtained by extending Coulomb's law; and the lower of the two numbers
+indicates the ratio which the torsional rigidity for a bar of the
+corresponding section bears to that of a bar of circular section of the
+same material and of equal sectional area. These results have an
+important practical application, inasmuch as they show that
+strengthening ribs and projections, such as are introduced in
+engineering to give stiffness to beams, have the reverse of a good
+effect when torsional stiffness is an object, although they are of great
+value in increasing the resistance to bending. The theory shows further
+that the resistance to torsion is very seriously diminished when there
+is in the surface any dent approaching to a re-entrant angle. At such a
+place the shearing strain tends to become infinite, and some permanent
+set is produced by torsion. In the case of a section of any form, the
+strain and stress are greatest at points on the contour, and these
+points are in many cases the points of the contour which are nearest to
+the centroid of the section. The theory has also been applied to show
+that a longitudinal flaw near the axis of a shaft transmitting a
+torsional couple has little influence on the strength of the shaft, but
+that in the neighbourhood of a similar flaw which is much nearer to the
+surface than to the axis the shearing strain may be nearly doubled, and
+thus the possibility of such flaws is a source of weakness against which
+special provision ought to be made.
+
+[Illustration: FIG. 8.--Diagrams showing Torsional Rigidities.
+
+  (1) Rectilineal square. .84346. .88326.
+  (2) Square with curved corners and hollow sides. .8186. .8666.
+  (3) Square with acute angles and hollow sides. .7783. .8276.
+  (4) Star with four rounded points, being a curve of the eighth degree.
+        .5374. .6745.
+  (5) Equilateral triangle. .60000. .72552.]
+
+[Illustration: FIG. 9.]
+
+46. _Bending of Beams._--As a second example of the application of the
+general theory we take the problem of the flexure of a beam. In this
+case also we begin by forming a simple intuition as to the nature of the
+strain and the stress. On the side of the beam towards the centre of
+curvature the longitudinal filaments must be contracted, and on the
+other side they must be extended. If we assume that the cross-sections
+remain plane, and that the central-line is unaltered in length, we see
+(at once from fig. 9) that the extensions (or contractions) are given by
+the formula y/R, where y denotes the distance of a longitudinal filament
+from the plane drawn through the unstrained central-line at right-angles
+to the plane of bending, and R is the radius of curvature of the curve
+into which this line is bent (shown by the dotted line in the figure).
+Corresponding to this strain there must be traction acting across the
+cross-sections. If we assume that there is no other stress, then the
+magnitude of the traction in question is Ey/R, where E is Young's
+modulus, and it is tension on the side where the filaments are extended
+and pressure on the side where they are contracted. If the plane of
+bending contains a set of principal axes of the cross-sections at their
+centroids, these tractions for the whole cross-section are equivalent to
+a couple of moment EI/R, where I now denotes the moment of inertia of
+the cross-section about an axis through its centroid at right angles to
+the plane of bending, and the plane of the couple is the plane of
+bending. Thus a beam of any form of section can be held bent in a
+"principal plane" by terminal couples of moment M, that is to say by a
+"bending moment" M; the central-line will take a curvature M/EI, so that
+it becomes an arc of a circle of radius EI/M; and the stress at any
+point will be tension of amount My/I, where y denotes distance (reckoned
+positive towards the side remote from the centre of curvature) from that
+plane which initially contains the central-line and is at right angles
+to the plane of the couple. This plane is called the "neutral plane."
+The restriction that the beam is bent in a principal plane means that
+the plane of bending contains one set of principal axes of the
+cross-sections at their centroids; in the case of a beam of rectangular
+section the plane would bisect two opposite edges at right angles. In
+order that the theory may hold good the radius of curvature must be very
+large.
+
+47. In this problem of the bending of a beam by terminal couples the
+stress is tension, determined as above, and the corresponding strain
+consists therefore of longitudinal extension of amount My/EI or y/R
+(contraction if y is negative), accompanied by lateral contraction of
+amount [sigma]My/EI or [sigma]y/R (extension if y is negative), [sigma]
+being Poisson's ratio for the material. Our intuition of the nature of
+the strain was imperfect, inasmuch as it took no account of these
+lateral strains. The necessity for introducing them was pointed out by
+Saint-Venant. The effect of them is a change of shape of the
+cross-sections in their own planes. This is shown in an exaggerated way
+in fig. 10, where the rectangle ABCD represents the cross-section of the
+unstrained beam, or a rectangular portion of this cross-section, and the
+curvilinear figure A'B'C'D' represents in an exaggerated fashion the
+cross-section (or the corresponding portion of the cross-section) of the
+same beam, when bent so that the centre of curvature of the central-line
+(which is at right angles to the plane of the figure) is on the line EF
+produced beyond F. The lines A'B' and C'D' are approximately circles of
+radii R/[sigma], when the central-line is a circle of radius R, and
+their centres are on the line FE produced beyond E. Thus the neutral
+plane, and each of the faces that is parallel to it, becomes strained
+into an _anticlastic surface_, whose principal curvatures are in the
+ratio [sigma] : 1. The general appearance of the bent beam is shown in
+an exaggerated fashion in fig. 11, where the traces of the surface into
+which the neutral plane is bent are dotted. The result that the ratio of
+the principal curvatures of the anticlastic surfaces, into which the top
+and bottom planes of the beam (of rectangular section) are bent, is
+Poisson's ratio [sigma], has been used for the experimental
+determination of [sigma]. The result that the radius of curvature of the
+bent central-line is EI/M is used in the experimental determination of
+E. The quantity EI is often called the "flexural rigidity" of the beam.
+There are two principal flexural rigidities corresponding to bending in
+the two principal planes (cf. § 62 below).
+
+[Illustration: FIG. 10.]
+
+[Illustration: FIG. 11.]
+
+[Illustration: FIG. 12.]
+
+48. That this theory requires modification, when the load does not
+consist simply of terminal couples, can be seen most easily by
+considering the problem of a beam loaded at one end with a weight W, and
+supported in a horizontal position at its other end. The forces that are
+exerted at any section p, to balance the weight W, must reduce
+statically to a vertical force W and a couple, and these forces arise
+from the action of the part Ap on the part Bp (see fig. 12), i.e. from
+the stresses across the section at p. The couple is equal to the moment
+of the applied load W about an axis drawn through the centroid of the
+section p at right angles to the plane of bending. This moment is called
+the "bending moment" at the section, it is the product of the load W and
+the distance of the section from the loaded end, so that it varies
+uniformly along the length of the beam. The stress that suffices in the
+simpler problem gives rise to no vertical force, and it is clear that in
+addition to longitudinal tensions and pressures there must be tangential
+tractions on the cross-sections. The resultant of these tangential
+tractions must be a force equal to W, and directed vertically; but the
+direction of the traction at a point of the cross-section need not in
+general be vertical. The existence of tangential traction on the
+cross-sections implies the existence of equal tangential traction,
+directed parallel to the central-line, on some planes or other which are
+parallel to this line, the two sets of tractions forming a shearing
+stress. We conclude that such shearing stress is a necessary constituent
+of the stress-system in the beam bent by terminal transverse load. We
+can develop a theory of this stress-system from the assumptions (i.)
+that the tension at any point of the cross-section is related to the
+bending moment at the section by the same law as in the case of uniform
+bending by terminal couples; (ii.) that, in addition to this tension,
+there is at any point shearing stress, involving tangential tractions
+acting in appropriate directions upon the elements of the
+cross-sections. When these assumptions are made it appears that there is
+one and only one distribution of shearing stress by which the conditions
+of the problem can be satisfied. The determination of the amount and
+direction of this shearing stress, and of the corresponding strains and
+displacements, was effected by Saint-Venant and R.F.A. Clebsch for a
+number of forms of section by means of an analysis of the same kind as
+that employed in the solution of the torsion problem.
+
+[Illustration: Fig. 13.]
+
+  49. Let l be the length of the beam, x the distance of the section p
+  from the fixed end A, y the distance of any point below the horizontal
+  plane through the centroid of the section at A, then the bending
+  moment at p is W(l - x), and the longitudinal tension P or X_x at any
+  point on the cross-section is - W(l - x)y/I, and this is related to
+  the bending moment exactly as in the simpler problem.
+
+  50. The expressions for the shearing stresses depend on the shape of
+  the cross-section. Taking the beam to be of isotropic material and the
+  cross-section to be an ellipse of semiaxes a and b (fig. 13), the a
+  axis being vertical in the unstrained state, and drawing the axis z at
+  right angles to the plane of flexure, we find that the vertical
+  shearing stress U or X_y at any point (y, z) on any cross-section is
+
+    2W[(a² - y²){2a²(1 + [sigma]) + b²} - z²a²(1 - 2[sigma])]
+    ---------------------------------------------------------.
+                 [pi]a³b(1 + [sigma])(3a² + b²)
+
+  The resultant of these stresses is W, but the amount at the centroid,
+  which is the maximum amount, exceeds the average amount, W/[pi]ab, in
+  the ratio
+
+    {4a²(1 + [sigma]) + 2b²}/(3a² + b²)(1 + [sigma]).
+
+  If [sigma] = ¼, this ratio is 7/5 for a circle, nearly 4/3 for a flat
+  elliptic bar with the longest diameter vertical, nearly 8/5 for a flat
+  elliptic bar with the longest diameter horizontal.
+
+  In the same problem the horizontal shearing stress T or Z_x at any
+  point on any cross-section is of amount
+
+      4Wyz{a²(1 + [sigma]) + b²[sigma]}
+    - ---------------------------------.
+       [pi]a³b(1 + [sigma])(3a² + b²)
+
+  The resultant of these stresses vanishes; but, taking as before
+  [sigma] = ¼, and putting for the three cases above a = b, a = 10b, b =
+  10a, we find that the ratio of the maximum of this stress to the
+  average vertical shearing stress has the values 3/5, nearly 1/15, and
+  nearly 4. Thus the stress T is of considerable importance when the
+  beam is a plank.
+
+  As another example we may consider a circular tube of external radius
+  r0 and internal radius r1. Writing P, U, T for X_x, X_y, Z_x, we find
+
+                  4W
+    P = - -----------------(l - x)y,
+          [pi](r0^4 - r1^4)
+                                         _
+                      W                 |                /
+    U = ------------------------------- |(3 + 2[sigma]) (r0² + r1² - y²
+        2(1 + [sigma])[pi](r0^4 - r1^4) |_               \
+                                                 _
+           r0²r1²            \                    |
+       - ---------- (y² - z²) ) - (1 - 2[sigma])z²|
+         (y² + z²)²          /                   _|
+
+                      W
+  T = - ------------------------------
+        (1 + [sigma])[pi](r0^4 - r1^4)
+     _                                         _
+    |                                 r0²r1²    |
+    | 1 + 2[sigma] + (3 + 2[sigma]) ----------  | yz;
+    |_                              (y² + z²)² _|
+
+  and for a tube of radius r and small thickness t the value of P and
+  the maximum values of U and T reduce approximately to
+
+    P = - W(l - x)y/[pi]r³t
+
+    U_max. = W/[pi]rt,  T_max. = W/2[pi]rt.
+
+  The greatest value of U is in this case approximately twice its
+  average value, but it is possible that these results for the bending
+  of very thin tubes may be seriously at fault if the tube is not
+  plugged, and if the load is not applied in the manner contemplated in
+  the theory (cf. § 55). In such cases the extensions and contractions
+  of the longitudinal filaments may be practically confined to a small
+  part of the material near the ends of the tube, while the rest of the
+  tube is deformed without stretching.
+
+51. The tangential tractions U, T on the cross-sections are necessarily
+accompanied by tangential tractions on the longitudinal sections, and on
+each such section the tangential traction is parallel to the central
+line; on a vertical section z = const. its amount at any point is T, and
+on a horizontal section y = const. its amount at any point is U.
+
+The internal stress at any point is completely determined by the
+components P, U, T, but these are not principal stresses (§ 7). Clebsch
+has given an elegant geometrical construction for determining the
+principal stresses at any point when the values of P, U, T are known.
+
+[Illustration: FIG. 14.]
+
+  From the point O (fig. 14) draw lines OP, OU, OT, to represent the
+  stresses P, U, T at O, on the cross-section through O, in magnitude,
+  direction and sense, and compound U and T into a resultant represented
+  by OE; the plane EOP is a principal plane of stress at O, and the
+  principal stress at right angles to this plane vanishes. Take M the
+  middle point of OP, and with centre M and radius ME describe a circle
+  cutting the line OP in A and B; then OA and OB represent the
+  magnitudes of the two remaining principal stresses. On AB describe a
+  rectangle ABDC so that DC passes through E; then OC is the direction
+  of the principal stress represented in magnitude by OA, and OD is the
+  direction of the principal stress represented in magnitude by OB.
+
+[Illustration: FIG. 15.]
+
+52. As regards the strain in the beam, the longitudinal and lateral
+extensions and contractions depend on the bending moment in the same way
+as in the simpler problem; but, the bending moment being variable, the
+anticlastic curvature produced is also variable. In addition to these
+extensions and contractions there are shearing strains corresponding to
+the shearing stresses T, U. The shearing strain corresponding to T
+consists of a relative sliding parallel to the central-line of different
+longitudinal linear elements combined with a relative sliding in a
+transverse horizontal direction of elements of different cross-sections;
+the latter of these is concerned in the production of those
+displacements by which the variable anticlastic curvature is brought
+about; to see the effect of the former we may most suitably consider,
+for the case of an elliptic cross-section, the distortion of the shape
+of a rectangular portion of a plane of the material which in the natural
+state was horizontal; all the boundaries of such a portion become
+parabolas of small curvature, which is variable along the length of the
+beam, and the particular effect under consideration is the change of the
+transverse horizontal linear elements from straight lines such as HK to
+parabolas such as H'K' (fig. 15); the lines HL and KM are parallel to
+the central-line, and the figure is drawn for a plane above the neutral
+plane. When the cross-section is not an ellipse the character of the
+strain is the same, but the curves are only approximately parabolic.
+
+The shearing strain corresponding to U is a distortion which has the
+effect that the straight vertical filaments become curved lines which
+cut the longitudinal filaments obliquely, and thus the cross-sections do
+not remain plane, but become curved surfaces, and the tangent plane to
+any one of these surfaces at the centroid cuts the central line
+obliquely (fig. 16). The angle between these tangent planes and the
+central-line is the same at all points of the line; and, if it is
+denoted by ½[pi] + s0, the value of s0 is expressible as
+
+  shearing stress at centroid
+  ---------------------------,
+    rigidity of material
+
+and it thus depends on the shape of the cross-section; for the elliptic
+section of § 50 its value is
+
+    4W    2a²(1 + [sigma]) + b²
+  ------- ---------------------;
+  E[pi]ab       3a² + b²
+
+for a circle (with [sigma] = ¼) this becomes 7W/2E[pi]a². The vertical
+filament through the centroid of any cross-section becomes a cubical
+parabola, as shown in fig. 16, and the contour lines of the curved
+surface into which any cross-section is distorted are shown in fig. 17
+for a circular section.
+
+[Illustration: FIG. 16.]
+
+53. The deflection of the beam is determined from the equation
+
+  curvature of central line = bending moment ÷ flexural rigidity,
+
+and the special conditions at the supported end; there is no alteration
+of this statement on account of the shears. As regards the special
+condition at an end which is _encastrée_, or built in, Saint-Venant
+proposed to assume that the central tangent plane of the cross-section
+at the end is vertical; with this assumption the tangent to the central
+line at the end is inclined downwards and makes an angle s0 with the
+horizontal (see fig. 18); it is, however, improbable that this condition
+is exactly realized in practice. In the application of the theory to the
+experimental determination of Young's modulus, the small angle which the
+central-line at the support makes with the horizontal is an unknown
+quantity, to be eliminated by observation of the deflection at two or
+more points.
+
+54. We may suppose the displacement in a bent beam to be produced by the
+following operations: (1) the central-line is deflected into its curved
+form, (2) the cross-sections are rotated about axes through their
+centroids at right angles to the plane of flexure so as to make angles
+equal to ½[pi] + s0 with the central-line, (3) each cross-section is
+distorted in its own plane in such a way that the appropriate variable
+anticlastic curvature is produced, (4) the cross-sections are further
+distorted into curved surfaces. The contour lines of fig. 17 show the
+disturbance from the central tangent plane, not from the original
+vertical plane.
+
+[Illustration: FIG. 17.]
+
+55. _Practical Application of Saint-Venant's Theory._--The theory above
+described is exact provided the forces applied to the loaded end, which
+have W for resultant, are distributed over the terminal section in a
+particular way, not likely to be realized in practice; and the
+application to practical problems depends on a principle due to
+Saint-Venant, to the effect that, except for comparatively small
+portions of the beam near to the loaded and fixed ends, the resultant
+only is effective, and its mode of distribution does not seriously
+affect the internal strain and stress. In fact, the actual stress is
+that due to forces with the required resultant distributed in the manner
+contemplated in the theory, superposed upon that due to a certain
+distribution of forces on each terminal section which, if applied to a
+rigid body, would keep it in equilibrium; according to Saint-Venant's
+principle, the stresses and strains due to such distributions of force
+are unimportant except near the ends. For this principle to be exactly
+applicable it is necessary that the length of the beam should be very
+great compared with any linear dimension of its cross-section; for the
+practical application it is sufficient that the length should be about
+ten times the greatest diameter.
+
+56. In recent years the problem of the bending of a beam by loads
+distributed along its length has been much advanced. It is now
+practically solved for the case of a load distributed uniformly, or
+according to any rational algebraic law, and it is also solved for the
+case where the thickness is small compared with the length and depth, as
+in a plate girder, and the load is distributed in any way. These
+solutions are rather complicated and difficult to interpret. The case
+which has been worked out most fully is that of a transverse load
+distributed uniformly along the length of the beam. In this case two
+noteworthy results have been obtained. The first of these is that the
+central-line in general suffers extension. This result had been found
+experimentally many years before. In the case of the plate girder loaded
+uniformly along the top, this extension is just half as great as the
+extension of the central-line of the same girder when free at the ends,
+supported along the base, and carrying the same load along the top. The
+second noteworthy result is that the curvature of the strained
+central-line is not proportional to the bending moment. Over and above
+the curvature which would be found from the ordinary relation--
+
+  curvature of central-line = bending moment ÷ flexural rigidity,
+
+there is an additional curvature which is the same at all the
+cross-sections. In ordinary cases, provided the length is large compared
+with any linear dimension of the cross-section, this additional
+curvature is small compared with that calculated from the ordinary
+formula, but it may become important in cases like that of suspension
+bridges, where a load carried along the middle of the roadway is
+supported by tensions in rods attached at the sides.
+
+[Illustration: FIG. 18.]
+
+57. When the ordinary relation between the curvature and the bending
+moment is applied to the calculation of the deflection of _continuous
+beams_ it must not be forgotten that a correction of the kind just
+mentioned may possibly be requisite. In the usual method of treating the
+problem such corrections are not considered, and the ordinary relation
+is made the basis of the theory. In order to apply this relation to the
+calculation of the deflection, it is necessary to know the bending
+moment at every point; and, since the pressures of the supports are not
+among the data of the problem, we require a method of determining the
+bending moments at the supports either by calculation or in some other
+way. The calculation of the bending moment can be replaced by a method
+of graphical construction, due to Mohr, and depending on the two
+following theorems:--
+
+(i.) The curve of the central-line of each span of a beam, when the
+bending moment M is given,[1] is identical with the catenary or
+funicular curve passing through the ends of the span under a
+(fictitious) load per unit length of the span equal to M/EI, the
+horizontal tension in the funicular being unity.
+
+(ii.) The directions of the tangents to this funicular curve at the ends
+of the span are the same for all statically equivalent systems of
+(fictitious) load.
+
+When M is known, the magnitude of the resultant shearing stress at any
+section is dM/dx, where x is measured along the beam.
+
+[Illustration: FIG. 19.]
+
+[Illustration: FIG. 20.]
+
+  58. Let l be the length of a span of a loaded beam (fig. 19), M1 and
+  M2 the bending moments at the ends, M the bending moment at a section
+  distant x from the end (M1), M' the bending moment at the same section
+  when the same span with the same load is simply supported; then M is
+  given by the formula
+
+                l - x      x
+    M = M' + M1 ----- + M2 --,
+                  l        l
+
+  and thus a fictitious load statically equivalent to M/EI can be easily
+  found when M' has been found. If we draw a curve (fig. 20) to pass
+  through the ends of the span, so that its ordinate represents the
+  value of M'/EI, the corresponding fictitious loads are statically
+  equivalent to a single load, of amount represented by the area of the
+  curve, placed at the point of the span vertically above the centre of
+  gravity of this area. If PN is the ordinate of this curve, and if at
+  the ends of the span we erect ordinates in the proper sense to
+  represent M1/EI and M2/EI, the bending moment at any point is
+  represented by the length PQ.[2] For a uniformly distributed load the
+  curve of M' is a parabola M' = ½wx(l - x), where w is the load per
+  unit of length; and the statically equivalent fictitious load is
+  (1/12)wl³/EI placed at the middle point G of the span; also the loads
+  statically equivalent to the fictitious loads M1(l - x)/lEI and
+  M2x/lEI are ½M1l/EI and ½M2l/EI placed at the points g, g' of
+  trisection of the span. The funicular polygon for the fictitious loads
+  can thus be drawn, and the direction of the central-line at the
+  supports is determined when the bending moments at the supports are
+  known.
+
+  [Illustration: FIG. 21.]
+
+  59. When there is more than one span the funiculars in question may be
+  drawn for each of the spans, and, if the bending moments at the ends
+  of the extreme spans are known, the intermediate ones can be
+  determined. This determination depends on two considerations: (1) the
+  fictitious loads corresponding to the bending moment at any support
+  are proportional to the lengths of the spans which abut on that
+  support; (2) the sides of two funiculars that end at any support
+  coincide in direction. Fig. 21 illustrates the method for the case of
+  a uniform beam on three supports A, B, C, the ends A and C being
+  freely supported. There will be an unknown bending moment M0 at B, and
+  the system[3] of fictitious loads is (1/12)wAB³/EI at G the middle
+  point of AB, (1/12)wBC³/EI at G' the middle point of BC, -½M0AB/EI at
+  g and -½M0BC/EI at g', where g and g' are the points of trisection
+  nearer to B of the spans AB, BC. The centre of gravity of the two
+  latter is a fixed point independent of M0, and the line VK of the
+  figure is the vertical through this point. We draw AD and CE to
+  represent the loads at G and G' in magnitude; then D and E are fixed
+  points. We construct any triangle UVW whose sides UV, UW pass through
+  D, B, and whose vertices lie on the verticals gU, VK, g'W; the point F
+  where VW meets DB is a fixed point, and the lines EF, DK are the two
+  sides (2, 4) of the required funiculars which do not pass through A, B
+  or C. The remaining sides (1, 3, 5) can then be drawn, and the side 3
+  necessarily passes through B; for the triangle UVW and the triangle
+  whose sides are 2, 3, 4 are in perspective.
+
+  [Illustration: FIG. 22.]
+
+  The bending moment M0 is represented in the figure by the vertical
+  line BH where H is on the continuation of the side 4, the scale being
+  given by
+
+    BH     ½M0BC
+    -- = ---------- ;
+    CE   (1/12)wBC³
+
+  this appears from the diagrams of forces, fig. 22, in which the
+  oblique lines are marked to correspond to the sides of the funiculars
+  to which they are parallel.
+
+  In the application of the method to more complicated cases there are
+  two systems of fixed points corresponding to F, by means of which the
+  sides of the funiculars are drawn.
+
+60. _Finite Bending of Thin Rod._--The equation
+
+  curvature = bending moment ÷ flexural rigidity
+
+may also be applied to the problem of the flexure in a principal plane
+of a very thin rod or wire, for which the curvature need not be small.
+When the forces that produce the flexure are applied at the ends only,
+the curve into which the central-line is bent is one of a definite
+family of curves, to which the name _elastica_ has been given, and there
+is a division of the family into two species according as the external
+forces are applied directly to the ends or are applied to rigid arms
+attached to the ends; the curves of the former species are characterized
+by the presence of inflections at all the points at which they cut the
+line of action of the applied forces.
+
+[Illustration: FIG. 23.]
+
+  We select this case for consideration. The problem of determining the
+  form of the curve (cf. fig. 23) is mathematically identical with the
+  problem of determining the motion of a simple circular pendulum
+  oscillating through a finite angle, as is seen by comparing the
+  differential equation of the curve
+
+       d²[phi]
+    EI ------- + W sin [phi] = 0
+         ds²
+
+  with the equation of motion of the pendulum
+
+      d²[phi]
+    l ------- + g sin [phi] = 0.
+        dt²
+
+  The length L of the curve between two inflections corresponds to the
+  time of oscillation of the pendulum from rest to rest, and we thus
+  have
+
+    L [root](W/EI) = 2K,
+
+  where K is the real quarter period of elliptic functions of modulus
+  sin ½[alpha], and [alpha] is the angle at which the curve cuts the
+  line of action of the applied forces. Unless the length of the rod
+  exceeds [pi][root](EI/W) it will not bend under the force, but when
+  the length is great enough there may be more than two points of
+  inflection and more than one bay of the curve; for n bays (n + 1
+  inflections) the length must exceed n[pi][root](EI/W). Some of the
+  forms of the curve are shown in fig. 24.
+
+  [Illustration: FIG. 24.]
+
+  For the form d, in which two bays make a figure of eight, we have
+
+    L[root](W/EI) = 4.6, [alpha] = 130°
+
+  approximately. It is noteworthy that whenever the length and force
+  admit of a sinuous form, such as [alpha] or b, with more than two
+  inflections, there is also possible a crossed form, like e, with two
+  inflections only; the latter form is stable and the former unstable.
+
+61. The particular case of the above for which [alpha] is very small is
+a curve of sines of small amplitude, and the result in this case has
+been applied to the problem of the buckling of struts under thrust. When
+the strut, of length L', is maintained upright at its lower end, and
+loaded at its upper end, it is simply contracted, unless L'²W >
+¼[pi]²EI, for the lower end corresponds to a point at which the tangent
+is vertical on an elastica for which the line of inflections is also
+vertical, and thus the length must be half of one bay (fig. 25, a). For
+greater lengths or loads the strut tends to bend or buckle under the
+load. For a very slight excess of L'²W above ¼[pi]²EI, the theory on
+which the above discussion is founded, is not quite adequate, as it
+assumes the central-line of the strut to be free from extension or
+contraction, and it is probable that bending without extension does not
+take place when the length or the force exceeds the critical value but
+slightly. It should be noted also that the formula has no application to
+short struts, as the theory from which it is derived is founded on the
+assumption that the length is great compared with the diameter (cf. §
+56).
+
+[Illustration: Fig. 25.]
+
+The condition of buckling, corresponding to the above, for a long strut,
+of length L', when both ends are free to turn is L'²W > [pi]²EI; for the
+central-line forms a complete bay (fig. 25, b); if both ends are
+maintained in the same vertical line, the condition is L'²W > 4[pi]²EI,
+the central-line forming a complete bay and two half bays (fig. 25, c).
+
+[Illustration: Fig. 26.]
+
+62. In our consideration of flexure it has so far been supposed that the
+bending takes place in a principal plane. We may remove this restriction
+by resolving the forces that tend to produce bending into systems of
+forces acting in the two principal planes. To each plane there
+corresponds a particular flexural rigidity, and the systems of forces in
+the two planes give rise to independent systems of stress, strain and
+displacement, which must be superposed in order to obtain the actual
+state. Applying this process to the problem of §§ 48-54, and supposing
+that one principal axis of a cross-section at its centroid makes an
+angle [theta] with the vertical, then for any shape of section the
+neutral surface or locus of unextended fibres cuts the section in a line
+DD', which is conjugate to the vertical diameter CP with respect to any
+ellipse of inertia of the section. The central-line is bent into a plane
+curve which is not in a vertical plane, but is in a plane through the
+line CY which is perpendicular to DD' (fig. 26).
+
+63. _Bending and Twisting of Thin Rods._--When a very thin rod or wire
+is bent and twisted by applied forces, the forces on any part of it
+limited by a normal section are balanced by the tractions across the
+section, and these tractions are statically equivalent to certain forces
+and couples at the centroid of the section; we shall call them the
+_stress-resultants_ and the _stress-couples_. The stress-couples consist
+of two flexural couples in the two principal planes, and the torsional
+couple about the tangent to the central-line. The torsional couple is
+the product of the torsional rigidity and the twist produced; the
+torsional rigidity is exactly the same as for a straight rod of the same
+material and section twisted without bending, as in Saint-Venant's
+torsion problem (§ 42). The twist [tau] is connected with the
+deformation of the wire in this way: if we suppose a very small ring
+which fits the cross-section of the wire to be provided with a pointer
+in the direction of one principal axis of the section at its centroid,
+and to move along the wire with velocity v, the pointer will rotate
+about the central-line with angular velocity [tau]v. The amount of the
+flexural couple for either principal plane at any section is the product
+of the flexural rigidity for that plane, and the resolved part in that
+plane of the curvature of the central line at the centroid of the
+section; the resolved part of the curvature along the normal to any
+plane is obtained by treating the curvature as a vector directed along
+the normal to the osculating plane and projecting this vector. The
+flexural couples reduce to a single couple in the osculating plane
+proportional to the curvature when the two flexural rigidities are
+equal, and in this case only.
+
+The stress-resultants across any section are tangential forces in the
+two principal planes, and a tension or thrust along the central-line;
+when the stress-couples and the applied forces are known these
+stress-resultants are determinate. The existence, in particular, of the
+resultant tension or thrust parallel to the central-line does not imply
+sensible extension or contraction of the central filament, and the
+tension per unit area of the cross-section to which it would be
+equivalent is small compared with the tensions and pressures in
+longitudinal filaments not passing through the centroid of the section;
+the moments of the latter tensions and pressures constitute the flexural
+couples.
+
+64. We consider, in particular, the case of a naturally straight spring
+or rod of circular section, radius c, and of homogeneous isotropic
+material. The torsional rigidity is ¼E[pi]c^4/(1 + [sigma]); and the
+flexural rigidity, which is the same for all planes through the
+central-line, is ¼E[pi]c^4; we shall denote these by C and A
+respectively. The rod may be held bent by suitable forces into a curve
+of double curvature with an amount of twist [tau], and then the
+torsional couple is C[tau], and the flexural couple in the osculating
+plane is A/[rho], where [rho] is the radius of circular curvature. Among
+the curves in which the rod can be held by forces and couples applied at
+its ends only, one is a circular helix; and then the applied forces and
+couples are equivalent to a wrench about the axis of the helix.
+
+  Let [alpha] be the angle and r the radius of the helix, so that [rho]
+  is r sec²[alpha]; and let R and K be the force and couple of the
+  wrench (fig. 27).
+
+  Then the couple formed by R and an equal and opposite force at any
+  section and the couple K are equivalent to the torsional and flexural
+  couples at the section, and this gives the equations for R and K
+
+          sin [alpha] cos³ [alpha]           cos [alpha]
+    R = A ------------------------ - C[tau] ------------,
+                    r²                            r
+
+          cos³ [alpha]
+    K = A ------------ + C[tau] sin [alpha].
+               r
+
+  The thrust across any section is R sin [alpha] parallel to the tangent
+  to the helix, and the shearing stress-resultant is R cos [alpha] at
+  right angles to the osculating plane.
+
+  [Illustration: FIG. 27.]
+
+  When the twist is such that, if the rod were simply unbent, it would
+  also be untwisted, [tau] is (sin [alpha] cos [alpha])/r, and then,
+  restoring the values of A and C, we have
+
+         E[pi]c^4   [sigma]
+    R =  -------- ----------- sin [alpha] cos² [alpha],
+           4r²    1 + [sigma]
+
+        E[pi]c^4  1 + [sigma] cos² [alpha]
+    K = --------  ------------------------ cos [alpha].
+            4r          1 + [sigma]
+
+  65. The theory of spiral springs affords an application of these
+  results. The stress-couples called into play when a naturally helical
+  spring ([alpha], r) is held in the form of a helix ([alpha]', r'), are
+  equal to the differences between those called into play when a
+  straight rod of the same material and section is held in the first
+  form, and those called into play when it is held in the second form.
+
+  Thus the torsional couple is
+
+       /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha] \
+    C ( ------------------------- - ------------------------ ),
+       \           r'                          r            /
+
+  and the flexural couple is
+
+       /cos² [alpha]'   cos² [alpha]\
+    A ( ------------- - ------------ ).
+       \     r'              r      /
+
+  The wrench (R, K) along the axis by which the spring can be held in
+  the form ([alpha]', r') is given by the equations
+
+          sin [alpha]'  /cos² [alpha]'   cos² [alpha]\
+    R = A ------------ ( ------------- - ------------ ) -
+              r'        \       r'            r      /
+
+         cos [alpha]'  /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha]\
+      C ------------- ( ------------------------- - ----------------------- ),
+              r'       \           r'                          r           /
+
+                        /cos² [alpha]'   cos² [alpha]\
+    K = A cos [alpha]' ( ------------- - ------------ ) +
+                        \     r'               r     /
+
+                      /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha]\
+      C sin [alpha]' ( ------------------------- - ----------------------- ).
+                      \           r'                           r          /
+
+  When the spring is slightly extended by an axial force F, = -R, and
+  there is no couple, so that K vanishes, and [alpha]', r' differ very
+  little from [alpha], r, it follows from these equations that the axial
+  elongation, [delta]x, is connected with the axial length x and the
+  force F by the equation
+
+        E[pi]c^4        sin [alpha]       [delta]x
+    F = -------- ------------------------ --------,
+          4r²    1 + [sigma] cos² [alpha]     x
+
+  and that the loaded end is rotated about the axis of the helix through
+  a small angle
+
+    4[sigma]Fxr cos [alpha]
+    -----------------------
+           E[pi]c^4
+
+  the sense of the rotation being such that the spring becomes more
+  tightly coiled.
+
+66. A horizontal pointer attached to a vertical spiral spring would be
+made to rotate by loading the spring, and the angle through which it
+turns might be used to measure the load, at any rate, when the load is
+not too great; but a much more sensitive contrivance is the twisted
+strip devised by W.E. Ayrton and J. Perry. A very thin, narrow
+rectangular strip of metal is given a permanent twist about its
+longitudinal middle line, and a pointer is attached to it at right
+angles to this line. When the strip is subjected to longitudinal tension
+the pointer rotates through a considerable angle. G.H. Bryan (_Phil.
+Mag._, December 1890) has succeeded in constructing a theory of the
+action of the strip, according to which it is regarded as a strip of
+_plating_ in the form of a right helicoid, which, after extension of the
+middle line, becomes a portion of a slightly different helicoid; on
+account of the thinness of the strip, the change of curvature of the
+surface is considerable, even when the extension is small, and the
+pointer turns with the generators of the helicoid.
+
+  If b stands for the breadth and t for the thickness of the strip, and
+  [tau] for the permanent twist, the approximate formula for the angle
+  [theta] through which the strip is untwisted on the application of a
+  load W was found to be
+
+                        Wb[tau](1 + [sigma])
+    [theta] = ---------------------------------------.
+                     /    (1 + [sigma])   b^4[tau]²\
+              2Et^3 ( 1 + ------------- - --------- )
+                     \        30              t²   /
+
+  The quantity b[tau] which occurs in the formula is the total twist in
+  a length of the strip equal to its breadth, and this will generally be
+  very small; if it is small of the same order as t/b, or a higher
+  order, the formula becomes ½Wb[tau](1+[sigma])/Et^3, with sufficient
+  approximation, and this result appears to be in agreement with
+  observations of the behaviour of such strips.
+
+67. _Thin Plate under Pressure._--The theory of the deformation of
+plates, whether plane or curved, is very intricate, partly because of
+the complexity of the kinematical relations involved. We shall here
+indicate the nature of the effects produced in a thin plane plate, of
+isotropic material, which is slightly bent by pressure. This theory
+should have an application to the stress produced in a ship's plates. In
+the problem of the cylinder under internal pressure (§ 77 below) the
+most important stress is the circumferential tension, counteracting the
+tendency of the circular filaments to expand under the pressure; but in
+the problem of a plane plate some of the filaments parallel to the plane
+of the plate are extended and others are contracted, so that the
+tensions and pressures along them give rise to resultant couples but not
+always to resultant forces. Whatever forces are applied to bend the
+plate, these couples are always expressible, at least approximately in
+terms of the principal curvatures produced in the surface which, before
+strain, was the middle plane of the plate. The simplest case is that of
+a rectangular plate, bent by a distribution of couples applied to its
+edges, so that the middle surface becomes a cylinder of large radius R;
+the requisite couple per unit of length of the straight edges is of
+amount C/R, where C is a certain constant; and the requisite couple per
+unit of length of the circular edges is of amount C[sigma]/R, the latter
+being required to resist the tendency to anticlastic curvature (cf. §
+47). If normal sections of the plate are supposed drawn through the
+generators and circular sections of the cylinder, the action of the
+neighbouring portions on any portion so bounded involves flexural
+couples of the above amounts. When the plate is bent in any manner, the
+curvature produced at each section of the middle surface may be regarded
+as arising from the superposition of two cylindrical curvatures; and the
+flexural couples across normal sections through the lines of curvature,
+estimated per unit of length of those lines, are C(1/R1 + [sigma]/R2)
+and C(1/R2 + [sigma]/R1), where R1 and R2 are the principal radii of
+curvature. The value of C for a plate of small thickness 2h is
+(2/3)Eh^3/(1 - [sigma]²). Exactly as in the problem of the beam (§§ 48,
+56), the action between neighbouring portions of the plate generally
+involves shearing stresses across normal sections as well as flexural
+couples; and the resultants of these stresses are determined by the
+conditions that, with the flexural couples, they balance the forces
+applied to bend the plate.
+
+[Illustration: FIG. 28.]
+
+  68. To express this theory analytically, let the middle plane of the
+  plate in the unstrained position be taken as the plane of (x, y), and
+  let normal sections at right angles to the axes of x and y be drawn
+  through any point. After strain let w be the displacement of this
+  point in the direction perpendicular to the plane, marked p in fig.
+  28. If the axes of x and y were parallel to the lines of curvature at
+  the point, the flexural couple acting across the section normal to x
+  (or y) would have the axis of y (or x) for its axis; but when the
+  lines of curvature are inclined to the axes of co-ordinates, the
+  flexural couple across a section normal to either axis has a component
+  about that axis as well as a component about the perpendicular axis.
+  Consider an element ABCD of the section at right angles to the axis of
+  x, contained between two lines near together and perpendicular to the
+  middle plane. The action of the portion of the plate to the right upon
+  the portion to the left, across the element, gives rise to a couple
+  about the middle line (y) of amount, estimated per unit of length of
+  that line, equal to
+
+       /dP²w          dP²w\
+    C ( ---- + [sigma]---- ), = G1,
+       \dPx²          dPy²/
+
+  say, and to a couple, similarly estimated, about the normal (x) of
+  amount
+
+                   dP²w
+    -C(1-[sigma]) ------, = H,
+                  dPxdPy
+
+  say. The corresponding couples on an element of a section at right
+  angles to the axis of y, estimated per unit of length of the axis of
+  x, are of amounts
+
+        /dP²w          dP²w\
+     -C( ---- + [sigma]---- ), = G2
+        \dPy²          dPx²/
+
+  say, and -H. The resultant S1 of the shearing stresses on the element
+  ABCD, estimated as before, is given by the equation
+
+         dPG1   dPH
+    S1 = ---- - ---
+         dPx    dPy
+
+  (cf. § 57), and the corresponding resultant S2 for an element
+  perpendicular to the axis of y is given by the equation
+
+          dPH   dPG2
+    S2= - --- - ----.
+          dPx   dPy
+
+  If the plate is bent by a pressure p per unit of area, the equation of
+  equilibrium is
+
+    dPS1   dPS2
+    ---- + ---- = p, or, in terms of w,
+    dPx    dPy
+
+    dP^4w   dP^4w     dP^4w     p
+    ----- + ----- + 2-------- = --.
+    dPx^4   dPy^4    dPx²dPy²   C
+
+  This equation, together with the special conditions at the rim,
+  suffices for the determination of w, and then all the quantities here
+  introduced are determined. Further, the most important of the
+  stress-components are those which act across elements of normal
+  sections: the tension in direction x, at a distance z from the middle
+  plane measured in the direction of p, is of amount
+
+      3Cz   /dP²w          dP²w\
+    - ---- ( ---- + [sigma]---- ),
+      2h^3  \dPx²          dPy²/
+
+  and there is a corresponding tension in direction y; the shearing
+  stress consisting of traction parallel to y on planes x = const., and
+  traction parallel to x on planes y = const., is of amount
+
+    3C(1 - [sigma])z  dP²w
+    ---------------- ------;
+          2h^3       dPxdPy
+
+  these tensions and shearing stresses are equivalent to two principal
+  tensions, in the directions of the lines of curvature of the surface
+  into which the middle plane is bent, and they give rise to the
+  flexural couples.
+
+  69. In the special example of a circular plate, of radius a, supported
+  at the rim, and held bent by a uniform pressure p, the value of w at a
+  point distant r from the axis is
+
+    1  p             /5 + [sigma]       \
+    -- -- (a² - r²) ( ----------- a² - r²),
+    64 C             \1 + [sigma]       /
+
+  and the most important of the stress components is the radial tension,
+  of which the amount at any point is (3/32)(3 + [sigma])pz(a² - r)/h³;
+  the maximum radial tension is about (1/3)(a/h)²p, and, when the
+  thickness is small compared with the diameter, this is a large
+  multiple of p.
+
+70. _General Theorems._--Passing now from these questions of flexure and
+torsion, we consider some results that can be deduced from the general
+equations of equilibrium of an elastic solid body.
+
+The form of the general expression for the potential energy (§ 27)
+stored up in the strained body leads, by a general property of quadratic
+functions, to a reciprocal theorem relating to the effects produced in
+the body by two different systems of forces, viz.: The whole work done
+by the forces of the first system, acting over the displacements
+produced by the forces of the second system, is equal to the whole work
+done by the forces of the second system, acting over the displacements
+produced by the forces of the first system. By a suitable choice of the
+second system of forces, the average values of the component stresses
+and strains produced by given forces, considered as constituting the
+first system, can be obtained, even when the distribution of the stress
+and strain cannot be determined.
+
+[Illustration: FIG. 29.]
+
+  Taking for example the problem presented by an isotropic body of any
+  form[4] pressed between two parallel planes distant l apart (fig. 29),
+  and denoting the resultant pressure by p, we find that the diminution
+  of volume -[delta]v is given by the equation
+
+    -[delta]v = lp/3k,
+
+  where k is the modulus of compression, equal to (1/3)E/(1 - 2[sigma]).
+  Again, take the problem of the changes produced in a heavy body by
+  different ways of supporting it; when the body is suspended from one
+  or more points in a horizontal plane its volume is increased by
+
+    [delta]v = Wh/3k,
+
+  where W is the weight of the body, and h the depth of its centre of
+  gravity below the plane; when the body is supported by upward
+  vertical pressures at one or more points in a horizontal plane the
+  volume is diminished by
+
+    -[delta]v = Wh'/3k,
+
+  where h' is the height of the centre of gravity above the plane; if
+  the body is a cylinder, of length l and section A, standing with its
+  base on a smooth horizontal plane, its length is shortened by an
+  amount
+
+    -[delta]l = Wl/2EA;
+
+  if the same cylinder lies on the plane with its generators horizontal,
+  its length is increased by an amount
+
+    [delta]l = [sigma]Wh'/EA.
+
+
+
+71. In recent years important results have been found by considering the
+effects produced in an elastic solid by forces applied at isolated
+points.
+
+  Taking the case of a single force F applied at a point in the
+  interior, we may show that the stress at a distance r from the point
+  consists of
+
+  (1) a radial pressure of amount
+
+    2 - [sigma]   F   cos [theta]
+    ----------- ----- -----------,
+    1 - [sigma] 4[pi]     r²
+
+  (2) tension in all directions at right angles to the radius of amount
+
+     1 - 2[sigma]  F cos [theta]
+    -------------- -------------,
+    2(1 - [sigma])    4[pi]r²
+
+  (3) shearing stress consisting of traction acting along the radius
+  dr on the surface of the cone [theta] = const. and traction acting
+  along the meridian d[theta] on the surface of the sphere r = const. of
+  amount
+
+     1 - 2[sigma]    F   sin [theta]
+    -------------- ----- -----------,
+    2(1 - [sigma]) 4[pi]     r²
+
+  where [theta] is the angle between the radius vector r and the line of
+  action of F. The line marked T in fig. 30 shows the direction of the
+  tangential traction on the spherical surface.
+
+  [Illustration: FIG. 30.]
+
+  Thus the lines of stress are in and perpendicular to the meridian
+  plane, and the direction of one of those in the meridian plane is
+  inclined to the radius vector r at an angle
+
+               /2 - 4[sigma]            \
+    ½tan^(-1) ( ------------ tan [theta] ).
+               \5 - 4[sigma]            /
+
+  The corresponding displacement at any point is compounded of a radial
+  displacement of amount
+
+     1 + [sigma]     F    cos [theta]
+    -------------- ------ -----------
+    2(1 - [sigma]) 4[pi]E      r
+
+  and a displacement parallel to the line of action of F of amount
+
+    (3 - 4[sigma])(1 + [sigma])   F    1
+    --------------------------- ------ --.
+          2(1 - [sigma])        4[pi]E r
+
+  The effects of forces applied at different points and in different
+  directions can be obtained by summation, and the effect of
+  continuously distributed forces can be obtained by integration.
+
+72. The stress system considered in § 71 is equivalent, on the plane
+through the origin at right angles to the line of action of F, to a
+resultant pressure of magnitude ½F at the origin and a radial traction
+of amount
+
+   1 - 2[sigma]     F
+  -------------- -------,
+  2(1 - [sigma]) 4[pi]r²
+
+and, by the application of this system of tractions to a solid bounded
+by a plane, the displacement just described would be produced. There is
+also another stress system for a solid so bounded which is equivalent,
+on the same plane, to a resultant pressure at the origin, and a radial
+traction proportional to 1/r², but these are in the ratio 2[pi]:r^(-2),
+instead of being in the ratio 4[pi](1 - [sigma]) : (1 - 2[sigma])r^(-2).
+
+[Illustration: FIG. 31.]
+
+  The second stress system (see fig. 31) consists of:
+
+  (1) radial pressure F'r^{-2},
+
+  (2) tension in the meridian plane across the radius vector of amount
+
+    F'r^(-2) cos [theta] /(1 + cos [theta]),
+
+  (3) tension across the meridian plane of amount
+
+    F'r^(-2)/(l + cos [theta]),
+
+  (4) shearing stress as in § 71 of amount
+
+    F'r^(-2) sin [theta]/(1 + cos [theta]),
+
+  and the stress across the plane boundary consists of a resultant
+  pressure of magnitude 2[pi]F' and a radial traction of amount
+  F'r^(-2). If then we superpose the component stresses of the last
+  section multiplied by 4(1 - [sigma])W/F, and the component stresses
+  here written down multiplied by -(1 - 2[sigma])W/2[pi]F', the stress
+  on the plane boundary will reduce to a single pressure W at the
+  origin. We shall thus obtain the stress system at any point due to
+  such a force applied at one point of the boundary.
+
+  In the stress system thus arrived at the traction across any plane
+  parallel to the boundary is directed away from the place where W is
+  supported, and its amount is 3W cos²[theta]/2[pi]r². The corresponding
+  displacement consists of
+
+  (1) a horizontal displacement radially outwards from the vertical
+  through the origin of amount
+
+    W(1 + [sigma]) sin [theta]  /               1 - 2[sigma]  \
+    -------------------------- ( cos [theta] - --------------- ),
+             2[pi]Er            \              1 + cos [theta]/
+
+  (2) a vertical displacement downwards of amount
+
+    W(1 + [sigma])
+    -------------- {2(1 - [sigma]) + cos²[theta]}.
+       2[pi]Er
+
+  The effects produced by a system of loads on a solid bounded by a
+  plane can be deduced.
+
+The results for a solid body bounded by an infinite plane may be
+interpreted as giving the local effects of forces applied to a small
+part of the surface of a body. The results show that pressure is
+transmitted into a body from the boundary in such a way that the
+traction at a point on a section parallel to the boundary is the same at
+all points of any sphere which touches the boundary at the point of
+pressure, and that its amount at any point is inversely proportional to
+the square of the radius of this sphere, while its direction is that of
+a line drawn from the point of pressure to the point at which the
+traction is estimated. The transmission of force through a solid body
+indicated by this result was strikingly demonstrated in an attempt that
+was made to measure the lunar deflexion of gravity; it was found that
+the weight of the observer on the floor of the laboratory produced a
+disturbance of the instrument sufficient to disguise completely the
+effect which the instrument had been designed to measure (see G.H.
+Darwin, _The Tides and Kindred Phenomena in the Solar System_, London,
+1898).
+
+73. There is a corresponding theory of two-dimensional systems, that is
+to say, systems in which either the displacement is parallel to a fixed
+plane, or there is no traction across any plane of a system of parallel
+planes. This theory shows that, when pressure is applied at a point of
+the edge of a plate in any direction in the plane of the plate, the
+stress developed in the plate consists exclusively of radial pressure
+across any circle having the point of pressure as centre, and the
+magnitude of this pressure is the same at all points of any circle which
+touches the edge at the point of pressure, and its amount at any point
+is inversely proportional to the radius of this circle. This result
+leads to a number of interesting solutions of problems relating to plane
+systems; among these may be mentioned the problem of a circular plate
+strained by any forces applied at its edge.
+
+74. The results stated in § 72 have been applied to give an account of
+the nature of the actions concerned in the impact of two solid bodies.
+The dissipation of energy involved in the impact is neglected, and the
+resultant pressure between the bodies at any instant during the impact
+is equal to the rate of destruction of momentum of either along the
+normal to the plane of contact drawn towards the interior of the other.
+It has been shown that in general the bodies come into contact over a
+small area bounded by an ellipse, and remain in contact for a time which
+varies inversely as the fifth root of the initial relative velocity.
+
+  For equal spheres of the same material, with [sigma] = ¼, impinging
+  directly with relative velocity v, the patches that come into contact
+  are circles of radius
+
+     /45[pi]\ ^(1/5)  /v \ ^(2/5)
+    ( ------ )       ( -- )      r,
+     \ 256  /         \V /
+
+  where r is the radius of either, and V the velocity of longitudinal
+  waves in a thin bar of the material. The duration of the impact is
+  approximately
+
+              /2025[pi]²\ ^(1/5)       r
+    (2.9432) ( --------- )      --------------- .
+              \   512   /       v^(1/5) V^(4/5)
+
+  For two steel spheres of the size of the earth impinging with a
+  velocity of 1 cm. per second the duration of the impact would be about
+  twenty-seven hours. The fact that the duration of impact is, for
+  moderate velocities, a considerable multiple of the time taken by a
+  wave of compression to travel through either of two impinging bodies
+  has been ascertained experimentally, and constitutes the reason for
+  the adequacy of the statical theory here described.
+
+75. _Spheres and Cylinders._--Simple results can be found for spherical
+and cylindrical bodies strained by radial forces.
+
+  For a sphere of radius a, and of homogeneous isotropic material of
+  density [rho], strained by the mutual gravitation of its parts, the
+  stress at a distance r from the centre consists of
+
+  (1) uniform hydrostatic pressure of amount (1/10)g[rho]a(3 -
+  [sigma])/(1 - [sigma]),
+
+  (2) radial tension of amount (1/10)g[rho](r²/a)(3 - [sigma])/(1
+  -[sigma]),
+
+  (3) uniform tension at right angles to the radius vector of amount
+
+    (1/10)g[rho](r²/a) (1 + 3[sigma])/(1 - [sigma]),
+
+  where g is the value of gravity at the surface. The corresponding
+  strains consist of
+
+  (1) uniform contraction of all lines of the body of amount
+
+    (1/30)k^(-1)g[rho]a(3 - [sigma])/(1 - [sigma]),
+
+  (2) radial extension of amount (1/10)k^(-1)g[rho](r²/a)(1 +
+  [sigma])/(1 - [sigma]),
+
+  (3) extension in any direction at right angles to the radius vector of
+  amount
+
+    (1/30)k^(-1)g[rho](r²/a) (1 + [sigma])/(1 - [sigma]),
+
+  where k is the modulus of compression. The volume is diminished by the
+  fraction g[rho]a/5k of itself. The parts of the radii vectors within
+  the sphere r = a{(3 - [sigma])/(3 + 3[sigma])}^½ are contracted, and
+  the parts without this sphere are extended. The application of the
+  above results to the state of the interior of the earth involves a
+  neglect of the caution emphasized in § 40, viz. that the strain
+  determined by the solution must be small if the solution is to be
+  accepted. In a body of the size and mass of the earth, and having a
+  resistance to compression and a rigidity equal to those of steel, the
+  radial contraction at the centre, as given by the above solution,
+  would be nearly 1/3, and the radial extension at the surface nearly
+  1/6, and these fractions can by no means be regarded as "small."
+
+  76. In a spherical shell of homogeneous isotropic material, of
+  internal radius r1 and external radius r0, subjected to pressure p0 on
+  the outer surface, and p1 on the inner surface, the stress at any
+  point distant r from the centre consists of
+
+                                                  p1r1³ - p0r0³
+  (1) uniform tension in all directions of amount -------------,
+                                                    r0³ - r1³
+
+                                 p1 - p0   r0³ r1³
+  (2) radial pressure of amount ---------  -------,
+                                r0³ - r1³     r³
+
+  (3) tension in all directions at right angles to the radius vector of
+  amount
+
+       p1 - p0  r0³ r1³
+    ½ --------- -------.
+      r0³ - r1³   r³
+
+  The corresponding strains consist of
+
+  (1) uniform extension of all lines of the body of amount
+
+    1  p1r1³ - p0r0³
+    -- -------------,
+    3k   r0³ - r1³
+
+                                   1   p1 - p0  r0³ r1³
+  (2) radial contraction of amount -- --------- -------,
+                                   2µ r0³ - r1³    r³
+
+  (3) extension in all directions at right angles to the radius vector
+  of amount
+
+    1   p1 - p0  r0³ r1³
+    -- --------- -------,
+    4µ r0³ - r1³    r³
+
+  where µ is the modulus of rigidity of the material, = ½E/(1 +
+  [sigma]). The volume included between the two surfaces of the body is
+  increased
+
+                  p1r1³ - p0r0³
+  by the fraction ------------- of itself, and the volume within the
+                  k(r0³ - r1³)
+
+  inner surface is increased by the fraction
+
+    3(p1 - p0)    r0³      p1r1³ - p0r0³
+    ---------- --------- + -------------
+        4µ     r0³ - r1³   k(r0³ - r1³)
+
+  of itself. For a shell subject only to internal pressure p the
+  greatest extension is the extension at right angles to the radius at
+  the inner surface, and its amount is
+
+       pr1³    / 1   1  r0³ \
+    --------- ( -- + -- ---  );
+    r0³ - r1³  \3k   4µ r1³ /
+
+  the greatest tension is the transverse tension at the inner surface,
+  and its amount is p(½r0³ + r1³)/(r0³ - r1³).
+
+  77. In the problem of a cylindrical shell under pressure a
+  complication may arise from the effects of the ends; but when the ends
+  are free from stress the solution is very simple. With notation
+  similar to that in § 76 it can be shown that the stress at a distance
+  r from the axis consists of
+
+  (1) uniform tension in all directions at right angles to the axis of
+  amount
+
+    p1r1² - p0r0²
+    -------------,
+      r0² - r1²
+
+                                 p1 - p0  r0² r1²
+  (2) radial pressure of amount --------- -------,
+                                r0² - r1²    r²
+
+  (3) hoop tension numerically equal to this radial pressure.
+
+  The corresponding strains consist of
+
+  (1) uniform extension of all lines of the material at right angles to
+  the axis of amount
+
+    1 - [sigma] p1r1² - p0r0²
+    ----------- -------------,
+         E        r0² - r1²
+
+  (2) radial contraction of amount
+
+    1 + [sigma]  p1 - p0  r0² r1²
+    ----------- --------- -------,
+         E      r0² - r1²   r²
+
+  (3) extension along the circular filaments numerically equal to this
+  radial contraction,
+
+  (4) uniform contraction of the longitudinal filaments of amount
+
+    2[sigma] p1r1² - p0r0²
+    -------- -------------.
+       E       r0² - r1²
+
+  For a shell subject only to internal pressure p the greatest extension
+  is the circumferential extension at the inner surface, and its amount
+  is
+
+    p   /r0² + r1²          \
+    -- ( --------- + [sigma] );
+    E   \r0² - r1²          /
+
+  the greatest tension is the hoop tension at the inner surface, and its
+  amount is p(r0² + r1^²)/(r0² - r1²).
+
+  78. When the ends of the tube, instead of being free, are closed by
+  disks, so that the tube becomes a closed cylindrical vessel, the
+  longitudinal extension is determined by the condition that the
+  resultant longitudinal tension in the walls balances the resultant
+  normal pressure on either end. This condition gives the value of the
+  extension of the longitudinal filaments as
+
+    (p1r1² - p0r0²)/3k(r0² - r1²),
+
+  where k is the modulus of compression of the material. The result may
+  be applied to the experimental determination of k, by measuring the
+  increase of length of a tube subjected to internal pressure (A.
+  Mallock, _Proc. R. Soc. London_, lxxiv., 1904, and C. Chree, _ibid._).
+
+79. The results obtained in § 77 have been applied to gun construction;
+we may consider that one cylinder is heated so as to slip over another
+upon which it shrinks by cooling, so that the two form a single body in
+a condition of initial stress.
+
+  We take P as the measure of the pressure between the two, and p for
+  the pressure within the inner cylinder by which the system is
+  afterwards strained, and denote by r' the radius of the common
+  surface. To obtain the stress at any point we superpose the
+
+                                         r1² r0² - r²
+  system consisting of radial pressure p --- --------- and hoop tension
+                                         r²  r0² - r1²
+
+     r1²  r0² + r²
+   p --- ---------  upon a system which, for the outer cylinder, consists
+     r²  r0² - r1²
+
+                       r'²  r0² - r²
+  of radial pressure P --- ---------
+                       r²  r0² - r'²
+
+                     r'²  r0² + r²
+  and hoop tension P --- ---------, and for the inner cylinder consists
+                     r²  r0² - r'²
+
+                        r'²  r² - r1²                    r'²  r² + r1²
+  of radial pressure  P --- --------- and hoop tension P --- ---------.
+                        r²  r'² - r1²                    r²  r'² - r1²
+
+  The hoop tension at the inner surface is less than it would be for a
+  tube of equal thickness without initial stress in the ratio
+
+        P     2r'²    r0² + r1²
+    1 - -- ---------  --------- : 1.
+        p  r0² + r1²  r'² - r1²
+
+  This shows how the strength of the tube is increased by the initial
+  stress. When the initial stress is produced by tightly wound wire, a
+  similar gain of strength accrues.
+
+80. In the problem of determining the distribution of stress and strain
+in a circular cylinder, rotating about its axis, simple solutions have
+been obtained which are sufficiently exact for the two special cases of
+a thin disk and a long shaft.
+
+  Suppose that a circular disk of radius a and thickness 2l, and of
+  density [rho], rotates about its axis with angular velocity [omega],
+  and consider the following systems of superposed stresses at any point
+  distant r from the axis and z from the middle plane:
+
+  (1) uniform tension in all directions at right angles to the axis of
+  amount (1/8)[omega]²[rho]a²(3 + [sigma]),
+
+  (2) radial pressure of amount (1/8)[omega]²[rho]r²(3 + [sigma]),
+
+  (3) pressure along the circular filaments of amount
+  (1/8)[omega]²[rho]r²(1 + 3[sigma]),
+
+  (4) uniform tension in all directions at right angles to the axis of
+  amount (1/6)[omega]²[rho](l²-3z²)[sigma](1 + [sigma])/(1 - [sigma]).
+
+  The corresponding strains may be expressed as
+
+  (1) uniform extension of all filaments at right angles to the axis of
+  amount
+
+    1 - [sigma]
+    ----------- (1/8)[omega]²[rho]a²(3 + [sigma]),
+         E
+
+  (2) radial contraction of amount
+
+    1 - [sigma]²
+    ------------ (3/8)[omega]²[rho]r²,
+         E
+
+  (3) contraction along the circular filaments of amount
+
+    1 - [sigma]²
+    ------------ (1/8)[omega]²[rho]r²,
+         E
+
+  (4) extension of all filaments at right angles to the axis of amount
+
+    (1/E)(1/6)[omega]²[rho][l² - (3_x)²][sigma](1+[sigma]),
+
+  (5) contraction of the filaments normal to the plane of the disk of
+  amount
+
+    2[sigma]
+    -------- (1/8)[omega]²[rho]a²(3 + [sigma])
+       E
+
+       [sigma]
+     - ------- ½ [omega]²[rho]r²(1 + [sigma])
+          E
+
+       2[sigma]                                      (1 + [sigma])
+     + -------- (1/6)[omega]²[rho](l^² - 3z²)[sigma] -------------.
+          E                                          (1 - [sigma])
+
+  The greatest extension is the circumferential extension near the
+  centre, and its amount is
+
+    (3 + [sigma])(1 - [sigma])                   [sigma](1 + [sigma])
+    -------------------------- [omega]²[rho]a² + -------------------- [omega]²[rho]l².
+                8E                                        6E
+
+  [Illustration: Fig. 32.]
+
+  The longitudinal contraction is required to make the plane faces of
+  the disk free from pressure, and the terms in l and z enable us to
+  avoid tangential traction on any cylindrical surface. The system of
+  stresses and strains thus expressed satisfies all the conditions,
+  except that there is a small radial tension on the bounding surface of
+  amount per unit area (1/6)[omega]²[rho](l² - 3z²)[sigma](1 +
+  [sigma])/(1 - [sigma]). The resultant of these tensions on any part of
+  the edge of the disk vanishes, and the stress in question is very
+  small in comparison with the other stresses involved when the disk is
+  thin; we may conclude that, for a thin disk, the expressions given
+  represent the actual condition at all points which are not very close
+  to the edge (cf. § 55). The effect to the longitudinal contraction is
+  that the plane faces become slightly concave (fig. 32).
+
+  81. The corresponding solution for a disk with a circular axle-hole
+  (radius b) will be obtained from that given in the last section by
+  superposing the following system of additional stresses:
+
+  (1) radial tension of amount (1/8)[omega]²[rho]b²(1 - a²/r²)(3 +
+  [sigma]),
+
+  (2) tension along the circular filaments of amount
+
+    (1/8)[omega]²[rho]b²(1 + a²/r²)(3 + [sigma]).
+
+  The corresponding additional strains are
+
+  (1) radial contraction of amount
+                 _                               _
+    3 + [sigma] |              a²                 |
+    ----------- | (1 + [sigma])-- - (1 - [sigma]) | [omega]²[rho]b²,
+        8E      |_             r²                _|
+
+  (2) extension along the circular filaments of amount
+                 _                              _
+    3 + [sigma] |             a²                 |
+    ----------- |(1 + [sigma])-- + (1 - [sigma]) | [omega]²[rho]b².
+        8E      |_            r²                _|
+
+  (3) contraction of the filaments parallel to the axis of amount
+
+    [sigma](3 + [sigma])
+    -------------------- [omega]²[rho]b².
+             4E
+
+  Again, the greatest extension is the circumferential extension at the
+  inner surface, and, when the hole is very small, its amount is nearly
+  double what it would be for a complete disk.
+
+  82. In the problem of the rotating shaft we have the following
+  stress-system:
+
+  (1) radial tension of amount
+
+    (1/8)[omega]²[rho](a² - r²)(3 - 2[sigma])/(1-[sigma]),
+
+  (2) circumferential tension of amount
+
+    (1/8)[omega]²[rho]{(a²(3 - 2[sigma])/(1-[sigma])
+      - r²(1 + 2[sigma])/(1 - [sigma])},
+
+  (3) longitudinal tension of amount
+
+    ¼[omega]²[rho](a² - 2r²)[sigma]/(1 - [sigma]).
+
+  The resultant longitudinal tension at any normal section vanishes, and
+  the radial tension vanishes at the bounding surface; and thus the
+  expressions here given may be taken to represent the actual condition
+  at all points which are not very close to the ends of the shaft. The
+  contraction of the longitudinal filaments is uniform and equal to
+  ½[omega]²[rho]a²[sigma]/E. The greatest extension in the rotating
+  shaft is the circumferential extension close to the axis, and its
+  amount is (1/8)[omega]²[rho]a²(3 - 5[sigma])/E(1 - [sigma]).
+
+  The value of any theory of the strength of long rotating shafts
+  founded on these formulae is diminished by the circumstance that at
+  sufficiently high speeds the shaft may tend to take up a curved form,
+  the straight form being unstable. The shaft is then said to _whirl_.
+  This occurs when the period of rotation of the shaft is very nearly
+  coincident with one of its periods of lateral vibration. The lowest
+  speed at which whirling can take place in a shaft of length l, freely
+  supported at its ends, is given by the formula
+
+    [omega]²[rho] = ¼Ea²([pi]/l)^4.
+
+  As in § 61, this formula should not be applied unless the length of
+  the shaft is a considerable multiple of its diameter. It implies that
+  whirling is to be expected whenever [omega] approaches this critical
+  value.
+
+83. When the forces acting upon a spherical or cylindrical body are not
+radial, the problem becomes more complicated. In the case of the sphere
+deformed by any forces it has been completely solved, and the solution
+has been applied by Lord Kelvin and Sir G.H. Darwin to many interesting
+questions of cosmical physics. The nature of the stress produced in the
+interior of the earth by the weight of continents and mountains, the
+spheroidal figure of a rotating solid planet, the rigidity of the earth,
+are among the questions which have in this way been attacked. Darwin
+concluded from his investigation that, to support the weight of the
+existing continents and mountain ranges, the materials of which the
+earth is composed must, at great depths (1600 kilometres), have at least
+the strength of granite. Kelvin concluded from his investigation that
+the actual heights of the tides in the existing oceans can be accounted
+for only on the supposition that the interior of the earth is solid, and
+of rigidity nearly as great as, if not greater than, that of steel.
+
+  84. Some interesting problems relating to the strains produced in a
+  cylinder of finite length by forces distributed symmetrically round
+  the axis have been solved. The most important is that of a cylinder
+  crushed between parallel planes in contact with its plane ends. The
+  solution was applied to explain the discrepancies that have been
+  observed in different tests of crushing strength according as the ends
+  of the test specimen are or are not prevented from spreading. It was
+  applied also to explain the fact that in such tests small conical
+  pieces are sometimes cut out at the ends subjected to pressure.
+
+85. _Vibrations and Waves._--When a solid body is struck, or otherwise
+suddenly disturbed, it is thrown into a state of vibration. There always
+exist dissipative forces which tend to destroy the vibratory motion, one
+cause of the subsidence of the motion being the communication of energy
+to surrounding bodies. When these dissipative forces are disregarded, it
+is found that an elastic solid body is capable of vibrating in such a
+way that the motion of any particle is simple harmonic motion, all the
+particles completing their oscillations in the same period and being at
+any instant in the same phase, and the displacement of any selected one
+in any particular direction bearing a definite ratio to the displacement
+of an assigned one in an assigned direction. When a body is moving in
+this way it is said to be _vibrating in a normal mode_. For example,
+when a tightly stretched string of negligible flexural rigidity, such as
+a violin string may be taken to be, is fixed at the ends, and vibrates
+transversely in a normal mode, the displacements of all the particles
+have the same direction, and their magnitudes are proportional at any
+instant to the ordinates of a curve of sines. Every body possesses an
+infinite number of normal modes of vibration, and the _frequencies_ (or
+numbers of vibrations per second) that belong to the different modes
+form a sequence of increasing numbers. For the string, above referred
+to, the fundamental tone and the various overtones form an harmonic
+scale, that is to say, the frequencies of the normal modes of vibration
+are proportional to the integers 1, 2, 3, .... In all these modes except
+the first the string vibrates as if it were divided into a number of
+equal pieces, each having fixed ends; this number is in each case the
+integer defining the frequency. In general the normal modes of vibration
+of a body are distinguished one from another by the number and situation
+of the surfaces (or other _loci_) at which some characteristic
+displacement or traction vanishes. The problem of determining the normal
+modes and frequencies of free vibration of a body of definite size,
+shape and constitution, is a mathematical problem of a similar character
+to the problem of determining the state of stress in the body when
+subjected to given forces. The bodies which have been most studied are
+strings and thin bars, membranes, thin plates and shells, including
+bells, spheres and cylinders. Most of the results are of special
+importance in their bearing upon the theory of sound.
+
+  86. The most complete success has attended the efforts of
+  mathematicians to solve the problem of free vibrations for an
+  isotropic sphere. It appears that the modes of vibration fall into two
+  classes: one characterized by the absence of a radial component of
+  displacement, and the other by the absence of a radial component of
+  rotation (§ 14). In each class there is a doubly infinite number of
+  modes. The displacement in any mode is determined in terms of a single
+  spherical harmonic function, so that there are modes of each class
+  corresponding to spherical harmonics of every integral degree; and for
+  each degree there is an infinite number of modes, differing from one
+  another in the number and position of the concentric spherical
+  surfaces at which some characteristic displacement vanishes. The most
+  interesting modes are those in which the sphere becomes slightly
+  spheroidal, being alternately prolate and oblate during the course of
+  a vibration; for these vibrations tend to be set up in a spherical
+  planet by tide-generating forces. In a sphere of the size of the
+  earth, supposed to be incompressible and as rigid as steel, the period
+  of these vibrations is 66 minutes.
+
+87. The theory of free vibrations has an important bearing upon the
+question of the strength of structures subjected to sudden blows or
+shocks. The stress and strain developed in a body by sudden applications
+of force may exceed considerably those which would be produced by a
+gradual application of the same forces. Hence there arises the general
+question of _dynamical resistance_, or of the resistance of a body to
+forces applied so quickly that the inertia of the body comes sensibly
+into play. In regard to this question we have two chief theoretical
+results. The first is that the strain produced by a force suddenly
+applied may be as much as twice the statical strain, that is to say, as
+the strain which would be produced by the same force when the body is
+held in equilibrium under its action; the second is that the sudden
+reversal of the force may produce a strain three times as great as the
+statical strain. These results point to the importance of specially
+strengthening the parts of any machine (e.g. screw propeller shafts)
+which are subject to sudden applications or reversals of load. The
+theoretical limits of twice, or three times, the statical strain are not
+in general attained. For example, if a thin bar hanging vertically from
+its upper end is suddenly loaded at its lower end with a weight equal to
+its own weight, the greatest dynamical strain bears to the greatest
+statical strain the ratio 1.63 : 1; when the attached weight is four
+times the weight of the bar the ratio becomes 1.84 : 1. The method by
+which the result just mentioned is reached has recently been applied to
+the question of the breaking of winding ropes used in mines. It appeared
+that, in order to bring the results into harmony with the observed
+facts, the strain in the supports must be taken into account as well as
+the strain in the rope (J. Perry, _Phil. Mag._, 1906 (vi.), vol. ii.).
+
+88. The immediate effect of a blow or shock, locally applied to a body,
+is the generation of a wave which travels through the body from the
+locality first affected. The question of the propagation of waves
+through an elastic solid body is historically of very great importance;
+for the first really successful efforts to construct a theory of
+elasticity (those of S.D. Poisson, A.L. Cauchy and G. Green) were
+prompted, at least in part, by Fresnel's theory of the propagation of
+light by transverse vibrations. For many years the luminiferous medium
+was identified with the isotropic solid of the theory of elasticity.
+Poisson showed that a disturbance communicated to the body gives rise to
+two waves which are propagated through it with different velocities; and
+Sir G.G. Stokes afterwards showed that the quicker wave is a wave of
+irrotational dilatation, and the slower wave is a wave of rotational
+distortion accompanied by no change of volume. The velocities of the two
+waves in a solid of density [rho] are [root]{([lambda] + 2µ)/[rho]} and
+[root](µ/[rho]), [lambda] and µ being the constants so denoted in § 26.
+When the surface of the body is free from traction, the waves on
+reaching the surface are reflected; and thus after a little time the
+body would, if there were no dissipative forces, be in a very complex
+state of motion due to multitudes of waves passing to and fro through
+it. This state can be expressed as a state of vibration, in which the
+motions belonging to the various normal modes (§ 85) are superposed,
+each with an appropriate amplitude and phase. The waves of dilatation
+and distortion do not, however, give rise to different modes of
+vibration, as was at one time supposed, but any mode of vibration in
+general involves both dilatation and rotation. There are exceptional
+results for solids of revolution; such solids possess normal modes of
+vibration which involve no dilatation. The existence of a boundary to
+the solid body has another effect, besides reflexion, upon the
+propagation of waves. Lord Rayleigh has shown that any disturbance
+originating at the surface gives rise to waves which travel away over
+the surface as well as to waves which travel through the interior; and
+any internal disturbance, on reaching the surface, also gives rise to
+such superficial waves. The velocity of the superficial waves is a
+little less than that of the waves of distortion: 0.9554
+[root](µ/[rho]) when the material is incompressible
+0.9194[root](µ/[rho]) when the Poisson's ratio belonging to the material
+is ¼.
+
+89. These results have an application to the propagation of earthquake
+shocks (see also EARTHQUAKE). An internal disturbance should, if the
+earth can be regarded as solid, give rise to three wave-motions: two
+propagated through the interior of the earth with different velocities,
+and a third propagated over the surface. The results of seismographic
+observations have independently led to the recognition of three phases
+of the recorded vibrations: a set of "preliminary tremors" which are
+received at different stations at such times as to show that they are
+transmitted directly through the interior of the earth with a velocity
+of about 10 km. per second, a second set of preliminary tremors which
+are received at different stations at such times as to show that they
+are transmitted directly through the earth with a velocity of about 5
+km. per second, and a "main shock," or set of large vibrations, which
+becomes sensible at different stations at such times as to show that a
+wave is transmitted over the surface of the earth with a velocity of
+about 3 km. per second. These results can be interpreted if we assume
+that the earth is a solid body the greater part of which is practically
+homogeneous, with high values for the rigidity and the resistance to
+compression, while the superficial portions have lower values for these
+quantities. The rigidity of the central portion would be about
+(1.4)10^12 dynes per square cm., which is considerably greater than that
+of steel, and the resistance to compression would be about (3.8)10^12
+dynes per square cm. which is much greater than that of any known
+material. The high value of the resistance to compression is not
+surprising when account is taken of the great pressures, due to
+gravitation, which must exist in the interior of the earth. The high
+value of the rigidity can be regarded as a confirmation of Lord Kelvin's
+estimate founded on tidal observations (§ 83).
+
+90. _Strain produced by Heat._--The mathematical theory of elasticity as
+at present developed takes no account of the strain which is produced in
+a body by unequal heating. It appears to be impossible in the present
+state of knowledge to form as in § 39 a system of differential equations
+to determine both the stress and the temperature at any point of a solid
+body the temperature of which is liable to variation. In the cases of
+isothermal and adiabatic changes, that is to say, when the body is
+slowly strained without variation of temperature, and also when the
+changes are effected so rapidly that there is no gain or loss of heat by
+any element, the internal energy of the body is sufficiently expressed
+by the strain-energy-function (§§ 27, 30). Thus states of equilibrium
+and of rapid vibration can be determined by the theory that has been
+explained above. In regard to thermal effects we can obtain some
+indications from general thermodynamic theory. The following passages
+extracted from the article "Elasticity" contributed to the 9th edition
+of the _Encyclopaedia Britannica_ by Sir W. Thomson (Lord Kelvin)
+illustrate the nature of these indications:--"From thermodynamic theory
+it is concluded that cold is produced whenever a solid is strained by
+opposing, and heat when it is strained by yielding to, any elastic force
+of its own, the strength of which would diminish if the temperature were
+raised; but that, on the contrary, heat is produced when a solid is
+strained against, and cold when it is strained by yielding to, any
+elastic force of its own, the strength of which would increase if the
+temperature were raised. When the strain is a condensation or
+dilatation, uniform in all directions, a fluid may be included in the
+statement. Hence the following propositions:--
+
+"(1) A cubical compression of any elastic fluid or solid in an ordinary
+condition causes an evolution of heat; but, on the contrary, a cubical
+compression produces cold in any substance, solid or fluid, in such an
+abnormal state that it would contract if heated while kept under
+constant pressure. Water below its temperature (3.9° Cent.) of maximum
+density is a familiar instance.
+
+"(2) If a wire already twisted be suddenly twisted further, always,
+however, within its limits of elasticity, cold will be produced; and if
+it be allowed suddenly to untwist, heat will be evolved from itself
+(besides heat generated externally by any work allowed to be wasted,
+which it does in untwisting). It is assumed that the torsional rigidity
+of the wire is diminished by an elevation of temperature, as the writer
+of this article had found it to be for copper, iron, platinum and other
+metals.
+
+"(3) A spiral spring suddenly drawn out will become lower in
+temperature, and will rise in temperature when suddenly allowed to draw
+in. [This result has been experimentally verified by Joule
+('Thermodynamic Properties of Solids,' _Phil. Trans._, 1858) and the
+amount of the effect found to agree with that calculated, according to
+the preceding thermodynamic theory, from the amount of the weakening of
+the spring which he found by experiment.]
+
+"(4) A bar or rod or wire of any substance with or without a weight hung
+on it, or experiencing any degree of end thrust, to begin with, becomes
+cooled if suddenly elongated by end pull or by diminution of end thrust,
+and warmed if suddenly shortened by end thrust or by diminution of end
+pull; except abnormal cases in which with constant end pull or end
+thrust elevation of temperature produces shortening; in every such case
+pull or diminished thrust produces elevation of temperature, thrust or
+diminished pull lowering of temperature.
+
+"(5) An india-rubber band suddenly drawn out (within its limits of
+elasticity) becomes warmer; and when allowed to contract, it becomes
+colder. Any one may easily verify this curious property by placing an
+india-rubber band in slight contact with the edges of the lips, then
+suddenly extending it--it becomes very perceptibly warmer: hold it for
+some time stretched nearly to breaking, and then suddenly allow it to
+shrink--it becomes quite startlingly colder, the cooling effect being
+sensible not merely to the lips but to the fingers holding the band. The
+first published statement of this curious observation is due to J. Gough
+(_Mem. Lit. Phil. Soc. Manchester_, 2nd series, vol. i. p. 288), quoted
+by Joule in his paper on 'Thermodynamic Properties of Solids' (cited
+above). The thermodynamic conclusion from it is that an india-rubber
+band, stretched by a constant weight of sufficient amount hung on it,
+must, when heated, pull up the weight, and, when cooled, allow the
+weight to descend: this Gough, independently of thermodynamic theory,
+had found to be actually the case. The experiment any one can make with
+the greatest ease by hanging a few pounds weight on a common
+india-rubber band, and taking a red-hot coal in a pair of tongs, or a
+red-hot poker, and moving it up and down close to the band. The way in
+which the weight rises when the red-hot body is near, and falls when it
+is removed, is quite startling. Joule experimented on the amount of
+shrinking per degree of elevation of temperature, with different weights
+hung on a band of vulcanized india-rubber, and found that they closely
+agreed with the amounts calculated by Thomson's theory from the heating
+effects of pull, and cooling effects of ceasing to pull, which he had
+observed in the same piece of india-rubber."
+
+91. _Initial Stress._--It has been pointed out above (§ 20) that the
+"unstressed" state, which serves as a zero of reckoning for strains and
+stresses is never actually attained, although the strain (measured from
+this state), which exists in a body to be subjected to experiment, may
+be very slight. This is the case when the "initial stress," or the
+stress existing before the experiment, is small in comparison with the
+stress developed during the experiment, and the limit of linear
+elasticity (§ 32) is not exceeded. The existence of initial stress has
+been correlated above with the existence of body forces such as the
+force of gravity, but it is not necessarily dependent upon such forces.
+A sheet of metal rolled into a cylinder, and soldered to maintain the
+tubular shape, must be in a state of considerable initial stress quite
+apart from the action of gravity. Initial stress is utilized in many
+manufacturing processes, as, for example, in the construction of
+ordnance, referred to in § 79, in the winding of golf balls by means of
+india-rubber in a state of high tension (see the report of the case _The
+Haskell Golf Ball Company_ v. _Hutchinson & Main_ in _The Times_ of
+March 1, 1906). In the case of a body of ordinary dimensions it is such
+internal stress as this which is especially meant by the phrase
+"initial stress." Such a body, when in such a state of internal stress,
+is sometimes described as "self-strained." It would be better described
+as "self-stressed." The somewhat anomalous behaviour of cast iron has
+been supposed to be due to the existence within the metal of initial
+stress. As the metal cools, the outer layers cool more rapidly than the
+inner, and thus the state of initial stress is produced. When cast iron
+is tested for tensile strength, it shows at first no sensible range
+either of perfect elasticity or of linear elasticity; but after it has
+been loaded and unloaded several times its behaviour begins to be more
+nearly like that of wrought iron or steel. The first tests probably
+diminish the initial stress.
+
+  92. From a mathematical point of view the existence of initial stress
+  in a body which is "self-stressed" arises from the fact that the
+  equations of equilibrium of a body free from body forces or surface
+  tractions, viz. the equations of the type
+
+    dPX_x   dPX_y   dPZ_x
+    ----- + ----- + ----- = 0,
+     dPx     dPy     dPz
+
+  possess solutions which differ from zero. If, in fact, [phi]1, [phi]2,
+  [phi]3 denote any arbitrary functions of x, y, z, the equations are
+  satisfied by putting
+
+          dP²[phi]3   dP²[phi]2               dP²[phi]1
+    X_x = --------- + ---------, ..., Y_z = - ---------, ...;
+             dPy²        dPz                    dPydPz
+
+  and it is clear that the functions [phi]1, [phi]2, [phi]3 can be
+  adjusted in an infinite number of ways so that the bounding surface of
+  the body may be free from traction.
+
+93. Initial stress due to body forces becomes most important in the case
+of a gravitating planet. Within the earth the stress that arises from
+the mutual gravitation of the parts is very great. If we assumed the
+earth to be an elastic solid body with moduluses of elasticity no
+greater than those of steel, the strain (measured from the unstressed
+state) which would correspond to the stress would be much too great to
+be calculated by the ordinary methods of the theory of elasticity (§
+75). We require therefore some other method of taking account of the
+initial stress. In many investigations, for example those of Lord Kelvin
+and Sir G.H. Darwin referred to in § 83, the difficulty is turned by
+assuming that the material may be treated as practically incompressible;
+but such investigations are to some extent incomplete, so long as the
+corrections due to a finite, even though high, resistance to compression
+remain unknown. In other investigations, such as those relating to the
+propagation of earthquake shocks and to gravitational instability, the
+possibility of compression is an essential element of the problem. By
+gravitational instability is meant the tendency of gravitating matter to
+condense into nuclei when slightly disturbed from a state of uniform
+diffusion; this tendency has been shown by J.H. Jeans (_Phil. Trans_. A.
+201, 1903) to have exerted an important influence upon the course of
+evolution of the solar system. For the treatment of such questions Lord
+Rayleigh (_Proc. R. Soc. London_, A. 77, 1906) has advocated a method
+which amounts to assuming that the initial stress is hydrostatic
+pressure, and that the actual state of stress is to be obtained by
+superposing upon this initial stress a stress related to the state of
+strain (measured from the initial state) by the same formulae as hold
+for an elastic solid body free from initial stress. The development of
+this method is likely to lead to results of great interest.
+
+  AUTHORITIES.--In regard to the analysis requisite to prove the results
+  set forth above, reference may be made to A.E.H. Love, _Treatise on
+  the Mathematical Theory of Elasticity_ (2nd ed., Cambridge, 1906),
+  where citations of the original authorities will also be found. The
+  following treatises may be mentioned: Navier, _Résumé des leçons sur
+  l'application de la mécanique_ (3rd ed., with notes by Saint-Venant,
+  Paris, 1864); G. Lamé, _Leçons sur la théorie mathématique de
+  l'élasticité des corps solides_ (Paris, 1852); A. Clebsch, _Theorie
+  der Elasticität fester Körper_ (Leipzig, 1862; French translation with
+  notes by Saint-Venant, Paris, 1883); F. Neumann, _Vorlesungen über die
+  Theorie der Elasticität_ (Leipzig, 1885); Thomson and Tait, _Natural
+  Philosophy_ (Cambridge, 1879, 1883); Todhunter and Pearson, _History
+  of the Elasticity and Strength of Materials_ (Cambridge, 1886-1893).
+  The article "Elasticity" by Sir W. Thomson (Lord Kelvin) in 9th ed. of
+  _Encyc. Brit_. (reprinted in his _Mathematical and Physical Papers_,
+  iii., Cambridge, 1890) is especially valuable, not only for the
+  exposition of the theory and its practical applications, but also for
+  the tables of physical constants which are there given.
+       (A. E. H. L.)
+
+
+FOOTNOTES:
+
+  [1] The sign of M is shown by the arrow-heads in fig. 19, for which,
+    with y downwards,
+
+         d²y
+      EI --- + M = 0.
+         dx²
+
+  [2] The figure is drawn for a case where the bending moment has the
+    same sign throughout.
+
+  [3] M0 is taken to have, as it obviously has, the opposite sense to
+    that shown in fig. 19.
+
+  [4] The line joining the points of contact must be normal to the
+    planes.
+
+
+
+
+ELATERITE, also termed ELASTIC BITUMEN and MINERAL CAOUTCHOUC, a mineral
+hydrocarbon, which occurs at Castleton in Derbyshire, in the lead mines
+of Odin and elsewhere. It varies somewhat in consistency, being
+sometimes soft, elastic and sticky; often closely resembling
+india-rubber; and occasionally hard and brittle. It is usually dark
+brown in colour and slightly translucent. A substance of similar
+physical character is found in the Coorong district of South Australia,
+and is hence termed coorongite, but Prof. Ralph Tate considers this to
+be a vegetable product.
+
+
+
+
+ELATERIUM, a drug consisting of a sediment deposited by the juice of the
+fruit of _Ecballium Elaterium_, the squirting cucumber, a native of the
+Mediterranean region. The plant, which is a member of the natural order
+Cucurbitaceae, resembles the vegetable marrow in its growth. The fruit
+resembles a small cucumber, and when ripe is highly turgid, and
+separates almost at a touch from the fruit stalk. The end of the stalk
+forms a stopper, on the removal of which the fluid contents of the
+fruit, together with the seeds, are squirted through the aperture by the
+sudden contraction of the wall of the fruit. To prepare the drug the
+fruit is sliced lengthwise and slightly pressed; the greenish and
+slightly turbid juice thus obtained is strained and set aside; and the
+deposit of elaterium formed after a few hours is collected on a linen
+filter, rapidly drained, and dried on porous tiles at a gentle heat.
+Elaterium is met with in commerce in light, thin, friable, flat or
+slightly incurved opaque cakes, of a greyish-green colour, bitter taste
+and tea-like smell.
+
+The drug is soluble in alcohol, but insoluble in water and ether. The
+official dose is 1/10-½ grain, and the British pharmacopeia directs that
+the drug is to contain from 20 to 25% of the active principle elaterinum
+or elaterin. A resin in the natural product aids its action. Elaterin is
+extracted from elaterium by chloroform and then precipitated by ether.
+It has the formula C_20H_28O5. It forms colourless scales which have a
+bitter taste, but it is highly inadvisable to taste either this
+substance or elaterium. Its dose is 1/40-1/10 grain, and the British
+pharmacopeia contains a useful preparation, the Pulvis Elaterini
+Compositus, which contains one part of the active principle in forty.
+
+The action of this drug resembles that of the saline aperients, but is
+much more powerful. It is the most active hydragogue purgative known,
+causing also much depression and violent griping. When injected
+subcutaneously it is inert, as its action is entirely dependent upon its
+admixture with the bile. The drug is undoubtedly valuable in cases of
+dropsy and Bright's disease, and also in cases of cerebral haemorrhage,
+threatened or present. It must not be used except in urgent cases, and
+must invariably be employed with the utmost care, especially if the
+state of the heart be unsatisfactory.
+
+
+
+
+ELBA (Gr. [Greek: Aithalia]; Lat. _Ilva_), an island off the W. coast of
+Italy, belonging to the province of Leghorn, from which it is 45 m. S.,
+and 7 m. S.W. of Piombino, the nearest point of the mainland. Pop.
+(1901) 25,043 (including Pianosa). It is about 19 m. long, 6½ m. broad,
+and 140 sq. m. in area; and its highest point is 3340 ft. (Monte
+Capanne). It forms, like Giglio and Monte Cristo, part of a sunken
+mountain range extending towards Corsica and Sardinia.
+
+The oldest rocks of Elba consist of schist and serpentine which in the
+eastern part of the island are overlaid by beds containing Silurian and
+Devonian fossils. The Permian may be represented, but the Trias is
+absent, and in general the older Palaeozoic rocks are overlaid directly
+by the Rhaetic and Lias. The Liassic beds are often metamorphosed and
+the limestones contain garnet and wollastonite. The next geological
+formation which is represented is the Eocene, consisting of nummulitic
+limestone, sandstone and schist. The Miocene and Pliocene are absent.
+The most remarkable feature in the geology of Elba is the extent of the
+granitic and ophiolitic eruptions of the Tertiary period. Serpentines,
+peridotites and diabases are interstratified with the Eocene deposits.
+The granite, which is intruded through the Eocene beds, is associated
+with a pegmatite containing tourmaline and cassiterite. The celebrated
+iron ore of Elba is of Tertiary age and occurs indifferently in all the
+older rocks. The deposits are superficial, resulting from the opening
+out of veins at the surface, and consist chiefly of haematite. These
+ores were worked by the ancients, but so inefficiently that their
+spoil-heaps can be smelted again with profit. This process is now gone
+through on the island itself. The granite was also quarried by the
+Romans, but is not now much worked.
+
+Parts of the island are fertile, and the cultivation of vines, and the
+tunny and sardine fishery, also give employment to a part of the
+population. The capital of the island is Portoferraio--pop. (1901)
+5987--in the centre of the N. coast, enclosed by an amphitheatre of
+lofty mountains, the slopes of which are covered with villas and
+gardens. This is the best harbour, the ancient _Portus Argous_. The town
+was built and fortified by Cosimo I. in 1548, who called it Cosmopolis.
+Above the harbour, between the forts Stella and Falcone, is the palace
+of Napoleon I., and 4 m. to the S.W. is his villa; while on the N. slope
+of Monte Capanne is another of his country houses. The other villages in
+the island are Campo nell' Elba, on the S. near the W. end, Marciana and
+Marciana Marina on the N. of the island near the W. extremity, Porto
+Longone, on the E. coast, with picturesque Spanish fortifications,
+constructed in 1602 by Philip III.; Rio dell' Elba and Rio Marina, both
+on the E. side of the island, in the mining district. At Le Grotte,
+between Portoferraio and Rio dell' Elba, and at Capo Castello, on the
+N.E. of the island, are ruins of Roman date.
+
+Elba was famous for its mines in early times, and the smelting furnaces
+gave it its Greek name of [Greek: A'thalia] ("soot island"). In Roman
+times, and until 1900, however, owing to lack of fuel, the smelting was
+done on the mainland. In 453 B.C. Elba was devastated by a Syracusan
+squadron. From the 11th to the 14th century it belonged to Pisa, and in
+1399 came under the dukes of Piombino. In 1548 it was ceded by them to
+Cosimo I. of Florence. In 1596 Porto Longone was taken by Philip III. of
+Spain, and retained until 1709, when it was ceded to Naples. In 1802 the
+island was given to France by the peace of Amiens. On Napoleon's
+deposition, the island was ceded to him with full sovereign rights, and
+he resided there from the 5th of May 1814 to the 26th of February 1815.
+After his fall it was restored to Tuscany, and passed with it to Italy
+in 1860.
+
+  See Sir R. Colt Hoare, _A Tour through the Island of Elba_ (London,
+  1814).
+
+
+
+
+ELBE (the _Albis_ of the Romans and the _Labe_ of the Czechs), a river
+of Germany, which rises in Bohemia not far from the frontiers of
+Silesia, on the southern side of the Riesengebirge, at an altitude of
+about 4600 ft. Of the numerous small streams (Seifen or Flessen as they
+are named in the district) whose confluent waters compose the infant
+river, the most important are the Weisswasser, or White Water, and the
+Elbseifen, which is formed in the same neighbourhood, but at a little
+lower elevation. After plunging down the 140 ft. of the Elbfall, the
+latter stream unites with the steep torrential Weisswasser at
+Mädelstegbaude, at an altitude of 2230 ft., and thereafter the united
+stream of the Elbe pursues a southerly course, emerging from the
+mountain glens at Hohenelbe (1495 ft.), and continuing on at a soberer
+pace to Pardubitz, where it turns sharply to the west, and at Kolin (730
+ft.), some 27 m. farther on, bends gradually towards the north-west. A
+little above Brandeis it picks up the Iser, which, like itself, comes
+down from the Riesengebirge, and at Melnik it has its stream more than
+doubled in volume by the Moldau, a river which winds northwards through
+the heart of Bohemia in a sinuous, trough-like channel carved through
+the plateaux. Some miles lower down, at Leitmeritz (433 ft.), the waters
+of the Elbe are tinted by the reddish Eger, a stream which drains the
+southern slopes of the Erzgebirge. Thus augmented, and swollen into a
+stream 140 yds. wide, the Elbe carves a path through the basaltic mass
+of the Mittelgebirge, churning its way through a deep, narrow rocky
+gorge. Then the river winds through the fantastically sculptured
+sandstone mountains of the "Saxon Switzerland," washing successively the
+feet of the lofty Lilienstein (932 ft. above the Elbe), the scene of one
+of Frederick the Great's military exploits in the Seven Years' War,
+Königstein (797 ft. above the Elbe), where in times of war Saxony has
+more than once stored her national purse for security, and the pinnacled
+rocky wall of the Bastei, towering 650 ft. above the surface of the
+stream. Shortly after crossing the Bohemian-Saxon frontier, and whilst
+still struggling through the sandstone defiles, the stream assumes a
+north-westerly direction, which on the whole it preserves right away to
+the North Sea. At Pirna the Elbe leaves behind it the stress and turmoil
+of the Saxon Switzerland, rolls through Dresden, with its noble river
+terraces, and finally, beyond Meissen, enters on its long journey across
+the North German plain, touching Torgau, Wittenberg, Magdeburg,
+Wittenberge, Hamburg, Harburg and Altona on the way, and gathering into
+itself the waters of the Mulde and Saale from the left, and those of the
+Schwarze Elster, Havel and Elde from the right. Eight miles above
+Hamburg the stream divides into the Norder (or Hamburg) Elbe and the
+Süder (or Harburg) Elbe, which are linked together by several
+cross-channels, and embrace in their arms the large island of
+Wilhelmsburg and some smaller ones. But by the time the river reaches
+Blankenese, 7 m. below Hamburg, all these anastomosing branches have
+been reunited, and the Elbe, with a width of 4 to 9 m. between bank and
+bank, travels on between the green marshes of Holstein and Hanover until
+it becomes merged in the North Sea off Cuxhaven. At Kolin the width is
+about 100 ft., at the mouth of the Moldau about 300, at Dresden 960, and
+at Magdeburg over 1000. From Dresden to the sea the river has a total
+fall of only 280 ft., although the distance is about 430 m. For the 75
+m. between Hamburg and the sea the fall is only 3¼ ft. One consequence
+of this is that the bed of the river just below Hamburg is obstructed by
+a bar, and still lower down is choked with sandbanks, so that navigation
+is confined to a relatively narrow channel down the middle of the
+stream. But unremitting efforts have been made to maintain a sufficient
+fairway up to Hamburg (q.v.). The tide advances as far as Geesthacht, a
+little more than 100 m. from the sea. The river is navigable as far as
+Melnik, that is, the confluence of the Moldau, a distance of 525 m., of
+which 67 are in Bohemia. Its total length is 725 m., of which 190 are in
+Bohemia, 77 in the kingdom of Saxony, and 350 in Prussia, the remaining
+108 being in Hamburg and other states of Germany. The area of the
+drainage basin is estimated at 56,000 sq. m.
+
+_Navigation._--Since 1842, but more especially since 1871, improvements
+have been made in the navigability of the Elbe by all the states which
+border upon its banks. As a result of these labours there is now in the
+Bohemian portion of the river a minimum depth of 2 ft. 8 in., whilst
+from the Bohemian frontier down to Magdeburg the minimum depth is 3 ft.,
+and from Magdeburg to Hamburg, 3 ft. 10 in. In 1896 and 1897 Prussia and
+Hamburg signed covenants whereby two channels are to be kept open to a
+depth of 9¾ ft., a width of 656 ft., and a length of 550 yds. between
+Bunthaus and Ortkathen, just above the bifurcation of the Norder Elbe
+and the Süder Elbe. In 1869 the maximum burden of the vessels which were
+able to ply on the upper Elbe was 250 tons; but in 1899 it was increased
+to 800 tons. The large towns through which the river flows have vied
+with one another in building harbours, providing shipping accommodation,
+and furnishing other facilities for the efficient navigation of the
+Elbe. In this respect the greatest efforts have naturally been made by
+Hamburg; but Magdeburg, Dresden, Meissen, Riesa, Tetschen, Aussig and
+other places have all done their relative shares, Magdeburg, for
+instance, providing a commercial harbour and a winter harbour. In spite,
+however, of all that has been done, the Elbe remains subject to serious
+inundations at periodic intervals. Among the worst floods were those of
+the years 1774, 1799, 1815, 1830, 1845, 1862, 1890 and 1909. The growth
+of traffic up and down the Elbe has of late years become very
+considerable. A towing chain, laid in the bed of the river, extends from
+Hamburg to Aussig, and by this means, as by paddle-tug haulage, large
+barges are brought from the port of Hamburg into the heart of Bohemia.
+The fleet of steamers and barges navigating the Elbe is in point of fact
+greater than on any other German river. In addition to goods thus
+conveyed, enormous quantities of timber are floated down the Elbe; the
+weight of the rafts passing the station of Schandau on the Saxon
+Bohemian frontier amounting in 1901 to 333,000 tons.
+
+A vast amount of traffic is directed to Berlin, by means of the
+Havel-Spree system of canals, to the Thuringian states and the Prussian
+province of Saxony, to the kingdom of Saxony and Bohemia, and to the
+various riverine states and provinces of the lower and middle Elbe. The
+passenger traffic, which is in the hands of the Sächsisch-Böhmische
+Dampfschifffahrtsgesellschaft is limited to Bohemia and Saxony, steamers
+plying up and down the stream from Dresden to Melnik, occasionally
+continuing the journey up the Moldau to Prague, and down the river as
+far as Riesa, near the northern frontier of Saxony, and on the average
+1½ million passengers are conveyed.
+
+In 1877-1879, and again in 1888-1895, some 100 m. of canal were dug, 5
+to 6½ ft. deep and of various widths, for the purpose of connecting the
+Elbe, through the Havel and the Spree, with the system of the Oder. The
+most noteworthy of these connexions are the Elbe Canal (14¼ m. long),
+the Reek Canal (9½ m.), the Rüdersdorfer Gewässer (11½ m.), the
+Rheinsberger Canal (11¼ m.), and the Sacrow-Paretzer Canal (10 m.),
+besides which the Spree has been canalized for a distance of 28 m., and
+the Elbe for a distance of 70 m. Since 1896 great improvements have been
+made in the Moldau and the Bohemian Elbe, with the view of facilitating
+communication between Prague and the middle of Bohemia generally on the
+one hand, and the middle and lower reaches of the Elbe on the other. In
+the year named a special commission was appointed for the regulation of
+the Moldau and Elbe between Prague and Aussig, at a cost estimated at
+about £1,000,000, of which sum two-thirds were to be borne by the
+Austrian empire and one-third by the kingdom of Bohemia. The regulation
+is effected by locks and movable dams, the latter so designed that in
+times of flood or frost they can be dropped flat on the bottom of the
+river. In 1901 the Austrian government laid before the Reichsrat a canal
+bill, with proposals for works estimated to take twenty years to
+complete, and including the construction of a canal between the Oder,
+starting at Prerau, and the upper Elbe at Pardubitz, and for the
+canalization of the Elbe from Pardubitz to Melnik (see AUSTRIA:
+_Waterways_). In 1900 Lübeck was put into direct communication with the
+Elbe at Lauenburg by the opening of the Elbe-Trave Canal, 42 m. in
+length, and constructed at a cost of £1,177,700, of which the state of
+Lübeck contributed £802,700, and the kingdom of Prussia £375,000. The
+canal has been made 72 ft. wide at the bottom, 105 to 126 ft. wide at
+the top, has a minimum depth of 8{1/6} ft., and is equipped with seven
+locks, each 262½ ft. long and 39¼ ft. wide. It is thus able to
+accommodate vessels up to 800 tons burden; and the passage from Lübeck
+to Lauenburg occupies 18 to 21 hours. In the first year of its being
+open (June 1900 to June 1901) a total of 115,000 tons passed through the
+canal.[1] A gigantic project has also been put forward for providing
+water communication between the Rhine and the Elbe, and so with the
+Oder, through the heart of Germany. This scheme is known as the Midland
+Canal. Another canal has been projected for connecting Kiel with the
+Elbe by means of a canal trained through the Plön Lakes.
+
+_Bridges._--The Elbe is crossed by numerous bridges, as at Königgrätz,
+Pardubitz, Kolin, Leitmeritz, Tetschen, Schandau, Pirna, Dresden,
+Meissen, Torgau, Wittenberg, Rosslau, Barby, Magdeburg, Rathenow,
+Wittenberge, Dömitz, Lauenburg, and Hamburg and Harburg. At all these
+places there are railway bridges, and nearly all, but more especially
+those in Bohemia, Saxony and the middle course of the river--these last
+on the main lines between Berlin and the west and south-west of the
+empire--possess a greater or less strategic value. At Leitmeritz there
+is an iron trellis bridge, 600 yds long. Dresden has four bridges, and
+there is a fifth bridge at Loschwitz, about 3 m. above the city. Meissen
+has a railway bridge, in addition to an old road bridge. Magdeburg is
+one of the most important railway centres in northern Germany; and the
+Elbe, besides being bridged--it divides there into three arms--several
+times for vehicular traffic, is also spanned by two fine railway
+bridges. At both Hamburg and Harburg, again, there are handsome railway
+bridges, the one (1868-1873 and 1894) crossing the northern Elbe, and
+the other (1900) the southern Elbe; and the former arm is also crossed
+by a fine triple-arched bridge (1888) for vehicular traffic.
+
+_Fish._--The river is well stocked with fish, both salt-water and
+fresh-water species being found in its waters, and several varieties of
+fresh-water fish in its tributaries. The kinds of greatest economic
+value are sturgeon, shad, salmon, lampreys, eels, pike and whiting.
+
+_Tolls._--In the days of the old German empire no fewer than thirty-five
+different tolls were levied between Melnik and Hamburg, to say nothing
+of the special dues and privileged exactions of various riparian owners
+and political authorities. After these had been _de facto_, though not
+_de jure_, in abeyance during the period of the Napoleonic wars, a
+commission of the various Elbe states met and drew up a scheme for their
+regulation, and the scheme, embodied in the Elbe Navigation Acts, came
+into force in 1822. By this a definite number of tolls, at fixed rates,
+was substituted for the often arbitrary tolls which had been exacted
+previously. Still further relief was afforded in 1844 and in 1850, on
+the latter occasion by the abolition of all tolls between Melnik and the
+Saxon frontier. But the number of tolls was only reduced to one, levied
+at Wittenberge, in 1863, about one year after Hanover was induced to
+give up the Stade or Brunsbüttel toll in return for a compensation of
+2,857,340 thalers. Finally, in 1870, 1,000,000 thalers were paid to
+Mecklenburg and 85,000 thalers to Anhalt, which thereupon abandoned all
+claims to levy tolls upon the Elbe shipping, and thus navigation on the
+river became at last entirely free.
+
+_History._--The Elbe cannot rival the Rhine in the picturesqueness of
+the scenery it travels through, nor in the glamour which its romantic
+and legendary associations exercise over the imagination. But it
+possesses much to charm the eye in the deep glens of the Riesengebirge,
+amid which its sources spring, and in the bizarre rock-carving of the
+Saxon Switzerland. It has been indirectly or directly associated with
+many stirring events in the history of the German peoples. In its lower
+course, whatever is worthy of record clusters round the historical
+vicissitudes of Hamburg--its early prominence as a missionary centre
+(Ansgar) and as a bulwark against Slav and marauding Northman, its
+commercial prosperity as a leading member of the Hanseatic League, and
+its sufferings during the Napoleonic wars, especially at the hands of
+the ruthless Davoût. The bridge over the river at Dessau recalls the hot
+assaults of the _condottiere_ Ernst von Mansfeld in April 1626, and his
+repulse by the crafty generalship of Wallenstein. But three years later
+this imperious leader was checked by the heroic resistance of the
+"Maiden" fortress of Magdeburg; though two years later still she lost
+her reputation, and suffered unspeakable horrors at the hands of Tilly's
+lawless and unlicensed soldiery. Mühlberg, just outside the Saxon
+frontier, is the place where Charles V. asserted his imperial authority
+over the Protestant elector of Saxony, John Frederick, the Magnanimous
+or Unfortunate, in 1547. Dresden, Aussig and Leitmeritz are all
+reminiscent of the fierce battles of the Hussite wars, and the last
+named of the Thirty Years' War. But the chief historical associations of
+the upper (i.e. the Saxon and Bohemian) Elbe are those which belong to
+the Seven Years' War, and the struggle of the great Frederick of Prussia
+against the power of Austria and her allies. At Pirna (and Lilienstein)
+in 1756 he caught the entire Saxon army in his fowler's net, after
+driving back at Lobositz the Austrian forces which were hastening to
+their assistance; but only nine months later he lost his reputation for
+"invincibility" by his crushing defeat at Kolin, where the great highway
+from Vienna to Dresden crosses the Elbe. Not many miles distant, higher
+up the stream, another decisive battle was fought between the same
+national antagonists, but with a contrary result, on the memorable 3rd
+of July 1866.
+
+  See M. Buchheister, "Die Elbe u. der Hafen von Hamburg," in _Mitteil.
+  d. Geog. Gesellsch. in Hamburg_ (1899), vol. xv. pp. 131-188; V. Kurs,
+  "Die künstlichen Wasserstrassen des deutschen Reichs," in _Geog.
+  Zeitschrift_ (1898), pp. 601-617; and (the official) _Der Elbstrom_
+  (1900); B. Weissenborn, _Die Elbzölle und Elbstapelplätze im
+  Mittelalter_ (Halle, 1900); Daniel, _Deutschland_; and A. Supan,
+  _Wasserstrassen und Binnenschifffahrt_ (Berlin, 1902).
+
+
+FOOTNOTE:
+
+  [1] See _Der Bau des Elbe-Trave Canals und seine Vorgeschichte_
+    (Lübeck, 1900).
+
+
+
+
+ELBERFELD, a manufacturing town of Germany, in the Prussian Rhine
+province, on the Wupper, and immediately west of and contiguous to
+Barmen (q.v.). Pop. (1816) 21,710; (1840) 31,514; (1885) 109,218; (1905)
+167,382. Elberfeld-Barmen, although administratively separate,
+practically form a single whole. It winds, a continuous strip of houses
+and factories, for 9 m. along the deep valley, on both banks of the
+Wupper, which is crossed by numerous bridges, the engirdling hills
+crowned with woods. Local intercommunication is provided by an electric
+tramway line and a novel hanging railway--on the Langen mono-rail
+system--suspended over the bed of the river, with frequent stations. In
+the centre of the town are a number of irregular and narrow streets, and
+the river, polluted by the refuse of dye-works and factories,
+constitutes a constant eyesore. Yet within recent years great
+alterations have been effected; in the newer quarters are several
+handsome streets and public buildings; in the centre many insanitary
+dwellings have been swept away, and their place occupied by imposing
+blocks of shops and business premises, and a magnificent new town-hall,
+erected in a dominant position. Among the most recent improvements must
+be mentioned the Brausenwerther Platz, flanked by the theatre, the
+public baths, and the railway station and administrative offices. There
+are eleven Evangelical and five Roman Catholic churches (noticeable
+among the latter the Suitbertuskirche), a synagogue, and chapels of
+various other sects. Among other public buildings may be enumerated the
+civic hall, the law courts and the old town-hall.
+
+The town is particularly rich in educational, industrial, philanthropic
+and religious institutions. The schools include the Gymnasium (founded
+in 1592 by the Protestant community as a Latin school), the
+Realgymnasium (founded in 1830, for "modern" subjects and Latin), the
+Oberrealschule and Realschule (founded 1893, the latter wholly
+"modern"), two girls' high schools, a girls' middle-class school, a
+large number of popular schools, a mechanics' and polytechnic school, a
+school of mechanics, an industrial drawing school, a commercial school,
+and a school for the deaf and dumb. There are also a theatre, an
+institute of music, a library, a museum, a zoological garden, and
+numerous scientific societies. The town is the seat of the Berg Bible
+Society. The majority of the inhabitants are Protestant, with a strong
+tendency towards Pietism; but the Roman Catholics number upwards of
+40,000, forming about one-fourth of the total population. The industries
+of Elberfeld are on a scale of great magnitude. It is the chief centre
+in Germany of the cotton, wool, silk and velvet manufactures, and of
+upholstery, drapery and haberdashery of all descriptions, of printed
+calicoes, of Turkey-red and other dyes, and of fine chemicals. Leather
+and rubber goods, gold, silver and aluminium wares, machinery,
+wall-paper, and stained glass are also among other of its staple
+products. Commerce is lively and the exports to foreign countries are
+very considerable. The railway system is well devised to meet the
+requirements of its rapidly increasing trade. Two main lines of railway
+traverse the valley; that on the south is the main line from
+Aix-la-Chapelle, Cologne and Düsseldorf to central Germany and Berlin,
+that on the north feeds the important towns of the Ruhr valley.
+
+The surroundings of Elberfeld are attractive, and public grounds and
+walks have been recently opened on the hills around with results
+eminently beneficial to the health of the population.
+
+In the 12th century the site of Elberfeld was occupied by the castle of
+the lords of Elverfeld, feudatories of the archbishops of Cologne. The
+fief passed later into the possession of the counts of Berg. The
+industrial development of the place started with a colony of bleachers,
+attracted by the clear waters of the Wupper, who in 1532 were granted
+the exclusive privilege of bleaching yarn. It was not, however, until
+1610 that Elberfeld was raised to the status of a town, and in 1640 was
+surrounded with walls. In 1760 the manufacture of silk was introduced,
+and dyeing with Turkey-red in 1780; but it was not till the end of the
+century that its industries developed into importance under the
+influence of Napoleon's continental system, which barred out British
+competition. In 1815 Elberfeld was assigned by the congress of Vienna,
+with the grand-duchy of Berg, to Prussia, and its prosperity rapidly
+developed under the Prussian Zollverein.
+
+  See Coutelle, _Elberfeld, topographisch-statistische Darstellung_
+  (Elberfeld, 1853); Schell, _Geschichte der Stadt Elberfeld_ (1900); A.
+  Shadwell, _Industrial Efficiency_ (London, 1906); and Jorde, _Führer
+  durch Elberfeld und seine Umgebung_ (1902).
+
+
+
+
+ELBEUF, a town of northern France in the department of Seine-Inférieure,
+14 m. S.S.W. of Rouen by the western railway. Pop. (1906) 17,800.
+Elbeuf, a town of wide, clean streets, with handsome houses and
+factories, stands on the left bank of the Seine at the foot of hills
+over which extends the forest of Elbeuf. A tribunal and chamber of
+commerce, a board of trade-arbitrators, a lycée, a branch of the Bank of
+France, a school of industry, a school of cloth manufacture and a museum
+of natural history are among its institutions. The churches of St
+Étienne and St Jean, both of the Renaissance period with later
+additions, preserve stained glass of the 16th century. The
+hôtel-de-ville and the Cercle du Commerce are the chief modern
+buildings. The town with its suburbs, Orival, Caudebec-lès-Elbeuf, St
+Aubin and St Pierre, is one of the principal and most ancient seats of
+the woollen manufacture in France; more than half the inhabitants are
+directly maintained by the staple industry and numbers more by the
+auxiliary crafts. As a river-port it has a brisk trade in the produce of
+the surrounding district as well as in the raw materials of its
+manufactures, especially in wool from La Plata, Australia and Germany.
+Two bridges, one of them a suspension-bridge, communicate with St Aubin
+on the opposite bank of the Seine, and steamboats ply regularly to
+Rouen.
+
+Elbeuf was, in the 13th century, the centre of an important fief held by
+the house of Harcourt, but its previous history goes back at least to
+the early years of the Norman occupation, when it appears under the name
+of Hollebof. It passed into the hands of the houses of Rieux and
+Lorraine, and was raised to the rank of a duchy in the peerage of France
+by Henry III. in favour of Charles of Lorraine (d. 1605), grandson of
+Claude, duke of Guise, master of the hounds and master of the horse of
+France. The last duke of Elbeuf was Charles Eugène of Lorraine, prince
+de Lambesc, who distinguished himself in 1789 by his energy in
+repressing risings of the people at Paris. He fought in the army of the
+Bourbons, and later in the service of Austria, and died in 1825.
+
+
+
+
+ELBING, a seaport town of Germany, in the kingdom of Prussia, 49 m. by
+rail E.S.E. of Danzig, on the Elbing, a small river which flows into the
+Frische Haff about 5 m. from the town, and is united with the Nogat or
+eastern arm of the Vistula by means of the Kraffohl canal. Pop. (1905)
+55,627. By the Elbing-Oberländischer canal, 110 m. long, constructed in
+1845-1860, Lakes Geserich and Drewenz are connected with Lake Drausen,
+and consequently with the port of Elbing. The old town was formerly
+surrounded by fortifications, but of these only a few fragments remain.
+There are several churches, among them the Marienkirche (dating from the
+15th century and restored in 1887), a classical school (Gymnasium)
+founded in 1536, a modern school (Realschule), a public library of over
+28,000 volumes, and several charitable institutions. The town-hall
+(1894) contains a historical museum.
+
+Elbing is a place of rapidly growing industries. At the great Schichau
+iron-works, which employ thousands of workmen, are built most of the
+torpedo-boats and destroyers for the German navy, as well as larger
+craft, locomotives and machinery. In addition to this there are at
+Elbing important iron foundries, and manufactories of machinery, cigars,
+lacquer and metal ware, flax and hemp yarn, cotton, linen, organs, &c.
+There is a considerable trade also in agricultural produce.
+
+The origin of Elbing was a colony of traders from Lübeck and Bremen,
+which established itself under the protection of a castle of the
+Teutonic Knights, built in 1237. In 1246 the town acquired "Lübeck
+rights," i.e. the full autonomy conceded by the charter of the emperor
+Frederick II. in 1226 (see LÜBECK), and it was early admitted to the
+Hanseatic League. In 1454 the town repudiated the overlordship of the
+Teutonic Order, and placed itself under the protection of the king of
+Poland, becoming the seat of a Polish voivode. From this event dates a
+decline in its prosperity, a decline hastened by the wars of the early
+18th century. In 1698, and again in 1703, it was seized by the elector
+of Brandenburg as security for a debt due to him by the Polish king. It
+was taken and held to ransom by Charles XII. of Sweden, and in 1710 was
+captured by the Russians. In 1772, when it fell to Prussia through the
+first partition of Poland, it was utterly decayed.
+
+  See Fuchs, _Gesch. der Stadt Elbing_ (Elbing, 1818-1852); Rhode, _Der
+  Elbinger Kreis in topographischer, historischer, und statistischer
+  Hinsicht_ (Danzig, 1871); Wernick, _Elbing_ (Elbing, 1888).
+
+
+
+
+ELBOW, in anatomy, the articulation of the _humerus_, the bone of the
+upper arm, and the _ulna_ and _radius_, the bones of the forearm (see
+JOINTS). The word is thus applied to things which are like this joint in
+shape, such as a sharp bend of a stream or river, an angle in a tube,
+&c. The word is derived from the O. Eng. _elnboga_, a combination of
+_eln_, the forearm, and _boga_, a bow or bend. This combination is
+common to many Teutonic languages, cf. Ger. _Ellbogen_. _Eln_ still
+survives in the name of a linear measure, the "ell," and is derived from
+the O. Teut. _alina_, cognate with Lat. _ulna_ and Gr. [Greek: ôlenê],
+the forearm. The use of the arm as a measure of length is illustrated by
+the uses of _ulna_, in Latin, cubit, and fathom.
+
+
+
+
+ELBURZ, or ALBURZ (from O. Pers. _Hara-bere-zaiti_, the "High
+Mountain"), a great chain of mountains in northern Persia, separating
+the Caspian depression from the Persian highlands, and extending without
+any break for 650 m. from the western shore of the Caspian Sea to
+north-eastern Khorasan. According to the direction, or strike, of its
+principal ranges the Elburz may be divided into three sections: the
+first 120 m. in length with a direction nearly N. to S., the second 240
+m. in length with a direction N.W. to S.E., and the third 290 m. in
+length striking S.W. to N.E. The first section, which is connected with
+the system of the Caucasus, and begins west of Lenkoran in 39° N. and
+45° E., is known as the Talish range and has several peaks 9000 to
+10,000 ft. in height. It runs almost parallel to the western shore of
+the Caspian, and west of Astara is only 10 or 12 m. distant from the
+sea. At the point west of Resht, where the direction of the principal
+range changes to one of N.W. to S.E., the second section of the Elburz
+begins, and extends from there to beyond Mount Demavend, east of
+Teheran. South of Resht this section is broken through at almost a right
+angle by the Safid Rud (White river), and along it runs the principal
+commercial road between the Caspian and inner Persia,
+Resht-Kazvin-Teheran. The Elburz then splits into three principal ranges
+running parallel to one another and connected at many places by
+secondary ranges and spurs. Many peaks of the ranges in this section
+have an altitude of 11,000 to 13,000 ft., and the elevation of the
+passes leading over the ranges varies between 7000 and 10,000 ft. The
+highest peaks are situated in the still unexplored district of Talikan,
+N.W. of Teheran, and thence eastwards to beyond Mount Demavend. The part
+of the Elburz immediately north of Teheran is known as the Kuh i Shimran
+(mountain of Shimran, from the name of the Shimran district on its
+southern slopes) and culminates in the Sar i Tochal (12,600 ft.). Beyond
+it, and between the border of Talikan in the N.W. and Mount Demavend in
+the N.E., are the ranges Azadbur, Kasil, Kachang, Kendevan, Shahzad,
+Varzeh, Derbend i Sar and others, with elevations of 12,000 to 13,500
+ft., while Demavend towers above them all with its altitude of 19,400
+ft. The eastern foot of Demavend is washed by the river Herhaz (called
+Lar river in its upper course), which there breaks through the Elburz in
+a S.-N. direction in its course to the Caspian, past the city of Amol.
+The third section of the Elburz, with its principal ranges striking S.W.
+to N.E., has a length of about 290 m., and ends some distance beyond
+Bujnurd in northern Khorasan, where it joins the Ala Dagh range, which
+has a direction to the S.E., and, continuing with various appellations
+to northern Afghanistan, unites with the Paropamisus. For about
+two-thirds of its length--from its beginning to Khush Yailak--the third
+section consists of three principal ranges connected by lateral ranges
+and spurs. It also has many peaks over 10,000 ft. in height, and the
+Nizva mountain on the southern border of the unexplored district of
+Hazarjirib, north of Semnan, and the Shahkuh, between Shahrud and
+Astarabad, have an elevation exceeding 13,000 ft. Beyond Khush Yailak
+(meaning "pleasant summer quarters"), with an elevation of 10,000 ft.,
+are the Kuh i Buhar (8000) and Kuh i Suluk (8000), which latter joins
+the Ala Dagh (11,000).
+
+The northern slopes of the Elburz and the lowlands which lie between
+them and the Caspian, and together form the provinces of Gilan,
+Mazandaran and Astarabad, are covered with dense forest and traversed by
+hundreds (Persian writers say 1362) of perennial rivers and streams. The
+breadth of the lowlands between the foot of the hills and the sea is
+from 2 to 25 m., the greatest breadth being in the meridian of Resht in
+Gilan, and in the districts of Amol, Sari and Barfurush in Mazandaran.
+The inner slopes and ranges of the Elburz south of the principal
+watershed, generally the central one of the three principal ranges which
+are outside of the fertilizing influence of the moisture brought from
+the sea, have little or no natural vegetation, and those farthest south
+are, excepting a few stunted cypresses, completely arid and bare.
+
+"North of the principal watershed forest trees and general verdure
+refresh the eye. Gurgling water, strips of sward and tall forest trees,
+backed by green hills, make a scene completely unlike the usual monotony
+of Persian landscape. The forest scenery much resembles that of England,
+with fine oaks and greensward. South of the watershed the whole aspect
+of the landscape is as hideous and disappointing as scenery in
+Afghanistan. Ridge after ridge of bare hill and curtain behind curtain
+of serrated mountain, certainly sometimes of charming greys and blues,
+but still all bare and naked, rugged and arid" ("Beresford Lovett,
+_Proc. R.G.S._, Feb. 1883).
+
+The higher ranges of the Elburz are snow-capped for the greater part of
+the year, and some, which are not exposed to the refracted heat from the
+arid districts of inner Persia, are rarely without snow. Water is
+plentiful in the Elburz, and situated in well-watered valleys and gorges
+are innumerable flourishing villages, embosomed in gardens and orchards,
+with extensive cultivated fields and meadows, and at higher altitudes
+small plateaus, under snow until March or April, afford cool camping
+grounds to the nomads of the plains, and luxuriant grazing to their
+sheep and cattle during the summer.     (A. H.-S.)
+
+
+
+
+ELCHE, a town of eastern Spain, in the province of Alicante, on the
+river Vinalapo. Pop. (1900) 27,308. Elche is the meeting-place of three
+railways, from Novelda, Alicante and Murcia. It contains no building of
+high architectural merit, except, perhaps, the collegiate church of
+Santa Maria, with its lofty blue-tiled dome and fine west doorway. But
+the costume and physiognomy of the inhabitants, the narrow streets and
+flat-roofed, whitewashed houses, and more than all, the thousands of
+palm-trees in its gardens and fields, give the place a strikingly
+Oriental aspect, and render it unique among the cities of Spain. The
+cultivation of the palm is indeed the principal occupation; and though
+the dates are inferior to those of the Barbary States, upwards of 22,500
+tons are annually exported. The blanched fronds are also sold in large
+quantities for the processions of Palm Sunday, and after they have
+received the blessing of the priest they are regarded throughout Spain
+as certain defences against lightning. Other thriving local industries
+include the manufacture of oil, soap, flour, leather, alcohol and
+esparto grass rugs. The harbour of Elche is Santa Pola (pop. 4100),
+situated 6 m. E.S.E., where the Vinalapo enters the Mediterranean, after
+forming the wide lagoon known as the Albufera de Elche.
+
+Elche is usually identified with the Iberian _Helike_, afterwards the
+Roman colony of _Ilici_ or _Illici_. From the 8th century to the 13th it
+was held by the Moors, who finally failed to recapture it from the
+Spaniards in 1332.
+
+
+
+
+ELCHINGEN, a village of Germany, in the kingdom of Bavaria, not far from
+the Danube, 5 m. N.E. from Ulm. Here, on the 14th of October 1805, the
+Austrians under Laudon were defeated by the French under Ney, who by
+taking the bridge decided the day and gained for himself the title of
+duke of Elchingen.
+
+
+
+
+ELDAD BEN MAHLI, also surnamed had-Dani, Abu-Dani, David-had-Dani, or
+the Danite, Jewish traveller, was the supposed author of a Jewish
+travel-narrative of the 9th century A.D., which enjoyed great authority
+in the middle ages, especially on the question of the Lost Ten Tribes.
+Eldad first set out to visit his Hebrew brethren in Africa and Asia. His
+vessel was wrecked, and he fell into the hands of cannibals; but he was
+saved by his leanness, and by the opportune invasion of a neighbouring
+tribe. After spending four years with his new captors, he was ransomed
+by a fellow-countryman, a merchant of the tribe of Issachar. He then
+(according to his highly fabulous narrative) visited the territory of
+Issachar, in the mountains of Media and Persia; he also describes the
+abodes of Zabulon, on the "other side" of the Paran Mountains, extending
+to Armenia and the Euphrates; of Reuben, on another side of the same
+mountains; of Ephraim and Half Manasseh, in Arabia, not far from Mecca;
+and of Simeon and the other Half of Manasseh, in Chorazin, six months'
+journey from Jerusalem. Dan, he declares, sooner than join in Jeroboam's
+scheme of an Israelite war against Judah, had migrated to Cush, and
+finally, with the help of Naphthali, Asher and Gad, had founded an
+independent Jewish kingdom in the Gold Land of Havila, beyond Abyssinia.
+The tribe of Levi had also been miraculously guided, from near Babylon,
+to Havila, where they were enclosed and protected by the mystic river
+Sambation or Sabbation, which on the Sabbath, though calm, was veiled in
+impenetrable mist, while on other days it ran with a fierce
+untraversable current of stones and sand.
+
+Apart from these tales, we have the genuine Eldad, a celebrated Jewish
+traveller and philologist; who flourished c. A.D. 830-890; to whom the
+work above noticed is ascribed; who was a native either of S. Arabia,
+Palestine or Media; who journeyed in Egypt, Mesopotamia, North Africa,
+and Spain; who spent several years at Kairawan in Tunis; who died on a
+visit to Cordova, and whose authority, as to the lost tribes, is
+supported by a great Hebrew doctor of his own time, Zemah Gaon, the
+rector of the Academy at Sura (A.D. 889-898). It is possible that a
+certain relationship exists (as suggested by Epstein and supported by
+D.H. Müller) between the famous apocryphal _Letter of Prester John_ (of
+c. A.D. 1165) and the narrative of Eldad; but the affinity is not close.
+Eldad is quoted as an authority on linguistic difficulties by the
+leading medieval Jewish grammarians and lexicographers.
+
+  The work ascribed to Eldad is in Hebrew, divided into six chapters,
+  probably abbreviated from the original text. The first edition
+  appeared at Mantua about 1480; the second at Constantinople in 1516;
+  this was reprinted at Venice in 1544 and 1605, and at Jessnitz in
+  1722. A Latin version by Gilb. Génébrard was published at Paris in
+  1563, under the title of _Eldad Danius ... de Judaeis clausis eorumque
+  in Aethiopia ... imperio_, and was afterwards incorporated in the
+  translator's _Chronologia Hebraeorum_ of 1584; a German version
+  appeared at Prague in 1695, and another at Jessnitz in 1723. In 1838
+  E. Carmoly edited and translated a fuller recension which he had found
+  in a MS. from the library of Eliezer Ben Hasan, forwarded to him by
+  David Zabach of Morocco (see _Relation d'Eldad le Danite_, Paris,
+  1838). Both forms are printed by Dr Jellinek in his _Bet-ha-Midrasch_,
+  vols. ii. p. 102, &c., and iii. p. 6, &c. (Leipzig, 1853-1855). See
+  also Bartolocci, _Bibliotheca magna Rabbinica_, i. 101-130; Fürst,
+  _Bibliotheca Judaica_, i. 30, &c.; Hirsch Graetz, _Geschichte der
+  Juden_ (3rd ed., Leipzig, 1895), v. 239-244; Rossi, _Dizionario degli
+  Ebrei_; Steinschneider, _Cat. librorum Hebraeorum in bibliotheca
+  Bodleiana_, cols. 923-925; Kitto's _Biblical Cyclopaedia_ (3rd
+  edition, _sub nomine_); Abr. Epstein, _Eldad ha-Dani_ (Pressburg,
+  1891); D.H. Müller, "Die Recensionen und Versionen des Eldad
+  had-Dani," in _Denkschriften d. Wiener Akad._ (Phil.-Hist. Cl.), vol.
+  xli. (1892), pp. 1-80.
+
+
+
+
+ELDER (Gr. [Greek: presbuteros]), the name given at different times to a
+ruler or officer in certain political and ecclesiastical systems of
+government.
+
+1. The office of elder is in its origin political and is a relic of the
+old patriarchal system. The unit of primitive society is always the
+family; the only tie that binds men together is that of kinship. "The
+eldest male parent," to quote Sir Henry Maine,[1] "is absolutely
+supreme in his household. His dominion extends to life and death and is
+as unqualified over his children and their houses as over his slaves."
+The tribe, which is a later development, is always an aggregate of
+families or clans, not a collection of individuals. "The union of
+several clans for common political action," as Robertson Smith says,
+"was produced by the pressure of practical necessity, and always tended
+towards dissolution when this practical pressure was withdrawn. The only
+organization for common action was that the leading men of the clans
+consulted together in time of need, and their influence led the masses
+with them. Out of these conferences arose the senates of elders found in
+the ancient states of Semitic and Aryan antiquity alike."[2] With the
+development of civilization there came a time when age ceased to be an
+indispensable condition of leadership. The old title was, however,
+generally retained, e.g. the [Greek: gerontes] so often mentioned in
+Homer, the [Greek: gerousia] of the Dorian states, the _senatus_ and the
+_patres conscripti_ of Rome, the sheikh or elder of Arabia, the alderman
+of an English borough, the seigneur (Lat. _senior_) of feudal France.
+
+2. It was through the influence of Judaism that the originally political
+office of elder passed over into the Christian Church and became
+ecclesiastical. The Israelites inherited the office from their Semitic
+ancestors (just as did the Moabites and the Midianites, of whose elders
+we read in Numbers xxii. 7), and traces of it are found throughout their
+history. Mention is made in Judges viii. 14 of the elders of Succoth
+whom "Gideon taught with thorns of the wilderness and with briers." It
+was to the elders of Israel in Egypt that Moses communicated the plan of
+Yahweh for the redemption of the people (Exodus iii. 16). During the
+sojourn in the wilderness the elders were the intermediaries between
+Moses and the people, and it was out of the ranks of these elders that
+Moses chose a council of seventy "to bear with him the burden of the
+people" (Numbers xi. 16). The elders were the governors of the people
+and the administrators of justice. There are frequent references to
+their work in the latter capacity in the book of Deuteronomy, especially
+in relation to the following crimes--the disobedience of sons; slander
+against a wife; the refusal of levirate marriage; manslaughter; and
+blood-revenge. Their powers were gradually curtailed by (a) the
+development of the monarchy, to which of course they were in subjection,
+and which became the court of appeal in questions of law;[3] (b) the
+appointment of special judges, probably chosen from amongst the elders
+themselves, though their appointment meant the loss of privilege to the
+general body; (c) the rise of the priestly orders, which usurped many of
+the prerogatives that originally belonged to the elders. But in spite of
+the rise of new authorities, the elders still retained a large amount of
+influence. We hear of them frequently in the Persian, Greek and Roman
+periods. In the New Testament the members of the Sanhedrin in Jerusalem
+are very frequently termed "elders" or [Greek: presbyteroi], and from
+them the name was taken over by the Church.
+
+3. The name "elder" was probably the first title bestowed upon the
+officers of the Christian Church--since the word deacon does not occur
+in connexion with the appointment of the Seven in Acts vi. Its universal
+adoption is due not only to its currency amongst the Jews, but also to
+the fact that it was frequently used as the title of magistrates in the
+cities and villages of Asia Minor. For the history of the office of
+elder in the early Church and the relation between elders and bishops
+see PRESBYTER.
+
+4. In modern times the use of the term is almost entirely confined to
+the Presbyterian church, the officers of which are always called elders.
+According to the Presbyterian theory of church government there are two
+classes of elders--"teaching elders," or those specially set apart to
+the pastoral office, and "ruling elders," who are laymen, chosen
+generally by the congregation and set apart by ordination to be
+associated with the pastor in the oversight and government of the
+church. When the word is used without any qualification it is
+understood to apply to the latter class alone. For an account of the
+duties, qualifications and powers of elders in the Presbyterian Church
+see PRESBYTERIANISM.
+
+  See W.R. Smith, _History of the Semites_; H. Maine, _Ancient Law_; E.
+  Schürer, _The Jewish People in the Time of Christ_; J. Wellhausen,
+  _History of Israel and Judah_; G.A. Deissmann, _Bible Studies_, p.
+  154.
+
+
+FOOTNOTES:
+
+  [1] _Ancient Law_, p. 126.
+
+  [2] _Religion of the Semites_, p. 34.
+
+  [3] There is a hint at this even in the Pentateuch, "every great
+    matter they shall bring unto thee, but every small matter they shall
+    judge themselves."
+
+
+
+
+ELDER (O. Eng. _ellarn_; Ger. _Holunder_; Fr. _sureau_), the popular
+designation of the deciduous shrubs and trees constituting the genus
+_Sambucus_ of the natural order Caprifoliaceae. The Common Elder, _S.
+nigra_, the bourtree of Scotland, is found in Europe, the north of
+Africa, Western Asia, the Caucasus, and Southern Siberia; in sheltered
+spots it attains a height of over 20 ft. The bark is smooth; the shoots
+are stout and angular, and the leaves glabrous, pinnate, with oval or
+elliptical leaflets. The flowers, which form dense flat-topped clusters
+(corymbose cymes), with five main branches, have a cream-coloured,
+gamopetalous, five-lobed corolla, five stamens, and three sessile
+stigmas; the berries are purplish-black, globular and three- or
+four-seeded, and ripen about September. The elder thrives best in moist,
+well-drained situations, but can be grown in a great diversity of soils.
+It grows readily from young shoots, which after a year are fit for
+transplantation. It is found useful for making screen-fences in bleak,
+exposed situations, and also as a shelter for other shrubs in the
+outskirts of plantations. By clipping two or three times a year, it may
+be made close and compact in growth. The young trees furnish a brittle
+wood, containing much pith; the wood of old trees is white, hard and
+close-grained, polishes well, and is employed for shoemakers' pegs,
+combs, skewers, mathematical instruments and turned articles. Young
+elder twigs deprived of pith have from very early times been in request
+for making whistles, popguns and other toys.
+
+The elder was known to the ancients for its medicinal properties, and in
+England the inner bark was formerly administered as a cathartic. The
+flowers (_sambuci flores_) contain a volatile oil, and serve for the
+distillation of elder-flower water (_aqua sambuci_), used in
+confectionery, perfumes and lotions. The leaves of the elder are
+employed to impart a green colour to fat and oil (_unguentum sambuci
+foliorum_ and _oleum viride_), and the berries for making wine, a common
+adulterant of port. The leaves and bark emit a sickly odour, believed to
+be repugnant to insects. Christopher Gullet (_Phil. Trans._, 1772, lxii.
+p. 348) recommends that cabbages, turnips, wheat and fruit trees, to
+preserve them from caterpillars, flies and blight, should be whipped
+with twigs of young elder. According to German folklore, the hat must be
+doffed in the presence of the elder-tree; and in certain of the English
+midland counties a belief was once prevalent that the cross of Christ
+was made from its wood, which should therefore never be used as fuel, or
+treated with disrespect (see _Quart. Rev._ cxiv. 233). It was, however,
+a common medieval tradition, alluded to by Ben Jonson, Shakespeare and
+other writers, that the elder was the tree on which Judas hanged
+himself; and on this account, probably, to be crowned with elder was in
+olden times accounted a disgrace. In Cymbeline (act iv. s. 2) "the
+stinking elder" is mentioned as a symbol of grief. In Denmark the tree
+is supposed by the superstitious to be under the protection of the
+"Elder-mother": its flowers may not be gathered without her leave; its
+wood must not be employed for any household furniture; and a child
+sleeping in an elder-wood cradle would certainly be strangled by the
+Elder-mother.
+
+Several varieties are known in cultivation: _aurea_, golden elder, has
+golden-yellow leaves; _laciniata_, parsley-leaved elder, has the
+leaflets cut into fine segments; _rotundifolia_ has rounded leaflets;
+forms also occur with variegated white and yellow leaves, and
+_virescens_ is a variety having white bark and green-coloured berries.
+The scarlet-berried elder, _S. racemosa_, is the handsomest species of
+the genus. It is a native of various parts of Europe, growing in Britain
+to a height of over 15 ft., but often producing no fruit. The dwarf
+elder or Danewort (supposed to have been introduced into Britain by the
+Danes), _S. Ebulus_, a common European species, reaches a height of
+about 6 ft. Its cyme is hairy, has three principal branches, and is
+smaller than that of _S. nigra_; the flowers are white tipped with
+pink. All parts of the plant are cathartic and emetic.
+
+
+
+
+ELDON, JOHN SCOTT, 1st EARL OF (1751-1838), lord high chancellor of
+England, was born at Newcastle on the 4th of June 1751. His grandfather,
+William Scott of Sandgate, a suburb of Newcastle, was clerk to a
+"fitter"--a sort of water-carrier and broker of coals. His father, whose
+name also was William, began life as an apprentice to a fitter, in which
+service he obtained the freedom of Newcastle, becoming a member of the
+gild of Hoastmen (coal-fitters); later in life he became a principal in
+the business, and attained a respectable position as a merchant in
+Newcastle, accumulating property worth nearly £20,000.
+
+John Scott was educated at the grammar school of his native town. He was
+not remarkable at school for application to his studies, though his
+wonderful memory enabled him to make good progress in them; he
+frequently played truant and was whipped for it, robbed orchards, and
+indulged in other questionable schoolboy freaks; nor did he always come
+out of his scrapes with honour and a character for truthfulness. When he
+had finished his education at the grammar school, his father thought of
+apprenticing him to his own business, to which an elder brother Henry
+had already devoted himself; and it was only through the interference of
+his elder brother William (afterwards Lord Stowell, q.v.), who had
+already obtained a fellowship at University College, Oxford, that it was
+ultimately resolved that he should continue the prosecution of his
+studies. Accordingly, in 1766, John Scott entered University College
+with the view of taking holy orders and obtaining a college living. In
+the year following he obtained a fellowship, graduated B.A. in 1770, and
+in 1771 won the prize for the English essay, the only university prize
+open in his time for general competition.
+
+His wife was the eldest daughter of Aubone Surtees, a Newcastle banker.
+The Surtees family objected to the match, and attempted to prevent it;
+but a strong attachment had sprung up between them. On the 18th November
+1772 Scott, with the aid of a ladder and an old friend, carried off the
+lady from her father's house in the Sandhill, across the border to
+Blackshiels, in Scotland, where they were married. The father of the
+bridegroom objected not to his son's choice, but to the time he chose to
+marry; for it was a blight on his son's prospects, depriving him of his
+fellowship and his chance of church preferment. But while the bride's
+family refused to hold intercourse with the pair, Mr Scott, like a
+prudent man and an affectionate father, set himself to make the best of
+a bad matter, and received them kindly, settling on his son £2000. John
+returned with his wife to Oxford, and continued to hold his fellowship
+for what is called the year of grace given after marriage, and added to
+his income by acting as a private tutor. After a time Mr Surtees was
+reconciled with his daughter, and made a liberal settlement on her.
+
+John Scott's year of grace closed without any college living falling
+vacant; and with his fellowship he gave up the church and turned to the
+study of law. He became a student at the Middle Temple in January 1773.
+In 1776 he was called to the bar, intending at first to establish
+himself as an advocate in his native town, a scheme which his early
+success led him to abandon, and he soon settled to the practice of his
+profession in London, and on the northern circuit. In the autumn of the
+year in which he was called to the bar his father died, leaving him a
+legacy of £1000 over and above the £2000 previously settled on him.
+
+In his second year at the bar his prospects began to brighten. His
+brother William, who by this time held the Camden professorship of
+ancient history, and enjoyed an extensive acquaintance with men of
+eminence in London, was in a position materially to advance his
+interests. Among his friends was the notorious Andrew Bowes of Gibside,
+to the patronage of whose house the rise of the Scott family was largely
+owing. Bowes having contested Newcastle and lost it, presented an
+election petition against the return of his opponent. Young Scott was
+retained as junior counsel in the case, and though he lost the petition
+he did not fail to improve the opportunity which it afforded for
+displaying his talents. This engagement, in the commencement of his
+second year at the bar, and the dropping in of occasional fees, must
+have raised his hopes; and he now abandoned the scheme of becoming a
+provincial barrister. A year or two of dull drudgery and few fees
+followed, and he began to be much depressed. But in 1780 we find his
+prospects suddenly improved, by his appearance in the case of _Ackroyd_
+v. _Smithson_, which became a leading case settling a rule of law; and
+young Scott, having lost his point in the inferior court, insisted on
+arguing it, on appeal, against the opinion of his clients, and carried
+it before Lord Thurlow, whose favourable consideration he won by his
+able argument. The same year Bowes again retained him in an election
+petition; and in the year following Scott greatly increased his
+reputation by his appearance as leading counsel in the Clitheroe
+election petition. From this time his success was certain. In 1782 he
+obtained a silk gown, and was so far cured of his early modesty that he
+declined accepting the king's counselship if precedence over him were
+given to his junior, Thomas (afterwards Lord) Erskine, though the latter
+was the son of a peer and a most accomplished orator. He was now on the
+high way to fortune. His health, which had hitherto been but
+indifferent, strengthened with the demands made upon it; his talents,
+his power of endurance, and his ambition all expanded together. He
+enjoyed a considerable practice in the northern part of his circuit,
+before parliamentary committees and at the chancery bar. By 1787 his
+practice at the equity bar had so far increased that he was obliged to
+give up the eastern half of his circuit (which embraced six counties)
+and attend it only at Lancaster.
+
+In 1782 he entered parliament for Lord Weymouth's close borough of
+Weobley, which Lord Thurlow obtained for him without solicitation. In
+parliament he gave a general and independent support to Pitt. His first
+parliamentary speeches were directed against Fox's India Bill. They were
+unsuccessful. In one he aimed at being brilliant; and becoming merely
+laboured and pedantic, he was covered with ridicule by Sheridan, from
+whom he received a lesson which he did not fail to turn to account. In
+1788 he was appointed solicitor-general, and was knighted, and at the
+close of this year he attracted attention by his speeches in support of
+Pitt's resolutions on the state of the king (George III., who then
+laboured under a mental malady) and the delegation of his authority. It
+is said that he drew the Regency Bill, which was introduced in 1789. In
+1793 Sir John Scott was promoted to the office of attorney-general, in
+which it fell to him to conduct the memorable prosecutions for high
+treason against British sympathizers with French republicanism,--amongst
+others, against the celebrated Horne Tooke. These prosecutions, in most
+cases, were no doubt instigated by Sir John Scott, and were the most
+important proceedings in which he was ever professionally engaged. He
+has left on record, in his _Anecdote Book_, a defence of his conduct in
+regard to them. A full account of the principal trials, and of the
+various legislative measures for repressing the expressions of popular
+opinion for which he was more or less responsible, will be found in
+Twiss's _Public and Private Life of the Lord Chancellor Eldon_, and in
+the _Lives of the Lord Chancellors_, by Lord Campbell.
+
+In 1799 the office of chief justice of the Court of Common Pleas falling
+vacant, Sir John Scott's claim to it was not overlooked; and after
+seventeen years' service in the Lower House, he entered the House of
+Peers as Baron Eldon. In February 1801 the ministry of Pitt was
+succeeded by that of Addington, and the chief justice now ascended the
+woolsack. The chancellorship was given to him professedly on account of
+his notorious anti-Catholic zeal. From the peace of Amiens (1802) till
+1804 Lord Eldon appears to have interfered little in politics. In the
+latter year we find him conducting the negotiations which resulted in
+the dismissal of Addington and the recall of Pitt to office as prime
+minister. Lord Eldon was continued in office as chancellor under Pitt;
+but the new administration was of short duration, for on the 23rd of
+January 1806 Pitt died, worn out with the anxieties of office, and his
+ministry was succeeded by a coalition, under Lord Grenville. The death
+of Fox, who became foreign secretary and leader of the House of Commons,
+soon, however, broke up the Grenville administration; and in the spring
+of 1807 Lord Eldon once more, under Lord Liverpool's administration,
+returned to the woolsack, which, from that time, he continued to occupy
+for about twenty years, swaying the cabinet, and being in all but name
+prime minister of England. It was not till April 1827, when the
+premiership, vacant through the paralysis of Lord Liverpool, fell to
+Canning, the chief advocate of Roman Catholic emancipation, that Lord
+Eldon, in the seventy-sixth year of his age, finally resigned the
+chancellorship. When, after the two short administrations of Canning and
+Goderich, it fell to the duke of Wellington to construct a cabinet, Lord
+Eldon expected to be included, if not as chancellor, at least in some
+important office, but he was overlooked, at which he was much chagrined.
+Notwithstanding his frequent protests that he did not covet power, but
+longed for retirement, we find him again, so late as 1835, within three
+years of his death, in hopes of office under Peel. He spoke in
+parliament for the last time in July 1834.
+
+In 1821 Lord Eldon had been created Viscount Encombe and earl of Eldon
+by George IV., whom he managed to conciliate, partly, no doubt, by
+espousing his cause against his wife, whose advocate he had formerly
+been, and partly through his reputation for zeal against the Roman
+Catholics. In the same year his brother William, who from 1798 had
+filled the office of judge of the High Court of Admiralty, was raised to
+the peerage under the title of Lord Stowell.
+
+Lord Eldon's wife, his dear "Bessy," his love for whom is a beautiful
+feature in his life, died before him, on the 28th of June 1831. By
+nature she was of simple character, and by habits acquired during the
+early portion of her husband's career almost a recluse. Two of their
+sons reached maturity--John, who died in 1805, and William Henry John,
+who died unmarried in 1832. Lord Eldon himself survived almost all his
+immediate relations. His brother William died in 1836. He himself died
+in London on the 13th of January 1838, leaving behind him two daughters,
+Lady Frances Bankes and Lady Elizabeth Repton, and a grandson John
+(1805-1854), who succeeded him as second earl, the title subsequently
+passing to the latter's son John (b. 1846).
+
+Lord Eldon was no legislator--his one aim in politics was to keep in
+office, and maintain things as he found them; and almost the only laws
+he helped to pass were laws for popular coercion. For nearly forty years
+he fought against every improvement in law, or in the
+constitution--calling God to witness, on the smallest proposal of
+reform, that he foresaw from it the downfall of his country. Without any
+political principles, properly so called, and without interest in or
+knowledge of foreign affairs, he maintained himself and his party in
+power for an unprecedented period by his great tact, and in virtue of
+his two great political properties--of zeal against every species of
+reform, and zeal against the Roman Catholics. To pass from his political
+to his judicial character is to shift to ground on which his greatness
+is universally acknowledged. His judgments, which have received as much
+praise for their accuracy as abuse for their clumsiness and uncouthness,
+fill a small library. But though intimately acquainted with every nook
+and cranny of the English law, he never carried his studies into foreign
+fields, from which to enrich our legal literature; and it must be added
+that against the excellence of his judgments, in too many cases, must be
+set off the hardships, worse than injustice, that arose from his
+protracted delays in pronouncing them. A consummate judge and the
+narrowest of politicians, he was doubt on the bench, and promptness
+itself in the political arena. For literature, as for art, he had no
+feeling. What intervals of leisure he enjoyed from the cares of office
+he filled up with newspapers and the gossip of old cronies. Nor were his
+intimate associates men of refinement and taste; they were rather good
+fellows who quietly enjoyed a good bottle and a joke; he uniformly
+avoided encounters of wit with his equals. He is said to have been
+parsimonious, and certainly he was quicker to receive than to
+reciprocate hospitalities; but his mean establishment and mode of life
+are explained by the retired habits of his wife, and her dislike of
+company. His manners were very winning and courtly, and in the circle of
+his immediate relatives he is said to have always been lovable and
+beloved.
+
+"In his person," says Lord Campbell, "Lord Eldon was about the middle
+size, his figure light and athletic, his features regular and handsome,
+his eye bright and full, his smile remarkably benevolent, and his whole
+appearance prepossessing. The advance of years rather increased than
+detracted from these personal advantages. As he sat on the
+judgment-seat, 'the deep thought betrayed in his furrowed brow--the
+large eyebrows, overhanging eyes that seemed to regard more what was
+taking place within than around him--his calmness, that would have
+assumed a character of sternness but for its perfect placidity--his
+dignity, repose and venerable age, tended at once to win confidence and
+to inspire respect' (Townsend). He had a voice both sweet and
+deep-toned, and its effect was not injured by his Northumbrian burr,
+which, though strong, was entirely free from harshness and vulgarity."
+
+  AUTHORITIES.--Horace Twiss, _Life of Lord Chancellor Eldon_ (1844);
+  W.E. Surtees, _Sketch of the Lives of Lords Stowell and Eldon_ (1846);
+  Lord Campbell, _Lives of the Chancellors_; W.C. Townsend, _Lives of
+  Twelve Eminent Judges_ (1846); _Greville Memoirs_.
+
+
+
+
+EL DORADO (Span. "the gilded one"), a name applied, first, to the king
+or chief priest of a South American tribe who was said to cover himself
+with gold dust at a yearly religious festival held near Santa Fé de
+Bogotá; next, to a legendary city called Manoa or Omoa; and lastly, to a
+mythical country in which gold and precious stones were found in
+fabulous abundance. The legend, which has never been traced to its
+ultimate source, had many variants, especially as regards the situation
+attributed to Manoa. It induced many Spanish explorers to lead
+expeditions in search of treasure, but all failed. Among the most famous
+were the expedition undertaken by Diego de Ordaz, whose lieutenant
+Martinez claimed to have been rescued from shipwreck, conveyed inland,
+and entertained at Omoa by "El Dorado" himself (1531); and the journeys
+of Orellana (1540-1541), who passed down the Rio Napo to the valley of
+the Amazon; that of Philip von Hutten (1541-1545), who led an exploring
+party from Coro on the coast of Caracas; and of Gonzalo Ximenes de
+Quesada (1569), who started from Santa Fé de Bogotá. Sir Walter Raleigh,
+who resumed the search in 1595, described Manoa as a city on Lake Parimá
+in Guiana. This lake was marked on English and other maps until its
+existence was disproved by A. von Humboldt (1769-1859). Meanwhile the
+name of El Dorado came to be used metaphorically of any place where
+wealth could be rapidly acquired. It was given to a county in
+California, and to towns and cities in various states. In literature
+frequent allusion is made to the legend, perhaps the best-known
+references being those in Milton's _Paradise Lost_ (vi. 411) and
+Voltaire's _Candide_ (chs. 18, 19).
+
+  See A.F.A. Bandelier, _The Gilded Man, El Dorado_ (New York, 1893).
+
+
+
+
+ELDUAYEN, JOSÉ DE, 1st Marquis del Pazo de la Merced (1823-1898),
+Spanish politician, was born in Madrid on the 22nd of June 1823. He was
+educated in the capital, took the degree of civil engineer, and as such
+directed important works in Asturias and Galicia, entered the Cortes in
+1856 as deputy for Vigo, and sat in all the parliaments until 1867 as
+member of the Union Liberal with Marshal O'Donnell. He attacked the
+Miraflores cabinet in 1864, and became under-secretary of the home
+office when Canovas was minister in 1865. He was made a councillor of
+state in 1866, and in 1868 assisted the other members of the Union
+Liberal in preparing the revolution. In the Cortes of 1872 he took much
+part in financial debates. He accepted office as member of the last
+Sagasta cabinet under King Amadeus. On the proclamation of the republic
+Elduayen very earnestly co-operated in the Alphonsist conspiracy, and
+endeavoured to induce the military and politicians to work together. He
+went abroad to meet and accompany the prince after the _pronunciamiento_
+of Marshal Campos, landed with him at Valencia, was made governor of
+Madrid, a marquis, grand cross of Charles III., and minister for the
+colonies in 1878. He accepted the portfolio of foreign affairs in the
+Canovas cabinet from 1883 to 1885, and was made a life senator. He
+always prided himself on having been one of the five members of the
+Cortes of 1870 who voted for Alphonso XII. when that parliament elected
+Amadeus of Savoy. He died at Madrid on the 24th of June 1898.
+
+
+
+
+ELEANOR OF AQUITAINE (c. 1122-1204), wife of the English king Henry II.,
+was the daughter and heiress of Duke William X. of Aquitaine, whom she
+succeeded in April 1137. In accordance with arrangements made by her
+father, she at once married Prince Louis, the heir to the French crown,
+and a month later her husband became king of France under the title of
+Louis VII. Eleanor bore Louis two daughters but no sons. This was
+probably the reason why their marriage was annulled by mutual consent in
+1151, but contemporary scandal-mongers attributed the separation to the
+king's jealousy. It was alleged that, while accompanying her husband on
+the Second Crusade (1146-1149), Eleanor had been unduly familiar with
+her uncle, Raymond of Antioch. Chronology is against this hypothesis,
+since Louis and she lived on good terms together for two years after the
+Crusade. There is still less ground for the supposition that Henry of
+Anjou, whom she married immediately after the divorce, had been her
+lover before it. This second marriage, with a youth some years her
+junior, was purely political. The duchy of Aquitaine required a strong
+ruler, and the union with Anjou was eminently desirable. Louis, who had
+hoped that Aquitaine would descend to his daughters, was mortified and
+alarmed by the Angevin marriage; all the more so when Henry of Anjou
+succeeded to the English crown in 1154. From this event dates the
+beginning of the secular strife between England and France which runs
+like a red thread through medieval history.
+
+Eleanor bore to her second husband five sons and three daughters; John,
+the youngest of their children, was born in 1167. But her relations with
+Henry passed gradually through indifference to hatred. Henry was an
+unfaithful husband, and Eleanor supported her sons in their great
+rebellion of 1173. Throughout the latter years of the reign she was kept
+in a sort of honourable confinement. It was during her captivity that
+Henry formed his connexion with Rosamond Clifford, the Fair Rosamond of
+romance. Eleanor, therefore, can hardly have been responsible for the
+death of this rival, and the romance of the poisoned bowl appears to be
+an invention of the next century.
+
+Under the rule of Richard and John the queen became a political
+personage of the highest importance. To both her sons the popularity
+which she enjoyed in Aquitaine was most valuable. But in other
+directions also she did good service. She helped to frustrate the
+conspiracy with France which John concocted during Richard's captivity.
+She afterwards reconciled the king and the prince, thus saving for John
+the succession which he had forfeited by his misconduct. In 1199 she
+crushed an Angevin rising in favour of John's nephew, Arthur of
+Brittany. In 1201 she negotiated a marriage between her grand-daughter,
+Blanche of Castile, and Louis of France, the grandson of her first
+husband. It was through her staunch defence of Mirabeau in Poitou that
+John got possession of his nephew's person. She died on the 1st of April
+1204, and was buried at Fontevrault. Although a woman of strong passions
+and great abilities she is, historically, less important as an
+individual than as the heiress of Aquitaine, a part of which was,
+through her second marriage, united to England for some four hundred
+years.
+
+  See the chronicles cited for the reigns of Henry II., Richard I. and
+  John. Also Sir J.H. Ramsay, _Angevin Empire_ (London, 1903); K.
+  Norgate, _England under the Angevin Kings_ (London, 1887); and A.
+  Strickland, _Lives of the Queens of England_, vol. i. (1841).
+       (H. W. C. D.)
+
+
+
+
+ELEATIC SCHOOL, a Greek school of philosophy which came into existence
+towards the end of the 6th century B.C., and ended with Melissus of
+Samos (fl. c. 450 B.C.). It took its name from Elea, a Greek city of
+lower Italy, the home of its chief exponents, Parmenides and Zeno. Its
+foundation is often attributed to Xenophanes of Colophon, but, although
+there is much in his speculations which formed part of the later Eleatic
+doctrine, it is probably more correct to regard Parmenides as the
+founder of the school. At all events, it was Parmenides who gave it its
+fullest development. The main doctrines of the Eleatics were evolved in
+opposition, on the one hand, to the physical theories of the early
+physical philosophers who explained all existence in terms of primary
+matter (see IONIAN SCHOOL), and, on the other hand, to the theory of
+Heraclitus that all existence may be summed up as perpetual change. As
+against these theories the Eleatics maintained that the true explanation
+of things lies in the conception of a universal unity of being. The
+senses with their changing and inconsistent reports cannot cognize this
+unity; it is by thought alone that we can pass beyond the false
+appearances of sense and arrive at the knowledge of being, at the
+fundamental truth that "the All is One." There can be no creation, for
+being cannot come from not-being; a thing cannot arise from that which
+is different from it. The errors of common opinion arise to a great
+extent from the ambiguous use of the verb "to be," which may imply
+existence or be merely the copula which connects subject and predicate.
+
+In these main contentions the Eleatic school achieved a real advance,
+and paved the way to the modern conception of metaphysics. Xenophanes in
+the middle of the 6th century had made the first great attack on the
+crude mythology of early Greece, including in his onslaught the whole
+anthropomorphic system enshrined in the poems of Homer and Hesiod. In
+the hands of Parmenides this spirit of free thought developed on
+metaphysical lines. Subsequently, whether from the fact that such bold
+speculations were obnoxious to the general sense of propriety in Elea,
+or from the inferiority of its leaders, the school degenerated into
+verbal disputes as to the possibility of motion, and similar academic
+trifling. The best work of the school was absorbed in the Platonic
+metaphysic (see E. Caird, _Evolution of Theology in the Greek
+Philosophers_, 1904).
+
+  See further the articles on XENOPHANES; PARMENIDES; ZENO (of Elea);
+  MELISSUS, with the works there quoted; also the histories of
+  philosophy by Zeller, Gomperz, Windelband, &c.
+
+
+
+
+ELECAMPANE (Med. Lat. _Enula Campana_), a perennial composite plant, the
+_Inula Helenium_ of botanists, which is common in many parts of Britain,
+and ranges throughout central and southern Europe, and in Asia as far
+eastwards as the Himalayas. It is a rather rigid herb, the stem of which
+attains a height of from 3 to 5 ft.; the leaves are large and toothed,
+the lower ones stalked, the rest embracing the stem; the flowers are
+yellow, 2 in. broad, and have many rays, each three-notched at the
+extremity. The root is thick, branching and mucilaginous, and has a
+warm, bitter taste and a camphoraceous odour. For medicinal purposes it
+should be procured from plants not more than two or three years old.
+Besides _inulin_, C_12H_20O_10, a body isomeric with starch, the root
+contains _helenin_, C6H8O, a stearoptene, which may be prepared in white
+acicular crystals, insoluble in water, but freely soluble in alcohol.
+When freed from the accompanying inula-camphor by repeated
+crystallization from alcohol, helenin melts at 110° C. By the ancients
+the root was employed both as a medicine and as a condiment, and in
+England it was formerly in great repute as an aromatic tonic and
+stimulant of the secretory organs. "The fresh roots of elecampane
+preserved with sugar, or made into a syrup or conserve," are recommended
+by John Parkinson in his _Theatrum Botanicum_ as "very effectual to warm
+a cold and windy stomack, and the pricking and stitches therein or in
+the sides caused by the Spleene, and to helpe the cough, shortnesse of
+breath, and wheesing in the Lungs." As a drug, however, the root is now
+seldom resorted to except in veterinary practice, though it is
+undoubtedly possessed of antiseptic properties. In France and
+Switzerland it is used in the manufacture of absinthe.
+
+
+
+
+ELECTION (from Lat. _eligere_, to pick out), the method by which a
+choice or selection is made by a constituent body (the electors or
+electorate) of some person to fill a certain office or dignity. The
+procedure itself is called an election. Election, as a special form of
+selection, is naturally a loose term covering many subjects; but except
+in the theological sense (the doctrine of election), as employed by
+Calvin and others, for the choice by God of His "elect," the legal sense
+(see ELECTION, _in law_, below), and occasionally as a synonym for
+personal choice (one's own "election"), it is confined to the selection
+by the preponderating vote of some properly constituted body of electors
+of one of two or more candidates, sometimes for admission only to some
+private social position (as in a club), but more particularly in
+connexion with public representative positions in political government.
+It is thus distinguished from arbitrary methods of appointment, either
+where the right of nominating rests in an individual, or where pure
+chance (such as selection by lot) dictates the result. The part played
+by different forms of election in history is alluded to in numerous
+articles in this work, dealing with various countries and various
+subjects. It is only necessary here to consider certain important
+features in the elections, as ordinarily understood, namely, the
+exercise of the right of voting for political and municipal offices in
+the United Kingdom and America. See also the articles PARLIAMENT;
+REPRESENTATION; VOTING; BALLOT, &c., and UNITED STATES: _Political
+Institutions_. For practical details as to the conduct of political
+elections in England reference must be made to the various text-books on
+the subject; the candidate and his election agent require to be on their
+guard against any false step which might invalidate his return.
+
+_Law in the United Kingdom._--Considerable alterations have been made in
+recent years in the law of Great Britain and Ireland relating to the
+procedure at parliamentary and municipal elections, and to election
+petitions.
+
+As regards parliamentary elections (which may be either the "general
+election," after a dissolution of parliament, or "by-elections," when
+casual vacancies occur during its continuance), the most important of
+the amending statutes is the Corrupt and Illegal Practices Act 1883.
+This act, and the Parliamentary Elections Act 1868, as amended by it,
+and other enactments dealing with corrupt practices, are temporary acts
+requiring annual renewal. As regards municipal elections, the Corrupt
+Practices (Municipal Elections) Act 1872 has been repealed by the
+Municipal Corporations Act 1882 for England, and by the Local Government
+(Ireland) Act 1898 for Ireland. The governing enactments for England are
+now the Municipal Corporations Act 1882, part iv., and the Municipal
+Elections (Corrupt and Illegal Practices) Act 1884, the latter annually
+renewable. The provisions of these enactments have been applied with
+necessary modifications to municipal and other local government
+elections in Ireland by orders of the Irish Local Government Board made
+under powers conferred by the Local Government (Ireland) Act 1898. In
+Scotland the law regulating municipal and other local government
+elections is now to be found in the Elections (Scotland) (Corrupt and
+Illegal Practices) Act 1890.
+
+The alterations in the law have been in the direction of greater
+strictness in regard to the conduct of elections, and increased control
+in the public interest over the proceedings on election petitions.
+Various acts and payments which were previously lawful in the absence of
+any corrupt bargain or motive are now altogether forbidden under the
+name of "illegal practices" as distinguished from "corrupt practices."
+Failure on the part of a parliamentary candidate or his election agent
+to comply with the requirements of the law in any particular is
+sufficient to invalidate the return (see the articles BRIBERY and
+CORRUPT PRACTICES). Certain relaxations are, however, allowed in
+consideration of the difficulty of absolutely avoiding all deviation
+from the strict rules laid down. Thus, where the judges who try an
+election petition report that there has been treating, undue influence,
+or any illegal practice by the candidate or his election agent, but that
+it was trivial, unimportant and of a limited character, and contrary to
+the orders and without the sanction or connivance of the candidate or
+his election agent, and that the candidate and his election agent took
+all reasonable means for preventing corrupt and illegal practices, and
+that the election was otherwise free from such practices on their part,
+the election will not be avoided. The court has also the power to
+relieve from the consequences of certain innocent contraventions of the
+law caused by inadvertence or miscalculation.
+
+
+  Election petitions.
+
+The inquiry into a disputed parliamentary election was formerly
+conducted before a committee of the House of Commons, chosen as nearly
+as possible from both sides of the House for that particular business.
+The decisions of these tribunals laboured under the suspicion of being
+prompted by party feeling, and by an act of 1868 the jurisdiction was
+finally transferred to judges of the High Court, notwithstanding the
+general unwillingness of the bench to accept a class of business which
+they feared might bring their integrity into dispute. Section 11 of the
+act ordered, _inter alia_, that the trial of every election petition
+shall be conducted before a _puisne judge_ of one of the common law
+courts at Westminster and Dublin; that the said courts shall each select
+a judge to be placed on the rota for the trial of election petitions;
+that the said judges shall try petitions standing for trial according to
+seniority or otherwise, as they may agree; that the trial shall take
+place in the county or borough to which the petition refers, unless the
+court should think it desirable to hold it elsewhere. The judge shall
+determine "whether the member whose return is complained of, or any and
+what other person, was duly returned and elected, or whether the
+election was void," and shall certify his determination to the speaker.
+When corrupt practices have been charged the judge shall also report (1)
+whether any such practice has been committed by or with the knowledge or
+consent of any candidate, and the nature thereof; (2) the names of
+persons proved to have been guilty of any corrupt practice; and (3)
+whether corrupt practices have extensively prevailed at the election.
+Questions of law were to be referred to the decision of the court of
+common pleas. On the abolition of that court by the Judicature Act 1873,
+the jurisdiction was transferred to the common pleas division, and again
+on the abolition of that division was transferred to the king's bench
+division, in whom it is now vested. The rota of judges for the trial of
+election petitions is also supplied by the king's bench division. The
+trial now takes place before two judges instead of one; and, when
+necessary, the number of judges on the rota may be increased. Both the
+judges who try a petition are to sign the certificates to be made to the
+speaker. If they differ as to the validity of a return, they are to
+state such difference in their certificate, and the return is to be held
+good; if they differ as to a report on any other matter, they are to
+certify their difference and make no report on such matter. The director
+of public prosecutions attends the trial personally or by
+representative. It is his duty to watch the proceedings in the public
+interest, to issue summonses to witnesses whose evidence is desired by
+the court, and to prosecute before the election court or elsewhere those
+persons whom he thinks to have been guilty of corrupt or illegal
+practices at the election in question. If an application is made for
+leave to withdraw a petition, copies of the affidavits in support are to
+be delivered to him; and he is entitled to be heard and to call evidence
+in opposition to such application. Witnesses are not excused from
+answering criminating questions; but their evidence cannot be used
+against them in any proceedings except criminal proceedings for perjury
+in respect of that evidence. If a witness answers truly all questions
+which he is required by the court to answer, he is entitled to receive a
+certificate of indemnity, which will save him from all proceedings for
+any offence under the Corrupt Practices Acts committed by him before the
+date of the certificate at or in relation to the election, except
+proceedings to enforce any incapacity incurred by such offence. An
+application for leave to withdraw a petition must be supported by
+affidavits from all the parties to the petition and their solicitors,
+and by the election agents of all of the parties who were candidates at
+the election. Each of these affidavits is to state that to the best of
+the deponent's knowledge and belief there has been no agreement and no
+terms or undertaking made or entered into as to the withdrawal, or, if
+any agreement has been made, shall state its terms. The applicant and
+his solicitor are also to state in their affidavits the grounds on which
+the petition is sought to be withdrawn. If any person makes an agreement
+for the withdrawal of a petition in consideration of a money payment, or
+of the promise that the seat shall be vacated or another petition
+withdrawn, or omits to state in his affidavit that he has made an
+agreement, lawful or unlawful, for the withdrawal, he is guilty of an
+indictable misdemeanour. The report of the judges to the speaker is to
+contain particulars as to illegal practices similar to those previously
+required as to corrupt practices; and they are to report further whether
+any candidate has been guilty by his agents of an illegal practice, and
+whether certificates of indemnity have been given to persons reported
+guilty of corrupt or illegal practices.
+
+The Corrupt Practices Acts apply, with necessary variations in details,
+to parliamentary elections in Scotland and Ireland.
+
+The amendments in the law as to municipal elections are generally
+similar to those which have been made in parliamentary election law. The
+procedure on trial of petitions is substantially the same, and wherever
+no other provision is made by the acts or rules the procedure on the
+trial of parliamentary election petitions is to be followed. Petitions
+against municipal elections were dealt with in 35 & 36 Vict. c. 60. The
+election judges appoint a number of barristers, not exceeding five, as
+commissioners to try such petitions. No barrister can be appointed who
+is of less than fifteen years' standing, or a member of parliament, or
+holder of any office of profit (other than that of recorder) under the
+crown; nor can any barrister try a petition in any borough in which he
+is recorder or in which he resides, or which is included in his circuit.
+The barrister sits without a jury. The provisions are generally similar
+to those relating to parliamentary elections. The petition may allege
+that the election was avoided as to the borough or ward on the ground of
+general bribery, &c., or that the election of the person petitioned
+against was avoided by corrupt practices, or by personal
+disqualification, or that he had not the majority of lawful votes. The
+commissioner who tries a petition sends to the High Court a certificate
+of the result, together with reports as to corrupt and illegal
+practices, &c., similar to those made to the speaker by the judges who
+try a parliamentary election petition. The Municipal Elections (Corrupt
+and Illegal Practices) Act 1884 applied to school board elections
+subject to certain variations, and has been extended by the Local
+Government Act 1888 to county council elections, and by the Local
+Government Act 1894 to elections by parochial electors. The law in
+Scotland is on the same lines, and extends to all non-parliamentary
+elections, and, as has been stated, the English statutes have been
+applied with adaptations to all municipal and local government elections
+in Ireland.
+
+_United States._--Elections are much more frequent in the United States
+than they are in Great Britain, and they are also more complicated. The
+terms of elective officers are shorter; and as there are also more
+offices to be filled, the number of persons to be voted for is
+necessarily much greater. In the year of a presidential election the
+citizen may be called upon to vote at one time for all of the following:
+(1) National candidates--president and vice-president (indirectly
+through the electoral college) and members of the House of
+Representatives; (2) state candidates--governor, members of the state
+legislature, attorney-general, treasurer, &c.; (3) county
+candidates--sheriff, county judges, district attorney, &c.; (4)
+municipal or town candidates--mayor, aldermen, selectmen, &c. The number
+of persons actually voted for may therefore be ten or a dozen, or it may
+be many more. In addition, the citizen is often called upon to vote yea
+or nay on questions such as amendments to the state constitutions,
+granting of licences, and approval or disapproval of new municipal
+undertakings. As there may be, and generally is, more than one candidate
+for each office, and as all elections are now, and have been for many
+years, conducted by ballot, the total number of names to appear on the
+ballot may be one hundred or may be several hundred. These names are
+arranged in different ways, according to the laws of the different
+states. Under the Massachusetts law, which is considered the best by
+reformers, the names of candidates for each office are arranged
+alphabetically on a "blanket" ballot, as it is called from its size, and
+the elector places a mark opposite the names of such candidates as he
+may wish to vote for. Other states, New York for example, have the
+blanket system, but the names of the candidates are arranged in party
+columns. Still other states allow the grouping on one ballot of all the
+candidates of a single party, and there would be therefore as many
+separate ballots in such states as there were parties in the field.
+
+The qualifications for voting, while varying in the different states in
+details, are in their main features the same throughout the Union. A
+residence in the state is required of from three months to two years.
+Residence is also necessary, but for a shorter period, in the county,
+city or town, or voting precinct. A few states require the payment of a
+poll tax. Some require that the voter shall be able to read and
+understand the Constitution. This latter qualification has been
+introduced into several of the Southern states, partly at least to
+disqualify the ignorant coloured voters. In all, or practically all, the
+states idiots, convicts and the insane are disqualified; in some states
+paupers; in some of the Western states the Chinese. In some states women
+are allowed to vote on certain questions, or for the candidates for
+certain offices, especially school officials; and in four of the Western
+states women have the same rights of suffrage as men. The number of
+those who are qualified to vote, but do not avail themselves of the
+right, varies greatly in the different states and according to the
+interest taken in the election. As a general rule, but subject to
+exceptions, the national elections call out the largest number, the
+state elections next, and the local elections the smallest number of
+voters. In an exciting national election between 80 and 90% of the
+qualified voters actually vote, a proportion considerably greater than
+in Great Britain or Germany.
+
+The tendency of recent years has been towards a decrease both in the
+number and in the frequency of elections. A president and vice-president
+are voted for every fourth year, in the years divisible by four, on the
+first Tuesday following the first Monday of November. Members of the
+national House of Representatives are chosen for two years on the
+even-numbered years. State and local elections take place in accordance
+with state laws, and may or may not be on the same day as the national
+elections. Originally the rule was for the states to hold annual
+elections; in fact, so strongly did the feeling prevail of the need in a
+democratic country for frequent elections, that the maxim "where annual
+elections end, tyranny begins," became a political proverb. But opinion
+gradually changed even in the older or Eastern states, and in 1909
+Massachusetts and Rhode Island were the only states in the Union holding
+annual elections for governor and both houses of the state legislature.
+In the Western states especially state officers are chosen for longer
+terms--in the case of the governor often for four years--and the number
+of elections has correspondingly decreased. Another cause of the
+decrease in the number of elections is the growing practice of holding
+all the elections of any year on one and the same day. Before the Civil
+War Pennsylvania held its state elections several months before the
+national elections. Ohio and Indiana, until 1885 and 1881 respectively,
+held their state elections early in October. Maine, Vermont and Arkansas
+keep to September. The selection of one day in the year for all
+elections held in that year has resulted in a considerable decrease in
+the total number.
+
+Another tendency of recent years, but not so pronounced, is to hold
+local elections in what is known as the "off" year; that is, on the
+odd-numbered year, when no national election is held. The object of this
+reform is to encourage independent voting. The average American citizen
+is only too prone to carry his national political predilections into
+local elections, and to vote for the local nominees of his party,
+without regard to the question of fitness of candidates and the
+fundamental difference of issues involved. This tendency to vote the
+entire party ticket is the more pronounced because under the system of
+voting in use in many of the states all the candidates of the party are
+arranged on one ticket, and it is much easier to vote a straight or
+unaltered ticket than to change or "scratch" it. Again, the voter,
+especially the ignorant one, refrains from scratching his ticket, lest
+in some way he should fail to comply with the technicalities of the law
+and his vote be lost. On the other hand, if local elections are held on
+the "off" or odd year, and there be no national or state candidates, the
+voter feels much more free to select only those candidates whom he
+considers best qualified for the various offices.
+
+On the important question of the purity of elections it is difficult to
+speak with precision. In many of the states, especially those with an
+enlightened public spirit, such as most of the New England states and
+many of the North-Western, the elections are fairly conducted, there
+being no intimidation at all, little or no bribery, and an honest count.
+It can safely be said that through the Union as a whole the tendency of
+recent years has been decidedly towards greater honesty of elections.
+This is owing to a number of causes: (1) The selection of a single day
+for all elections, and the consequent immense number voting on that day.
+Some years ago, when for instance the Ohio and Indiana elections were
+held a few weeks before the general election, each party strained every
+nerve to carry them, for the sake of prestige and the influence on other
+states. In fact, presidential elections were often felt to turn on the
+result in these early voting states, and the party managers were none
+too scrupulous in the means employed to carry them. Bribery has
+decreased in such states since the change of election day to that of the
+rest of the country. (2) The enactment in most of the states of the
+Australian or secret ballot (q.v.) laws. These have led to the secrecy
+of the ballot, and hence to a greater or less extent have prevented
+intimidation and bribery. (3) Educational or other such test, more
+particularly in the Southern states, the object of which is to exclude
+the coloured, and especially the ignorant coloured, voters from the
+polls. In those southern states in which the coloured vote was large,
+and still more in those in which it was the majority, it was felt among
+the whites that intimidation or ballot-box stuffing was justified by the
+necessity of white supremacy. With the elimination of the coloured vote
+by educational or other tests the honesty of elections has increased.
+(4) The enactment of new and more stringent registration laws. Under
+these laws only those persons are allowed to vote whose names have been
+placed on the rolls a certain number of days or months before election.
+These rolls are open to public inspection, and the names may be
+challenged at the polls, and "colonization" or repeating is therefore
+almost impossible. (5) The reform of the civil service and the gradual
+elimination of the vicious principle of "to the victors belong the
+spoils." With the reform of the civil service elections become less a
+scramble for office and more a contest of political or economic
+principle. They bring into the field, therefore, a better class of
+candidates. (6) The enactment in a number of states of various other
+laws for the prevention of corrupt practices, for the publication of
+campaign expenses, and for the prohibition of party workers from coming
+within a certain specified distance of the polls. In the state of
+Massachusetts, for instance, an act passed in 1892, and subsequently
+amended, provides that political committees shall file a full statement,
+duly sworn to, of all campaign expenditures made by them. The act
+applies to all public elections except that of town officers, and also
+covers nominations by caucuses and conventions as well. Apart from his
+personal expenses such as postage, travelling expenses, &c., a candidate
+is prohibited from spending anything himself to promote either his
+nomination or his election, but he is allowed to contribute to the
+treasury of the political committee. The law places no limit on the
+amount that these committees may spend. The reform sought by the law is
+thorough publicity, and not only are details of receipts and
+expenditures to be published, but the names of contributors and the
+amount of their contributions. In the state of New York the act which
+seeks to prevent corrupt practices relies in like manner on the efficacy
+of publicity, but it is less effective than the Massachusetts law in
+that it provides simply for the filing by the candidates themselves of
+sworn statements of their own expenses. There is nothing to prevent
+their contributing to political committees, and the financial methods
+and the amounts expended by such committees are not made public. But
+behind all these causes that have led to more honest elections lies the
+still greater one of a healthier public spirit. In the reaction
+following the Civil War all reforms halted. In recent years, however, a
+new and healthier interest has sprung up in things political; and one
+result of this improved civic spirit is seen in the various laws for
+purification of elections. It may now be safely affirmed that in the
+majority of states the elections are honestly conducted; that
+intimidation, bribery, stuffing of the ballot boxes or other forms of
+corruption, when they exist, are owing in large measure to temporary or
+local causes; and that the tendency of recent years has been towards a
+decrease in all forms of corruption.
+
+The expenses connected with elections, such as the renting and preparing
+of the polling-places, the payment of the clerks and other officers who
+conduct the elections and count the vote, are borne by the community. A
+candidate therefore is not, as far as the law is concerned, liable to
+any expense whatever. As a matter of fact he does commonly contribute to
+the party treasury, though in the case of certain candidates,
+particularly those for the presidency and for judicial offices,
+financial contributions are not general. The amount of a candidate's
+contribution varies greatly, according to the office sought, the state
+in which he lives, and his private wealth. On one occasion, in a
+district in New York, a candidate for Congress is credibly believed to
+have spent at one election $50,000. On the other hand, in a
+Congressional election in a certain district in Massachusetts, the only
+expenditure of one of the candidates was for the two-cent stamp placed
+on his letter of acceptance. No estimate of the average amount expended
+can be made. It is, however, the conclusion of Mr Bryce, in his
+_American Commonwealth_, that as a rule a seat in Congress costs the
+candidate less than a seat for a county division in the House of
+Commons. (See also BALLOT.)
+
+
+
+
+ELECTION, in English law, the obligation imposed upon a party by courts
+of equity to choose between two inconsistent or alternative rights or
+claims in cases where there is a clear intention of the person from whom
+he derives one that he should not enjoy both. Thus a testator died
+seized of property in fee simple and in fee tail--he had two daughters,
+and devised the fee simple property to one and the entailed property to
+the other; the first one claimed to have her share of the entailed
+property as coparcener and also to retain the benefit she took under the
+will. It was held that she was put to her election whether she would
+take under the will and renounce her claim to the entailed property or
+take against the will, in which case she must renounce the benefits she
+took under the will in so far as was necessary to compensate her sister.
+As the essence of the doctrine is compensation, a person electing
+against a document does not lose all his rights under it, but the court
+will sequester so much only of the benefit intended for him as will
+compensate the persons disappointed by his election. For the same reason
+it is necessary that there should be a free and disposable fund passing
+by the instrument from which compensation can be made in the event of
+election against the will. If, therefore, a man having a special power
+of appointment appoint the fund equally between two persons, one being
+an object of the power and the other not an object, no question of
+election arises, but the appointment to the person not an object is bad.
+
+Election, though generally arising in cases of wills, may also arise in
+the case of a deed. There is, however, a distinction to be observed. In
+the case of a will a clear intention on the part of the testator that he
+meant to dispose of property not his own must be shown, and parol
+evidence is not admissible as to this. In the case of a deed, however,
+no such intention need be shown, for if a deed confers a benefit and
+imposes a liability on the same person he cannot be allowed to accept
+the one and reject the other, but this must be distinguished from cases
+where two separate gifts are given to a person, one beneficial and the
+other onerous. In such a case no question of election arises and he may
+take the one and reject the other, unless, indeed, there are words used
+which make the one conditional on the acceptance of the other.
+
+Election is either express, e.g. by deed, or implied; in the latter case
+it is often a question of considerable difficulty whether there has in
+fact been an election or not; each case must depend upon the particular
+circumstances, but quite generally it may be said that the person who
+has elected must have been capable of electing, aware of the existence
+of the doctrine of election, and have had the opportunity of satisfying
+himself of the relative value of the properties between which he has
+elected. In the case of infants the court will sometimes elect after an
+inquiry as to which course is the most advantageous, or if there is no
+immediate urgency, will allow the matter to stand over till the infant
+attains his majority. In the cases of married women and lunatics the
+courts will exercise the right for them. It sometimes happens that the
+parties have so dealt with the property that it would be inequitable to
+disturb it; in such cases the court will not interfere in order to allow
+of election.
+
+
+
+
+ELECTORAL COMMISSION, in United States history, a commission created to
+settle the disputed presidential election of 1876. In this election
+Samuel J. Tilden, the Democratic candidate, received 184 uncontested
+electoral votes, and Rutherford B. Hayes, the Republican candidate,
+163.[1] The states of Florida, Louisiana, Oregon and South Carolina,
+with a total of 22 votes, each sent in two sets of electoral ballots,[2]
+and from each of these states except Oregon one set gave the whole vote
+to Tilden and the other gave the whole vote to Hayes. From Oregon one
+set of ballots gave the three electoral votes of the state to Hayes; the
+other gave two votes to Hayes and one to Tilden.
+
+The election of a president is a complex proceeding, the method being
+indicated partly in the Constitution, and being partly left to Congress
+and partly to the states. The manner of selecting the electors is left
+to state law; the electoral ballots are sent to the president of the
+Senate, who "shall, in the presence of the Senate and House of
+Representatives, open all certificates, and the votes shall then be
+counted." Concerning this provision many questions of vital importance
+arose in 1876: Did the president of the Senate count the votes, the
+houses being mere witnesses; or did the houses count them, the
+president's duties being merely ministerial? Did counting imply the
+determination of what should be counted, or was it a mere arithmetical
+process; that is, did the Constitution itself afford a method of
+settling disputed returns, or was this left to legislation by Congress?
+Might Congress or an officer of the Senate go behind a state's
+certificate and review the acts of its certifying officials? Might it go
+further and examine into the choice of electors? And if it had such
+powers, might it delegate them to a commission? As regards the procedure
+of Congress, it seems that, although in early years the president of the
+Senate not only performed or overlooked the electoral count but also
+exercised discretion in some matters very important in 1876, Congress
+early began to assert power, and, at least from 1821 onward, controlled
+the count, claiming complete power. The fact, however, that the Senate
+in 1876 was controlled by the Republicans and the House by the
+Democrats, lessened the chances of any harmonious settlement of these
+questions by Congress. The country seemed on the verge of civil war.
+Hence it was that by an act of the 29th of January 1877, Congress
+created the Electoral Commission to pass upon the contested returns,
+giving it "the same powers, if any" possessed by itself in the premises,
+the decisions to stand unless rejected by the two houses separately. The
+commission was composed of five Democratic and five Republican
+Congressmen, two justices of the Supreme Court of either party, and a
+fifth justice chosen by these four. As its members of the commission the
+Senate chose G.F. Edmunds of Vermont, O.P. Morton of Indiana, and F.T.
+Frelinghuysen of New Jersey (Republicans); and A.G. Thurman of Ohio and
+T.F. Bayard of Delaware (Democrats). The House chose Henry B. Payne of
+Ohio, Eppa Hunton of Virginia, and Josiah G. Abbott of Massachusetts
+(Democrats); and George F. Hoar of Massachusetts and James A. Garfield
+of Ohio (Republicans). The Republican judges were William Strong and
+Samuel F. Miller; the Democratic, Nathan Clifford and Stephen J. Field.
+These four chose as the fifteenth member Justice Joseph P. Bradley, a
+Republican but the only member not selected avowedly as a partisan. As
+counsel for the Democratic candidate there appeared before the
+commission at different times Charles O'Conor of New York, Jeremiah S.
+Black of Pennsylvania, Lyman Trumbull of Illinois, R.T. Merrick of the
+District of Columbia, Ashbel Green of New Jersey, Matthew H. Carpenter
+of Wisconsin, George Hoadley of Ohio, and W.C. Whitney of New York. W.M.
+Evarts and E.W. Stoughton of New York and Samuel Shellabarger and
+Stanley Matthews of Ohio appeared regularly in behalf of Mr Hayes.
+
+The popular vote seemed to indicate that Hayes had carried South
+Carolina and Oregon, and Tilden Florida and Louisiana. It was evident,
+however, that Hayes could secure the 185 votes necessary to elect only
+by gaining every disputed ballot. As the choice of Republican electors
+in Louisiana had been accomplished by the rejection of several thousand
+Democratic votes by a Republican returning board, the Democrats insisted
+that the commission should go behind the returns and correct injustice;
+the Republicans declared that the state's action was final, and that to
+go behind the returns would be invading its sovereignty. When this
+matter came before the commission it virtually accepted the Republican
+contention, ruling that it could not go behind the returns except on the
+superficial issues of manifest fraud therein or the eligibility of
+electors to their office under the Constitution; that is, it could not
+investigate antecedents of fraud or misconduct of state officials in the
+results certified. All vital questions were settled by the votes of
+eight Republicans and seven Democrats; and as the Republican Senate
+would never concur with the Democratic House in overriding the
+decisions, all the disputed votes were awarded to Mr Hayes, who
+therefore was declared elected.
+
+The strictly partisan votes of the commission and the adoption by
+prominent Democrats and Republicans, both within and without the
+commission, of an attitude toward states-rights principles quite
+inconsistent with party tenets and tendencies, have given rise to much
+severe criticism. The Democrats and the country, however, quietly
+accepted the decision. The judgments underlying it were two: (1) That
+Congress rightly claimed the power to settle such contests within the
+limits set; (2) that, as Justice Miller said regarding these limits, the
+people had never at any time intended to give to Congress the power, by
+naming the electors, to "decide who are to be the president and
+vice-president of the United States."
+
+There is no doubt that Mr Tilden was morally entitled to the presidency,
+and the correction of the Louisiana frauds would certainly have given
+satisfaction then and increasing satisfaction later, in the retrospect,
+to the country. The commission might probably have corrected the frauds
+without exceeding its Congressional precedents. Nevertheless, the
+principles of its decisions must be recognized by all save
+ultra-nationalists as truer to the spirit of the Constitution and
+promising more for the good of the country than would have been the
+principles necessary to a contrary decision.
+
+By an act of the 3rd of February 1887 the electoral procedure is
+regulated in great detail. Under this act determination by a state of
+electoral disputes is conclusive, subject to certain formalities that
+guarantee definite action and accurate certification. These formalities
+constitute "regularity," and are in all cases judgable by Congress. When
+Congress is forced by the lack or evident inconclusiveness of state
+action, or by conflicting state action, to decide disputes, votes are
+lost unless both houses concur.
+
+  AUTHORITIES.--J.F. Rhodes, _History of the United States_, vol. 7,
+  covering 1872-1877 (New York, 1906); P.L. Haworth, _The Hayes-Tilden
+  disputed Presidential Election of 1876_ (Cleveland, 1906); J.W.
+  Burgess, _Political Science Quarterly_, vol. 3 (1888), pp. 633-653,
+  "The Law of the Electoral Count"; and for the sources. Senate
+  Miscellaneous Document No. 5 (vol. 1), and House Miscel. Doc. No. 13
+  (vol. 2), 44 Congress, 2 Session,--_Count of the Electoral Vote.
+  Proceedings of Congress and Electoral Commission_,--the latter
+  identical with _Congressional Record_, vol. 5, pt. 4, 44 Cong., 2
+  Session; also about twenty volumes of evidence on the state elections
+  involved. The volume called _The Presidential Counts_ (New York, 1877)
+  was compiled by Mr. Tilden and his secretary.
+
+
+FOOTNOTES:
+
+  [1] The election of a vice-president was, of course, involved also.
+    William A. Wheeler was the Republican candidate, and Thomas A.
+    Hendricks the Democratic.
+
+  [2] A second set of electoral ballots had also been sent in from
+    Vermont, where Hayes had received a popular majority vote of 24,000.
+    As these ballots had been transmitted in an irregular manner, the
+    president of the Senate refused to receive them, and was sustained in
+    this action by the upper House.
+
+
+
+
+ELECTORS (Ger. _Kurfürsten_, from _Küren_, O.H.G. _kiosan_, choose,
+elect, and _Fürst_, prince), a body of German princes, originally seven
+in number, with whom rested the election of the German king, from the
+13th until the beginning of the 19th century. The German kings, from the
+time of Henry the Fowler (919-936) till the middle of the 13th century,
+succeeded to their position partly by heredity, and partly by election.
+Primitive Germanic practice had emphasized the element of heredity.
+_Reges ex nobilitate sumunt_: the man whom a German tribe recognized as
+its king must be in the line of hereditary descent from Woden; and
+therefore the genealogical trees of early Teutonic kings (as, for
+instance, in England those of the Kentish and West Saxon sovereigns) are
+carefully constructed to prove that descent from the god which alone
+will constitute a proper title for his descendants. Even from the first,
+however, there had been some opening for election; for the principle of
+primogeniture was not observed, and there might be several competing
+candidates, all of the true Woden stock. One of these competing
+candidates would have to be recognized (as the Anglo-Saxons said,
+_geceosan_); and to this limited extent Teutonic kings may be termed
+elective from the very first. In the other nations of western Europe
+this element of election dwindled, and the principle of heredity alone
+received legal recognition; in medieval Germany, on the contrary, the
+principle of heredity, while still exercising an inevitable natural
+force, sank formally into the background, and legal recognition was
+finally given to the elective principle. _De facto_, therefore, the
+principle of heredity exercises in Germany a great influence, an
+influence never more striking than in the period which follows on the
+formal recognition of the elective principle, when the Habsburgs (like
+the Metelli at Rome) _fato imperatores fiunt: de jure_, each monarch
+owes his accession simply and solely to the vote of an electoral
+college.
+
+This difference between the German monarchy and the other monarchies of
+western Europe may be explained by various considerations. Not the least
+important of these is what seems a pure accident. Whereas the Capetian
+monarchs, during the three hundred years that followed on the election
+of Hugh Capet in 987, always left an heir male, and an heir male of full
+age, the German kings again and again, during the same period, either
+left a minor to succeed to their throne, or left no issue at all. The
+principle of heredity began to fail because there were no heirs. Again
+the strength of tribal feeling in Germany made the monarchy into a
+prize, which must not be the apanage of any single tribe, but must
+circulate, as it were, from Franconian to Saxon, from Saxon to Bavarian,
+from Bavarian to Franconian, from Franconian to Swabian; while the
+growing power of the baronage, and its habit of erecting anti-kings to
+emphasize its opposition to the crown (as, for instance, in the reign of
+Henry IV.), coalesced with and gave new force to the action of tribal
+feeling. Lastly, the fact that the German kings were also Roman emperors
+finally and irretrievably consolidated the growing tendency towards the
+elective principle. The principle of heredity had never held any great
+sway under the ancient Roman Empire (see under EMPEROR); and the
+medieval Empire, instituted as it was by the papacy, came definitely
+under the influence of ecclesiastical prepossessions in favour of
+election. The church had substituted for that descent from Woden, which
+had elevated the old pagan kings to their thrones, the conception that
+the monarch derived his crown from the choice of God, after the manner
+of Saul; and the theoretical choice of God was readily turned into the
+actual choice of the church, or, at any rate, of the general body of
+churchmen. If an ordinary king is thus regarded by the church as
+essentially elected, much more will the emperor, connected as he is with
+the church as one of its officers, be held to be also elected; and as a
+bishop is chosen by the chapter of his diocese, so, it will be thought,
+must the emperor be chosen by some corresponding body in his empire.
+Heredity might be tolerated in a mere matter of kingship: the precious
+trust of imperial power could not be allowed to descend according to the
+accidents of family succession. To Otto of Freising (_Gesta Frid._ ii.
+1) it is already a point of right vindicated for itself by the
+excellency of the Roman Empire, as a matter of singular prerogative,
+that it should not descend _per sanguinis propaginem, sed per principum
+electionem_.
+
+The accessions of Conrad II. (see Wipo, _Vita Cuonradi_, c. 1-2), of
+Lothair II. (see _Narratio de electione Lotharii_, M.G.H. _Scriptt._
+xii. p. 510), of Conrad III. (see Otto of Freising, _Chronicon_, vii.
+22) and of Frederick I. (see Otto of Freising, _Gesta Frid._ ii. 1) had
+all been marked by an element, more or less pronounced, of election.
+That element is perhaps most considerable in the case of Lothair, who
+had no rights of heredity to urge. Here we read of ten princes being
+selected from the princes of the various duchies, to whose choice the
+rest promise to assent, and of these ten selecting three candidates, one
+of whom, Lothair, is finally chosen (apparently by the whole assembly)
+in a somewhat tumultuary fashion. In this case the electoral assembly
+would seem to be, in the last resort, the whole diet of all the princes.
+But a _de facto_ pre-eminence in the act of election is already, during
+the 12th century, enjoyed by the three Rhenish archbishops, probably
+because of the part they afterwards played at the coronation, and also
+by the dukes of the great duchies--possibly because of the part they too
+played, as vested for the time with the great offices of the household,
+at the coronation feast.[1] Thus at the election of Lothair it is the
+archbishop of Mainz who conducts the proceedings; and the election is
+not held to be final until the duke of Bavaria has given his assent. The
+fact is that, votes being weighed by quality as well as by quantity (see
+DIET), the votes of the archbishops and dukes, which would first be
+taken, would of themselves, if unanimous, decide the election. To
+prevent tumultuary elections, it was well that the election should be
+left exclusively with these great dignitaries; and this is what, by the
+middle of the 13th century, had eventually been done.
+
+The chaos of the interregnum from 1198 to 1212 showed the way for the
+new departure; the chaos of the great interregnum (1250-1273) led to its
+being finally taken. The decay of the great duchies, and the narrowing
+of the class of princes into a close corporation, some of whose members
+were the equals of the old dukes in power, introduced difficulties and
+doubts into the practice of election which had been used in the 12th
+century. The contested election of the interregnum of 1198-1212 brought
+these difficulties and doubts into strong relief. The famous bull of
+Innocent III. (_Venerabilem_), in which he decided for Otto IV. against
+Philip of Swabia, on the ground that, though he had fewer votes than
+Philip, he had a majority of the votes of those _ad quos principaliter
+spectat electio_, made it almost imperative that there should be some
+definition of these principal electors. The most famous attempt at such
+a definition is that of the _Sachsenspiegel_, which was followed, or
+combated, by many other writers in the first half of the 13th century.
+Eventually the contested election of 1257 brought light and definition.
+Here we find seven potentates acting--the same seven whom the Golden
+Bull recognizes in 1356; and we find these seven described in an
+official letter to the pope, as _principes vocem in hujusmodi electione
+habentes, qui sunt septem numero_. The doctrine thus enunciated was at
+once received. The pope acknowledged it in two bulls (1263); a cardinal,
+in a commentary on the bull _Venerabilem_ of Innocent III., recognized
+it about the same time; and the erection of statues of the seven
+electors at Aix-la-Chapelle gave the doctrine a visible and outward
+expression.
+
+By the date of the election of Rudolph of Habsburg (1273) the seven
+electors may be regarded as a definite body, with an acknowledged right.
+But the definition and the acknowledgment were still imperfect. (1) The
+composition of the electoral body was uncertain in two respects. The
+duke of Bavaria claimed as his right the electoral vote of the king of
+Bohemia; and the practice of _partitio_ in electoral families tended to
+raise further difficulties about the exercise of the vote. The Golden
+Bull of 1356 settled both these questions. Bohemia (of which Charles
+IV., the author of the Golden Bull, was himself the king) was assigned
+the electoral vote in preference to Bavaria; and a provision annexing
+the electoral vote to a definite territory, declaring that territory
+indivisible, and regulating its descent by the rule of primogeniture
+instead of partition, swept away the old difficulties which the custom
+of partition had raised. After 1356 the seven electors are regularly the
+three Rhenish archbishops, Mainz, Cologne and Trier, and four lay
+magnates, the palatine of the Rhine, the duke of Saxony, the margrave of
+Brandenburg, and the king of Bohemia; the three former being vested with
+the three archchancellorships, and the four latter with the four offices
+of the royal household (see HOUSEHOLD). (2) The rights of the seven
+electors, in their collective capacity as an electoral college, were a
+matter of dispute with the papacy. The result of the election, whether
+made, as at first, by the princes generally or, as after 1257, by the
+seven electors exclusively, was in itself simply the creation of a
+German king--an _electio in regem_. But since 962 the German king was
+also, after coronation by the pope, Roman emperor. Therefore the
+election had a double result: the man elected was not only _electus in
+regem_, but also _promovendus ad imperium_. The difficulty was to define
+the meaning of the term _promovendus_. Was the king elect _inevitably_
+to become emperor? or did the _promotio_ only follow at the discretion
+of the pope, if he thought the king elect fit for promotion? and if so,
+to what extent, and according to what standard, did the pope judge of
+such fitness? Innocent III. had already claimed, in the bull
+_Venerabilem_, (1) that the electors derived their power of election, so
+far as it made an emperor, from the Holy See (which had originally
+"translated" the Empire from the East to the West), and (2) that the
+papacy had a _jus et auctoritas examinandi personam electam in regem et
+promovendam ad imperium_. The latter claim he had based on the fact that
+he anointed, consecrated and crowned the emperor--in other words, that
+he gave a spiritual office according to spiritual methods, which
+entitled him to inquire into the fitness of the recipient of that
+office, as a bishop inquires into the fitness of a candidate for
+ordination. Innocent had put forward this claim as a ground for deciding
+between competing candidates: Boniface VIII. pressed the claim against
+Albert I. in 1298, even though his election was unanimous; while John
+XXII. exercised it in its harshest form, when in 1324 he ex-communicated
+Louis IV. for using the title and exerting the rights even of king
+without previous papal confirmation. This action ultimately led to a
+protest from the electors themselves, whose right of election would have
+become practically meaningless, if such assumptions had been tolerated.
+A meeting of the electors (_Kurverein_) at Rense in 1338 declared (and
+the declaration was reaffirmed by a diet at Frankfort in the same year)
+that _postquam aliquis eligitur in Imperatorem sive Regem ab Electoribus
+Imperii concorditer, vel majori parte eorundem, statim ex sola electione
+est Rex verus et Imperator Romanus censendus ... nec Papae sive Sedis
+Apostolicae ... approbatione ... indiget_. The doctrine thus positively
+affirmed at Rense is negatively reaffirmed in the Golden Bull, in which
+a significant silence is maintained in regard to papal rights. But the
+doctrine was not in practice followed: Sigismund himself did not venture
+to dispense with papal approbation.
+
+By the end of the 14th century the position of the electors, both
+individually and as a corporate body, had become definite and precise.
+Individually, they were distinguished from all other princes, as we have
+seen, by the indivisibility of their territories and by the custom of
+primogeniture which secured that indivisibility; and they were still
+further distinguished by the fact that their person, like that of the
+emperor himself, was protected by the law of treason, while their
+territories were only subject to the jurisdiction of their own courts.
+They were independent territorial sovereigns; and their position was at
+once the envy and the ideal of the other princes of Germany. Such had
+been the policy of Charles IV.; and thus had he, in the Golden Bull,
+sought to magnify the seven electors, and himself as one of the seven,
+in his capacity of king of Bohemia, even at the expense of the Empire,
+and of himself in his capacity of emperor. Powerful as they were,
+however, in their individual capacity, the electors showed themselves no
+less powerful as a corporate body. As such a corporate body, they may be
+considered from three different points of view, and as acting in three
+different capacities. They are an electoral body, choosing each
+successive emperor; they are one of the three colleges of the imperial
+diet (see DIET); and they are also an electoral union
+(_Kurfürstenverein_), acting as a separate and independent political
+organ even after the election, and during the reign, of the monarch. It
+was in this last capacity that they had met at Rense in 1338; and in the
+same capacity they acted repeatedly during the 15th century. According
+to the Golden Bull, such meetings were to be annual, and their
+deliberations were to concern "the safety of the Empire and the world."
+Annual they never were; but occasionally they became of great
+importance. In 1424, during the attempt at reform occasioned by the
+failure of German arms against the Hussites, the _Kurfürstenverein_
+acted, or at least it claimed to act, as the predominant partner in a
+duumvirate, in which the unsuccessful Sigismund was relegated to a
+secondary position. During the long reign of Frederick III.--a reign in
+which the interests of Austria were cherished, and the welfare of the
+Empire neglected, by that apathetic yet tenacious emperor--the electors
+once more attempted, in the year 1453, to erect a new central government
+in place of the emperor, a government which, if not conducted by
+themselves directly in their capacity of a _Kurfürstenverein_, should at
+any rate be under their influence and control. So, they hoped, Germany
+might be able to make head against that papal aggression, to which
+Frederick had yielded, and to take a leading part in that crusade
+against the Turks, which he had neglected. Like the previous attempt at
+reform during the Hussite wars, the scheme came to nothing; the forces
+of disunion in Germany were too strong for any central government,
+whether monarchical and controlled by the emperor, or oligarchical and
+controlled by the electors. But a final attempt, the most strenuous of
+all, was made in the reign of Maximilian I., and under the influence of
+Bertold, elector and archbishop of Mainz. The council of 1500, in which
+the electors (with the exception of the king of Bohemia) were to have
+sat, and which would have been under their control, represents the last
+effective attempt at a real _Reichsregiment_. Inevitably, however, it
+shipwrecked on the opposition of Maximilian; and though the attempt was
+again made between 1521 and 1530, the idea of a real central government
+under the control of the electors perished, and the development of local
+administration by the circle took its place.
+
+In the course of the 16th century a new right came to be exercised by
+the electors. As an electoral body (that is to say, in the first of the
+three capacities distinguished above), they claimed, at the election of
+Charles V. in 1519 and at subsequent elections, to impose conditions on
+the elected monarch, and to determine the terms on which he should
+exercise his office in the course of his reign. This _Wahlcapitulation_,
+similar to the _Pacta Conventa_ which limited the elected kings of
+Poland, was left by the diet to the discretion of the electors, though
+after the treaty of Westphalia an attempt was made, with some little
+success,[2] to turn the capitulation into a matter of legislative
+enactment by the diet. From this time onwards the only fact of
+importance in the history of the electors is the change which took place
+in the composition of their body during the 17th and 18th centuries.
+From the Golden Bull to the treaty of Westphalia (1356-1648) the
+composition of the electoral body had remained unchanged. In 1623,
+however, in the course of the Thirty Years' War, the vote of the count
+palatine of the Rhine had been transferred to the duke of Bavaria; and
+at the treaty of Westphalia the vote, with the office of imperial butler
+which it carried, was left to Bavaria, while an eighth vote, along with
+the new office of imperial treasurer, was created for the count
+palatine. In 1708 a ninth vote, along with the office of imperial
+standard-bearer, was created for Hanover; while finally, in 1778, the
+vote of Bavaria and the office of imperial butler returned to the counts
+palatine, as heirs of the duchy, on the extinction of the ducal line,
+while the new vote created for the Palatinate in 1648, with the office
+of imperial treasurer, was transferred to Brunswick-Lüneburg (Hanover)
+in lieu of the one which this house already held. In 1806, on the
+dissolution of the Holy Roman Empire, the electors ceased to exist.
+
+  LITERATURE.--T. Lindner, _Die deutschen Königswahlen und die
+  Entstehung des Kurfürstentums_ (1893), and _Der Hergang bei den
+  deutschen Königswahlen_ (1899); R. Kirchhöfer, _Zur Entstehung des
+  Kurkollegiums_ (1893); W. Maurenbrecher, _Geschichte der deutschen
+  Königswahlen_ (1889); and G. Blondel, _Étude sur Frédéric II_, p. 27
+  sqq. See also J. Bryce, _Holy Roman Empire_ (edition of 1904), c. ix.;
+  and R. Schröder, _Lehrbuch der deutschen Rechtsgeschichte_, pp.
+  471-481 and 819-820.     (E. Br.)
+
+
+FOOTNOTES:
+
+  [1] This is the view of the _Sachsenspiegel_, and also of Albert of
+    Stade (quoted in Schröder, p. 476, n. 27): "Palatinus eligit, quia
+    dapifer est; dux Saxoniae, quia marescalcus," &c. Schröder points out
+    (p. 479, n. 45) that "participation in the coronation feast is an
+    express recognition of the king"; and those who are to discharge
+    their office in the one must have had a prominent voice in the other.
+
+  [2] See Schröder's _Lehrbuch der deutschen Rechtsgeschichte_, p. 820.
+
+
+
+
+ELECTRA ([Greek: Elektra]), "the bright one," in Greek mythology. (1)
+One of the seven Pleiades, daughter of Atlas and Pleïone. She is closely
+connected with the old constellation worship and the religion of
+Samothrace, the chief seat of the Cabeiri (q.v.), where she was
+generally supposed to dwell. By Zeus she was the mother of Dardanus,
+Iasion (or Eëtion), and Harmonia; but in the Italian tradition, which
+represented Italy as the original home of the Trojans, Dardanus was her
+son by a king of Italy named Corythus. After her amour with Zeus,
+Electra fled to the Palladium as a suppliant, but Athena, enraged that
+it had been touched by one who was no longer a maiden, flung Electra and
+the image from heaven to earth, where it was found by Ilus, and taken by
+him to Ilium; according to another tradition, Electra herself took it to
+Ilium, and gave it to her son Dardanus (Schol. Eurip. _Phoen._ 1136). In
+her grief at the destruction of the city she plucked out her hair and
+was changed into a comet; in another version Electra and her six sisters
+had been placed among the stars as the Pleiades, and the star which she
+represented lost its brilliancy after the fall of Troy. Electra's
+connexion with Samothrace (where she was also called Electryone and
+Strategis) is shown by the localization of the carrying off of her
+reputed daughter Harmonia by Cadmus, and by the fact that, according to
+Athenicon (the author of a work on Samothrace quoted by the scholiast on
+Apollonius Rhodius i. 917), the Cabeiri were Dardanus and Iasion. The
+gate Electra at Thebes and the fabulous island Electris were said to
+have been called after her (Apollodorus iii. 10. 12; Servius on _Aen._
+iii. 167, vii. 207, x. 272, _Georg._ i. 138).
+
+(2) Daughter of Agamemnon and Clytaemnestra, sister of Orestes and
+Iphigeneia. She does not appear in Homer, although according to Xanthus
+(regarded by some as a fictitious personage), to whom Stesichorus was
+indebted for much in his _Oresteia_, she was identical with the Homeric
+Laodice, and was called Electra because she remained so long unmarried
+([Greek: 'A-lektra]). She was said to have played an important part in
+the poem of Stesichorus, and subsequently became a favourite figure in
+tragedy. After the murder of her father on his return from Troy by her
+mother and Aegisthus, she saved the life of her brother Orestes by
+sending him out of the country to Strophius, king of Phanote in Phocis,
+who had him brought up with his own son Pylades. Electra, cruelly
+ill-treated by Clytaemnestra and her paramour, never loses hope that her
+brother will return to avenge his father. When grown up, Orestes, in
+response to frequent messages from his sister, secretly repairs with
+Pylades to Argos, where he pretends to be a messenger from Strophius
+bringing the news of the death of Orestes. Being admitted to the palace,
+he slays both Aegisthus and Clytaemnestra. According to another story
+(Hyginus, _Fab._ 122), Electra, having received a false report that
+Orestes and Pylades had been sacrificed to Artemis in Tauris, went to
+consult the oracle at Delphi. In the meantime Aletes, the son of
+Aegisthus, seized the throne of Mycenae. Her arrival at Delphi coincided
+with that of Orestes and Iphigeneia. The same messenger, who had already
+communicated the false report of the death of Orestes, informed her that
+he had been slain by Iphigeneia. Electra in her rage seized a burning
+brand from the altar, intending to blind her sister; but at the critical
+moment Orestes appeared, recognition took place, and the brother and
+sister returned to Mycenae. Aletes was slain by Orestes, and Electra
+became the wife of Pylades. The story of Electra is the subject of the
+_Choëphori_ of Aeschylus, the _Electra_ of Sophocles and the _Electra_
+of Euripides. It is in the Sophoclean play that Electra is most
+prominent.
+
+  There are many variations in the treatment of the legend, for which,
+  as also for a discussion of the modern plays on the subject by
+  Voltaire and Alfieri, see Jebb's Introduction to his edition of the
+  _Electra_ of Sophocles.
+
+
+
+
+ELECTRICAL (or ELECTROSTATIC) MACHINE, a machine operating by manual or
+other power for transforming mechanical work into electric energy in the
+form of electrostatic charges of opposite sign delivered to separate
+conductors. Electrostatic machines are of two kinds: (1) Frictional, and
+(2) Influence machines.
+
+[Illustration: FIG. 1.--Ramsden's electrical machine.]
+
+_Frictional Machines._--A primitive form of frictional electrical
+machine was constructed about 1663 by Otto von Guericke (1602-1686). It
+consisted of a globe of sulphur fixed on an axis and rotated by a winch,
+and it was electrically excited by the friction of warm hands held
+against it. Sir Isaac Newton appears to have been the first to use a
+glass globe instead of sulphur (_Optics_, 8th Query). F. Hawksbee in
+1709 also used a revolving glass globe. A metal chain resting on the
+globe served to collect the charge. Later G.M. Bose (1710-1761), of
+Wittenberg, added the prime conductor, an insulated tube or cylinder
+supported on silk strings, and J.H. Winkler (1703-1770), professor of
+physics at Leipzig, substituted a leather cushion for the hand. Andreas
+Gordon (1712-1751) of Erfurt, a Scotch Benedictine monk, first used a
+glass cylinder in place of a sphere. Jesse Ramsden (1735-1800) in 1768
+constructed his well-known form of plate electrical machine (fig. 1). A
+glass plate fixed to a wooden or metal shaft is rotated by a winch. It
+passes between two rubbers made of leather, and is partly covered with
+two silk aprons which extend over quadrants of its surface. Just below
+the places where the aprons terminate, the glass is embraced by two
+insulated metal forks having the sharp points projecting towards the
+glass, but not quite touching it. The glass is excited positively by
+friction with the rubbers, and the charge is drawn off by the action of
+the points which, when acted upon inductively, discharge negative
+electricity against it. The insulated conductor to which the points are
+connected therefore becomes positively electrified. The cushions must be
+connected to earth to remove the negative electricity which accumulates
+on them. It was found that the machine acted better if the rubbers were
+covered with bisulphide of tin or with F. von Kienmayer's amalgam,
+consisting of one part of zinc, one of tin and two of mercury. The
+cushions were greased and the amalgam in a state of powder spread over
+them. Edward Nairne's electrical machine (1787) consisted of a glass
+cylinder with two insulated conductors, called prime conductors, on
+glass legs placed near it. One of these carried the leather exacting
+cushions and the other the collecting metal points, a silk apron
+extending over the cylinder from the cushion almost to the points. The
+rubber was smeared with amalgam. The function of the apron is to prevent
+the escape of electrification from the glass during its passage from the
+rubber to the collecting points. Nairne's machine could give either
+positive or negative electricity, the first named being collected from
+the prime conductor carrying the collecting points and the second from
+the prime conductor carrying the cushion.
+
+[Illustration: FIG. 2.]
+
+_Influence Machines._--Frictional machines are, however, now quite
+superseded by the second class of instrument mentioned above, namely,
+influence machines. These operate by electrostatic induction and convert
+mechanical work into electrostatic energy by the aid of a small initial
+charge which is continually being replenished or reinforced. The general
+principle of all the machines described below will be best understood by
+considering a simple ideal case. Imagine two Leyden jars with large
+brass knobs, A and B, to stand on the ground (fig. 2). Let one jar be
+initially charged with positive electricity on its inner coating and the
+other with negative, and let both have their outsides connected to
+earth. Imagine two insulated balls A' and B' so held that A' is near A
+and B' is near B. Then the positive charge on A induces two charges on
+A', viz.: a negative on the side nearest and a positive on the side most
+removed. Likewise the negative charge on B induces a positive charge on
+the side of B' nearest to it and repels negative electricity to the far
+side. Next let the balls A' and B' be connected together for a moment by
+a wire N called a neutralizing conductor which is subsequently removed.
+Then A' will be left negatively electrified and B' will be left
+positively electrified. Suppose that A' and B' are then made to change
+places. To do this we shall have to exert energy to remove A' against
+the attraction of A and B' against the attraction of B. Finally let A'
+be brought in contact with B and B' with A. The ball A' will give up its
+charge of negative electricity to the Leyden jar B, and the ball B' will
+give up its positive charge to the Leyden jar A. This transfer will take
+place because the inner coatings of the Leyden jars have greater
+capacity with respect to the earth than the balls. Hence the charges of
+the jars will be increased. The balls A' and B' are then practically
+discharged, and the above cycle of operations may be repeated. Hence,
+however small may be the initial charges of the Leyden jars, by a
+principle of accumulation resembling that of compound interest, they can
+be increased as above shown to any degree. If this series of operations
+be made to depend upon the continuous rotation of a winch or handle, the
+arrangement constitutes an electrostatic influence machine. The
+principle therefore somewhat resembles that of the self-exciting dynamo.
+
+
+  Bennet's Doubler.
+
+The first suggestion for a machine of the above kind seems to have grown
+out of the invention of Volta's electrophorus. Abraham Bennet, the
+inventor of the gold leaf electroscope, described a doubler or machine
+for multiplying electric charges (_Phil. Trans._, 1787).
+
+  The principle of this apparatus may be explained thus. Let A and C be
+  two fixed disks, and B a disk which can be brought at will within a
+  very short distance of either A or C. Let us suppose all the plates to
+  be equal, and let the capacities of A and C in presence of B be each
+  equal to p, and the coefficient of induction between A and B, or C and
+  B, be q. Let us also suppose that the plates A and C are so distant
+  from each other that there is no mutual influence, and that p' is the
+  capacity of one of the disks when it stands alone. A small charge Q is
+  communicated to A, and A is insulated, and B, uninsulated, is brought
+  up to it; the charge on B will be--(q/p)Q. B is now uninsulated and
+  brought to face C, which is uninsulated; the charge on C will be
+  (q/p)²Q. C is now insulated and connected with A, which is always
+  insulated. B is then brought to face A and uninsulated, so that the
+  charge on A becomes rQ, where
+
+           p      /    q²\
+    r = -------- ( 1 + -- ).
+        (p + p')  \    p²/
+
+  A is now disconnected from C, and here the first operation ends. It is
+  obvious that at the end of n such operations the charge on A will be
+  r^_(n)Q, so that the charge goes on increasing in geometrical
+  progression. If the distance between the disks could be made
+  infinitely small each time, then the multiplier r would be 2, and the
+  charge would be doubled each time. Hence the name of the apparatus.
+
+[Illustration: FIG. 3.--Nicholson's Revolving Doubler.]
+
+
+  Nicholson's doubler.
+
+Erasmus Darwin, B. Wilson, G.C. Bohnenberger and J.C.E. Peclet devised
+various modifications of Bennet's instrument (see S.P. Thompson, "The
+Influence Machine from 1788 to 1888," _Journ. Soc. Tel. Eng._, 1888, 17,
+p. 569). Bennet's doubler appears to have given a suggestion to William
+Nicholson (_Phil. Trans._, 1788, p. 403) of "an instrument which by
+turning a winch produced the two states of electricity without friction
+or communication with the earth." This "revolving doubler," according to
+the description of Professor S.P. Thompson (_loc. cit._), consists of
+two fixed plates of brass A and C (fig. 3), each two inches in diameter
+and separately supported on insulating arms in the same plane, so that a
+third revolving plate B may pass very near them without touching. A
+brass ball D two inches in diameter is fixed on the end of the axis that
+carries the plate B, and is loaded within at one side, so as to act as a
+counterpoise to the revolving plate B. The axis P N is made of varnished
+glass, and so are the axes that join the three plates with the brass
+axis N O. The axis N O passes through the brass piece M, which stands on
+an insulating pillar of glass, and supports the plates A and C. At one
+extremity of this axis is the ball D, and the other is connected with a
+rod of glass, N P, upon which is fixed the handle L, and also the piece
+G H, which is separately insulated. The pins E, F rise out of the back
+of the fixed plates A and C, at unequal distances from the axis. The
+piece K is parallel to G H, and both of them are furnished at their ends
+with small pieces of flexible wire that they may touch the pins E, F in
+certain points of their revolution. From the brass piece M there stands
+out a pin I, to touch against a small flexible wire or spring which
+projects sideways from the rotating plate B when it comes opposite A.
+The wires are so adjusted by bending that B, at the moment when it is
+opposite A, communicates with the ball D, and A communicates with C
+through GH; and half a revolution later C, when B comes opposite to it,
+communicates with the ball D through the contact of K with F. In all
+other positions A, B, C and D are completely disconnected from each
+other. Nicholson thus described the operation of his machine:--
+
+  "When the plates A and B are opposite each other, the two fixed plates
+  A and C may be considered as one mass, and the revolving plate B,
+  together with the ball D, will constitute another mass. All the
+  experiments yet made concur to prove that these two masses will not
+  possess the same electric state.... The redundant electricities in the
+  masses under consideration will be unequally distributed; the plate A
+  will have about ninety-nine parts, and the plate C one; and, for the
+  same reason, the revolving plate B will have ninety-nine parts of the
+  opposite electricity, and the ball D one. The rotation, by destroying
+  the contacts, preserves this unequal distribution, and carries B from
+  A to C at the same time that the tail K connects the ball with the
+  plate C. In this situation, the electricity in B acts upon that in C,
+  and produces the contrary state, by virtue of the communication
+  between C and the ball; which last must therefore acquire an
+  electricity of the same kind with that of the revolving plate. But the
+  rotation again destroys the contact and restores B to its first
+  situation opposite A. Here, if we attend to the effect of the whole
+  revolution, we shall find that the electric states of the respective
+  masses have been greatly increased; for the ninety-nine parts in A and
+  B remain, and the one part of electricity in C has been increased so
+  as nearly to compensate ninety-nine parts of the opposite electricity
+  in the revolving plate B, while the communication produced an opposite
+  mutation in the electricity of the ball. A second rotation will, of
+  course, produce a proportional augmentation of these increased
+  quantities; and a continuance of turning will soon bring the
+  intensities to their maximum, which is limited by an explosion between
+  the plates" (_Phil. Trans._, 1788, p. 405).
+
+[Illustration: FIG. 4.--Belli's Doubler.]
+
+
+  Belli's doubler.
+
+Nicholson described also another apparatus, the "spinning condenser,"
+which worked on the same principle. Bennet and Nicholson were followed
+by T. Cavallo, John Read, Bohnenberger, C.B. Désormes and J.N.P.
+Hachette and others in the invention of various forms of rotating
+doubler. A simple and typical form of doubler, devised in 1831 by G.
+Belli (fig. 4), consisted of two curved metal plates between which
+revolved a pair of balls carried on an insulating stem. Following the
+nomenclature usual in connexion with dynamos we may speak of the
+conductors which carry the initial charges as the field plates, and of
+the moving conductors on which are induced the charges which are
+subsequently added to those on the field plates, as the carriers. The
+wire which connects two armature plates for a moment is the neutralizing
+conductor. The two curved metal plates constitute the field plates and
+must have original charges imparted to them of opposite sign. The
+rotating balls are the carriers, and are connected together for a moment
+by a wire when in a position to be acted upon inductively by the field
+plates, thus acquiring charges of opposite sign. The moment after they
+are separated again. The rotation continuing the ball thus negatively
+charged is made to give up this charge to that negatively electrified
+field plate, and the ball positively charged its charge to the
+positively electrified field plate, by touching little contact springs.
+In this manner the field plates accumulate charges of opposite sign.
+
+[Illustration: FIG. 5.--Varley's Machine.]
+
+
+  Varley's machine.
+
+Modern types of influence machine may be said to date from 1860 when
+C.F. Varley patented a type of influence machine which has been the
+parent of numerous subsequent forms (_Brit. Pat. Spec._ No. 206 of
+1860). In it the field plates were sheets of tin-foil attached to a
+glass plate (fig. 5). In front of them a disk of ebonite or glass,
+having carriers of metal fixed to its edge, was rotated by a winch. In
+the course of their rotation two diametrically opposite carriers touched
+against the ends of a neutralizing conductor so as to form for a moment
+one conductor, and the moment afterwards these two carriers were
+insulated, one carrying away a positive charge and the other a negative.
+Continuing their rotation, the positively charged carrier gave up its
+positive charge by touching a little knob attached to the positive field
+plate, and similarly for the negative charge carrier. In this way the
+charges on the field plates were continually replenished and reinforced.
+Varley also constructed a multiple form of influence machine having six
+rotating disks, each having a number of carriers and rotating between
+field plates. With this apparatus he obtained sparks 6 in. long, the
+initial source of electrification being a single Daniell cell.
+
+
+  Toepler machine.
+
+Varley was followed by A.J.I. Toepler, who in 1865 constructed an
+influence machine consisting of two disks fixed on the same shaft and
+rotating in the same direction. Each disk carried two strips of tin-foil
+extending nearly over a semi-circle, and there were two field plates,
+one behind each disk; one of the plates was positively and the other
+negatively electrified. The carriers which were touched under the
+influence of the positive field plate passed on and gave up a portion of
+their negative charge to increase that of the negative field plate; in
+the same way the carriers which were touched under the influence of the
+negative field plate sent a part of their charge to augment that of the
+positive field plate. In this apparatus one of the charging rods
+communicated with one of the field plates, but the other with the
+neutralizing brush opposite to the other field plate. Hence one of the
+field plates would always remain charged when a spark was taken at the
+transmitting terminals.
+
+[Illustration: FIG. 6.--Holtz's Machine.]
+
+
+  Holtz machine.
+
+Between 1864 and 1880, W.T.B. Holtz constructed and described a large
+number of influence machines which were for a long time considered the
+most advanced development of this type of electrostatic machine. In one
+form the Holtz machine consisted of a glass disk mounted on a horizontal
+axis F (fig. 6) which could be made to rotate at a considerable speed by
+a multiplying gear, part of which is seen at X. Close behind this disk
+was fixed another vertical disk of glass in which were cut two windows
+B, B. On the side of the fixed disk next the rotating disk were pasted
+two sectors of paper A, A, with short blunt points attached to them
+which projected out into the windows on the side away from the rotating
+disk. On the other side of the rotating disk were placed two metal combs
+C, C, which consisted of sharp points set in metal rods and were each
+connected to one of a pair of discharge balls E, D, the distance between
+which could be varied. To start the machine the balls were brought in
+contact, one of the paper armatures electrified, say, with positive
+electricity, and the disk set in motion. Thereupon very shortly a
+hissing sound was heard and the machine became harder to turn as if the
+disk were moving through a resisting medium. After that the discharge
+balls might be separated a little and a continuous series of sparks or
+brush discharges would take place between them. If two Leyden jars L, L
+were hung upon the conductors which supported the combs, with their
+outer coatings put in connexion with one another by M, a series of
+strong spark discharges passed between the discharge balls. The action
+of the machine is as follows: Suppose one paper armature to be charged
+positively, it acts by induction on the right hand comb, causing
+negative electricity to issue from the comb points upon the glass
+revolving disk; at the same time the positive electricity passes through
+the closed discharge circuit to the left comb and issues from its teeth
+upon the part of the glass disk at the opposite end of the diameter.
+This positive electricity electrifies the left paper armature by
+induction, positive electricity issuing from the blunt point upon the
+side farthest from the rotating disk. The charges thus deposited on the
+glass disk are carried round so that the upper half is electrified
+negatively on both sides and the lower half positively on both sides,
+the sign of the electrification being reversed as the disk passes
+between the combs and the armature by discharges issuing from them
+respectively. If it were not for leakage in various ways, the
+electrification would go on everywhere increasing, but in practice a
+stationary state is soon attained. Holtz's machine is very uncertain in
+its action in a moist climate, and has generally to be enclosed in a
+chamber in which the air is kept artificially dry.
+
+
+  Voss's machine.
+
+Robert Voss, a Berlin instrument maker, in 1880 devised a form of
+machine in which he claimed that the principles of Toepler and Holtz
+were combined. On a rotating glass or ebonite disk were placed carriers
+of tin-foil or metal buttons against which neutralizing brushes touched.
+This armature plate revolved in front of a field plate carrying two
+pieces of tin-foil backed up by larger pieces of varnished paper. The
+studs on the armature plate were charged inductively by being connected
+for a moment by a neutralizing wire as they passed in front of the field
+plates, and then gave up their charges partly to renew the field charges
+and partly to collecting combs connected to discharge balls. In general
+design and construction, the manner of moving the rotating plate and in
+the use of the two Leyden jars in connexion with the discharge balls,
+Voss borrowed his ideas from Holtz.
+
+
+  Wimshurst machine.
+
+All the above described machines, however, have been thrown into the
+shade by the invention of a greatly improved type of influence machine
+first constructed by James Wimshurst about 1878. Two glass disks are
+mounted on two shafts in such a manner that, by means of two belts and
+pulleys worked from a winch shaft, the disks can be rotated rapidly in
+opposite directions close to each other (fig. 7). These glass disks
+carry on them a certain number (not less than 16 or 20) tin-foil
+carriers which may or may not have brass buttons upon them. The glass
+plates are well varnished, and the carriers are placed on the outer
+sides of the two glass plates. As therefore the disks revolve, these
+carriers travel in opposite directions, coming at intervals in
+opposition to each other. Each upright bearing carrying the shafts of
+the revolving disks also carries a neutralizing conductor or wire ending
+in a little brush of gilt thread. The neutralizing conductors for each
+disk are placed at right angles to each other. In addition there are
+collecting combs which occupy an intermediate position and have sharp
+points projecting inwards, and coming near to but not touching the
+carriers. These combs on opposite sides are connected respectively to
+the inner coatings of two Leyden jars whose outer coatings are in
+connexion with one another.
+
+[Illustration: FIG. 7.--Wimshurst's Machine.]
+
+The operation of the machine is as follows: Let us suppose that one of
+the studs on the back plate is positively electrified and one at the
+opposite end of a diameter is negatively electrified, and that at that
+moment two corresponding studs on the front plate passing opposite to
+these back studs are momentarily connected together by the neutralizing
+wire belonging to the front plate. The positive stud on the back plate
+will act inductively on the front stud and charge it negatively, and
+similarly for the other stud, and as the rotation continues these
+charged studs will pass round and give up most of their charge through
+the combs to the Leyden jars. The moment, however, a pair of studs on
+the front plate are charged, they act as field plates to studs on the
+back plate which are passing at the moment, provided these last are
+connected by the back neutralizing wire. After a few revolutions of the
+disks half the studs on the front plate at any moment are charged
+negatively and half positively and the same on the back plate, the
+neutralizing wires forming the boundary between the positively and
+negatively charged studs. The diagram in fig. 8, taken by permission
+from S.P. Thompson's paper (_loc. cit._), represents a view of the
+distribution of these charges on the front and back plates respectively.
+It will be seen that each stud is in turn both a field plate and a
+carrier having a charge induced on it, and then passing on in turn
+induces further charges on other studs. Wimshurst constructed numerous
+very powerful machines of this type, some of them with multiple plates,
+which operate in almost any climate, and rarely fail to charge
+themselves and deliver a torrent of sparks between the discharge balls
+whenever the winch is turned. He also devised an alternating current
+electrical machine in which the discharge balls were alternately
+positive and negative. Large Wimshurst multiple plate influence machines
+are often used instead of induction coils for exciting Röntgen ray tubes
+in medical work. They give very steady illumination on fluorescent
+screens.
+
+[Illustration: FIG. 8.--Action of the Wimshurst Machine.]
+
+In 1900 it was found by F. Tudsbury that if an influence machine is
+enclosed in a metallic chamber containing compressed air, or better,
+carbon dioxide, the insulating properties of compressed gases enable a
+greatly improved effect to be obtained owing to the diminution of the
+leakage across the plates and from the supports. Hence sparks can be
+obtained of more than double the length at ordinary atmospheric
+pressure. In one case a machine with plates 8 in. in diameter which
+could give sparks 2.5 in. at ordinary pressure gave sparks of 5, 7, and
+8 in. as the pressure was raised to 15, 30 and 45 lb. above the normal
+atmosphere.
+
+[Illustration: FIG. 9.--Lord Kelvin's Replenisher.
+
+  C, C, Metal carriers fixed to ebonite cross-arm.
+  F, F, Brass field-plates or conductors.
+  a, a, Receiving springs.
+  n, n, Connecting springs or neutralizing brushes.]
+
+The action of Lord Kelvin's replenisher (fig. 9) used by him in
+connexion with his electrometers for maintaining their charge, closely
+resembles that of Belli's doubler and will be understood from fig. 9.
+Lord Kelvin also devised an influence machine, commonly called a "mouse
+mill," for electrifying the ink in connexion with his siphon recorder.
+It was an electrostatic and electromagnetic machine combined, driven by
+an electric current and producing in turn electrostatic charges of
+electricity. In connexion with this subject mention must also be made of
+the water dropping influence machine of the same inventor.[1]
+
+The action and efficiency of influence machines have been investigated
+by F. Rossetti, A. Righi and F.W.G. Kohlrausch. The electromotive force
+is practically constant no matter what the velocity of the disks, but
+according to some observers the internal resistance decreases as the
+velocity increases. Kohlrausch, using a Holtz machine with a plate 16
+in. in diameter, found that the current given by it could only
+electrolyse acidulated water in 40 hours sufficient to liberate one
+cubic centimetre of mixed gases. E.E.N. Mascart, A. Roiti, and E.
+Bouchotte have also examined the efficiency and current producing power
+of influence machines.
+
+  BIBLIOGRAPHY.--In addition to S.P. Thompson's valuable paper on
+  influence machines (to which this article is much indebted) and other
+  references given, see J. Clerk Maxwell, _Treatise on Electricity and
+  Magnetism_ (2nd ed., Oxford, 1881), vol. i. p. 294; J.D. Everett,
+  _Electricity_ (expansion of part iii. of Deschanel's _Natural
+  Philosophy_) (London, 1901), ch. iv. p. 20; A. Winkelmann, _Handbuch
+  der Physik_ (Breslau, 1905), vol. iv. pp. 50-58 (contains a large
+  number of references to original papers); J. Gray, _Electrical
+  Influence Machines, their Development and Modern Forms_ (London,
+  1903).     (J. A. F.)
+
+
+FOOTNOTE:
+
+  [1] See Lord Kelvin, _Reprint of Papers on Electrostatics and
+    Magnetism_ (1872); "Electrophoric Apparatus and Illustrations of
+    Voltaic Theory," p. 319; "On Electric Machines Founded on Induction
+    and Convection," p. 330; "The Reciprocal Electrophorus," p. 337.
+
+
+
+
+ELECTRIC EEL (_Gymnotus electricus_), a member of the family of fishes
+known as _Gymnotidae_. In spite of their external similarity the
+_Gymnotidae_ have nothing to do with the eels (_Anguilla_). They
+resemble the latter in the elongation of the body, the large number of
+vertebrae (240 in _Gymnotus_), and the absence of pelvic fins; but they
+differ in all the more important characters of internal structure. They
+are in fact allied to the carps or _Cyprinidae_ and the cat-fishes or
+_Siluridae_. In common with these two families and the _Characinidae_ of
+Africa and South America, the _Gymnotidae_ possess the peculiar
+structures called _ossicula auditus_ or Weberian ossicles. These are a
+chain of small bones belonging to the first four vertebrae, which are
+much modified, and connecting the air-bladder with the auditory organs.
+Such an agreement in the structure of so complicated and specialized an
+apparatus can only be the result of a community of descent of the
+families possessing it. Accordingly these families are now placed
+together in a distinct sub-order, the Ostariophysi. The _Gymnotidae_ are
+strongly modified and degraded _Characinidae_. In them the dorsal and
+caudal fins are very rudimentary or absent, and the anal is very long,
+extending from the anus, which is under the head or throat, to the end
+of the body.
+
+_Gymnotus_ is the only genus of the family which possesses electric
+organs. These extend the whole length of the tail, which is four-fifths
+of the body. They are modifications of the lateral muscles and are
+supplied with numerous branches of the spinal nerves. They consist of
+longitudinal columns, each composed of an immense number of "electric
+plates." The posterior end of the organ is positive, the anterior
+negative, and the current passes from the tail to the head. The maximum
+shock is given when the head and tail of the _Gymnotus_ are in contact
+with different points in the surface of some other animal. _Gymnotus
+electricus_ attains a length of 3 ft. and the thickness of a man's
+thigh, and frequents the marshes of Brazil and the Guianas, where it is
+regarded with terror, owing to the formidable electrical apparatus with
+which it is provided. When this natural battery is discharged in a
+favourable position, it is sufficiently powerful to stun the largest
+animal; and according to A. von Humboldt, it has been found necessary to
+change the line of certain roads passing through the pools frequented by
+the electric eels. These fish are eaten by the Indians, who, before
+attempting to capture them, seek to exhaust their electrical power by
+driving horses into the ponds. By repeated discharges upon these they
+gradually expend this marvellous force; after which, being defenceless,
+they become timid, and approach the edge for shelter, when they fall an
+easy prey to the harpoon. It is only after long rest and abundance of
+food that the fish is able to resume the use of its subtle weapon.
+Humboldt's description of this method of capturing the fish has not,
+however, been verified by recent travellers.
+
+
+
+
+ELECTRICITY. This article is devoted to a general sketch of the history
+of the development of electrical knowledge on both the theoretical and
+the practical sides. The two great branches of electrical theory which
+concern the phenomena of electricity at rest, or "frictional" or
+"static" electricity, and of electricity in motion, or electric
+currents, are treated in two separate articles, ELECTROSTATICS and
+ELECTROKINETICS. The phenomena attendant on the passage of electricity
+through solids, through liquids and through gases, are described in the
+article CONDUCTION, ELECTRIC, and also ELECTROLYSIS, and the propagation
+of electrical vibrations in ELECTRIC WAVES. The interconnexion of
+magnetism (which has an article to itself) and electricity is discussed
+in ELECTROMAGNETISM, and these manifestations in nature in ATMOSPHERIC
+ELECTRICITY; AURORA POLARIS and MAGNETISM, TERRESTRIAL. The general
+principles of electrical engineering will be found in ELECTRICITY
+SUPPLY, and further details respecting the generation and use of
+electrical power are given in such articles as DYNAMO; MOTORS, ELECTRIC;
+TRANSFORMERS; ACCUMULATOR; POWER TRANSMISSION: _Electric_; TRACTION;
+LIGHTING: _Electric_; ELECTROCHEMISTRY and ELECTROMETALLURGY. The
+principles of telegraphy (land, submarine and wireless) and of telephony
+are discussed in the articles TELEGRAPH and TELEPHONE, and various
+electrical instruments are treated in separate articles such as
+AMPEREMETER; ELECTROMETER; GALVANOMETER; VOLTMETER; WHEATSTONE'S BRIDGE;
+POTENTIOMETER; METER, ELECTRIC; ELECTROPHORUS; LEYDEN JAR; &c.
+
+The term "electricity" is applied to denote the physical agency which
+exhibits itself by effects of attraction and repulsion when particular
+substances are rubbed or heated, also in certain chemical and
+physiological actions and in connexion with moving magnets and metallic
+circuits. The name is derived from the word _electrica_, first used by
+William Gilbert (1544-1603) in his epoch-making treatise _De magnete,
+magneticisque corporibus, et de magno magnete tellure_, published in
+1600,[1] to denote substances which possess a similar property to amber
+(= _electrum_, from [Greek: êlektron]) of attracting light objects when
+rubbed. Hence the phenomena came to be collectively called electrical, a
+term first used by William Barlowe, archdeacon of Salisbury, in 1618,
+and the study of them, electrical science.
+
+
+_Historical Sketch._
+
+Gilbert was the first to conduct systematic scientific experiments on
+electrical phenomena. Prior to his date the scanty knowledge possessed
+by the ancients and enjoyed in the middle ages began and ended with
+facts said to have been familiar to Thales of Miletus (600 B.C.) and
+mentioned by Theophrastus (321 B.C.) and Pliny (A.D. 70), namely, that
+amber, jet and one or two other substances possessed the power, when
+rubbed, of attracting fragments of straw, leaves or feathers. Starting
+with careful and accurate observations on facts concerning the
+mysterious properties of amber and the lodestone, Gilbert laid the
+foundations of modern electric and magnetic science on the true
+experimental and inductive basis. The subsequent history of electricity
+may be divided into four well-marked periods. The first extends from the
+date of publication of Gilbert's great treatise in 1600 to the invention
+by Volta of the voltaic pile and the first production of the electric
+current in 1799. The second dates from Volta's discovery to the
+discovery by Faraday in 1831 of the induction of electric currents and
+the creation of currents by the motion of conductors in magnetic fields,
+which initiated the era of modern electrotechnics. The third covers the
+period between 1831 and Clerk Maxwell's enunciation of the
+electromagnetic theory of light in 1865 and the invention of the
+self-exciting dynamo, which marks another great epoch in the development
+of the subject; and the fourth comprises the modern development of
+electric theory and of absolute quantitative measurements, and above
+all, of the applications of this knowledge in electrical engineering. We
+shall sketch briefly the historical progress during these various
+stages, and also the growth of electrical theories of electricity during
+that time.
+
+FIRST PERIOD.--Gilbert was probably led to study the phenomena of the
+attraction of iron by the lodestone in consequence of his conversion to
+the Copernican theory of the earth's motion, and thence proceeded to
+study the attractions produced by amber. An account of his electrical
+discoveries is given in the _De magnete_, lib. ii. cap. 2.[2] He
+invented the _versorium_ or electrical needle and proved that
+innumerable bodies he called _electrica_, when rubbed, can attract the
+needle of the versorium (see ELECTROSCOPE). Robert Boyle added many new
+facts and gave an account of them in his book, _The Origin of
+Electricity_. He showed that the attraction between the rubbed body and
+the test object is mutual. Otto von Guericke (1602-1686) constructed the
+first electrical machine with a revolving ball of sulphur (see
+ELECTRICAL MACHINE), and noticed that light objects were repelled after
+being attracted by excited electrics. Sir Isaac Newton substituted a
+ball of glass for sulphur in the electrical machine and made other not
+unimportant additions to electrical knowledge. Francis Hawksbee (d.
+1713) published in his book _Physico-Mechanical Experiments_ (1709), and
+in several Memoirs in the _Phil. Trans._ about 1707, the results of his
+electrical inquiries. He showed that light was produced when mercury was
+shaken up in a glass tube exhausted of its air. Dr Wall observed the
+spark and crackling sound when warm amber was rubbed, and compared them
+with thunder and lightning (_Phil. Trans._, 1708, 26, p. 69). Stephen
+Gray (1696-1736) noticed in 1720 that electricity could be excited by
+the friction of hair, silk, wool, paper and other bodies. In 1729 Gray
+made the important discovery that some bodies were conductors and others
+non-conductors of electricity. In conjunction with his friend Granville
+Wheeler (d. 1770), he conveyed the electricity from rubbed glass, a
+distance of 886 ft., along a string supported on silk threads (_Phil.
+Trans._, 1735-1736, 39, pp. 16, 166 and 400). Jean Théophile Desaguliers
+(1683-1744) announced soon after that electrics were non-conductors, and
+conductors were non-electrics. C.F. de C. du Fay (1699-1739) made the
+great discovery that electricity is of two kinds, vitreous and resinous
+(_Phil. Trans._, 1733, 38, p. 263), the first being produced when glass,
+crystal, &c. are rubbed with silk, and the second when resin, amber,
+silk or paper, &c. are excited by friction with flannel. He also
+discovered that a body charged with positive or negative electricity
+repels a body free to move when the latter is charged with electricity
+of like sign, but attracts it if it is charged with electricity of
+opposite sign, i.e. positive repels positive and negative repels
+negative, but positive attracts negative. It is to du Fay also that we
+owe the abolition of the distinction between electrics and
+non-electrics. He showed that all substances could be electrified by
+friction, but that to electrify conductors they must be insulated or
+supported on non-conductors. Various improvements were made in the
+electrical machine, and thereby experimentalists were provided with the
+means of generating strong electrification; C.F. Ludolff (1707-1763) of
+Berlin in 1744 succeeded in igniting ether with the electric spark
+(_Phil. Trans._, 1744, 43, p. 167).
+
+  For a very full list of the papers and works of these early electrical
+  philosophers, the reader is referred to the bibliography on
+  Electricity in Dr Thomas Young's _Natural Philosophy_, vol. ii. p.
+  415.
+
+In 1745 the important invention of the Leyden jar or condenser was made
+by E.G. von Kleist of Kammin, and almost simultaneously by Cunaeus and
+Pieter van Musschenbroek (1692-1761) of Leiden (see LEYDEN JAR). Sir
+William Watson (1715-1787) in England first observed the flash of light
+when a Leyden jar is discharged, and he and Dr John Bevis (1695-1771)
+suggested coating the jar inside and outside with tinfoil. Watson
+carried out elaborate experiments to discover how far the electric
+discharge of the jar could be conveyed along metallic wires and was able
+to accomplish it for a distance of 2 m., making the important
+observation that the electricity appeared to be transmitted
+instantaneously.
+
+_Franklin's Researches._--Benjamin Franklin (1706-1790) was one of the
+great pioneers of electrical science, and made the ever-memorable
+experimental identification of lightning and electric spark. He argued
+that electricity is not created by friction, but merely collected from
+its state of diffusion through other matter by which it is attracted. He
+asserted that the glass globe, when rubbed, attracted the electrical
+fire, and took it from the rubber, the same globe being disposed, when
+the friction ceases, to give out its electricity to any body which has
+less. In the case of the charged Leyden jar, he asserted that the inner
+coating of tinfoil had received more than its ordinary quantity of
+electricity, and was therefore electrified positively, or plus, while
+the outer coating of tinfoil having had its ordinary quantity of
+electricity diminished, was electrified negatively, or minus. Hence the
+cause of the shock and spark when the jar is discharged, or when the
+superabundant or plus electricity of the inside is transferred by a
+conducting body to the defective or minus electricity of the outside.
+This theory of the Leyden phial Franklin supported very ingeniously by
+showing that the outside and the inside coating possessed electricities
+of opposite sign, and that, in charging it, exactly as much electricity
+is added on one side as is subtracted from the other. The abundant
+discharge of electricity by points was observed by Franklin is his
+earliest experiments, and also the power of points to conduct it
+copiously from an electrified body. Hence he was furnished with a simple
+method of collecting electricity from other bodies, and he was enabled
+to perform those remarkable experiments which are chiefly connected with
+his name. Hawksbee, Wall and J.A. Nollet (1700-1770) had successively
+suggested the identity of lightning and the electric spark, and of
+thunder and the snap of the spark. Previously to the year 1750, Franklin
+drew up a statement, in which he showed that all the general phenomena
+and effects which were produced by electricity had their counterparts in
+lightning. After waiting some time for the erection of a spire at
+Philadelphia, by means of which he hoped to bring down the electricity
+of a thunderstorm, he conceived the idea of sending up a kite among
+thunder-clouds. With this view he made a small cross of two small light
+strips of cedar, the arms being sufficiently long to reach to the four
+corners of a large thin silk handkerchief when extended. The corners of
+the handkerchief were tied to the extremities of the cross, and when the
+body of the kite was thus formed, a tail, loop and string were added to
+it. The body was made of silk to enable it to bear the violence and wet
+of a thunderstorm. A very sharp pointed wire was fixed at the top of the
+upright stick of the cross, so as to rise a foot or more above the wood.
+A silk ribbon was tied to the end of the twine next the hand, and a key
+suspended at the junction of the twine and silk. In company with his
+son, Franklin raised the kite like a common one, in the first
+thunderstorm, which happened in the month of June 1752. To keep the silk
+ribbon dry, he stood within a door, taking care that the twine did not
+touch the frame of the door; and when the thunder-clouds came over the
+kite he watched the state of the string. A cloud passed without any
+electrical indications, and he began to despair of success. At last,
+however, he saw the loose filaments of the twine standing out every way,
+and he found them to be attracted by the approach of his finger. The
+suspended key gave a spark on the application of his knuckle, and when
+the string had become wet with the rain the electricity became abundant.
+A Leyden jar was charged at the key, and by the electric fire thus
+obtained spirits were inflamed, and many other experiments performed
+which had been formerly made by excited electrics. In subsequent trials
+with another apparatus, he found that the clouds were sometimes
+positively and sometimes negatively electrified, and so demonstrated the
+perfect identity of lightning and electricity. Having thus succeeded in
+drawing the electric fire from the clouds, Franklin conceived the idea
+of protecting buildings from lightning by erecting on their highest
+parts pointed iron wires or conductors communicating with the ground.
+The electricity of a hovering or a passing cloud would thus be carried
+off slowly and silently; and if the cloud was highly charged, the
+lightning would strike in preference the elevated conductors.[3] The
+most important of Franklin's electrical writings are his _Experiments
+and Observations on Electricity made at Philadelphia_, 1751-1754; his
+_Letters on Electricity_; and various memoirs and letters in the _Phil.
+Trans._ from 1756 to 1760.
+
+About the same time that Franklin was making his kite experiment in
+America, T.F. Dalibard (1703-1779) and others in France had erected a
+long iron rod at Marli, and obtained results agreeing with those of
+Franklin. Similar investigations were pursued by many others, among whom
+Father G.B. Beccaria (1716-1781) deserves especial mention. John Canton
+(1718-1772) made the important contribution to knowledge that
+electricity of either sign could be produced on nearly any body by
+friction with appropriate substances, and that a rod of glass roughened
+on one half was excited negatively in the rough part and positively in
+the smooth part by friction with the same rubber. Canton first suggested
+the use of an amalgam of mercury and tin for use with glass cylinder
+electrical machines to improve their action. His most important
+discovery, however, was that of electrostatic induction, the fact that
+one electrified body can produce charges of electricity upon another
+insulated body, and that when this last is touched it is left
+electrified with a charge of opposite sign to that of the inducing
+charge (_Phil. Trans._, 1753-1754). We shall make mention lower down of
+Canton's contributions to electrical theory. Robert Symmer (d. 1763)
+showed that quite small differences determined the sign of the
+electrification that was generated by the friction of two bodies one
+against the other. Thus wearing a black and a white silk stocking one
+over the other, he found they were electrified oppositely when rubbed
+and drawn off, and that such a rubbed silk stocking when deposited in a
+Leyden jar gave up its electrification to the jar (_Phil. Trans._,
+1759). Ebenezer Kinnersley (1711-1778) of Philadelphia made useful
+observations on the elongation and fusion of iron wires by electrical
+discharges (_Phil. Trans._, 1763). A contemporary of Canton and
+co-discoverer with him of the facts of electrostatic induction was the
+Swede, Johann Karl Wilcke (1732-1796), then resident in Germany, who in
+1762 published an account of experiments in which a metal plate held
+above the upper surface of a glass table was subjected to the action of
+a charge on an electrified metal plate held below the glass (_Kon.
+Schwedische Akad. Abhandl._, 1762, 24, p. 213).
+
+_Pyro-electricity._--The subject of pyro-electricity, or the power
+possessed by some minerals of becoming electrified when merely heated,
+and of exhibiting positive and negative electricity, now began to
+attract notice. It is possible that the _lyncurium_ of the ancients,
+which according to Theophrastus attracted light bodies, was tourmaline,
+a mineral found in Ceylon, which had been christened by the Dutch with
+the name of _aschentrikker_, or the attractor of ashes. In 1717 Louis
+Lémery exhibited to the Paris Academy of Sciences a stone from Ceylon
+which attracted light bodies; and Linnaeus in mentioning his experiments
+gives the stone the name of _lapis electricus_. Giovanni Caraffa, duca
+di Noja (1715-1768), was led in 1758 to purchase some of the stones
+called tourmaline in Holland, and, assisted by L.J.M. Daubenton and
+Michel Adanson, he made a series of experiments with them, a description
+of which he gave in a letter to G.L.L. Buffon in 1759. The subject,
+however, had already engaged the attention of the German philosopher,
+F.U.T. Aepinus, who published an account of them in 1756. Hitherto
+nothing had been said respecting the necessity of heat to excite the
+tourmaline; but it was shown by Aepinus that a temperature between 99½°
+and 212° Fahr. was requisite for the development of its attractive
+powers. Benjamin Wilson (_Phil. Trans._, 1763, &c.), J. Priestley, and
+Canton continued the investigation, but it was reserved for the Abbé
+Haüy to throw a clear light on this curious branch of the science
+(_Traité de minéralogie_, 1801). He found that the electricity of the
+tourmaline decreased rapidly from the summits or poles towards the
+middle of the crystal, where it was imperceptible; and he discovered
+that if a tourmaline is broken into any number of fragments, each
+fragment, when excited, has two opposite poles. Haüy discovered the same
+property in the Siberian and Brazilian topaz, borate of magnesia,
+mesotype, prehnite, sphene and calamine. He also found that the polarity
+which minerals receive from heat has a relation to the secondary forms
+of their crystals--the tourmaline, for example, having its resinous pole
+at the summit of the crystal which has three faces. In the other
+pyro-electric crystals above mentioned, Haüy detected the same deviation
+from the rules of symmetry in their secondary crystals which occurs in
+tourmaline. C.P. Brard (1788-1838) discovered that pyro-electricity was
+a property of axinite; and it was afterwards detected in other minerals.
+In repeating and extending the experiments of Haüy much later, Sir David
+Brewster discovered that various artificial salts were pyro-electric,
+and he mentions the tartrates of potash and soda and tartaric acid as
+exhibiting this property in a very strong degree. He also made many
+experiments with the tourmaline when cut into thin slices, and reduced
+to the finest powder, in which state each particle preserved its
+pyro-electricity; and he showed that scolezite and mesolite, even when
+deprived of their water of crystallization and reduced to powder, retain
+their property of becoming electrical by heat. When this white powder is
+heated and stirred about by any substance whatever, it collects in
+masses like new-fallen snow, and adheres to the body with which it is
+stirred.
+
+  For Sir David Brewster's work on pyro-electricity, see _Trans. Roy.
+  Soc. Edin._, 1845, also _Phil. Mag._, Dec. 1847. The reader will also
+  find a full discussion on the subject in the _Treatise on
+  Electricity_, by A. de la Rive, translated by C.V. Walker (London,
+  1856), vol. ii. part v. ch. i.
+
+_Animal electricity._--The observation that certain animals could give
+shocks resembling the shock of a Leyden jar induced a closer examination
+of these powers. The ancients were acquainted with the benumbing power
+of the torpedo-fish, but it was not till 1676 that modern naturalists
+had their attention again drawn to the fact. E. Bancroft was the first
+person who distinctly suspected that the effects of the torpedo were
+electrical. In 1773 John Walsh (d. 1795) and Jan Ingenhousz (1730-1799)
+proved by many curious experiments that the shock of the torpedo was an
+electrical one (_Phil. Trans._, 1773-1775); and John Hunter (id. 1773,
+1775) examined and described the anatomical structure of its electrical
+organs. A. von Humboldt and Gay-Lussac (_Ann. Chim._, 1805), and Etienne
+Geoffroy Saint-Hilaire (_Gilb. Ann._, 1803) pursued the subject with
+success; and Henry Cavendish (_Phil. Trans._, 1776) constructed an
+artificial torpedo, by which he imitated the actions of the living
+animal. The subject was also investigated (_Phil. Trans._, 1812, 1817)
+by Dr T.J. Todd (1789-1840), Sir Humphry Davy (id. 1829), John Davy (id.
+1832, 1834, 1841) and Faraday (_Exp. Res._, vol. ii.). The power of
+giving electric shocks has been discovered also in the _Gymnotus
+electricus_ (electric eel), the _Malapterurus electricus_, the
+_Trichiurus electricus_, and the _Tetraodon electricus_. The most
+interesting and the best known of these singular fishes is the
+_Gymnotus_ or Surinam eel. Humboldt gives a very graphic account of the
+combats which are carried on in South America between the gymnoti and
+the wild horses in the vicinity of Calabozo.
+
+_Cavendish's Researches._--The work of Henry Cavendish (1731-1810)
+entitles him to a high place in the list of electrical investigators. A
+considerable part of Cavendish's work was rescued from oblivion in 1879
+and placed in an easily accessible form by Professor Clerk Maxwell, who
+edited the original manuscripts in the possession of the duke of
+Devonshire.[4] Amongst Cavendish's important contributions were his
+exact measurements of electrical capacity. The leading idea which
+distinguishes his work from that of his predecessors was his use of the
+phrase "degree of electrification" with a clear scientific definition
+which shows it to be equivalent in meaning to the modern term "electric
+potential." Cavendish compared the capacity of different bodies with
+those of conducting spheres of known diameter and states these
+capacities in "globular inches," a globular inch being the capacity of a
+sphere 1 in. in diameter. Hence his measurements are all directly
+comparable with modern electrostatic measurements in which the unit of
+capacity is that of a sphere 1 centimetre in radius. Cavendish measured
+the capacity of disks and condensers of various forms, and proved that
+the capacity of a Leyden pane is proportional to the surface of the
+tinfoil and inversely as the thickness of the glass. In connexion with
+this subject he anticipated one of Faraday's greatest discoveries,
+namely, the effect of the dielectric or insulator upon the capacity of a
+condenser formed with it, in other words, made the discovery of specific
+inductive capacity (see _Electrical Researches_, p. 183). He made many
+measurements of the electric conductivity of different solids and
+liquids, by comparing the intensity of the electric shock taken through
+his body and various conductors. He seems in this way to have educated
+in himself a very precise "electrical sense," making use of his own
+nervous system as a kind of physiological galvanometer. One of the most
+important investigations he made in this way was to find out, as he
+expressed it, "what power of the velocity the resistance is proportional
+to." Cavendish meant by the term "velocity" what we now call the
+current, and by "resistance" the electromotive force which maintains the
+current. By various experiments with liquids in tubes he found this
+power was nearly unity. This result thus obtained by Cavendish in
+January 1781, that the current varies in direct proportion to the
+electromotive force, was really an anticipation of the fundamental law
+of electric flow, discovered independently by G.S. Ohm in 1827, and
+since known as Ohm's Law. Cavendish also enunciated in 1776 all the laws
+of division of electric current between circuits in parallel, although
+they are generally supposed to have been first given by Sir C.
+Wheatstone. Another of his great investigations was the determination of
+the law according to which electric force varies with the distance.
+Starting from the fact that if an electrified globe, placed within two
+hemispheres which fit over it without touching, is brought in contact
+with these hemispheres, it gives up the whole of its charge to them--in
+other words, that the charge on an electrified body is wholly on the
+surface--he was able to deduce by most ingenious reasoning the law that
+electric force varies inversely as the square of the distance. The
+accuracy of his measurement, by which he established within 2% the above
+law, was only limited by the sensibility, or rather insensibility, of
+the pith ball electrometer, which was his only means of detecting the
+electric charge.[5] In the accuracy of his quantitative measurements and
+the range of his researches and his combination of mathematical and
+physical knowledge, Cavendish may not inaptly be described as the Kelvin
+of the 18th century. Nothing but his curious indifference to the
+publication of his work prevented him from securing earlier recognition
+for it.
+
+_Coulomb's Work._--Contemporary with Cavendish was C.A. Coulomb
+(1736-1806), who in France addressed himself to the same kind of exact
+quantitative work as Cavendish in England. Coulomb has made his name for
+ever famous by his invention and application of his torsion balance to
+the experimental verification of the fundamental law of electric
+attraction, in which, however, he was anticipated by Cavendish, namely,
+that the force of attraction between two small electrified spherical
+bodies varies as the product of their charges and inversely as the
+square of the distance of their centres. Coulomb's work received better
+publication than Cavendish's at the time of its accomplishment, and
+provided a basis on which mathematicians could operate. Accordingly the
+close of the 18th century drew into the arena of electrical
+investigation on its mathematical side P.S. Laplace, J.B. Biot, and
+above all, S.D. Poisson. Adopting the hypothesis of two fluids, Coulomb
+investigated experimentally and theoretically the distribution of
+electricity on the surface of bodies by means of his proof plane. He
+determined the law of distribution between two conducting bodies in
+contact; and measured with his proof plane the density of the
+electricity at different points of two spheres in contact, and
+enunciated an important law. He ascertained the distribution of
+electricity among several spheres (whether equal or unequal) placed in
+contact in a straight line; and he measured the distribution of
+electricity on the surface of a cylinder, and its distribution between
+a sphere and cylinder of different lengths but of the same diameter. His
+experiments on the dissipation of electricity possess also a high value.
+He found that the momentary dissipation was proportional to the degree
+of electrification at the time, and that, when the charge was moderate,
+its dissipation was not altered in bodies of different kinds or shapes.
+The temperature and pressure of the atmosphere did not produce any
+sensible change; but he concluded that the dissipation was nearly
+proportional to the cube of the quantity of moisture in the air.[6] In
+examining the dissipation which takes place along imperfectly insulating
+substances, he found that a thread of gum-lac was the most perfect of
+all insulators; that it insulated ten times as well as a dry silk
+thread; and that a silk thread covered with fine sealing-wax insulated
+as powerfully as gum-lac when it had four times its length. He found
+also that the dissipation of electricity along insulators was chiefly
+owing to adhering moisture, but in some measure also to a slight
+conducting power. For his memoirs see _Mém. de math. et phys. de l'acad.
+de sc._, 1785, &c.
+
+SECOND PERIOD.--We now enter upon the second period of electrical
+research inaugurated by the epoch-making discovery of Alessandro Volta
+(1745-1827). L. Galvani had made in 1790 his historic observations on
+the muscular contraction produced in the bodies of recently killed frogs
+when an electrical machine was being worked in the same room, and
+described them in 1791 (_De viribus electricitatis in motu musculari
+commentarius_, Bologna, 1791). Volta followed up these observations with
+rare philosophic insight and experimental skill. He showed that all
+conductors liquid and solid might be divided into two classes which he
+called respectively conductors of the first and of the second class, the
+first embracing metals and carbon in its conducting form, and the second
+class, water, aqueous solutions of various kinds, and generally those
+now called electrolytes. In the case of conductors of the first class he
+proved by the use of the condensing electroscope, aided probably by some
+form of multiplier or doubler, that a difference of potential (see
+ELECTROSTATICS) was created by the mere contact of two such conductors,
+one of them being positively electrified and the other negatively. Volta
+showed, however, that if a series of bodies of the first class, such as
+disks of various metals, are placed in contact, the potential difference
+between the first and the last is just the same as if they are
+immediately in contact. There is no accumulation of potential. If,
+however, pairs of metallic disks, made, say, of zinc and copper, are
+alternated with disks of cloth wetted with a conductor of the second
+class, such, for instance, as dilute acid or any electrolyte, then the
+effect of the feeble potential difference between one pair of copper and
+zinc disks is added to that of the potential difference between the next
+pair, and thus by a sufficiently long series of pairs any required
+difference of potential can be accumulated.
+
+_The Voltaic Pile._--This led him about 1799 to devise his famous
+voltaic pile consisting of disks of copper and zinc or other metals with
+wet cloth placed between the pairs. Numerous examples of Volta's
+original piles at one time existed in Italy, and were collected together
+for an exhibition held at Como in 1899, but were unfortunately destroyed
+by a disastrous fire on the 8th of July 1899. Volta's description of his
+pile was communicated in a letter to Sir Joseph Banks, president of the
+Royal Society of London, on the 20th of March 1800, and was printed in
+the _Phil. Trans._, vol. 90, pt. 1, p. 405. It was then found that when
+the end plates of Volta's pile were connected to an electroscope the
+leaves diverged either with positive or negative electricity. Volta also
+gave his pile another form, the _couronne des tasses_ (crown of cups),
+in which connected strips of copper and zinc were used to bridge between
+cups of water or dilute acid. Volta then proved that all metals could be
+arranged in an electromotive series such that each became positive when
+placed in contact with the one next below it in the series. The origin
+of the electromotive force in the pile has been much discussed, and
+Volta's discoveries gave rise to one of the historic controversies of
+science. Volta maintained that the mere contact of metals was sufficient
+to produce the electrical difference of the end plates of the pile. The
+discovery that chemical action was involved in the process led to the
+advancement of the chemical theory of the pile and this was strengthened
+by the growing insight into the principle of the conservation of energy.
+In 1851 Lord Kelvin (Sir W. Thomson), by the use of his then
+newly-invented electrometer, was able to confirm Volta's observations on
+contact electricity by irrefutable evidence, but the contact theory of
+the voltaic pile was then placed on a basis consistent with the
+principle of the conservation of energy. A.A. de la Rive and Faraday
+were ardent supporters of the chemical theory of the pile, and even at
+the present time opinions of physicists can hardly be said to be in
+entire accordance as to the source of the electromotive force in a
+voltaic couple or pile.[7]
+
+Improvements in the form of the voltaic pile were almost immediately
+made by W. Cruickshank (1745-1800), Dr W.H. Wollaston and Sir H. Davy,
+and these, together with other eminent continental chemists, such as
+A.F. de Fourcroy, L.J. Thénard and J.W. Ritter (1776-1810), ardently
+prosecuted research with the new instrument. One of the first
+discoveries made with it was its power to electrolyse or chemically
+decompose certain solutions. William Nicholson (1753-1815) and Sir
+Anthony Carlisle (1768-1840) in 1800 constructed a pile of silver and
+zinc plates, and placing the terminal wires in water noticed the
+evolution from these wires of bubbles of gas, which they proved to be
+oxygen and hydrogen. These two gases, as Cavendish and James Watt had
+shown in 1784, were actually the constituents of water. From that date
+it was clearly recognized that a fresh implement of great power had been
+given to the chemist. Large voltaic piles were then constructed by
+Andrew Crosse (1784-1855) and Sir H. Davy, and improvements initiated by
+Wollaston and Robert Hare (1781-1858) of Philadelphia. In 1806 Davy
+communicated to the Royal Society of London a celebrated paper on some
+"Chemical Agencies of Electricity," and after providing himself at the
+Royal Institution of London with a battery of several hundred cells, he
+announced in 1807 his great discovery of the electrolytic decomposition
+of the alkalis, potash and soda, obtaining therefrom the metals
+potassium and sodium. In July 1808 Davy laid a request before the
+managers of the Royal Institution that they would set on foot a
+subscription for the purchase of a specially large voltaic battery; as a
+result he was provided with one of 2000 pairs of plates, and the first
+experiment performed with it was the production of the electric arc
+light between carbon poles. Davy followed up his initial work with a
+long and brilliant series of electrochemical investigations described
+for the most part in the _Phil. Trans._ of the Royal Society.
+
+_Magnetic Action of Electric Current._--Noticing an analogy between the
+polarity of the voltaic pile and that of the magnet, philosophers had
+long been anxious to discover a relation between the two, but twenty
+years elapsed after the invention of the pile before Hans Christian
+Oersted (1777-1851), professor of natural philosophy in the university
+of Copenhagen, made in 1819 the discovery which has immortalized his
+name. In the _Annals of Philosophy_ (1820, 16, p. 273) is to be found an
+English translation of Oersted's original Latin essay (entitled
+"Experiments on the Effect of a Current of Electricity on the Magnetic
+Needle"), dated the 21st of July 1820, describing his discovery. In it
+Oersted describes the action he considers is taking place around the
+conductor joining the extremities of the pile; he speaks of it as the
+electric conflict, and says: "It is sufficiently evident that the
+electric conflict is not confined to the conductor, but is dispersed
+pretty widely in the circumjacent space. We may likewise conclude that
+this conflict performs circles round the wire, for without this
+condition it seems impossible that one part of the wire when placed
+below the magnetic needle should drive its pole to the east, and when
+placed above it, to the west." Oersted's important discovery was the
+fact that when a wire joining the end plates of a voltaic pile is held
+near a pivoted magnet or compass needle, the latter is deflected and
+places itself more or less transversely to the wire, the direction
+depending upon whether the wire is above or below the needle, and on the
+manner in which the copper or zinc ends of the pile are connected to it.
+It is clear, moreover, that Oersted clearly recognized the existence of
+what is now called the magnetic field round the conductor. This
+discovery of Oersted, like that of Volta, stimulated philosophical
+investigation in a high degree.
+
+_Electrodynamics._--On the 2nd of October 1820, A.M. Ampère presented to
+the French Academy of Sciences an important memoir,[8] in which he
+summed up the results of his own and D.F.J. Arago's previous
+investigations in the new science of electromagnetism, and crowned that
+labour by the announcement of his great discovery of the dynamical
+action between conductors conveying the electric currents. Ampère in
+this paper gave an account of his discovery that conductors conveying
+electric currents exercise a mutual attraction or repulsion on one
+another, currents flowing in the same direction in parallel conductors
+attracting, and those in opposite directions repelling. Respecting this
+achievement when developed in its experimental and mathematical
+completeness, Clerk Maxwell says that it was "perfect in form and
+unassailable in accuracy." By a series of well-chosen experiments Ampère
+established the laws of this mutual action, and not only explained
+observed facts by a brilliant train of mathematical analysis, but
+predicted others subsequently experimentally realized. These
+investigations led him to the announcement of the fundamental law of
+action between elements of current, or currents in infinitely short
+lengths of linear conductors, upon one another at a distance; summed up
+in compact expression this law states that the action is proportional to
+the product of the current strengths of the two elements, and the
+lengths of the two elements, and inversely proportional to the square of
+the distance between the two elements, and also directly proportional to
+a function of the angles which the line joining the elements makes with
+the directions of the two elements respectively. Nothing is more
+remarkable in the history of discovery than the manner in which Ampère
+seized upon the right clue which enabled him to disentangle the
+complicated phenomena of electrodynamics and to deduce them all as a
+consequence of one simple fundamental law, which occupies in
+electrodynamics the position of the Newtonian law of gravitation in
+physical astronomy.
+
+In 1821 Michael Faraday (1791-1867), who was destined later on to do so
+much for the science of electricity, discovered electromagnetic
+rotation, having succeeded in causing a wire conveying a voltaic current
+to rotate continuously round the pole of a permanent magnet.[9] This
+experiment was repeated in a variety of forms by A.A. De la Rive, Peter
+Barlow (1776-1862), William Ritchie (1790-1837), William Sturgeon
+(1783-1850), and others; and Davy (_Phil. Trans._, 1823) showed that
+when two wires connected with the pole of a battery were dipped into a
+cup of mercury placed on the pole of a powerful magnet, the fluid
+rotated in opposite directions about the two electrodes.
+
+_Electromagnetism._--In 1820 Arago (_Ann. Chim. Phys._, 1820, 15, p. 94)
+and Davy (_Annals of Philosophy_, 1821) discovered independently the
+power of the electric current to magnetize iron and steel. Félix Savary
+(1797-1841) made some very curious observations in 1827 on the
+magnetization of steel needles placed at different distances from a wire
+conveying the discharge of a Leyden jar (_Ann. Chim. Phys._, 1827, 34).
+W. Sturgeon in 1824 wound a copper wire round a bar of iron bent in the
+shape of a horseshoe, and passing a voltaic current through the wire
+showed that the iron became powerfully magnetized as long as the
+connexion with the pile was maintained (_Trans. Soc. Arts_, 1825). These
+researches gave us the electromagnet, almost as potent an instrument of
+research and invention as the pile itself (see ELECTROMAGNETISM).
+
+Ampère had already previously shown that a spiral conductor or solenoid
+when traversed by an electric current possesses magnetic polarity, and
+that two such solenoids act upon one another when traversed by electric
+currents as if they were magnets. Joseph Henry, in the United States,
+first suggested the construction of what were then called intensity
+electromagnets, by winding upon a horseshoe-shaped piece of soft iron
+many superimposed windings of copper wire, insulated by covering it with
+silk or cotton, and then sending through the coils the current from a
+voltaic battery. The dependence of the intensity of magnetization on the
+strength of the current was subsequently investigated (_Pogg. Ann.
+Phys._, 1839, 47) by H.F.E. Lenz (1804-1865) and M.H. von Jacobi
+(1801-1874). J.P. Joule found that magnetization did not increase
+proportionately with the current, but reached a maximum (_Sturgeon's
+Annals of Electricity_, 1839, 4). Further investigations on this subject
+were carried on subsequently by W.E. Weber (1804-1891), J.H.J. Müller
+(1809-1875), C.J. Dub (1817-1873), G.H. Wiedemann (1826-1899), and
+others, and in modern times by H.A. Rowland (1848-1901), Shelford
+Bidwell (b. 1848), John Hopkinson (1849-1898), J.A. Ewing (b. 1855) and
+many others. Electric magnets of great power were soon constructed in
+this manner by Sturgeon, Joule, Henry, Faraday and Brewster. Oersted's
+discovery in 1819 was indeed epoch-making in the degree to which it
+stimulated other research. It led at once to the construction of the
+galvanometer as a means of detecting and measuring the electric current
+in a conductor. In 1820 J.S.C. Schweigger (1779-1857) with his
+"multiplier" made an advance upon Oersted's discovery, by winding the
+wire conveying the electric current many times round the pivoted
+magnetic needle and thus increasing the deflection; and L. Nobili
+(1784-1835) in 1825 conceived the ingenious idea of neutralizing the
+directive effect of the earth's magnetism by employing a pair of
+magnetized steel needles fixed to one axis, but with their magnetic
+poles pointing in opposite directions. Hence followed the astatic
+multiplying galvanometer.
+
+_Electrodynamic Rotation._--The study of the relation between the magnet
+and the circuit conveying an electric current then led Arago to the
+discovery of the "magnetism of rotation." He found that a vibrating
+magnetic compass needle came to rest sooner when placed over a plate of
+copper than otherwise, and also that a plate of copper rotating under a
+suspended magnet tended to drag the magnet in the same direction. The
+matter was investigated by Charles Babbage, Sir J.F.W. Herschel, Peter
+Barlow and others, but did not receive a final explanation until after
+the discovery of electromagnetic induction by Faraday in 1831. Ampère's
+investigations had led electricians to see that the force acting upon a
+magnetic pole due to a current in a neighbouring conductor was such as
+to tend to cause the pole to travel round the conductor. Much ingenuity
+had, however, to be expended before a method was found of exhibiting
+such a rotation. Faraday first succeeded by the simple but ingenious
+device of using a light magnetic needle tethered flexibly to the bottom
+of a cup containing mercury so that one pole of the magnet was just
+above the surface of the mercury. On bringing down on to the mercury
+surface a wire conveying an electric current, and allowing the current
+to pass through the mercury and out at the bottom, the magnetic pole at
+once began to rotate round the wire (_Exper. Res._, 1822, 2, p. 148).
+Faraday and others then discovered, as already mentioned, means to make
+the conductor conveying the current rotate round a magnetic pole, and
+Ampère showed that a magnet could be made to rotate on its own axis when
+a current was passed through it. The difficulty in this case consisted
+in discovering means by which the current could be passed through one
+half of the magnet without passing it through the other half. This,
+however, was overcome by sending the current out at the centre of the
+magnet by means of a short length of wire dipping into an annular groove
+containing mercury. Barlow, Sturgeon and others then showed that a
+copper disk could be made to rotate between the poles of a horseshoe
+magnet when a current was passed through the disk from the centre to the
+circumference, the disk being rendered at the same time freely movable
+by making a contact with the circumference by means of a mercury trough.
+These experiments furnished the first elementary forms of electric
+motor, since it was then seen that rotatory motion could be produced in
+masses of metal by the mutual action of conductors conveying electric
+current and magnetic fields. By his discovery of thermo-electricity in
+1822 (_Pogg. Ann. Phys._, 6), T.J. Seebeck (1770-1831) opened up a new
+region of research (see THERMOELECTRICITY). James Cumming (1777-1861) in
+1823 (_Annals of Philosophy_, 1823) found that the thermo-electric
+series varied with the temperature, and J.C.A. Peltier (1785-1845) in
+1834 discovered that a current passed across the junction of two metals
+either generated or absorbed heat.
+
+_Ohm's Law._--In 1827 Dr G.S. Ohm (1787-1854) rendered a great service
+to electrical science by his mathematical investigation of the voltaic
+circuit, and publication of his paper, _Die galvanische Kette
+mathematisch bearbeitet_. Before his time, ideas on the measurable
+quantities with which we are concerned in an electric circuit were
+extremely vague. Ohm introduced the clear idea of current strength as an
+effect produced by electromotive force acting as a cause in a circuit
+having resistance as its quality, and showed that the current was
+directly proportional to the electromotive force and inversely as the
+resistance. Ohm's law, as it is called, was based upon an analogy with
+the flow of heat in a circuit, discussed by Fourier. Ohm introduced the
+definite conception of the distribution along the circuit of
+"electroscopic force" or tension (_Spannung_), corresponding to the
+modern term potential. Ohm verified his law by the aid of
+thermo-electric piles as sources of electromotive force, and Davy,
+C.S.M. Pouillet (1791-1868), A.C. Becquerel (1788-1878), G.T. Fechner
+(1801-1887), R.H.A. Kohlrausch (1809-1858) and others laboured at its
+confirmation. In more recent times, 1876, it was rigorously tested by G.
+Chrystal (b. 1851) at Clerk Maxwell's instigation (see _Brit. Assoc.
+Report_, 1876, p. 36), and although at its original enunciation its
+meaning was not at first fully apprehended, it soon took its place as
+the expression of the fundamental law of electrokinetics.
+
+_Induction of Electric Currents._--In 1831 Faraday began the
+investigations on electromagnetic induction which proved more fertile in
+far-reaching practical consequences than any of those which even his
+genius gave to the world. These advances all centre round his supreme
+discovery of the induction of electric currents. Fully familiar with the
+fact that an electric charge upon one conductor could produce a charge
+of opposite sign upon a neighbouring conductor, Faraday asked himself
+whether an electric current passing through a conductor could not in any
+like manner induce an electric current in some neighbouring conductor.
+His first experiments on this subject were made in the month of November
+1825, but it was not until the 29th of August 1831 that he attained
+success. On that date he had provided himself with an iron ring, over
+which he had wound two coils of insulated copper wire. One of these
+coils was connected with the voltaic battery and the other with the
+galvanometer. He found that at the moment the current in the battery
+circuit was started or stopped, transitory currents appeared in the
+galvanometer circuit in opposite directions. In ten days of brilliant
+investigation, guided by clear insight from the very first into the
+meaning of the phenomena concerned, he established experimentally the
+fact that a current may be induced in a conducting circuit simply by the
+variation in a magnetic field, the lines of force of which are linked
+with that circuit. The whole of Faraday's investigations on this
+subject can be summed up in the single statement that if a conducting
+circuit is placed in a magnetic field, and if either by variation of the
+field or by movement or variation of the form of the circuit the total
+magnetic flux linked with the circuit is varied, an electromotive force
+is set up in that circuit which at any instant is measured by the rate
+at which the total flux linked with the circuit is changing.
+
+Amongst the memorable achievements of the ten days which Faraday devoted
+to this investigation was the discovery that a current could be induced
+in a conducting wire simply by moving it in the neighbourhood of a
+magnet. One form which this experiment took was that of rotating a
+copper disk between the poles of a powerful electric magnet. He then
+found that a conductor, the ends of which were connected respectively
+with the centre and edge of the disk, was traversed by an electric
+current. This important fact laid the foundation for all subsequent
+inventions which finally led to the production of electromagnetic or
+dynamo-electric machines.
+
+THIRD PERIOD.--With this supremely important discovery of Faraday's we
+enter upon the third period of electrical research, in which that
+philosopher himself was the leading figure. He not only collected the
+facts concerning electromagnetic induction so industriously that nothing
+of importance remained for future discovery, and embraced them all in
+one law of exquisite simplicity, but he introduced his famous conception
+of lines of force which changed entirely the mode of regarding
+electrical phenomena. The French mathematicians, Coulomb, Biot, Poisson
+and Ampère, had been content to accept the fact that electric charges or
+currents in conductors could exert forces on other charges or conductors
+at a distance without inquiring into the means by which this action at a
+distance was produced. Faraday's mind, however, revolted against this
+notion; he felt intuitively that these distance actions must be the
+result of unseen operations in the interposed medium. Accordingly when
+he sprinkled iron filings on a card held over a magnet and revealed the
+curvilinear system of lines of force (see MAGNETISM), he regarded these
+fragments of iron as simple indicators of a physical state in the space
+already in existence round the magnet. To him a magnet was not simply a
+bar of steel; it was the core and origin of a system of lines of
+magnetic force attached to it and moving with it. Similarly he came to
+see an electrified body as a centre of a system of lines of
+electrostatic force. All the space round magnets, currents and electric
+charges was therefore to Faraday the seat of corresponding lines of
+magnetic or electric force. He proved by systematic experiments that the
+electromotive forces set up in conductors by their motions in magnetic
+fields or by the induction of other currents in the field were due to
+the secondary conductor _cutting_ lines of magnetic force. He invented
+the term "electrotonic state" to signify the total magnetic flux due to
+a conductor conveying a current, which was linked with any secondary
+circuit in the field or even with itself.
+
+_Faraday's Researches._--Space compels us to limit our account of the
+scientific work done by Faraday in the succeeding twenty years, in
+elucidating electrical phenomena and adding to the knowledge thereon, to
+the very briefest mention. We must refer the reader for further
+information to his monumental work entitled _Experimental Researches on
+Electricity_, in three volumes, reprinted from the _Phil. Trans._
+between 1831 and 1851. Faraday divided these researches into various
+series. The 1st and 2nd concern the discovery of magneto-electric
+induction already mentioned. The 3rd series (1833) he devoted to
+discussion of the identity of electricity derived from various sources,
+frictional, voltaic, animal and thermal, and he proved by rigorous
+experiments the identity and similarity in properties of the electricity
+generated by these various methods. The 5th series (1833) is occupied
+with his electrochemical researches. In the 7th series (1834) he defines
+a number of new terms, such as electrolyte, electrolysis, anode and
+cathode, &c., in connexion with electrolytic phenomena, which were
+immediately adopted into the vocabulary of science. His most important
+contribution at this date was the invention of the voltameter and his
+enunciation of the laws of electrolysis. The voltameter provided a means
+of measuring quantity of electricity, and in the hands of Faraday and
+his successors became an appliance of fundamental importance. The 8th
+series is occupied with a discussion of the theory of the voltaic pile,
+in which Faraday accumulates evidence to prove that the source of the
+energy of the pile must be chemical. He returns also to this subject in
+the 16th series. In the 9th series (1834) he announced the discovery of
+the important property of electric conductors, since called their
+self-induction or inductance, a discovery in which, however, he was
+anticipated by Joseph Henry in the United States. The 11th series (1837)
+deals with electrostatic induction and the statement of the important
+fact of the specific inductive capacity of insulators or dielectrics.
+This discovery was made in November 1837 when Faraday had no knowledge
+of Cavendish's previous researches into this matter. The 19th series
+(1845) contains an account of his brilliant discovery of the rotation of
+the plane of polarized light by transparent dielectrics placed in a
+magnetic field, a relation which established for the first time a
+practical connexion between the phenomena of electricity and light. The
+20th series (1845) contains an account of his researches on the
+universal action of magnetism and diamagnetic bodies. The 22nd series
+(1848) is occupied with the discussion of magneto-crystallic force and
+the abnormal behaviour of various crystals in a magnetic field. In the
+25th series (1850) he made known his discovery of the magnetic character
+of oxygen gas, and the important principle that the terms paramagnetic
+and diamagnetic are relative. In the 26th series (1850) he returned to a
+discussion of magnetic lines of force, and illuminated the whole subject
+of the magnetic circuit by his transcendent insight into the intricate
+phenomena concerned. In 1855 he brought these researches to a conclusion
+by a general article on magnetic philosophy, having placed the whole
+subject of magnetism and electromagnetism on an entirely novel and solid
+basis. In addition to this he provided the means for studying the
+phenomena not only qualitatively, but also quantitatively, by the
+profoundly ingenious instruments he invented for that purpose.
+
+_Electrical Measurement._--Faraday's ideas thus pressed upon
+electricians the necessity for the quantitative measurement of
+electrical phenomena.[10] It has been already mentioned that Schweigger
+invented in 1820 the "multiplier," and Nobili in 1825 the astatic
+galvanometer. C.S.M. Pouillet in 1837 contributed the sine and tangent
+compass, and W.E. Weber effected great improvements in them and in the
+construction and use of galvanometers. In 1849 H. von Helmholtz devised
+a tangent galvanometer with two coils. The measurement of electric
+resistance then engaged the attention of electricians. By his Memoirs in
+the _Phil. Trans._ in 1843, Sir Charles Wheatstone gave a great impulse
+to this study. He invented the rheostat and improved the resistance
+balance, invented by S.H. Christie (1784-1865) in 1833, and subsequently
+called the Wheatstone Bridge. (See his _Scientific Papers_, published by
+the Physical Society of London, p. 129.) Weber about this date invented
+the electrodynamometer, and applied the mirror and scale method of
+reading deflections, and in co-operation with C.F. Gauss introduced a
+system of absolute measurement of electric and magnetic phenomena. In
+1846 Weber proceeded with improved apparatus to test Ampère's laws of
+electrodynamics. In 1845 H.G. Grassmann (1809-1877) published (_Pogg.
+Ann._ vol. 64) his "Neue Theorie der Electrodynamik," in which he gave
+an elementary law differing from that of Ampère but leading to the same
+results for closed circuits. In the same year F.E. Neumann published
+another law. In 1846 Weber announced his famous hypothesis concerning
+the connexion of electrostatic and electrodynamic phenomena. The work of
+Neumann and Weber had been stimulated by that of H.F.E. Lenz
+(1804-1865), whose researches (_Pogg. Ann._, 1834, 31; 1835, 34) among
+other results led him to the statement of the law by means of which the
+direction of the induced current can be predicted from the theory of
+Ampère, the rule being that the direction of the induced current is
+always such that its electrodynamic action tends to oppose the motion
+which produces it.
+
+Neumann in 1845 did for electromagnetic induction what Ampère did for
+electrodynamics, basing his researches upon the experimental laws of
+Lenz. He discovered a function, which has been called the potential of
+one circuit on another, from which he deduced a theory of induction
+completely in accordance with experiment. Weber at the same time deduced
+the mathematical laws of induction from his elementary law of electrical
+action, and with his improved instruments arrived at accurate
+verifications of the law of induction, which by this time had been
+developed mathematically by Neumann and himself. In 1849 G.R. Kirchhoff
+determined experimentally in a certain case the absolute value of the
+current induced by one circuit in another, and in the same year Erik
+Edland (1819-1888) made a series of careful experiments on the induction
+of electric currents which further established received theories. These
+labours laid the foundation on which was subsequently erected a complete
+system for the absolute measurement of electric and magnetic quantities,
+referring them all to the fundamental units of mass, length and time.
+Helmholtz gave at the same time a mathematical theory of induced
+currents and a valuable series of experiments in support of them (_Pogg.
+Ann._, 1851). This great investigator and luminous expositor just before
+that time had published his celebrated essay, _Die Erhaltung der Kraft_
+("The Conservation of Energy"), which brought to a focus ideas which had
+been accumulating in consequence of the work of J.P. Joule, J.R. von
+Mayer and others, on the transformation of various forms of physical
+energy, and in particular the mechanical equivalent of heat. Helmholtz
+brought to bear upon the subject not only the most profound mathematical
+attainments, but immense experimental skill, and his work in connexion
+with this subject is classical.
+
+_Lord Kelvin's Work._--About 1842 Lord Kelvin (then William Thomson)
+began that long career of theoretical and practical discovery and
+invention in electrical science which revolutionized every department of
+pure and applied electricity. His early contributions to electrostatics
+and electrometry are to be found described in his _Reprint of Papers on
+Electrostatics and Magnetism_ (1872), and his later work in his
+collected _Mathematical and Physical Papers_. By his studies in
+electrostatics, his elegant method of electrical images, his development
+of the theory of potential and application of the principle of
+conservation of energy, as well as by his inventions in connexion with
+electrometry, he laid the foundations of our modern knowledge of
+electrostatics. His work on the electrodynamic qualities of metals,
+thermo-electricity, and his contributions to galvanometry, were not less
+massive and profound. From 1842 onwards to the end of the 19th century,
+he was one of the great master workers in the field of electrical
+discovery and research.[11] In 1853 he published a paper "On Transient
+Electric Currents" (_Phil. Mag._, 1853 [4], 5, p. 393), in which he
+applied the principle of the conservation of energy to the discharge of
+a Leyden jar. He added definiteness to the idea of the self-induction or
+inductance of an electric circuit, and gave a mathematical expression
+for the current flowing out of a Leyden jar during its discharge. He
+confirmed an opinion already previously expressed by Helmholtz and by
+Henry, that in some circumstances this discharge is oscillatory in
+nature, consisting of an alternating electric current of high frequency.
+These theoretical predictions were confirmed and others, subsequently,
+by the work of B.W. Feddersen (b. 1832), C.A. Paalzow (b. 1823), and it
+was then seen that the familiar phenomena of the discharge of a Leyden
+jar provided the means of generating electric oscillations of very high
+frequency.
+
+_Telegraphy._--Turning to practical applications of electricity, we may
+note that electric telegraphy took its rise in 1820, beginning with a
+suggestion of Ampère immediately after Oersted's discovery. It was
+established by the work of Weber and Gauss at Göttingen in 1836, and
+that of C.A. Steinheil (1801-1870) of Munich, Sir W.F. Cooke (1806-1879)
+and Sir C. Wheatstone in England, Joseph Henry and S.F.B. Morse
+(1791-1872) in the United States in 1837. In 1845 submarine telegraphy
+was inaugurated by the laying of an insulated conductor across the
+English Channel by the brothers Brett, and their temporary success was
+followed by the laying in 1851 of a permanent Dover-Calais cable by T.R.
+Crampton. In 1856 the project for an Atlantic submarine cable took shape
+and the Atlantic Telegraph Company was formed with a capital of
+£350,000, with Sir Charles Bright as engineer-in-chief and E.O.W.
+Whitehouse as electrician. The phenomena connected with the propagation
+of electric signals by underground insulated wires had already engaged
+the attention of Faraday in 1854, who pointed out the Leyden-jar-like
+action of an insulated subterranean wire. Scientific and practical
+questions connected with the possibility of laying an Atlantic submarine
+cable then began to be discussed, and Lord Kelvin was foremost in
+developing true scientific knowledge on this subject, and in the
+invention of appliances for utilizing it. One of his earliest and most
+useful contributions (in 1858) was the invention of the mirror
+galvanometer. Abandoning the long and somewhat heavy magnetic needles
+that had been used up to that date in galvanometers, he attached to the
+back of a very small mirror made of microscopic glass a fragment of
+magnetized watch-spring, and suspended the mirror and needle by means of
+a cocoon fibre in the centre of a coil of insulated wire. By this simple
+device he provided a means of measuring small electric currents far in
+advance of anything yet accomplished, and this instrument proved not
+only most useful in pure scientific researches, but at the same time was
+of the utmost value in connexion with submarine telegraphy. The history
+of the initial failures and final success in laying the Atlantic cable
+has been well told by Mr. Charles Bright (see _The Story of the Atlantic
+Cable_, London, 1903).[12] The first cable laid in 1857 broke on the
+11th of August during laying. The second attempt in 1858 was successful,
+but the cable completed on the 5th of August 1858 broke down on the 20th
+of October 1858, after 732 messages had passed through it. The third
+cable laid in 1865 was lost on the 2nd of August 1865, but in 1866 a
+final success was attained and the 1865 cable also recovered and
+completed. Lord Kelvin's mirror galvanometer was first used in receiving
+signals through the short-lived 1858 cable. In 1867 he invented his
+beautiful siphon-recorder for receiving and recording the signals
+through long cables. Later, in conjunction with Prof. Fleeming Jenkin,
+he devised his automatic curb sender, an appliance for sending signals
+by means of punched telegraphic paper tape. Lord Kelvin's contributions
+to the science of exact electric measurement[13] were enormous. His
+ampere-balances, voltmeters and electrometers, and double bridge, are
+elsewhere described in detail (see AMPEREMETER; ELECTROMETER, and
+WHEATSTONE'S BRIDGE).
+
+_Dynamo._--The work of Faraday from 1831 to 1851 stimulated and
+originated an immense mass of scientific research, but at the same time
+practical inventors had not been slow to perceive that it was capable of
+purely technical application. Faraday's copper disk rotated between the
+poles of a magnet, and producing thereby an electric current, became the
+parent of innumerable machines in which mechanical energy was directly
+converted into the energy of electric currents. Of these machines,
+originally called magneto-electric machines, one of the first was
+devised in 1832 by H. Pixii. It consisted of a fixed horseshoe armature
+wound over with insulated copper wire in front of which revolved about a
+vertical axis a horseshoe magnet. Pixii, who invented the split tube
+commutator for converting the alternating current so produced into a
+continuous current in the external circuit, was followed by J. Saxton,
+E.M. Clarke, and many others in the development of the above-described
+magneto-electric machine. In 1857 E.W. Siemens effected a great
+improvement by inventing a shuttle armature and improving the shape of
+the field magnet. Subsequently similar machines with electromagnets were
+introduced by Henry Wilde (b. 1833), Siemens, Wheatstone, W. Ladd and
+others, and the principle of self-excitation was suggested by Wilde,
+C.F. Varley (1828-1883), Siemens and Wheatstone (see DYNAMO). These
+machines about 1866 and 1867 began to be constructed on a commercial
+scale and were employed in the production of the electric light. The
+discovery of electric-current induction also led to the production of
+the induction coil (q.v.), improved and brought to its present
+perfection by W. Sturgeon, E.R. Ritchie, N.J. Callan, H.D. Rühmkorff
+(1803-1877), A.H.L. Fizeau, and more recently by A. Apps and modern
+inventors. About the same time Fizeau and J.B.L. Foucault devoted
+attention to the invention of automatic apparatus for the production of
+Davy's electric arc (see LIGHTING: _ELECTRIC_), and these appliances in
+conjunction with magneto-electric machines were soon employed in
+lighthouse work. With the advent of large magneto-electric machines the
+era of electrotechnics was fairly entered, and this period, which may be
+said to terminate about 1867 to 1869, was consummated by the theoretical
+work of Clerk Maxwell.
+
+_Maxwell's Researches._--James Clerk Maxwell (1831-1879) entered on his
+electrical studies with a desire to ascertain if the ideas of Faraday,
+so different from those of Poisson and the French mathematicians, could
+be made the foundation of a mathematical method and brought under the
+power of analysis.[14] Maxwell started with the conception that all
+electric and magnetic phenomena are due to effects taking place in the
+dielectric or in the ether if the space be vacuous. The phenomena of
+light had compelled physicists to postulate a space-filling medium, to
+which the name ether had been given, and Henry and Faraday had long
+previously suggested the idea of an electromagnetic medium. The
+vibrations of this medium constitute the agency called light. Maxwell
+saw that it was unphilosophical to assume a multiplicity of ethers or
+media until it had been proved that one would not fulfil all the
+requirements. He formulated the conception, therefore, of electric
+charge as consisting in a displacement taking place in the dielectric or
+electromagnetic medium (see ELECTROSTATICS). Maxwell never committed
+himself to a precise definition of the physical nature of electric
+displacement, but considered it as defining that which Faraday had
+called the polarization in the insulator, or, what is equivalent, the
+number of lines of electrostatic force passing normally through a unit
+of area in the dielectric. A second fundamental conception of Maxwell
+was that the electric displacement whilst it is changing is in effect an
+electric current, and creates, therefore, magnetic force. The total
+current at any point in a dielectric must be considered as made up of
+two parts: first, the true conduction current, if it exists; and second,
+the rate of change of dielectric displacement. The fundamental fact
+connecting electric currents and magnetic fields is that the line
+integral of magnetic force taken once round a conductor conveying an
+electric current is equal to 4 [pi]-times the surface integral of the
+current density, or to 4 [pi]-times the total current flowing through
+the closed line round which the integral is taken (see ELECTROKINETICS).
+A second relation connecting magnetic and electric force is based upon
+Faraday's fundamental law of induction, that the rate of change of the
+total magnetic flux linked with a conductor is a measure of the
+electromotive force created in it (see ELECTROKINETICS). Maxwell also
+introduced in this connexion the notion of the vector potential.
+Coupling together these ideas he was finally enabled to prove that the
+propagation of electric and magnetic force takes place through space
+with a certain velocity determined by the dielectric constant and the
+magnetic permeability of the medium. To take a simple instance, if we
+consider an electric current as flowing in a conductor it is, as Oersted
+discovered, surrounded by closed lines of magnetic force. If we imagine
+the current in the conductor to be instantaneously reversed in
+direction, the magnetic force surrounding it would not be instantly
+reversed everywhere in direction, but the reversal would be propagated
+outwards through space with a certain velocity which Maxwell showed was
+inversely as the square root of the product of the magnetic permeability
+and the dielectric constant or specific inductive capacity of the
+medium.
+
+These great results were announced by him for the first time in a paper
+presented in 1864 to the Royal Society of London and printed in the
+_Phil. Trans._ for 1865, entitled "A Dynamical Theory of the
+Electromagnetic Field." Maxwell showed in this paper that the velocity
+of propagation of an electromagnetic impulse through space could also be
+determined by certain experimental methods which consisted in measuring
+the same electric quantity, capacity, resistance or potential in two
+ways. W.E. Weber had already laid the foundations of the absolute system
+of electric and magnetic measurement, and proved that a quantity of
+electricity could be measured either by the force it exercises upon
+another static or stationary quantity of electricity, or magnetically by
+the force this quantity of electricity exercises upon a magnetic pole
+when flowing through a neighbouring conductor. The two systems of
+measurement were called respectively the electrostatic and the
+electromagnetic systems (see UNITS, PHYSICAL). Maxwell suggested new
+methods for the determination of this ratio of the electrostatic to the
+electromagnetic units, and by experiments of great ingenuity was able to
+show that this ratio, which is also that of the velocity of the
+propagation of an electromagnetic impulse through space, is identical
+with that of light. This great fact once ascertained, it became clear
+that the notion that electric phenomena are affections of the
+luminiferous ether was no longer a mere speculation but a scientific
+theory capable of verification. An immediate deduction from Maxwell's
+theory was that in transparent dielectrics, the dielectric constant or
+specific inductive capacity should be numerically equal to the square of
+the refractive index for very long electric waves. At the time when
+Maxwell developed his theory the dielectric constants of only a few
+transparent insulators were known and these were for the most part
+measured with steady or unidirectional electromotive force. The only
+refractive indices which had been measured were the optical refractive
+indices of a number of transparent substances. Maxwell made a comparison
+between the optical refractive index and the dielectric constant of
+paraffin wax, and the approximation between the numerical values of the
+square of the first and that of the last was sufficient to show that
+there was a basis for further work. Maxwell's electric and magnetic
+ideas were gathered together in a great mathematical treatise on
+electricity and magnetism which was published in 1873.[15] This book
+stimulated in a most remarkable degree theoretical and practical
+research into the phenomena of electricity and magnetism. Experimental
+methods were devised for the further exact measurements of the
+electromagnetic velocity and numerous determinations of the dielectric
+constants of various solids, liquids and gases, and comparisons of these
+with the corresponding optical refractive indices were conducted. This
+early work indicated that whilst there were a number of cases in which
+the square of optical refractive index for long waves and the
+dielectric constant of the same substance were sufficiently close to
+afford an apparent confirmation of Maxwell's theory, yet in other cases
+there were considerable divergencies. L. Boltzmann (1844-1907) made a
+large number of determinations for solids and for gases, and the
+dielectric constants of many solid and liquid substances were determined
+by N.N. Schiller (b. 1848), P.A. Silow (b. 1850), J. Hopkinson and
+others. The accumulating determinations of the numerical value of the
+electromagnetic velocity (v) from the earliest made by Lord Kelvin (Sir
+W. Thomson) with the aid of King and M^cKichan, or those of Clerk
+Maxwell, W.E. Ayrton and J. Perry, to more recent ones by J.J. Thomson,
+F. Himstedt, H.A. Rowland, E.B. Rosa, J.S.H. Pellat and H.A. Abraham,
+showed it to be very close to the best determinations of the velocity of
+light (see UNITS, PHYSICAL). On the other hand, the divergence in some
+cases between the square of the optical refractive index and the
+dielectric constant was very marked. Hence although Maxwell's theory of
+electrical action when first propounded found many adherents in Great
+Britain, it did not so much dominate opinion on the continent of Europe.
+
+FOURTH PERIOD.--With the publication of Clerk Maxwell's treatise in
+1873, we enter fully upon the fourth and modern period of electrical
+research. On the technical side the invention of a new form of armature
+for dynamo electric machines by Z.T. Gramme (1826-1901) inaugurated a
+departure from which we may date modern electrical engineering. It will
+be convenient to deal with technical development first.
+
+_Technical Development._--As far back as 1841 large magneto-electric
+machines driven by steam power had been constructed, and in 1856 F.H.
+Holmes had made a magneto machine with multiple permanent magnets which
+was installed in 1862 in Dungeness lighthouse. Further progress was made
+in 1867 when H. Wilde introduced the use of electromagnets for the field
+magnets. In 1860 Dr Antonio Pacinotti invented what is now called the
+toothed ring winding for armatures and described it in an Italian
+journal, but it attracted little notice until reinvented in 1870 by
+Gramme. In this new form of bobbin, the armature consisted of a ring of
+iron wire wound over with an endless coil of wire and connected to a
+commutator consisting of copper bars insulated from one another. Gramme
+dynamos were then soon made on the self-exciting principle. In 1873 at
+Vienna the fact was discovered that a dynamo machine of the Gramme type
+could also act as an electric motor and was set in rotation when a
+current was passed into it from another similar machine. Henceforth the
+electric transmission of power came within the possibilities of
+engineering.
+
+_Electric Lighting._--In 1876, Paul Jablochkov (1847-1894), a Russian
+officer, passing through Paris, invented his famous electric candle,
+consisting of two rods of carbon placed side by side and separated from
+one another by an insulating material. This invention in conjunction
+with an alternating current dynamo provided a new and simple form of
+electric arc lighting. Two years afterwards C.F. Brush, in the United
+States, produced another efficient form of dynamo and electric arc lamp
+suitable for working in series (see LIGHTING: _Electric_), and these
+inventions of Brush and Jablochkov inaugurated commercial arc lighting.
+The so-called subdivision of electric light by incandescent lighting
+lamps then engaged attention. E.A. King in 1845 and W.E. Staite in 1848
+had made incandescent electric lamps of an elementary form, and T.A.
+Edison in 1878 again attacked the problem of producing light by the
+incandescence of platinum. It had by that time become clear that the
+most suitable material for an incandescent lamp was carbon contained in
+a good vacuum, and St G. Lane Fox and Sir J.W. Swan in England, and T.A.
+Edison in the United States, were engaged in struggling with the
+difficulties of producing a suitable carbon incandescence electric lamp.
+Edison constructed in 1879 a successful lamp of this type consisting of
+a vessel wholly of glass containing a carbon filament made by
+carbonizing paper or some other carbonizable material, the vessel being
+exhausted and the current led into the filament through platinum wires.
+In 1879 and 1880, Edison in the United States, and Swan in conjunction
+with C.H. Stearn in England, succeeded in completely solving the
+practical problems. From and after that date incandescent electric
+lighting became commercially possible, and was brought to public notice
+chiefly by an electrical exhibition held at the Crystal Palace, near
+London, in 1882. Edison, moreover, as well as Lane-Fox, had realized the
+idea of a public electric supply station, and the former proceeded to
+establish in Pearl Street, New York, in 1881, the first public electric
+supply station. A similar station in England was opened in the basement
+of a house in Holborn Viaduct, London, in March 1882. Edison, with
+copious ingenuity, devised electric meters, electric mains, lamp
+fittings and generators complete for the purpose. In 1881 C.A. Faure
+made an important improvement in the lead secondary battery which G.
+Planté (1834-1889) had invented in 1859, and storage batteries then
+began to be developed as commercial appliances by Faure, Swan, J.S.
+Sellon and many others (see ACCUMULATOR). In 1882, numerous electric
+lighting companies were formed for the conduct of public and private
+lighting, but an electric lighting act passed in that year greatly
+hindered commercial progress in Great Britain. Nevertheless the delay
+was utilized in the completion of inventions necessary for the safe and
+economical distribution of electric current for the purpose of electric
+lighting.
+
+_Telephone._--Going back a few years we find the technical applications
+of electrical invention had developed themselves in other directions.
+Alexander Graham Bell in 1876 invented the speaking telephone (q.v.),
+and Edison and Elisha Gray in the United States followed almost
+immediately with other telephonic inventions for electrically
+transmitting speech. About the same time D.E. Hughes in England invented
+the microphone. In 1879 telephone exchanges began to be developed in the
+United States, Great Britain and other countries.
+
+_Electric Power._--Following on the discovery in 1873 of the reversible
+action of the dynamo and its use as a motor, efforts began to be made to
+apply this knowledge to transmission of power, and S.D. Field, T.A.
+Edison, Leo Daft, E.M. Bentley and W.H. Knight, F.J. Sprague, C.J. Van
+Depoele and others between 1880 and 1884 were the pioneers of electric
+traction. One of the earliest electric tram cars was exhibited by E.W.
+and W. Siemens in Paris in 1881. In 1883 Lucien Gaulard, following a
+line of thought opened by Jablochkov, proposed to employ high pressure
+alternating currents for electric distributions over wide areas by means
+of transformers. His ideas were improved by Carl Zipernowsky and O.T.
+Bláthy in Hungary and by S.Z. de Ferranti in England, and the
+alternating current transformer (see TRANSFORMERS) came into existence.
+Polyphase alternators were first exhibited at the Frankfort electrical
+exhibition in 1891, developed as a consequence of scientific researches
+by Galileo Ferraris (1847-1897), Nikola Tesla, M.O. von
+Dolivo-Dobrowolsky and C.E.L. Brown, and long distance transmission of
+electrical power by polyphase electrical currents (see POWER
+TRANSMISSION: _Electric_) was exhibited in operation at Frankfort in
+1891. Meanwhile the early continuous current dynamos devised by Gramme,
+Siemens and others had been vastly improved in scientific principle and
+practical construction by the labours of Siemens, J. Hopkinson, R.E.B.
+Crompton, Elihu Thomson, Rudolf Eickemeyer, Thomas Parker and others,
+and the theory of the action of the dynamo had been closely studied by
+J. and E. Hopkinson, G. Kapp, S.P. Thompson, C.P. Steinmetz and J.
+Swinburne, and great improvements made in the alternating current dynamo
+by W.M. Mordey, S.Z. de Ferranti and Messrs Ganz of Budapest. Thus in
+twenty years from the invention of the Gramme dynamo, electrical
+engineering had developed from small beginnings into a vast industry.
+The amendment, in 1888, of the Electric Lighting Act of 1882, before
+long caused a huge development of public electric lighting in Great
+Britain. By the end of the 19th century every large city in Europe and
+in North and South America was provided with a public electric supply
+for the purposes of electric lighting. The various improvements in
+electric illuminants, such as the Nernst oxide lamp, the tantalum and
+osmium incandescent lamps, and improved forms of arc lamp, enclosed,
+inverted and flame arcs, are described under LIGHTING: _Electric_.
+
+Between 1890 and 1900, electric traction advanced rapidly in the United
+States of America but more slowly in England. In 1902 the success of
+deep tube electric railways in Great Britain was assured, and in 1904
+main line railways began to abandon, at least experimentally, the steam
+locomotive and substitute for it the electric transmission of power.
+Long distance electrical transmission had been before that time
+exemplified in the great scheme of utilizing the falls of Niagara. The
+first projects were discussed in 1891 and 1892 and completed practically
+some ten years later. In this scheme large turbines were placed at the
+bottom of hydraulic fall tubes 150 ft. deep, the turbines being coupled
+by long shafts with 5000 H.P. alternating current dynamos on the
+surface. By these electric current was generated and transmitted to
+towns and factories around, being sent overhead as far as Buffalo, a
+distance of 18 m. At the end of the 19th century electrochemical
+industries began to be developed which depended on the possession of
+cheap electric energy. The production of aluminium in Switzerland and
+Scotland, carborundum and calcium carbide in the United States, and soda
+by the Castner-Kellner process, began to be conducted on an immense
+scale. The early work of Sir W. Siemens on the electric furnace was
+continued and greatly extended by Henri Moissan and others on its
+scientific side, and electrochemistry took its place as one of the most
+promising departments of technical research and invention. It was
+stimulated and assisted by improvements in the construction of large
+dynamos and increased knowledge concerning the control of powerful
+electric currents.
+
+In the early part of the 20th century the distribution in bulk of
+electric energy for power purposes in Great Britain began to assume
+important proportions. It was seen to be uneconomical for each city and
+town to manufacture its own supply since, owing to the intermittent
+nature of the demand for current for lighting, the price had to be kept
+up to 4d. and 6d. per unit. It was found that by the manufacture in
+bulk, even by steam engines, at primary centres the cost could be
+considerably reduced, and in numerous districts in England large power
+stations began to be erected between 1903 and 1905 for the supply of
+current for power purposes. This involved almost a revolution in the
+nature of the tools used, and in the methods of working, and may
+ultimately even greatly affect the factory system and the concentration
+of population in large towns which was brought about in the early part
+of the 19th century by the invention of the steam engine.
+
+
+_Development of Electric Theory._
+
+Turning now to the theory of electricity, we may note the equally
+remarkable progress made in 300 years in scientific insight into the
+nature of the agency which has so recast the face of human society.
+There is no need to dwell upon the early crude theories of the action of
+amber and lodestone. In a true scientific sense no hypothesis was
+possible, because few facts had been accumulated. The discoveries of
+Stephen Gray and C.F. de C. du Fay on the conductivity of some bodies
+for the electric agency and the dual character of electrification gave
+rise to the first notions of electricity as an imponderable fluid, or
+non-gravitative subtile matter, of a more refined and penetrating kind
+than ordinary liquids and gases. Its duplex character, and the fact that
+the electricity produced by rubbing glass and vitreous substances was
+different from that produced by rubbing sealing-wax and resinous
+substances, seemed to necessitate the assumption of two kinds of
+electric fluid; hence there arose the conception of _positive_ and
+_negative_ electricity, and the two-fluid theory came into existence.
+
+_Single-fluid Theory._--The study of the phenomena of the Leyden jar and
+of the fact that the inside and outside coatings possessed opposite
+electricities, so that in charging the jar as much positive electricity
+is added to one side as negative to the other, led Franklin about 1750
+to suggest a modification called the single fluid theory, in which the
+two states of electrification were regarded as not the results of two
+entirely different fluids but of the addition or subtraction of one
+electric fluid from matter, so that positive electrification was to be
+looked upon as the result of increase or addition of something to
+ordinary matter and negative as a subtraction. The positive and negative
+electrifications of the two coatings of the Leyden jar were therefore to
+be regarded as the result of a transformation of something called
+electricity from one coating to the other, by which process a certain
+measurable quantity became so much less on one side by the same amount
+by which it became more on the other. A modification of this single
+fluid theory was put forward by F.U.T. Aepinus which was explained and
+illustrated in his _Tentamen theoriae electricitatis et magnetismi_,
+published in St Petersburg in 1759. This theory was founded on the
+following principles:--(1) the particles of the electric fluid repel
+each other with a force decreasing as the distance increases; (2) the
+particles of the electric fluid attract the atoms of all bodies and are
+attracted by them with a force obeying the same law; (3) the electric
+fluid exists in the pores of all bodies, and while it moves without any
+obstruction in conductors such as metals, water, &c., it moves with
+extreme difficulty in so-called non-conductors such as glass, resin,
+&c.; (4) electrical phenomena are produced either by the transference of
+the electric fluid of a body containing more to one containing less, or
+from its attraction and repulsion when no transference takes place.
+Electric attractions and repulsions were, however, regarded as
+differential actions in which the mutual repulsion of the particles of
+electricity operated, so to speak, in antagonism to the mutual
+attraction of particles of matter for one another and of particles of
+electricity for matter. Independently of Aepinus, Henry Cavendish put
+forward a single-fluid theory of electricity (_Phil. Trans._, 1771, 61,
+p. 584), in which he considered it in more precise detail.
+
+_Two-fluid Theory._--In the elucidation of electrical phenomena,
+however, towards the end of the 18th century, a modification of the
+two-fluid theory seems to have been generally preferred. The notion then
+formed of the nature of electrification was something as follows:--All
+bodies were assumed to contain a certain quantity of a so-called neutral
+fluid made up of equal quantities of positive and negative electricity,
+which when in this state of combination neutralized one another's
+properties. The neutral fluid could, however, be divided up or separated
+into its two constituents, and these could be accumulated on separate
+conductors or non-conductors. This view followed from the discovery of
+the facts of electric induction of J. Canton (1753, 1754). When, for
+instance, a positively electrified body was found to induce upon another
+insulated conductor a charge of negative electricity on the side nearest
+to it, and a charge of positive electricity on the side farthest from
+it, this was explained by saying that the particles of each of the two
+electric fluids repelled one another but attracted those of the positive
+fluid. Hence the operation of the positive charge upon the neutral fluid
+was to draw towards the positive the negative constituent of the neutral
+charge and repel to the distant parts of the conductor the positive
+constituent.
+
+C.A. Coulomb experimentally proved that the law of attraction and
+repulsion of simple electrified bodies was that the force between them
+varied inversely as the square of the distance and thus gave
+mathematical definiteness to the two-fluid hypothesis. It was then
+assumed that each of the two constituents of the neutral fluid had an
+atomic structure and that the so-called particles of one of the electric
+fluids, say positive, repelled similar particles with a force varying
+inversely as a square of the distance and attracted those of the
+opposite fluid according to the same law. This fact and hypothesis
+brought electrical phenomena within the domain of mathematical analysis
+and, as already mentioned, Laplace, Biot, Poisson, G.A.A. Plana
+(1781-1846), and later Robert Murphy (1806-1843), made them the subject
+of their investigations on the mode in which electricity distributes
+itself on conductors when in equilibrium.
+
+_Faraday's Views._--The two-fluid theory may be said to have held the
+field until the time when Faraday began his researches on electricity.
+After he had educated himself by the study of the phenomena of lines of
+magnetic force in his discoveries on electromagnetic induction, he
+applied the same conception to electrostatic phenomena, and thus created
+the notion of lines of electrostatic force and of the important function
+of the dielectric or non-conductor in sustaining them. Faraday's notion
+as to the nature of electrification, therefore, about the middle of the
+19th century came to be something as follows:--He considered that the
+so-called charge of electricity on a conductor was in reality nothing on
+the conductor or in the conductor itself, but consisted in a state of
+strain or polarization, or a physical change of some kind in the
+particles of the dielectric surrounding the conductor, and that it was
+this physical state in the dielectric which constituted electrification.
+Since Faraday was well aware that even a good vacuum can act as a
+dielectric, he recognized that the state he called dielectric
+polarization could not be wholly dependent upon the presence of
+gravitative matter, but that there must be an electromagnetic medium of
+a supermaterial nature. In the 13th series of his _Experimental
+Researches on Electricity_ he discussed the relation of a vacuum to
+electricity. Furthermore his electrochemical investigations, and
+particularly his discovery of the important law of electrolysis, that
+the movement of a certain quantity of electricity through an electrolyte
+is always accompanied by the transfer of a certain definite quantity of
+matter from one electrode to another and the liberation at these
+electrodes of an equivalent weight of the ions, gave foundation for the
+idea of a definite atomic charge of electricity. In fact, long
+previously to Faraday's electrochemical researches, Sir H. Davy and J.J.
+Berzelius early in the 19th century had advanced the hypothesis that
+chemical combination was due to electric attractions between the
+electric charges carried by chemical atoms. The notion, however, that
+electricity is atomic in structure was definitely put forward by Hermann
+von Helmholtz in a well-known Faraday lecture. Helmholtz says: "If we
+accept the hypothesis that elementary substances are composed of atoms,
+we cannot well avoid concluding that electricity also is divided into
+elementary portions which behave like atoms of electricity."[16] Clerk
+Maxwell had already used in 1873 the phrase, "a molecule of
+electricity."[17] Towards the end of the third quarter of the 19th
+century it therefore became clear that electricity, whatever be its
+nature, was associated with atoms of matter in the form of exact
+multiples of an indivisible minimum electric charge which may be
+considered to be "Nature's unit of electricity." This ultimate unit of
+electric quantity Professor Johnstone Stoney called an _electron_.[18]
+The formulation of electrical theory as far as regards operations in
+space free from matter was immensely assisted by Maxwell's mathematical
+theory. Oliver Heaviside after 1880 rendered much assistance by reducing
+Maxwell's mathematical analysis to more compact form and by introducing
+greater precision into terminology (see his _Electrical Papers_, 1892).
+This is perhaps the place to refer also to the great services of Lord
+Rayleigh to electrical science. Succeeding Maxwell as Cavendish
+professor of physics at Cambridge in 1880, he soon devoted himself
+especially to the exact redetermination of the practical electrical
+units in absolute measure. He followed up the early work of the British
+Association Committee on electrical units by a fresh determination of
+the ohm in absolute measure, and in conjunction with other work on the
+electrochemical equivalent of silver and the absolute electromotive
+force of the Clark cell may be said to have placed exact electrical
+measurement on a new basis. He also made great additions to the theory
+of alternating electric currents, and provided fresh appliances for
+other electrical measurements (see his _Collected Scientific Papers_,
+Cambridge, 1900).
+
+_Electro-optics._--For a long time Faraday's observation on the rotation
+of the plane of polarized light by heavy glass in a magnetic field
+remained an isolated fact in electro-optics. Then M.E. Verdet
+(1824-1860) made a study of the subject and discovered that a solution
+of ferric perchloride in methyl alcohol rotated the plane of
+polarization in an opposite direction to heavy glass (_Ann. Chim.
+Phys._, 1854, 41, p. 370; 1855, 43, p. 37; _Com. Rend._, 1854, 39, p.
+548). Later A.A.E.E. Kundt prepared metallic films of iron, nickel and
+cobalt, and obtained powerful negative optical rotation with them
+(_Wied. Ann._, 1884, 23, p. 228; 1886, 27, p. 191). John Kerr
+(1824-1907) discovered that a similar effect was produced when plane
+polarized light was reflected from the pole of a powerful magnet (_Phil.
+Mag._, 1877, [5], 3, p. 321, and 1878, 5, p. 161). Lord Kelvin showed
+that Faraday's discovery demonstrated that some form of rotation was
+taking place along lines of magnetic force when passing through a
+medium.[19] Many observers have given attention to the exact
+determination of Verdet's constant of rotation for standard substances,
+e.g. Lord Rayleigh for carbon bisulphide,[20] and Sir W.H. Perkin for an
+immense range of inorganic and organic bodies.[21] Kerr also discovered
+that when certain homogeneous dielectrics were submitted to electric
+strain, they became birefringent (_Phil. Mag._, 1875, 50, pp. 337 and
+446). The theory of electro-optics received great attention from Kelvin,
+Maxwell, Rayleigh, G.F. Fitzgerald, A. Righi and P.K.L. Drude, and
+experimental contributions from innumerable workers, such as F.T.
+Trouton, O.J. Lodge and J.L. Howard, and many others.
+
+_Electric Waves._--In the decade 1880-1890, the most important advance
+in electrical physics was, however, that which originated with the
+astonishing researches of Heinrich Rudolf Hertz (1857-1894). This
+illustrious investigator was stimulated, by a certain problem brought to
+his notice by H. von Helmholtz, to undertake investigations which had
+for their object a demonstration of the truth of Maxwell's principle
+that a variation in electric displacement was in fact an electric
+current and had magnetic effects. It is impossible to describe here the
+details of these elaborate experiments; the reader must be referred to
+Hertz's own papers, or the English translation of them by Prof. D.E.
+Jones. Hertz's great discovery was an experimental realization of a
+suggestion made by G.F. Fitzgerald (1851-1901) in 1883 as to a method of
+producing electric waves in space. He invented for this purpose a
+radiator consisting of two metal rods placed in one line, their inner
+ends being provided with poles nearly touching and their outer ends with
+metal plates. Such an arrangement constitutes in effect a condenser, and
+when the two plates respectively are connected to the secondary
+terminals of an induction coil in operation, the plates are rapidly and
+alternately charged, and discharged across the spark gap with electrical
+oscillations (see ELECTROKINETICS). Hertz then devised a wave detecting
+apparatus called a resonator. This in its simplest form consisted of a
+ring of wire nearly closed terminating in spark balls very close
+together, adjustable as to distance by a micrometer screw. He found that
+when the resonator was placed in certain positions with regard to the
+oscillator, small sparks were seen between the micrometer balls, and
+when the oscillator was placed at one end of a room having a sheet of
+zinc fixed against the wall at the other end, symmetrical positions
+could be found in the room at which, when the resonator was there
+placed, either no sparks or else very bright sparks occurred at the
+poles. These effects, as Hertz showed, indicated the establishment of
+stationary electric waves in space and the propagation of electric and
+magnetic force through space with a finite velocity. The other
+additional phenomena he observed finally contributed an all but
+conclusive proof of the truth of Maxwell's views. By profoundly
+ingenious methods Hertz showed that these invisible electric waves could
+be reflected and refracted like waves of light by mirrors and prisms,
+and that familiar experiments in optics could be repeated with electric
+waves which could not affect the eye. Hence there arose a new science of
+electro-optics, and in all parts of Europe and the United States
+innumerable investigators took possession of the novel field of research
+with the greatest delight. O.J. Lodge,[22] A. Righi,[23] J.H.
+Poincaré,[24] V.F.K. Bjerknes, P.K.L. Drude, J.J. Thomson,[25] John
+Trowbridge, Max Abraham, and many others, contributed to its
+elucidation.
+
+In 1892, E. Branly of Paris devised an appliance for detecting these
+waves which subsequently proved to be of immense importance. He
+discovered that they had the power of affecting the electric
+conductivity of materials when in a state of powder, the majority of
+metallic filings increasing in conductivity. Lodge devised a similar
+arrangement called a coherer, and E. Rutherford invented a magnetic
+detector depending on the power of electric oscillations to demagnetize
+iron or steel. The sum total of all these contributions to electrical
+knowledge had the effect of establishing Maxwell's principles on a firm
+basis, but they also led to technical inventions of the very greatest
+utility. In 1896 G. Marconi applied a modified and improved form of
+Branly's wave detector in conjunction with a novel form of radiator for
+the telegraphic transmission of intelligence through space without
+wires, and he and others developed this new form of telegraphy with the
+greatest rapidity and success into a startling and most useful means of
+communicating through space electrically without connecting wires.
+
+_Electrolysis._--The study of the transfer of electricity through
+liquids had meanwhile received much attention. The general facts and
+laws of electrolysis (q.v.) were determined experimentally by Davy and
+Faraday and confirmed by the researches of J.F. Daniell, R.W. Bunsen and
+Helmholtz. The modern theory of electrolysis grew up under the hands of
+R.J.E. Clausius, A.W. Williamson and F.W.G. Kohlrausch, and received a
+great impetus from the work of Svante Arrhenius, J.H. Van't Hoff, W.
+Ostwald, H.W. Nernst and many others. The theory of the ionization of
+salts in solution has raised much discussion amongst chemists, but the
+general fact is certain that electricity only moves through liquids in
+association with matter, and simultaneously involves chemical
+dissociation of molecular groups.
+
+_Discharge through Gases._--Many eminent physicists had an instinctive
+feeling that the study of the passage of electricity through gases would
+shed much light on the intrinsic nature of electricity. Faraday devoted
+to a careful examination of the phenomena the XIII^th series of his
+_Experimental Researches_, and among the older workers in this field
+must be particularly mentioned J. Plücker, J.W. Hittorf, A.A. de la
+Rive, J.P. Gassiot, C.F. Varley, and W. Spottiswoode and J. Fletcher
+Moulton. It has long been known that air and other gases at the pressure
+of the atmosphere were very perfect insulators, but that when they were
+rarefied and contained in glass tubes with platinum electrodes sealed
+through the glass, electricity could be passed through them under
+sufficient electromotive force and produced a luminous appearance known
+as the electric glow discharge. The so-called vacuum tubes constructed
+by H. Geissler (1815-1879) containing air, carbonic acid, hydrogen, &c.,
+under a pressure of one or two millimetres, exhibit beautiful
+appearances when traversed by the high tension current produced by the
+secondary circuit of an induction coil. Faraday discovered the existence
+of a dark space round the negative electrode which is usually known as
+the "Faraday dark space." De la Rive added much to our knowledge of the
+subject, and J. Plücker and his disciple J.W. Hittorf examined the
+phenomena exhibited in so-called high vacua, that is, in exceedingly
+rarefied gases. C.F. Varley discovered the interesting fact that no
+current could be sent through the rarefied gas unless a certain minimum
+potential difference of the electrodes was excited. Sir William Crookes
+took up in 1872 the study of electric discharge through high vacua,
+having been led to it by his researches on the radiometer. The
+particular details of the phenomena observed will be found described in
+the article CONDUCTION, ELECTRIC (§ III.). The main fact discovered by
+researches of Plücker, Hittorf and Crookes was that in a vacuum tube
+containing extremely rarefied air or other gas, a luminous discharge
+takes place from the negative electrode which proceeds in lines normal
+to the surface of the negative electrode and renders phosphorescent both
+the glass envelope and other objects placed in the vacuum tube when it
+falls upon them. Hittorf made in 1869 the discovery that solid objects
+could cast shadows or intercept this cathode discharge. The cathode
+discharge henceforth engaged the attention of many physicists. Varley
+had advanced tentatively the hypothesis that it consisted in an actual
+projection of electrified matter from the cathode, and Crookes was led
+by his researches in 1870, 1871 and 1872 to embrace and confirm this
+hypothesis in a modified form and announce the existence of a fourth
+state of matter, which he called radiant matter, demonstrating by many
+beautiful and convincing experiments that there was an actual projection
+of material substance of some kind possessing inertia from the surface
+of the cathode. German physicists such as E. Goldstein were inclined to
+take another view. Sir J.J. Thomson, the successor of Maxwell and Lord
+Rayleigh in the Cavendish chair of physics in the university of
+Cambridge, began about the year 1899 a remarkable series of
+investigations on the cathode discharge, which finally enabled him to
+make a measurement of the ratio of the electric charge to the mass of
+the particles of matter projected from the cathode, and to show that
+this electric charge was identical with the atomic electric charge
+carried by a hydrogen ion in the act of electrolysis, but that the mass
+of the cathode particles, or "corpuscles" as he called them, was far
+less, viz. about 1/2000th part of the mass of a hydrogen atom.[26] The
+subject was pursued by Thomson and the Cambridge physicists with great
+mathematical and experimental ability, and finally the conclusion was
+reached that in a high vacuum tube the electric charge is carried by
+particles which have a mass only a fraction, as above mentioned, of that
+of the hydrogen atom, but which carry a charge equal to the unit
+electric charge of the hydrogen ion as found by electrochemical
+researches.[27] P.E.A. Lenard made in 1894 (_Wied. Ann. Phys._, 51, p.
+225) the discovery that these cathode particles or corpuscles could pass
+through a window of thin sheet aluminium placed in the wall of the
+vacuum tube and give rise to a class of radiation called the Lenard
+rays. W.C. Röntgen of Munich made in 1896 his remarkable discovery of
+the so-called X or Röntgen rays, a class of radiation produced by the
+impact of the cathode particles against an impervious metallic screen or
+anticathode placed in the vacuum tube. The study of Röntgen rays was
+ardently pursued by the principal physicists in Europe during the years
+1897 and 1898 and subsequently. The principal property of these Röntgen
+rays which attracted public attention was their power of passing through
+many solid bodies and affecting a photographic plate. Hence some
+substances were opaque to them and others transparent. The astonishing
+feat of photographing the bones of the living animal within the tissues
+soon rendered the Röntgen rays indispensable in surgery and directed an
+army of investigators to their study.
+
+_Radioactivity._--One outcome of all this was the discovery by H.
+Becquerel in 1896 that minerals containing uranium, and particularly the
+mineral known as pitchblende, had the power of affecting sensitive
+photographic plates enclosed in a black paper envelope when the mineral
+was placed on the outside, as well as of discharging a charged
+electroscope (_Com. Rend._, 1896, 122, p. 420). This research opened a
+way of approach to the phenomena of radioactivity, and the history of
+the steps by which P. Curie and Madame Curie were finally led to the
+discovery of radium is one of the most fascinating chapters in the
+history of science. The study of radium and radioactivity (see
+RADIOACTIVITY) led before long to the further remarkable knowledge that
+these so-called radioactive materials project into surrounding space
+particles or corpuscles, some of which are identical with those
+projected from the cathode in a high vacuum tube, together with others
+of a different nature. The study of radioactivity was pursued with great
+ability not only by the Curies and A. Debierne, who associated himself
+with them, in France, but by E. Rutherford and F. Soddy in Canada, and
+by J.J. Thomson, Sir William Crookes, Sir William Ramsay and others in
+England.
+
+_Electronic Theory._--The final outcome of these investigations was the
+hypothesis that Thomson's corpuscles or particles composing the cathode
+discharge in a high vacuum tube must be looked upon as the ultimate
+constituent of what we call negative electricity; in other words, they
+are atoms of negative electricity, possessing, however, inertia, and
+these negative electrons are components at any rate of the chemical
+atom. Each electron is a point-charge of negative electricity equal to
+3.9×10^{-10} of an electrostatic unit or to 1.3×10^{-20} of an
+electromagnetic unit, and the ratio of its charge to its mass is nearly
+2×10^7 using E.M. units. For the hydrogen atom the ratio of charge to
+mass as deduced from electrolysis is about 10^4. Hence the mass of an
+electron is 1/2000th of that of a hydrogen atom. No one has yet been
+able to isolate positive electrons, or to give a complete demonstration
+that the whole inertia of matter is only electric inertia due to what
+may be called the inductance of the electrons. Prof. Sir J. Larmor
+developed in a series of very able papers (_Phil. Trans._, 1894, 185;
+1895, 186; 1897, 190), and subsequently in his book _Aether and Matter_
+(1900), a remarkable hypothesis of the structure of the electron or
+corpuscle, which he regards as simply a strain centre in the aether or
+electromagnetic medium, a chemical atom being a collection of positive
+and negative electrons or strain centres in stable orbital motion round
+their common centre of mass (see AETHER). J.J. Thomson also developed
+this hypothesis in a profoundly interesting manner, and we may therefore
+summarize very briefly the views held on the nature of electricity and
+matter at the beginning of the 20th century by saying that the term
+electricity had come to be regarded, in part at least, as a collective
+name for electrons, which in turn must be considered as constituents of
+the chemical atom, furthermore as centres of certain lines of
+self-locked and permanent strain existing in the universal aether or
+electromagnetic medium. Atoms of matter are composed of congeries of
+electrons and the inertia of matter is probably therefore only the
+inertia of the electromagnetic medium.[28] Electric waves are produced
+wherever electrons are accelerated or retarded, that is, whenever the
+velocity of an electron is changed or accelerated positively or
+negatively. In every solid body there is a continual atomic
+dissociation, the result of which is that mixed up with the atoms of
+chemical matter composing them we have a greater or less percentage of
+free electrons. The operation called an electric current consists in a
+diffusion or movement of these electrons through matter, and this is
+controlled by laws of diffusion which are similar to those of the
+diffusion of liquids or gases. Electromotive force is due to a
+difference in the density of the electronic population in different or
+identical conducting bodies, and whilst the electrons can move freely
+through so-called conductors their motion is much more hindered or
+restricted in non-conductors. Electric charge consists, therefore, in an
+excess or deficit of negative electrons in a body. In the hands of H.A.
+Lorentz, P.K.L. Drude, J. J, Thomson, J. Larmor and many others, the
+electronic hypothesis of matter and of electricity has been developed in
+great detail and may be said to represent the outcome of modern
+researches upon electrical phenomena.
+
+The reader may be referred for an admirable summary of the theories of
+electricity prior to the advent of the electronic hypothesis to J.J.
+Thomson's "Report on Electrical Theories" (_Brit. Assoc. Report_, 1885),
+in which he divides electrical theories enunciated during the 19th
+century into four classes, and summarizes the opinions and theories of
+A.M. Ampère, H.G. Grassman, C.F. Gauss, W.E. Weber, G.F.B. Riemann,
+R.J.E. Clausius, F.E. Neumann and H. von Helmholtz.
+
+  BIBLIOGRAPHY.--M. Faraday, _Experimental Researches in Electricity_ (3
+  vols., London, 1839, 1844, 1855); A.A. De la Rive, _Treatise on
+  Electricity_ (3 vols., London, 1853, 1858); J. Clerk Maxwell, _A
+  Treatise on Electricity and Magnetism_ (2 vols., 3rd ed., 1892); id.,
+  _Scientific Papers_ (2 vols., edited by Sir W.J. Niven, Cambridge,
+  1890); H.M. Noad, _A Manual of Electricity_ (2 vols., London, 1855,
+  1857); J.J. Thomson, _Recent Researches in Electricity and Magnetism_
+  (Oxford, 1893); id., _Conduction of Electricity through Gases_
+  (Cambridge, 1903); id., _Electricity and Matter_ (London, 1904); O.
+  Heaviside, _Electromagnetic Theory_ (London, 1893); O.J. Lodge,
+  _Modern Views of Electricity_ (London, 1889); E. Mascart and J.
+  Joubert, _A Treatise on Electricity and Magnetism_, English trans. by
+  E. Atkinson (2 vols., London, 1883); Park Benjamin, _The Intellectual
+  Rise in Electricity_ (London, 1895); G.C. Foster and A.W. Porter,
+  _Electricity and Magnetism_ (London, 1903); A. Gray, _A Treatise on
+  Magnetism and Electricity_ (London, 1898); H.W. Watson and S.H.
+  Burbury, _The Mathematical Theory of Electricity and Magnetism_ (2
+  vols., 1885); Lord Kelvin (Sir William Thomson), _Mathematical and
+  Physical Papers_ (3 vols., Cambridge, 1882); Lord Rayleigh,
+  _Scientific Papers_ (4 vols., Cambridge, 1903); A. Winkelmann,
+  _Handbuch der Physik_, vols. iii. and iv. (Breslau, 1903 and 1905; a
+  mine of wealth for references to original papers on electricity and
+  magnetism from the earliest date up to modern times). For particular
+  information on the modern Electronic theory the reader may consult W.
+  Kaufmann, "The Developments of the Electron Idea." _Physikalische
+  Zeitschrift_ (1st of Oct. 1901), or _The Electrician_ (1901), 48, p.
+  95; H.A. Lorentz, _The Theory of Electrons_ (1909); E.E. Fournier
+  d'Albe, _The Electron Theory_ (London, 1906); H. Abraham and P.
+  Langevin, _Ions, Electrons, Corpuscles_ (Paris, 1905); J.A. Fleming,
+  "The Electronic Theory of Electricity," _Popular Science Monthly_ (May
+  1902); Sir Oliver J. Lodge, _Electrons, or the Nature and Properties
+  of Negative Electricity_ (London, 1907).     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] Gilbert's work, _On the Magnet, Magnetic Bodies and the Great
+    Magnet, the Earth_, has been translated from the rare folio Latin
+    edition of 1600, but otherwise reproduced in its original form by the
+    chief members of the Gilbert Club of England, with a series of
+    valuable notes by Prof. S.P. Thompson (London, 1900). See also _The
+    Electrician_, February 21, 1902.
+
+  [2] See _The Intellectual Rise in Electricity_, ch. x., by Park
+    Benjamin (London, 1895).
+
+  [3] See Sir Oliver Lodge, "Lightning, Lightning Conductors and
+    Lightning Protectors," _Journ. Inst. Elec. Eng._ (1889), 18, p. 386,
+    and the discussion on the subject in the same volume; also the book
+    by the same author on _Lightning Conductors and Lightning Guards_
+    (London, 1892).
+
+  [4] _The Electrical Researches of the Hon. Henry Cavendish
+    1771-1781_, edited from the original manuscripts by J. Clerk Maxwell,
+    F.R.S. (Cambridge, 1879).
+
+  [5] In 1878 Clerk Maxwell repeated Cavendish's experiments with
+    improved apparatus and the employment of a Kelvin quadrant
+    electrometer as a means of detecting the absence of charge on the
+    inner conductor after it had been connected to the outer case, and
+    was thus able to show that if the law of electric attraction varies
+    inversely as the nth power of the distance, then the exponent n must
+    have a value of 2±{1/21600}. See Cavendish's _Electrical Researches_,
+    p. 419.
+
+  [6] Modern researches have shown that the loss of charge is in fact
+    dependent upon the ionization of the air, and that, provided the
+    atmospheric moisture is prevented from condensing on the insulating
+    supports, water vapour in the air does not _per se_ bestow on it
+    conductance for electricity.
+
+  [7] Faraday discussed the chemical theory of the pile and arguments
+    in support of it in the 8th and 16th series of his _Experimental
+    Researches on Electricity_. De la Rive reviews the subject in his
+    large _Treatise on Electricity and Magnetism_, vol. ii. ch. iii. The
+    writer made a contribution to the discussion in 1874 in a paper on
+    "The Contact Theory of the Galvanic Cell," _Phil. Mag._, 1874, 47, p.
+    401. Sir Oliver Lodge reviewed the whole position in a paper in 1885,
+    "On the Seat of the Electromotive Force in a Voltaic Cell," _Journ.
+    Inst. Elec. Eng._, 1885, 14, p. 186.
+
+  [8] "Mémoire sur la théorie mathématique des phénomènes
+    électrodynamiques," _Mémoires de l'institut_, 1820, 6; see also _Ann.
+    de Chim._, 1820, 15.
+
+  [9] See M. Faraday, "On some new Electro-Magnetical Motions and on
+    the Theory of Magnetism," _Quarterly Journal of Science_, 1822, 12,
+    p. 74; or _Experimental Researches on Electricity_, vol. ii. p. 127.
+
+  [10] Amongst the most important of Faraday's quantitative researches
+    must be included the ingenious and convincing proofs he provided that
+    the production of any quantity of electricity of one sign is always
+    accompanied by the production of an equal quantity of electricity of
+    the opposite sign. See _Experimental Researches on Electricity_, vol.
+    i. § 1177.
+
+  [11] In this connexion the work of George Green (1793-1841) must not
+    be forgotten. Green's _Essay on the Application of Mathematical
+    Analysis to the Theories of Electricity and Magnetism_, published in
+    1828, contains the first exposition of the theory of potential. An
+    important theorem contained in it is known as Green's theorem, and is
+    of great value.
+
+  [12] See also his _Submarine Telegraphs_ (London, 1898).
+
+  [13] The quantitative study of electrical phenomena has been
+    enormously assisted by the establishment of the absolute system of
+    electrical measurement due originally to Gauss and Weber. The British
+    Association for the advancement of science appointed in 1861 a
+    committee on electrical units, which made its first report in 1862
+    and has existed ever since. In this work Lord Kelvin took a leading
+    part. The popularization of the system was greatly assisted by the
+    publication by Prof. J.D. Everett of _The C.G.S. System of Units_
+    (London, 1891).
+
+  [14] The first paper in which Maxwell began to translate Faraday's
+    conceptions into mathematical language was "On Faraday's Lines of
+    Force," read to the Cambridge Philosophical Society on the 10th of
+    December 1855 and the 11th of February 1856. See Maxwell's _Collected
+    Scientific Papers_, i. 155.
+
+  [15] _A Treatise on Electricity and Magnetism_ (2 vols.), by James
+    Clerk Maxwell, sometime professor of experimental physics in the
+    university of Cambridge. A second edition was edited by Sir W.D.
+    Niven in 1881 and a third by Prof. Sir J.J. Thomson in 1891.
+
+  [16] H. von Helmholtz, "On the Modern Development of Faraday's
+    Conception of Electricity," _Journ. Chem. Soc._, 1881, 39, p. 277.
+
+  [17] See Maxwell's _Electricity and Magnetism_, vol. i. p. 350 (2nd
+    ed., 1881).
+
+  [18] "On the Physical Units of Nature," _Phil. Mag._, 1881, [5], 11,
+    p. 381. Also _Trans. Roy. Soc._ (Dublin, 1891), 4, p. 583.
+
+  [19] See Sir W. Thomson, _Proc. Roy. Soc. Lond._, 1856, 8, p. 152; or
+    Maxwell, _Elect. and Mag._, vol. ii. p. 831.
+
+  [20] See Lord Rayleigh, _Proc. Roy. Soc. Lond._, 1884, 37, p. 146;
+    Gordon, _Phil. Trans._, 1877, 167, p. 1; H. Becquerel, _Ann. Chim.
+    Phys._, 1882, [3], 27, p. 312.
+
+  [21] Perkin's Papers are to be found in the _Journ. Chem. Soc.
+    Lond._, 1884, p. 421; 1886, p. 177; 1888, p. 561; 1889, p. 680; 1891,
+    p. 981; 1892, p. 800; 1893, p. 75.
+
+  [22] _The Work of Hertz_ (London, 1894).
+
+  [23] _L'Ottica delle oscillazioni elettriche_ (Bologna, 1897).
+
+  [24] _Les Oscillations électriques_ (Paris, 1894).
+
+  [25] _Recent Researches in Electricity and Magnetism_ (Oxford, 1892).
+
+  [26] See J.J. Thomson, _Proc. Roy. Inst. Lond._, 1897, 15, p. 419;
+   also _Phil. Mag._, 1899, [5], 48, p. 547.
+
+  [27] Later results show that the mass of a hydrogen atom is not far
+    from 1.3 × 10^-24 gramme and that the unit atomic charge or natural
+    unit of electricity is 1.3 × 10^-20 of an electromagnetic C.G.S.
+    unit. The mass of the electron or corpuscle is 7.0 × 10^-28 gramme
+    and its diameter is 3 × 10^-13 centimetre. The diameter of a chemical
+    atom is of the order of 10^-7 centimetre.
+
+    See H.A. Lorentz, "The Electron Theory," _Elektrotechnische
+    Zeitschrift_, 1905, 26, p. 584; or _Science Abstracts_, 1905, 8, A,
+    p. 603.
+
+  [28] See J.J. Thomson, _Electricity and Matter_ (London, 1904).
+
+
+
+
+ELECTRICITY SUPPLY. I. _General Principles._--The improvements made in
+the dynamo and electric motor between 1870 and 1880 and also in the
+details of the arc and incandescent electric lamp towards the close of
+that decade, induced engineers to turn their attention to the question
+of the private and public supply of electric current for the purpose of
+lighting and power. T.A. Edison[1] and St G. Lane Fox[2] were among the
+first to see the possibilities and advantages of public electric supply,
+and to devise plans for its practical establishment. If a supply of
+electric current has to be furnished to a building the option exists in
+many cases of drawing from a public supply or of generating it by a
+private plant.
+
+_Private Plants._--In spite of a great amount of ingenuity devoted to
+the development of the primary battery and the thermopile, no means of
+generation of large currents can compete in economy with the dynamo.
+Hence a private electric generating plant involves the erection of a
+dynamo which may be driven either by a steam, gas or oil engine, or by
+power obtained by means of a turbine from a low or high fall of water.
+It may be either directly coupled to the motor, or driven by a belt; and
+it may be either a continuous-current machine or an alternator, and if
+the latter, either single-phase or polyphase. The convenience of being
+able to employ storage batteries in connexion with a private-supply
+system is so great that unless power has to be transmitted long
+distances, the invariable rule is to employ a continuous-current dynamo.
+Where space is valuable this is always coupled direct to the motor; and
+if a steam-engine is employed, an enclosed engine is most cleanly and
+compact. Where coal or heating gas is available, a gas-engine is
+exceedingly convenient, since it requires little attention. Where coal
+gas is not available, a Dowson gas-producer can be employed. The
+oil-engine has been so improved that it is extensively used in
+combination with a direct-coupled or belt-driven dynamo and thus forms a
+favourite and easily-managed plant for private electric lighting. Lead
+storage cells, however, as at present made, when charged by a
+steam-driven dynamo deteriorate less rapidly than when an oil-engine is
+employed, the reason being that the charging current is more irregular
+in the latter case, since the single cylinder oil-engine only makes an
+impulse every other revolution. In connexion with the generator, it is
+almost the invariable custom to put down a secondary battery of storage
+cells, to enable the supply to be given after the engine has stopped.
+This is necessary, not only as a security for the continuity of supply,
+but because otherwise the costs of labour in running the engine night
+and day become excessive. The storage battery gives its supply
+automatically, but the dynamo and engine require incessant skilled
+attendance. If the building to be lighted is at some distance from the
+engine-house the battery should be placed in the basement of the
+building, and underground or overhead conductors, to convey the charging
+current, brought to it from the dynamo.
+
+It is usual, in the case of electric lighting installations, to reckon
+all lamps in their equivalent number of 8 candle power (c.p.)
+incandescent lamps. In lighting a private house or building, the first
+thing to be done is to settle the total number of incandescent lamps and
+their size, whether 32 c.p., 16 c.p. or 8 c.p. Lamps of 5 c.p. can be
+used with advantage in small bedrooms and passages. Each candle-power in
+the case of a carbon filament lamp can be taken as equivalent to 3.5
+watts, or the 8 c.p. lamp as equal to 30 watts, the 16 c.p. lamp to 60
+watts, and so on. In the case of metallic filament lamps about 1.0 or
+1.25 watts. Hence if the equivalent of 100 carbon filament 8 c.p. lamps
+is required in a building the maximum electric power-supply available
+must be 3000 watts or 3 kilowatts. The next matter to consider is the
+pressure of supply. If the battery can be in a position near the
+building to be lighted, it is best to use 100-volt incandescent lamps
+and enclosed arc lamps, which can be worked singly off the 100-volt
+circuit. If, however, the lamps are scattered over a wide area, or in
+separate buildings somewhat far apart, as in a college or hospital, it
+may be better to select 200 volts as the supply pressure. Arc lamps can
+then be worked three in series with added resistance. The third step is
+to select the size of the dynamo unit and the amount of spare plant. It
+is desirable that there should be at least three dynamos, two of which
+are capable of taking the whole of the full load, the third being
+reserved to replace either of the others when required. The total power
+to be absorbed by the lamps and motors (if any) being given, together
+with an allowance for extensions, the size of the dynamos can be
+settled, and the power of the engines required to drive them determined.
+A good rule to follow is that the indicated horse-power (I.H.P.) of the
+engine should be double the dynamo full-load output in kilowatts; that
+is to say, for a 10-kilowatt dynamo an engine should be capable of
+giving 20 indicated (not nominal) H.P. From the I.H.P. of the engine, if
+a steam engine, the size of the boiler required for steam production
+becomes known. For small plants it is safe to reckon that, including
+water waste, boiler capacity should be provided equal to evaporating 40
+lb. of water per hour for every I.H.P. of the engine. The locomotive
+boiler is a convenient form; but where large amounts of steam are
+required, some modification of the Lancashire boiler or the water-tube
+boiler is generally adopted. In settling the electromotive force of the
+dynamo to be employed, attention must be paid to the question of
+charging secondary cells, if these are used. If a secondary battery is
+employed in connexion with 100-volt lamps, it is usual to put in 53 or
+54 cells. The electromotive force of these cells varies between 2.2 and
+1.8 volts as they discharge; hence the above number of cells is
+sufficient for maintaining the necessary electromotive force. For
+charging, however, it is necessary to provide 2.5 volts per cell, and
+the dynamo must therefore have an electromotive force of 135 volts,
+_plus_ any voltage required to overcome the fall of potential in the
+cable connecting the dynamo with the secondary battery. Supposing this
+to be 10 volts, it is safe to install dynamos having an electromotive
+force of 150 volts, since by means of resistance in the field circuits
+this electromotive force can be lowered to 110 or 115 if it is required
+at any time to dispense with the battery. The size of the secondary cell
+will be determined by the nature of the supply to be given after the
+dynamos have been stopped. It is usual to provide sufficient storage
+capacity to run all the lamps for three or four hours without assistance
+from the dynamo.
+
+  As an example taken from actual practice, the following figures give
+  the capacity of the plant put down to supply 500 8 c.p. lamps in a
+  hospital. The dynamos were 15-unit machines, having a full-load
+  capacity of 100 amperes at 150 volts, each coupled direct to an engine
+  of 25 H.P.; and a double plant of this description was supplied from
+  two steel locomotive boilers, each capable of evaporating 800 lb. of
+  water per hour. One dynamo during the day was used for charging the
+  storage battery of 54 cells; and at night the discharge from the
+  cells, together with the current from one of the dynamos, supplied the
+  lamps until the heaviest part of the load had been taken; after that
+  the current was drawn from the batteries alone. In working such a
+  plant it is necessary to have the means of varying the electromotive
+  force of the dynamo as the charging of the cells proceeds. When they
+  are nearly exhausted, their electromotive force is less than 2 volts;
+  but as the charging proceeds, a counter-electromotive force is
+  gradually built up, and the engineer-in-charge has to raise the
+  voltage of the dynamo in order to maintain a constant charging
+  current. This is effected by having the dynamos designed to give
+  normally the highest E.M.F. required, and then inserting resistance in
+  their field circuits to reduce it as may be necessary. The space and
+  attendance required for an oil-engine plant are much less than for a
+  steam-engine.
+
+_Public Supply._--The methods at present in successful operation for
+public electric supply fall into two broad divisions:--(1)
+continuous-current systems and (2) alternating-current systems.
+Continuous-current systems are either low- or high-pressure. In the
+former the current is generated by dynamos at some pressure less than
+500 volts, generally about 460 volts, and is supplied to users at half
+this pressure by means of a three-wire system (see below) of
+distribution, with or without the addition of storage batteries.
+
+
+  Low-pressure continuous supply.
+
+The general arrangements of a low-pressure continuous-current town
+supply station are as follows:--If steam is the motive power selected,
+it is generated under all the best conditions of economy by a battery of
+boilers, and supplied to engines which are now almost invariably coupled
+direct, each to its own dynamo, on one common bedplate; a multipolar
+dynamo is most usually employed, coupled direct to an enclosed engine.
+Parsons or Curtis steam turbines (see STEAM-ENGINE) are frequently
+selected, since experience has shown that the costs of oil and
+attendance are far less for this type than for the reciprocating engine,
+whilst the floor space and, therefore, the building cost are greatly
+reduced. In choosing the size of unit to be adopted, the engineer has
+need of considerable experience and discretion, and also a full
+knowledge of the nature of the public demand for electric current. The
+rule is to choose as large units as possible, consistent with security,
+because they are proportionately more economical than small ones. The
+over-all efficiency of a steam dynamo--that is, the ratio between the
+electrical power output, reckoned say in kilowatts, and the I.H.P. of
+the engine, reckoned in the same units--is a number which falls rapidly
+as the load decreases, but at full load may reach some such value as 80
+or 85%. It is common to specify the efficiency, as above defined, which
+must be attained by the plant at full-load, and also the efficiencies at
+quarter- and half-load which must be reached or exceeded. Hence in the
+selection of the size of the units the engineer is guided by the
+consideration that whatever units are in use shall be as nearly as
+possible fully loaded. If the demand on the station is chiefly for
+electric lighting, it varies during the hours of the day and night with
+tolerable regularity. If the output of the station, either in amperes or
+watts, is represented by the ordinates of a curve, the abscissae of
+which represent the hours of the day, this load diagram for a supply
+station with lighting load only, is a curve such as is shown in fig. 1,
+having a high peak somewhere between 6 and 8 P.M. The area enclosed by
+this load-diagram compared with the area of the circumscribing rectangle
+is called the _load-factor_ of the station. This varies from day to day
+during the year, but on the average for a simple lighting load is not
+generally above 10 or 12%, and may be lower. Thus the total output from
+the station is only some 10% on an average of that which it would be if
+the supply were at all times equal to the maximum demand. Roughly
+speaking, therefore, the total output of an electric supply station,
+furnishing current chiefly for electric lighting, is at best equal to
+about two hours' supply during the day at full load. Hence during the
+greater part of the twenty-four hours a large part of the plant is lying
+idle. It is usual to provide certain small sets of steam dynamos, called
+the daylight machines, for supplying the demand during the day and later
+part of the evening, the remainder of the machines being called into
+requisition only for a short time. Provision must be made for sufficient
+reserve of plant, so that the breakdown of one or more sets will not
+cripple the output of the station.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+
+  Three-wire system.
+
+Assuming current to be supplied at about 460 volts by different and
+separate steam dynamos, Dy1, Dy2 (fig. 2), the machines are connected
+through proper amperemeters and voltmeters with _omnibus bars_, O1, O2,
+O3, on a main switchboard, so that any dynamo can be put in connexion or
+removed. The switchboard is generally divided into three parts--one
+panel for the connexions of the positive feeders, F1, with the positive
+terminals of the generators; one for the negative feeders, F3, and
+negative generator terminals; while from the third (or middle-wire
+panel) proceed an equal number of middle-wire feeders, F2. These sets of
+conductors are led out into the district to be supplied with current,
+and are there connected into a distributing system, consisting of three
+separate insulated conductors, D1, D2, D3, respectively called the
+positive, middle and negative distributing mains. The lamps in the
+houses, H1, H2, &c., are connected between the middle and negative, and
+the middle and positive, mains by smaller supply and service wires. As
+far as possible the numbers of lamps installed on the two sides of the
+system are kept equal; but since it is not possible to control the
+consumption of current, it becomes necessary to provide at the station
+two small dynamos called the _balancing machines_, B1, B2, connected
+respectively between the middle and positive and the middle and negative
+omnibus bars. These machines may have their shafts connected together,
+or they may be driven by separate steam dynamos; their function is to
+supply the difference in the total current circulating through the whole
+of the lamps respectively on the two opposite sides of the middle wire.
+If storage batteries are employed in the station, it is usual to install
+two complete batteries, S1, S2, which are placed in a separate battery
+room and connected between the middle omnibus bar and the two outer
+omnibus bars. The extra electromotive force required to charge these
+batteries is supplied by two small dynamos b1, b2, called _boosters_. It
+is not unusual to join together the two balancing dynamos and the two
+boosters on one common bedplate, the shafts being coupled and in line,
+and to employ the balancing machines as electromotors to drive the
+boosters as required. By the use of _reversible boosters_, such as those
+made by the Lancashire Dynamo & Motor Company under the patents of
+Turnbull & M^cLeod, having four field windings on the booster magnets
+(see _The Electrician_, 1904, p. 303), it is possible to adjust the
+relative duty of the dynamos and battery so that the load on the supply
+dynamos is always constant. Under these conditions the main engines can
+be worked all the time at their maximum steam economy and a smaller
+engine plant employed. If the load in the station rises above the fixed
+amount, the batteries discharge in parallel with the station dynamos; if
+it falls below, the batteries are charged and the station dynamos take
+the external load.
+
+[Illustration: From _The Electrician_.
+
+FIGS. 3 and 4.--Low-pressure Supply Station.]
+
+
+  Generating stations.
+
+The general arrangements of a low-pressure supply station are shown in
+figs. 3 and 4. It consists of a boiler-house containing a bank of
+boilers, either Lancashire or Babcock & Wilcox being generally used (see
+BOILER), which furnish steam to the engines and dynamos, provision
+being made by duplicate steam-pipes or a ring main so that the failure
+of a single engine or dynamo does not cripple the whole supply. The
+furnace gases are taken through an economizer (generally Green's) so
+that they give up their heat to the cold feed water. If condensing water
+is available the engines are worked condensing, and this is an essential
+condition of economy when steam turbines are employed. Hence, either a
+condensing water pond or a cooling tower has to be provided to cool the
+condensing water and enable it to be used over and over again.
+Preferably the station should be situated near a river or canal and a
+railway siding. The steam dynamos are generally arranged in an
+engine-room so as to be overlooked from a switchboard gallery (fig. 3),
+from which all the control is carried out. The boiler furnaces are
+usually stoked by automatic stokers. Owing to the relatively small load
+factor (say 8 or 10%) of a station giving electric supply for lighting
+only, the object of every station engineer is to cultivate a demand for
+electric current for power during the day-time by encouraging the use of
+electric motors for lifts and other purposes, but above all to create a
+demand for traction purposes. Hence most urban stations now supply
+current not only for electric lighting but for running the town tramway
+system, and this traction load being chiefly a daylight load serves to
+keep the plant employed and remunerative. It is usual to furnish a
+continuous current supply for traction at 500 or 600 volts, although
+some station engineers are advocating the use of higher voltages. In
+those stations which supply current for traction, but which have a
+widely scattered lighting load, _double current_ dynamos are often
+employed, furnishing from one and the same armature a continuous current
+for traction purposes, and an alternating current for lighting purposes.
+
+
+  High-pressure continuous supply.
+
+In some places a high voltage system of electric supply by continuous
+current is adopted. In this case the current is generated at a pressure
+of 1000 or 2000 volts, and transmitted from the generating station by
+conductors, called high-pressure feeders, to certain sub-centres or
+transformer centres, which are either buildings above ground or cellars
+or excavations under the ground. In these transformer centres are placed
+machines, called _continuous-current transformers_, which transform the
+electric energy and create a secondary electric current at a lower
+pressure, perhaps 100 or 150 volts, to be supplied by distributing mains
+to users (see TRANSFORMERS). From these sub-centres insulated conductors
+are run back to the generating station, by which the engineer can start
+or stop the continuous-current rotatory transformers, and at the same
+time inform himself as to their proper action and the electromotive
+force at the secondary terminals. This system was first put in practice
+in Oxford, England, and hence has been sometimes called by British
+engineers "the Oxford system." It is now in operation in a number of
+places in England, such as Wolverhampton, Walsall, and Shoreditch in
+London. It has the advantage that in connexion with the low-pressure
+distributing system secondary batteries can be employed, so that a
+storage of electric energy is effected. Further, continuous-current arc
+lamps can be worked in series off the high-pressure mains, that is to
+say, sets of 20 to 40 arc lamps can be operated for the purpose of
+street lighting by means of the high-pressure continuous current.
+
+
+  Alternating supply.
+
+The alternating current systems in operation at the present time are the
+_single-phase_ system, with distributing transformers or transformer
+sub-centres, and the _polyphase_ systems, in which the alternating
+current is transformed down into an alternating current of low pressure,
+or, by means of rotatory transformers, into a continuous current. The
+general arrangement of a _single-phase_ alternating-current system is as
+follows: The generating station contains a number of alternators, A1 A2
+(fig. 5), producing single-phase alternating current, either at 1000,
+2000, or sometimes, as at Deptford and other places, 10,000 volts. This
+current is distributed from the station either at the pressure at which
+it is generated, or after being transformed up to a higher pressure by
+the transformer T. The alternators are sometimes worked in parallel,
+that is to say, all furnish their current to two common omnibus bars on
+a high-pressure switchboard, and each is switched into circuit at the
+moment when it is brought into step with the other machines, as shown by
+some form of _phase-indicator_. In some cases, instead of the
+high-pressure feeders starting from omnibus bars, each alternator works
+independently and the feeders are grouped together on the various
+alternators as required. A number of high-pressure feeders are carried
+from the main switchboard to various transformer sub-centres or else run
+throughout the district to which current is to be furnished. If the
+system laid down is the transformer sub-centre system, then at each of
+these sub-centres is placed a battery of alternating-current
+transformers, T1 T2 T3, having their primary circuits all joined in
+parallel to the terminals of the high-pressure feeders, and their
+secondary circuits all joined in parallel on a distributing main,
+suitable switches and cut-outs being interposed. The pressure of the
+current is then transformed down by these transformers to the required
+supply pressure. The secondary circuits of these transformers are
+generally provided with three terminals, so as to supply the
+low-pressure side on a three-wire system. It is not advisable to connect
+together directly the secondary circuits of all the different
+sub-centres, because then a fault or short circuit on one secondary
+system affects all the others. In banking together transformers in this
+manner in a sub-station it is necessary to take care that the
+transformation ratio and secondary drop (see TRANSFORMERS) are exactly
+the same, otherwise one transformer will take more than its full share
+of the load and will become overheated. The transformer sub-station
+system can only be adopted where the area of supply is tolerably
+compact. Where the consumers lie scattered over a large area, it is
+necessary to carry the high-pressure mains throughout the area, and to
+place a separate transformer or transformers in each building. From a
+financial point of view, this "house-to-house system" of
+alternating-current supply, generally speaking, is less satisfactory in
+results than the transformer sub-centre system. In the latter some of
+the transformers can be switched off, either by hand or by automatic
+apparatus, during the time when the load is light, and then no power is
+expended in magnetizing their cores. But with the house-to-house system
+the whole of the transformers continually remain connected with the
+high-pressure circuits; hence in the case of supply stations which have
+only an ordinary electric lighting load, and therefore a load-factor not
+above 10%, the efficiency of distribution is considerably diminished.
+
+[Illustration: FIG. 5.]
+
+The single-phase alternating-current system is defective in that it
+cannot be readily combined with secondary batteries for the storage of
+electric energy. Hence in many places preference is now given to the
+_polyphase system_. In such a system a polyphase alternating current,
+either two- or three-phase, is transmitted from the generating station
+at a pressure of 5000 to 10,000 volts, or sometimes higher, and at
+various sub-stations is transformed down, first by static transformers
+into an alternating current of lower pressure, say 500 volts, and then
+by means of rotatory transformers into a continuous current of 500
+volts or lower for use for lighting or traction.
+
+In the case of large cities such as London, New York, Chicago, Berlin
+and Paris the use of small supply stations situated in the interior of
+the city has gradually given way to the establishment of large supply
+stations outside the area; in these alternating current is generated on
+the single or polyphase system at a high voltage and transmitted by
+underground cables to sub-stations in the city, at which it is
+transformed down for distribution for private and public electric
+lighting and for urban electric traction.
+
+Owing to the high relative cost of electric power when generated in
+small amounts and the great advantages of generating it in proximity to
+coal mines and waterfalls, the supply of electric power in bulk to small
+towns and manufacturing districts has become a great feature in modern
+electrical engineering. In Great Britain, where there is little useful
+water power but abundance of coal, electric supply stations for supply
+in bulk have been built in the coal-producing districts of South Wales,
+the Midlands, the Clyde valley and Yorkshire. In these cases the current
+is a polyphase current generated at a high voltage, 5000 to 10,000
+volts, and sometimes raised again in pressure to 20,000 or 40,000 volts
+and transmitted by overhead lines to the districts to be supplied. It is
+there reduced in voltage by transformers and employed as an alternating
+current, or is used to drive polyphase motors coupled to direct current
+generators to reproduce the power in continuous current form. It is then
+distributed for local lighting, street or railway traction, driving
+motors, and metallurgical or electrochemical applications. Experience
+has shown that it is quite feasible to distribute in all directions for
+25 miles round a high-pressure generating station, which thus supplies
+an area of nearly 2000 sq. m. At such stations, employing large turbine
+engines and alternators, electric power may be generated at a works cost
+of 0.375d. per kilowatt (K.W.), the coal cost being less than 0.125d.
+per K.W., and the selling price to large load-factor users not more than
+0.5d. per K.W. The average price of supply from the local generating
+stations in towns and cities is from 3d. to 4d. per unit, electric
+energy for power and heating being charged at a lower rate than that for
+lighting only.
+
+
+  Conductors.
+
+We have next to consider the structure and the arrangement of the
+conductors employed to convey the currents from their place of creation
+to that of utilization. The conductors themselves for the most part
+consist of copper having a conductivity of not less than 98% according
+to Matthiessen's standard. They are distinguished as (1) _External
+conductors_, which are a part of the public supply and belong to the
+corporation or company supplying the electricity; (2) _Internal
+conductors_, or house wiring, forming a part of the structure of the
+house or building supplied and usually the property of its owner.
+
+
+  External conductors.
+
+The external conductors may be overhead or underground. _Overhead_
+conductors may consist of bare stranded copper cables carried on
+porcelain insulators mounted on stout iron or wooden poles. If the
+current is a high-pressure one, these insulators must be carefully
+tested, and are preferably of the pattern known as oil insulators. In
+and near towns it is necessary to employ insulated overhead conductors,
+generally india-rubber-covered stranded copper cables, suspended by
+leather loops from steel bearer wires which take the weight. The British
+Board of Trade have issued elaborate rules for the construction of
+overhead lines to transmit large electric currents. Where telephone and
+telegraph wires pass over such overhead electric lighting wires, they
+have to be protected from falling on the latter by means of guard wires.
+
+By far the largest part, however, of the external electric distribution
+is now carried out by _underground conductors_, which are either bare or
+insulated. Bare copper conductors may be carried underground in culverts
+or chases, air being in this case the insulating material, as in the
+overhead system. A culvert and covered chase is constructed under the
+road or side-walk, and properly shaped oak crossbars are placed in it
+carrying glass or porcelain insulators, on which stranded copper
+cables, or, preferably, copper strips placed edgeways, are stretched and
+supported. The advantages of this method of construction are cheapness
+and the ease with which connexions can be made with service-lines for
+house supply; the disadvantages are the somewhat large space in which
+coal-gas leaking out of gas-pipes can accumulate, and the difficulty of
+keeping the culverts at all times free from rain-water. Moisture has a
+tendency to collect on the negative insulators, and hence to make a dead
+earth on the negative side of the main; while unless the culverts are
+well ventilated, explosions from mixtures of coal-gas and air are liable
+to occur. Insulated cables are insulated either with a material which is
+in itself waterproof, or with one which is only waterproof in so far as
+it is enclosed in a waterproof tube, e.g. of lead. Gutta-percha and
+india-rubber are examples of materials of the former kind. Gutta-percha,
+although practically everlasting when in darkness and laid under water,
+as in the case of submarine cables, has not been found satisfactory for
+use with large systems of electric distribution, although much employed
+for telephone and telegraph work. Insulated underground external
+conductors are of three types:--(a) _Insulated Cables drawn into
+Pipes._--In this system of distribution cast-iron or stoneware pipes, or
+special stoneware conduits, or conduits made of a material called
+bitumen concrete, are first laid underground in the street. These
+contain a number of holes or "ways," and at intervals drawing-in boxes
+are placed which consist of a brick or cast-iron box having a
+water-tight lid, by means of which access is gained to a certain section
+of the conduit. Wires are used to draw in the cables, which are covered
+with either india-rubber or lead, the copper being insulated by means of
+paper, impregnated jute, or other similar material. The advantages of a
+drawing-in system are that spare ways can be left when the conduits are
+put in, so that at a future time fresh cables can be added without
+breaking up the roadway. (b) _Cables in Bitumen._--One of the earliest
+systems of distribution employed by T.A. Edison consisted in fixing two
+segment-shaped copper conductors in a steel tube, the interspace between
+the conductors and the tube being filled in with a bitumen compound. A
+later plan is to lay down an iron trough, in which the cables are
+supported by wooden bearers at proper distances, and fill in the whole
+with natural bitumen. This system has been carried out extensively by
+the Callendar Cable Company. Occasionally concentric lead-covered and
+armoured cables are laid in this way, and then form an expensive but
+highly efficient form of insulated conductor. In selecting a system of
+distribution regard must be paid to the nature of the soil in which the
+cables are laid. Lead is easily attacked by soft water, although under
+some conditions it is apparently exceedingly durable, and an atmosphere
+containing coal-gas is injurious to india-rubber. (c) _Armoured
+Cables._--In a very extensively used system of distribution armoured
+cables are employed. In this case the copper conductors, two, three or
+more in number, may be twisted together or arranged concentrically, and
+insulated by means of specially prepared jute or paper insulation,
+overlaid with a continuous tube of lead. Over the lead, but separated by
+a hemp covering, is put a steel armour consisting of two layers of steel
+strip, wound in opposite directions and kept in place by an external
+covering. Such a cable can be laid directly in the ground without any
+preparation other than the excavation of a simple trench, junction-boxes
+being inserted at intervals to allow of branch cables being taken off.
+The armoured cable used is generally of the concentric pattern (fig. 6).
+It consists of a stranded copper cable composed of a number of wires
+twisted together and overlaid with an insulating material. Outside this
+a tubular arrangement of copper wires and a second layer of insulation,
+and finally a protective covering of lead and steel wires or armour are
+placed. In some cases three concentric cylindrical conductors are formed
+by twisting wires or copper strips with insulating material between. In
+others two or three cables of stranded copper are embedded in insulating
+material and included in a lead sheath. This last type of cable is
+usually called a _two-_ or _three-core_ pattern cable (fig. 7).
+
+[Illustration: FIG. 6.--Armoured Concentric Cable (Section).
+
+  IC, Inner conductor.
+  OC, Outer conductor.
+  I, Insulation.
+  L, Lead sheath.
+  S, Steel armour.
+  H, Hemp covering.]
+
+[Illustration: FIG. 7.--Triple Conductor Armoured Cable (Section).
+
+  C, Copper conductor.
+  I, Insulation.
+  L, Lead sheath.
+  H, Hemp covering.
+  S, Steel armour.]
+
+The arrangement and nature of the external conductors depends on the
+system of electric supply in which they are used. In the case of
+continuous-current supply for incandescent electric lighting and motive
+power in small units, when the external conductors are laid down on the
+three-wire system, each main or branch cable in the street consists of a
+set of three conductors called the positive, middle and negative. Of
+these triple conductors some run from the supply station to various
+points in the area of supply without being tapped, and are called the
+_feeders_; others, called the _distributing mains_, are used for making
+connexions with the service lines of the consumers, one service line, as
+already explained, being connected to the middle conductor, and the
+other to either the positive or the negative one. Since the middle
+conductor serves to convey only the difference between the currents
+being used on the two sides of the system, it is smaller in section than
+the positive and negative ones. In laying out the system great judgment
+has to be exercised as to the selection of the points of attachment of
+the feeders to the distributing mains, the object being to keep a
+constant electric pressure or voltage between the two service-lines in
+all the houses independently of the varying demand for current. Legally
+the suppliers are under regulations to keep the supply voltage constant
+within 4% either way above or below the standard pressure. As a matter
+of fact very few stations do maintain such good regulation. Hence a
+considerable variation in the light given by the incandescent lamps is
+observed, since the candle-power of carbon glow lamps varies as the
+fifth or sixth power of the voltage of supply, i.e. a variation of only
+2% in the supply pressure affects the resulting candle-power of the
+lamps to the extent of 10 or 12%. This variation is, however, less in
+the case of metallic filament lamps (see LIGHTING: _Electric_). In the
+service-lines are inserted the meters for measuring the electric energy
+supplied to the customer (see METER, ELECTRIC).
+
+
+  Interior wiring.
+
+In the interior of houses and buildings the conductors generally consist
+of india-rubber-covered cables laid in wood casing. The copper wire must
+be tinned and then covered, first with a layer of unvulcanized pure
+india-rubber, then with a layer of vulcanized rubber, and lastly with
+one or more layers of protective cotton twist or tape. No conductor of
+this character employed for interior house-wiring should have a smaller
+insulation resistance than 300 megohms per mile when tested with a
+pressure of 600 volts after soaking 24 hours in water. The wood casing
+should, if placed in damp positions or under plaster, be well varnished
+with waterproof varnish. As far as possible all joints in the run of the
+cable should be avoided by the use of the so-called looping-in system,
+and after the wiring is complete, careful tests for insulation should be
+made. The Institution of Electrical Engineers of Great Britain have
+drawn up rules to be followed in interior house-wiring, and the
+principal Fire Insurance offices, following the lead of the Phoenix Fire
+Office, of London, have made regulations which, if followed, are a
+safeguard against bad workmanship and resulting possibility of damage by
+fire. Where fires having an electric origin have taken place, they have
+invariably been traced to some breach of these rules. Opinions differ,
+however, as to the value and security of this method of laying interior
+conductors in buildings, and two or three alternative systems have been
+much employed. In one of these, called the _interior conduit_ system,
+highly insulating waterproof and practically fireproof tubes or conduits
+replace the wooden casing; these, being either of plain insulating
+material, or covered with brass or steel armour, may be placed under
+plaster or against walls. They are connected by bends or joint-boxes.
+The insulated wires being drawn into them, any short circuit or heating
+of the wire cannot give rise to a fire, as it can only take place in the
+interior of a non-inflammable tube. A third system of electric light
+wiring is the safety concentric system, in which concentric conductors
+are used. The inner one, which is well insulated, consists of a
+copper-stranded cable. The outer may be a galvanized iron strand, a
+copper tape or braid, or a brass tube, and is therefore necessarily
+connected with the earth. A fourth system consists in the employment of
+twin insulated wires twisted together and sheathed with a lead tube; the
+conductor thus formed can be fastened by staples against walls, or laid
+under plaster or floors.
+
+The general arrangement for distributing current to the different
+portions of a building for the purpose of electric lighting is to run up
+one or more rising mains, from which branches are taken off to
+distributing boxes on each floor, and from these boxes to carry various
+branch circuits to the lamps. At the distributing boxes are collected
+the cut-outs and switches controlling the various circuits. When
+alternating currents are employed, it is usual to select as a type of
+conductor either twin-twisted conductor or concentric; and the
+employment of these types of cable, rather than two separate cables, is
+essential in any case where there are telephone or telegraph wires in
+proximity, for otherwise the alternating current would create inductive
+disturbances in the telephone circuit. The house-wiring also comprises
+the details of _switches_ for controlling the lamps, _cut-outs_ or fuses
+for preventing an excess of current passing, and fixtures or supports
+for lamps often of an ornamental character. For the details of these,
+special treatises on electric interior wiring must be consulted.
+
+  For further information the reader may be referred to the following
+  books:--C.H. Wordingham, _Central Electrical Stations_ (London, 1901);
+  A. Gay and C.Y. Yeaman, _Central Station Electricity Supply_ (London,
+  1906); S.P. Thompson, _Dynamo Electric Machinery_ (2 vols., London,
+  1905); E. Tremlett Carter and T. Davies, _Motive Power and Gearing_
+  (London, 1906); W.C. Clinton, _Electric Wiring_ (2nd ed., London,
+  1906); W. Perren Maycock, _Electric Wiring, Fitting, Switches and
+  Lamps_ (London, 1899); D. Salomons, _Electric Light Installations_
+  (London, 1894); Stuart A. Russell, _Electric Light Cables_ (London,
+  1901); F.A.C. Perrine, _Conductors for Electrical Distribution_
+  (London, 1903); E. Rosenberg, W.W. Haldane Gee and C. Kinzbrunner,
+  _Electrical Engineering_ (London, 1903); E.C. Metcalfe, _Practical
+  Electric Wiring for Lighting Installations_ (London, 1905); F.C.
+  Raphael, _The Wireman's Pocket Book_ (London, 1903).     (J. A. F.)
+
+
+  History.
+
+II. _Commercial Aspects._--To enable the public supply enterprises
+referred to in the foregoing section to be carried out in England,
+statutory powers became necessary to break up the streets. In the early
+days a few small stations were established for the supply of electricity
+within "block" buildings, or by means of overhead wires within
+restricted areas, but the limitations proved uneconomical and the
+installations were for the most part merged into larger undertakings
+sanctioned by parliamentary powers. In the year 1879 the British
+government had its attention directed for the first time to electric
+lighting as a possible subject for legislation, and the consideration of
+the then existing state of electric lighting was referred to a select
+committee of the House of Commons. No legislative action, however, was
+taken at that time. In fact the invention of the incandescent lamp was
+incomplete--Edison's British master-patent was only filed in Great
+Britain in November 1879. In 1881 and 1882 electrical exhibitions were
+held in Paris and at the Crystal Palace, London, where the improved
+electric incandescent lamp was brought before the general public. In
+1882 parliament passed the first Electric Lighting Act, and considerable
+speculation ensued. The aggregate capital of the companies registered in
+1882-1883 to carry out the public supply of electricity in the United
+Kingdom amounted to £15,000,000, but the onerous conditions of the act
+deterred investors from proceeding with the enterprise. Not one of the
+sixty-two provisional orders granted to companies in 1883 under the act
+was carried out. In 1884 the Board of Trade received only four
+applications for provisional orders, and during the subsequent four
+years only one order was granted. Capitalists declined to go on with a
+business which if successful could be taken away from them by local
+authorities at the end of twenty-one years upon terms of paying only the
+then value of the plant, lands and buildings, without regard to past or
+future profits, goodwill or other considerations. The electrical
+industry in Great Britain ripened at a time when public opinion was
+averse to the creation of further monopolies, the general belief being
+that railway, water and gas companies had in the past received valuable
+concessions on terms which did not sufficiently safeguard the interests
+of the community. The great development of industries by means of
+private enterprise in the early part of the 19th century produced a
+reaction which in the latter part of the century had the effect of
+discouraging the creation by private enterprise of undertakings
+partaking of the nature of monopolies; and at the same time efforts were
+made to strengthen local and municipal institutions by investing them
+with wider functions. There were no fixed principles governing the
+relations between the state or municipal authorities and commercial
+companies rendering monopoly services. The new conditions imposed on
+private enterprise for the purpose of safeguarding the interests of the
+public were very tentative, and a former permanent secretary of the
+Board of Trade has stated that the efforts made by parliament in these
+directions have sometimes proved injurious alike to the public and to
+investors. One of these tentative measures was the Tramways Act 1870,
+and twelve years later it was followed by the first Electric Lighting
+Act.
+
+It was several years before parliament recognized the harm that had been
+done by the passing of the Electric Lighting Act 1882. A select
+committee of the House of Lords sat in 1886 to consider the question of
+reform, and as a result the Electric Lighting Act 1888 was passed. This
+amending act altered the period of purchase from twenty-one to forty-two
+years, but the terms of purchase were not materially altered in favour
+of investors. The act, while stipulating for the consent of local
+authorities to the granting of provisional orders, gives the Board of
+Trade power in exceptional cases to dispense with the consent, but this
+power has been used very sparingly. The right of vetoing an undertaking,
+conferred on local authorities by the Electric Lighting Acts and also by
+the Tramways Act 1870, has frequently been made use of to exact unduly
+onerous conditions from promoters, and has been the subject of complaint
+for years. Although, in the opinion of ministers of the Crown, the
+exercise of the veto by local authorities has on several occasions led
+to considerable scandals, no government has so far been able, owing to
+the very great power possessed by local authorities, to modify the law
+in this respect. After 1888 electric lighting went ahead in Great
+Britain for the first time, although other countries where legislation
+was different had long previously enjoyed its benefits. The developments
+proceeded along three well-defined lines. In London, where none of the
+gas undertakings was in the hands of local authorities, many of the
+districts were allotted to companies, and competition was permitted
+between two and sometimes three companies. In the provinces the cities
+and larger towns were held by the municipalities, while the smaller
+towns, in cases where consents could be obtained, were left to the
+enterprise of companies. Where consents could not be obtained these
+towns were for some time left without supply.
+
+  Some statistics showing the position of the electricity supply
+  business respectively in 1896 and 1906 are interesting as indicating
+  the progress made and as a means of comparison between these two
+  periods of the state of the industry as a whole. In 1896 thirty-eight
+  companies were at work with an aggregate capital of about £6,000,000,
+  and thirty-three municipalities with electric lighting loans of nearly
+  £2,000,000. The figures for 1906, ten years later, show that 187
+  electricity supply companies were in operation with a total investment
+  of close on £32,000,000, and 277 municipalities with loans amounting
+  to close on £36,000,000. The average return on the capital invested in
+  the companies at the later period was 5.1% per annum. In 1896 the
+  average capital expenditure was about £100 per kilowatt of plant
+  installed; and £50 per kilowatt was regarded as a very low record. For
+  1906 the average capital expenditure per kilowatt installed was about
+  £81. The main divisions of the average expenditure are:--
+
+                             1896.   1906.
+    Land and buildings       22.3%   17.8%
+    Plant and machinery      36.7    36.5
+    Mains                    32.2    35.5
+    Meters and instruments    4.6     5.7
+    Provisional orders, &c.   3.2     2.8
+
+  The load connected, expressed in equivalents of eight candle-power
+  lamps, was 2,000,000 in 1896 and 24,000,000 in 1906. About one-third
+  of this load would be for power purposes and about two-thirds for
+  lighting. The Board of Trade units sold were 30,200,000 in 1896 and
+  533,600,000 in 1906, and the average prices per unit obtained were
+  5.7d. and 2.7d. respectively, or a revenue of £717,250 in 1896 and
+  over £6,000,000 in 1906. The working expenses per Board of Trade unit
+  sold, excluding depreciation, sinking fund and interest were as
+  follows:--
+
+                                   1896.    1906.
+    Generation and distribution    2.81d.   .99d.
+    Rent, rates and taxes           .35     .14
+    Management                      .81     .18
+    Sundries                        .10     .02
+                                   ------  ------
+                 Total             4.07d.  1.33d.
+
+  In 1896 the greatest output at one station was about 5½ million units,
+  while in 1906 the station at Manchester had the largest output of over
+  40 million units.
+
+  The capacity of the plants installed in the United Kingdom in 1906
+  was:--
+
+                               K.W.
+    Continuous current         417,000     / Provinces    333,000
+                                           \ London        84,000
+    Alternating current        132,000     / Provinces     83,000
+                                           \ London        49,000
+    Continuous current and \
+      alternating current   >  480,000     / Provinces    366,000
+      combined             /               \ London       114,000
+                             ---------
+                             1,029,000 k.w.
+
+
+  Economics.
+
+The economics of electric lighting were at first assumed to be similar
+to those of gas lighting. Experience, however, soon proved that there
+were important differences, one being that gas may be stored in
+gasometers without appreciable loss and the work of production carried
+on steadily without reference to fluctuations of demand. Electricity
+cannot be economically stored to the same extent, and for the most part
+it has to be used as it is generated. The demand for electric light is
+practically confined to the hours between sunset and midnight, and it
+rises sharply to a "peak" during this period. Consequently the
+generating station has to be equipped with plant of sufficient capacity
+to cope with the maximum load, although the peak does not persist for
+many minutes--a condition which is very uneconomical both as regards
+capital expenditure and working costs (see LIGHTING: _Electric_). In
+order to obviate the unproductiveness of the generating plant during the
+greater part of the day, electricity supply undertakings sought to
+develop the "daylight" load. This they did by supplying electricity for
+traction purposes, but more particularly for industrial power purposes.
+The difficulties in the way of this line of development, however, were
+that electric power could not be supplied cheaply enough to compete with
+steam, hydraulic, gas and other forms of power, unless it was generated
+on a very large scale, and this large demand could not be developed
+within the restricted areas for which provisional orders were granted
+and under the restrictive conditions of these orders in regard to
+situation of power-house and other matters.
+
+The leading factors which make for economy in electricity supply are the
+magnitude of the output, the load factor, and the diversity factor,
+also the situation of the power house, the means of distribution, and
+the provision of suitable, trustworthy and efficient plant. These
+factors become more favourable the larger the area and the greater and
+more varied the demand to be supplied. Generally speaking, as the output
+increases so the cost per unit diminishes, but the ratio (called the
+load factor) which the output during any given period bears to the
+_maximum_ possible output during the same period has a very important
+influence on costs. The ideal condition would be when a power station is
+working at its normal _maximum_ output continuously night and day. This
+would give a load-factor of 100%, and represents the ultimate ideal
+towards which the electrical engineer strives by increasing the area of
+his operations and consequently also the load and the variety of the
+overlapping demands. It is only by combining a large number of demands
+which fluctuate at different times--that is by achieving a high
+diversity factor--that the supplier of electricity can hope to approach
+the ideal of continuous and steady output. Owing to the dovetailing of
+miscellaneous demands the actual demand on a power station at any moment
+is never anything like the aggregate of all the maximum demands. One
+large station would require a plant of 36,000 k.w. capacity if all the
+demands came upon the station simultaneously, but the maximum demand on
+the generating plant is only 15,000 kilowatts. The difference between
+these two figures may be taken to represent the economy effected by
+combining a large number of demands on one station. In short, the
+keynote of progress in cheap electricity is increased and diversified
+demand combined with concentration of load. The average load-factor of
+all the British electricity stations in 1907 was 14.5%--a figure which
+tends to improve.
+
+
+  Power companies.
+
+Several electric power supply companies have been established in the
+United Kingdom to give practical effect to these principles. The
+Electric Lighting Acts, however, do not provide for the establishment of
+large power companies, and special acts of parliament have had to be
+promoted to authorize these undertakings. In 1898 several bills were
+introduced in parliament for these purposes. They were referred to a
+joint committee of both Houses of Parliament presided over by Lord
+Cross. The committee concluded that, where sufficient public advantages
+are shown, powers should be given for the supply of electricity over
+areas including the districts of several local authorities and involving
+the use of exceptional plant; that the usual conditions of purchase of
+the undertakings by the local authorities did not apply to such
+undertakings; that the period of forty-two years was "none too long" a
+tenure; and that the terms of purchase should be reconsidered. With
+regard to the provision of the Electric Lighting Acts which requires
+that the consent of the local authority should be obtained as a
+condition precedent to the granting of a provisional order, the
+committee was of opinion that the local authority should be entitled to
+be heard by the Board of Trade, but should not have the power of veto.
+No general legislation took place as a result of these recommendations,
+but the undermentioned special acts constituting power supply companies
+were passed.
+
+In 1902 the president of the Board of Trade stated that a bill had been
+drafted which he thought "would go far to meet all the reasonable
+objections that had been urged against the present powers by the local
+authorities." In 1904 the government introduced the Supply of
+Electricity Bill, which provided for the removal of some of the minor
+anomalies in the law relating to electricity. The bill passed through
+all its stages in the House of Lords but was not proceeded with in the
+House of Commons. In 1905 the bill was again presented to parliament but
+allowed to lie on the table. In the words of the president of the Board
+of Trade, there was "difficulty of dealing with this question so long as
+local authorities took so strong a view as to the power which ought to
+be reserved to them in connexion with this enterprise." In the official
+language of the council of the Institution of Electrical Engineers, the
+development of electrical science in the United Kingdom is in a backward
+condition as compared with other countries in respect of the practical
+application to the industrial and social requirements of the nation,
+notwithstanding that Englishmen have been among the first in inventive
+genius. The cause of such backwardness is largely due to the conditions
+under which the electrical industry has been carried on in the country,
+and especially to the restrictive character of the legislation governing
+the initiation and development of electrical power and traction
+undertakings, and to the powers of obstruction granted to local
+authorities. Eventually The Electric Lighting Act 1909 was passed. This
+Act provides:--(1) for the granting of provisional orders authorizing
+any local authority or company to supply electricity in bulk; (2) for
+the exercise of electric lighting powers by local authorities jointly
+under provisional order; (3) for the supply of electricity to railways,
+canals and tramways outside the area of supply with the consent of the
+Board of Trade; (4) for the compulsory acquisition of land for
+generating stations by provisional order; (5) for the exemption of
+agreements for the supply of electricity from stamp duty; and (6) for
+the amendment of regulations relating to July notices, revision of
+maximum price, certification of meters, transfer of powers of
+undertakers, auditors' reports, and other matters.
+
+The first of the Power Bills was promoted in 1898, under which it was
+proposed to erect a large generating station in the Midlands from which
+an area of about two thousand square miles would be supplied. Vigorous
+opposition was organized against the bill by the local authorities and
+it did not pass. The bill was revived in 1899, but was finally crushed.
+In 1900 and following years several power bills were successfully
+promoted, and the following are the areas over which the powers of these
+acts extend:
+
+In Scotland, (1) the Clyde Valley, (2) the county of Fife, (3) the
+districts described as "Scottish Central," comprising Linlithgow,
+Clackmannan, and portions of Dumbarton and Stirling, and (4) the
+Lothians, which include portions of Midlothian, East Lothian, Peebles
+and Lanark.
+
+In England there are companies operating in (1) Northumberland, (2)
+Durham county, (3) Lancashire, (4) South Wales and Carmarthenshire, (5)
+Derbyshire and Nottinghamshire, (6) Leicestershire and Warwickshire, (7)
+Yorkshire, (8) Shropshire, Worcestershire and Staffordshire, (9)
+Somerset, (10) Kent, (11) Cornwall, (12) portions of Gloucestershire,
+(13) North Wales, (14) North Staffordshire, Derbyshire, Denbighshire and
+Flintshire, (15) West Cumberland, (16) the Cleveland district, (17) the
+North Metropolitan district, and (18) the West Metropolitan area. An
+undertaking which may be included in this category, although it is not a
+Power Act company, is the Midland Electric Corporation in South
+Staffordshire. The systems of generation and distribution are generally
+10,000 or 11,000 volts three-phase alternating current.
+
+The powers conferred by these acts were much restricted as a result of
+opposition offered to them. In many cases the larger towns were cut out
+of the areas of supply altogether, but the general rule was that the
+power company was prohibited from supplying direct to a power consumer
+in the area of an authorized distributor without the consent of the
+latter, subject to appeal to the Board of Trade. Even this restricted
+power of direct supply was not embodied in all the acts, the power of
+taking supply in bulk being left only to certain authorized distributors
+and to authorized users such as railways and tramways. Owing chiefly to
+the exclusion of large towns and industrial centres from their areas,
+these power supply companies did not all prove as successful as was
+expected.
+
+In the case of one of the power companies which has been in a favourable
+position for the development of its business, the theoretical
+conclusions in regard to the economy of large production above stated
+have been amply demonstrated in practice. In 1901, when this company was
+emerging from the stage of a simple electric lighting company, the total
+costs per unit were 1.05d. with an output of about 2½ million units per
+annum. In 1905 the output rose to over 30 million units mostly for power
+and traction purposes, and the costs fell to 0.56d. per unit.
+
+An interesting phase of the power supply question has arisen in London.
+Under the general acts it was stipulated that the power-house should be
+erected within the area of supply, and amalgamation of undertakings was
+prohibited. After less than a decade of development several of the
+companies in London found themselves obliged to make considerable
+additions to their generating plants. But their existing buildings were
+full to their utmost capacity, and the difficulties of generating
+cheaply on crowded sites had increased instead of diminished during the
+interval. Several of the companies had to promote special acts of
+parliament to obtain relief, but the idea of a general combination was
+not considered to be within the range of practical politics until 1905,
+when the Administrative County of London Electric Power Bill was
+introduced. Compared with other large cities, the consumption of
+electricity in London is small. The output of electricity in New York
+for all purposes is 971 million units per annum or 282 units per head of
+population. The output of electricity in London is only 42 units per
+head per annum. There are in London twelve local authorities and
+fourteen companies carrying on electricity supply undertakings. The
+capital expenditure is £3,127,000 by the local authorities and
+£12,530,000 by the companies, and their aggregate capacity of plant is
+165,000 k.w. The total output is about 160,000,000 units per annum, the
+total revenue is over £2,000,000, and the gross profit before providing
+for interest and sinking fund charges is £1,158,000. The general average
+cost of production is 1.55d. per unit, and the average price per unit
+sold is 3.16d., but some of the undertakers have already supplied
+electricity to large power consumers at below 1d. per unit. By
+generating on a large scale for a wide variety of demands the promoters
+of the new scheme calculated to be able to offer electrical energy in
+bulk to electricity supply companies and local authorities at prices
+substantially below their costs of production at separate stations, and
+also to provide them and power users with electricity at rates which
+would compete with other forms of power. The authorized capital was
+fixed at £6,666,000, and the initial outlay on the first plant of 90,000
+k.w., mains, &c., was estimated at £2,000,000. The costs of generation
+were estimated at 0.15d. per unit, and the total cost at 0.52d. per unit
+sold. The output by the year 1911 was estimated at 133,500,000 units at
+an average selling price of 0.7d. per unit, to be reduced to 0.55d. by
+1916 when the output was estimated at 600,000,000 units. The bill
+underwent a searching examination before the House of Lords committee
+and was passed in an amended form. At the second reading in the House of
+Commons a strong effort was made to throw it out, but it was allowed to
+go to committee on the condition--contrary to the general
+recommendations of the parliamentary committee of 1898--that a purchase
+clause would be inserted; but amendments were proposed to such an extent
+that the bill was not reported for third reading until the eve of the
+prorogation of parliament. In the following year (1906) the
+Administrative Company's bill was again introduced in parliament, but
+the London County Council, which had previously adopted an attitude both
+hostile and negative, also brought forward a similar bill. Among other
+schemes, one known as the Additional Electric Power Supply Bill was to
+authorize the transmission of current from St Neots in Hunts. This bill
+was rejected by the House of Commons because the promoters declined to
+give precedence to the bill of the London County Council. The latter
+bill was referred to a hybrid committee with instructions to consider
+the whole question of London power supply, but it was ultimately
+rejected. The same result attended a second bill which was promoted by
+the London County Council in 1907. The question was settled by the
+London Electric Supply Act 1908, which constitutes the London County
+Council the purchasing authority (in the place of the local authorities)
+for the electric supply companies in London. This Act also enabled the
+Companies and other authorized undertakers to enter into agreements for
+the exchange of current and the linking-up of stations.
+
+
+  Legislation and regulations.
+
+The general supply of electricity is governed primarily by the two acts
+of parliament passed in 1882 and 1888, which apply to the whole of the
+United Kingdom. Until 1899 the other statutory provisions relating to
+electricity supply were incorporated in provisional orders granted by
+the Board of Trade and confirmed by parliament in respect of each
+undertaking, but in that year an Electric Lighting Clauses Act was
+passed by which the clauses previously inserted in each order were
+standardized. Under these acts the Board of Trade made rules with
+respect to applications for licences and provisional orders, and
+regulations for the protection of the public, and of the electric lines
+and works of the post office, and others, and also drew up a model form
+for provisional orders.
+
+Until the passing of the Electric Lighting Acts, wires could be placed
+wherever permission for doing so could be obtained, but persons breaking
+up streets even with the consent of the local authority were liable to
+indictment for nuisance. With regard to overhead wires crossing the
+streets, the local authorities had no greater power than any member of
+the public, but a road authority having power to make a contract for
+lighting the road could authorize others to erect poles and wires for
+the purpose. A property owner, however, was able to prevent wires from
+being taken over his property. The act of 1888 made all electric lines
+or other works for the supply of electricity, not entirely enclosed
+within buildings or premises in the same occupation, subject to
+regulations of the Board of Trade. The postmaster-general may also
+impose conditions for the protection of the post office. Urban
+authorities, the London County Council, and some other corporations have
+now powers to make by-laws for prevention of obstruction from posts and
+overhead wires for telegraph, telephone, lighting or signalling
+purposes; and electric lighting stations are now subject to the
+provisions of the Factory Acts.
+
+Parliamentary powers to supply electricity can now be obtained by (A)
+Special Act, (B) Licence, or (C) Provisional order.
+
+A. _Special Act._--Prior to the report of Lord Cross's joint committee
+of 1898 (referred to above), only one special act was passed. The
+provisions of the Electric Power Acts passed subsequently are not
+uniform, but the following are some of the usual provisions:--
+
+The company shall not supply electricity for lighting purposes except to
+authorized undertakers, provided that the energy supplied to any person
+for power may be used for lighting any premises on which the power is
+utilized. The company shall not supply energy (except to authorized
+undertakers) in any area which forms part of the area of supply of any
+authorized distributors without their consent, such consent not to be
+unreasonably withheld. The company is bound to supply authorized
+undertakers upon receiving notice and upon the applicants agreeing to
+pay for at least seven years an amount sufficient to yield 20% on the
+outlay (excluding generating plant or wires already installed). Other
+persons to whom the company is authorized to supply may require it upon
+terms to be settled, if not agreed, by the Board of Trade. Dividends are
+usually restricted to 8%, with a provision that the rate may be
+increased upon the average price charged being reduced. The maximum
+charges are usually limited to 3d. per unit for any quantity up to 400
+hours' supply, and 2d. per unit beyond. No preference is to be shown
+between consumers in like circumstances. Many provisions of the general
+Electric Lighting Acts are excluded from these special acts, in
+particular the clause giving the local authority the right to purchase
+the undertaking compulsorily.
+
+B. _Licence._--The only advantages of proceeding by licence are that it
+can be expeditiously obtained and does not require confirmation by
+parliament; but some of the provisions usually inserted in provisional
+orders would be _ultra vires_ in a licence, and the Electric Lighting
+Clauses Act 1899 does not extend to licences. The term of a licence does
+not exceed seven years, but is renewable. The consent of the local
+authority is necessary even to an application for a licence. None of the
+licences that have been granted is now in force.
+
+C. _Provisional Order._--An intending applicant for a provisional order
+must serve notice of his intention on every local authority within the
+proposed area of supply on or before the 1st of July prior to the
+session in which application is to be made to the Board of Trade. This
+provision has given rise to much complaint, as it gives the local
+authorities a long time for bargaining and enables them to supersede
+the company's application by themselves applying for provisional orders.
+The Board of Trade generally give preference to the applications of
+local authorities.
+
+In 1905 the Board of Trade issued a memorandum stating that, in view of
+the revocation of a large number of provisional orders which had been
+obtained by local authorities, or in regard to which local authorities
+had entered into agreements with companies for carrying the orders into
+effect (which agreements were in many cases _ultra vires_ or at least of
+doubtful validity), it appeared undesirable that a local authority
+should apply for a provisional order without having a definite intention
+of exercising the powers, and that in future the Board of Trade would
+not grant an order to a local authority unless the board were satisfied
+that the powers would be exercised within a specified period.
+
+Every undertaking authorized by provisional order is subject to the
+provision of the general act entitling the local authority to purchase
+compulsorily at the end of forty-two years (or shorter period), or after
+the expiration of every subsequent period of ten years (unless varied by
+agreement between the parties with the consent of the Board of Trade),
+so much of the undertaking as is within the jurisdiction of the
+purchasing authority upon the terms of paying the then value of all
+lands, buildings, works, materials and plant, suitable to and used for
+the purposes of the undertaking; provided that the value of such lands,
+&c., shall be deemed to be their fair market value at the time of
+purchase, due regard being had to the nature and then condition and
+state of repair thereof, and to the circumstance that they are in such
+positions as to be ready for immediate working, and to the suitability
+of the same to the purposes of the undertaking, and where a part only of
+the undertaking is purchased, to any loss occasioned by severance, but
+without any addition in respect of compulsory purchase or of goodwill,
+or of any profits which may or might have been or be made from the
+undertaking or any similar consideration. Subject to this right of
+purchase by the local authority, a provisional order (but not a licence)
+may be for such period as the Board of Trade may think proper, but so
+far no limit has been imposed, and unless purchased by a local authority
+the powers are held in perpetuity. No monopoly is granted to
+undertakers, and since 1889 the policy of the Board of Trade has been to
+sanction two undertakings in the same metropolitan area, preferably
+using different systems, but to discourage competing schemes within the
+same area in the provinces. Undertakers must within two years lay mains
+in certain specified streets. After the first eighteen months they may
+be required to lay mains in other streets upon conditions specified in
+the order, and any owner or occupier of premises within 50 yds. of a
+distributing main may require the undertakers to give a supply to his
+premises; but the consumer must pay the cost of the lines laid upon his
+property and of so much outside as exceeds 60 ft. from the main, and he
+must also contract for two and in some cases for three years' supply.
+But undertakers are prohibited in making agreements for supply from
+showing any undue preference. The maximum price in London is 13s. 4d.
+per quarter for any quantity up to 20 units, and beyond that 8d. per
+unit, but 11s. 8d. per quarter up to 20 units and 7d. per unit beyond is
+the more general maximum. The "Bermondsey clause" requires the
+undertakers (local authority) so to fix their charges (not exceeding the
+specified maximum) that the revenue shall not be less than the
+expenditure.
+
+There is no statutory obligation on municipalities to provide for
+depreciation of electricity supply undertakings, but after providing for
+all expenses, interest on loans, and sinking fund instalments, the local
+authority may create a reserve fund until it amounts, with interest, to
+one-tenth of the aggregate capital expenditure. Any deficiency when not
+met out of reserve is payable out of the local rates.
+
+The principle on which the Local Government Board sanctions municipal
+loans for electric lighting undertakings is that the period of the loan
+shall not exceed the life of the works, and that future ratepayers shall
+not be unduly burdened. The periods of the loans vary from ten years for
+accumulators and arc lamps to sixty years for lands. Within the county
+of London the loans raised by the metropolitan borough councils for
+electrical purposes are sanctioned by the London County Council, and
+that body allows a minimum period of twenty years for repayment. Up to
+1904-1905, 245 loans had been granted by the council amounting in the
+aggregate to £4,045,067.
+
+
+  Standardization.
+
+In 1901 the Institution of Civil Engineers appointed a committee to
+consider the advisability of standardizing various kinds of iron and
+steel sections. Subsequently the original reference was enlarged, and in
+1902 the Institution of Electrical Engineers was invited to co-operate.
+The treasury, as well as railway companies, manufacturers and others,
+have made grants to defray the expenses. The committee on electrical
+plant has ten sub-committees. In August 1904 an interim report was
+issued by the sub-committee on generators, motors and transformers,
+dealing with pressures and frequencies, rating of generators and motors,
+direct-current generators, alternating-current generators, and motors.
+
+In 1903 the specification for British standard tramway rails and
+fish-plates was issued, and in 1904 a standard specification for tubular
+tramway poles was issued. A sectional committee was formed in 1904 to
+correspond with foreign countries with regard to the formation of an
+electrical international commission to study the question of an
+international standardization of nomenclature and ratings of electrical
+apparatus and machinery.
+
+
+  The electrical industry.
+
+The electrical manufacturing branch, which is closely related to the
+electricity supply and other operating departments of the electrical
+industry, only dates from about 1880. Since that time it has undergone
+many vicissitudes. It began with the manufacture of small arc lighting
+equipments for railway stations, streets and public buildings. When the
+incandescent lamp became a commercial article, ship-lighting sets and
+installations for theatres and mansions constituted the major portion of
+the electrical work. The next step was the organization of
+house-to-house distribution of electricity from small "central
+stations," ultimately leading to the comprehensive public supply in
+large towns, which involved the manufacture of generating and
+distributing plants of considerable magnitude and complexity. With the
+advent of electric traction about 1896, special machinery had to be
+produced, and at a later stage the manufacturer had to solve problems in
+connexion with bulk supply in large areas and for power purposes. Each
+of these main departments involved changes in ancillary manufactures,
+such as cables, switches, transformers, meters, &c., so that the
+electrical manufacturing industry has been in a constant state of
+transition. At the beginning of the period referred to Germany and
+America were following the lead of England in theoretical developments,
+and for some time Germany obtained electrical machinery from England.
+Now scarcely any electrical apparatus is exported to Germany, and
+considerable imports are received by England from that country and
+America. The explanation is to be found mainly in the fact that the
+adverse legislation of 1882 had the effect of restricting enterprise,
+and while British manufacturers were compulsorily inert during periods
+of impeded growth of the two most important branches of the
+industry--electric lighting and traction--manufacturers in America and
+on the continent of Europe, who were in many ways encouraged by their
+governments, devoted their resources to the establishment of factories
+and electrical undertakings, and to the development of efficient selling
+organizations at home and abroad. When after the amendment of the
+adverse legislation in 1888 a demand for electrical machinery arose in
+England, the foreign manufacturers were fully organized for trade on a
+large scale, and were further aided by fiscal conditions to undersell
+English manufacturers, not only in neutral markets, but even in their
+own country. Successful manufacture on a large scale is possible only by
+standardizing the methods of production. English manufacturers were not
+able to standardize because they had not the necessary output. There had
+been no repetitive demand, and there was no production on a large scale.
+Foreign manufacturers, however, were able to standardize by reason of
+the large uniform demand which existed for their manufactures.
+Statistics are available showing the extent to which the growth of the
+electrical manufacturing industry in Great Britain was delayed. Nearly
+twenty years after the inception of the industry there were only
+twenty-four manufacturing companies registered in the United Kingdom,
+having an aggregate subscribed capital of under £7,000,000. But in 1907
+there were 292 companies with over £42,000,000 subscribed capital. The
+cable and incandescent lamp sections show that when the British
+manufacturers are allowed opportunities they are not slow to take
+advantage of them. The cable-making branch was established under the
+more encouraging conditions of the telegraph industry, and the lamp
+industry was in the early days protected by patents. Other departments
+not susceptible to foreign competition on account of freightage, such as
+the manufacture of storage batteries and rolling stock, are also fairly
+prosperous. In departments where special circumstances offer a prospect
+of success, the technical skill, commercial enterprise and general
+efficiency of British manufacturers manifest themselves by positive
+progress and not merely by the continuance of a struggle against adverse
+conditions. The normal posture of the British manufacturer of electrical
+machinery has been described as one of desperate defence of his home
+trade; that of the foreign manufacturer as one of vigorous attack upon
+British and other open markets. In considering the position of English
+manufacturers as compared with their foreign rivals, some regard should
+be had to the patent laws. One condition of a grant of a patent in most
+foreign countries is that the patent shall be worked in those countries
+within a specified period. But a foreign inventor was until 1907 able to
+secure patent protection in Great Britain without any obligation to
+manufacture there. The effect of this was to encourage the manufacture
+of patented apparatus in foreign countries, and to stimulate their
+exportation to Great Britain in competition with British products. With
+regard to the electrochemical industry the progress which has been
+achieved by other nations, notably Germany, is very marvellous by
+comparison with the advance made by England, but to state the reasons
+why this industry has had such extraordinary development in Germany,
+notwithstanding that many of the fundamental inventions were made in
+England, would require a statement of the marked differences in the
+methods by which industrial progress is promoted in the two countries.
+
+There has been very little solidarity among those interested in the
+commercial development of electricity, and except for the discussion of
+scientific subjects there has been very little organization with the
+object of protecting and promoting common interests. (E. GA.)
+
+
+FOOTNOTES:
+
+  [1] British Patent Specification, No. 5306 of 1878, and No. 602 of
+    1880.
+
+  [2] Ibid. No. 3988 of 1878.
+
+
+
+
+ELECTRIC WAVES. § 1. Clerk Maxwell proved that on his theory
+electromagnetic disturbances are propagated as a wave motion through the
+dielectric, while Lord Kelvin in 1853 (_Phil. Mag._ [4] 5, p. 393)
+proved from electromagnetic theory that the discharge of a condenser is
+oscillatory, a result which Feddersen (_Pogg. Ann._ 103, p. 69, &c.)
+verified by a beautiful series of experiments. The oscillating discharge
+of a condenser had been inferred by Henry as long ago as 1842 from his
+experiments on the magnetization produced in needles by the discharge of
+a condenser. From these two results it follows that electric waves must
+be passing through the dielectric surrounding a condenser in the act of
+discharging, but it was not until 1887 that the existence of such waves
+was demonstrated by direct experiment. This great step was made by Hertz
+(_Wied. Ann._ 34, pp. 155, 551, 609; _Ausbreitung der elektrischen
+Kraft_, Leipzig, 1892), whose experiments on this subject form one of
+the greatest contributions ever made to experimental physics. The
+difficulty which had stood in the way of the observations of these waves
+was the absence of any method of detecting electrical and magnetic
+forces, reversed some millions of times per second, and only lasting for
+an exceedingly short time. This was removed by Hertz, who showed that
+such forces would produce small sparks between pieces of metal very
+nearly in contact, and that these sparks were sufficiently regular to be
+used to detect electric waves and to investigate their properties. Other
+and more delicate methods have subsequently been discovered, but the
+results obtained by Hertz with his detector were of such signal
+importance, that we shall begin our account of experiments on these
+waves by a description of some of Hertz's more fundamental experiments.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+To produce the waves Hertz used two forms of vibrator. The first is
+represented in fig. 1. A and B are two zinc plates about 40 cm. square;
+to these brass rods, C, D, each about 30 cm. long, are soldered,
+terminating in brass balls E and F. To get good results it is necessary
+that these balls should be very brightly polished, and as they get
+roughened by the sparks which pass between them it is necessary to
+repolish them at short intervals; they should be shaded from light and
+from sparks, or other source of ultra-violet light. In order to excite
+the waves, C and D are connected to the two poles of an induction coil;
+sparks cross the air-gap which becomes a conductor, and the charges on
+the plates oscillate backwards and forwards like the charges on the
+coatings of a Leyden jar when it is short-circuited. The object of
+polishing the balls and screening off light is to get a sudden and sharp
+discharge; if the balls are rough there will be sharp points from which
+the charge will gradually leak, and the discharge will not be abrupt
+enough to start electrical vibrations, as these have an exceedingly
+short period. From the open form of this vibrator we should expect the
+radiation to be very large and the rate of decay of the amplitude very
+rapid. Bjerknes (_Wied. Ann._ 44, p. 74) found that the amplitude fell
+to 1/e of the original value, after a time 4T where T was the period of
+the electrical vibrations. Thus after a few vibrations the amplitude
+becomes inappreciable. To detect the waves produced by this vibrator
+Hertz used a piece of copper wire bent into a circle, the ends being
+furnished with two balls, or a ball and a point connected by a screw, so
+that the distance between them admitted of very fine adjustment. The
+radius of the circle for use with the vibrator just described was 35
+cm., and was so chosen that the free period of the detector might be the
+same as that of the vibrator, and the effects in it increased by
+resonance. It is evident, however, that with a primary system as greatly
+damped as the vibrator used by Hertz, we could not expect very marked
+resonance effects, and as a matter of fact the accurate timing of
+vibrator and detector in this case is not very important. With
+electrical vibrators which can maintain a large number of vibrations,
+resonance effects are very striking, as is beautifully shown by the
+following experiment due to Lodge (_Nature_, 41, p. 368), whose
+researches have greatly advanced our knowledge of electric waves. A and
+C (fig. 2) are two Leyden jars, whose inner and outer coatings are
+connected by wires, B and D, bent so as to include a considerable area.
+There is an air-break in the circuit connecting the inside and outside
+of one of the jars, A, and electrical oscillations are started in A by
+joining the inside and outside with the terminals of a coil or
+electrical machine. The circuit in the jar C is provided with a sliding
+piece, F, by means of which the self-induction of the discharging
+circuit, and, therefore, the time of an electrical oscillation of the
+jar, can be adjusted. The inside and outside of this jar are put almost,
+but not quite, into electrical contact by means of a piece of tin-foil,
+E, bent over the lip of the jar. The jars are placed face to face so
+that the circuits B and D are parallel to each other, and approximately
+at right angles to the line joining their centres. When the electrical
+machine is in action sparks pass across the air-break in the circuit in
+A, and by moving the slider F it is possible to find one position for it
+in which sparks pass from the inside to the outside of C across the
+tin-foil, while when the slider is moved a short distance on either side
+of this position the sparks cease.
+
+Hertz found that when he held his detector in the neighbourhood of the
+vibrator minute sparks passed between the balls. These sparks were not
+stopped when a large plate of non-conducting substance, such as the wall
+of a room, was interposed between the vibrator and detector, but a large
+plate of very thin metal stopped them completely.
+
+To illustrate the analogy between electric waves and waves of light
+Hertz found another form of apparatus more convenient. The vibrator
+consisted of two equal brass cylinders, 12 cm. long and 3 cm. in
+diameter, placed with their axes coincident, and in the focal line of a
+large zinc parabolic mirror about 2 m. high, with a focal length of 12.5
+cm. The ends of the cylinders nearest each other, between which the
+sparks passed, were carefully polished. The detector, which was placed
+in the focal line of an equal parabolic mirror, consisted of two lengths
+of wire, each having a straight piece about 50 cm. long and a curved
+piece about 15 cm. long bent round at right angles so as to pass through
+the back of the mirror. The ends which came through the mirror were
+connected with a spark micrometer, the sparks being observed from behind
+the mirror. The mirrors are shown, in fig. 3.
+
+[Illustration: FIG. 3.]
+
+§ 2. _Reflection and Refraction._--To show the reflection of the waves
+Hertz placed the mirrors side by side, so that their openings looked in
+the same direction, and their axes converged at a point about 3 m. from
+the mirrors. No sparks were then observed in the detector when the
+vibrator was in action. When, however, a large zinc plate about 2 m.
+square was placed at right angles to the line bisecting the angle
+between the axes of the mirrors sparks became visible, but disappeared
+again when the metal plate was twisted through an angle of about 15° to
+either side. This experiment showed that electric waves are reflected,
+and that, approximately at any rate, the angle of incidence is equal to
+the angle of reflection. To show refraction Hertz used a large prism
+made of hard pitch, about 1.5 m. high, with a slant side of 1.2 m. and
+an angle of 30°. When the waves from the vibrator passed through this
+the sparks in the detector were not excited when the axes of the two
+mirrors were parallel, but appeared when the axis of the mirror
+containing the detector made a certain angle with the axis of that
+containing the vibrator. When the system was adjusted for minimum
+deviation the sparks were most vigorous when the angle between the axes
+of the mirrors was 22°. This corresponds to an index of refraction of
+1.69.
+
+§ 3. _Analogy to a Plate of Tourmaline._--If a screen be made by winding
+wire round a large rectangular framework, so that the turns of the wire
+are parallel to one pair of sides of the frame, and if this screen be
+interposed between the parabolic mirrors when placed so as to face each
+other, there will be no sparks in the detector when the turns of the
+wire are parallel to the focal lines of the mirror; but if the frame is
+turned through a right angle so that the wires are perpendicular to the
+focal lines of the mirror the sparks will recommence. If the framework
+is substituted for the metal plate in the experiment on the reflection
+of electric waves, sparks will appear in the detector when the wires are
+parallel to the focal lines of the mirrors, and will disappear when the
+wires are at right angles to these lines. Thus the framework reflects
+but does not transmit the waves when the electric force in them is
+parallel to the wires, while it transmits but does not reflect waves in
+which the electric force is at right angles to the wires. The wire
+framework behaves towards the electric waves exactly as a plate of
+tourmaline does to waves of light. Du Bois and Rubens (_Wied. Ann._ 49,
+p. 593), by using a framework wound with very fine wire placed very
+close together, have succeeded in polarizing waves of radiant heat,
+whose wave length, although longer than that of ordinary light, is very
+small compared with that of electric waves.
+
+§ 4. _Angle of Polarization._--When light polarized at right angles to
+the plane of incidence falls on a refracting substance at an angle
+tan^{-1}µ, where µ is the refractive index of the substance, all the
+light is refracted and none reflected; whereas when light is polarized
+in the plane of incidence, some of the light is always reflected
+whatever the angle of incidence. Trouton (_Nature_, 39, p. 391) showed
+that similar effects take place with electric waves. From a paraffin
+wall 3 ft. thick, reflection always took place when the electric force
+in the incident wave was at right angles to the plane of incidence,
+whereas at a certain angle of incidence there was no reflection when the
+vibrator was turned, so that the electric force was in the plane of
+incidence. This shows that on the electromagnetic theory of light the
+electric force is at right angles to the plane of polarization.
+
+[Illustration: FIG. 4.]
+
+§ 5. _Stationary Electrical Vibrations._--Hertz (_Wied. Ann._ 34, p.
+609) made his experiments on these in a large room about 15 m. long. The
+vibrator, which was of the type first described, was placed at one end
+of the room, its plates being parallel to the wall, at the other end a
+piece of sheet zinc about 4 m. by 2 m. was placed vertically against the
+wall. The detector--the circular ring previously described--was held so
+that its plane was parallel to the metal plates of the vibrator, its
+centre on the line at right angles to the metal plate bisecting at right
+angles the spark gap of the vibrator, and with the spark gap of the
+detector parallel to that of the vibrator. The following effects were
+observed when the detector was moved about. When it was close up to the
+zinc plate there were no sparks, but they began to pass feebly as soon
+as it was moved forward a little way from the plate, and increased
+rapidly in brightness until it was about 1.8 m. from the plate, when
+they attained their maximum. When its distance was still further
+increased they diminished in brightness, and vanished again at a
+distance of about 4 m. from the plate. When the distance was still
+further increased they reappeared, attained another maximum, and so on.
+They thus exhibited a remarkable periodicity similar to that which
+occurs when stationary vibrations are produced by the interference of
+direct waves with those reflected from a surface placed at right angles
+to the direction of propagation. Similar periodic alterations in the
+spark were observed by Hertz when the waves, instead of passing freely
+through the air and being reflected by a metal plate at the end of the
+room, were led along wires, as in the arrangement shown in fig. 4. L and
+K are metal plates placed parallel to the plates of the vibrator, long
+parallel wires being attached to act as guides to the waves which were
+reflected from the isolated end. (Hertz used only one plate and one
+wire, but the double set of plates and wires introduced by Sarasin and
+De la Rive make the results more definite.) In this case the detector is
+best placed so that its plane is at right angles to the wires, while the
+air space is parallel to the plane containing the wires. The sparks
+instead of vanishing when the detector is at the far end of the wire are
+a maximum in this position, but wax and wane periodically as the
+detector is moved along the wires. The most obvious interpretation of
+these experiments was the one given by Hertz--that there was
+interference between the direct waves given out by the vibrator and
+those reflected either from the plate or from the ends of the wire, this
+interference giving rise to stationary waves. The places where the
+electric force was a maximum were the places where the sparks were
+brightest, and the places where the electric force was zero were the
+places where the sparks vanished. On this explanation the distance
+between two consecutive places where the sparks vanished would be half
+the wave length of the waves given out by the vibrator.
+
+Some very interesting experiments made by Sarasin and De la Rive
+(_Comptes rendus_, 115, p. 489) showed that this explanation could not
+be the true one, since by using detectors of different sizes they found
+that the distance between two consecutive places where the sparks
+vanished depended mainly upon the size of the detector, and very little
+upon that of the vibrator. With small detectors they found the distance
+small, with large detectors, large; in fact it is directly proportional
+to the diameter of the detector. We can see that this result is a
+consequence of the large damping of the oscillations of the vibrator and
+the very small damping of those of the detector. Bjerknes showed that
+the time taken for the amplitude of the vibrations of the vibrator to
+sink to 1/e of their original value was only 4T, while for the detector
+it was 500T', when T and T' are respectively the times of vibration of
+the vibrator and the detector. The rapid decay of the oscillations of
+the vibrator will stifle the interference between the direct and the
+reflected wave, as the amplitude of the direct wave will, since it is
+emitted later, be much smaller than that of the reflected one, and not
+able to annul its effects completely; while the well-maintained
+vibrations of the detector will interfere and produce the effects
+observed by Sarasin and De la Rive. To see this let us consider the
+extreme case in which the oscillations of the vibrator are absolutely
+dead-beat. Here an impulse, starting from the vibrator on its way to the
+reflector, strikes against the detector and sets it in vibration; it
+then travels up to the plate and is reflected, the electric force in the
+impulse being reversed by reflection. After reflection the impulse again
+strikes the detector, which is still vibrating from the effects of the
+first impact; if the phase of this vibration is such that the reflected
+impulse tends to produce a current round the detector in the same
+direction as that which is circulating from the effects of the first
+impact, the sparks will be increased, but if the reflected impulse tends
+to produce a current in the opposite direction the sparks will be
+diminished. Since the electric force is reversed by reflection, the
+greatest increase in the sparks will take place when the impulse finds,
+on its return, the detector in the opposite phase to that in which it
+left it; that is, if the time which has elapsed between the departure
+and return of the impulse is equal to an odd multiple of half the time
+of vibration of the detector. If d is the distance of the detector from
+the reflector when the sparks are brightest, and V the velocity of
+propagation of electromagnetic disturbance, then 2d/V = (2n + 1)(T'/2);
+where n is an integer and T' the time of vibration of the detector, the
+distance between two spark maxima will be VT'/2, and the places where
+the sparks are a minimum will be midway between the maxima. Sarasin and
+De la Rive found that when the same detector was used the distance
+between two spark maxima was the same with the waves through air
+reflected from a metal plate and with those guided by wires and
+reflected from the free ends of the wire, the inference being that the
+velocity of waves along wires is the same as that through the air. This
+result, which follows from Maxwell's theory, when the wires are not too
+fine, had been questioned by Hertz on account of some of his
+experiments on wires.
+
+§ 6. _Detectors._--The use of a detector with a period of vibration of
+its own thus tends to make the experiments more complicated, and many
+other forms of detector have been employed by subsequent experimenters.
+For example, in place of the sparks in air the luminous discharge
+through a rarefied gas has been used by Dragoumis, Lecher (who used
+tubes without electrodes laid across the wires in an arrangement
+resembling that shown in fig. 7) and Arons. A tube containing neon at a
+low pressure is especially suitable for this purpose. Zehnder (_Wied.
+Ann._ 47, p. 777) used an exhausted tube to which an external
+electromotive force almost but not quite sufficient of itself to produce
+a discharge was applied; here the additional electromotive force due to
+the waves was sufficient to start the discharge. Detectors depending on
+the heat produced by the rapidly alternating currents have been used by
+Paalzow and Rubens, Rubens and Ritter, and I. Klemencic. Rubens measured
+the heat produced by a bolometer arrangement, and Klemencic used a
+thermo-electric method for the same purpose; in consequence of the great
+increase in the sensitiveness of galvanometers these methods are now
+very frequently resorted to. Boltzmann used an electroscope as a
+detector. The spark gap consisted of a ball and a point, the ball being
+connected with the electroscope and the point with a battery of 200 dry
+cells. When the spark passed the cells charged up the electroscope.
+Ritter utilized the contraction of a frog's leg as a detector, Lucas and
+Garrett the explosion produced by the sparks in an explosive mixture of
+hydrogen and oxygen; while Bjerknes and Franke used the mechanical
+attraction between oppositely charged conductors. If the two sides of
+the spark gap are connected with the two pairs of quadrants of a very
+delicate electrometer, the needle of which is connected with one pair of
+quadrants, there will be a deflection of the electrometer when the
+detector is struck by electric waves. A very efficient detector is that
+invented by E. Rutherford (_Trans. Roy. Soc._ A. 1897, 189, p. 1); it
+consists of a bundle of fine iron wires magnetized to saturation and
+placed inside a small magnetizing coil, through which the electric waves
+cause rapidly alternating currents to pass which demagnetize the soft
+iron. If the instrument is used to detect waves in air, long straight
+wires are attached to the ends of the demagnetizing coil to collect the
+energy from the field; to investigate waves in wires it is sufficient to
+make a loop or two in the wire and place the magnetized piece of iron
+inside it. The amount of demagnetization which can be observed by the
+change in the deflection of a magnetometer placed near the iron,
+measures the intensity of the electric waves, and very accurate
+determinations can be made with ease with this apparatus. It is also
+very delicate, though in this respect it does not equal the detector to
+be next described, the coherer; Rutherford got indications in 1895 when
+the vibrator was ¾ of a mile away from the detector, and where the waves
+had to traverse a thickly populated part of Cambridge. It can also be
+used to measure the coefficient of damping of the electric waves, for
+since the wire is initially magnetized to saturation, if the direction
+of the current when it first begins to flow in the magnetizing coil is
+such as to tend to increase the magnetization of the wire, it will
+produce no effect, and it will not be until the current is reversed that
+the wire will lose some of its magnetization. The effect then gives the
+measure of the intensity half a period after the commencement of the
+waves. If the wire is put in the coil the opposite way, i.e. so that the
+magnetic force due to the current begins at once to demagnetize the
+wire, the demagnetization gives a measure of the initial intensity of
+the waves. Comparing this result with that obtained when the wires were
+reversed, we get the coefficient of damping. A very convenient detector
+of electric waves is the one discovered almost simultaneously by
+Fessenden (_Electrotech. Zeits._, 1903, 24, p. 586) and Schlömilch
+(_ibid._ p. 959). This consists of an electrolytic cell in which one of
+the electrodes is an exceedingly fine point. The electromotive force in
+the circuit is small, and there is large polarization in the circuit
+with only a small current. When the circuit is struck by electric waves
+there is an increase in the currents due to the depolarization of the
+circuit. If a galvanometer is in the circuit, the increased deflection
+of the instrument will indicate the presence of the waves.
+
+§ 7. _Coherers._--The most sensitive detector of electric waves is the
+"coherer," although for metrical work it is not so suitable as that just
+described. It depends upon the fact discovered by Branly (_Comptes
+rendus_, 111, p. 785; 112, p. 90) that the resistance between loose
+metallic contacts, such as a pile of iron turnings, diminishes when they
+are struck by an electric wave. One of the forms made by Lodge (_The
+Work of Hertz and some of his Successors_, 1894) on this principle
+consists simply of a glass tube containing iron turnings, in contact
+with which are wires led into opposite ends of the tube. The arrangement
+is placed in series with a galvanometer (one of the simplest kind will
+do) and a battery; when the iron turnings are struck by electric waves
+their resistance is diminished and the deflection of the galvanometer is
+increased. Thus the deflection of the galvanometer can be used to
+indicate the arrival of electric waves. The tube must be tapped between
+each experiment, and the deflection of the galvanometer brought back to
+about its original value. This detector is marvellously delicate, but
+not metrical, the change produced in the resistance depending upon so
+many things besides the intensity of the waves that the magnitude of the
+galvanometer deflection is to some extent a matter of chance. Instead of
+the iron turnings we may use two iron wires, one resting on the other;
+the resistance of this contact will be altered by the incidence of the
+waves. To get greater regularity Bose uses, instead of the iron
+turnings, spiral springs, which are pushed against each other by means
+of a screw until the most sensitive state is attained. The sensitiveness
+of the coherer depends on the electromotive force put in the
+galvanometer circuit. Very sensitive ones can be made by using springs
+of very fine silver wire coated electrolytically with nickel. Though the
+impact of electric waves generally produces a diminution of resistance
+with these loose contacts, yet there are exceptions to the rule. Thus
+Branly showed that with lead peroxide, PbO2, there is an increase in
+resistance. Aschkinass proved the same to be true with copper sulphide,
+CuS; and Bose showed that with potassium there is an increase of
+resistance and great power of self-recovery of the original resistance
+after the waves have ceased. Several theories of this action have been
+proposed. Branly (_Lumière électrique_, 40, p. 511) thought that the
+small sparks which certainly pass between adjacent portions of metal
+clear away layers of oxide or some other kind of non-conducting film,
+and in this way improve the contact. It would seem that if this theory
+is true the films must be of a much more refined kind than layers of
+oxide or dirt, for the coherer effect has been observed with clean
+non-oxidizable metals. Lodge explains the effect by supposing that the
+heat produced by the sparks fuses adjacent portions of metal into
+contact and hence diminishes the resistance; it is from this view of the
+action that the name coherer is applied to the detector. Auerbeck
+thought that the effect was a mechanical one due to the electrostatic
+attractions between the various small pieces of metal. It is probable
+that some or all of these causes are at work in some cases, but the
+effects of potassium make us hesitate to accept any of them as the
+complete explanation. Blanc (_Ann. chim. phys._, 1905, [8] 6, p. 5), as
+the result of a long series of experiments, came to the conclusion that
+coherence is due to pressure. He regarded the outer layers as different
+from the mass of the metal and having a much greater specific
+resistance. He supposed that when two pieces of metal are pressed
+together the molecules diffuse across the surface, modifying the surface
+layers and increasing their conductivity.
+
+  § 8. _Generators of Electric Waves._--Bose (_Phil. Mag._ 43, p. 55)
+  designed an instrument which generates electric waves with a length of
+  not more than a centimetre or so, and therefore allows their
+  properties to be demonstrated with apparatus of moderate dimensions.
+  The waves are excited by sparking between two platinum beads carried
+  by jointed electrodes; a platinum sphere is placed between the beads,
+  and the distance between the beads and the sphere can be adjusted by
+  bending the electrodes. The diameter of the sphere is 8 mm., and the
+  wave length of the shortest electrical waves generated is said to be
+  about 6 mm. The beads are connected with the terminals of a small
+  induction coil, which, with the battery to work it and the sparking
+  arrangement, are enclosed in a metal box, the radiation passing out
+  through a metal tube opposite to the spark gap. The ordinary vibrating
+  break of the coil is not used, a single spark made by making and
+  breaking the circuit by means of a button outside the box being
+  employed instead. The detector is one of the spiral spring coherers
+  previously described; it is shielded from external disturbance by
+  being enclosed in a metal box provided with a funnel-shaped opening to
+  admit the radiation. The wires leading from the coherers to the
+  galvanometer are also surrounded by metal tubes to protect them from
+  stray radiation. The radiating apparatus and the receiver are mounted
+  on stands sliding in an optical bench. If a parallel beam of radiation
+  is required, a cylindrical lens of ebonite or sulphur is mounted in a
+  tube fitting on to the radiator tube and stopped by a guide when the
+  spark is at the principal focal line of the lens. For experiments
+  requiring angular measurements a spectrometer circle is mounted on one
+  of the sliding stands, the receiver being carried on a radial arm and
+  pointing to the centre of the circle. The arrangement is represented
+  in fig. 5.
+
+  [Illustration: FIG. 5.]
+
+  With this apparatus the laws of reflection, refraction and
+  polarization can readily be verified, and also the double refraction
+  of crystals, and of bodies possessing a fibrous or laminated structure
+  such as jute or books. (The double refraction of electric waves seems
+  first to have been observed by Righi, and other researches on this
+  subject have been made by Garbasso and Mack.) Bose showed the rotation
+  of the plane of polarization by means of pieces of twisted jute rope;
+  if the pieces were arranged so that their twists were all in one
+  direction and placed in the path of the radiation, they rotated the
+  plane of polarization in a direction depending upon the direction of
+  twist; if they were mixed so that there were as many twisted in one
+  direction as the other, there was no rotation.
+
+  [Illustration: FIG. 6.]
+
+  A series of experiments showing the complete analogy between electric
+  and light waves is described by Righi in his book _L'Ottica delle
+  oscillazioni elettriche_. Righi's exciter, which is especially
+  convenient when large statical electric machines are used instead of
+  induction coils, is shown in fig. 6. E and F are balls connected with
+  the terminals of the machine, and AB and CD are conductors insulated
+  from each other, the ends B, C, between which the sparks pass, being
+  immersed in vaseline oil. The period of the vibrations given out by
+  the system is adjusted by means of metal plates M and N attached to AB
+  and CD. When the waves are produced by induction coils or by
+  electrical machines the intervals between the emission of different
+  sets of waves occupy by far the largest part of the time. Simon
+  (_Wied. Ann._, 1898, 64, p. 293; _Phys. Zeit._, 1901, 2, p. 253),
+  Duddell (_Electrician_, 1900, 46, p. 269) and Poulsen (_Electrotech.
+  Zeits._, 1906, 27, p. 1070) reduced these intervals very considerably
+  by using the electric arc to excite the waves, and in this way
+  produced electrical waves possessing great energy. In these methods
+  the terminals between which the arc is passing are connected through
+  coils with self-induction L to the plates of a condenser of capacity
+  C. The arc is not steady, but is continually varying. This is
+  especially the case when it passes through hydrogen. These variations
+  excite vibrations with a period 2[pi][root](LC) in the circuit
+  containing the capacity of the self-induction. By this method Duddell
+  produced waves with a frequency of 40,000. Poulsen, who cooled the
+  terminals of the arc, produced waves with a frequency of 1,000,000,
+  while Stechodro (_Ann. der Phys._ 27, p. 225) claims to have produced
+  waves with three hundred times this frequency, i.e. having a wave
+  length of about a metre. When the self-induction and capacity are
+  large so that the frequency comes within the limits of the frequency
+  of audible notes, the system gives out a musical note, and the
+  arrangement is often referred to as the singing arc.
+
+  [Illustration: FIG. 7.]
+
+  [Illustration: FIG. 8.]
+
+  § _9. Waves in Wires._--Many problems on electric waves along wires
+  can readily be investigated by a method due to Lecher (_Wied. Ann._
+  41, p. 850), and known as Lecher's bridge, which furnishes us with a
+  means of dealing with waves of a definite and determinable
+  wave-length. In this arrangement (fig. 7) two large plates A and B
+  are, as in Hertz's exciter, connected with the terminals of an
+  induction coil; opposite these and insulated from them are two smaller
+  plates D, E, to which long parallel wires DFH, EGJ are attached. These
+  wires are bridged across by a wire LM, and their farther ends H, J,
+  may be insulated, or connected together, or with the plates of a
+  condenser. To detect the waves in the circuit beyond the bridge,
+  Lecher used an exhausted tube placed across the wires, and Rubens a
+  bolometer, but Rutherford's detector is the most convenient and
+  accurate. If this detector is placed in a fixed position at the end of
+  the circuit, it is found that the deflections of this detector depend
+  greatly upon the position of the bridge LM, rising rapidly to a
+  maximum for some positions, and falling rapidly away when the bridge
+  is displaced. As the bridge is moved from the coil end towards the
+  detector the deflections show periodic variations, such as are
+  represented in fig. 8 when the ordinates represent the deflections of
+  the detector and the abscissae the distance of the bridge from the
+  ends D, E. The maximum deflections of the detector correspond to the
+  positions in which the two circuits DFLMGE, HLMJ (in which the
+  vibrations are but slightly damped) are in resonance. For since the
+  self-induction and resistance of the bridge LM is very small compared
+  with that of the circuit beyond, it follows from the theory of
+  circuits in parallel that only a small part of the current will in
+  general flow round the longer circuit; it is only when the two
+  circuits DFLMGE, HLMJ are in resonance that a considerable current
+  will flow round the latter. Hence when we get a maximum effect in the
+  detector we know that the waves we are dealing with are those
+  corresponding to the free periods of the system HLMJ, so that if we
+  know the free periods of this circuit we know the wave length of the
+  electric waves under consideration. Thus if the ends of the wires H, J
+  are free and have no capacity, the current along them must vanish at H
+  and J, which must be in opposite electric condition. Hence half the
+  wave length must be an odd submultiple of the length of the circuit
+  HLMJ. If H and J are connected together the wave length must be a
+  submultiple of the length of this circuit. When the capacity at the
+  ends is appreciable the wave length of the circuit is determined by a
+  somewhat complex expression. To facilitate the determination of the
+  wave length in such cases, Lecher introduced a second bridge L'M', and
+  moved this about until the deflection of the detector was a maximum;
+  when this occurs the wave length is one of those corresponding to the
+  closed circuit LMM'L', and must therefore be a submultiple of the
+  length of the circuit. Lecher showed that if instead of using a single
+  wire LM to form the bridge, he used two parallel wires PQ, LM, placed
+  close together, the currents in the further circuit were hardly
+  appreciably diminished when the main wires were cut between PL and QM.
+  Blondlot used a modification of this apparatus better suited for the
+  production of short waves. In his form (fig. 9) the exciter consists
+  of two semicircular arms connected with the terminals of an induction
+  coil, and the long wires, instead of being connected with the small
+  plates, form a circuit round the exciter.
+
+  As an example of the use of Lecher's arrangement, we may quote Drude's
+  application of the method to find the specific induction capacity of
+  dielectrics under electric oscillations of varying frequency. In this
+  application the ends of the wire are connected to the plates of a
+  condenser, the space between whose plates can be filled with the
+  liquid whose specific inductive capacity is required, and the bridge
+  is moved until the detector at the end of the circuit gives the
+  maximum deflection. Then if [lambda] is the wave length of the waves,
+  [lambda] is the wave length of one of the free vibrations of the
+  system HLMJ; hence if C is the capacity of the condenser at the end in
+  electrostatic measure we have
+
+         2[pi]l
+    cot --------
+        [lambda]    C
+    ------------ = ---
+       2[pi]l      C'l
+      --------
+      [lambda]
+
+  where l is the distance of the condenser from the bridge and C' is the
+  capacity of unit length of the wire. In the condenser part of the
+  lines of force will pass through air and part through the dielectric;
+  hence C will be of the form C0+KC1 where K is the specific inductive
+  capacity of the dielectric. Hence if l is the distance of maximum
+  deflection when the dielectric is replaced by air, l' when filled with
+  a dielectric whose specific inductive capacity is known to be K', and
+  l" the distance when filled with the dielectric whose specific
+  inductive capacity is required, we easily see that--
+
+         2[pi]l        2[pi]l'
+    cot -------- - cot --------
+        [lambda]       [lambda]   1 - K'
+    --------------------------- = ------
+         2[pi]l        2[pi]l"    1 - K
+    cot -------- - cot --------
+        [lambda]       [lambda]
+
+  an equation by means of which K can be determined. It was in this way
+  that Drude investigated the specific inductive capacity with varying
+  frequency, and found a falling off in the specific inductive capacity
+  with increase of frequency when the dielectrics contained the radicle
+  OH. In another method used by him the wires were led through long
+  tanks filled with the liquid whose specific inductive capacity was
+  required; the velocity of propagation of the electric waves along the
+  wires in the tank being the same as the velocity of propagation of an
+  electromagnetic disturbance through the liquid filling the tank, if we
+  find the wave length of the waves along the wires in the tank, due to
+  a vibration of a given frequency, and compare this with the wave
+  lengths corresponding to the same frequency when the wires are
+  surrounded by air, we obtain the velocity of propagation of
+  electromagnetic disturbance through the fluid, and hence the specific
+  inductive capacity of the fluid.
+
+  [Illustration: FIG. 9.]
+
+  § 10. _Velocity of Propagation of Electromagnetic Effects through
+  Air._--The experiments of Sarasin and De la Rive already described
+  (see § 5) have shown that, as theory requires, the velocity of
+  propagation of electric effects through air is the same as along
+  wires. The same result had been arrived at by J.J. Thomson, although
+  from the method he used greater differences between the velocities
+  might have escaped detection than was possible by Sarasin and De la
+  Rive's method. The velocity of waves along wires has been directly
+  determined by Blondlot by two different methods. In the first the
+  detector consisted of two parallel plates about 6 cm. in diameter
+  placed a fraction of a millimetre apart, and forming a condenser whose
+  capacity C was determined in electromagnetic measure by Maxwell's
+  method. The plates were connected by a rectangular circuit whose
+  self-induction L was calculated from the dimensions of the rectangle
+  and the size of the wire. The time of vibration T is equal to
+  2[pi][root](LC). (The wave length corresponding to this time is long
+  compared with the length of the circuit, so that the use of this
+  formula is legitimate.) This detector is placed between two parallel
+  wires, and the waves produced by the exciter are reflected from a
+  movable bridge. When this bridge is placed just beyond the detector
+  vigorous sparks are observed, but as the bridge is pushed away a place
+  is reached where the sparks disappear; this place is distance
+  2/[lambda] from the detector, when [lambda] is the wave length of the
+  vibration given out by the detector. The sparks again disappear when
+  the distance of the bridge from the detector is 3[lambda]/4. Thus by
+  measuring the distance between two consecutive positions of the bridge
+  at which the sparks disappear [lambda] can be determined, and v, the
+  velocity of propagation, is equal to [lambda]/T. As the means of a
+  number of experiments Blondlot found v to be 3.02 × 10^10 cm./sec.,
+  which, within the errors of experiment, is equal to 3 × 10^10
+  cm./sec., the velocity of light. A second method used by Blondlot, and
+  one which does not involve the calculation of the period, is as
+  follows:--A and A' (fig. 10) are two equal Leyden jars coated inside
+  and outside with tin-foil. The outer coatings form two separate rings
+  a, a1; a', a'1, and the inner coatings are connected with the poles of
+  the induction coil by means of the metal pieces b, b'. The sharply
+  pointed conductors p and p', the points of which are about ½ mm.
+  apart, are connected with the rings of the tin-foil a and a', and two
+  long copper wires pca1, p'c'a'1, 1029 cm. long, connect these points
+  with the other rings a1, a1'. The rings aa', a1a1', are connected by
+  wet strings so as to charge up the jars. When a spark passes between b
+  and b', a spark at once passes between pp', and this is followed by
+  another spark when the waves travelling by the paths a1cp, a'1c'p'
+  reach p and p'. The time between the passage of these sparks, which is
+  the time taken by the waves to travel 1029 cm., was observed by means
+  of a rotating mirror, and the velocity measured in 15 experiments
+  varied between 2.92 × 10^10 and 3.03 × 10^10 cm./sec., thus agreeing
+  well with that deduced by the preceding method. Other determinations
+  of the velocity of electromagnetic propagation have been made by Lodge
+  and Glazebrook, and by Saunders.
+
+  [Illustration: FIG. 10.]
+
+  On Maxwell's electromagnetic theory the velocity of propagation of
+  electromagnetic disturbances should equal the velocity of light, and
+  also the ratio of the electromagnetic unit of electricity to the
+  electrostatic unit. A large number of determinations of this ratio
+  have been made:--
+
+        Observer.            Date.    Ratio 10^10×.
+    Klemencic                1884    3.019 cm./sec.
+    Himstedt                 1888    3.009 cm./sec.
+    Rowland                  1889    2.9815 cm./sec.
+    Rosa                     1889    2.9993 cm./sec.
+    J.J. Thomson and Searle  1890    2.9955 cm./sec.
+    Webster                  1891    2.987 cm./sec.
+    Pellat                   1891    3.009 cm./sec.
+    Abraham                  1892    2.992 cm./sec.
+    Hurmuzescu               1895    3.002 cm./sec.
+    Rosa                     1908    2.9963 cm./sec.
+
+  The mean of these determinations is 3.001 × 10^10 cm./sec., while the
+  mean of the last five determinations of the velocity of light in air
+  is given by Himstedt as 3.002 × 10^10 cm./sec. From these experiments
+  we conclude that the velocity of propagation of an electromagnetic
+  disturbance is equal to the velocity of light, and to the velocity
+  required by Maxwell's theory.
+
+  In experimenting with electromagnetic waves it is in general more
+  difficult to measure the period of the oscillations than their wave
+  length. Rutherford used a method by which the period of the vibration
+  can easily be determined; it is based upon the theory of the
+  distribution of alternating currents in two circuits ACB, ADB in
+  parallel. If A and B are respectively the maximum currents in the
+  circuits ACB, ADB, then
+
+    A           / S² + (N - M)²p² \
+    -- = [root](  ---------------  )
+    B           \ R² + (L - M)²p² /
+
+  when R and S are the resistances, L and N the coefficients of
+  self-induction of the circuits ACB, ADB respectively, M the
+  coefficient of mutual induction between the circuits, and p the
+  frequency of the currents. Rutherford detectors were placed in the two
+  circuits, and the circuits adjusted until they showed that A = B; when
+  this is the case
+
+               R² - S²
+    p² = -------------------.
+         N² - L² - 2M(N - L)
+
+  If we make one of the circuits, ADB, consist of a short length of a
+  high liquid resistance, so that S is large and N small, and the
+  other circuit ACB of a low metallic resistance bent to have
+  considerable self-induction, the preceding equation becomes
+  approximately p = S/L, so that when S and L are known p is readily
+  determined.     (J. J. T.)
+
+
+
+
+ELECTROCHEMISTRY. The present article deals with processes that involve
+the electrolysis of aqueous solutions, whilst those in which electricity
+is used in the manufacture of chemical products at furnace temperatures
+are treated under ELECTROMETALLURGY, although, strictly speaking, in
+some cases (e.g. calcium carbide and phosphorus manufacture) they are
+not truly metallurgical in character. For the theory and elemental laws
+of electro-deposition see ELECTROLYSIS; and for the construction and use
+of electric generators see DYNAMO and BATTERY: _Electric_. The
+importance of the subject may be gauged by the fact that all the
+aluminium, magnesium, sodium, potassium, calcium carbide, carborundum
+and artificial graphite, now placed on the market, is made by electrical
+processes, and that the use of such processes for the refining of copper
+and silver, and in the manufacture of phosphorus, potassium chlorate and
+bleach, already pressing very heavily on the older non-electrical
+systems, is every year extending. The convenience also with which the
+energy of waterfalls can be converted into electric energy has led to
+the introduction of chemical industries into countries and districts
+where, owing to the absence of coal, they were previously unknown.
+Norway and Switzerland have become important producers of chemicals, and
+pastoral districts such as those in which Niagara or Foyers are situated
+manufacturing centres. In this way the development of the
+electrochemical industry is in a marked degree altering the distribution
+of trade throughout the world.
+
+_Electrolytic Refining of Metals._--The principle usually followed in
+the electrolytic refining of metals is to cast the impure metal into
+plates, which are exposed as anodes in a suitable solvent, commonly a
+salt of the metal under treatment. On passing a current of electricity,
+of which the volume and pressure are adjusted to the conditions of the
+electrolyte and electrodes, the anode slowly dissolves, leaving the
+insoluble impurities in the form of a sponge, if the proportion be
+considerable, but otherwise as a mud or slime which becomes detached
+from the anode surface and must be prevented from coming into contact
+with the cathode. The metal to be refined passing into solution is
+concurrently deposited at the cathode. Soluble impurities which are more
+electro-negative than the metal under treatment must, if present, be
+removed by a preliminary process, and the voltage and other conditions
+must be so selected that none of the more electro-positive metals are
+co-deposited with the metal to be refined. From these and other
+considerations it is obvious that (1) the electrolyte must be such as
+will freely dissolve the metal to be refined; (2) the electrolyte must
+be able to dissolve the major portion of the anode, otherwise the mass
+of insoluble matter on the outer layer will prevent access of
+electrolyte to the core, which will thus escape refining; (3) the
+electrolyte should, if possible, be incapable of dissolving metals more
+electro-negative than that to be refined; (4) the proportion of soluble
+electro-positive impurities must not be excessive, or these substances
+will accumulate too rapidly in the solution and necessitate its frequent
+purification; (5) the current density must be so adjusted to the
+strength of the solution and to other conditions that no relatively
+electro-positive metal is deposited, and that the cathode deposit is
+physically suitable for subsequent treatment; (6) the current density
+should be as high as is consistent with the production of a pure and
+sound deposit, without undue expense of voltage, so that the operation
+may be rapid and the "turnover" large; (7) the electrolyte should be as
+good a conductor of electricity as possible, and should not, ordinarily,
+be altered chemically by exposure to air; and (8) the use of porous
+partitions should be avoided, as they increase the resistance and
+usually require frequent renewal. For details of the practical methods
+see GOLD; SILVER; COPPER and headings for other metals.
+
+_Electrolytic Manufacture of Chemical Products._--When an aqueous
+solution of the salt of an alkali metal is electrolysed, the metal
+reacts with the water, as is well known, forming caustic alkali, which
+dissolves in the solution, and hydrogen, which comes off as a gas. So
+early as 1851 a patent was taken out by Cooke for the production of
+caustic alkali without the use of a separate current, by immersing iron
+and copper plates on opposite sides of a porous (biscuit-ware) partition
+in a suitable cell, containing a solution of the salt to be
+electrolysed, at 21°-65° C. (70°-150° F.). The solution of the iron
+anode was intended to afford the necessary energy. In the same year
+another patent was granted to C. Watt for a similar process, involving
+the employment of an externally generated current. When an alkaline
+chloride, say sodium chloride, is electrolysed with one electrode
+immersed in a porous cell, while caustic soda is formed at the cathode,
+chlorine is deposited at the anode. If the latter be insoluble, the gas
+diffuses into the solution and, when this becomes saturated, escapes
+into the air. If, however, no porous division be used to prevent the
+intermingling by diffusion of the anode and cathode solutions, a
+complicated set of subsidiary reactions takes place. The chlorine reacts
+with the caustic soda, forming sodium hypochlorite, and this in turn,
+with an excess of chlorine and at higher temperatures, becomes for the
+most part converted into chlorate, whilst any simultaneous electrolysis
+of a hydroxide or water and a chloride (so that hydroxyl and chlorine
+are simultaneously liberated at the anode) also produces oxygen-chlorine
+compounds direct. At the same time, the diffusion of these compounds
+into contact with the cathode leads to a partial reduction to chloride,
+by the removal of combined oxygen by the instrumentality of the hydrogen
+there evolved. In proportion as the original chloride is thus
+reproduced, the efficiency of the process is of course diminished. It is
+obvious that, with suitable methods and apparatus, the electrolysis of
+alkaline chlorides may be made to yield chlorine, hypochlorites
+(bleaching liquors), chlorates or caustic alkali, but that great care
+must be exercised if any of these products is to be obtained pure and
+with economy. Many patents have been taken out in this branch of
+electrochemistry, but it is to be remarked that that granted to C. Watt
+traversed the whole of the ground. In his process a current was passed
+through a tank divided into two or three cells by porous partitions,
+hoods and tubes were arranged to carry off chlorine and hydrogen
+respectively, and the whole was heated to 120° F. by a steam jacket when
+caustic alkali was being made. Hypochlorites were made, at ordinary
+temperatures, and chlorates at higher temperatures, in a cell without a
+partition in which the cathode was placed horizontally immediately above
+the anode, to favour the mixing of the ascending chlorine with the
+descending caustic solution.
+
+  The relation between the composition of the electrolyte and the
+  various conditions of current-density, temperature and the like has
+  been studied by F. Oettel (_Zeitschrift f. Elektrochem._, 1894, vol.
+  i. pp. 354 and 474) in connexion with the production of hypochlorites
+  and chlorates in tanks without diaphragms, by C. Häussermann and W.
+  Naschold (_Chemiker Zeitung_, 1894, vol. xviii. p. 857) for their
+  production in cells with porous diaphragms, and by F. Haber and S.
+  Grinberg (_Zeitschrift f. anorgan. Chem._, 1898, vol. xvi. pp. 198,
+  329, 438) in connexion with the electrolysis of hydrochloric acid.
+  Oettel, using a 20% solution of potassium chloride, obtained the best
+  yield of hypochlorite with a high current-density, but as soon as 1¼%
+  of bleaching chlorine (as hypochlorite) was present, the formation of
+  chlorate commenced. The yield was at best very low as compared with
+  that theoretically possible. The best yield of chlorate was obtained
+  when from 1 to 4% of caustic potash was present. With high
+  current-density, heating the solution tended to increase the
+  proportion of chlorate to hypochlorite, but as the proportion of water
+  decomposed is then higher, the amount of chlorine produced must be
+  less and the total chlorine efficiency lower. He also traced a
+  connexion between alkalinity, temperature and current-density, and
+  showed that these conditions should be mutually adjusted. With a
+  current-density of 130 to 140 amperes per sq. ft., at 3 volts, passing
+  between platinum electrodes, he attained to a current-efficiency of
+  52%, and each (British) electrical horse-power hour was equivalent to
+  a production of 1378.5 grains of potassium chlorate. In other words,
+  each pound of chlorate would require an expenditure of nearly 5.1
+  e.h.p. hours. One of the earliest of the more modern processes was
+  that of E. Hermite, which consisted in the production of
+  bleach-liquors by the electrolysis (according to the 1st edition of
+  the 1884 patent) of magnesium or calcium chloride between platinum
+  anodes carried in wooden frames, and zinc cathodes. The solution,
+  containing hypochlorites and chlorates, was then applied to the
+  bleaching of linen, paper-pulp or the like, the solution being used
+  over and over again. Many modifications have been patented by Hermite,
+  that of 1895 specifying the use of platinum gauze anodes, held in
+  ebonite or other frames. Rotating zinc cathodes were used, with
+  scrapers to prevent the accumulation of a layer of insoluble magnesium
+  compounds, which would otherwise increase the electrical resistance
+  beyond reasonable limits. The same inventor has patented the
+  application of electrolysed chlorides to the purification of starch by
+  the oxidation of less stable organic bodies, to the bleaching of oils,
+  and to the purification of coal gas, spirit and other substances. His
+  system for the disinfection of sewage and similar matter by the
+  electrolysis of chlorides, or of sea-water, has been tried, but for
+  the most part abandoned on the score of expense. Reference may be made
+  to papers written in the early days of the process by C.F. Cross and
+  E.J. Bevan (_Journ. Soc. Chem. Industry_, 1887, vol. vi. p. 170, and
+  1888, vol. vii. p. 292), and to later papers by P. Schoop
+  (_Zeitschrift f. Elektrochem._, 1895, vol. ii. pp. 68, 88, 107, 209,
+  289).
+
+  E. Kellner, who in 1886 patented the use of cathode (caustic soda) and
+  anode (chlorine) liquors in the manufacture of cellulose from
+  wood-fibre, and has since evolved many similar processes, has produced
+  an apparatus that has been largely used. It consists of a stoneware
+  tank with a thin sheet of platinum-iridium alloy at either end forming
+  the primary electrodes, and between them a number of glass plates
+  reaching nearly to the bottom, each having a platinum gauze sheet on
+  either side; the two sheets belonging to each plate are in metallic
+  connexion, but insulated from all the others, and form intermediary or
+  bi-polar electrodes. A 10-12% solution of sodium chloride is caused to
+  flow upwards through the apparatus and to overflow into troughs, by
+  which it is conveyed (if necessary through a cooling apparatus) back
+  to the circulating pump. Such a plant has been reported as giving
+  0.229 gallon of a liquor containing 1% of available chlorine per
+  kilowatt hour, or 0.171 gallon per e.h.p. hour. Kellner has also
+  patented a "bleaching-block," as he terms it, consisting of a frame
+  carrying parallel plates similar in principle to those last described.
+  The block is immersed in the solution to be bleached, and may be
+  lifted in or out as required. O. Knöfler and Gebauer have also a
+  system of bi-polar electrodes, mounted in a frame in appearance
+  resembling a filter-press.
+
+_Other Electrochemical Processes._--It is obvious that electrolytic
+iodine and bromine, and oxygen compounds of these elements, may be
+produced by methods similar to those applied to chlorides (see ALKALI
+MANUFACTURE and CHLORATES), and Kellner and others have patented
+processes with this end in view. _Hydrogen_ and _oxygen_ may also be
+produced electrolytically as gases, and their respective reducing and
+oxidizing powers at the moment of deposition on the electrode are
+frequently used in the laboratory, and to some extent industrially,
+chiefly in the field of organic chemistry. Similarly, the formation of
+organic halogen products may be effected by electrolytic chlorine, as,
+for example, in the production of _chloral_ by the gradual introduction
+of alcohol into an anode cell in which the electrolyte is a strong
+solution of potassium chloride. Again, anode reactions, such as are
+observed in the electrolysis of the fatty acids, may be utilized, as,
+for example, when the radical CH3CO2--deposited at the anode in the
+electrolysis of acetic acid--is dissociated, two of the groups react to
+give one molecule of _ethane_, C2H6, and two of carbon dioxide. This,
+which has long been recognized as a class-reaction, is obviously capable
+of endless variation. Many electrolytic methods have been proposed for
+the purification of _sugar_; in some of them soluble anodes are used for
+a few minutes in weak alkaline solutions, so that the caustic alkali
+from the cathode reaction may precipitate chemically the hydroxide of
+the anode metal dissolved in the liquid, the precipitate carrying with
+it mechanically some of the impurities present, and thus clarifying the
+solution. In others the current is applied for a longer time to the
+original sugar-solution with insoluble (e.g. carbon) anodes. F. Peters
+has found that with these methods the best results are obtained when
+ozone is employed in addition to electrolytic oxygen. Use has been made
+of electrolysis in _tanning_ operations, the current being passed
+through the tan-liquors containing the hides. The current, by
+endosmosis, favours the passage of the solution into the hide-substance,
+and at the same time appears to assist the chemical combinations there
+occurring; hence a great reduction in the time required for the
+completion of the process. Many patents have been taken out in this
+direction, one of the best known being that of Groth, experimented upon
+by S. Rideal and A.P. Trotter (_Journ. Soc. Chem. Indust._, 1891, vol.
+x. p. 425), who employed copper anodes, 4 sq. ft. in area, with
+current-densities of 0.375 to 1 (ranging in some cases to 7.5) ampere
+per sq. ft., the best results being obtained with the smaller
+current-densities. Electrochemical processes are often indirectly used,
+as for example in the Villon process (_Elec. Rev._, New York, 1899, vol.
+xxxv. p. 375) applied in Russia to the manufacture of alcohol, by a
+series of chemical reactions starting from the production of acetylene
+by the action of water upon calcium carbide. The production of _ozone_
+in small quantities during electrolysis, and by the so-called silent
+discharge, has long been known, and the Siemens induction tube has been
+developed for use industrially. The Siemens and Halske ozonizer, in form
+somewhat resembling the old laboratory instrument, is largely used in
+Germany; working with an alternating current transformed up to 6500
+volts, it has been found to give 280 grains or more of ozone per e.h.p.
+hour. E. Andreoli (whose first British ozone patent was No. 17,426 of
+1891) uses flat aluminium plates and points, and working with an
+alternating current of 3000 volts is said to have obtained 1440 grains
+per e.h.p. hour. Yarnold's process, using corrugated glass plates coated
+on one side with gold or other metal leaf, is stated to have yielded as
+much as 2700 grains per e.h.p. hour. The ozone so prepared has numerous
+uses, as, for example, in bleaching oils, waxes, fabrics, &c.,
+sterilizing drinking-water, maturing wines, cleansing foul beer-casks,
+oxidizing oil, and in the manufacture of vanillin.
+
+  For further information the following books, among others, may be
+  consulted:--Haber, _Grundriss der technischen Elektrochemie_ (München,
+  1898); Borchers and M'Millan, _Electric Smelting and Refining_
+  (London, 1904); E.D. Peters, _Principles of Copper Smelting_ (New
+  York, 1907); F. Peters, _Angewandte Elektrochemie_, vols. ii. and iii.
+  (Leipzig, 1900); Gore, _The Art of Electrolytic Separation of Metals_
+  (London, 1890); Blount, _Practical Electro-Chemistry_ (London, 1906);
+  G. Langbein, _Vollständiges Handbuch der galvanischen
+  Metall-Niederschläge_ (Leipzig, 1903), Eng. trans. by W.T. Brannt
+  (1909); A. Watt, _Electro-Plating and Electro-Refining of Metals_
+  (London, 1902); W.H. Wahl, _Practical Guide to the Gold and Silver
+  Electroplater, &c._ (Philadelphia, 1883); Wilson, _Stereotyping and
+  Electrotyping_ (London); Lunge, _Sulphuric Acid and Alkali_, vol. iii.
+  (London, 1909). Also papers in various technical periodicals. The
+  industrial aspect is treated in a Gartside Report, _Some
+  Electro-Chemical Centres_ (Manchester, 1908), by J.N. Pring.
+       (W. G. M.)
+
+
+
+
+ELECTROCUTION (an anomalous derivative from "electro-execution"; syn.
+"electrothanasia"), the popular name, invented in America, for the
+infliction of the death penalty on criminals (see CAPITAL PUNISHMENT) by
+passing through the body of the condemned a sufficient current of
+electricity to cause death. The method was first adopted by the state of
+New York, a law making this method obligatory having been passed and
+approved by the governor on the 4th of June 1888. The law provides that
+there shall be present, in addition to the warden, two physicians,
+twelve reputable citizens of full age, seven deputy sheriffs, and such
+ministers, priests or clergymen, not exceeding two, as the criminal may
+request. A post-mortem examination of the body of the convict is
+required, and the body, unless claimed by relatives, is interred in the
+prison cemetery with a sufficient quantity of quicklime to consume it.
+The law became effective in New York on the 1st of January 1889. The
+first criminal to be executed by electricity was William Kemmler, on the
+6th of August 1890, at Auburn prison. The validity of the New York law
+had previously been attacked in regard to this case (_Re Kemmler_, 1889;
+136 U.S. 436), as providing "a cruel and unusual punishment" and
+therefore being contrary to the Constitution; but it was sustained in
+the state courts and finally in the Federal courts. By 1906 about one
+hundred and fifteen murderers had been successfully executed by
+electricity in New York state in Sing Sing, Auburn and Dannemora
+prisons. The method has also been adopted by the states of Ohio (1896),
+Massachusetts (1898), New Jersey (1906), Virginia (1908) and North
+Carolina (1910).
+
+The apparatus consists of a stationary engine, an alternating dynamo
+capable of generating a current at a pressure of 2000 volts, a
+"death-chair" with adjustable head-rest, binding straps and adjustable
+electrodes devised by E.F. Davis, the state electrician of New York. The
+voltmeter, ammeter and switch-board controlling the current are located
+in the execution-room; the dynamo-room is communicated with by electric
+signals. Before each execution the entire apparatus is thoroughly
+tested. When everything is in readiness the criminal is brought in and
+seats himself in the death-chair. His head, chest, arms and legs are
+secured by broad straps; one electrode thoroughly moistened with
+salt-solution is affixed to the head, and another to the calf of one
+leg, both electrodes being moulded so as to secure good contact. The
+application of the current is usually as follows: the contact is made
+with a high voltage (1700-1800 volts) for 5 to 7 seconds, reduced to 200
+volts until a half-minute has elapsed; raised to high voltage for 3 to 5
+seconds, again reduced to low voltage for 3 to 5 seconds, again reduced
+to a low voltage until one minute has elapsed, when it is again raised
+to the high voltage for a few seconds and the contact broken. The
+ammeter usually shows that from 7 to 10 amperes pass through the
+criminal's body. A second or even a third brief contact is sometimes
+made, partly as a precautionary measure, but rather the more completely
+to abolish reflexes in the dead body. Calculations have shown that by
+this method of execution from 7 to 10 h. p. of energy are liberated in
+the criminal's body. The time consumed by the strapping-in process is
+usually about 45 seconds, and the first contact is made about 70 seconds
+after the criminal has entered the death-chamber.
+
+When properly performed the effect is painless and instantaneous death.
+The mechanism of life, circulation and respiration cease with the first
+contact. Consciousness is blotted out instantly, and the prolonged
+application of the current ensures permanent derangement of the vital
+functions beyond recovery. Occasionally the drying of the sponges
+through undue generation of heat causes desquamation or superficial
+blistering of the skin at the site of the electrodes. Post-mortem
+discoloration, or post-mortem lividity, often appears during the first
+contact. The pupils of the eyes dilate instantly and remain dilated
+after death.
+
+The post-mortem examination of "electrocuted" criminals reveals a number
+of interesting phenomena. The temperature of the body rises promptly
+after death to a very high point. At the site of the leg electrode a
+temperature of over 128° F. was registered within fifteen minutes in
+many cases. After the removal of the brain the temperature recorded in
+the spinal canal was often over 120° F. The development of this high
+temperature is to be regarded as resulting from the active metabolism of
+tissues not (somatically) dead within a body where all vital mechanisms
+have been abolished, there being no circulation to carry off the
+generated heat. The heart, at first flaccid when exposed soon after
+death, gradually contracts and assumes a tetanized condition; it empties
+itself of all blood and takes the form of a heart in systole. The lungs
+are usually devoid of blood and weigh only 7 or 8 ounces (avoird.) each.
+The blood is profoundly altered biochemically; it is of a very dark
+colour and it rarely coagulates.     (E. A. S.*)
+
+
+
+
+ELECTROKINETICS, that part of electrical science which is concerned with
+the properties of electric currents.
+
+_Classification of Electric Currents._--Electric currents are classified
+into (a) conduction currents, (b) convection currents, (c) displacement
+or dielectric currents. In the case of conduction currents electricity
+flows or moves through a stationary material body called the conductor.
+In convection currents electricity is carried from place to place with
+and on moving material bodies or particles. In dielectric currents there
+is no continued movement of electricity, but merely a limited
+displacement through or in the mass of an insulator or dielectric. The
+path in which an electric current exists is called an electric circuit,
+and may consist wholly of a conducting body, or partly of a conductor
+and insulator or dielectric, or wholly of a dielectric. In cases in
+which the three classes of currents are present together the true
+current is the sum of each separately. In the case of conduction
+currents the circuit consists of a conductor immersed in a
+non-conductor, and may take the form of a thin wire or cylinder, a
+sheet, surface or solid. Electric conduction currents may take place in
+space of one, two or three dimensions, but for the most part the
+circuits we have to consider consist of thin cylindrical wires or tubes
+of conducting material surrounded with an insulator; hence the case
+which generally presents itself is that of electric flow in space of one
+dimension. Self-closed electric currents taking place in a sheet of
+conductor are called "eddy currents."
+
+Although in ordinary language the current is said to flow in the
+conductor, yet according to modern views the real pathway of the energy
+transmitted is the surrounding dielectric, and the so-called conductor
+or wire merely guides the transmission of energy in a certain direction.
+The presence of an electric current is recognized by three qualities or
+powers: (1) by the production of a magnetic field, (2) in the case of
+conduction currents, by the production of heat in the conductor, and (3)
+if the conductor is an electrolyte and the current unidirectional, by
+the occurrence of chemical decomposition in it. An electric current may
+also be regarded as the result of a movement of electricity across each
+section of the circuit, and is then measured by the quantity conveyed
+per unit of time. Hence if dq is the quantity of electricity which flows
+across any section of the conductor in the element of time dt, the
+current i = dq/dt.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+Electric currents may be also classified as constant or variable and as
+unidirectional or "direct," that is flowing always in the same
+direction, or "alternating," that is reversing their direction at
+regular intervals. In the last case the variation of current may follow
+any particular law. It is called a "periodic current" if the cycle of
+current values is repeated during a certain time called the periodic
+time, during which the current reaches a certain maximum value, first in
+one direction and then in the opposite, and in the intervals between has
+a zero value at certain instants. The frequency of the periodic current
+is the number of periods or cycles in one second, and alternating
+currents are described as low frequency or high frequency, in the latter
+case having some thousands of periods per second. A periodic current may
+be represented either by a wave diagram, or by a polar diagram.[1] In
+the first case we take a straight line to represent the uniform flow of
+time, and at small equidistant intervals set up perpendiculars above or
+below the time axis, representing to scale the current at that instant
+in one direction or the other; the extremities of these ordinates then
+define a wavy curve which is called the wave form of the current (fig.
+1). It is obvious that this curve can only be a single valued curve. In
+one particular and important case the form of the current curve is a
+simple harmonic curve or simple sine curve. If T represents the periodic
+time in which the cycle of current values takes place, whilst n is the
+frequency or number of periods per second and p stands for 2[pi]n, and i
+is the value of the current at any instant t, and I its maximum value,
+then in this case we have i = I sin pt. Such a current is called a "sine
+current" or simple periodic current.
+
+In a polar diagram (fig. 2) a number of radial lines are drawn from a
+point at small equiangular intervals, and on these lines are set off
+lengths proportional to the current value of a periodic current at
+corresponding intervals during one complete period represented by four
+right angles. The extremities of these radii delineate a polar curve.
+The polar form of a simple sine current is obviously a circle drawn
+through the origin. As a consequence of Fourier's theorem it follows
+that any periodic curve having any wave form can be imitated by the
+superposition of simple sine currents differing in maximum value and in
+phase.
+
+_Definitions of Unit Electric Current._--In electrokinetic
+investigations we are most commonly limited to the cases of
+unidirectional continuous and constant currents (C.C. or D.C.), or of
+simple periodic currents, or alternating currents of sine form (A.C.). A
+continuous electric current is measured either by the magnetic effect it
+produces at some point outside its circuit, or by the amount of
+electrochemical decomposition it can perform in a given time on a
+selected standard electrolyte. Limiting our consideration to the case of
+linear currents or currents flowing in thin cylindrical wires, a
+definition may be given in the first place of the unit electric current
+in the centimetre, gramme, second (C.G.S.) of electromagnetic
+measurement (see UNITS, PHYSICAL). H.C. Oersted discovered in 1820 that
+a straight wire conveying an electric current is surrounded by a
+magnetic field the lines of which are self-closed lines embracing the
+electric circuit (see ELECTRICITY and ELECTROMAGNETISM). The unit
+current in the electromagnetic system of measurement is defined as the
+current which, flowing in a thin wire bent into the form of a circle of
+one centimetre in radius, creates a magnetic field having a strength of
+2[pi] units at the centre of the circle, and therefore would exert a
+mechanical force of 2[pi] dynes on a unit magnetic pole placed at that
+point (see MAGNETISM). Since the length of the circumference of the
+circle of unit radius is 2[pi] units, this is equivalent to stating that
+the unit current on the electromagnetic C.G.S. system is a current such
+that unit length acts on unit magnetic pole with a unit force at a unit
+of distance. Another definition, called the electrostatic unit of
+current, is as follows: Let any conductor be charged with electricity
+and discharged through a thin wire at such a rate that one electrostatic
+unit of quantity (see ELECTROSTATICS) flows past any section of the wire
+in one unit of time. The electromagnetic unit of current defined as
+above is 3 × 10^10 times larger than the electrostatic unit.
+
+In the selection of a practical unit of current it was considered that
+the electromagnetic unit was too large for most purposes, whilst the
+electrostatic unit was too small; hence a practical unit of current
+called 1 ampere was selected, intended originally to be {1/10} of the
+absolute electromagnetic C.G.S. unit of current as above defined. The
+practical unit of current, called the international ampere, is, however,
+legally defined at the present time as the continuous unidirectional
+current which when flowing through a neutral solution of silver nitrate
+deposits in one second on the cathode or negative pole 0.001118 of a
+gramme of silver. There is reason to believe that the international unit
+is smaller by about one part in a thousand, or perhaps by one part in
+800, than the theoretical ampere defined as 1/10 part of the absolute
+electromagnetic unit. A periodic or alternating current is said to have
+a value of 1 ampere if when passed through a fine wire it produces in
+the same time the same heat as a unidirectional continuous current of 1
+ampere as above electrochemically defined. In the case of a simple
+periodic alternating current having a simple sine wave form, the maximum
+value is equal to that of the equiheating continuous current multiplied
+by [root]2. This equiheating continuous current is called the effective
+or root-mean-square (R.M.S.) value of the alternating one.
+
+_Resistance._--A current flows in a circuit in virtue of an
+electromotive force (E.M.F.), and the numerical relation between the
+current and E.M.F. is determined by three qualities of the circuit
+called respectively, its resistance (R), inductance (L), and capacity
+(C). If we limit our consideration to the case of continuous
+unidirectional conduction currents, then the relation between current
+and E.M.F. is defined by Ohm's law, which states that the numerical
+value of the current is obtained as the quotient of the electromotive
+force by a certain constant of the circuit called its resistance, which
+is a function of the geometrical form of the circuit, of its nature,
+i.e. material, and of its temperature, but is independent of the
+electromotive force or current. The resistance (R) is measured in units
+called ohms and the electromotive force in volts (V); hence for a
+continuous current the value of the current in amperes (A) is obtained
+as the quotient of the electromotive force acting in the circuit
+reckoned in volts by the resistance in ohms, or A = V/R. Ohm established
+his law by a course of reasoning which was similar to that on which
+J.B.J. Fourier based his investigations on the uniform motion of heat in
+a conductor. As a matter of fact, however, Ohm's law merely states the
+direct proportionality of steady current to steady electromotive force
+in a circuit, and asserts that this ratio is governed by the numerical
+value of a quality of the conductor, called its resistance, which is
+independent of the current, provided that a correction is made for the
+change of temperature produced by the current. Our belief, however, in
+its universality and accuracy rests upon the close agreement between
+deductions made from it and observational results, and although it is
+not derivable from any more fundamental principle, it is yet one of the
+most certainly ascertained laws of electrokinetics.
+
+Ohm's law not only applies to the circuit as a whole but to any part of
+it, and provided the part selected does not contain a source of
+electromotive force it may be expressed as follows:--The difference of
+potential (P.D.) between any two points of a circuit including a
+resistance R, but not including any source of electromotive force, is
+proportional to the product of the resistance and the current i in the
+element, provided the conductor remains at the same temperature and the
+current is constant and unidirectional. If the current is varying we
+have, however, to take into account the electromotive force (E.M.F.)
+produced by this variation, and the product Ri is then equal to the
+difference between the observed P.D. and induced E.M.F.
+
+We may otherwise define the resistance of a circuit by saying that it is
+that physical quality of it in virtue of which energy is dissipated as
+heat in the circuit when a current flows through it. The power
+communicated to any electric circuit when a current i is created in it
+by a continuous unidirectional electromotive force E is equal to Ei, and
+the energy dissipated as heat in that circuit by the conductor in a
+small interval of time dt is measured by Ei dt. Since by Ohm's law E =
+Ri, where R is the resistance of the circuit, it follows that the energy
+dissipated as heat per unit of time in any circuit is numerically
+represented by Ri², and therefore the resistance is measured by the heat
+produced per unit of current, provided the current is unvarying.
+
+_Inductance._--As soon as we turn our attention, however, to alternating
+or periodic currents we find ourselves compelled to take into account
+another quality of the circuit, called its "inductance." This may be
+defined as that quality in virtue of which energy is stored up in
+connexion with the circuit in a magnetic form. It can be experimentally
+shown that a current cannot be created instantaneously in a circuit by
+any finite electromotive force, and that when once created it cannot be
+annihilated instantaneously. The circuit possesses a quality analogous
+to the inertia of matter. If a current i is flowing in a circuit at any
+moment, the energy stored up in connexion with the circuit is measured
+by ½Li², where L, the inductance of the circuit, is related to the
+current in the same manner as the quantity called the mass of a body is
+related to its velocity in the expression for the ordinary kinetic
+energy, viz. ½Mv². The rate at which this conserved energy varies with
+the current is called the "electrokinetic momentum" of this circuit (=
+Li). Physically interpreted this quantity signifies the number of lines
+of magnetic flux due to the current itself which are self-linked with
+its own circuit.
+
+_Magnetic Force and Electric Currents._--In the case of every circuit
+conveying a current there is a certain magnetic force (see MAGNETISM) at
+external points which can in some instances be calculated. Laplace
+proved that the magnetic force due to an element of length dS of a
+circuit conveying a current I at a point P at a distance r from the
+element is expressed by IdS sin [theta]/r², where [theta] is the angle
+between the direction of the current element and that drawn between the
+element and the point. This force is in a direction perpendicular to the
+radius vector and to the plane containing it and the element of current.
+Hence the determination of the magnetic force due to any circuit is
+reduced to a summation of the effects due to all the elements of length.
+For instance, the magnetic force at the centre of a circular circuit of
+radius r carrying a steady current I is 2[pi]I/r, since all elements
+are at the same distance from the centre. In the same manner, if we take
+a point in a line at right angles to the plane of the circle through its
+centre and at a distance d, the magnetic force along this line is
+expressed by 2[pi]r²I/(r² + d²)(3/2). Another important case is that of
+an infinitely long straight current. By summing up the magnetic force
+due to each element at any point P outside the continuous straight
+current I, and at a distance d from it, we can show that it is equal to
+2I/d or is inversely proportional to the distance of the point from the
+wire. In the above formula the current I is measured in absolute
+electromagnetic units. If we reckon the current in amperes A, then I =
+A/10.
+
+It is possible to make use of this last formula, coupled with an
+experimental fact, to prove that the magnetic force due to an element of
+current varies inversely as the square of the distance. If a flat
+circular disk is suspended so as to be free to rotate round a straight
+current which passes through its centre, and two bar magnets are placed
+on it with their axes in line with the current, it is found that the
+disk has no tendency to rotate round the current. This proves that the
+force on each magnetic pole is inversely as its distance from the
+current. But it can be shown that this law of action of the whole
+infinitely long straight current is a mathematical consequence of the
+fact that each element of the current exerts a magnetic force which
+varies inversely as the square of the distance. If the current flows N
+times round the circuit instead of once, we have to insert NA/10 in
+place of I in all the above formulae. The quantity NA is called the
+"ampere-turns" on the circuit, and it is seen that the magnetic field at
+any point outside a circuit is proportional to the ampere-turns on it
+and to a function of its geometrical form and the distance of the point.
+
+[Illustration: FIG. 3.]
+
+[Illustration: FIG. 4.]
+
+There is therefore a distribution of magnetic force in the field of
+every current-carrying conductor which can be delineated by lines of
+magnetic force and rendered visible to the eye by iron filings (see
+Magnetism). If a copper wire is passed vertically through a hole in a
+card on which iron filings are sprinkled, and a strong electric current
+is sent through the circuit, the filings arrange themselves in
+concentric circular lines making visible the paths of the lines of
+magnetic force (fig. 3). In the same manner, by passing a circular wire
+through a card and sending a strong current through the wire we can
+employ iron filings to delineate for us the form of the lines of
+magnetic force (fig. 4). In all cases a magnetic pole of strength M,
+placed in the field of an electric current, is urged along the lines of
+force with a mechanical force equal to MH, where H is the magnetic
+force. If then we carry a unit magnetic pole against the direction in
+which it would naturally move we do _work_. The lines of magnetic force
+embracing a current-carrying conductor are always loops or endless
+lines.
+
+  The work done in carrying a unit magnetic pole once round a circuit
+  conveying a current is called the "line integral of magnetic force"
+  along that path. If, for instance, we carry a unit pole in a circular
+  path of radius r once round an infinitely long straight filamentary
+  current I, the line integral is 4[pi]I. It is easy to prove that this
+  is a general law, and that if we have any currents flowing in a
+  conductor the line integral of magnetic force taken once round a path
+  linked with the current circuit is 4[pi] times the total current
+  flowing through the circuit. Let us apply this to the case of an
+  endless solenoid. If a copper wire insulated or covered with cotton or
+  silk is twisted round a thin rod so as to make a close spiral, this
+  forms a "solenoid," and if the solenoid is bent round so that its two
+  ends come together we have an endless solenoid. Consider such a
+  solenoid of mean length l and N turns of wire. If it is made endless,
+  the magnetic force H is the same everywhere along the central axis and
+  the line integral along the axis is Hl. If the current is denoted by
+  I, then NI is the total current, and accordingly 4[pi]NI = Hl, or H =
+  4[pi]NI/l. For a thin endless solenoid the axial magnetic force is
+  therefore 4[pi] times the current-turns per unit of length. This holds
+  good also for a long straight solenoid provided its length is large
+  compared with its diameter. It can be shown that if insulated wire is
+  wound round a sphere, the turns being all parallel to lines of
+  latitude, the magnetic force in the interior is constant and the lines
+  of force therefore parallel. The magnetic force at a point outside a
+  conductor conveying a current can by various means be measured or
+  compared with some other standard magnetic forces, and it becomes then
+  a means of measuring the current. Instruments called galvanometers and
+  ammeters for the most part operate on this principle.
+
+_Thermal Effects of Currents._--J.P. Joule proved that the heat produced
+by a constant current in a given time in a wire having a constant
+resistance is proportional to the square of the strength of the current.
+This is known as Joule's law, and it follows, as already shown, as an
+immediate consequence of Ohm's law and the fact that the power
+dissipated electrically in a conductor, when an electromotive force E is
+applied to its extremities, producing thereby a current I in it, is
+equal to EI.
+
+  If the current is alternating or periodic, the heat produced in any
+  time T is obtained by taking the sum at equidistant intervals of time
+  of all the values of the quantities Ri²dt, where dt represents a small
+  interval of time and i is the current at that instant. The quantity
+           _
+          / T
+   T^(-1) |    i²dt is called the mean-square-value of the variable
+         _/ 0
+
+  current, i being the instantaneous value of the current, that is, its
+  value at a particular instant or during a very small interval of time
+  dt. The square root of the above quantity, or
+     _        _      _
+    |        / T      | ½,
+    | T^(-1) |  i²dt  |
+    |_      _/ 0     _|
+
+  is called the root-mean-square-value, or the effective value of the
+  current, and is denoted by the letters R.M.S.
+
+Currents have equal heat-producing power in conductors of identical
+resistance when they have the same R.M.S. values. Hence periodic or
+alternating currents can be measured as regards their R.M.S. value by
+ascertaining the continuous current which produces in the same time the
+same heat in the same conductor as the periodic current considered.
+Current measuring instruments depending on this fact, called hot-wire
+ammeters, are in common use, especially for measuring alternating
+currents. The maximum value of the periodic current can only be
+determined from the R.M.S. value when we know the wave form of the
+current. The thermal effects of electric currents in conductors are
+dependent upon the production of a state of equilibrium between the heat
+produced electrically in the wire and the causes operative in removing
+it. If an ordinary round wire is heated by a current it loses heat, (1)
+by radiation, (2) by air convection or cooling, and (3) by conduction of
+heat out of the ends of the wire. Generally speaking, the greater part
+of the heat removal is effected by radiation and convection.
+
+  If a round sectioned metallic wire of uniform diameter d and length l
+  made of a material of resistivity [rho] has a current of A amperes
+  passed through it, the heat in watts produced in any time t seconds is
+  represented by the value of 4A²[rho]lt/10^9[pi]d², where d and l must
+  be measured in centimetres and [rho] in absolute C.G.S.
+  electromagnetic units. The factor 10^9 enters because one ohm is 10^9
+  absolute electromagnetic C.G.S. units (see UNITS, PHYSICAL). If the
+  wire has an emissivity e, by which is meant that e units of heat
+  reckoned in joules or watt-seconds are radiated per second from unit
+  of surface, then the power removed by radiation in the time t is
+  expressed by [pi]dlet. Hence when thermal equilibrium is established
+  we have 4A²[rho]lt/10^9[pi]d² = [pi]dlet, or A² = 10^9[pi]²ed³/4[rho].
+  If the diameter of the wire is reckoned in mils (1 mil = .001 in.),
+  and if we take e to have a value 0.1, an emissivity which will
+  generally bring the wire to about 60° C., we can put the above formula
+  in the following forms for circular sectioned copper, iron or
+  platinoid wires, viz.
+
+    A = [root](d³/500) for copper wires
+    A = [root](d³/4000) for iron wires
+    A = [root](d³/5000) for platinoid wires.
+
+  These expressions give the ampere value of the current which will
+  bring bare, straight or loosely coiled wires of d mils in diameter to
+  about 60° C. when the steady state of temperature is reached. Thus,
+  for instance, a bare straight copper wire 50 mils in diameter (=0.05
+  in.) will be brought to a steady temperature of about 60° C. if a
+  current of [root]50³/500 = [root]250 = 16 amperes (nearly) is passed
+  through it, whilst a current of [root]25 = 5 amperes would bring a
+  platinoid wire to about the same temperature.
+
+A wire has therefore a certain safe current-carrying capacity which is
+determined by its specific resistance and emissivity, the latter being
+fixed by its form, surface and surroundings. The emissivity increases
+with the temperature, else no state of thermal equilibrium could be
+reached. It has been found experimentally that whilst for fairly thick
+wires from 8 to 60 mils in diameter the safe current varies
+approximately as the 1.5th power of the diameter, for fine wires of 1 to
+3 mils it varies more nearly as the diameter.
+
+_Action of one Current on Another._--The investigations of Ampère in
+connexion with electric currents are of fundamental importance in
+electrokinetics. Starting from the discovery of Oersted, Ampère made
+known the correlative fact that not only is there a mechanical action
+between a current and a magnet, but that two conductors conveying
+electric currents exert mechanical forces on each other. Ampère devised
+ingenious methods of making one portion of a circuit movable so that he
+might observe effects of attraction or repulsion between this circuit
+and some other fixed current. He employed for this purpose an astatic
+circuit B, consisting of a wire bent into a double rectangle round which
+a current flowed first in one and then in the opposite direction (fig.
+5). In this way the circuit was removed from the action of the earth's
+magnetic field, and yet one portion of it could be submitted to the
+action of any other circuit C. The astatic circuit was pivoted by
+suspending it in mercury cups q, p, one of which was in electrical
+connexion with the tubular support A, and the other with a strong
+insulated wire passing up it.
+
+[Illustration: FIG. 5.]
+
+Ampère devised certain crucial experiments, and the theory deduced from
+them is based upon four facts and one assumption.[2] He showed (1) that
+wire conveying a current bent back on itself produced no action upon a
+proximate portion of a movable astatic circuit; (2) that if the return
+wire was bent zig-zag but close to the outgoing straight wire the
+circuit produced no action on the movable one, showing that the effect
+of an element of the circuit was proportional to its projected length;
+(3) that a closed circuit cannot cause motion in an element of another
+circuit free to move in the direction of its length; and (4) that the
+action of two circuits on one and the same movable circuit was null if
+one of the two fixed circuits was n times greater than the other but n
+times further removed from the movable circuit. From this last
+experiment by an ingenious line of reasoning he proved that the action
+of an element of current on another element of current varies inversely
+as a square of their distance. These experiments enabled him to
+construct a mathematical expression of the law of action between two
+elements of conductors conveying currents. They also enabled him to
+prove that an element of current may be resolved like a force into
+components in different directions, also that the force produced by any
+element of the circuit on an element of any other circuit was
+perpendicular to the line joining the elements and inversely as the
+square of their distance. Also he showed that this force was an
+attraction if the currents in the elements were in the same direction,
+but a repulsion if they were in opposite directions. From these
+experiments and deductions from them he built up a complete formula for
+the action of one element of a current of length dS of one conductor
+conveying a current I upon another element dS' of another circuit
+conveying another current I' the elements being at a distance apart
+equal to r.
+
+  If [theta] and [theta]' are the angles the elements make with the line
+  joining them, and [phi] the angle they make with one another, then
+  Ampère's expression for the mechanical force f the elements exert on
+  one another is
+
+    f = 2II'r^(-2) {cos [phi] - (3/2)cos [theta] cos [theta]'}dSdS'.
+
+  This law, together with that of Laplace already mentioned, viz. that
+  the magnetic force due to an element of length dS of a current I at a
+  distance r, the element making an angle [theta] with the radius vector
+  o is IdS sin [theta]/r², constitute the fundamental laws of
+  electrokinetics.
+
+Ampère applied these with great mathematical skill to elucidate the
+mechanical actions of currents on each other, and experimentally
+confirmed the following deductions: (1) Currents in parallel circuits
+flowing in the same direction attract each other, but if in opposite
+directions repel each other. (2) Currents in wires meeting at an angle
+attract each other more into parallelism if both flow either to or from
+the angle, but repel each other more widely apart if they are in
+opposite directions. (3) A current in a small circular conductor exerts
+a magnetic force in its centre perpendicular to its plane and is in all
+respects equivalent to a magnetic shell or a thin circular disk of steel
+so magnetized that one face is a north pole and the other a south pole,
+the product of the area of the circuit and the current flowing in it
+determining the magnetic moment of the element. (4) A closely wound
+spiral current is equivalent as regards external magnetic force to a
+polar magnet, such a circuit being called a finite solenoid. (5) Two
+finite solenoid circuits act on each other like two polar magnets,
+exhibiting actions of attraction or repulsion between their ends.
+
+Ampère's theory was wholly built up on the assumption of action at a
+distance between elements of conductors conveying the electric currents.
+Faraday's researches and the discovery of the fact that the insulating
+medium is the real seat of the operations necessitates a change in the
+point of view from which we regard the facts discovered by Ampère.
+Maxwell showed that in any field of magnetic force there is a tension
+along the lines of force and a pressure at right angles to them; in
+other words, lines of magnetic force are like stretched elastic threads
+which tend to contract.[3] If, therefore, two conductors lie parallel
+and have currents in them in the same direction they are impressed by a
+certain number of lines of magnetic force which pass round the two
+conductors, and it is the tendency of these to contract which draws the
+circuits together. If, however, the currents are in opposite directions
+then the lateral pressure of the similarly contracted lines of force
+between them pushes the conductors apart. Practical application of
+Ampère's discoveries was made by W.E. Weber in inventing the
+electrodynamometer, and later Lord Kelvin devised ampere balances for
+the measurement of electric currents based on the attraction between
+coils conveying electric currents.
+
+_Induction of Electric Currents._--Faraday[4] in 1831 made the important
+discovery of the induction of electric currents (see ELECTRICITY). If
+two conductors are placed parallel to each other, and a current in one
+of them, called the primary, started or stopped or changed in strength,
+every such alteration causes a transitory current to appear in the other
+circuit, called the secondary. This is due to the fact that as the
+primary current increases or decreases, its own embracing magnetic field
+alters, and lines of magnetic force are added to or subtracted from its
+fields. These lines do not appear instantly in their place at a
+distance, but are propagated out from the wire with a velocity equal to
+that of light; hence in their outward progress they cut through the
+secondary circuit, just as ripples made on the surface of water in a
+lake by throwing a stone on to it expand and cut through a stick held
+vertically in the water at a distance from the place of origin of the
+ripples. Faraday confirmed this view of the phenomena by proving that
+the mere motion of a wire transversely to the lines of magnetic force of
+a permanent magnet gave rise to an induced electromotive force in the
+wire. He embraced all the facts in the single statement that if there
+be any circuit which by movement in a magnetic field, or by the creation
+or change in magnetic fields round it, experiences a change in the
+number of lines of force linked with it, then an electromotive force is
+set up in that circuit which is proportional at any instant to the rate
+at which the total magnetic flux linked with it is changing. Hence if Z
+represents the total number of lines of magnetic force linked with a
+circuit of N turns, then -N(dZ/dt) represents the electromotive force
+set up in that circuit. The operation of the induction coil (q.v.) and
+the transformer (q.v.) are based on this discovery. Faraday also found
+that if a copper disk A (fig. 6) is rotated between the poles of a
+magnet NO so that the disk moves with its plane perpendicular to the
+lines of magnetic force of the field, it has created in it an
+electromotive force directed from the centre to the edge or vice versa.
+The action of the dynamo (q.v.) depends on similar processes, viz. the
+cutting of the lines of magnetic force of a constant field produced by
+certain magnets by certain moving conductors called armature bars or
+coils in which an electromotive force is thereby created.
+
+[Illustration: FIG 6.]
+
+  In 1834 H.F.E. Lenz enunciated a law which connects together the
+  mechanical actions between electric circuits discovered by Ampère and
+  the induction of electric currents discovered by Faraday. It is as
+  follows: If a constant current flows in a primary circuit P, and if by
+  motion of P a secondary current is created in a neighbouring circuit
+  S, the direction of the secondary current will be such as to oppose
+  the relative motion of the circuits. Starting from this, F.E. Neumann
+  founded a mathematical theory of induced currents, discovering a
+  quantity M, called the "potential of one circuit on another," or
+  generally their "coefficient of mutual inductance." Mathematically M
+  is obtained by taking the sum of all such quantities as ff dSdS' cos
+  [phi]/r, where dS and dS' are the elements of length of the two
+  circuits, r is their distance, and [phi] is the angle which they make
+  with one another; the summation or integration must be extended over
+  every possible pair of elements. If we take pairs of elements in the
+  same circuit, then Neumann's formula gives us the coefficient of
+  self-induction of the circuit or the potential of the circuit on
+  itself. For the results of such calculations on various forms of
+  circuit the reader must be referred to special treatises.
+
+  H. von Helmholtz, and later on Lord Kelvin, showed that the facts of
+  induction of electric currents discovered by Faraday could have been
+  predicted from the electrodynamic actions discovered by Ampère
+  assuming the principle of the conservation of energy. Helmholtz takes
+  the case of a circuit of resistance R in which acts an electromotive
+  force due to a battery or thermopile. Let a magnet be in the
+  neighbourhood, and the potential of the magnet on the circuit be V, so
+  that if a current I existed in the circuit the work done on the magnet
+  in the time dt is I(dV/dt)dt. The source of electromotive force
+  supplies in the time dt work equal to EIdt, and according to Joule's
+  law energy is dissipated equal to RI²dt. Hence, by the conservation of
+  energy,
+
+    EIdt = RI²dt + I(dV/dt)dt.
+
+  If then E = 0, we have I = -(dV/dt)/R, or there will be a current due
+  to an induced electromotive force expressed by -dV/dt. Hence if the
+  magnet moves, it will create a current in the wire provided that such
+  motion changes the potential of the magnet with respect to the
+  circuit. This is the effect discovered by Faraday.[5]
+
+_Oscillatory Currents._--In considering the motion of electricity in
+conductors we find interesting phenomena connected with the discharge of
+a condenser or Leyden jar (q.v.). This problem was first mathematically
+treated by Lord Kelvin in 1853 (_Phil. Mag._, 1853, 5, p. 292).
+
+  If a conductor of capacity C has its terminals connected by a wire of
+  resistance R and inductance L, it becomes important to consider the
+  subsequent motion of electricity in the wire. If Q is the quantity of
+  electricity in the condenser initially, and q that at any time t after
+  completing the circuit, then the energy stored up in the condenser at
+  that instant is ½q²/C, and the energy associated with the circuit is
+  ½L(dq/dt)², and the rate of dissipation of energy by resistance is
+  R(dq/dt)², since dq/dt = i is the discharge current. Hence we can
+  construct an equation of energy which expresses the fact that at any
+  instant the power given out by the condenser is partly stored in the
+  circuit and partly dissipated as heat in it. Mathematically this is
+  expressed as follows:--
+          _    _        _         _
+      d  |   q² |   d  |     /dq\² |      /dq\²
+    - -- | ½ -- | = -- | ½L ( -- ) | + R ( -- )
+      dt |_  C _|   dt |_    \dt/ _|      \dt/
+
+  or
+
+    d²q   R  dq   1
+    --- + -- -- + -- q = 0.
+    dt²   L  dt   LC
+
+  The above equation has two solutions according as R²/4L² is greater or
+  less than 1/LC. In the first case the current i in the circuit can be
+  expressed by the equation
+
+         [alpha]²+ß²
+    i= Q ------------ e^(-[alpha]t) [e^(ßt) - e^(-ßt)],
+             2ß
+                               ________
+                              /R²    1
+  where [alpha] = R/2L, ß =  / --- - --, Q is the value of q when t = 0,
+                           \/  4L²   LC
+
+  and e is the base of Napierian logarithms; and in the second case
+  by the equation
+
+          [alpha]²+ß²
+    i = Q ----------- e^(-[alpha]t) sin ßt
+            ß
+                                   ________
+                                  /1    R²
+  where [alpha] = R/2L, and ß =  / -- - ---.
+                               \/  LC   4L²
+
+
+  These expressions show that in the first case the discharge current of
+  the jar is always in the same direction and is a transient
+  unidirectional current. In the second case, however, the current is an
+  oscillatory current gradually decreasing in amplitude, the frequency n
+  of the oscillation being given by the expression
+                  ________
+          1      /1     R²
+    n = -----   / -- - ---.
+        2[pi] \/  LC   4L²
+
+  In those cases in which the resistance of the discharge circuit is
+  very small, the expression for the frequency n and for the time period
+  of oscillation R take the simple forms n = 1, 2[pi][root]LC, or T =
+  1/n = 2[pi][root]LC.
+
+The above investigation shows that if we construct a circuit consisting
+of a condenser and inductance placed in series with one another, such
+circuit has a natural electrical time period of its own in which the
+electrical charge in it oscillates if disturbed. It may therefore be
+compared with a pendulum of any kind which when displaced oscillates
+with a time period depending on its inertia and on its restoring force.
+
+The study of these electrical oscillations received a great impetus
+after H.R. Hertz showed that when taking place in electric circuits of a
+certain kind they create electromagnetic waves (see ELECTRIC WAVES) in
+the dielectric surrounding the oscillator, and an additional interest
+was given to them by their application to telegraphy. If a Leyden jar
+and a circuit of low resistance but some inductance in series with it
+are connected across the secondary spark gap of an induction coil, then
+when the coil is set in action we have a series of bright noisy sparks,
+each of which consists of a train of oscillatory electric discharges
+from the jar. The condenser becomes charged as the secondary
+electromotive force of the coil is created at each break of the primary
+current, and when the potential difference of the condenser coatings
+reaches a certain value determined by the spark-ball distance a
+discharge happens. This discharge, however, is not a single movement of
+electricity in one direction but an oscillatory motion with gradually
+decreasing amplitude. If the oscillatory spark is photographed on a
+revolving plate or a rapidly moving film, we have evidence in the
+photograph that such a spark consists of numerous intermittent sparks
+gradually becoming feebler. As the coil continues to operate, these
+trains of electric discharges take place at regular intervals. We can
+cause a train of electric oscillations in one circuit to induce similar
+oscillations in a neighbouring circuit, and thus construct an
+oscillation transformer or high frequency induction coil.
+
+_Alternating Currents._--The study of alternating currents of
+electricity began to attract great attention towards the end of the 19th
+century by reason of their application in electrotechnics and
+especially to the transmission of power. A circuit in which a simple
+periodic alternating current flows is called a single phase circuit. The
+important difference between such a form of current flow and steady
+current flow arises from the fact that if the circuit has inductance
+then the periodic electric current in it is not in step with the
+terminal potential difference or electromotive force acting in the
+circuit, but the current lags behind the electromotive force by a
+certain fraction of the periodic time called the "phase difference." If
+two alternating currents having a fixed difference in phase flow in two
+connected separate but related circuits, the two are called a two-phase
+current. If three or more single-phase currents preserving a fixed
+difference of phase flow in various parts of a connected circuit, the
+whole taken together is called a polyphase current. Since an electric
+current is a vector quantity, that is, has direction as well as
+magnitude, it can most conveniently be represented by a line denoting
+its maximum value, and if the alternating current is a simple periodic
+current then the root-mean-square or effective value of the current is
+obtained by dividing the maximum value by [root]2. Accordingly when we
+have an electric circuit or circuits in which there are simple periodic
+currents we can draw a vector diagram, the lines of which represent the
+relative magnitudes and phase differences of these currents.
+
+  A vector can most conveniently be represented by a symbol such as a +
+  ib, where a stands for any length of a units measured horizontally and
+  b for a length b units measured vertically, and the symbol i is a sign
+  of perpendicularity, and equivalent analytically[6] to [root]-1.
+  Accordingly if E represents the periodic electromotive force (maximum
+  value) acting in a circuit of resistance R and inductance L and
+  frequency n, and if the current considered as a vector is represented
+  by I, it is easy to show that a vector equation exists between these
+  quantities as follows:--
+
+    E = RI + [iota]2[pi]nLI.
+
+  Since the absolute magnitude of a vector a + [iota]b is [root](a² +
+  b²), it follows that considering merely magnitudes of current and
+  electromotive force and denoting them by symbols (E) (I), we have the
+  following equation connecting (I) and (E):--
+
+    (I) = (E)[root](R² + p²L²),
+
+  where p stands for 2[pi]n. If the above equation is compared with the
+  symbolic expression of Ohm's law, it will be seen that the quantity
+  [root](R² + p²L²) takes the place of resistance R in the expression of
+  Ohm. This quantity [root](R² + p²L²) is called the "impedance" of the
+  alternating circuit. The quantity pL is called the "reactance" of the
+  alternating circuit, and it is therefore obvious that the current in
+  such a circuit lags behind the electromotive force by an angle, called
+  the angle of lag, the tangent of which is pL/R.
+
+  _Currents in Networks of Conductors._--In dealing with problems
+  connected with electric currents we have to consider the laws which
+  govern the flow of currents in linear conductors (wires), in plane
+  conductors (sheets), and throughout the mass of a material
+  conductor.[7] In the first case consider the collocation of a number
+  of linear conductors, such as rods or wires of metal, joined at their
+  ends to form a network of conductors. The network consists of a number
+  of conductors joining certain points and forming meshes. In each
+  conductor a current may exist, and along each conductor there is a
+  fall of potential, or an active electromotive force may be acting in
+  it. Each conductor has a certain resistance. To find the current in
+  each conductor when the individual resistances and electromotive
+  forces are given, proceed as follows:--Consider any one mesh. The sum
+  of all the electromotive forces which exist in the branches bounding
+  that mesh must be equal to the sum of all the products of the
+  resistances into the currents flowing along them, or [Sigma](E) =
+  [Sigma](C.R.). Hence if we consider each mesh as traversed by
+  imaginary currents all circulating in the same direction, the real
+  currents are the sums or differences of these imaginary cyclic
+  currents in each branch. Hence we may assign to each mesh a cycle
+  symbol x, y, z, &c., and form a cycle equation. Write down the cycle
+  symbol for a mesh and prefix as coefficient the sum of all the
+  resistances which bound that cycle, then subtract the cycle symbols of
+  each adjacent cycle, each multiplied by the value of the bounding or
+  common resistances, and equate this sum to the total electromotive
+  force acting round the cycle. Thus if x y z are the cycle currents,
+  and a b c the resistances bounding the mesh x, and b and c those
+  separating it from the meshes y and z, and E an electromotive force in
+  the branch a, then we have formed the cycle equation x(a + b + c) -
+  by - cz = E. For each mesh a similar equation may be formed. Hence we
+  have as many linear equations as there are meshes, and we can obtain
+  the solution for each cycle symbol, and therefore for the current in
+  each branch. The solution giving the current in such branch of the
+  network is therefore always in the form of the quotient of two
+  determinants. The solution of the well-known problem of finding the
+  current in the galvanometer circuit of the arrangement of linear
+  conductors called Wheatstone's Bridge is thus easily obtained. For if
+  we call the cycles (see fig. 7) (x + y), y and z, and the resistances
+  P, Q, R, S, G and B, and if E be the electromotive force in the
+  battery circuit, we have the cycle equations
+
+    (P + G + R)(x + y) - Gy - Rz = 0,
+    (Q + G + S)y - G(x + y) - Sz = 0,
+    (R + S + B)z - R(x + y) - Sy = E.
+
+  [Illustration: FIG. 7.]
+
+  From these we can easily obtain the solution for (x + y) - y = x,
+  which is the current through the galvanometer circuit in the form
+
+    x = E(PS - RQ)[Delta].
+
+  where [Delta] is a certain function of P, Q, R, S, B and G.
+
+  _Currents in Sheets._--In the case of current flow in plane sheets, we
+  have to consider certain points called sources at which the current
+  flows into the sheet, and certain points called sinks at which it
+  leaves. We may investigate, first, the simple case of one source and
+  one sink in an infinite plane sheet of thickness [delta] and
+  conductivity k. Take any point P in the plane at distances R and r
+  from the source and sink respectively. The potential V at P is
+  obviously given by
+
+              Q            r1
+    V = -------------log_e --,
+        2[pi]k[delta]      r2
+
+  where Q is the quantity of electricity supplied by the source per
+  second. Hence the equation to the equipotential curve is r1r2 = a
+  constant.
+
+  If we take a point half-way between the sink and the source as the
+  origin of a system of rectangular co-ordinates, and if the distance
+  between sink and source is equal to p, and the line joining them is
+  taken as the axis of x, then the equation to the equipotential line is
+
+    y² + (x + p)²
+    ------------- = a constant.
+    y² + (x - p)²
+
+  This is the equation of a family of circles having the axis of y for a
+  common radical axis, one set of circles surrounding the sink and
+  another set of circles surrounding the source. In order to discover
+  the form of the stream of current lines we have to determine the
+  orthogonal trajectories to this family of coaxial circles. It is easy
+  to show that the orthogonal trajectory of the system of circles is
+  another system of circles all passing through the sink and the source,
+  and as a corollary of this fact, that the electric resistance of a
+  circular disk of uniform thickness is the same between any two points
+  taken anywhere on its circumference as sink and source. These
+  equipotential lines may be delineated experimentally by attaching the
+  terminals of a battery or batteries to small wires which touch at
+  various places a sheet of tinfoil. Two wires attached to a
+  galvanometer may then be placed on the tinfoil, and one may be kept
+  stationary and the other may be moved about, so that the galvanometer
+  is not traversed by any current. The moving terminal then traces out
+  an equipotential curve. If there are n sinks and sources in a plane
+  conducting sheet, and if r, r', r" be the distances of any point from
+  the sinks, and t, t', t" the distances of the sources, then
+
+    r r' r" ...
+    ----------- = a constant,
+    t t' t" ...
+
+  is the equation to the equipotential lines. The orthogonal
+  trajectories or stream lines have the equation
+
+    [Sigma]([theta] - [theta]') = a constant,
+
+  where [theta] and [theta]' are the angles which the lines drawn from
+  any point in the plane to the sink and corresponding source make with
+  the line joining that sink and source. Generally it may be shown that
+  if there are any number of sinks and sources in an infinite
+  plane-conducting sheet, and if r, [theta] are the polar co-ordinates
+  of any one, then the equation to the equipotential surfaces is given
+  by the equation
+
+    [Sigma](A log_er) = a constant,
+
+  where A is a constant; and the equation to the stream of current lines
+  is
+
+    [Sigma]([theta]) = a constant.
+
+  In the case of electric flow in three dimensions the electric
+  potential must satisfy Laplace's equation, and a solution is therefore
+  found in the form [Sigma](A/r) = a constant, as the equation to an
+  equipotential surface, where r is the distance of any point on that
+  surface from a source or sink.
+
+_Convection Currents._--The subject of convection electric currents has
+risen to great importance in connexion with modern electrical
+investigations. The question whether a statically electrified body in
+motion creates a magnetic field is of fundamental importance.
+Experiments to settle it were first undertaken in the year 1876 by H.A.
+Rowland, at a suggestion of H. von Helmholtz.[8] After preliminary
+experiments, Rowland's first apparatus for testing this hypothesis was
+constructed, as follows:--An ebonite disk was covered with radial strips
+of gold-leaf and placed between two other metal plates which acted as
+screens. The disk was then charged with electricity and set in rapid
+rotation. It was found to affect a delicately suspended pair of astatic
+magnetic needles hung in proximity to the disk just as would, by
+Oersted's rule, a circular electric current coincident with the
+periphery of the disk. Hence the statically-charged but rotating disk
+becomes in effect a circular electric current.
+
+The experiments were repeated and confirmed by W.C. Röntgen (_Wied.
+Ann._, 1888, 35, p. 264; 1890, 40, p. 93) and by F. Himstedt (_Wied.
+Ann._, 1889, 38, p. 560). Later V. Crémieu again repeated them and
+obtained negative results (_Com. rend._, 1900, 130, p. 1544, and 131,
+pp. 578 and 797; 1901, 132, pp. 327 and 1108). They were again very
+carefully reconducted by H. Pender (_Phil. Mag._, 1901, 2, p. 179) and
+by E.P. Adams (id. ib., 285). Pender's work showed beyond any doubt that
+electric convection does produce a magnetic effect. Adams employed
+charged copper spheres rotating at a high speed in place of a disk, and
+was able to prove that the rotation of such spheres produced a magnetic
+field similar to that due to a circular current and agreeing numerically
+with the theoretical value. It has been shown by J.J. Thomson (_Phil.
+Mag._, 1881, 2, p. 236) and O. Heaviside (_Electrical Papers_, vol. ii.
+p. 205) that an electrified sphere, moving with a velocity v and
+carrying a quantity of electricity q, should produce a magnetic force H,
+at a point at a distance [rho] from the centre of the sphere, equal to
+qv sin [theta]/[rho]², where [theta] is the angle between the direction
+of [rho] and the motion of the sphere. Adams found the field produced by
+a known electric charge rotating at a known speed had a strength not
+very different from that predetermined by the above formula. An
+observation recorded by R.W. Wood (_Phil. Mag._, 1902, 2, p. 659)
+provides a confirmatory fact. He noticed that if carbon-dioxide strongly
+compressed in a steel bottle is allowed to escape suddenly the cold
+produced solidifies some part of the gas, and the issuing jet is full of
+particles of carbon-dioxide snow. These by friction against the nozzle
+are electrified positively. Wood caused the jet of gas to pass through a
+glass tube 2.5 mm. in diameter, and found that these particles of
+electrified snow were blown through it with a velocity of 2000 ft. a
+second. Moreover, he found that a magnetic needle hung near the tube was
+deflected as if held near an electric current. Hence the positively
+electrified particles in motion in the tube create a magnetic field
+round it.
+
+_Nature of an Electric Current._--The question, What is an electric
+current? is involved in the larger question of the nature of
+electricity. Modern investigations have shown that negative electricity
+is identical with the electrons or corpuscles which are components of
+the chemical atom (see MATTER and ELECTRICITY). Certain lines of
+argument lead to the conclusion that a solid conductor is not only
+composed of chemical atoms, but that there is a certain proportion of
+free electrons present in it, the electronic density or number per unit
+of volume being determined by the material, its temperature and other
+physical conditions. If any cause operates to add or remove electrons at
+one point there is an immediate diffusion of electrons to re-establish
+equilibrium, and this electronic movement constitutes an electric
+current. This hypothesis explains the reason for the identity between
+the laws of diffusion of matter, of heat and of electricity.
+Electromotive force is then any cause making or tending to make an
+inequality of electronic density in conductors, and may arise from
+differences of temperature, i.e. thermoelectromotive force (see
+THERMOELECTRICITY), or from chemical action when part of the circuit is
+an electrolytic conductor, or from the movement of lines of magnetic
+force across the conductor.
+
+  BIBLIOGRAPHY.--For additional information the reader may be referred
+  to the following books: M. Faraday, _Experimental Researches in
+  Electricity_ (3 vols., London, 1839, 1844, 1855); J. Clerk Maxwell,
+  _Electricity and Magnetism_ (2 vols., Oxford, 1892); W. Watson and
+  S.H. Burbury, _Mathematical Theory of Electricity and Magnetism_, vol.
+  ii. (Oxford, 1889); E. Mascart and J. Joubert, _A Treatise on
+  Electricity and Magnetism_ (2 vols., London, 1883); A. Hay,
+  _Alternating Currents_ (London, 1905); W.G. Rhodes, _An Elementary
+  Treatise on Alternating Currents_ (London, 1902); D.C. Jackson and
+  J.P. Jackson, _Alternating Currents and Alternating Current Machinery_
+  (1896, new ed. 1903); S.P. Thompson, _Polyphase Electric Currents_
+  (London, 1900); _Dynamo-Electric Machinery_, vol. ii., "Alternating
+  Currents" (London, 1905); E.E. Fournier d'Albe, _The Electron Theory_
+  (London, 1906).     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] See J.A. Fleming, _The Alternate Current Transformer_, vol. i. p.
+    519.
+
+  [2] See Maxwell, _Electricity and Magnetism_, vol. ii. chap. ii.
+
+  [3] See Maxwell, _Electricity and Magnetism_, vol. ii. 642.
+
+  [4] _Experimental Researches_, vol. i. ser. 1.
+
+  [5] See Maxwell, _Electricity and Magnetism_, vol. ii. § 542, p. 178.
+
+  [6] See W.G. Rhodes, _An Elementary Treatise on Alternating Currents_
+    (London, 1902), chap. vii.
+
+  [7] See J.A. Fleming, "Problems on the Distribution of Electric
+    Currents in Networks of Conductors," _Phil. Mag_. (1885), or Proc.
+    Phys. Soc. Lond. (1885), 7; also Maxwell, _Electricity and Magnetism_
+    (2nd ed.), vol. i. p. 374, § 280, 282b.
+
+  [8] See _Berl. Acad. Ber._, 1876, p. 211; also H.A. Rowland and C.T.
+    Hutchinson, "On the Electromagnetic Effect of Convection Currents,"
+    _Phil. Mag._, 1889, 27, p. 445.
+
+
+
+
+ELECTROLIER, a fixture, usually pendent from the ceiling, for holding
+electric lamps. The word is analogous to chandelier, from which indeed
+it was formed.
+
+
+
+
+ELECTROLYSIS (formed from Gr. [Greek: lyein], to loosen). When the
+passage of an electric current through a substance is accompanied by
+definite chemical changes which are independent of the heating effects
+of the current, the process is known as _electrolysis_, and the
+substance is called an _electrolyte_. As an example we may take the case
+of a solution of a salt such as copper sulphate in water, through which
+an electric current is passed between copper plates. We shall then
+observe the following phenomena. (1) The bulk of the solution is
+unaltered, except that its temperature may be raised owing to the usual
+heating effect which is proportional to the square of the strength of
+the current. (2) The copper plate by which the current is said to enter
+the solution, i.e. the plate attached to the so-called positive terminal
+of the battery or other source of current, dissolves away, the copper
+going into solution as copper sulphate. (3) Copper is deposited on the
+surface of the other plate, being obtained from the solution. (4)
+Changes in concentration are produced in the neighbourhood of the two
+plates or electrodes. In the case we have chosen, the solution becomes
+stronger near the anode, or electrode at which the current enters, and
+weaker near the cathode, or electrode at which it leaves the solution.
+If, instead of using copper electrodes, we take plates of platinum,
+copper is still deposited on the cathode; but, instead of the anode
+dissolving, free sulphuric acid appears in the neighbouring solution,
+and oxygen gas is evolved at the surface of the platinum plate.
+
+With other electrolytes similar phenomena appear, though the primary
+chemical changes may be masked by secondary actions. Thus, with a dilute
+solution of sulphuric acid and platinum electrodes, hydrogen gas is
+evolved at the cathode, while, as the result of a secondary action on
+the anode, sulphuric acid is there re-formed, and oxygen gas evolved.
+Again, with the solution of a salt such as sodium chloride, the sodium,
+which is primarily liberated at the cathode, decomposes the water and
+evolves hydrogen, while the chlorine may be evolved as such, may
+dissolve the anode, or may liberate oxygen from the water, according to
+the nature of the plate and the concentration of the solution.
+
+_Early History of Electrolysis._--Alessandro Volta of Pavia discovered
+the electric battery in the year 1800, and thus placed the means of
+maintaining a steady electric current in the hands of investigators,
+who, before that date, had been restricted to the study of the isolated
+electric charges given by frictional electric machines. Volta's cell
+consists essentially of two plates of different metals, such as zinc and
+copper, connected by an electrolyte such as a solution of salt or acid.
+Immediately on its discovery intense interest was aroused in the new
+invention, and the chemical effects of electric currents were speedily
+detected. W. Nicholson and Sir A. Carlisle found that hydrogen and
+oxygen were evolved at the surfaces of gold and platinum wires connected
+with the terminals of a battery and dipped in water. The volume of the
+hydrogen was about double that of the oxygen, and, since this is the
+ratio in which these elements are combined in water, it was concluded
+that the process consisted essentially in the decomposition of water.
+They also noticed that a similar kind of chemical action went on in the
+battery itself. Soon afterwards, William Cruickshank decomposed the
+magnesium, sodium and ammonium chlorides, and precipitated silver and
+copper from their solutions--an observation which led to the process of
+electroplating. He also found that the liquid round the anode became
+acid, and that round the cathode alkaline. In 1804 W. Hisinger and J.J.
+Berzelius stated that neutral salt solutions could be decomposed by
+electricity, the acid appearing at one pole and the metal at the other.
+This observation showed that nascent hydrogen was not, as had been
+supposed, the primary cause of the separation of metals from their
+solutions, but that the action consisted in a direct decomposition into
+metal and acid. During the earliest investigation of the subject it was
+thought that, since hydrogen and oxygen were usually evolved, the
+electrolysis of solutions of acids and alkalis was to be regarded as a
+direct decomposition of water. In 1806 Sir Humphry Davy proved that the
+formation of acid and alkali when water was electrolysed was due to
+saline impurities in the water. He had shown previously that
+decomposition of water could be effected although the two poles were
+placed in separate vessels connected by moistened threads. In 1807 he
+decomposed potash and soda, previously considered to be elements, by
+passing the current from a powerful battery through the moistened
+solids, and thus isolated the metals potassium and sodium.
+
+The electromotive force of Volta's simple cell falls off rapidly when
+the cell is used, and this phenomenon was shown to be due to the
+accumulation at the metal plates of the products of chemical changes in
+the cell itself. This reverse electromotive force of polarization is
+produced in all electrolytes when the passage of the current changes the
+nature of the electrodes. In batteries which use acids as the
+electrolyte, a film of hydrogen tends to be deposited on the copper or
+platinum electrode; but, to obtain a constant electromotive force,
+several means were soon devised of preventing the formation of the film.
+Constant cells may be divided into two groups, according as their action
+is chemical (as in the bichromate cell, where the hydrogen is converted
+into water by an oxidizing agent placed in a porous pot round the carbon
+plate) or electrochemical (as in Daniell's cell, where a copper plate is
+surrounded by a solution of copper sulphate, and the hydrogen, instead
+of being liberated, replaces copper, which is deposited on the plate
+from the solution).
+
+[Illustration: FIG. 1.]
+
+_Faraday's Laws._--The first exact quantitative study of electrolytic
+phenomena was made about 1830 by Michael Faraday (_Experimental
+Researches_, 1833). When an electric current flows round a circuit,
+there is no accumulation of electricity anywhere in the circuit, hence
+the current strength is everywhere the same, and we may picture the
+current as analogous to the flow of an incompressible fluid. Acting on
+this view, Faraday set himself to examine the relation between the flow
+of electricity round the circuit and the amount of chemical
+decomposition. He passed the current driven by a voltaic battery ZnPt
+(fig. 1) through two branches containing the two electrolytic cells A
+and B. The reunited current was then led through another cell C, in
+which the strength of the current must be the sum of those in the arms A
+and B. Faraday found that the mass of substance liberated at the
+electrodes in the cell C was equal to the sum of the masses liberated in
+the cells A and B. He also found that, for the same current, the amount
+of chemical action was independent of the size of the electrodes and
+proportional to the time that the current flowed. Regarding the current
+as the passage of a certain amount of electricity per second, it will be
+seen that the results of all these experiments may be summed up in the
+statement that the amount of chemical action is proportional to the
+quantity of electricity which passes through the cell.
+
+Faraday's next step was to pass the same current through different
+electrolytes in series. He found that the amounts of the substances
+liberated in each cell were proportional to the chemical equivalent
+weights of those substances. Thus, if the current be passed through
+dilute sulphuric acid between hydrogen electrodes, and through a
+solution of copper sulphate, it will be found that the mass of hydrogen
+evolved in the first cell is to the mass of copper deposited in the
+second as 1 is to 31.8. Now this ratio is the same as that which gives
+the relative chemical equivalents of hydrogen and copper, for 1 gramme
+of hydrogen and 31.8 grammes of copper unite chemically with the same
+weight of any acid radicle such as chlorine or the sulphuric group, SO4.
+Faraday examined also the electrolysis of certain fused salts such as
+lead chloride and silver chloride. Similar relations were found to hold
+and the amounts of chemical change to be the same for the same electric
+transfer as in the case of solutions.
+
+We may sum up the chief results of Faraday's work in the statements
+known as Faraday's laws: The mass of substance liberated from an
+electrolyte by the passage of a current is proportional (1) to the total
+quantity of electricity which passes through the electrolyte, and (2) to
+the chemical equivalent weight of the substance liberated.
+
+Since Faraday's time his laws have been confirmed by modern research,
+and in favourable cases have been shown to hold good with an accuracy of
+at least one part in a thousand. The principal object of this more
+recent research has been the determination of the quantitative amount of
+chemical change associated with the passage for a given time of a
+current of strength known in electromagnetic units. It is found that the
+most accurate and convenient apparatus to use is a platinum bowl filled
+with a solution of silver nitrate containing about fifteen parts of the
+salt to one hundred of water. Into the solution dips a silver plate
+wrapped in filter paper, and the current is passed from the silver plate
+as anode to the bowl as cathode. The bowl is weighed before and after
+the passage of the current, and the increase gives the mass of silver
+deposited. The mean result of the best determinations shows that when a
+current of one ampere is passed for one second, a mass of silver is
+deposited equal to 0.001118 gramme. So accurate and convenient is this
+determination that it is now used conversely as a practical definition
+of the ampere, which (defined theoretically in terms of magnetic force)
+is defined practically as the current which in one second deposits 1.118
+milligramme of silver.
+
+Taking the chemical equivalent weight of silver, as determined by
+chemical experiments, to be 107.92, the result described gives as the
+electrochemical equivalent of an ion of unit chemical equivalent the
+value 1.036 × 10^(-5). If, as is now usual, we take the equivalent
+weight of oxygen as our standard and call it 16, the equivalent weight
+of hydrogen is 1.008, and its electrochemical equivalent is 1.044 ×
+10^(-5). The electrochemical equivalent of any other substance, whether
+element or compound, may be found by multiplying its chemical equivalent
+by 1.036 × 10^(-5). If, instead of the ampere, we take the C.G.S.
+electromagnetic unit of current, this number becomes 1.036 × 10^(-4).
+
+_Chemical Nature of the Ions._--A study of the products of decomposition
+does not necessarily lead directly to a knowledge of the ions actually
+employed in carrying the current through the electrolyte. Since the
+electric forces are active throughout the whole solution, all the ions
+must come under its influence and therefore move, but their separation
+from the electrodes is determined by the electromotive force needed to
+liberate them. Thus, as long as every ion of the solution is present in
+the layer of liquid next the electrode, the one which responds to the
+least electromotive force will alone be set free. When the amount of
+this ion in the surface layer becomes too small to carry all the current
+across the junction, other ions must also be used, and either they or
+their secondary products will appear also at the electrode. In aqueous
+solutions, for instance, a few hydrogen (H) and hydroxyl (OH) ions
+derived from the water are always present, and will be liberated if the
+other ions require a higher decomposition voltage and the current be
+kept so small that hydrogen and hydroxyl ions can be formed fast enough
+to carry all the current across the junction between solution and
+electrode.
+
+The issue is also obscured in another way. When the ions are set free at
+the electrodes, they may unite with the substance of the electrode or
+with some constituent of the solution to form secondary products. Thus
+the hydroxyl mentioned above decomposes into water and oxygen, and the
+chlorine produced by the electrolysis of a chloride may attack the metal
+of the anode. This leads us to examine more closely the part played by
+water in the electrolysis of aqueous solutions. Distilled water is a
+very bad conductor, though, even when great care is taken to remove all
+dissolved bodies, there is evidence to show that some part of the trace
+of conductivity remaining is due to the water itself. By careful
+redistillation F. Kohlrausch has prepared water of which the
+conductivity compared with that of mercury was only 0.40 × 10^(-11) at
+18° C. Even here some little impurity was present, and the conductivity
+of chemically pure water was estimated by thermodynamic reasoning as
+0.36 × 10^(-11) at 18° C. As we shall see later, the conductivity of
+very dilute salt solutions is proportional to the concentration, so that
+it is probable that, in most cases, practically all the current is
+carried by the salt. At the electrodes, however, the small quantity of
+hydrogen and hydroxyl ions from the water are liberated first in cases
+where the ions of the salt have a higher decomposition voltage. The
+water being present in excess, the hydrogen and hydroxyl are re-formed
+at once and therefore are set free continuously. If the current be so
+strong that new hydrogen and hydroxyl ions cannot be formed in time,
+other substances are liberated; in a solution of sulphuric acid a strong
+current will evolve sulphur dioxide, the more readily as the
+concentration of the solution is increased. Similar phenomena are seen
+in the case of a solution of hydrochloric acid. When the solution is
+weak, hydrogen and oxygen are evolved; but, as the concentration is
+increased, and the current raised, more and more chlorine is liberated.
+
+  An interesting example of secondary action is shown by the common
+  technical process of electroplating with silver from a bath of
+  potassium silver cyanide. Here the ions are potassium and the group
+  Ag(CN)2.[1] Each potassium ion as it reaches the cathode precipitates
+  silver by reacting with the solution in accordance with the chemical
+  equation
+
+    K + KAg(CN)2 = 2KCN + Ag,
+
+  while the anion Ag(CN)2 dissolves an atom of silver from the anode,
+  and re-forms the complex cyanide KAg(CN)2 by combining with the 2KCN
+  produced in the reaction described in the equation. If the anode
+  consist of platinum, cyanogen gas is evolved thereat from the anion
+  Ag(CN)2, and the platinum becomes covered with the insoluble silver
+  cyanide, AgCN, which soon stops the current. The coating of silver
+  obtained by this process is coherent and homogeneous, while that
+  deposited from a solution of silver nitrate, as the result of the
+  primary action of the current, is crystalline and easily detached.
+
+  In the electrolysis of a concentrated solution of sodium acetate,
+  hydrogen is evolved at the cathode and a mixture of ethane and carbon
+  dioxide at the anode. According to H. Jahn,[2] the processes at the
+  anode can be represented by the equations
+
+    2CH3·COO + H2O = 2CH3·COOH + O
+
+    2CH3·COOH + O = C2H6 + 2CO2 + H2O.
+
+  The hydrogen at the cathode is developed by the secondary action
+
+    2Na + 2H2O = 2NaOH + H2.
+
+  Many organic compounds can be prepared by taking advantage of
+  secondary actions at the electrodes, such as reduction by the cathodic
+  hydrogen, or oxidation at the anode (see ELECTROCHEMISTRY).
+
+  It is possible to distinguish between double salts and salts of
+  compound acids. Thus J.W. Hittorf showed that when a current was
+  passed through a solution of sodium platino-chloride, the platinum
+  appeared at the anode. The salt must therefore be derived from an
+  acid, chloroplatinic acid, H2PtCl6, and have the formula Na2PtCl6, the
+  ions being Na and PtCl6", for if it were a double salt it would
+  decompose as a mixture of sodium chloride and platinum chloride and
+  both metals would go to the cathode.
+
+_Early Theories of Electrolysis._--The obvious phenomena to be explained
+by any theory of electrolysis are the liberation of the products of
+chemical decomposition at the two electrodes while the intervening
+liquid is unaltered. To explain these facts, Theodor Grotthus
+(1785-1822) in 1806 put forward an hypothesis which supposed that the
+opposite chemical constituents of an electrolyte interchanged partners
+all along the line between the electrodes when a current passed. Thus,
+if the molecule of a substance in solution is represented by AB,
+Grotthus considered a chain of AB molecules to exist from one electrode
+to the other. Under the influence of an applied electric force, he
+imagined that the B part of the first molecule was liberated at the
+anode, and that the A part thus isolated united with the B part of the
+second molecule, which, in its turn, passed on its A to the B of the
+third molecule. In this manner, the B part of the last molecule of the
+chain was seized by the A of the last molecule but one, and the A part
+of the last molecule liberated at the surface of the cathode.
+
+Chemical phenomena throw further light on this question. If two
+solutions containing the salts AB and CD be mixed, double decomposition
+is found to occur, the salts AD and CB being formed till a certain part
+of the first pair of substances is transformed into an equivalent amount
+of the second pair. The proportions between the four salts AB, CD, AD
+and CB, which exist finally in solution, are found to be the same
+whether we begin with the pair AB and CD or with the pair AD and CB. To
+explain this result, chemists suppose that both changes can occur
+simultaneously, and that equilibrium results when the rate at which AB
+and CD are transformed into AD and CB is the same as the rate at which
+the reverse change goes on. A freedom of interchange is thus indicated
+between the opposite parts of the molecules of salts in solution, and it
+follows reasonably that with the solution of a single salt, say sodium
+chloride, continual interchanges go on between the sodium and chlorine
+parts of the different molecules.
+
+These views were applied to the theory of electrolysis by R.J.E.
+Clausius. He pointed out that it followed that the electric forces did
+not cause the interchanges between the opposite parts of the dissolved
+molecules but only controlled their direction. Interchanges must be
+supposed to go on whether a current passes or not, the function of the
+electric forces in electrolysis being merely to determine in what
+direction the parts of the molecules shall work their way through the
+liquid and to effect actual separation of these parts (or their
+secondary products) at the electrodes. This conclusion is supported also
+by the evidence supplied by the phenomena of electrolytic conduction
+(see CONDUCTION, ELECTRIC, § II.). If we eliminate the reverse
+electromotive forces of polarization at the two electrodes, the
+conduction of electricity through electrolytes is found to conform to
+Ohm's law; that is, once the polarization is overcome, the current is
+proportional to the electromotive force applied to the bulk of the
+liquid. Hence there can be no reverse forces of polarization inside the
+liquid itself, such forces being confined to the surface of the
+electrodes. No work is done in separating the parts of the molecules
+from each other. This result again indicates that the parts of the
+molecules are effectively separate from each other, the function of the
+electric forces being merely directive.
+
+_Migration of the Ions._--The opposite parts of an electrolyte, which
+work their way through the liquid under the action of the electric
+forces, were named by Faraday the ions--the travellers. The changes of
+concentration which occur in the solution near the two electrodes were
+referred by W. Hittorf (1853) to the unequal speeds with which he
+supposed the two opposite ions to travel. It is clear that, when two
+opposite streams of ions move past each other, equivalent quantities are
+liberated at the two ends of the system. If the ions move at equal
+rates, the salt which is decomposed to supply the ions liberated must be
+taken equally from the neighbourhood of the two electrodes. But if one
+ion, say the anion, travels faster through the liquid than the other,
+the end of the solution from which it comes will be more exhausted of
+salt than the end towards which it goes. If we assume that no other
+cause is at work, it is easy to prove that, with non-dissolvable
+electrodes, the ratio of salt lost at the anode to the salt lost at the
+cathode must be equal to the ratio of the velocity of the cation to the
+velocity of the anion. This result may be illustrated by fig. 2. The
+black circles represent one ion and the white circles the other. If the
+black ions move twice as fast as the white ones, the state of things
+after the passage of a current will be represented by the lower part of
+the figure. Here the middle part of the solution is unaltered and the
+number of ions liberated is the same at either end, but the amount of
+salt left at one end is less than that at the other. On the right,
+towards which the faster ion travels, five molecules of salt are left,
+being a loss of two from the original seven. On the left, towards which
+the slower ion moves, only three molecules remain--a loss of four. Thus,
+the ratio of the losses at the two ends is two to one--the same as the
+ratio of the assumed ionic velocities. It should be noted, however, that
+another cause would be competent to explain the unequal dilution of the
+two solutions. If either ion carried with it some of the unaltered salt
+or some of the solvent, concentration or dilution of the liquid would be
+produced where the ion was liberated. There is reason to believe that in
+certain cases such complex ions do exist, and interfere with the results
+of the differing ionic velocities.
+
+[Illustration: FIG. 2.]
+
+Hittorf and many other observers have made experiments to determine the
+unequal dilution of a solution round the two electrodes when a current
+passes. Various forms of apparatus have been used, the principle of them
+all being to secure efficient separation of the two volumes of solution
+in which the changes occur. In some cases porous diaphragms have been
+employed; but such diaphragms introduce a new complication, for the
+liquid as a whole is pushed through them by the action of the current,
+the phenomenon being known as electric endosmose. Hence experiments
+without separating diaphragms are to be preferred, and the apparatus may
+be considered effective when a considerable bulk of intervening solution
+is left unaltered in composition. It is usual to express the results in
+terms of what is called the migration constant of the anion, that is,
+the ratio of the amount of salt lost by the anode vessel to the whole
+amount lost by both vessels. Thus the statement that the migration
+constant or transport number for a decinormal solution of copper
+sulphate is 0.632 implies that of every gramme of copper sulphate lost
+by a solution containing originally one-tenth of a gramme equivalent per
+litre when a current is passed through it between platinum electrodes,
+0.632 gramme is taken from the cathode vessel and 0.368 gramme from the
+anode vessel. For certain concentrated solutions the transport number is
+found to be greater than unity; thus for a normal solution of cadmium
+iodide its value is 1.12. On the theory that the phenomena are wholly
+due to unequal ionic velocities this result would mean that the cation
+like the anion moved against the conventional direction of the current.
+That a body carrying a positive electric charge should move against the
+direction of the electric intensity is contrary to all our notions of
+electric forces, and we are compelled to seek some other explanation. An
+alternative hypothesis is given by the idea of complex ions. If some of
+the anions, instead of being simple iodine ions represented chemically
+by the symbol I, are complex structures formed by the union of iodine
+with unaltered cadmium iodide--structures represented by some such
+chemical formula as I(CdI2), the concentration of the solution round the
+anode would be increased by the passage of an electric current, and the
+phenomena observed would be explained. It is found that, in such cases
+as this, where it seems necessary to imagine the existence of complex
+ions, the transport number changes rapidly as the concentration of the
+original solution is changed. Thus, diminishing the concentration of the
+cadmium iodine solution from normal to one-twentieth normal changes the
+transport number from 1.12 to 0.64. Hence it is probable that in cases
+where the transport number keeps constant with changing concentration
+the hypothesis of complex ions is unnecessary, and we may suppose that
+the transport number is a true migration constant from which the
+relative velocities of the two ions may be calculated in the matter
+suggested by Hittorf and illustrated in fig. 2. This conclusion is
+confirmed by the results of the direct visual determination of ionic
+velocities (see CONDUCTION, ELECTRIC, § II.), which, in cases where the
+transport number remains constant, agree with the values calculated from
+those numbers. Many solutions in which the transport numbers vary at
+high concentration often become simple at greater dilution. For
+instance, to take the two solutions to which we have already referred,
+we have--
+
+  +----------------------------------+------+------+------+------+------+------+------+-----+-----------+
+  |Concentration                     | 2.0  | 1.5  | 1.0  | 0.5  | 0.2  | 0.1  | 0.05 | 0.02|0.01 normal|
+  |Copper sulphate transport numbers | 0.72 | 0.714| 0.696| 0.668| 0.643| 0.632| 0.626| 0.62|     ..    |
+  |Cadmium iodide     "         "    | 1.22 | 1.18 | 1.12 | 1.00 | 0.83 | 0.71 | 0.64 | 0.59|0.56       |
+  +----------------------------------+------+------+------+------+------+------+------+-----+-----------+
+
+It is probable that in both these solutions complex ions exist at fairly
+high concentrations, but gradually gets less in number and finally
+disappear as the dilution is increased. In such salts as potassium
+chloride the ions seem to be simple throughout a wide range of
+concentration since the transport numbers for the same series of
+concentrations as those used above run--
+
+  Potassium chloride--
+  0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.507, 0.506.
+
+The next important step in the theory of the subject was made by F.
+Kohlrausch in 1879. Kohlrausch formulated a theory of electrolytic
+conduction based on the idea that, under the action of the electric
+forces, the oppositely charged ions moved in opposite directions through
+the liquid, carrying their charges with them. If we eliminate the
+polarization at the electrodes, it can be shown that an electrolyte
+possesses a definite electric resistance and therefore a definite
+conductivity. The conductivity gives us the amount of electricity
+conveyed per second under a definite electromotive force. On the view of
+the process of conduction described above, the amount of electricity
+conveyed per second is measured by the product of the number of ions,
+known from the concentration of the solution, the charge carried by each
+of them, and the velocity with which, on the average, they move through
+the liquid. The concentration is known, and the conductivity can be
+measured experimentally; thus the average velocity with which the ions
+move past each other under the existent electromotive force can be
+estimated. The velocity with which the ions move past each other is
+equal to the sum of their individual velocities, which can therefore be
+calculated. Now Hittorf's transport number, in the case of simple salts
+in moderately dilute solution, gives us the ratio between the two ionic
+velocities. Hence the absolute velocities of the two ions can be
+determined, and we can calculate the actual speed with which a certain
+ion moves through a given liquid under the action of a given potential
+gradient or electromotive force. The details of the calculation are
+given in the article CONDUCTION, ELECTRIC, § II., where also will be
+found an account of the methods which have been used to measure the
+velocities of many ions by direct visual observation. The results go to
+show that, where the existence of complex ions is not indicated by
+varying transport numbers, the observed velocities agree with those
+calculated on Kohlrausch's theory.
+
+_Dissociation Theory._--The verification of Kohlrausch's theory of ionic
+velocity verifies also the view of electrolysis which regards the
+electric current as due to streams of ions moving in opposite directions
+through the liquid and carrying their opposite electric charges with
+them. There remains the question how the necessary migratory freedom of
+the ions is secured. As we have seen, Grotthus imagined that it was the
+electric forces which sheared the ions past each other and loosened the
+chemical bonds holding the opposite parts of each dissolved molecule
+together. Clausius extended to electrolysis the chemical ideas which
+looked on the opposite parts of the molecule as always changing partners
+independently of any electric force, and regarded the function of the
+current as merely directive. Still, the necessary freedom was supposed
+to be secured by interchanges of ions between molecules at the instants
+of molecular collision only; during the rest of the life of the ions
+they were regarded as linked to each other to form electrically neutral
+molecules.
+
+In 1887 Svante Arrhenius, professor of physics at Stockholm, put forward
+a new theory which supposed that the freedom of the opposite ions from
+each other was not a mere momentary freedom at the instants of molecular
+collision, but a more or less permanent freedom, the ions moving
+independently of each other through the liquid. The evidence which led
+Arrhenius to this conclusion was based on van 't Hoff's work on the
+osmotic pressure of solutions (see SOLUTION). If a solution, let us say
+of sugar, be confined in a closed vessel through the walls of which the
+solvent can pass but the solution cannot, the solvent will enter till a
+certain equilibrium pressure is reached. This equilibrium pressure is
+called the osmotic pressure of the solution, and thermodynamic theory
+shows that, in an ideal case of perfect separation between solvent and
+solute, it should have the same value as the pressure which a number of
+molecules equal to the number of solute molecules in the solution would
+exert if they could exist as a gas in a space equal to the volume of the
+solution, provided that the space was large enough (i.e. the solution
+dilute enough) for the intermolecular forces between the dissolved
+particles to be inappreciable. Van 't Hoff pointed out that measurements
+of osmotic pressure confirmed this value in the case of dilute solutions
+of cane sugar.
+
+Thermodynamic theory also indicates a connexion between the osmotic
+pressure of a solution and the depression of its freezing point and its
+vapour pressure compared with those of the pure solvent. The freezing
+points and vapour pressures of solutions of sugar are also in conformity
+with the theoretical numbers. But when we pass to solutions of mineral
+salts and acids--to solutions of electrolytes in fact--we find that the
+observed values of the osmotic pressures and of the allied phenomena are
+greater than the normal values. Arrhenius pointed out that these
+exceptions would be brought into line if the ions of electrolytes were
+imagined to be separate entities each capable of producing its own
+pressure effects just as would an ordinary dissolved molecule.
+
+Two relations are suggested by Arrhenius' theory. (1) In very dilute
+solutions of simple substances, where only one kind of dissociation is
+possible and the dissociation of the ions is complete, the number of
+pressure-producing particles necessary to produce the observed osmotic
+effects should be equal to the number of ions given by a molecule of the
+salt as shown by its electrical properties. Thus the osmotic pressure,
+or the depression of the freezing point of a solution of potassium
+chloride should, at extreme dilution, be twice the normal value, but of
+a solution of sulphuric acid three times that value, since the potassium
+salt contains two ions and the acid three. (2) As the concentration of
+the solutions increases, the ionization as measured electrically and the
+dissociation as measured osmotically might decrease more or less
+together, though, since the thermodynamic theory only holds when the
+solution is so dilute that the dissolved particles are beyond each
+other's sphere of action, there is much doubt whether this second
+relation is valid through any appreciable range of concentration.
+
+At present, measurements of freezing point are more convenient and
+accurate than those of osmotic pressure, and we may test the validity of
+Arrhenius' relations by their means. The theoretical value for the
+depression of the freezing point of a dilute solution per
+gramme-equivalent of solute per litre is 1.857° C. Completely ionized
+solutions of salts with two ions should give double this number or
+3.714°, while electrolytes with three ions should have a value of 5.57°.
+
+The following results are given by H.B. Loomis for the concentration of
+0.01 gramme-molecule of salt to one thousand grammes of water. The salts
+tabulated are those of which the equivalent conductivity reaches a
+limiting value indicating that complete ionization is reached as
+dilution is increased. With such salts alone is a valid comparison
+possible.
+
+  _Molecular Depressions of the Freezing Point._
+
+  _Electrolytes with two Ions._
+
+  Potassium chloride  3.60
+  Sodium chloride     3.67
+  Potassium hydrate   3.71
+  Hydrochloric acid   3.61
+  Nitric acid         3.73
+  Potassium nitrate   3.46
+  Sodium nitrate      3.55
+  Ammonium nitrate    3.58
+
+  _Electrolytes with three Ions._
+
+  Sulphuric acid      4.49
+  Sodium sulphate     5.09
+  Calcium chloride    5.04
+  Magnesium chloride  5.08
+
+At the concentration used by Loomis the electrical conductivity
+indicates that the ionization is not complete, particularly in the case
+of the salts with divalent ions in the second list. Allowing for
+incomplete ionization the general concordance of these numbers with the
+theoretical ones is very striking.
+
+The measurements of freezing points of solutions at the extreme dilution
+necessary to secure complete ionization is a matter of great difficulty,
+and has been overcome only in a research initiated by E.H. Griffiths.[3]
+Results have been obtained for solutions of sugar, where the
+experimental number is 1.858, and for potassium chloride, which gives a
+depression of 3.720. These numbers agree with those indicated by theory,
+viz. 1.857 and 3.714, with astonishing exactitude. We may take
+Arrhenius' first relation as established for the case of potassium
+chloride.
+
+The second relation, as we have seen, is not a strict consequence of
+theory, and experiments to examine it must be treated as an
+investigation of the limits within which solutions are dilute within the
+thermodynamic sense of the word, rather than as a test of the soundness
+of the theory. It is found that divergence has begun before the
+concentration has become great enough to enable freezing points to be
+measured with any ordinary apparatus. The freezing point curve usually
+lies below the electrical one, but approaches it as dilution is
+increased.[4]
+
+Returning once more to the consideration of the first relation, which
+deals with the comparison between the number of ions and the number of
+pressure-producing particles in dilute solution, one caution is
+necessary. In simple substances like potassium chloride it seems evident
+that one kind of dissociation only is possible. The electrical phenomena
+show that there are two ions to the molecule, and that these ions are
+electrically charged. Corresponding with this result we find that the
+freezing point of dilute solutions indicates that two pressure-producing
+particles per molecule are present. But the converse relation does not
+necessarily follow. It would be possible for a body in solution to be
+dissociated into non-electrical parts, which would give osmotic pressure
+effects twice or three times the normal value, but, being uncharged,
+would not act as ions and impart electrical conductivity to the
+solution. L. Kahlenberg (_Jour. Phys. Chem._, 1901, v. 344, 1902, vi.
+43) has found that solutions of diphenylamine in methyl cyanide possess
+an excess of pressure-producing particles and yet are non-conductors of
+electricity. It is possible that in complicated organic substances we
+might have two kinds of dissociation, electrical and non-electrical,
+occurring simultaneously, while the possibility of the association of
+molecules accompanied by the electrical dissociation of some of them
+into new parts should not be overlooked. It should be pointed out that
+no measurements on osmotic pressures or freezing points can do more than
+tell us that an excess of particles is present; such experiments can
+throw no light on the question whether or not those particles are
+electrically charged. That question can only be answered by examining
+whether or not the particles move in an electric field.
+
+The dissociation theory was originally suggested by the osmotic pressure
+relations. But not only has it explained satisfactorily the electrical
+properties of solutions, but it seems to be the only known hypothesis
+which is consistent with the experimental relation between the
+concentration of a solution and its electrical conductivity (see
+CONDUCTION, ELECTRIC, § II., "Nature of Electrolytes"). It is probable
+that the electrical effects constitute the strongest arguments in favour
+of the theory. It is necessary to point out that the dissociated ions of
+such a body as potassium chloride are not in the same condition as
+potassium and chlorine in the free state. The ions are associated with
+very large electric charges, and, whatever their exact relations with
+those charges may be, it is certain that the energy of a system in such
+a state must be different from its energy when unelectrified. It is not
+unlikely, therefore, that even a compound as stable in the solid form as
+potassium chloride should be thus dissociated when dissolved. Again,
+water, the best electrolytic solvent known, is also the body of the
+highest specific inductive capacity (dielectric constant), and this
+property, to whatever cause it may be due, will reduce the forces
+between electric charges in the neighbourhood, and may therefore enable
+two ions to separate.
+
+This view of the nature of electrolytic solutions at once explains many
+well-known phenomena. Other physical properties of these solutions, such
+as density, colour, optical rotatory power, &c., like the
+conductivities, are _additive_, i.e. can be calculated by adding
+together the corresponding properties of the parts. This again suggests
+that these parts are independent of each other. For instance, the colour
+of a salt solution is the colour obtained by the superposition of the
+colours of the ions and the colour of any undissociated salt that may be
+present. All copper salts in dilute solution are blue, which is
+therefore the colour of the copper ion. Solid copper chloride is brown
+or yellow, so that its concentrated solution, which contains both ions
+and undissociated molecules, is green, but changes to blue as water is
+added and the ionization becomes complete. A series of equivalent
+solutions all containing the same coloured ion have absorption spectra
+which, when photographed, show identical absorption bands of equal
+intensity.[5] The colour changes shown by many substances which are used
+as indicators (q.v.) of acids or alkalis can be explained in a similar
+way. Thus para-nitrophenol has colourless molecules, but an intensely
+yellow negative ion. In neutral, and still more in acid solutions, the
+dissociation of the indicator is practically nothing, and the liquid is
+colourless. If an alkali is added, however, a highly dissociated salt of
+para-nitrophenol is formed, and the yellow colour is at once evident. In
+other cases, such as that of litmus, both the ion and the undissociated
+molecule are coloured, but in different ways.
+
+Electrolytes possess the power of coagulating solutions of colloids such
+as albumen and arsenious sulphide. The mean values of the relative
+coagulative powers of sulphates of mono-, di-, and tri-valent metals
+have been shown experimentally to be approximately in the ratios
+1:35:1023. The dissociation theory refers this to the action of electric
+charges carried by the free ions. If a certain minimum charge must be
+collected in order to start coagulation, it will need the conjunction of
+6n monovalent, or 3n divalent, to equal the effect of 2n tri-valent
+ions. The ratios of the coagulative powers can thus be calculated to be
+1:x:x², and putting x = 32 we get 1:32:1024, a satisfactory agreement
+with the numbers observed.[6]
+
+The question of the application of the dissociation theory to the case
+of fused salts remains. While it seems clear that the conduction in this
+case is carried on by ions similar to those of solutions, since
+Faraday's laws apply equally to both, it does not follow necessarily
+that semi-permanent dissociation is the only way to explain the
+phenomena. The evidence in favour of dissociation in the case of
+solutions does not apply to fused salts, and it is possible that, in
+their case, a series of molecular interchanges, somewhat like Grotthus's
+chain, may represent the mechanism of conduction.
+
+An interesting relation appears when the electrolytic conductivity of
+solutions is compared with their chemical activity. The readiness and
+speed with which electrolytes react are in sharp contrast with the
+difficulty experienced in the case of non-electrolytes. Moreover, a
+study of the chemical relations of electrolytes indicates that it is
+always the electrolytic ions that are concerned in their reactions. The
+tests for a salt, potassium nitrate, for example, are the tests not for
+KNO3, but for its ions K and NO3, and in cases of double decomposition
+it is always these ions that are exchanged for those of other
+substances. If an element be present in a compound otherwise than as an
+ion, it is not interchangeable, and cannot be recognized by the usual
+tests. Thus neither a chlorate, which contains the ion ClO3, nor
+monochloracetic acid, shows the reactions of chlorine, though it is, of
+course, present in both substances; again, the sulphates do not answer
+to the usual tests which indicate the presence of sulphur as sulphide.
+The chemical activity of a substance is a quantity which may be measured
+by different methods. For some substances it has been shown to be
+independent of the particular reaction used. It is then possible to
+assign to each body a specific coefficient of affinity. Arrhenius has
+pointed out that the coefficient of affinity of an acid is proportional
+to its electrolytic ionization.
+
+  The affinities of acids have been compared in several ways. W. Ostwald
+  (_Lehrbuch der allg. Chemie_, vol. ii., Leipzig, 1893) investigated
+  the relative affinities of acids for potash, soda and ammonia, and
+  proved them to be independent of the base used. The method employed
+  was to measure the changes in volume caused by the action. His results
+  are given in column I. of the following table, the affinity of
+  hydrochloric acid being taken as one hundred. Another method is to
+  allow an acid to act on an insoluble salt, and to measure the quantity
+  which goes into solution. Determinations have been made with calcium
+  oxalate, CaC2O4+H2O, which is easily decomposed by acids, oxalic acid
+  and a soluble calcium salt being formed. The affinities of acids
+  relative to that of oxalic acid are thus found, so that the acids can
+  be compared among themselves (column II.). If an aqueous solution of
+  methyl acetate be allowed to stand, a slow decomposition goes on. This
+  is much quickened by the presence of a little dilute acid, though the
+  acid itself remains unchanged. It is found that the influence of
+  different acids on this action is proportional to their specific
+  coefficients of affinity. The results of this method are given in
+  column III. Finally, in column IV. the electrical conductivities of
+  normal solutions of the acids have been tabulated. A better basis of
+  comparison would be the ratio of the actual to the limiting
+  conductivity, but since the conductivity of acids is chiefly due to
+  the mobility of the hydrogen ions, its limiting value is nearly the
+  same for all, and the general result of the comparison would be
+  unchanged.
+
+    +-----------------+---------+---------+---------+---------+
+    |      Acid.      |    I.   |   II.   |   III.  |   IV.   |
+    +-----------------+---------+---------+---------+---------+
+    | Hydrochloric    |  100    |  100    |  100    |  100    |
+    | Nitric          |  102    |  110    |   92    |   99.6  |
+    | Sulphuric       |   68    |   67    |   74    |   65.1  |
+    | Formic          |    4.0  |    2.5  |    1.3  |    1.7  |
+    | Acetic          |    1.2  |    1.0  |    0.3  |    0.4  |
+    | Propionic       |    1.1  |     ..  |    0.3  |    0.3  |
+    | Monochloracetic |    7.2  |    5.1  |    4.3  |    4.9  |
+    | Dichloracetic   |   34    |   18    |   23.0  |   25.3  |
+    | Trichloracetic  |   82    |   63    |   68.2  |   62.3  |
+    | Malic           |   3.0   |    5.0  |    1.2  |    1.3  |
+    | Tartaric        |   5.3   |    6.3  |    2.3  |    2.3  |
+    | Succinic        |   0.1   |    0.2  |    0.5  |    0.6  |
+    +-----------------+---------+---------+---------+---------+
+
+  It must be remembered that, the solutions not being of quite the same
+  strength, these numbers are not strictly comparable, and that the
+  experimental difficulties involved in the chemical measurements are
+  considerable. Nevertheless, the remarkable general agreement of the
+  numbers in the four columns is quite enough to show the intimate
+  connexion between chemical activity and electrical conductivity. We
+  may take it, then, that only that portion of these bodies is
+  chemically active which is electrolytically active--that ionization is
+  necessary for such chemical activity as we are dealing with here, just
+  as it is necessary for electrolytic conductivity.
+
+  The ordinary laws of chemical equilibrium have been applied to the
+  case of the dissociation of a substance into its ions. Let x be the
+  number of molecules which dissociate per second when the number of
+  undissociated molecules in unit volume is unity, then in a dilute
+  solution where the molecules do not interfere with each other, xp is
+  the number when the concentration is p. Recombination can only occur
+  when two ions meet, and since the frequency with which this will
+  happen is, in dilute solution, proportional to the square of the ionic
+  concentration, we shall get for the number of molecules re-formed in
+  one second yq² where q is the number of dissociated molecules in one
+  cubic centimetre. When there is equilibrium, xp = yq². If µ be the
+  molecular conductivity, and µ_([oo]) its value at infinite dilution,
+  the fractional number of molecules dissociated is µ/µ_([oo]), which
+  we may write as [alpha]. The number of undissociated molecules is then
+  1 - [alpha], so that if V be the volume of the solution containing 1
+  gramme-molecule of the dissolved substance, we get
+
+    q = [alpha]/V and p = (1 - [alpha])/V,
+
+  hence   x(1 - [alpha])V = ya²/V²,
+
+           [alpha]²      x
+  and   -------------- = -- = constant = k.
+        V(1 - [alpha])   y
+
+  This constant k gives a numerical value for the chemical affinity, and
+  the equation should represent the effect of dilution on the molecular
+  conductivity of binary electrolytes.
+
+  In the case of substances like ammonia and acetic acid, where the
+  dissociation is very small, 1 - [alpha] is nearly equal to unity, and
+  only varies slowly with dilution. The equation then becomes [alpha]²/V
+  = k, or [alpha] = [root](Vk), so that the molecular conductivity is
+  proportional to the square root of the dilution. Ostwald has confirmed
+  the equation by observation on an enormous number of weak acids
+  (_Zeits. physikal. Chemie_, 1888, ii. p. 278; 1889, iii. pp. 170, 241,
+  369). Thus in the case of cyanacetic acid, while the volume V changed
+  by doubling from 16 to 1024 litres, the values of k were 0.00 (376,
+  373, 374, 361, 362, 361, 368). The mean values of k for other common
+  acids were--formic, 0.0000214; acetic, 0.0000180; monochloracetic,
+  0.00155; dichloracetic, 0.051; trichloracetic, 1.21; propionic,
+  0.0000134. From these numbers we can, by help of the equation,
+  calculate the conductivity of the acids for any dilution. The value of
+  k, however, does not keep constant so satisfactorily in the case of
+  highly dissociated substances, and empirical formulae have been
+  constructed to represent the effect of dilution on them. Thus the
+  values of the expressions [alpha]²/(1 - [alpha][root]V) (Rudolphi,
+  _Zeits. physikal. Chemie_, 1895, vol. xvii. p. 385) and [alpha]³/(1 -
+  [alpha])²V (van 't Hoff, ibid., 1895, vol. xviii. p. 300) are found to
+  keep constant as V changes. Van 't Hoff's formula is equivalent to
+  taking the frequency of dissociation as proportional to the square of
+  the concentration of the molecules, and the frequency of recombination
+  as proportional to the cube of the concentration of the ions. An
+  explanation of the failure of the usual dilution law in these cases
+  may be given if we remember that, while the electric forces between
+  bodies like undissociated molecules, each associated with equal and
+  opposite charges, will vary inversely as the fourth power of the
+  distance, the forces between dissociated ions, each carrying one
+  charge only, will be inversely proportional to the square of the
+  distance. The forces between the ions of a strongly dissociated
+  solution will thus be considerable at a dilution which makes forces
+  between undissociated molecules quite insensible, and at the
+  concentrations necessary to test Ostwald's formula an electrolyte will
+  be far from dilute in the thermodynamic sense of the term, which
+  implies no appreciable intermolecular or interionic forces.
+
+  When the solutions of two substances are mixed, similar considerations
+  to those given above enable us to calculate the resultant changes in
+  dissociation. (See Arrhenius, loc. cit.) The simplest and most
+  important case is that of two electrolytes having one ion in common,
+  such as two acids. It is evident that the undissociated part of each
+  acid must eventually be in equilibrium with the free hydrogen ions,
+  and, if the concentrations are not such as to secure this condition,
+  readjustment must occur. In order that there should be no change in
+  the states of dissociation on mixing, it is necessary, therefore, that
+  the concentration of the hydrogen ions should be the same in each
+  separate solution. Such solutions were called by Arrhenius
+  "isohydric." The two solutions, then, will so act on each other when
+  mixed that they become isohydric. Let us suppose that we have one very
+  active acid like hydrochloric, in which dissociation is nearly
+  complete, another like acetic, in which it is very small. In order
+  that the solutions of these should be isohydric and the concentrations
+  of the hydrogen ions the same, we must have a very large quantity of
+  the feebly dissociated acetic acid, and a very small quantity of the
+  strongly dissociated hydrochloric, and in such proportions alone will
+  equilibrium be possible. This explains the action of a strong acid on
+  the salt of a weak acid. Let us allow dilute sodium acetate to react
+  with dilute hydrochloric acid. Some acetic acid is formed, and this
+  process will go on till the solutions of the two acids are isohydric:
+  that is, till the dissociated hydrogen ions are in equilibrium with
+  both. In order that this should hold, we have seen that a considerable
+  quantity of acetic acid must be present, so that a corresponding
+  amount of the salt will be decomposed, the quantity being greater the
+  less the acid is dissociated. This "replacement" of a "weak" acid by a
+  "strong" one is a matter of common observation in the chemical
+  laboratory. Similar investigations applied to the general case of
+  chemical equilibrium lead to an expression of exactly the same form as
+  that given by C.M. Guldberg and P. Waage, which is universally
+  accepted as an accurate representation of the facts.
+
+The temperature coefficient of conductivity has approximately the same
+value for most aqueous salt solutions. It decreases both as the
+temperature is raised and as the concentration is increased, ranging
+from about 3.5% per degree for extremely dilute solutions (i.e.
+practically pure water) at 0° to about 1.5 for concentrated solutions
+at 18°. For acids its value is usually rather less than for salts at
+equivalent concentrations. The influence of temperature on the
+conductivity of solutions depends on (1) the ionization, and (2) the
+frictional resistance of the liquid to the passage of the ions, the
+reciprocal of which is called the ionic fluidity. At extreme dilution,
+when the ionization is complete, a variation in temperature cannot
+change its amount. The rise of conductivity with temperature, therefore,
+shows that the fluidity becomes greater when the solution is heated. As
+the concentration is increased and un-ionized molecules are formed, a
+change in temperature begins to affect the ionization as well as the
+fluidity. But the temperature coefficient of conductivity is now
+generally less than before; thus the effect of temperature on ionization
+must be of opposite sign to its effect on fluidity. The ionization of a
+solution, then, is usually diminished by raising the temperature, the
+rise in conductivity being due to the greater increase in fluidity.
+Nevertheless, in certain cases, the temperature coefficient of
+conductivity becomes negative at high temperatures, a solution of
+phosphoric acid, for example, reaching a maximum conductivity at 75° C.
+
+The dissociation theory gives an immediate explanation of the fact that,
+in general, no heat-change occurs when two neutral salt solutions are
+mixed. Since the salts, both before and after mixture, exist mainly as
+dissociated ions, it is obvious that large thermal effects can only
+appear when the state of dissociation of the products is very different
+from that of the reagents. Let us consider the case of the
+neutralization of a base by an acid in the light of the dissociation
+theory. In dilute solution such substances as hydrochloric acid and
+potash are almost completely dissociated, so that, instead of
+representing the reaction as
+
+  HCl + KOH = KCl + H2O,
+
+we must write
+
+  +   -    +   -    +   -
+  H + Cl + K + OH = K + Cl + H2O.
+
+The ions K and Cl suffer no change, but the hydrogen of the acid and the
+hydroxyl (OH) of the potash unite to form water, which is only very
+slightly dissociated. The heat liberated, then, is almost exclusively
+that produced by the formation of water from its ions. An exactly
+similar process occurs when any strongly dissociated acid acts on any
+strongly dissociated base, so that in all such cases the heat evolution
+should be approximately the same. This is fully borne out by the
+experiments of Julius Thomsen, who found that the heat of neutralization
+of one gramme-molecule of a strong base by an equivalent quantity of a
+strong acid was nearly constant, and equal to 13,700 or 13,800 calories.
+In the case of weaker acids, the dissociation of which is less complete,
+divergences from this constant value will occur, for some of the
+molecules have to be separated into their ions. For instance, sulphuric
+acid, which in the fairly strong solutions used by Thomsen is only about
+half dissociated, gives a higher value for the heat of neutralization,
+so that heat must be evolved when it is ionized. The heat of formation
+of a substance from its ions is, of course, very different from that
+evolved when it is formed from its elements in the usual way, since the
+energy associated with an ion is different from that possessed by the
+atoms of the element in their normal state. We can calculate the heat of
+formation from its ions for any substance dissolved in a given liquid,
+from a knowledge of the temperature coefficient of ionization, by means
+of an application of the well-known thermodynamical process, which also
+gives the latent heat of evaporation of a liquid when the temperature
+coefficient of its vapour pressure is known. The heats of formation thus
+obtained may be either positive or negative, and by using them to
+supplement the heat of formation of water, Arrhenius calculated the
+total heats of neutralization of soda by different acids, some of them
+only slightly dissociated, and found values agreeing well with
+observation (_Zeits. physikal. Chemie_, 1889, 4, p. 96; and 1892, 9, p.
+339).
+
+_Voltaic Cells._--When two metallic conductors are placed in an
+electrolyte, a current will flow through a wire connecting them provided
+that a difference of any kind exists between the two conductors in the
+nature either of the metals or of the portions of the electrolyte which
+surround them. A current can be obtained by the combination of two
+metals in the same electrolyte, of two metals in different electrolytes,
+of the same metal in different electrolytes, or of the same metal in
+solutions of the same electrolyte at different concentrations. In
+accordance with the principles of energetics (q.v.), any change which
+involves a decrease in the total available energy of the system will
+tend to occur, and thus the necessary and sufficient condition for the
+production of electromotive force is that the available energy of the
+system should decrease when the current flows.
+
+In order that the current should be maintained, and the electromotive
+force of the cell remain constant during action, it is necessary to
+ensure that the changes in the cell, chemical or other, which produce
+the current, should neither destroy the difference between the
+electrodes, nor coat either electrode with a non-conducting layer
+through which the current cannot pass. As an example of a fairly
+constant cell we may take that of Daniell, which consists of the
+electrical arrangement--zinc | zinc sulphate solution | copper sulphate
+solution | copper,--the two solutions being usually separated by a pot
+of porous earthenware. When the zinc and copper plates are connected
+through a wire, a current flows, the conventionally positive electricity
+passing from copper to zinc in the wire and from zinc to copper in the
+cell. Zinc dissolves at the anode, an equal amount of zinc replaces an
+equivalent amount of copper on the other side of the porous partition,
+and the same amount of copper is deposited on the cathode. This process
+involves a decrease in the available energy of the system, for the
+dissolution of zinc gives out more energy than the separation of copper
+absorbs. But the internal rearrangements which accompany the production
+of a current do not cause any change in the original nature of the
+electrodes, fresh zinc being exposed at the anode, and copper being
+deposited on copper at the cathode. Thus as long as a moderate current
+flows, the only variation in the cell is the appearance of zinc sulphate
+in the liquid on the copper side of the porous wall. In spite of this
+appearance, however, while the supply of copper is maintained, copper,
+being more easily separated from the solution than zinc, is deposited
+alone at the cathode, and the cell remains constant.
+
+It is necessary to observe that the condition for change in a system is
+that the total available energy of the whole system should be decreased
+by the change. We must consider what change is allowed by the mechanism
+of the system, and deal with the sum of all the alterations in energy.
+Thus in the Daniell cell the dissolution of copper as well as of zinc
+would increase the loss in available energy. But when zinc dissolves,
+the zinc ions carry their electric charges with them, and the liquid
+tends to become positively electrified. The electric forces then soon
+stop further action unless an equivalent quantity of positive ions are
+removed from the solution. Hence zinc can only dissolve when some more
+easily separable substance is present in solution to be removed pari
+passu with the dissolution of zinc. The mechanism of such systems is
+well illustrated by an experiment devised by W. Ostwald. Plates of
+platinum and pure or amalgamated zinc are separated by a porous pot, and
+each surrounded by some of the same solution of a salt of a metal more
+oxidizable than zinc, such as potassium. When the plates are connected
+together by means of a wire, no current flows, and no appreciable amount
+of zinc dissolves, for the dissolution of zinc would involve the
+separation of potassium and a gain in available energy. If sulphuric
+acid be added to the vessel containing the zinc, these conditions are
+unaltered and still no zinc is dissolved. But, on the other hand, if a
+few drops of acid be placed in the vessel with the platinum, bubbles of
+hydrogen appear, and a current flows, zinc dissolving at the anode, and
+hydrogen being liberated at the cathode. In order that positively
+electrified ions may enter a solution, an equivalent amount of other
+positive ions must be removed or negative ions be added, and, for the
+process to occur spontaneously, the possible action at the two
+electrodes must involve a decrease in the total available energy of the
+system.
+
+Considered thermodynamically, voltaic cells must be divided into
+reversible and non-reversible systems. If the slow processes of
+diffusion be ignored, the Daniell cell already described may be taken as
+a type of a reversible cell. Let an electromotive force exactly equal to
+that of the cell be applied to it in the reverse direction. When the
+applied electromotive force is diminished by an infinitesimal amount,
+the cell produces a current in the usual direction, and the ordinary
+chemical changes occur. If the external electromotive force exceed that
+of the cell by ever so little, a current flows in the opposite
+direction, and all the former chemical changes are reversed, copper
+dissolving from the copper plate, while zinc is deposited on the zinc
+plate. The cell, together with this balancing electromotive force, is
+thus a reversible system in true equilibrium, and the thermodynamical
+reasoning applicable to such systems can be used to examine its
+properties.
+
+Now a well-known relation connects the available energy of a reversible
+system with the corresponding change in its total internal energy.
+
+  The available energy A is the amount of external work obtainable by an
+  infinitesimal, reversible change in the system which occurs at a
+  constant temperature T. If I be the change in the internal energy, the
+  relation referred to gives us the equation
+
+    A = I + T(dA/dT),
+
+  where dA/dT denotes the rate of change of the available energy of the
+  system per degree change in temperature. During a small electric
+  transfer through the cell, the external work done is Ee, where E is
+  the electromotive force. If the chemical changes which occur in the
+  cell were allowed to take place in a closed vessel without the
+  performance of electrical or other work, the change in energy would be
+  measured by the heat evolved. Since the final state of the system
+  would be the same as in the actual processes of the cell, the same
+  amount of heat must give a measure of the change in internal energy
+  when the cell is in action. Thus, if L denote the heat corresponding
+  with the chemical changes associated with unit electric transfer, Le
+  will be the heat corresponding with an electric transfer e, and will
+  also be equal to the change in internal energy of the cell. Hence we
+  get the equation
+
+    Ee = Le + Te(dE/dT) or E = L + T(dE/dT),
+
+  as a particular case of the general thermodynamic equation of
+  available energy. This equation was obtained in different ways by J.
+  Willard Gibbs and H. von Helmholtz.
+
+  It will be noticed that when dE/dT is zero, that is, when the
+  electromotive force of the cell does not change with temperature, the
+  electromotive force is measured by the heat of reaction per unit of
+  electrochemical change. The earliest formulation of the subject, due
+  to Lord Kelvin, assumed that this relation was true in all cases, and,
+  calculated in this way, the electromotive force of Daniell's cell,
+  which happens to possess a very small temperature coefficient, was
+  found to agree with observation.
+
+  When one gramme of zinc is dissolved in dilute sulphuric acid, 1670
+  thermal units or calories are evolved. Hence for the electrochemical
+  unit of zinc or 0.003388 gramme, the thermal evolution is 5.66
+  calories. Similarly, the heat which accompanies the dissolution of one
+  electrochemical unit of copper is 3.00 calories. Thus, the thermal
+  equivalent of the unit of resultant electrochemical change in
+  Daniell's cell is 5.66 - 3.00 = 2.66 calories. The dynamical
+  equivalent of the calorie is 4.18 × 10^7 ergs or C.G.S. units of work,
+  and therefore the electromotive force of the cell should be 1.112 ×
+  10^8 C.G.S. units or 1.112 volts--a close agreement with the
+  experimental result of about 1.08 volts. For cells in which the
+  electromotive force varies with temperature, the full equation given
+  by Gibbs and Helmholtz has also been confirmed experimentally.
+
+As stated above, an electromotive force is set up whenever there is a
+difference of any kind at two electrodes immersed in electrolytes. In
+ordinary cells the difference is secured by using two dissimilar metals,
+but an electromotive force exists if two plates of the same metal are
+placed in solutions of different substances, or of the same substance at
+different concentrations. In the latter case, the tendency of the metal
+to dissolve in the more dilute solution is greater than its tendency to
+dissolve in the more concentrated solution, and thus there is a decrease
+in available energy when metal dissolves in the dilute solution and
+separates in equivalent quantity from the concentrated solution. An
+electromotive force is therefore set up in this direction, and, if we
+can calculate the change in available energy due to the processes of the
+cell, we can foretell the value of the electromotive force. Now the
+effective change produced by the action of the current is the
+concentration of the more dilute solution by the dissolution of metal in
+it, and the dilution of the originally stronger solution by the
+separation of metal from it. We may imagine these changes reversed in
+two ways. We may evaporate some of the solvent from the solution which
+has become weaker and thus reconcentrate it, condensing the vapour on
+the solution which had become stronger. By this reasoning Helmholtz
+showed how to obtain an expression for the work done. On the other hand,
+we may imagine the processes due to the electrical transfer to be
+reversed by an osmotic operation. Solvent may be supposed to be squeezed
+out from the solution which has become more dilute through a
+semi-permeable wall, and through another such wall allowed to mix with
+the solution which in the electrical operation had become more
+concentrated. Again, we may calculate the osmotic work done, and, if the
+whole cycle of operations be supposed to occur at the same temperature,
+the osmotic work must be equal and opposite to the electrical work of
+the first operation.
+
+  The result of the investigation shows that the electrical work Ee is
+  given by the equation
+          _
+         / p2
+    Ee = |   vdp,
+        _/ p1
+
+  where v is the volume of the solution used and p its osmotic pressure.
+  When the solutions may be taken as effectively dilute, so that the gas
+  laws apply to the osmotic pressure, this relation reduces to
+
+        nrRT               c1
+    E = ---- log_[epsilon] --
+         ey                c2
+
+  where n is the number of ions given by one molecule of the salt, r the
+  transport ratio of the anion, R the gas constant, T the absolute
+  temperature, y the total valency of the anions obtained from one
+  molecule, and c1 and c2 the concentrations of the two solutions.
+
+  If we take as an example a concentration cell in which silver plates
+  are placed in solutions of silver nitrate, one of which is ten times
+  as strong as the other, this equation gives
+
+    E = 0.060 × 10^8 C.G.S. units
+      = 0.060 volts.
+
+W. Nernst, to whom this theory is due, determined the electromotive
+force of this cell experimentally, and found the value 0.055 volt.
+
+The logarithmic formulae for these concentration cells indicate that
+theoretically their electromotive force can be increased to any extent
+by diminishing without limit the concentration of the more dilute
+solution, log c1/c2 then becoming very great. This condition may be
+realized to some extent in a manner that throws light on the general
+theory of the voltaic cell. Let us consider the arrangement--silver |
+silver chloride with potassium chloride solution | potassium nitrate
+solution | silver nitrate solution | silver. Silver chloride is a very
+insoluble substance, and here the amount in solution is still further
+reduced by the presence of excess of chlorine ions of the potassium
+salt. Thus silver, at one end of the cell in contact with many silver
+ions of the silver nitrate solution, at the other end is in contact with
+a liquid in which the concentration of those ions is very small indeed.
+The result is that a high electromotive force is set up, which has been
+calculated as 0.52 volt, and observed as 0.51 volt. Again, Hittorf has
+shown that the effect of a cyanide round a copper electrode is to
+combine with the copper ions. The concentration of the simple copper
+ions is then so much diminished that the copper plate becomes an anode
+with regard to zinc. Thus the cell--copper | potassium cyanide solution
+| potassium sulphate solution--zinc sulphate solution | zinc--gives a
+current which carries copper into solution and deposits zinc. In a
+similar way silver could be made to act as anode with respect to
+cadmium.
+
+It is now evident that the electromotive force of an ordinary chemical
+cell such as that of Daniell depends on the concentration of the
+solutions as well as on the nature of the metals. In ordinary cases
+possible changes in the concentrations only affect the electromotive
+force by a few parts in a hundred, but, by means such as those indicated
+above, it is possible to produce such immense differences in the
+concentrations that the electromotive force of the cell is not only
+changed appreciably but even reversed in direction. Once more we see
+that it is the total impending change in the available energy of the
+system which controls the electromotive force.
+
+Any reversible cell can theoretically be employed as an accumulator,
+though, in practice, conditions of general convenience are more sought
+after than thermodynamic efficiency. The effective electromotive force
+of the common lead accumulator (q.v.) is less than that required to
+charge it. This drop in the electromotive force has led to the belief
+that the cell is not reversible. F. Dolezalek, however, has attributed
+the difference to mechanical hindrances, which prevent the equalization
+of acid concentration in the neighbourhood of the electrodes, rather
+than to any essentially irreversible chemical action. The fact that the
+Gibbs-Helmholtz equation is found to apply also indicates that the lead
+accumulator is approximately reversible in the thermodynamic sense of
+the term.
+
+_Polarization and Contact Difference of Potential._--If we connect
+together in series a single Daniell's cell, a galvanometer, and two
+platinum electrodes dipping into acidulated water, no visible chemical
+decomposition ensues. At first a considerable current is indicated by
+the galvanometer; the deflexion soon diminishes, however, and finally
+becomes very small. If, instead of using a single Daniell's cell, we
+employ some source of electromotive force which can be varied as we
+please, and gradually raise its intensity, we shall find that, when it
+exceeds a certain value, about 1.7 volt, a permanent current of
+considerable strength flows through the solution, and, after the initial
+period, shows no signs of decrease. This current is accompanied by
+chemical decomposition. Now let us disconnect the platinum plates from
+the battery and join them directly with the galvanometer. A current will
+flow for a while in the reverse direction; the system of plates and
+acidulated water through which a current has been passed, acts as an
+accumulator, and will itself yield a current in return. These phenomena
+are explained by the existence of a reverse electromotive force at the
+surface of the platinum plates. Only when the applied electromotive
+force exceeds this reverse force of polarization, will a permanent
+steady current pass through the liquid, and visible chemical
+decomposition proceed. It seems that this reverse electromotive force of
+polarization is due to the deposit on the electrodes of minute
+quantities of the products of chemical decomposition. Differences
+between the two electrodes are thus set up, and, as we have seen above,
+an electromotive force will therefore exist between them. To pass a
+steady current in the direction opposite to this electromotive force of
+polarization, the applied electromotive force E must exceed that of
+polarization E', and the excess E - E' is the effective electromotive
+force of the circuit, the current being, in accordance with Ohm's law,
+proportional to the applied electromotive force and represented by (E -
+E')/R, where R is a constant called the resistance of the circuit.
+
+When we use platinum electrodes in acidulated water, hydrogen and oxygen
+are evolved. The opposing force of polarization is about 1.7 volt, but,
+when the plates are disconnected and used as a source of current, the
+electromotive force they give is only about 1.07 volt. This
+irreversibility is due to the work required to evolve bubbles of gas at
+the surface of bright platinum plates. If the plates be covered with a
+deposit of platinum black, in which the gases are absorbed as fast as
+they are produced, the minimum decomposition point is 1.07 volt, and the
+process is reversible. If secondary effects are eliminated, the
+deposition of metals also is a reversible process; the decomposition
+voltage is equal to the electromotive force which the metal itself gives
+when going into solution. The phenomena of polarization are thus seen to
+be due to the changes of surface produced, and are correlated with the
+differences of potential which exist at any surface of separation
+between a metal and an electrolyte.
+
+Many experiments have been made with a view of separating the two
+potential-differences which must exist in any cell made of two metals
+and a liquid, and of determining each one individually. If we regard the
+thermal effect at each junction as a measure of the potential-difference
+there, as the total thermal effect in the cell undoubtedly is of the sum
+of its potential-differences, in cases where the temperature coefficient
+is negligible, the heat evolved on solution of a metal should give the
+electrical potential-difference at its surface. Hence, if we assume
+that, in the Daniell's cell, the temperature coefficients are negligible
+at the individual contacts as well as in the cell as a whole, the sign
+of the potential-difference ought to be the same at the surface of the
+zinc as it is at the surface of the copper. Since zinc goes into
+solution and copper comes out, the electromotive force of the cell will
+be the difference between the two effects. On the other hand, it is
+commonly thought that the single potential-differences at the surface of
+metals and electrolytes have been determined by methods based on the use
+of the capillary electrometer and on others depending on what is called
+a dropping electrode, that is, mercury dropping rapidly into an
+electrolyte and forming a cell with the mercury at rest in the bottom of
+the vessel. By both these methods the single potential-differences found
+at the surfaces of the zinc and copper have opposite signs, and the
+effective electromotive force of a Daniell's cell is the sum of the two
+effects. Which of these conflicting views represents the truth still
+remains uncertain.
+
+_Diffusion of Electrolytes and Contact Difference of Potential between
+Liquids._--An application of the theory of ionic velocity due to W.
+Nernst[7] and M. Planck[8] enables us to calculate the diffusion
+constant of dissolved electrolytes. According to the molecular theory,
+diffusion is due to the motion of the molecules of the dissolved
+substance through the liquid. When the dissolved molecules are uniformly
+distributed, the osmotic pressure will be the same everywhere throughout
+the solution, but, if the concentration vary from point to point, the
+pressure will vary also. There must, then, be a relation between the
+rate of change of the concentration and the osmotic pressure gradient,
+and thus we may consider the osmotic pressure gradient as a force
+driving the solute through a viscous medium. In the case of
+non-electrolytes and of all non-ionized molecules this analogy
+completely represents the facts, and the phenomena of diffusion can be
+deduced from it alone. But the ions of an electrolytic solution can move
+independently through the liquid, even when no current flows, as the
+consequences of Ohm's law indicate. The ions will therefore diffuse
+independently, and the faster ion will travel quicker into pure water in
+contact with a solution. The ions carry their charges with them, and, as
+a matter of fact, it is found that water in contact with a solution
+takes with respect to it a positive or negative potential, according as
+the positive or negative ion travels the faster. This process will go on
+until the simultaneous separation of electric charges produces an
+electrostatic force strong enough to prevent further separation of ions.
+We can therefore calculate the rate at which the salt as a whole will
+diffuse by examining the conditions for a steady transfer, in which the
+ions diffuse at an equal rate, the faster one being restrained and the
+slower one urged forward by the electric forces. In this manner the
+diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3
+= 2.27, NaCl = 1.12), the unit of time being the day. By experiments on
+diffusion this constant has been found by Scheffer, and the numbers
+observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl =
+1.11).
+
+As we have seen above, when a solution is placed in contact with water
+the water will take a positive or negative potential with regard to the
+solution, according as the cation or anion has the greater specific
+velocity, and therefore the greater initial rate of diffusion. The
+difference of potential between two solutions of a substance at
+different concentrations can be calculated from the equations used to
+give the diffusion constants. The results give equations of the same
+logarithmic form as those obtained in a somewhat different manner in the
+theory of concentration cells described above, and have been verified by
+experiment.
+
+The contact differences of potential at the interfaces of metals and
+electrolytes have been co-ordinated by Nernst with those at the surfaces
+of separation between different liquids. In contact with a solvent a
+metal is supposed to possess a definite solution pressure, analogous to
+the vapour pressure of a liquid. Metal goes into solution in the form of
+electrified ions. The liquid thus acquires a positive charge, and the
+metal a negative charge. The electric forces set up tend to prevent
+further separation, and finally a state of equilibrium is reached, when
+no more ions can go into solution unless an equivalent number are
+removed by voltaic action. On the analogy between this case and that of
+the interface between two solutions, Nernst has arrived at similar
+logarithmic expressions for the difference of potential, which becomes
+proportional to log (P1/P2) where P2 is taken to mean the osmotic
+pressure of the cations in the solution, and P1 the osmotic pressure of
+the cations in the substance of the metal itself. On these lines the
+equations of concentration cells, deduced above on less hypothetical
+grounds, may be regained.
+
+_Theory of Electrons._--Our views of the nature of the ions of
+electrolytes have been extended by the application of the ideas of the
+relations between matter and electricity obtained by the study of
+electric conduction through gases. The interpretation of the phenomena
+of gaseous conduction was rendered possible by the knowledge previously
+acquired of conduction through liquids; the newer subject is now
+reaching a position whence it can repay its debt to the older.
+
+Sir J.J. Thomson has shown (see CONDUCTION, ELECTRIC, § III.) that the
+negative ions in certain cases of gaseous conduction are much more
+mobile than the corresponding positive ions, and possess a mass of about
+the one-thousandth part of that of a hydrogen atom. These negative
+particles or corpuscles seem to be the ultimate units of negative
+electricity, and may be identified with the electrons required by the
+theories of H.A. Lorentz and Sir J. Larmor. A body containing an excess
+of these particles is negatively electrified, and is positively
+electrified if it has parted with some of its normal number. An electric
+current consists of a moving stream of electrons. In gases the electrons
+sometimes travel alone, but in liquids they are always attached to
+matter, and their motion involves the movement of chemical atoms or
+groups of atoms. An atom with an extra corpuscle is a univalent negative
+ion, an atom with one corpuscle detached is a univalent positive ion. In
+metals the electrons can slip from one atom to the next, since a current
+can pass without chemical action. When a current passes from an
+electrolyte to a metal, the electron must be detached from the atom it
+was accompanying and chemical action be manifested at the electrode.
+
+  BIBLIOGRAPHY.--Michael Faraday, _Experimental Researches in
+  Electricity_ (London, 1844 and 1855); W. Ostwald, _Lehrbuch der
+  allgemeinen Chemie_, 2te Aufl. (Leipzig, 1891); _Elektrochemie_
+  (Leipzig, 1896); W Nernst, _Theoretische Chemie_, 3te Aufl.
+  (Stuttgart, 1900; English translation, London, 1904); F. Kohlrausch
+  and L. Holborn, _Das Leitvermögen der Elektrolyte_ (Leipzig, 1898);
+  W.C.D. Whetham, _The Theory of Solution and Electrolysis_ (Cambridge,
+  1902); M. Le Blanc, _Elements of Electrochemistry_ (Eng. trans.,
+  London, 1896); S. Arrhenius, _Text-Book of Electrochemistry_ (Eng.
+  trans., London, 1902); H.C. Jones, _The Theory of Electrolytic
+  Dissociation_ (New York, 1900); N. Munroe Hopkins, _Experimental
+  Electrochemistry_ (London, 1905); Lüphe, _Grundzüge der Elektrochemie_
+  (Berlin, 1896).
+
+  Some of the more important papers on the subject have been reprinted
+  for Harper's _Series of Scientific Memoirs in Electrolytic Conduction_
+  (1899) and the _Modern Theory of Solution_ (1899). Several journals
+  are published specially to deal with physical chemistry, of which
+  electrochemistry forms an important part. Among them may be mentioned
+  the _Zeitschrift für physikalische Chemie_ (Leipzig); and the _Journal
+  of Physical Chemistry_ (Cornell University). In these periodicals will
+  be found new work on the subject and abstracts of papers which appear
+  in other physical and chemical publications.     (W. C. D. W.)
+
+
+FOOTNOTES:
+
+  [1] See Hittorf, _Pogg. Ann._ cvi. 517 (1859).
+
+  [2] _Grundriss der Elektrochemie_ (1895), p. 292; see also F. Kaufler
+    and C. Herzog, _Ber._, 1909, 42, p. 3858.
+
+  [3] _Brit. Ass. Rep._, 1906, Section A, Presidential Address.
+
+  [4] See _Theory of Solution_, by W.C.D. Whetham (1902), p. 328.
+
+  [5] W. Ostwald, _Zeits. physikal. Chemie_, 1892, vol. IX. p. 579; T.
+    Ewan, _Phil. Mag._ (5), 1892, vol. xxxiii. p. 317; G.D. Liveing,
+    _Cambridge Phil. Trans._, 1900, vol. xviii. p. 298.
+
+  [6] See W.B. Hardy, _Journal of Physiology_, 1899, vol. xxiv. p. 288;
+    and W.C.D. Whetham, _Phil. Mag._, November 1899.
+
+  [7] _Zeits. physikal. Chem._ 2, p. 613.
+
+  [8] _Wied. Ann._, 1890, 40, p. 561.
+
+
+
+
+ELECTROMAGNETISM, that branch of physical science which is concerned
+with the interconnexion of electricity and magnetism, and with the
+production of magnetism by means of electric currents by devices called
+electromagnets.
+
+_History._--The foundation was laid by the observation first made by
+Hans Christian Oersted (1777-1851), professor of natural philosophy in
+Copenhagen, who discovered in 1820 that a wire uniting the poles or
+terminal plates of a voltaic pile has the property of affecting a
+magnetic needle[1] (see ELECTRICITY). Oersted carefully ascertained
+that the nature of the wire itself did not influence the result but saw
+that it was due to the electric conflict, as he called it, round the
+wire; or in modern language, to the magnetic force or magnetic flux
+round the conductor. If a straight wire through which an electric
+current is flowing is placed above and parallel to a magnetic compass
+needle, it is found that if the current is flowing in the conductor in a
+direction from south to north, the north pole of the needle under the
+conductor deviates to the left hand, whereas if the conductor is placed
+under the needle, the north pole deviates to the right hand; if the
+conductor is doubled back over the needle, the effects of the two sides
+of the loop are added together and the deflection is increased. These
+results are summed up in the mnemonic rule: _Imagine yourself swimming
+in the conductor with the current, that is, moving in the direction of
+the positive electricity, with your face towards the magnetic needle;
+the north pole will then deviate to your left hand._ The deflection of
+the magnetic needle can therefore reveal the existence of an electric
+current in a neighbouring circuit, and this fact was soon utilized in
+the construction of instruments called galvanometers (q.v.).
+
+Immediately after Oersted's discovery was announced, D.F.J. Arago and
+A.M. Ampère began investigations on the subject of electromagnetism. On
+the 18th of September 1820, Ampère read a paper before the Academy of
+Sciences in Paris, in which he announced that the voltaic pile itself
+affected a magnetic needle as did the uniting wire, and he showed that
+the effects in both cases were consistent with the theory that electric
+current was a circulation round a circuit, and equivalent in magnetic
+effect to a very short magnet with axis placed at right angles to the
+plane of the circuit. He then propounded his brilliant hypothesis that
+the magnetization of iron was due to molecular electric currents. This
+suggested to Arago that wire wound into a helix carrying electric
+current should magnetize a steel needle placed in the interior. In the
+_Ann. Chim._ (1820, 15, p. 94), Arago published a paper entitled
+"Expériences relatives à l'aimantation du fer et de l'acier par l'action
+du courant voltaïque," announcing that the wire conveying the current,
+even though of copper, could magnetize steel needles placed across it,
+and if plunged into iron filings it attracted them. About the same time
+Sir Humphry Davy sent a communication to Dr W.H. Wollaston, read at the
+Royal Society on the 16th of November 1820 (reproduced in the _Annals of
+Philosophy_ for August 1821, p. 81), "On the Magnetic Phenomena produced
+by Electricity," in which he announced his independent discovery of the
+same fact. With a large battery of 100 pairs of plates at the Royal
+Institution, he found in October 1820 that the uniting wire became
+strongly magnetic and that iron filings clung to it; also that steel
+needles placed across the wire were permanently magnetized. He placed a
+sheet of glass over the wire and sprinkling iron filings on it saw that
+they arranged themselves in straight lines at right angles to the wire.
+He then proved that Leyden jar discharges could produce the same
+effects. Ampère and Arago then seem to have experimented together and
+magnetized a steel needle wrapped in paper which was enclosed in a
+helical wire conveying a current. All these facts were rendered
+intelligible when it was seen that a wire when conveying an electric
+current becomes surrounded by a magnetic field. If the wire is a long
+straight one, the lines of magnetic force are circular and concentric
+with centres on the wire axis, and if the wire is bent into a circle the
+lines of magnetic force are endless loops surrounding and linked with
+the electric circuit. Since a magnetic pole tends to move along a line
+of magnetic force it was obvious that it should revolve round a wire
+conveying a current. To exhibit this fact involved, however, much
+ingenuity. It was first accomplished by Faraday in October 1821 (_Exper.
+Res._ ii. p. 127). Since the action is reciprocal a current free to move
+tends to revolve round a magnetic pole. The fact is most easily shown by
+a small piece of apparatus made as follows: In a glass cylinder (see
+fig. 1) like a lamp chimney are fitted two corks. Through the bottom one
+is passed the north end of a bar magnet which projects up above a little
+mercury lying in the cork. Through the top cork is passed one end of a
+wire from a battery, and a piece of wire in the cylinder is flexibly
+connected to it, the lower end of this last piece just touching the
+mercury. When a current is passed in at the top wire and out at the
+lower end of the bar magnet, the loose wire revolves round the magnet
+pole. All text-books on physics contain in their chapters on
+electromagnetism full accounts of various forms of this experiment.
+
+[Illustration: FIG. 1.]
+
+In 1825 another important step forward was taken when William Sturgeon
+(1783-1850) of London produced the electromagnet. It consisted of a
+horseshoe-shaped bar of soft iron, coated with varnish, on which was
+wrapped a spiral coil of bare copper wire, the turns not touching each
+other. When a voltaic current was passed through the wire the iron
+became a powerful magnet, but on severing the connexion with the
+battery, the soft iron lost immediately nearly all its magnetism.[2]
+
+At that date Ohm had not announced his law of the electric circuit, and
+it was a matter of some surprise to investigators to find that
+Sturgeon's electromagnet could not be operated at a distance through a
+long circuit of wire with such good results as when close to the
+battery. Peter Barlow, in January 1825, published in the _Edinburgh
+Philosophical Journal_, a description of such an experiment made with a
+view of applying Sturgeon's electromagnet to telegraphy, with results
+which were unfavourable. Sturgeon's experiments, however, stimulated
+Joseph Henry (q.v.) in the United States, and in 1831 he gave a
+description of a method of winding electromagnets which at once put a
+new face upon matters (_Silliman's Journal_, 1831, 19, p. 400). Instead
+of insulating the iron core, he wrapped the copper wire round with silk
+and wound in numerous turns and many layers upon the iron horseshoe in
+such fashion that the current went round the iron always in the same
+direction. He then found that such an electromagnet wound with a long
+fine wire, if worked with a battery consisting of a large number of
+cells in series, could be operated at a considerable distance, and he
+thus produced what were called at that time _intensity electromagnets_,
+and which subsequently rendered the electric telegraph a possibility. In
+fact, Henry established in 1831, in Albany, U.S.A., an electromagnetic
+telegraph, and in 1835 at Princeton even used an earth return, thereby
+anticipating the discovery (1838) of C.A. Steinheil (1801-1870) of
+Munich.
+
+[Illustration: FIG. 2.]
+
+Inventors were then incited to construct powerful electromagnets as
+tested by the weight they could carry from their armatures. Joseph Henry
+made a magnet for Yale College, U.S.A., which lifted 3000 lb.
+(_Silliman's Journal_, 1831, 20, p. 201), and one for Princeton which
+lifted 3000 with a very small battery. Amongst others J.P. Joule, ever
+memorable for his investigations on the mechanical equivalent of heat,
+gave much attention about 1838-1840 to the construction of
+electromagnets and succeeded in devising some forms remarkable for their
+lifting power. One form was constructed by cutting a thick soft iron
+tube longitudinally into two equal parts. Insulated copper wire was then
+wound longitudinally over one of both parts (see fig. 2) and a current
+sent through the wire. In another form two iron disks with teeth at
+right angles to the disk had insulated wire wound zigzag between the
+teeth; when a current was sent through the wire, the teeth were so
+magnetized that they were alternately N. and S. poles. If two such
+similar disks were placed with teeth of opposite polarity in contact, a
+very large force was required to detach them, and with a magnet and
+armature weighing in all 11.575 lb. Joule found that a weight of 2718
+was supported. Joule's papers on this subject will be found in his
+_Collected Papers_ published by the Physical Society of London, and in
+_Sturgeon's Annals of Electricity_, 1838-1841, vols. 2-6.
+
+  _The Magnetic Circuit._--The phenomena presented by the electromagnet
+  are interpreted by the aid of the notion of the magnetic circuit. Let
+  us consider a thin circular sectioned ring of iron wire wound over
+  with a solenoid or spiral of insulated copper wire through which a
+  current of electricity can be passed. If the solenoid or wire windings
+  existed alone, a current having a strength A amperes passed through it
+  would create in the interior of the solenoid a magnetic force H,
+  numerically equal to 4[pi]/10 multiplied by the number of windings N
+  on the solenoid, and by the current in amperes A, and divided by the
+  mean length of the solenoid l, or H = 4[pi]AN/10l. The product AN is
+  called the "ampere-turns" on the solenoid. The product Hl of the
+  magnetic force H and the length l of the magnetic circuit is called
+  the "magnetomotive force" in the magnetic circuit, and from the above
+  formula it is seen that the magnetomotive force denoted by (M.M.F.) is
+  equal to 4[pi]/10 (= 1.25 nearly) times the ampere-turns (A.N.) on the
+  exciting coil or solenoid. Otherwise (A.N.) = 0.8(M.M.F.). The
+  magnetomotive force is regarded as creating an effect called magnetic
+  flux (Z) in the magnetic circuit, just as electromotive force E.M.F.
+  produces electric current (A) in the electric circuit, and as by Ohm's
+  law (see ELECTROKINETICS) the current varies as the E.M.F. and
+  inversely as a quality of the electric circuit called its
+  "resistance," so in the magnetic circuit the magnetic flux varies as
+  the magnetomotive force and inversely as a quality of the magnetic
+  circuit called its "reluctance." The great difference between the
+  electric circuit and the magnetic circuit lies in the fact that
+  whereas the electric resistance of a solid or liquid conductor is
+  independent of the current and affected only by the temperature, the
+  magnetic reluctance varies with the magnetic flux and cannot be
+  defined except by means of a curve which shows its value for different
+  flux densities. The quotient of the total magnetic flux, Z, in a
+  circuit by the cross section, S, of the circuit is called the mean
+  "flux density," and the reluctance of a magnetic circuit one
+  centimetre long and one square centimetre in cross section is called
+  the "reluctivity" of the material. The relation between reluctivity
+  [rho] = 1/µ magnetic force H, and flux density B, is defined by the
+  equation H = [rho]B, from which we have Hl = Z([rho]l/S) = M.M.F.
+  acting on the circuit. Again, since the ampere-turns (AN) on the
+  circuit are equal to 0.8 times the M.M.F., we have finally AN/l =
+  0.8(Z/µS). This equation tells us the exciting force reckoned in
+  ampere-turns, AN, which must be put on the ring core to create a total
+  magnetic flux Z in it, the ring core having a mean perimeter l and
+  cross section S and reluctivity [rho] = 1/µ corresponding to a flux
+  density Z/S. Hence before we can make use of the equation for
+  practical purposes we need to possess a curve for the particular
+  material showing us the value of the reluctivity corresponding to
+  various values of the possible flux density. The reciprocal of [rho]
+  is usually called the "permeability" of the material and denoted by µ.
+  Curves showing the relation of 1/[rho] and ZS or µ and B, are called
+  "permeability curves." For air and all other non-magnetic matter the
+  permeability has the same value, taken arbitrarily as unity. On the
+  other hand, for iron, nickel and cobalt the permeability may in some
+  cases reach a value of 2000 or 2500 for a value of B = 5000 in C.G.S.
+  measure (see UNITS, PHYSICAL). The process of taking these curves
+  consists in sending a current of known strength through a solenoid of
+  known number of turns wound on a circular iron ring of known
+  dimensions, and observing the time-integral of the secondary current
+  produced in a secondary circuit of known turns and resistance R wound
+  over the iron core N times. The secondary electromotive force is by
+  Faraday's law (see ELECTROKINETICS) equal to the time rate of change
+  of the total flux, or E = NdZ/dt. But by Ohm's law E = Rdq/dt, where q
+  is the quantity of electricity set flowing in the secondary circuit by
+  a change dZ in the co-linked total flux. Hence if 2Q represents this
+  total quantity of electricity set flowing in the secondary circuit by
+  suddenly reversing the direction of the magnetic flux Z in the iron
+  core we must have
+
+    RQ = NZ or Z = RQ/N.
+
+  The measurement of the total quantity of electricity Q can be made by
+  means of a ballistic galvanometer (q.v.), and the resistance R of the
+  secondary circuit includes that of the coil wound on the iron core and
+  the galvanometer as well. In this manner the value of the total flux Z
+  and therefore of Z/S = B or the flux density, can be found for a given
+  magnetizing force H, and this last quantity is determined when we know
+  the magnetizing current in the solenoid and its turns and dimensions.
+  The curve which delineates the relation of H and B is called the
+  magnetization curve for the material in question. For examples of
+  these curves see MAGNETISM.
+
+  The fundamental law of the non-homogeneous magnetic circuit traversed
+  by one and the same total magnetic flux Z is that the sum of all the
+  magnetomotive forces acting in the circuit is numerically equal to the
+  product of the factor 0.8, the total flux in the circuit, and the sum
+  of all the reluctances of the various parts of the circuit. If then
+  the circuit consists of materials of different permeability and it is
+  desired to know the ampere-turns required to produce a given total of
+  flux round the circuit, we have to calculate from the magnetization
+  curves of the material of each part the necessary magnetomotive forces
+  and add these forces together. The practical application of this
+  principle to the predetermination of the field windings of dynamo
+  magnets was first made by Drs J. and E. Hopkinson (_Phil. Trans._,
+  1886, 177, p. 331).
+
+  We may illustrate the principles of this predetermination by a simple
+  example. Suppose a ring of iron has a mean diameter of 10 cms. and a
+  cross section of 2 sq. cms., and a transverse cut on air gap made in
+  it 1 mm. wide. Let us inquire the ampere-turns to be put upon the ring
+  to create in it a total flux of 24,000 C.G.S. units. The total length
+  of the iron part of the circuit is (10[pi] - 0.1) cms., and its
+  section is 2 sq. cms., and the flux density in it is to be 12,000.
+  From Table II. below we see that the permeability of pure iron
+  corresponding to a flux density of 12,000 is 2760. Hence the
+  reluctance of the iron circuits is equal to
+
+    10[pi] - 0.1    220
+    ------------ = ----- C.G.S. units.
+      2760 × 2     38640
+
+  The length of the air gap is 0.1 cm., its section 2 sq. cms., and its
+  permeability is unity. Hence the reluctance of the air gap is
+
+     0.1     1
+    ----- = -- C.G.S. unit.
+    1 × 2   20
+
+  Accordingly the magnetomotive force in ampere-turns required to
+  produce the required flux is equal to
+
+                 / 1    220 \
+    0.8(24,000) ( -- + ----- ) = 1070 nearly.
+                 \20   38640/
+
+  It follows that the part of the magnetomotive force required to
+  overcome the reluctance of the narrow air gap is about nine times that
+  required for the iron alone.
+
+  In the above example we have for simplicity assumed that the flux in
+  passing across the air gap does not spread out at all. In dealing with
+  electromagnet design in dynamo construction we have, however, to take
+  into consideration the spreading as well as the leakage of flux across
+  the circuit (see DYNAMO). It will be seen, therefore, that in order
+  that we may predict the effect of a certain kind of iron or steel when
+  used as the core of an electromagnet, we must be provided with tables
+  or curves showing the reluctivity or permeability corresponding to
+  various flux densities or--which comes to the same thing--with (B, H)
+  curves for the sample.
+
+_Iron and Steel for Electromagnetic Machinery._--In connexion with the
+technical application of electromagnets such as those used in the field
+magnets of dynamos (q.v.), the testing of different kinds of iron and
+steel for magnetic permeability has therefore become very important.
+Various instruments called permeameters and hysteresis meters have been
+designed for this purpose, but much of the work has been done by means
+of a ballistic galvanometer and test ring as above described. The
+"hysteresis" of an iron or steel is that quality of it in virtue of
+which energy is dissipated as heat when the magnetization is reversed or
+carried through a cycle (see MAGNETISM), and it is generally measured
+either in ergs per cubic centimetre of metal per cycle of magnetization,
+or in watts per lb. per 50 or 100 cycles per second at or corresponding
+to a certain maximum flux density, say 2500 or 600 C.G.S. units. For the
+details of various forms of permeameter and hysteresis meter technical
+books must be consulted.[3]
+
+An immense number of observations have been carried out on the magnetic
+permeability of different kinds of iron and steel, and in the following
+tables are given some typical results, mostly from experiments made by
+J.A. Ewing (see _Proc. Inst. C.E._, 1896, 126, p. 185) in which the
+ballistic method was employed to determine the flux density
+corresponding to various magnetizing forces acting upon samples of iron
+and steel in the form of rings.
+
+  The figures under heading I. are values given in a paper by A.W.S.
+  Pocklington and F. Lydall (_Proc. Roy. Soc_., 1892-1893, 52, pp. 164
+  and 228) as the results of a magnetic test of an exceptionally pure
+  iron supplied for the purpose of experiment by Colonel Dyer, of the
+  Elswick Works. The substances other than iron in this sample were
+  stated to be: carbon, _trace_; silicon, _trace_; phosphorus, _none_;
+  sulphur, 0.013%; manganese, 0.1%. The other five specimens, II. to
+  VI., are samples of commercial iron or steel. No. II. is a sample of
+  Low Moor bar iron forged into a ring, annealed and turned. No. III. is
+  a steel forging furnished by Mr R. Jenkins as a sample of forged
+  ingot-metal for dynamo magnets. No. IV. is a steel casting for dynamo
+  magnets, unforged, made by Messrs Edgar Allen & Company by a special
+  pneumatic process under the patents of Mr A. Tropenas. No. V. is also
+  an unforged steel casting for dynamo magnets, made by Messrs Samuel
+  Osborne & Company by the Siemens process. No. VI. is also an unforged
+  steel casting for dynamo magnets, made by Messrs Fried. Krupp, of
+  Essen.
+
+    TABLE I.--_Magnetic Flux Density corresponding to various Magnetizing
+    Forces in the case of certain Samples of Iron and Steel_ (_Ewing_).
+
+    +------------+-----------------------------------------------------+
+    |Magnetizing |                                                     |
+    |   Force    |                                                     |
+    |  H (C.G.S. |       Magnetic Flux Density B (C.G.S. Units).       |
+    |   Units).  |                                                     |
+    +------------+--------+--------+--------+--------+--------+--------+
+    |            |   I.   |   II.  |  III.  |   IV.  |   V.   |   VI.  |
+    +------------+--------+--------+--------+--------+--------+--------+
+    |      5     | 12,700 | 10,900 | 12,300 |  4,700 |  9,600 | 10,900 |
+    |     10     | 14,980 | 13,120 | 14,920 | 12,250 | 13,050 | 13,320 |
+    |     15     | 15,800 | 14,010 | 15,800 | 14,000 | 14,600 | 14,350 |
+    |     20     | 16,300 | 14,580 | 16,280 | 15,050 | 15,310 | 14,950 |
+    |     30     | 16,950 | 15,280 | 16,810 | 16,200 | 16,000 | 15,660 |
+    |     40     | 17,350 | 15,760 | 17,190 | 16,800 | 16,510 | 16,150 |
+    |     50     |   ..   | 16,060 | 17,500 | 17,140 | 16,900 | 16,480 |
+    |     60     |   ..   | 16,340 | 17,750 | 17,450 | 17,180 | 16,780 |
+    |     70     |   ..   | 16,580 | 17,970 | 17,750 | 17,400 | 17,000 |
+    |     80     |   ..   | 16,800 | 18,180 | 18,040 | 17,620 | 17,200 |
+    |     90     |   ..   | 17,000 | 18,390 | 18,230 | 17,830 | 17,400 |
+    |    100     |   ..   | 17,200 | 18,600 | 18,420 | 18,030 | 17,600 |
+    +------------+--------+--------+--------+--------+--------+--------+
+
+  It will be seen from the figures and the description of the materials
+  that the steel forgings and castings have a remarkably high
+  permeability under small magnetizing force.
+
+Table II. shows the magnetic qualities of some of these materials as
+found by Ewing when tested with small magnetizing forces.
+
+  TABLE II.--_Magnetic Permeability of Samples of Iron and Steel under
+  Weak Magnetizing Forces._
+
+  +-----------------+-------------+----------------+---------------+
+  |  Magnetic Flux  |      I.     |      III.      |       VI.     |
+  |    Density B    |  Pure Iron. | Steel Forging. | Steel Casting.|
+  | (C.G.S. Units). |             |                |               |
+  +-----------------+-------------+----------------+---------------+
+  |                 |  H      µ   |   H       µ    |  H       µ    |
+  |      2,000      | 0.90   2220 |  1.38    1450  | 1.18    1690  |
+  |      4,000      | 1.40   2850 |  1.91    2090  | 1.66    2410  |
+  |      6,000      | 1.85   3240 |  2.38    2520  | 2.15    2790  |
+  |      8,000      | 2.30   3480 |  2.92    2740  | 2.83    2830  |
+  |     10,000      | 3.10   3220 |  3.62    2760  | 4.05    2470  |
+  |     12,000      | 4.40   2760 |  4.80    2500  | 6.65    1810  |
+  +-----------------+-------------+----------------+---------------+
+
+The numbers I., III. and VI. in the above table refer to the samples
+mentioned in connexion with Table I.
+
+It is a remarkable fact that certain varieties of low carbon steel
+(commonly called mild steel) have a higher permeability than even
+annealed Swedish wrought iron under large magnetizing forces. The term
+_steel_, however, here used has reference rather to the mode of
+production than the final chemical nature of the material. In some of
+the mild-steel castings used for dynamo electromagnets it appears that
+the total foreign matter, including carbon, manganese and silicon, is
+not more than 0.3% of the whole, the material being 99.7% pure iron.
+This valuable magnetic property of steel capable of being cast is,
+however, of great utility in modern dynamo building, as it enables field
+magnets of very high permeability to be constructed, which can be
+fashioned into shape by casting instead of being built up as formerly
+out of masses of forged wrought iron. The curves in fig. 3 illustrate
+the manner in which the flux density or, as it is usually called, the
+magnetization curve of this mild cast steel crosses that of Swedish
+wrought iron, and enables us to obtain a higher flux density
+corresponding to a given magnetizing force with the steel than with the
+iron.
+
+From the same paper by Ewing we extract a number of results relating to
+permeability tests of thin sheet iron and sheet steel, such as is used
+in the construction of dynamo armatures and transformer cores.
+
+  No. VII. is a specimen of good transformer-plate, 0.301 millimetre
+  thick, rolled from Swedish iron by Messrs Sankey of Bilston. No. VIII.
+  is a specimen of specially thin transformer-plate rolled from scrap
+  iron. No. IX. is a specimen of transformer-plate rolled from
+  ingot-steel. No. X. is a specimen of the wire which was used by J.
+  Swinburne to form the core of his "hedgehog" transformers. Its
+  diameter was 0.602 millimetre. All these samples were tested in the
+  form of rings by the ballistic method, the rings of sheet-metal being
+  stamped or turned in the flat. The wire ring No. X. was coiled and
+  annealed after coiling.
+
+  [Illustration: FIG. 3.]
+
+    TABLE III.--_Permeability Tests of Transformer Plate and Wire_.
+
+    +---------+--------------+--------------+--------------+--------------+
+    |Magnetic |     VII.     |     VIII.    |      IX.     |      X.      |
+    |  Flux   | Transformer- | Transformer- | Transformer- | Transformer- |
+    |Density B|   plate of   |   plate of   |   plate of   |     wire.    |
+    | (C.G.S. | Swedish Iron.|  Scrap Iron. |   of Steel.  |              |
+    | Units). |              |              |              |              |
+    +---------+--------------+--------------+--------------+--------------+
+    |         |   H      µ   |   H      µ   |   H      µ   |   H      µ   |
+    |  1,000  |  0.81   1230 |  1.08    920 |  0.60   1470 |  1.71    590 |
+    |  2,000  |  1.05   1900 |  1.46   1370 |  0.90   2230 |  2.10    950 |
+    |  3,000  |  1.26   2320 |  1.77   1690 |  1.04   2880 |  2.30   1300 |
+    |  4,000  |  1.54   2600 |  2.10   1900 |  1.19   3360 |  2.50   1600 |
+    |  5,000  |  1.82   2750 |  2.53   1980 |  1.38   3620 |  2.70   1850 |
+    |  6,000  |  2.14   2800 |  3.04   1970 |  1.59   3770 |  2.92   2070 |
+    |  7,000  |  2.54   2760 |  3.62   1930 |  1.89   3700 |  3.16   2210 |
+    |  8,000  |  3.09   2590 |  4.37   1830 |  2.25   3600 |  3.43   2330 |
+    |  9,000  |  3.77   2390 |  5.3    1700 |  2.72   3310 |  3.77   2390 |
+    | 10,000  |  4.6    2170 |  6.5    1540 |  3.33   3000 |  4.17   2400 |
+    | 11,000  |  5.7    1930 |  7.9    1390 |  4.15   2650 |  4.70   2340 |
+    | 12,000  |  7.0    1710 |  9.8    1220 |  5.40   2220 |  5.45   2200 |
+    | 13,000  |  8.5    1530 | 11.9    1190 |  7.1    1830 |  6.5    2000 |
+    | 14,000  | 11.0    1270 | 15.0     930 | 10.0    1400 |  8.4    1670 |
+    | 15,000  | 15.1     990 | 19.5     770 |   ..     ..  | 11.9    1260 |
+    | 16,000  | 21.4     750 | 27.5     580 |   ..     ..  | 21.0     760 |
+    +---------+--------------+--------------+--------------+--------------+
+
+Some typical flux-density curves of iron and steel as used in dynamo and
+transformer building are given in fig. 4.
+
+[Illustration: FIG. 4.]
+
+The numbers in Table III. well illustrate the fact that the
+permeability, µ = B/H has a maximum value corresponding to a certain
+flux density. The tables are also explanatory of the fact that mild
+steel has gradually replaced iron in the manufacture of dynamo
+electromagnets and transformer-cores.
+
+Broadly speaking, the materials which are now employed in the
+manufacture of the cores of electromagnets for technical purposes of
+various kinds may be said to fall into three classes, namely, forgings,
+castings and stampings. In some cases the iron or steel core which is to
+be magnetized is simply a mass of iron hammered or pressed into shape by
+hydraulic pressure; in other cases it has to be fused and cast; and for
+certain other purposes it must be rolled first into thin sheets, which
+are subsequently stamped out into the required forms.
+
+[Illustration: FIG. 5.]
+
+For particular purposes it is necessary to obtain the highest possible
+magnetic permeability corresponding to a high, or the highest attainable
+flux density. This is generally the case in the electromagnets which are
+employed as the field magnets in dynamo machines. It may generally be
+said that whilst the best wrought iron, such as annealed Low Moor or
+Swedish iron, is more permeable for low flux densities than steel
+castings, the cast steel may surpass the wrought metal for high flux
+density. For most electro-technical purposes the best magnetic results
+are given by the employment of forged ingot-iron. This material is
+probably the most permeable throughout the whole scale of attainable
+flux densities. It is slightly superior to wrought iron, and it only
+becomes inferior to the highest class of cast steel when the flux
+density is pressed above 18,000 C.G.S. units (see fig. 5). For flux
+densities above 13,000 the forged ingot-iron has now practically
+replaced for electric engineering purposes the Low Moor or Swedish iron.
+Owing to the method of its production, it might in truth be called a
+soft steel with a very small percentage of combined carbon. The best
+description of this material is conveyed by the German term
+"Flusseisen," but its nearest British equivalent is "ingot-iron."
+Chemically speaking, the material is for all practical purposes very
+nearly pure iron. The same may be said of the cast steels now much
+employed for the production of dynamo magnet cores. The cast steel which
+is in demand for this purpose has a slightly lower permeability than the
+ingot-iron for low flux densities, but for flux densities above 16,000
+the required result may be more cheaply obtained with a steel casting
+than with a forging. When high tensile strength is required in addition
+to considerable magnetic permeability, it has been found advantageous to
+employ a steel containing 5% of nickel. The rolled sheet iron and sheet
+steel which is in request for the construction of magnet cores,
+especially those in which the exciting current is an alternating
+current, are, generally speaking, produced from Swedish iron. Owing to
+the mechanical treatment necessary to reduce the material to a thin
+sheet, the permeability at low flux densities is rather higher than,
+although at high flux densities it is inferior to, the same iron and
+steel when tested in bulk. For most purposes, however, where a laminated
+iron magnet core is required, the flux density is not pressed up above
+6000 units, and it is then more important to secure small hysteresis
+loss than high permeability. The magnetic permeability of cast iron is
+much inferior to that of wrought or ingot-iron, or the mild steels taken
+at the same flux densities.
+
+The following Table IV. gives the flux density and permeability of a
+typical cast iron taken by J.A. Fleming by the ballistic method:--
+
+  TABLE IV.--_Magnetic Permeability and Magnetization Curve of Cast
+  Iron._
+
+  +------+------+-----++-------+------+-----++--------+--------+-----+
+  |  H   |  B   |  µ  ||   H   |  B   |  µ  ||    H   |   B    |  µ  |
+  |  .19 |  27  | 139 ||  8.84 | 4030 | 456 ||  44.65 |  8,071 | 181 |
+  |  .41 |   62 | 150 || 10.60 | 4491 | 424 ||  56.57 |  8,548 | 151 |
+  | 1.11 |  206 | 176 || 12.33 | 4884 | 396 ||  71.98 |  9,097 | 126 |
+  | 2.53 |  768 | 303 || 13.95 | 5276 | 378 ||  88.99 |  9,600 | 108 |
+  | 3.41 | 1251 | 367 || 15.61 | 5504 | 353 || 106.35 | 10,066 |  95 |
+  | 4.45 | 1898 | 427 || 18.21 | 5829 | 320 || 120.60 | 10,375 |  86 |
+  | 5.67 | 2589 | 456 || 26.37 | 6814 | 258 || 140.37 | 10,725 |  76 |
+  | 7.16 | 3350 | 468 || 36.54 | 7580 | 207 || 152.73 | 10,985 |  72 |
+  +------+------+-----++-------+------+-----++--------+--------+-----+
+
+The metal of which the tests are given in Table IV. contained 2% of
+silicon, 2.85% of total carbon, and 0.5% of manganese. It will be seen
+that a magnetizing force of about 5 C.G.S. units is sufficient to impart
+to a wrought-iron ring a flux density of 18,000 C.G.S. units, but the
+same force hardly produces more than one-tenth of this flux density in
+cast iron.
+
+The testing of sheet iron and steel for magnetic hysteresis loss has
+developed into an important factory process, giving as it does a means
+of ascertaining the suitability of the metal for use in the manufacture
+of transformers and cores of alternating-current electromagnets.
+
+In Table V. are given the results of hysteresis tests by Ewing on
+samples of commercial sheet iron and steel. The numbers VII., VIII., IX.
+and X. refer to the same samples as those for which permeability results
+are given in Table III.
+
+  TABLE V.--_Hysteresis Loss in Transformer-iron._
+
+  +-------+------------------------------+-------------------------------+
+  |       |  Ergs per Cubic Centimetre   | Watts per lb. at a Frequency  |
+  |       |          per Cycle.          |            of 100.            |
+  |Maximum+-------+-------+-------+------+-------+-------+-------+-------+
+  | Flux  |  VII. | VIII. |  IX.  |  X.  |       |       |       |       |
+  |Density|Swedish| Forged| Ingot-| Soft |       |       |       |       |
+  |   B.  | Iron. |Scrap- | steel.| Iron |  VII. | VIII. |  IX.  |   X.  |
+  |       |       | iron. |       | Wire.|       |       |       |       |
+  +-------+-------+-------+-------+------+-------+-------+-------+-------+
+  | 2000  |  240  |  400  |  215  |  600 | 0.141 | 0.236 | 0.127 | 0.356 |
+  | 3000  |  520  |  790  |  430  | 1150 | 0.306 | 0.465 | 0.253 | 0.630 |
+  | 4000  |  830  | 1220  |  700  | 1780 | 0.490 | 0.720 | 0.410 | 1.050 |
+  | 5000  | 1190  | 1710  | 1000  | 2640 | 0.700 | 1.010 | 0.590 | 1.550 |
+  | 6000  | 1600  | 2260  | 1350  | 3360 | 0.940 | 1.330 | 0.790 | 1.980 |
+  | 7000  | 2020  | 2940  | 1730  | 4300 | 1.200 | 1.730 | 1.020 | 2.530 |
+  | 8000  | 2510  | 3710  | 2150  | 5300 | 1.480 | 2.180 | 1.270 | 3.120 |
+  | 9000  | 3050  | 4560  | 2620  | 6380 | 1.800 | 2.680 | 1.540 | 3.750 |
+  +-------+-------+-------+-------+------+-------+-------+-------+-------+
+
+In Table VI. are given the results of a magnetic test of some
+exceedingly good transformer-sheet rolled from Swedish iron.
+
+  TABLE VI.--_Hysteresis Loss in Strip of Transformer-plate rolled
+  Swedish Iron._
+
+  +------------+---------------------------+--------------------+
+  |Maximum Flux| Ergs per Cubic Centimetre | Watts per lb. at a |
+  |Density B.  |         per Cycle.        |  Frequency of 100. |
+  +------------+---------------------------+--------------------+
+  |    2000    |            220            |       0.129        |
+  |    3000    |            410            |       0.242        |
+  |    4000    |            640            |       0.376        |
+  |    5000    |            910            |       0.535        |
+  |    6000    |           1200            |       0.710        |
+  |    7000    |           1520            |       0.890        |
+  |    8000    |           1900            |       1.120        |
+  |    9000    |           2310            |       1.360        |
+  +------------+---------------------------+--------------------+
+
+In Table VII. are given some values obtained by Fleming for the
+hysteresis loss in the sample of cast iron, the permeability test of
+which is recorded in Table IV.
+
+  TABLE VII.--_Observations on the Magnetic Hysteresis of Cast Iron._
+
+  +------+---------+-----------------------------------+
+  |      |         |         Hysteresis Loss.          |
+  |      |         +-------------+---------------------+
+  | Loop.| B (max.)| Ergs per cc.|  Watts per lb. per. |
+  |      |         |  per Cycle. | 100 Cycles per sec. |
+  +------+---------+-------------+---------------------+
+  |   I. |  1475   |      466    |         .300        |
+  |  II. |  2545   |    1,288    |         .829        |
+  | III. |  3865   |    2,997    |        1.934        |
+  |  IV. |  5972   |    7,397    |        4.765        |
+  |   V. |  8930   |   13,423    |        8.658        |
+  +------+---------+-------------+---------------------+
+
+For most practical purposes the constructor of electromagnetic machinery
+requires his iron or steel to have some one of the following
+characteristics. If for dynamo or magnet making, it should have the
+highest possible permeability at a flux density corresponding to
+practically maximum magnetization. If for transformer or
+alternating-current magnet building, it should have the smallest
+possible hysteresis loss at a maximum flux density of 2500 C.G.S. units
+during the cycle. If required for permanent magnet making, it should
+have the highest possible coercivity combined with a high retentivity.
+Manufacturers of iron and steel are now able to meet these demands in a
+very remarkable manner by the commercial production of material of a
+quality which at one time would have been considered a scientific
+curiosity.
+
+It is usual to specify iron and steel for the first purpose by naming
+the minimum permeability it should possess corresponding to a flux
+density of 18,000 C.G.S. units; for the second, by stating the
+hysteresis loss in watts per lb. per 100 cycles per second,
+corresponding to a maximum flux density of 2500 C.G.S. units during the
+cycle; and for the third, by mentioning the coercive force required to
+reduce to zero magnetization a sample of the metal in the form of a long
+bar magnetized to a stated magnetization. In the cyclical reversal of
+magnetization of iron we have two modes to consider. In the first case,
+which is that of the core of the alternating transformer, the magnetic
+force passes through a cycle of values, the iron remaining stationary,
+and the direction of the magnetic force being always the same. In the
+other case, that of the dynamo armature core, the direction of the
+magnetic force in the iron is constantly changing, and at the same time
+undergoing a change in magnitude.
+
+It has been shown by F.G. Baily (_Proc. Roy. Soc._, 1896) that if a mass
+of laminated iron is rotating in a magnetic field which remains constant
+in direction and magnitude in any one experiment, the hysteresis loss
+rises to a maximum as the magnitude of the flux density in the iron is
+increased and then falls away again to nearly zero value. These
+observations have been confirmed by other observers. The question has
+been much debated whether the values of the hysteresis loss obtained by
+these two different methods are identical for magnetic cycles in which
+the flux density reaches the same maximum value. This question is also
+connected with another one, namely, whether the hysteresis loss per
+cycle is or is not a function of the speed with which the cycle is
+traversed. Early experiments by C.P. Steinmetz and others seemed to show
+that there was a difference between slow-speed and high-speed hysteresis
+cycles, but later experiments by J. Hopkinson and by A. Tanakadaté,
+though not absolutely exhaustive, tend to prove that up to 400 cycles
+per second the hysteresis loss per cycle is practically unchanged.
+
+Experiments made in 1896 by R. Beattie and R.C. Clinker on magnetic
+hysteresis in rotating fields were partly directed to determine whether
+the hysteresis loss at moderate flux densities, such as are employed in
+transformer work, was the same as that found by measurements made with
+alternating-current fields on the same iron and steel specimens (see
+_The Electrician_, 1896, 37, p. 723). These experiments showed that
+over moderate ranges of induction, such as may be expected in
+electro-technical work, the hysteresis loss per cycle per cubic
+centimetre was practically the same when the iron was tested in an
+alternating field with a periodicity of 100, the field remaining
+constant in direction, and when the iron was tested in a rotating field
+giving the same maximum flux density.
+
+With respect to the variation of hysteresis loss in magnetic cycles
+having different maximum values for the flux density, Steinmetz found
+that the hysteresis loss (W), as measured by the area of the complete
+(B, H) cycle and expressed in ergs per centimetre-cube per cycle, varies
+proportionately to a constant called the _hysteretic constant_, and to
+the 1.6th power of the maximum flux density (B), or W = [eta]B^(1.6).
+
+The hysteretic constants ([eta]) for various kinds of iron and steel are
+given in the table below:--
+
+    Metal.                                  Hysteretic Constant.
+
+  Swedish wrought iron, well annealed         .0010 to .0017
+  Annealed cast steel of good quality; small
+    percentage of carbon                      .0017 to .0029
+  Cast Siemens-Martin steel                   .0019 to .0028
+  Cast ingot-iron                             .0021 to .0026
+  Cast steel, with higher percentages of
+    carbon, or inferior qualities of wrought
+    iron                                      .0031 to .0054
+
+Steinmetz's law, though not strictly true for very low or very high
+maximum flux densities, is yet a convenient empirical rule for obtaining
+approximately the hysteresis loss at any one maximum flux density and
+knowing it at another, provided these values fall within a range varying
+say from 1 to 9000 C.G.S. units. (See MAGNETISM.)
+
+The standard maximum flux density which is adopted in electro-technical
+work is 2500, hence in the construction of the cores of
+alternating-current electromagnets and transformers iron has to be
+employed having a known hysteretic constant at the standard flux
+density. It is generally expressed by stating the number of watts per
+lb. of metal which would be dissipated for a frequency of 100 cycles,
+and a maximum flux density (B max.) during the cycle of 2500. In the
+case of good iron or steel for transformer-core making, it should not
+exceed 1.25 watt per lb. per 100 cycles per 2500 B (maximum value).
+
+It has been found that if the sheet iron employed for cores of
+alternating electromagnets or transformers is heated to a temperature
+somewhere in the neighbourhood of 200° C. the hysteresis loss is very
+greatly increased. It was noticed in 1894 by G.W. Partridge that
+alternating-current transformers which had been in use some time had a
+very considerably augmented core loss when compared with their initial
+condition. O.T. Bláthy and W.M. Mordey in 1895 showed that this
+augmentation in hysteresis loss in iron was due to heating. H.F.
+Parshall investigated the effect up to moderate temperatures, such as
+140° C., and an extensive series of experiments was made in 1898 by S.R.
+Roget (_Proc. Roy. Soc._, 1898, 63, p. 258, and 64, p. 150). Roget found
+that below 40° C. a rise in temperature did not produce any augmentation
+in the hysteresis loss in iron, but if it is heated to between 40° C.
+and 135° C. the hysteresis loss increases continuously with time, and
+this increase is now called "ageing" of the iron. It proceeds more
+slowly as the temperature is higher. If heated to above 135° C., the
+hysteresis loss soon attains a maximum, but then begins to decrease.
+Certain specimens heated to 160° C. were found to have their hysteresis
+loss doubled in a few days. The effect seems to come to a maximum at
+about 180° C. or 200° C. Mere lapse of time does not remove the
+increase, but if the iron is reannealed the augmentation in hysteresis
+disappears. If the iron is heated to a higher temperature, say between
+300° C. and 700° C., Roget found the initial rise of hysteresis happens
+more quickly, but that the metal soon settles down into a state in which
+the hysteresis loss has a small but still augmented constant value. The
+augmentation in value, however, becomes more nearly zero as the
+temperature approaches 700° C. Brands of steel are now obtainable which
+do not age in this manner, but these _non-ageing_ varieties of steel
+have not generally such low initial hysteresis values as the "Swedish
+Iron," commonly considered best for the cores of transformers and
+alternating-current magnets.
+
+The following conclusions have been reached in the matter:--(1) Iron and
+mild steel in the annealed state are more liable to change their
+hysteresis value by heating than when in the harder condition; (2) all
+changes are removed by re-annealing; (3) the changes thus produced by
+heating affect not only the amount of the hysteresis loss, but also the
+form of the lower part of the (B, H) curve.
+
+_Forms of Electromagnet._--The form which an electromagnet must take
+will greatly depend upon the purposes for which it is to be used. A
+design or form of electromagnet which will be very suitable for some
+purposes will be useless for others. Supposing it is desired to make an
+electromagnet which shall be capable of undergoing very rapid changes of
+strength, it must have such a form that the coercivity of the material
+is overcome by a self-demagnetizing force. This can be achieved by
+making the magnet in the form of a short and stout bar rather than a
+long thin one. It has already been explained that the ends or poles of a
+polar magnet exert a demagnetizing power upon the mass of the metal in
+the interior of the bar. If then the electromagnet has the form of a
+long thin bar, the length of which is several hundred times its
+diameter, the poles are very far removed from the centre of the bar, and
+the demagnetizing action will be very feeble; such a long thin
+electromagnet, although made of very soft iron, retains a considerable
+amount of magnetism after the magnetizing force is withdrawn. On the
+other hand, a very thick bar very quickly demagnetizes itself, because
+no part of the metal is far removed from the action of the free poles.
+Hence when, as in many telegraphic instruments, a piece of soft iron,
+called an armature, has to be attracted to the poles of a
+horseshoe-shaped electromagnet, this armature should be prevented from
+quite touching the polar surfaces of the magnet. If a soft iron mass
+does quite touch the poles, then it completes the magnetic circuit and
+abolishes the free poles, and the magnet is to a very large extent
+deprived of its self-demagnetizing power. This is the explanation of the
+well-known fact that after exciting the electromagnet and then stopping
+the current, it still requires a good pull to detach the "keeper"; but
+when once the keeper has been detached, the magnetism is found to have
+nearly disappeared. An excellent form of electromagnet for the
+production of very powerful fields has been designed by H. du Bois (fig.
+6).
+
+[Illustration: FIG. 6.--Du Bois's Electromagnet.]
+
+Various forms of electromagnets used in connexion with dynamo machines
+are considered in the article DYNAMO, and there is, therefore, no
+necessity to refer particularly to the numerous different shapes and
+types employed in electrotechnics.
+
+  BIBLIOGRAPHY.--For additional information on the above subject the
+  reader may be referred to the following works and original papers:--
+
+  H. du Bois, _The Magnetic Circuit in Theory and Practice_; S.P.
+  Thompson, _The Electromagnet_; J.A. Fleming, _Magnets and Electric
+  Currents_; J.A. Ewing, _Magnetic Induction in Iron and other Metals_;
+  J.A. Fleming, "The Ferromagnetic Properties of Iron and Steel,"
+  _Proceedings of Sheffield Society of Engineers and Metallurgists_
+  (Oct. 1897); J.A. Ewing, "The Magnetic Testing of Iron and Steel,"
+  _Proc. Inst. Civ. Eng._, 1896, 126, p. 185; H.F. Parshall, "The
+  Magnetic Data of Iron and Steel," _Proc. Inst. Civ. Eng._, 1896, 126,
+  p. 220; J.A. Ewing, "The Molecular Theory of Induced Magnetism,"
+  _Phil. Mag._, Sept. 1890; W.M. Mordey, "Slow Changes in the
+  Permeability of Iron," _Proc. Roy. Soc._ 57, p. 224; J.A. Ewing,
+  "Magnetism," James Forrest Lecture, _Proc. Inst. Civ. Eng._ 138; S.P.
+  Thompson, "Electromagnetic Mechanism," _Electrician_, 26, pp. 238,
+  269, 293; J.A. Ewing, "Experimental Researches in Magnetism," _Phil.
+  Trans._, 1885, part ii.; Ewing and Klassen, "Magnetic Qualities of
+  Iron," _Proc. Roy. Soc._, 1893.     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] In the _Annals of Philosophy_ for November 1821 is a long article
+    entitled "Electromagnetism" by Oersted, in which he gives a detailed
+    account of his discovery. He had his thoughts turned to it as far
+    back as 1813, but not until the 20th of July 1820 had he actually
+    made his discovery. He seems to have been arranging a compass needle
+    to observe any deflections during a storm, and placed near it a
+    platinum wire through which a galvanic current was passed.
+
+  [2] See _Trans. Soc. Arts_, 1825, 43, p. 38, in which a figure of
+    Sturgeon's electromagnet is given as well as of other pieces of
+    apparatus for which the Society granted him a premium and a silver
+    medal.
+
+  [3] See S.P. Thompson, _The Electromagnet_ (London, 1891); J.A.
+    Fleming, _A Handbook for the Electrical Laboratory and Testing Room_,
+    vol. 2 (London, 1903); J.A. Ewing, _Magnetic Induction in Iron and
+    other Metals_ (London, 1903, 3rd ed.).
+
+
+
+
+ELECTROMETALLURGY. The present article, as explained under
+ELECTROCHEMISTRY, treats only of those processes in which electricity is
+applied to the production of chemical reactions or molecular changes at
+furnace temperatures. In many of these the application of heat is
+necessary to bring the substances used into the liquid state for the
+purpose of electrolysis, aqueous solutions being unsuitable. Among the
+earliest experiments in this branch of the subject were those of Sir H.
+Davy, who in 1807 (_Phil. Trans._, 1808, p. 1), produced the alkali
+metals by passing an intense current of electricity from a platinum wire
+to a platinum dish, through a mass of fused caustic alkali. The action
+was started in the cold, the alkali being slightly moistened to render
+it a conductor; then, as the current passed, heat was produced and the
+alkali fused, the metal being deposited in the liquid condition. Later,
+A. Matthiessen (_Quarterly Journ. Chem. Soc._ viii. 30) obtained
+potassium by the electrolysis of a mixture of potassium and calcium
+chlorides fused over a lamp. There are here foreshadowed two types of
+electrolytic furnace-operations: (a) those in which external heating
+maintains the electrolyte in the fused condition, and (b) those in which
+a current-density is applied sufficiently high to develop the heat
+necessary to effect this object unaided. Much of the earlier
+electro-metallurgical work was done with furnaces of the (a) type, while
+nearly all the later developments have been with those of class (b).
+There is a third class of operations, exemplified by the manufacture of
+calcium carbide, in which electricity is employed solely as a heating
+agent; these are termed _electrothermal_, as distinguished from
+_electrolytic_. In certain electrothermal processes (e.g. calcium
+carbide production) the heat from the current is employed in raising
+mixtures of substances to the temperature at which a desired chemical
+reaction will take place between them, while in others (e.g. the
+production of graphite from coke or gas-carbon) the heat is applied
+solely to the production of molecular or physical changes. In ordinary
+electrolytic work only the continuous current may of course be used, but
+in electrothermal work an alternating current is equally available.
+
+_Electric Furnaces._--Independently of the question of the application
+of external heating, the furnaces used in electrometallurgy may be
+broadly classified into (i.) arc furnaces, in which the intense heat of
+the electric arc is utilized, and (ii.) resistance and incandescence
+furnaces, in which the heat is generated by an electric current
+overcoming the resistance of an inferior conductor.
+
+
+  Arc furnaces.
+
+Excepting such experimental arrangements as that of C.M. Despretz
+(_C.R._, 1849, 29) for use on a small scale in the laboratory, Pichou in
+France and J.H. Johnson in England appear, in 1853, to have introduced
+the earliest practical form of furnace. In these arrangements, which
+were similar if not identical, the furnace charge was crushed to a fine
+powder and passed through two or more electric arcs in succession. When
+used for ore smelting, the reduced metal and the accompanying slag were
+to be caught, after leaving the arc and while still liquid, in a hearth
+fired with ordinary fuel. Although this primitive furnace could be made
+to act, its efficiency was low, and the use of a separate fire was
+disadvantageous. In 1878 Sir William Siemens patented a form of
+furnace[1] which is the type of a very large number of those designed by
+later inventors.
+
+  In the best-known form a plumbago crucible was used with a hole cut in
+  the bottom to receive a carbon rod, which was ground in so as to make
+  a tight joint. This rod was connected with the positive pole of the
+  dynamo or electric generator. The crucible was fitted with a cover in
+  which were two holes; one at the side to serve at once as sight-hole
+  and charging door, the other in the centre to allow a second carbon
+  rod to pass freely (without touching) into the interior. This rod was
+  connected with the negative pole of the generator, and was suspended
+  from one arm of a balance-beam, while from the other end of the beam
+  was suspended a vertical hollow iron cylinder, which could be moved
+  into or out of a wire coil or solenoid joined as a shunt across the
+  two carbon rods of the furnace. The solenoid was above the iron
+  cylinder, the supporting rod of which passed through it as a core.
+  When the furnace with this well-known regulating device was to be
+  used, say, for the melting of metals or other conductors of
+  electricity, the fragments of metal were placed in the crucible and
+  the positive electrode was brought near them. Immediately the current
+  passed through the solenoid it caused the iron cylinder to rise, and,
+  by means of its supporting rod, forced the end of the balance beam
+  upwards, so depressing the other end that the negative carbon rod was
+  forced downwards into contact with the metal in the crucible. This
+  action completed the furnace-circuit, and current passed freely from
+  the positive carbon through the fragments of metal to the negative
+  carbon, thereby reducing the current through the shunt. At once the
+  attractive force of the solenoid on the iron cylinder was
+  automatically reduced, and the falling of the latter caused the
+  negative carbon to rise, starting an arc between it and the metal in
+  the crucible. A counterpoise was placed on the solenoid end of the
+  balance beam to act against the attraction of the solenoid, the
+  position of the counterpoise determining the length of the arc in the
+  crucible. Any change in the resistance of the arc, either by
+  lengthening, due to the sinking of the charge in the crucible, or by
+  the burning of the carbon, affected the proportion of current flowing
+  in the two shunt circuits, and so altered the position of the iron
+  cylinder in the solenoid that the length of arc was, within limits,
+  automatically regulated. Were it not for the use of some such device
+  the arc would be liable to constant fluctuation and to frequent
+  extinction. The crucible was surrounded with a bad conductor of heat
+  to minimize loss by radiation. The positive carbon was in some cases
+  replaced by a water-cooled metal tube, or ferrule, closed, of course,
+  at the end inserted in the crucible. Several modifications were
+  proposed, in one of which, intended for the heating of non-conducting
+  substances, the electrodes were passed horizontally through
+  perforations in the upper part of the crucible walls, and the charge
+  in the lower part of the crucible was heated by radiation.
+
+The furnace used by Henri Moissan in his experiments on reactions at
+high temperatures, on the fusion and volatilization of refractory
+materials, and on the formation of carbides, silicides and borides of
+various metals, consisted, in its simplest form, of two superposed
+blocks of lime or of limestone with a central cavity cut in the lower
+block, and with a corresponding but much shallower inverted cavity in
+the upper block, which thus formed the lid of the furnace. Horizontal
+channels were cut on opposite walls, through which the carbon poles or
+electrodes were passed into the upper part of the cavity. Such a
+furnace, to take a current of 4 H.P. (say, of 60 amperes and 50 volts),
+measured externally about 6 by 6 by 7 in., and the electrodes were about
+0.4 in. in diameter, while for a current of 100 H.P. (say, of 746
+amperes and 100 volts) it measured about 14 by 12 by 14 in., and the
+electrodes were about 1.5 in. in diameter. In the latter case the
+crucible, which was placed in the cavity immediately beneath the arc,
+was about 3 in. in diameter (internally), and about 3½ in. in height.
+The fact that energy is being used at so high a rate as 100 H.P. on so
+small a charge of material sufficiently indicates that the furnace is
+only used for experimental work, or for the fusion of metals which, like
+tungsten or chromium, can only be melted at temperatures attainable by
+electrical means. Moissan succeeded in fusing about ¾ lb. of either of
+these metals in 5 or 6 minutes in a furnace similar to that last
+described. He also arranged an experimental tube-furnace by passing a
+carbon tube horizontally beneath the arc in the cavity of the lime
+blocks. When prolonged heating is required at very high temperatures it
+is found necessary to line the furnace-cavity with alternate layers of
+magnesia and carbon, taking care that the lamina next to the lime is of
+magnesia; if this were not done the lime in contact with the carbon
+crucible would form calcium carbide and would slag down, but magnesia
+does not yield a carbide in this way. Chaplet has patented a muffle or
+tube furnace, similar in principle, for use on a larger scale, with a
+number of electrodes placed above and below the muffle-tube. The arc
+furnaces now widely used in the manufacture of calcium carbide on a
+large scale are chiefly developments of the Siemens furnace. But
+whereas, from its construction, the Siemens furnace was intermittent in
+operation, necessitating stoppage of the current while the contents of
+the crucible were poured out, many of the newer forms are specially
+designed either to minimize the time required in effecting the
+withdrawal of one charge and the introduction of the next, or to ensure
+absolute continuity of action, raw material being constantly charged in
+at the top and the finished substance and by-products (slag, &c.)
+withdrawn either continuously or at intervals, as sufficient quantity
+shall have accumulated. In the King furnace, for example, the crucible,
+or lowest part of the furnace, is made detachable, so that when full it
+may be removed and an empty crucible substituted. In the United States a
+revolving furnace is used which is quite continuous in action.
+
+
+  Incandescence furnaces.
+
+The class of furnaces heated by electrically incandescent materials has
+been divided by Borchers into two groups: (1) those in which the
+substance is heated by contact with a substance offering a high
+resistance to the current passing through it, and (2) those in which the
+substance to be heated itself affords the resistance to the passage of
+the current whereby electric energy is converted into heat. Practically
+the first of these furnaces was that of Despretz, in which the mixture
+to be heated was placed in a carbon tube rendered incandescent by the
+passage of a current through its substance from end to end. In 1880 W.
+Borchers introduced his resistance-furnace, which, in one sense, is the
+converse of the Despretz apparatus. A thin carbon pencil, forming a
+bridge between two stout carbon rods, is set in the midst of the mixture
+to be heated. On passing a current through the carbon the small rod is
+heated to incandescence, and imparts heat to the surrounding mass. On a
+larger scale several pencils are used to make the connexions between
+carbon blocks which form the end walls of the furnace, while the side
+walls are of fire-brick laid upon one another without mortar. Many of
+the furnaces now in constant use depend mainly on this principle, a core
+of granular carbon fragments stamped together in the direct line between
+the electrodes, as in Acheson's carborundum furnace, being substituted
+for the carbon pencils. In other cases carbon fragments are mixed
+throughout the charge, as in E.H. and A.H. Cowles's zinc-smelting
+retort. In practice, in these furnaces, it is possible for small local
+arcs to be temporarily set up by the shifting of the charge, and these
+would contribute to the heating of the mass. In the remaining class of
+furnace, in which the electrical resistance of the charge itself is
+utilized, are the continuous-current furnaces, such as are used for the
+smelting of aluminium, and those alternating-current furnaces, (e.g. for
+the production of calcium carbide) in which a portion of the charge is
+first actually fused, and then maintained in the molten condition by the
+current passing through it, while the reaction between further portions
+of the charge is proceeding.
+
+
+  Uses and advantages.
+
+For ordinary metallurgical work the electric furnace, requiring as it
+does (excepting where waterfalls or other cheap sources of power are
+available) the intervention of the boiler and steam-engine, or of the
+gas or oil engine, with a consequent loss of energy, has not usually
+proved so economical as an ordinary direct fired furnace. But in some
+cases in which the current is used for electrolysis and for the
+production of extremely high temperatures, for which the calorific
+intensity of ordinary fuel is insufficient, the electric furnace is
+employed with advantage. The temperature of the electric furnace,
+whether of the arc or incandescence type, is practically limited to
+that at which the least easily vaporized material available for
+electrodes is converted into vapour. This material is carbon, and as its
+vaporizing point is (estimated at) over 3500° C., and less than 4000°
+C., the temperature of the electric furnace cannot rise much above 3500°
+C. (6330° F.); but H. Moissan showed that at this temperature the most
+stable of mineral combinations are dissociated, and the most refractory
+elements are converted into vapour, only certain borides, silicides and
+metallic carbides having been found to resist the action of the heat. It
+is not necessary that all electric furnaces shall be run at these high
+temperatures; obviously, those of the incandescence or resistance type
+may be worked at any convenient temperature below the maximum. The
+electric furnace has several advantages as compared with some of the
+ordinary types of furnace, arising from the fact that the heat is
+generated from within the mass of material operated upon, and (unlike
+the blast-furnace, which presents the same advantage) without a large
+volume of gaseous products of combustion and atmospheric nitrogen being
+passed through it. In ordinary reverberatory and other heating furnaces
+the burning fuel is without the mass, so that the vessel containing the
+charge, and other parts of the plant, are raised to a higher temperature
+than would otherwise be necessary, in order to compensate for losses by
+radiation, convection and conduction. This advantage is especially
+observed in some cases in which the charge of the furnace is liable to
+attack the containing vessel at high temperatures, as it is often
+possible to maintain the outer walls of the electric furnace relatively
+cool, and even to keep them lined with a protecting crust of unfused
+charge. Again, the construction of electric furnaces may often be
+exceedingly crude and simple; in the carborundum furnace, for example,
+the outer walls are of loosely piled bricks, and in one type of furnace
+the charge is simply heaped on the ground around the carbon resistance
+used for heating, without containing-walls of any kind. There is,
+however, one (not insuperable) drawback in the use of the electric
+furnace for the smelting of pure metals. Ordinarily carbon is used as
+the electrode material, but when carbon comes in contact at high
+temperatures with any metal that is capable of forming a carbide a
+certain amount of combination between them is inevitable, and the carbon
+thus introduced impairs the mechanical properties of the ultimate
+metallic product. Aluminium, iron, platinum and many other metals may
+thus take up so much carbon as to become brittle and unforgeable. It is
+for this reason that Siemens, Borchers and others substituted a hollow
+water-cooled metal block for the carbon cathode upon which the melted
+metal rests while in the furnace. Liquid metal coming in contact with
+such a surface forms a crust of solidified metal over it, and this crust
+thickens up to a certain point, namely, until the heat from within the
+furnace just overbalances that lost by conduction through the solidified
+crust and the cathode material to the flowing water. In such an
+arrangement, after the first instant, the melted metal in the furnace
+does not come in contact with the cathode material.
+
+
+  Aluminium alloys.
+
+_Electrothermal Processes._--In these processes the electric current is
+used solely to generate heat, either to induce chemical reactions
+between admixed substances, or to produce a physical (allotropic)
+modification of a given substance. Borchers predicted that, at the high
+temperatures available with the electric furnace, every oxide would
+prove to be reducible by the action of carbon, and this prediction has
+in most instances been justified. Alumina and lime, for example, which
+cannot be reduced at ordinary furnace temperatures, readily give up
+their oxygen to carbon in the electric furnace, and then combine with an
+excess of carbon to form metallic carbides. In 1885 the brothers Cowles
+patented a process for the electrothermal reduction of oxidized ores by
+exposure to an intense current of electricity when admixed with carbon
+in a retort. Later in that year they patented a process for the
+reduction of aluminium by carbon, and in 1886 an electric furnace with
+sliding carbon rods passed through the end walls to the centre of a
+rectangular furnace. The impossibility of working with just sufficient
+carbon to reduce the alumina, without using any excess which would be
+free to form at least so much carbide as would suffice, when diffused
+through the metal, to render it brittle, practically restricts the use
+of such processes to the production of aluminium alloys. Aluminium
+bronze (aluminium and copper) and ferro-aluminium (aluminium and iron)
+have been made in this way; the latter is the more satisfactory product,
+because a certain proportion of carbon is expected in an alloy of this
+character, as in ferromanganese and cast iron, and its presence is not
+objectionable. The furnace is built of fire-brick, and may measure
+(internally) 5 ft. in length by 1 ft. 8 in. in width, and 3 ft. in
+height. Into each end wall is built a short iron tube sloping downwards
+towards the centre, and through this is passed a bundle of five 3-in.
+carbon rods, bound together at the outer end by being cast into a head
+of cast iron for use with iron alloys, or of cast copper for aluminium
+bronze. This head slides freely in the cast iron tubes, and is connected
+by a copper rod with one of the terminals of the dynamo supplying the
+current. The carbons can thus, by the application of suitable mechanism,
+be withdrawn from or plunged into the furnace at will. In starting the
+furnace, the bottom is prepared by ramming it with charcoal-powder that
+has been soaked in milk of lime and dried, so that each particle is
+coated with a film of lime, which serves to reduce the loss of current
+by conduction through the lining when the furnace becomes hot. A sheet
+iron case is then placed within the furnace, and the space between it
+and the walls rammed with limed charcoal; the interior is filled with
+fragments of the iron or copper to be alloyed, mixed with alumina and
+coarse charcoal, broken pieces of carbon being placed in position to
+connect the electrodes. The iron case is then removed, the whole is
+covered with charcoal, and a cast iron cover with a central flue is
+placed above all. The current, either continuous or alternating, is then
+started, and continued for about 1 to 1½ hours, until the operation is
+complete, the carbon rods being gradually withdrawn as the action
+proceeds. In such a furnace a continuous current, for example, of 3000
+amperes, at 50 to 60 volts, may be used at first, increasing to 5000
+amperes in about half an hour. The reduction is not due to electrolysis,
+but to the action of carbon on alumina, a part of the carbon in the
+charge being consumed and evolved as carbon monoxide gas, which burns at
+the orifice in the cover so long as reduction is taking place. The
+reduced aluminium alloys itself immediately with the fused globules of
+metal in its midst, and as the charge becomes reduced the globules of
+alloy unite until, in the end, they are run out of the tap-hole after
+the current has been diverted to another furnace. It was found in
+practice (in 1889) that the expenditure of energy per pound of reduced
+aluminium was about 23 H.P.-hours, a number considerably in excess of
+that required at the present time for the production of pure aluminium
+by the electrolytic process described in the article ALUMINIUM. Calcium
+carbide, graphite (q.v.), phosphorus (q.v.) and carborundum (q.v.) are
+now extensively manufactured by the operations outlined above.
+
+_Electrolytic Processes._--The isolation of the metals sodium and
+potassium by Sir Humphry Davy in 1807 by the electrolysis of the fused
+hydroxides was one of the earliest applications of the electric current
+to the extraction of metals. This pioneering work showed little
+development until about the middle of the 19th century. In 1852
+magnesium was isolated electrolytically by R. Bunsen, and this process
+subsequently received much attention at the hands of Moissan and
+Borchers. Two years later Bunsen and H.E. Sainte Claire Deville working
+independently obtained aluminium (q.v.) by the electrolysis of the fused
+double sodium aluminium chloride. Since that date other processes have
+been devised and the electrolytic processes have entirely replaced the
+older methods of reduction with sodium. Methods have also been
+discovered for the electrolytic manufacture of calcium (q.v.), which
+have had the effect of converting a laboratory curiosity into a product
+of commercial importance. Barium and strontium have also been produced
+by electro-metallurgical methods, but the processes have only a
+laboratory interest at present. Lead, zinc and other metals have also
+been reduced in this manner.
+
+  For further information the following books, in addition to those
+  mentioned at the end of the article ELECTROCHEMISTRY, may be
+  consulted: Borchers, _Handbuch der Elektrochemie_; _Electric Furnaces_
+  (Eng. trans. by H.G. Solomon, 1908); Moissan, _The Electric Furnace_
+  (1904); J. Escard, _Fours électriques_ (1905); _Les Industries
+  électrochimiques_ (1907).     (W. G. M.)
+
+
+FOOTNOTE:
+
+  [1] Cf. Siemens's account of the use of this furnace for experimental
+    purposes in _British Association Report_ for 1882.
+
+
+
+
+ELECTROMETER, an instrument for measuring difference of potential, which
+operates by means of electrostatic force and gives the measurement
+either in arbitrary or in absolute units (see UNITS, PHYSICAL). In the
+last case the instrument is called an absolute electrometer. Lord Kelvin
+has classified electrometers into (1) Repulsion, (2) Attracted disk, and
+(3) Symmetrical electrometers (see W. Thomson, _Brit. Assoc. Report_,
+1867, or _Reprinted Papers on Electrostatics and Magnetization_, p.
+261).
+
+_Repulsion Electrometers._--The simplest form of repulsion electrometer
+is W. Henley's pith ball electrometer (_Phil. Trans._, 1772, 63, p. 359)
+in which the repulsion of a straw ending in a pith ball from a fixed
+stem is indicated on a graduated arc (see ELECTROSCOPE). A double pith
+ball repulsion electrometer was employed by T. Cavallo in 1777.
+
+  It may be pointed out that such an arrangement is not merely an
+  arbitrary electrometer, but may become an absolute electrometer within
+  certain rough limits. Let two spherical pith balls of radius r and
+  weight W, covered with gold-leaf so as to be conducting, be suspended
+  by parallel silk threads of length l so as just to touch each other.
+  If then the balls are both charged to a potential V they will repel
+  each other, and the threads will stand out at an angle 2[theta], which
+  can be observed on a protractor. Since the electrical repulsion of the
+  balls is equal to C²V²4l² sin²[theta] dynes, where C = r is the
+  capacity of either ball, and this force is balanced by the restoring
+  force due to their weight, Wg dynes, where g is the acceleration of
+  gravity, it is easy to show that we have
+
+        2l sin [theta] [root](Wg tan [theta])
+    V = -------------------------------------
+                         r
+
+  as an expression for their common potential V, provided that the balls
+  are small and their distance sufficiently great not sensibly to
+  disturb the uniformity of electric charge upon them. Observation of
+  [theta] with measurement of the value of l and r reckoned in
+  centimetres and W in grammes gives us the potential difference of the
+  balls in absolute C.G.S. or electrostatic units. The gold-leaf
+  electroscope invented by Abraham Bennet (see ELECTROSCOPE) can in like
+  manner, by the addition of a scale to observe the divergence of the
+  gold-leaves, be made a repulsion electrometer.
+
+[Illustration: FIG. 1.--Snow-Harris's Disk Electrometer.]
+
+_Attracted Disk Electrometers._--A form of attracted disk absolute
+electrometer was devised by A. Volta. It consisted of a plane conducting
+plate forming one pan of a balance which was suspended over another
+insulated plate which could be electrified. The attraction between the
+two plates was balanced by a weight put in the opposite pan. A similar
+electric balance was subsequently devised by Sir W. Snow-Harris,[1] one
+of whose instruments is shown in fig. 1. C is an insulated disk over
+which is suspended another disk attached to the arm of a balance. A
+weight is put in the opposite scale pan and a measured charge of
+electricity is given to the disk C just sufficient to tip over the
+balance. Snow-Harris found that this charge varied as the square root of
+the weight in the opposite pan, thus showing that the attraction
+between the disks at given distance apart varies as the square of their
+difference of potential.
+
+The most important improvements in connexion with electrometers are due,
+however, to Lord Kelvin, who introduced the guard plate and used gravity
+or the torsion of a wire as a means for evaluating the electrical
+forces.
+
+[Illustration: FIG. 2.--Kelvin's Portable Electrometer.]
+
+[Illustration: FIG. 3.]
+
+  His portable electrometer is shown in fig. 2. H H (see fig. 3) is a
+  plane disk of metal called the guard plate, fixed to the inner coating
+  of a small Leyden jar (see fig. 2). At F a square hole is cut out of H
+  H, and into this fits loosely without touching, like a trap door, a
+  square piece of aluminium foil having a projecting tail, which carries
+  at its end a stirrup L, crossed by a fine hair (see fig. 3). The
+  square piece of aluminium is pivoted round a horizontal stretched
+  wire. If then another horizontal disk G is placed over the disk H H
+  and a difference of potential made between G and H H, the movable
+  aluminium trap door F will be attracted by the fixed plate G. Matters
+  are so arranged by giving a torsion to the wire carrying the aluminium
+  disk F that for a certain potential difference between the plates H
+  and G, the movable part F comes into a definite sighted position,
+  which is observed by means of a small lens. The plate G (see fig. 2)
+  is moved up and down, parallel to itself, by means of a screw. In
+  using the instrument the conductor, whose potential is to be tested,
+  is connected to the plate G. Let this potential be denoted by V, and
+  let v be the potential of the guard plate and the aluminium flap. This
+  last potential is maintained constant by guard plate and flap being
+  part of the interior coating of a charged Leyden jar. Since the
+  distribution of electricity may be considered to be constant over the
+  surface S of the attracted disk, the mechanical force f on it is given
+  by the expression,[2]
+
+        S(V - v)²
+    f = ---------,
+         8[pi]d²
+
+  where d is the distance between the two plates. If this distance is
+  varied until the attracted disk comes into a definite sighted position
+  as seen by observing the end of the index through the lens, then since
+  the force f is constant, being due to the torque applied by the wire
+  for a definite angle of twist, it follows that the difference of
+  potential of the two plates varies as their distance. If then two
+  experiments are made, first with the upper plate connected to earth,
+  and secondly, connected to the object being tested, we get an
+  expression for the potential V of this conductor in the form
+
+    V = A(d' - d),
+
+  where d and d' are the distances of the fixed and movable plates from
+  one another in the two cases, and A is some constant. We thus find V
+  in terms of the constant and the difference of the two screw readings.
+
+  [Illustration: FIG. 4.--Kelvin's Absolute Electrometer.]
+
+  Lord Kelvin's absolute electrometer (fig. 4) involves the same
+  principle. There is a certain fixed guard disk B having a hole in it
+  which is loosely occupied by an aluminium trap door plate, shielded by
+  D and suspended on springs, so that its surface is parallel with that
+  of the guard plate. Parallel to this is a second movable plate A, the
+  distances between the two being measurable by means of a screw. The
+  movable plate can be drawn down into a definite sighted position when
+  a difference of potential is made between the two plates. This
+  sighted position is such that the surface of the trap door plate is
+  level with that of the guard plate, and is determined by observations
+  made with the lenses H and L. The movable plate can be thus depressed
+  by placing on it a certain standard weight W grammes.
+
+  Suppose it is required to measure the difference of potentials V and
+  V' of two conductors. First one and then the other conductor is
+  connected with the electrode of the lower or movable plate, which is
+  moved by the screw until the index attached to the attracted disk
+  shows it to be in the sighted position. Let the screw readings in the
+  two cases be d and d'. If W is the weight required to depress the
+  attracted disk into the same sighted position when the plates are
+  unelectrified and g is the acceleration of gravity, then the
+  difference of potentials of the conductors tested is expressed by the
+  formula
+                         _______
+                        /8[pi]gW
+    V - V' = (d - d')  / -------,
+                     \/     S
+
+  where S denotes the area of the attracted disk.
+
+  The difference of potentials is thus determined in terms of a weight,
+  an area and a distance, in absolute C.G.S. measure or electrostatic
+  units.
+
+[Illustration: FIG. 5.]
+
+_Symmetrical Electrometers_ include the dry pile electrometer and
+Kelvin's quadrant electrometer. The principle underlying these
+instruments is that we can measure differences of potential by means of
+the motion of an electrified body in a symmetrical field of electric
+force. In the dry pile electrometer a single gold-leaf is hung up
+between two plates which are connected to the opposite terminals of a
+dry pile so that a certain constant difference of potential exists
+between these plates. The original inventor of this instrument was
+T.G.B. Behrens (_Gilb. Ann._, 1806, 23), but it generally bears the name
+of J.G.F. von Bohnenberger, who slightly modified its form. G.T. Fechner
+introduced the important improvement of using only one pile, which he
+removed from the immediate neighbourhood of the suspended leaf. W.G.
+Hankel still further improved the dry pile electrometer by giving a slow
+motion movement to the two plates, and substituted a galvanic battery
+with a large number of cells for the dry pile, and also employed a
+divided scale to measure the movements of the gold-leaf (_Pogg. Ann._,
+1858, 103). If the gold-leaf is unelectrified, it is not acted upon by
+the two plates placed at equal distances on either side of it, but if
+its potential is raised or lowered it is attracted by one disk and
+repelled by the other, and the displacement becomes a measure of its
+potential.
+
+[Illustration: FIG. 6.--Kelvin's Quadrant Electrometer.]
+
+A vast improvement in this instrument was made by the invention of the
+quadrant electrometer by Lord Kelvin, which is the most sensitive form
+of electrometer yet devised. In this instrument (see fig. 5) a flat
+paddle-shaped needle of aluminium foil U is supported by a bifilar
+suspension consisting of two cocoon fibres. This needle is suspended in
+the interior of a glass vessel partly coated with tin-foil on the
+outside and inside, forming therefore a Leyden jar (see fig. 6). In the
+bottom of the vessel is placed some sulphuric acid, and a platinum wire
+attached to the suspended needle dips into this acid. By giving a charge
+to this Leyden jar the needle can thus be maintained at a certain
+constant high potential. The needle is enclosed by a sort of flat box
+divided into four insulated quadrants A, B, C, D (fig. 5), whence the
+name. The opposite quadrants are connected together by thin platinum
+wires. These quadrants are insulated from the needle and from the case,
+and the two pairs are connected to two electrodes. When the instrument
+is to be used to determine the potential difference between two
+conductors, they are connected to the two opposite pairs of quadrants.
+The needle in its normal position is symmetrically placed with regard to
+the quadrants, and carries a mirror by means of which its displacement
+can be observed in the usual manner by reflecting the ray of light from
+it. If the two quadrants are at different potentials, the needle moves
+from one quadrant towards the other, and the image of a spot of light on
+the scale is therefore displaced. Lord Kelvin provided the instrument
+with two necessary adjuncts, viz. a replenisher or rotating
+electrophorus (q.v.), by means of which the charge of the Leyden jar
+which forms the enclosing vessel can be increased or diminished, and
+also a small aluminium balance plate or gauge, which is in principle the
+same as the attracted disk portable electrometer by means of which the
+potential of the inner coating of the Leyden jar is preserved at a known
+value.
+
+  According to the mathematical theory of the instrument,[3] if V and V'
+  are the potentials of the quadrants and v is the potential of the
+  needle, then the torque acting upon the needle to cause rotation is
+  given by the expression,
+
+    C(V - V') {v - ½(V + V')},
+
+  where C is some constant. If v is very large compared with the mean
+  value of the potentials of the two quadrants, as it usually is, then
+  the above expression indicates that the couple varies as the
+  difference of the potentials between the quadrants.
+
+  Dr J. Hopkinson found, however, before 1885, that the above formula
+  does not agree with observed facts (_Proc. Phys. Soc. Lond._, 1885, 7,
+  p. 7). The formula indicates that the sensibility of the instrument
+  should increase with the charge of the Leyden jar or needle, whereas
+  Hopkinson found that as the potential of the needle was increased by
+  working the replenisher of the jar, the deflection due to three volts
+  difference between the quadrants first increased and then diminished.
+  He found that when the potential of the needle exceeded a certain
+  value, of about 200 volts, for the particular instrument he was using
+  (made by White of Glasgow), the above formula did not hold good. W.E.
+  Ayrton, J. Perry and W.E. Sumpner, who in 1886 had noticed the same
+  fact as Hopkinson, investigated the matter in 1891 (_Proc. Roy. Soc._,
+  1891, 50, p. 52; _Phil. Trans._, 1891, 182, p. 519). Hopkinson had
+  been inclined to attribute the anomaly to an increase in the tension
+  of the bifilar threads, owing to a downward pull on the needle, but
+  they showed that this theory would not account for the discrepancy.
+  They found from observations that the particular quadrant electrometer
+  they used might be made to follow one or other of three distinct laws.
+  If the quadrants were near together there were certain limits between
+  which the potential of the needle might vary without producing more
+  than a small change in the deflection corresponding with the fixed
+  potential difference of the quadrants. For example, when the quadrants
+  were about 2.5 mm. apart and the suspended fibres near together at the
+  top, the deflection produced by a P.D. of 1.45 volts between the
+  quadrants only varied about 11% when the potential of the needle
+  varied from 896 to 3586 volts. When the fibres were far apart at the
+  top a similar flatness was obtained in the curve with the quadrants
+  about 1 mm. apart. In this case the deflection of the needle was
+  practically quite constant when its potential varied from 2152 to 3227
+  volts. When the quadrants were about 3.9 mm. apart, the deflection for
+  a given P.D. between the quadrants was almost directly proportional to
+  the potential of the needle. In other words, the electrometer nearly
+  obeyed the theoretical law. Lastly, when the quadrants were 4 mm. or
+  more apart, the deflection increased much more rapidly than the
+  potential, so that a maximum sensibility bordering on instability was
+  obtained. Finally, these observers traced the variation to the fact
+  that the wire supporting the aluminium needle as well as the wire
+  which connects the needle with the sulphuric acid in the Leyden jar in
+  the White pattern of Leyden jar is enclosed in a metallic guard tube
+  to screen the wire from external action. In order that the needle may
+  project outside the guard tube, openings are made in its two sides;
+  hence the moment the needle is deflected each half of it becomes
+  unsymmetrically placed relatively to the two metallic pieces which
+  join the upper and lower half of the guard tube. Guided by these
+  experiments, Ayrton, Perry and Sumpner constructed an improved
+  unifilar quadrant electrometer which was not only more sensitive than
+  the White pattern, but fulfilled the theoretical law of working. The
+  bifilar suspension was abandoned, and instead a new form of adjustable
+  magnetic control was adopted. All the working parts of the instrument
+  were supported on the base, so that on removing a glass shade which
+  serves as a Leyden jar they can be got at and adjusted in position.
+  The conclusion to which the above observers came was that any quadrant
+  electrometer made in any manner does not necessarily obey a law of
+  deflection making the deflections proportional to the potential
+  difference of the quadrants, but that an electrometer can be
+  constructed which does fulfil the above law.
+
+  The importance of this investigation resides in the fact that an
+  electrometer of the above pattern can be used as a wattmeter (q.v.),
+  provided that the deflection of the needle is proportional to the
+  potential difference of the quadrants. This use of the instrument was
+  proposed simultaneously in 1881 by Professors Ayrton and G.F.
+  Fitzgerald and M.A. Potier. Suppose we have an inductive and a
+  non-inductive circuit in series, which is traversed by a periodic
+  current, and that we desire to know the power being absorbed to the
+  inductive circuit. Let v1, v2, v3 be the instantaneous potentials of
+  the two ends and middle of the circuit; let a quadrant electrometer be
+  connected first with the quadrants to the two ends of the inductive
+  circuit and the needle to the far end of the non-inductive circuit,
+  and then secondly with the needle connected to one of the quadrants
+  (see fig. 5). Assuming the electrometer to obey the above-mentioned
+  theoretical law, the first reading is proportional to
+
+             /     v1 + v2\
+    v1 - v2 ( v3 - ------- )
+             \        2   /
+
+  and the second to
+
+             /     v1 + v2\
+    v1 - v2 ( v2 - ------- ).
+             \        2   /
+
+  The difference of the readings is then proportional to
+
+    (v1 - v2)(v2 - v3).
+
+  But this last expression is proportional to the instantaneous power
+  taken up in the inductive circuit, and hence the difference of the two
+  readings of the electrometer is proportional to the mean power taken
+  up in the circuit (_Phil. Mag._, 1891, 32, p. 206). Ayrton and Perry
+  and also P.R. Blondlot and P. Curie afterwards suggested that a single
+  electrometer could be constructed with two pairs of quadrants and a
+  duplicate needle on one stem, so as to make two readings
+  simultaneously and produce a deflection proportional at once to the
+  power being taken up in the inductive circuit.
+
+[Illustration: FIG. 7.--Quadrant Electrometer. Dolezalek Pattern.]
+
+Quadrant electrometers have also been designed especially for measuring
+extremely small potential differences. An instrument of this kind has
+been constructed by Dr. F. Dolezalek (fig. 7). The needle and quadrants
+are of small size, and the electrostatic capacity is correspondingly
+small. The quadrants are mounted on pillars of amber which afford a very
+high insulation. The needle, a piece of paddle-shaped paper thinly
+coated with silver foil, is suspended by a quartz fibre, its extreme
+lightness making it possible to use a very feeble controlling force
+without rendering the period of oscillation unduly great. The resistance
+offered by the air to a needle of such light construction suffices to
+render the motion nearly dead-beat. Throughout a wide range the
+deflections are proportional to the potential difference producing them.
+The needle is charged to a potential of 50 to 200 volts by means of a
+dry pile or voltaic battery, or from a lighting circuit. To facilitate
+the communication of the charge to the needle, the quartz fibre and its
+attachments are rendered conductive by a thin film of solution of
+hygroscopic salt such as calcium chloride. The lightness of the needle
+enables the instrument to be moved without fear of damaging the
+suspension. The upper end of the quartz fibre is rotated by a torsion
+head, and a metal cover serves to screen the instrument from stray
+electrostatic fields. With a quartz fibre 0.009 mm. thick and 60 mm.
+long, the needle being charged to 110 volts, the period and swing of the
+needle was 18 seconds. With the scale at a distance of two metres, a
+deflection of 130 mm. was produced by an electromotive force of 0.1
+volt. By using a quartz fibre of about half the above diameter the
+sensitiveness was much increased. An instrument of this form is valuable
+in measuring small alternating currents by the fall of potential
+produced down a known resistance. In the same way it may be employed to
+measure high potentials by measuring the fall of potential down a
+fraction of a known non-inductive resistance. In this last case,
+however, the capacity of the electrometer used must be small, otherwise
+an error is introduced.[4]
+
+  See, in addition to references already given, A. Gray, _Absolute
+  Measurements in Electricity and Magnetism_ (London, 1888), vol. i. p.
+  254; A. Winkelmann, _Handbuch der Physik_ (Breslau, 1905), pp. 58-70,
+  which contains a large number of references to original papers on
+  electrometers.     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] It is probable that an experiment of this kind had been made as
+    far back as 1746 by Daniel Gralath, of Danzig, who has some claims to
+    have suggested the word "electrometer" in connexion with it. See Park
+    Benjamin, _The Intellectual Rise in Electricity_ (London, 1895), p.
+    542.
+
+  [2] See Maxwell, _Treatise on Electricity and Magnetism_ (2nd ed.),
+    i. 308.
+
+  [3] See Maxwell, _Electricity and Magnetism_ (2nd ed., Oxford, 1881),
+    vol. i. p. 311.
+
+  [4] See J.A. Fleming, _Handbook for the Electrical Laboratory and
+    Testing Room_, vol. i. p. 448 (London, 1901).
+
+
+
+
+ELECTRON, the name suggested by Dr G. Johnstone Stoney in 1891 for the
+natural unit of electricity to which he had drawn attention in 1874, and
+subsequently applied to the ultra-atomic particles carrying negative
+charges of electricity, of which Professor Sir J.J. Thomson proved in
+1897 that the cathode rays consisted. The electrons, which Thomson at
+first called corpuscles, are point charges of negative electricity,
+their inertia showing them to have a mass equal to about {1/2000} that
+of the hydrogen atom. They are apparently derivable from all kinds of
+matter, and are believed to be components at any rate of the chemical
+atom. The electronic theory of the chemical atom supposes, in fact, that
+atoms are congeries of electrons in rapid orbital motion. The size of
+the electron is to that of an atom roughly in the ratio of a pin's head
+to the dome of St Paul's cathedral. The electron is always associated
+with the unit charge of negative electricity, and it has been suggested
+that its inertia is wholly electrical. For further details see the
+articles on ELECTRICITY; MAGNETISM; MATTER; RADIOACTIVITY; CONDUCTION,
+ELECTRIC; _The Electron Theory_, E. Fournier d'Albe (London, 1907); and
+the original papers of Dr G. Johnstone Stoney, _Proc. Brit. Ass._
+(Belfast, August 1874), "On the Physical Units of Nature," and _Trans.
+Royal Dublin Society_ (1891), 4, p. 583.
+
+
+
+
+ELECTROPHORUS, an instrument invented by Alessandro Volta in 1775, by
+which mechanical work is transformed into electrostatic charge by the
+aid of a small initial charge of electricity. The operation depends on
+the facts of electrostatic induction discovered by John Canton in 1753,
+and, independently, by J.K. Wilcke in 1762 (see ELECTRICITY). Volta, in
+a letter to J. Priestley on the 10th of June 1775 (see _Collezione dell'
+opere_, ed. 1816, vol. i. p. 118), described the invention of a device
+he called an _elettroforo perpetuo_, based on the fact that a conductor
+held near an electrified body and touched by the finger was found, when
+withdrawn, to possess an electric charge of opposite sign to that of the
+electrified body. His electrophorus in one form consisted of a disk of
+non-conducting material, such as pitch or resin, placed between two
+metal sheets, one being provided with an insulating handle. For the
+pitch or resin may be substituted a sheet of glass, ebonite,
+india-rubber or any other good dielectric placed upon a metallic sheet,
+called the sole-plate. To use the apparatus the surface of the
+dielectric is rubbed with a piece of warm flannel, silk or catskin, so
+as to electrify it, and the upper metal plate is then placed upon it.
+Owing to the irregularities in the surfaces of the dielectric and upper
+plate the two are only in contact at a few points, and owing to the
+insulating quality of the dielectric its surface electrical charge
+cannot move over it. It therefore acts inductively upon the upper plate
+and induces on the adjacent surface an electric charge of opposite sign.
+Suppose, for instance, that the dielectric is a plate of resin rubbed
+with catskin, it will then be negatively electrified and will act by
+induction on the upper plate across the film of air separating the upper
+resin surface and lower surface of the upper metal plate. If the upper
+plate is touched with the finger or connected to earth for a moment, a
+negative charge will escape from the metal plate to earth at that
+moment. The arrangement thus constitutes a condenser; the upper plate on
+its under surface carries a charge of positive electricity and the resin
+plate a charge of negative electricity on its upper surface, the air
+film between them being the dielectric of the condenser. If, therefore,
+the upper plate is elevated, mechanical work has to be done to separate
+the two electric charges. Accordingly on raising the upper plate, the
+charge on it, in old-fashioned nomenclature, becomes _free_ and can be
+communicated to any other insulated conductor at a lower potential, the
+upper plate thereby becoming more or less discharged. On placing the
+upper plate again on the resin and touching it for a moment, the process
+can be repeated, and so at the expense of mechanical work done in
+lifting the upper plate against the mutual attraction of two electric
+charges of opposite sign, an indefinitely large electric charge can be
+accumulated and given to any other suitable conductor. In course of
+time, however, the surface charge of the resin becomes dissipated and it
+then has to be again excited. To avoid the necessity for touching the
+upper plate every time it is put down on the resin, a metal pin may be
+brought through the insulator from the sole-plate so that each time that
+the upper plate is put down on the resin it is automatically connected
+to earth. We are thus able by a process of merely lifting the upper
+plate repeatedly to convey a large electrical charge to some conductor
+starting from the small charge produced by friction on the resin. The
+above explanation does not take into account the function of the
+sole-plate, which is important. The sole-plate serves to increase the
+electrical capacity of the upper plate when placed down upon the resin
+or excited insulator. Hence when so placed it takes a larger charge.
+When touched by the finger the upper plate is brought to zero potential.
+If then the upper plate is lifted by its insulating handle its capacity
+becomes diminished. Since, however, it carries with it the charge it had
+when resting on the resin, its potential becomes increased as its
+capacity becomes less, and it therefore rises to a high potential, and
+will give a spark if the knuckle is approached to it when it is lifted
+after having been touched and raised.
+
+The study of Volta's electrophorus at once suggested the performance of
+these cyclical operations by some form of rotation instead of elevation,
+and led to the invention of various forms of doubler or multiplier. The
+instrument was thus the first of a long series of machines for
+converting mechanical work into electrostatic energy, and the
+predecessor of the modern type of influence machine (see ELECTRICAL
+MACHINE). Volta himself devised a double and reciprocal electrophorus
+and also made mention of the subject of multiplying condensers in a
+paper published in the _Phil. Trans._ for 1782 (p. 237, and appendix, p.
+vii.). He states, however, that the use of a condenser in connexion with
+an electrophorus to make evident and multiply weak charges was due to T.
+Cavallo (_Phil. Trans._, 1788).
+
+  For further information see S.P. Thompson, "The Influence Machine from
+  1788 to 1888," _Journ. Inst. Tel. Eng._, 1888, 17, p. 569. Many
+  references to original papers connected with the electrophorus will be
+  found in A. Winkelmann's _Handbuch der Physik_ (Breslau, 1905), vol.
+  iv. p. 48.     (J. A. F.)
+
+
+
+
+ELECTROPLATING, the art of depositing metals by the electric current. In
+the article ELECTROLYSIS it is shown how the passage of an electric
+current through a solution containing metallic ions involves the
+deposition of the metal on the cathode. Sometimes the metal is deposited
+in a pulverulent form, at others as a firm tenacious film, the nature of
+the deposit being dependent upon the particular metal, the concentration
+of the solution, the difference of potential between the electrodes, and
+other experimental conditions. As the durability of the
+electro-deposited coat on plated wares of all kinds is of the utmost
+importance, the greatest care must be taken to ensure its complete
+adhesion. This can only be effected if the surface of the metal on which
+the deposit is to be made is chemically clean. Grease must be removed by
+potash, whiting or other means, and tarnish by an acid or potassium
+cyanide, washing in plenty of water being resorted to after each
+operation. The vats for depositing may be of enamelled iron, slate,
+glazed earthenware, glass, lead-lined wood, &c. The current densities
+and potential differences frequently used for some of the commoner
+metals are given in the following table, taken from M'Millan's _Treatise
+on Electrometallurgy_. It must be remembered, however, that variations
+in conditions modify the electromotive force required for any given
+process. For example, a rise in temperature of the bath causes an
+increase in its conductivity, so that a lower E.M.F. will suffice to
+give the required current density; on the other hand, an abnormally
+great distance between the electrodes, or a diminution in acidity of an
+acid bath, or in the strength of the solution used, will increase the
+resistance, and so require the application of a higher E.M.F.
+
+  +----------------------+------------------------------------+---------------+
+  |                      |               Amperes.             |               |
+  |                      +-------------------+----------------+ Volts between |
+  |        Metal.        | Per sq. decimetre | Per sq. in. of |   Anode and   |
+  |                      |    of Cathode     |    Cathode     |    Cathode.   |
+  |                      |      Surface.     |    Surface.    |               |
+  +----------------------+-------------------+----------------+---------------+
+  | Antimony             |      0.4-0.5      |    0.02-0.03   |    1.0-1.2    |
+  | Brass                |      0.5-0.8      |    0.03-0.05   |    3.0-4.0    |
+  | Copper, acid bath    |      1.0-1.5      |   0.065-0.10   |    0.5-1.5    |
+  |   "     alkaline bath|      0.3-0.5      |    0.02-0.03   |    3.0-5.0    |
+  | Gold                 |        0.1        |     0.006      |    0.5-4.0    |
+  | Iron                 |        0.5        |      0.03      |      1.0      |
+  | Nickel, at first     |      1.4-1.5      |    0.09-0.10   |      5.0      |
+  |   "     after        |      0.2-0.3      |   0.015-0.02   |    1.5-2.0    |
+  |   "     on zinc      |        0.4        |     0.025      |    4.0-5.0    |
+  | Silver               |      0.2-0.5      |   0.015-0.03   |   0.75-1.0    |
+  | Zinc                 |      0.3-0.6      |    0.02-0.04   |    2.5-3.0    |
+  +----------------------+-------------------+----------------+---------------+
+
+Large objects are suspended in the tanks by hooks or wires, care being
+taken to shift their position and so avoid wire-marks. Small objects are
+often heaped together in perforated trays or ladles, the cathode
+connecting-rod being buried in the midst of them. These require constant
+shifting because the objects are in contact at many points, and because
+the top ones shield those below from the depositing action of the
+current. Hence processes have been patented in which the objects to be
+plated are suspended in revolving drums between the anodes, the rotation
+of the drum causing the constant renewal of surfaces and affording a
+burnishing action at the same time. Care must be taken not to expose
+goods in the plating-bath to too high a current density, else they may
+be "burnt"; they must never be exposed one at a time to the full anode
+surface, with the current flowing in an empty bath, but either one piece
+at a time should be replaced, or some of the anodes should be
+transferred temporarily to the place of the cathodes, in order to
+distribute the current over a sufficient cathode-area. Burnt deposits
+are dark-coloured, or even pulverulent and useless. The strength of the
+current may also be regulated by introducing lengths of German silver or
+iron wire, carbon rod, or other inferior conductors in the path of the
+current, and a series of such resistances should always be provided
+close to the tanks. Ammeters to measure the volume, and voltmeters to
+determine the pressure of current supplied to the baths, should also be
+provided. Very irregular surfaces may require the use of specially
+shaped anodes in order that the distance between the electrodes may be
+fairly uniform, otherwise the portion of the cathode lying nearest to
+the anode may receive an undue share of the current, and therefore a
+greater thickness of coat. Supplementary anodes are sometimes used in
+difficult cases of this kind. Large metallic surfaces (especially
+external surfaces) are sometimes plated by means of a "doctor," which,
+in its simplest form, is a brush constantly wetted with the electrolyte,
+with a wire anode buried amid the hairs or bristles; this brush is
+painted slowly over the surface of the metal to be coated, which must be
+connected to the negative terminal of the electrical generator. Under
+these conditions electrolysis of the solution in the brush takes place.
+Iron ships' plates have recently been coated with copper in sections (to
+prevent the adhesion of barnacles), by building up a temporary trough
+against the side of the ship, making the thoroughly cleansed plate act
+both as cathode and as one side of the trough. Decorative plating-work
+in several colours (e.g. "parcel-gilding") is effected by painting a
+portion of an object with a stopping-out (i.e. a non-conducting)
+varnish, such as copal varnish, so that this portion is not coated. The
+varnish is then removed, a different design stopped out, and another
+metal deposited. By varying this process, designs in metals of different
+colours may readily be obtained.
+
+Reference must be made to the textbooks (see ELECTROCHEMISTRY) for a
+fuller account of the very varied solutions and methods employed for
+electroplating with silver, gold, copper, iron and nickel. It should be
+mentioned here, however, that solutions which would deposit their metal
+on any object by simple immersion should not be generally used for
+electroplating that object, as the resulting deposit is usually
+non-adhesive. For this reason the acid copper-bath is not used for iron
+or zinc objects, a bath containing copper cyanide or oxide dissolved in
+potassium cyanide being substituted. This solution, being an inferior
+conductor of electricity, requires a much higher electromotive force to
+drive the current through it, and is therefore more costly in use. It
+is, however, commonly employed hot, whereby its resistance is reduced.
+_Zinc_ is commonly deposited by electrolysis on iron or steel goods
+which would ordinarily be "galvanized," but which for any reason may not
+conveniently be treated by the method of immersion in fused zinc. The
+zinc cyanide bath may be used for small objects, but for heavy goods the
+sulphate bath is employed. Sherard Cowper-Coles patented a process in
+which, working with a high current density, a lead anode is used, and
+powdered zinc is kept suspended in the solution to maintain the
+proportion of zinc in the electrolyte, and so to guard against the
+gradual acidification of the bath. _Cobalt_ is deposited by a method
+analogous to that used for its sister-metal nickel. _Platinum_,
+_palladium_ and _tin_ are occasionally deposited for special purposes.
+In the deposition of _gold_ the colour of the deposit is influenced by
+the presence of impurities in the solution; when copper is present, some
+is deposited with the gold, imparting to it a reddish colour, whilst a
+little silver gives it a greenish shade. Thus so-called coloured-gold
+deposits may be produced by the judicious introduction of suitable
+impurities. Even pure gold, it may be noted, is darker or lighter in
+colour according as a stronger or a weaker current is used. The
+electro-deposition of _brass_--mainly on iron ware, such as bedstead
+tubes--is now very widely practised, the bath employed being a mixture
+of copper, zinc and potassium cyanides, the proportions of which vary
+according to the character of the brass required, and to the mode of
+treatment. The colour depends in part upon the proportion of copper and
+zinc, and in part upon the current density, weaker currents tending to
+produce a redder or yellower metal. Other alloys may be produced, such
+as bronze, or German silver, by selecting solutions (usually cyanides)
+from which the current is able to deposit the constituent metals
+simultaneously.
+
+Electrolysis has in a few instances been applied to processes of
+manufacture. For example, Wilde produced copper printing surfaces for
+calico printing-rollers and the like by immersing rotating iron
+cylinders as cathodes in a copper bath. Elmore, Dumoulin, Cowper-Coles
+and others have prepared copper cylinders and plates by depositing
+copper on rotating mandrels with special arrangements. Others have
+arranged a means of obtaining high conductivity wire from cathode-copper
+without fusion, by depositing the metal in the form of a spiral strip on
+a cylinder, the strip being subsequently drawn down in the usual way; at
+present, however, the ordinary methods of wire production are found to
+be cheaper. J.W. Swan (_Journ. Inst. Elec. Eng._, 1898, vol. xxvii. p.
+16) also worked out, but did not proceed with, a process in which a
+copper wire whilst receiving a deposit of copper was continuously passed
+through the draw-plate, and thus indefinitely extended in length.
+Cowper-Coles (_Journ. Inst. Elec. Eng._, 1898, 27, p. 99) very
+successfully produced true parabolic reflectors for projectors, by
+depositing copper upon carefully ground and polished glass surfaces
+rendered conductive by a film of deposited silver.
+
+
+
+
+ELECTROSCOPE, an instrument for detecting differences of electric
+potential and hence electrification. The earliest form of scientific
+electroscope was the _versorium_ or electrical needle of William Gilbert
+(1544-1603), the celebrated author of the treatise _De magnete_ (see
+ELECTRICITY). It consisted simply of a light metallic needle balanced on
+a pivot like a compass needle. Gilbert employed it to prove that
+numerous other bodies besides amber are susceptible of being electrified
+by friction.[1] In this case the visible indication consisted in the
+attraction exerted between the electrified body and the light pivoted
+needle which was acted upon and electrified by induction. The next
+improvement was the invention of simple forms of repulsion electroscope.
+Two similarly electrified bodies repel each other. Benjamin Franklin
+employed the repulsion of two linen threads, C.F. de C. du Fay, J.
+Canton, W. Henley and others devised the pith ball, or double straw
+electroscope (fig. 1). T. Cavallo about 1770 employed two fine silver
+wires terminating in pith balls suspended in a glass vessel having
+strips of tin-foil pasted down the sides (fig. 2). The object of the
+thimble-shaped dome was to keep moisture from the stem from which the
+pith balls were supported, so that the apparatus could be used in the
+open air even in the rainy weather. Abraham Bennet (_Phil. Trans._,
+1787, 77, p. 26) invented the modern form of gold-leaf electroscope.
+Inside a glass shade he fixed to an insulated wire a pair of strips of
+gold-leaf (fig. 3). The wire terminated in a plate or knob outside the
+vessel. When an electrified body was held near or in contact with the
+knob, repulsion of the gold leaves ensued. Volta added the condenser
+(_Phil. Trans._, 1782), which greatly increased the power of the
+instrument. M. Faraday, however, showed long subsequently that to bestow
+upon the indications of such an electroscope definite meaning it was
+necessary to place a cylinder of metallic gauze connected to the earth
+inside the vessel, or better still, to line the glass shade with
+tin-foil connected to the earth and observe through a hole the
+indications of the gold leaves (fig. 4). Leaves of aluminium foil may
+with advantage be substituted for gold-leaf, and a scale is sometimes
+added to indicate the angular divergence of the leaves.
+
+[Illustration: FIG. 1.--Henley's Electroscope.]
+
+[Illustration: FIG. 2.--Cavallo's Electroscope.]
+
+[Illustration: FIG. 3.--Bennet's Electroscope.]
+
+The uses of an electroscope are, first, to ascertain if any body is in a
+state of electrification, and secondly, to indicate the sign of that
+charge. In connexion with the modern study of radioactivity, the
+electroscope has become an instrument of great usefulness, far
+outrivalling the spectroscope in sensibility. Radio-active bodies are
+chiefly recognized by the power they possess of rendering the air in
+their neighbourhood conductive; hence the electroscope detects the
+presence of a radioactive body by losing an electric charge given to it
+more quickly than it would otherwise do. A third great use of the
+electroscope is therefore to detect electric conductivity either in the
+air or in any other body.
+
+[Illustration: FIG. 4.--Gold-Leaf Electroscope.]
+
+To detect electrification it is best to charge the electroscope by
+induction. If an electrified body is held near the gold-leaf
+electroscope the leaves diverge with electricity of the same sign as
+that of the body being tested. If, without removing the electrified
+body, the plate or knob of the electroscope is touched, the leaves
+collapse. If the electroscope is insulated once more and the electrified
+body removed, the leaves again diverge with electricity of the opposite
+sign to that of the body being tested. The sign of charge is then
+determined by holding near the electroscope a glass rod rubbed with silk
+or a sealing-wax rod rubbed with flannel. If the approach of the glass
+rod causes the leaves in their final state to collapse, then the charge
+in the rod was positive, but if it causes them to expand still more the
+charge was negative, and vice versa for the sealing-wax rod. When
+employing a Volta condensing electroscope, the following is the method
+of procedure:--The top of the electroscope consists of a flat, smooth
+plate of lacquered brass on which another plate of brass rests,
+separated from it by three minute fragments of glass or shellac, or a
+film of shellac varnish. If the electrified body is touched against the
+upper plate whilst at the same time the lower plate is put to earth, the
+condenser formed of the two plates and the film of air or varnish
+becomes charged with positive electricity on the one plate and negative
+on the other. On insulating the lower plate and raising the upper plate
+by the glass handle, the capacity of the condenser formed by the plates
+is vastly decreased, but since the charge on the lower plate including
+the gold leaves attached to it remains the same, as the capacity of the
+system is reduced the potential is raised and therefore the gold leaves
+diverge widely. Volta made use of such an electroscope in his celebrated
+experiments (1790-1800) to prove that metals placed in contact with one
+another are brought to different potentials, in other words to prove the
+existence of so-called contact electricity. He was assisted to detect
+the small potential differences then in question by the use of a
+multiplying condenser or revolving doubler (see ELECTRICAL MACHINE). To
+employ the electroscope as a means of detecting radioactivity, we have
+first to test the leakage quality of the electroscope itself. Formerly
+it was usual to insulate the rod of the electroscope by passing it
+through a hole in a cork or mass of sulphur fixed in the top of the
+glass vessel within which the gold leaves were suspended. A further
+improvement consisted in passing the metal wire to which the gold leaves
+were attached through a glass tube much wider than the rod, the latter
+being fixed concentrically in the glass tube by means of solid shellac
+melted and run in. This insulation, however, is not sufficiently good
+for an electroscope intended for the detection of radioactivity; for
+this purpose it must be such that the leaves will remain for hours or
+days in a state of steady divergence when an electrical charge has been
+given to them.
+
+In their researches on radioactivity M. and Mme P. Curie employed an
+electroscope made as follows:--A metal case (fig. 5), having two holes
+in its sides, has a vertical brass strip B attached to the inside of the
+lid by a block of sulphur SS or any other good insulator. Joined to the
+strip is a transverse wire terminating at one end in a knob C, and at
+the other end in a condenser plate P'. The strip B carries also a strip
+of gold-leaf L, and the metal case is connected to earth. If a charge is
+given to the electroscope, and if any radioactive material is placed on
+a condenser plate P attached to the outer case, then this substance
+bestows conductivity on the air between the plates P and P', and the
+charge of the electroscope begins to leak away. The collapse of the
+gold-leaf is observed through an aperture in the case by a microscope,
+and the time taken by the gold-leaf to fall over a certain distance is
+proportional to the ionizing current, that is, to the intensity of the
+radioactivity of the substance.
+
+[Illustration: FIG. 5.--Curie's Electroscope.]
+
+A very similar form of electroscope was employed by J.P.L.J. Elster and
+H.F.K. Geitel (fig. 6), and also by C.T.R. Wilson (see _Proc. Roy.
+Soc._, 1901, 68, p. 152). A metal box has a metal strip B suspended from
+a block or insulator by means of a bit of sulphur or amber S, and to it
+is fastened a strip of gold-leaf L. The electroscope is provided with a
+charging rod C. In a dry atmosphere sulphur or amber is an early perfect
+insulator, and hence if the air in the interior of the box is kept dry
+by calcium chloride, the electroscope will hold its charge for a long
+time. Any divergence or collapse of the gold-leaf can be viewed by a
+microscope through an aperture in the side of the case.
+
+[Illustration: FIG. 6.--Elster and Geitel Electroscope.]
+
+[Illustration: FIG. 7.--Wilson's Electroscope.]
+
+Another type of sensitive electroscope is one devised by C.T.R. Wilson
+(_Proc. Cam. Phil. Soc._, 1903, 12, part 2). It consists of a metal box
+placed on a tilting stand (fig. 7). At one end is an insulated plate P
+kept at a potential of 200 volts or so above the earth by a battery. At
+the other end is an insulated metal wire having attached to it a thin
+strip of gold-leaf L. If the plate P is electrified it attracts the
+strip which stretches out towards it. Before use the strip is for one
+moment connected to the case, and the arrangement is then tilted until
+the strip extends at a certain angle. If then the strip of gold-leaf is
+raised or lowered in potential it moves to or from the plate P, and its
+movement can be observed by a microscope through a hole in the side of
+the box. There is a particular angle of tilt of the case which gives a
+maximum sensitiveness. Wilson found that with the plate electrified to
+207 volts and with a tilt of the case of 30°, if the gold-leaf was
+raised one volt in potential above the case, it moved over 200 divisions
+of the micrometer scale in the eye-piece of the microscope, 54 divisions
+being equal to one millimetre. In using the instrument the insulated rod
+to which the gold-leaf is attached is connected to the conductor, the
+potential of which is being examined. In the use of all these
+electroscopic instruments it is essential to bear in mind (as first
+pointed out by Lord Kelvin) that what a gold-leaf electroscope really
+indicates is the difference of potential between the gold-leaf and the
+solid walls enclosing the air space in which they move.[2] If these
+enclosing walls are made of anything else than perfectly conducting
+material, then the indications of the instrument may be uncertain and
+meaningless. As already mentioned, Faraday remedied this defect by
+coating the inside of the glass vessel in which the gold-leaves were
+suspended to form an electroscope with tinfoil (see fig. 4). In spite of
+these admonitions all but a few instrument makers have continued to make
+the vicious type of instrument consisting of a pair of gold-leaves
+suspended within a glass shade or bottle, no means being provided for
+keeping the walls of the vessel continually at zero potential.
+
+  See J. Clerk Maxwell, _Treatise on Electricity and Magnetism_, vol. i.
+  p. 300 (2nd ed., Oxford, 1881); H.M. Noad, _A Manual of Electricity_,
+  vol. i. p. 25 (London, 1855); E. Rutherford, _Radioactivity_.
+       (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] See the English translation by the Gilbert Club of Gilbert's _De
+    magnete_, p. 49 (London, 1900).
+
+  [2] See Lord Kelvin, "Report on Electrometers and Electrostatic
+    Measurements," _Brit. Assoc. Report_ for 1867, or Lord Kelvin's
+    _Reprint of Papers on Electrostatics and Magnetism_, p. 260.
+
+
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 9, Slice 2, by Various
+
+*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 9 SL 2 ***
+
+***** This file should be named 35092-8.txt or 35092-8.zip *****
+This and all associated files of various formats will be found in:
+        https://www.gutenberg.org/3/5/0/9/35092/
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+Updated editions will replace the previous one--the old editions
+will be renamed.
+
+Creating the works from public domain print editions means that no
+one owns a United States copyright in these works, so the Foundation
+(and you!) can copy and distribute it in the United States without
+permission and without paying copyright royalties.  Special rules,
+set forth in the General Terms of Use part of this license, apply to
+copying and distributing Project Gutenberg-tm electronic works to
+protect the PROJECT GUTENBERG-tm concept and trademark.  Project
+Gutenberg is a registered trademark, and may not be used if you
+charge for the eBooks, unless you receive specific permission.  If you
+do not charge anything for copies of this eBook, complying with the
+rules is very easy.  You may use this eBook for nearly any purpose
+such as creation of derivative works, reports, performances and
+research.  They may be modified and printed and given away--you may do
+practically ANYTHING with public domain eBooks.  Redistribution is
+subject to the trademark license, especially commercial
+redistribution.
+
+
+
+*** START: FULL LICENSE ***
+
+THE FULL PROJECT GUTENBERG LICENSE
+PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK
+
+To protect the Project Gutenberg-tm mission of promoting the free
+distribution of electronic works, by using or distributing this work
+(or any other work associated in any way with the phrase "Project
+Gutenberg"), you agree to comply with all the terms of the Full Project
+Gutenberg-tm License (available with this file or online at
+https://gutenberg.org/license).
+
+
+Section 1.  General Terms of Use and Redistributing Project Gutenberg-tm
+electronic works
+
+1.A.  By reading or using any part of this Project Gutenberg-tm
+electronic work, you indicate that you have read, understand, agree to
+and accept all the terms of this license and intellectual property
+(trademark/copyright) agreement.  If you do not agree to abide by all
+the terms of this agreement, you must cease using and return or destroy
+all copies of Project Gutenberg-tm electronic works in your possession.
+If you paid a fee for obtaining a copy of or access to a Project
+Gutenberg-tm electronic work and you do not agree to be bound by the
+terms of this agreement, you may obtain a refund from the person or
+entity to whom you paid the fee as set forth in paragraph 1.E.8.
+
+1.B.  "Project Gutenberg" is a registered trademark.  It may only be
+used on or associated in any way with an electronic work by people who
+agree to be bound by the terms of this agreement.  There are a few
+things that you can do with most Project Gutenberg-tm electronic works
+even without complying with the full terms of this agreement.  See
+paragraph 1.C below.  There are a lot of things you can do with Project
+Gutenberg-tm electronic works if you follow the terms of this agreement
+and help preserve free future access to Project Gutenberg-tm electronic
+works.  See paragraph 1.E below.
+
+1.C.  The Project Gutenberg Literary Archive Foundation ("the Foundation"
+or PGLAF), owns a compilation copyright in the collection of Project
+Gutenberg-tm electronic works.  Nearly all the individual works in the
+collection are in the public domain in the United States.  If an
+individual work is in the public domain in the United States and you are
+located in the United States, we do not claim a right to prevent you from
+copying, distributing, performing, displaying or creating derivative
+works based on the work as long as all references to Project Gutenberg
+are removed.  Of course, we hope that you will support the Project
+Gutenberg-tm mission of promoting free access to electronic works by
+freely sharing Project Gutenberg-tm works in compliance with the terms of
+this agreement for keeping the Project Gutenberg-tm name associated with
+the work.  You can easily comply with the terms of this agreement by
+keeping this work in the same format with its attached full Project
+Gutenberg-tm License when you share it without charge with others.
+
+1.D.  The copyright laws of the place where you are located also govern
+what you can do with this work.  Copyright laws in most countries are in
+a constant state of change.  If you are outside the United States, check
+the laws of your country in addition to the terms of this agreement
+before downloading, copying, displaying, performing, distributing or
+creating derivative works based on this work or any other Project
+Gutenberg-tm work.  The Foundation makes no representations concerning
+the copyright status of any work in any country outside the United
+States.
+
+1.E.  Unless you have removed all references to Project Gutenberg:
+
+1.E.1.  The following sentence, with active links to, or other immediate
+access to, the full Project Gutenberg-tm License must appear prominently
+whenever any copy of a Project Gutenberg-tm work (any work on which the
+phrase "Project Gutenberg" appears, or with which the phrase "Project
+Gutenberg" is associated) is accessed, displayed, performed, viewed,
+copied or distributed:
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+1.E.2.  If an individual Project Gutenberg-tm electronic work is derived
+from the public domain (does not contain a notice indicating that it is
+posted with permission of the copyright holder), the work can be copied
+and distributed to anyone in the United States without paying any fees
+or charges.  If you are redistributing or providing access to a work
+with the phrase "Project Gutenberg" associated with or appearing on the
+work, you must comply either with the requirements of paragraphs 1.E.1
+through 1.E.7 or obtain permission for the use of the work and the
+Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or
+1.E.9.
+
+1.E.3.  If an individual Project Gutenberg-tm electronic work is posted
+with the permission of the copyright holder, your use and distribution
+must comply with both paragraphs 1.E.1 through 1.E.7 and any additional
+terms imposed by the copyright holder.  Additional terms will be linked
+to the Project Gutenberg-tm License for all works posted with the
+permission of the copyright holder found at the beginning of this work.
+
+1.E.4.  Do not unlink or detach or remove the full Project Gutenberg-tm
+License terms from this work, or any files containing a part of this
+work or any other work associated with Project Gutenberg-tm.
+
+1.E.5.  Do not copy, display, perform, distribute or redistribute this
+electronic work, or any part of this electronic work, without
+prominently displaying the sentence set forth in paragraph 1.E.1 with
+active links or immediate access to the full terms of the Project
+Gutenberg-tm License.
+
+1.E.6.  You may convert to and distribute this work in any binary,
+compressed, marked up, nonproprietary or proprietary form, including any
+word processing or hypertext form.  However, if you provide access to or
+distribute copies of a Project Gutenberg-tm work in a format other than
+"Plain Vanilla ASCII" or other format used in the official version
+posted on the official Project Gutenberg-tm web site (www.gutenberg.org),
+you must, at no additional cost, fee or expense to the user, provide a
+copy, a means of exporting a copy, or a means of obtaining a copy upon
+request, of the work in its original "Plain Vanilla ASCII" or other
+form.  Any alternate format must include the full Project Gutenberg-tm
+License as specified in paragraph 1.E.1.
+
+1.E.7.  Do not charge a fee for access to, viewing, displaying,
+performing, copying or distributing any Project Gutenberg-tm works
+unless you comply with paragraph 1.E.8 or 1.E.9.
+
+1.E.8.  You may charge a reasonable fee for copies of or providing
+access to or distributing Project Gutenberg-tm electronic works provided
+that
+
+- You pay a royalty fee of 20% of the gross profits you derive from
+     the use of Project Gutenberg-tm works calculated using the method
+     you already use to calculate your applicable taxes.  The fee is
+     owed to the owner of the Project Gutenberg-tm trademark, but he
+     has agreed to donate royalties under this paragraph to the
+     Project Gutenberg Literary Archive Foundation.  Royalty payments
+     must be paid within 60 days following each date on which you
+     prepare (or are legally required to prepare) your periodic tax
+     returns.  Royalty payments should be clearly marked as such and
+     sent to the Project Gutenberg Literary Archive Foundation at the
+     address specified in Section 4, "Information about donations to
+     the Project Gutenberg Literary Archive Foundation."
+
+- You provide a full refund of any money paid by a user who notifies
+     you in writing (or by e-mail) within 30 days of receipt that s/he
+     does not agree to the terms of the full Project Gutenberg-tm
+     License.  You must require such a user to return or
+     destroy all copies of the works possessed in a physical medium
+     and discontinue all use of and all access to other copies of
+     Project Gutenberg-tm works.
+
+- You provide, in accordance with paragraph 1.F.3, a full refund of any
+     money paid for a work or a replacement copy, if a defect in the
+     electronic work is discovered and reported to you within 90 days
+     of receipt of the work.
+
+- You comply with all other terms of this agreement for free
+     distribution of Project Gutenberg-tm works.
+
+1.E.9.  If you wish to charge a fee or distribute a Project Gutenberg-tm
+electronic work or group of works on different terms than are set
+forth in this agreement, you must obtain permission in writing from
+both the Project Gutenberg Literary Archive Foundation and Michael
+Hart, the owner of the Project Gutenberg-tm trademark.  Contact the
+Foundation as set forth in Section 3 below.
+
+1.F.
+
+1.F.1.  Project Gutenberg volunteers and employees expend considerable
+effort to identify, do copyright research on, transcribe and proofread
+public domain works in creating the Project Gutenberg-tm
+collection.  Despite these efforts, Project Gutenberg-tm electronic
+works, and the medium on which they may be stored, may contain
+"Defects," such as, but not limited to, incomplete, inaccurate or
+corrupt data, transcription errors, a copyright or other intellectual
+property infringement, a defective or damaged disk or other medium, a
+computer virus, or computer codes that damage or cannot be read by
+your equipment.
+
+1.F.2.  LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right
+of Replacement or Refund" described in paragraph 1.F.3, the Project
+Gutenberg Literary Archive Foundation, the owner of the Project
+Gutenberg-tm trademark, and any other party distributing a Project
+Gutenberg-tm electronic work under this agreement, disclaim all
+liability to you for damages, costs and expenses, including legal
+fees.  YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
+LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
+PROVIDED IN PARAGRAPH 1.F.3.  YOU AGREE THAT THE FOUNDATION, THE
+TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
+LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
+INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
+DAMAGE.
+
+1.F.3.  LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
+defect in this electronic work within 90 days of receiving it, you can
+receive a refund of the money (if any) you paid for it by sending a
+written explanation to the person you received the work from.  If you
+received the work on a physical medium, you must return the medium with
+your written explanation.  The person or entity that provided you with
+the defective work may elect to provide a replacement copy in lieu of a
+refund.  If you received the work electronically, the person or entity
+providing it to you may choose to give you a second opportunity to
+receive the work electronically in lieu of a refund.  If the second copy
+is also defective, you may demand a refund in writing without further
+opportunities to fix the problem.
+
+1.F.4.  Except for the limited right of replacement or refund set forth
+in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER
+WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
+WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE.
+
+1.F.5.  Some states do not allow disclaimers of certain implied
+warranties or the exclusion or limitation of certain types of damages.
+If any disclaimer or limitation set forth in this agreement violates the
+law of the state applicable to this agreement, the agreement shall be
+interpreted to make the maximum disclaimer or limitation permitted by
+the applicable state law.  The invalidity or unenforceability of any
+provision of this agreement shall not void the remaining provisions.
+
+1.F.6.  INDEMNITY - You agree to indemnify and hold the Foundation, the
+trademark owner, any agent or employee of the Foundation, anyone
+providing copies of Project Gutenberg-tm electronic works in accordance
+with this agreement, and any volunteers associated with the production,
+promotion and distribution of Project Gutenberg-tm electronic works,
+harmless from all liability, costs and expenses, including legal fees,
+that arise directly or indirectly from any of the following which you do
+or cause to occur: (a) distribution of this or any Project Gutenberg-tm
+work, (b) alteration, modification, or additions or deletions to any
+Project Gutenberg-tm work, and (c) any Defect you cause.
+
+
+Section  2.  Information about the Mission of Project Gutenberg-tm
+
+Project Gutenberg-tm is synonymous with the free distribution of
+electronic works in formats readable by the widest variety of computers
+including obsolete, old, middle-aged and new computers.  It exists
+because of the efforts of hundreds of volunteers and donations from
+people in all walks of life.
+
+Volunteers and financial support to provide volunteers with the
+assistance they need are critical to reaching Project Gutenberg-tm's
+goals and ensuring that the Project Gutenberg-tm collection will
+remain freely available for generations to come.  In 2001, the Project
+Gutenberg Literary Archive Foundation was created to provide a secure
+and permanent future for Project Gutenberg-tm and future generations.
+To learn more about the Project Gutenberg Literary Archive Foundation
+and how your efforts and donations can help, see Sections 3 and 4
+and the Foundation web page at https://www.pglaf.org.
+
+
+Section 3.  Information about the Project Gutenberg Literary Archive
+Foundation
+
+The Project Gutenberg Literary Archive Foundation is a non profit
+501(c)(3) educational corporation organized under the laws of the
+state of Mississippi and granted tax exempt status by the Internal
+Revenue Service.  The Foundation's EIN or federal tax identification
+number is 64-6221541.  Its 501(c)(3) letter is posted at
+https://pglaf.org/fundraising.  Contributions to the Project Gutenberg
+Literary Archive Foundation are tax deductible to the full extent
+permitted by U.S. federal laws and your state's laws.
+
+The Foundation's principal office is located at 4557 Melan Dr. S.
+Fairbanks, AK, 99712., but its volunteers and employees are scattered
+throughout numerous locations.  Its business office is located at
+809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email
+business@pglaf.org.  Email contact links and up to date contact
+information can be found at the Foundation's web site and official
+page at https://pglaf.org
+
+For additional contact information:
+     Dr. Gregory B. Newby
+     Chief Executive and Director
+     gbnewby@pglaf.org
+
+
+Section 4.  Information about Donations to the Project Gutenberg
+Literary Archive Foundation
+
+Project Gutenberg-tm depends upon and cannot survive without wide
+spread public support and donations to carry out its mission of
+increasing the number of public domain and licensed works that can be
+freely distributed in machine readable form accessible by the widest
+array of equipment including outdated equipment.  Many small donations
+($1 to $5,000) are particularly important to maintaining tax exempt
+status with the IRS.
+
+The Foundation is committed to complying with the laws regulating
+charities and charitable donations in all 50 states of the United
+States.  Compliance requirements are not uniform and it takes a
+considerable effort, much paperwork and many fees to meet and keep up
+with these requirements.  We do not solicit donations in locations
+where we have not received written confirmation of compliance.  To
+SEND DONATIONS or determine the status of compliance for any
+particular state visit https://pglaf.org
+
+While we cannot and do not solicit contributions from states where we
+have not met the solicitation requirements, we know of no prohibition
+against accepting unsolicited donations from donors in such states who
+approach us with offers to donate.
+
+International donations are gratefully accepted, but we cannot make
+any statements concerning tax treatment of donations received from
+outside the United States.  U.S. laws alone swamp our small staff.
+
+Please check the Project Gutenberg Web pages for current donation
+methods and addresses.  Donations are accepted in a number of other
+ways including including checks, online payments and credit card
+donations.  To donate, please visit: https://pglaf.org/donate
+
+
+Section 5.  General Information About Project Gutenberg-tm electronic
+works.
+
+Professor Michael S. Hart was the originator of the Project Gutenberg-tm
+concept of a library of electronic works that could be freely shared
+with anyone.  For thirty years, he produced and distributed Project
+Gutenberg-tm eBooks with only a loose network of volunteer support.
+
+
+Project Gutenberg-tm eBooks are often created from several printed
+editions, all of which are confirmed as Public Domain in the U.S.
+unless a copyright notice is included.  Thus, we do not necessarily
+keep eBooks in compliance with any particular paper edition.
+
+
+Most people start at our Web site which has the main PG search facility:
+
+     https://www.gutenberg.org
+
+This Web site includes information about Project Gutenberg-tm,
+including how to make donations to the Project Gutenberg Literary
+Archive Foundation, how to help produce our new eBooks, and how to
+subscribe to our email newsletter to hear about new eBooks.
diff --git a/35092-8.zip b/35092-8.zip
new file mode 100644
index 0000000..5aecee9
--- /dev/null
+++ b/35092-8.zip
diff --git a/35092-h.zip b/35092-h.zip
new file mode 100644
index 0000000..6ad0792
--- /dev/null
+++ b/35092-h.zip
diff --git a/35092-h/35092-h.htm b/35092-h/35092-h.htm
new file mode 100644
index 0000000..6e4c24a
--- /dev/null
+++ b/35092-h/35092-h.htm
@@ -0,0 +1,18615 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
+
+  <head>
+    <meta http-equiv="Content-Type" content=
+    "text/html; charset=iso-8859-1" />
+
+    <title>
+      The Project Gutenberg eBook of Encyclop&aelig;dia Britannica, Volume IX Slice II - Ehud to Electroscope.
+    </title>
+
+    <style type="text/css">
+
+    body    { margin-left: 12%; margin-right: 12%; text-align: justify; }
+    p       { margin-top: .75em; margin-bottom: .75em; text-indent: 1em; line-height: 1.4em;}
+    p.c     { margin-top: .25em; margin-bottom: .25em; text-indent: 1em; padding-left: 1em; line-height: 1.4em;}
+    p.noind { margin-top: .75em; margin-bottom: .75em; text-indent: 0; }
+
+    h2,h3        { text-align: center; }
+    hr           { margin-left: auto; margin-right: auto; text-align: center; width: 70%; height: 5px; background-color: #dcdcdc; border:none; }
+    hr.art       { margin-left: auto; margin-right: auto; width: 40%; height: 5px; background-color: #778899;
+                          margin-top: 2em; margin-bottom: 6em }
+    hr.foot      {margin-left: 2em; width: 16%; background-color: black; margin-top: 1em; margin-bottom: 0; height: 1px; }
+    hr.full      {width: 100%}
+
+    table.ws      {white-space: nowrap; border-collapse: collapse; margin-left: auto; margin-right: auto;
+                   margin-top: 2em; margin-bottom: 2em;}
+    table.reg     { margin-left: auto; margin-right: auto; clear: both;}
+    table.reg td  { white-space: normal;}
+    table.nobctr  { margin-left: auto; margin-right: auto; border-collapse: collapse; }
+    table.flt     { border-collapse: collapse; }
+    table.pic     { margin-left: auto; margin-right: auto; }
+    table.math0   { vertical-align: middle; margin-left: auto; margin-right: auto; border-collapse: collapse;}
+    table.math0l  { vertical-align: middle; margin-left: 3em; border-collapse: collapse;}
+    table.math0 td, table.math0l td  {text-align: center;}
+    table.math0 td.np {text-align: center; padding-left: 0; padding-right: 0;}
+
+    table.reg p     {text-indent: 1em; margin-left: 1.5em; text-align: justify;}
+    table.reg td.tc5p  { padding-left: 2em; text-indent: 0em; white-space: normal;}
+    table.nobctr td, table.flt td { white-space: normal; }
+    table.pic td    { white-space: normal; text-indent: 1em; padding-left: 2em; padding-right: 1em;}
+    table.nobctr p, table.flt p  {text-indent: -1.5em; margin-left: 1.5em;}
+    table.pic td p  {text-indent: -1.5em; margin-left: 1.5em;}
+
+    td            { white-space: nowrap; padding-right: 0.3em; padding-left: 0.3em;}
+    td.norm       { white-space: normal; }
+    td.denom      { border-top: 1px solid black; text-align: center; padding-right: 0.3em; padding-left: 0.3em;}
+
+    td.tcc        { padding-right: 0.5em; padding-left: 0.5em; text-align: center; vertical-align: top;}
+    td.tccm       { padding-right: 0.5em; padding-left: 0.5em; text-align: center; vertical-align: middle;}
+    td.tccb       { padding-right: 0.5em; padding-left: 0.5em; text-align: center; vertical-align: bottom;}
+    td.tcr        { padding-right: 0.5em; padding-left: 0.5em; text-align: right; vertical-align: top;}
+    td.tcrb       { padding-right: 0.5em; padding-left: 0.5em; text-align: right; vertical-align: bottom;}
+    td.tcrm       { padding-right: 0.5em; padding-left: 0.5em; text-align: right; vertical-align: middle;}
+    td.tcl        { padding-right: 0.5em; padding-left: 0.5em; text-align: left; vertical-align: top;}
+    td.tclb       { padding-right: 0.5em; padding-left: 0.5em; text-align: left; vertical-align: bottom;}
+    td.tclm       { padding-right: 0.5em; padding-left: 0.5em; text-align: left; vertical-align: middle;}
+    td.vb         { vertical-align: bottom; }
+
+      .caption    { font-size: 0.9em; text-align: center; padding-bottom: 1em; padding-left: 1em; padding-right: 1em;}
+      .caption1   { font-size: 0.9em; text-align: left; padding-bottom: 1em; padding-left: 3em; padding-right: 2em;}
+
+    td.lb       {border-left: black 1px solid;}
+    td.ltb      {border-left: black 1px solid; border-top: black 1px solid;}
+    td.rb       {border-right: black 1px solid;}
+    td.rb2      {border-right: black 2px solid;}
+    td.tb, span.tb  {border-top: black 1px solid;}
+    td.bb       {border-bottom: black 1px solid;}
+    td.bb1      {border-bottom: #808080 3px solid; padding-top: 1em; padding-bottom: 1em;}
+    td.rlb      {border-right: black 1px solid; border-left : black 1px solid;}
+    td.allb     {border: black 1px solid;}
+    td.cl       {background-color: #e8e8e8}
+
+    table p       { margin: 0;}
+
+    a:link, a:visited, link  {text-decoration:none}
+
+    .author   {text-align: right; margin-top: -1em; margin-right: 1em; font-variant: small-caps;}
+    .author1  {text-align: right; margin-top: -1em; margin-right: 1em; }
+    .center   {text-align: center; text-indent: 0;}
+    .center1  {text-align: center; text-indent: 0; margin-top: 1em; margin-bottom: 1em;}
+    .grk      {font-style: normal; font-family:"Palatino Linotype","New Athena Unicode",Gentium,"Lucida Grande", Galilee, "Arial Unicode MS", sans-serif;}
+
+    .f80      {font-size: 80%}
+    .f90      {font-size: 90%}
+    .f150     {font-size: 150%}
+    .f200     {font-size: 200%}
+
+    .sp       {position: relative; bottom: 0.5em; font-size: 0.75em;}
+    .sp1      {position: relative; bottom: 1.2em; font-size: 0.75em;}
+    .su       {position: relative; top: 0.3em; font-size: 0.75em;}
+    .su1      {position: relative; top: 0.5em; font-size: 0.75em; margin-left: -1.2ex;}
+    .spp      {position: relative; bottom: 0.5em; font-size: 0.6em;}
+    .suu      {position: relative; top: 0.2em; font-size: 0.6em;}
+    .sc       {font-variant: small-caps;}
+    .scs      {text-transform: lowercase; font-variant: small-caps;}
+    .ov       {text-decoration: overline}
+    .un       {text-decoration: underline}
+    .cl       {background-color: #f5f5f5;}
+    .bk       {padding-left: 0; font-size: 80%;}
+    .bk1      {margin-left: -1em;}
+
+    .pagenum  {position: absolute; right: 5%; text-align: right; font-size: 10pt;
+                  background-color: #f5f5f5; color: #778899; text-indent: 0;
+                  padding-left: 0.5em; padding-right: 0.5em; font-style: normal; }
+    span.sidenote {width: 8em; margin-bottom: 1em; margin-top: 1.7em; margin-right: 2em;
+	           font-size: 85%; float: left; clear: left; font-weight: bold;
+                   font-style: italic; text-align: left; text-indent: 0;
+                   background-color: #f5f5f5; color: black; }
+    .note     {margin-left: 2em; margin-right: 2em; font-size: 0.9em; }
+    .fn       { position: absolute; left: 12%; text-align: left; background-color: #f5f5f5;
+                text-indent: 0; padding-left: 0.2em; padding-right: 0.2em; }
+    span.correction {border-bottom: 1px dashed red;}
+
+    div.poemr        { margin-top: .75em; margin-bottom: .75em;}
+    div.poemr p      { margin-left: 0; padding-left: 3em; text-indent: -3em; margin-top: 0em; margin-bottom: 0em; }
+    div.poemr p.s     { margin-top: 1.5em; }
+    div.poemr p.i05   { margin-left: 0.4em; }
+    div.poemr p.i1    { margin-left: 1em; }
+    div.poemr p.i2    { margin-left: 2em; }
+
+    .figright1 { padding-right: 1em; padding-left: 2em; padding-top: 1.5em; text-align: center; }
+    .figleft1  { padding-right: 2em; padding-left: 1em; padding-top: 1.5em; text-align: center; }
+    .figcenter   {text-align: center; margin: auto; margin-left: auto; margin-right: auto; padding-top: 1.5em;}
+    .figcenter1  {text-align: center; margin-left: auto; margin-right: auto; padding-top: 2em; padding-bottom: 2em;}
+    .figure      {text-align: center; padding-left: 1.5em; padding-right: 1.5em; padding-top: 1.5em; padding-bottom: 0;}
+    .bold        {font-weight: bold; }
+
+     div.minind   {text-align: justify;}
+     div.condensed, div.condensed1  { line-height: 1.3em; margin-left: 3%; margin-right: 3%; font-size: 95%; }
+     div.condensed1 p  {margin-left: 0; padding-left: 2em; text-indent: -2em;}
+     div.condensed span.sidenote {font-size: 90%}
+
+     div.list   {margin-left: 0;}
+     div.list p {padding-left: 4em; text-indent: -2em;}
+     div.list1   {margin-left: 0;}
+     div.list1 p {padding-left: 5em; text-indent: -3em;}
+
+    .pt05       {padding-top: 0.5em;}
+    .pt1        {padding-top: 1em;}
+    .pt2        {padding-top: 2em;}
+    .ptb1       {padding-top: 1em; padding-bottom: 1em;}
+    td.prl      {padding-left: 10%; padding-right: 7em; text-align: left; vertical-align: top;}
+
+    </style>
+   </head>
+<body>
+
+
+<pre>
+
+The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
+Volume 9, Slice 2, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2
+       "Ehud" to "Electroscope"
+
+Author: Various
+
+Release Date: January 27, 2011 [EBook #35092]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 9 SL 2 ***
+
+
+
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+
+
+
+
+</pre>
+
+
+
+<table border="0" cellpadding="10" style="background-color: #dcdcdc; color: #696969; " summary="Transcriber's note">
+<tr>
+<td style="width:25%; vertical-align:top">
+Transcriber&rsquo;s note:
+</td>
+<td class="norm">
+A few typographical errors have been corrected. They
+appear in the text <span class="correction" title="explanation will pop up">like this</span>, and the
+explanation will appear when the mouse pointer is moved over the marked
+passage. Sections in Greek will yield a transliteration
+when the pointer is moved over them, and words using diacritic characters in the
+Latin Extended Additional block, which may not display in some fonts or browsers, will
+display an unaccented version. <br /><br />
+<a name="artlinks">Links to other EB articles:</a> Links to articles residing in other EB volumes will
+be made available when the respective volumes are introduced online.
+</td>
+</tr>
+</table>
+<div style="padding-top: 3em; ">&nbsp;</div>
+
+<h2>THE ENCYCLOP&AElig;DIA BRITANNICA</h2>
+
+<h2>A DICTIONARY OF ARTS, SCIENCES, LITERATURE AND GENERAL INFORMATION</h2>
+
+<h3>ELEVENTH EDITION</h3>
+<div style="padding-top: 3em; ">&nbsp;</div>
+
+<hr class="full" />
+<h3>VOLUME IX SLICE II<br /><br />
+Ehud to Electroscope</h3>
+<hr class="full" />
+<div style="padding-top: 3em; ">&nbsp;</div>
+
+<p class="center1" style="font-size: 150%; font-family: 'verdana';">Articles in This Slice</p>
+<table class="reg" style="width: 90%; font-size: 90%; border: gray 2px solid;" cellspacing="8" summary="Contents">
+
+<tr><td class="tcl"><a href="#ar1">EHUD</a></td> <td class="tcl"><a href="#ar40">ELBERFELD</a></td></tr>
+<tr><td class="tcl"><a href="#ar2">EIBENSTOCK</a></td> <td class="tcl"><a href="#ar41">ELBEUF</a></td></tr>
+<tr><td class="tcl"><a href="#ar3">EICHBERG, JULIUS</a></td> <td class="tcl"><a href="#ar42">ELBING</a></td></tr>
+<tr><td class="tcl"><a href="#ar4">EICHENDORFF, JOSEPH, FREIHERR VON</a></td> <td class="tcl"><a href="#ar43">ELBOW</a></td></tr>
+<tr><td class="tcl"><a href="#ar5">EICHHORN, JOHANN GOTTFRIED</a></td> <td class="tcl"><a href="#ar44">ELBURZ</a></td></tr>
+<tr><td class="tcl"><a href="#ar6">EICHHORN, KARL FRIEDRICH</a></td> <td class="tcl"><a href="#ar45">ELCHE</a></td></tr>
+<tr><td class="tcl"><a href="#ar7">EICHSTÄTT</a></td> <td class="tcl"><a href="#ar46">ELCHINGEN</a></td></tr>
+<tr><td class="tcl"><a href="#ar8">EICHWALD, KARL EDUARD VON</a></td> <td class="tcl"><a href="#ar47">ELDAD BEN MA&#7716;LI</a></td></tr>
+<tr><td class="tcl"><a href="#ar9">EIDER</a> (river of Prussia)</td> <td class="tcl"><a href="#ar48">ELDER</a> (ruler or officer)</td></tr>
+<tr><td class="tcl"><a href="#ar10">EIDER</a> (duck)</td> <td class="tcl"><a href="#ar49">ELDER</a> (shrubs and trees)</td></tr>
+<tr><td class="tcl"><a href="#ar11">EIFEL</a></td> <td class="tcl"><a href="#ar50">ELDON, JOHN SCOTT</a></td></tr>
+<tr><td class="tcl"><a href="#ar12">EIFFEL TOWER</a></td> <td class="tcl"><a href="#ar51">EL DORADO</a></td></tr>
+<tr><td class="tcl"><a href="#ar13">EILDON HILLS</a></td> <td class="tcl"><a href="#ar52">ELDUAYEN, JOSÉ DE</a></td></tr>
+<tr><td class="tcl"><a href="#ar14">EILENBURG</a></td> <td class="tcl"><a href="#ar53">ELEANOR OF AQUITAINE</a></td></tr>
+<tr><td class="tcl"><a href="#ar15">EINBECK</a></td> <td class="tcl"><a href="#ar54">ELEATIC SCHOOL</a></td></tr>
+<tr><td class="tcl"><a href="#ar16">EINDHOVEN</a></td> <td class="tcl"><a href="#ar55">ELECAMPANE</a></td></tr>
+<tr><td class="tcl"><a href="#ar17">EINHARD</a></td> <td class="tcl"><a href="#ar56">ELECTION</a> (politics)</td></tr>
+<tr><td class="tcl"><a href="#ar18">EINHORN, DAVID</a></td> <td class="tcl"><a href="#ar57">ELECTION</a> (English law choice)</td></tr>
+<tr><td class="tcl"><a href="#ar19">EINSIEDELN</a></td> <td class="tcl"><a href="#ar58">ELECTORAL COMMISSION</a></td></tr>
+<tr><td class="tcl"><a href="#ar20">EISENACH</a></td> <td class="tcl"><a href="#ar59">ELECTORS</a></td></tr>
+<tr><td class="tcl"><a href="#ar21">EISENBERG</a></td> <td class="tcl"><a href="#ar60">ELECTRA</a></td></tr>
+<tr><td class="tcl"><a href="#ar22">EISENERZ</a></td> <td class="tcl"><a href="#ar61">ELECTRICAL MACHINE</a></td></tr>
+<tr><td class="tcl"><a href="#ar23">EISLEBEN</a></td> <td class="tcl"><a href="#ar62">ELECTRIC EEL</a></td></tr>
+<tr><td class="tcl"><a href="#ar24">EISTEDDFOD</a></td> <td class="tcl"><a href="#ar63">ELECTRICITY</a></td></tr>
+<tr><td class="tcl"><a href="#ar25">EJECTMENT</a></td> <td class="tcl"><a href="#ar64">ELECTRICITY SUPPLY</a></td></tr>
+<tr><td class="tcl"><a href="#ar26">EKATERINBURG</a></td> <td class="tcl"><a href="#ar65">ELECTRIC WAVES</a></td></tr>
+<tr><td class="tcl"><a href="#ar27">EKATERINODAR</a></td> <td class="tcl"><a href="#ar66">ELECTROCHEMISTRY</a></td></tr>
+<tr><td class="tcl"><a href="#ar28">EKATERINOSLAV</a> (government of Russia)</td> <td class="tcl"><a href="#ar67">ELECTROCUTION</a></td></tr>
+<tr><td class="tcl"><a href="#ar29">EKATERINOSLAV</a> (town of Russia)</td> <td class="tcl"><a href="#ar68">ELECTROKINETICS</a></td></tr>
+<tr><td class="tcl"><a href="#ar30">EKHOF, KONRAD</a></td> <td class="tcl"><a href="#ar69">ELECTROLIER</a></td></tr>
+<tr><td class="tcl"><a href="#ar31">EKRON</a></td> <td class="tcl"><a href="#ar70">ELECTROLYSIS</a></td></tr>
+<tr><td class="tcl"><a href="#ar32">ELABUGA</a></td> <td class="tcl"><a href="#ar71">ELECTROMAGNETISM</a></td></tr>
+<tr><td class="tcl"><a href="#ar33">ELAM</a></td> <td class="tcl"><a href="#ar72">ELECTROMETALLURGY</a></td></tr>
+<tr><td class="tcl"><a href="#ar34">ELAND</a></td> <td class="tcl"><a href="#ar73">ELECTROMETER</a></td></tr>
+<tr><td class="tcl"><a href="#ar35">ELASTICITY</a></td> <td class="tcl"><a href="#ar74">ELECTRON</a></td></tr>
+<tr><td class="tcl"><a href="#ar36">ELATERITE</a></td> <td class="tcl"><a href="#ar75">ELECTROPHORUS</a></td></tr>
+<tr><td class="tcl"><a href="#ar37">ELATERIUM</a></td> <td class="tcl"><a href="#ar76">ELECTROPLATING</a></td></tr>
+<tr><td class="tcl"><a href="#ar38">ELBA</a></td> <td class="tcl"><a href="#ar77">ELECTROSCOPE</a></td></tr>
+<tr><td class="tcl"><a href="#ar39">ELBE</a></td> <td>&nbsp;</td></tr>
+</table>
+
+<hr class="art" />
+<p><span class="pagenum"><a name="page131" id="page131"></a>131</span></p>
+<p><span class="bold">EHUD<a name="ar1" id="ar1"></a></span>, in the Bible, a &ldquo;judge&rdquo; who delivered Israel from
+the Moabites (Judg. iii. 12-30). He was sent from Ephraim to
+bear tribute to Eglon king of Moab, who had crossed over the
+Jordan and seized the district around Jericho. Being, like the
+Benjamites, left-handed (cf. xx. 16), he was able to conceal a
+dagger and strike down the king before his intentions were suspected.
+He locked Eglon in his chamber and escaped. The
+men from Mt Ephraim collected under his leadership and by
+seizing the fords of the Jordan were able to cut off the Moabites.
+He is called the son of Gera a Benjamite, but since both Ehud
+and Gera are tribal names (2 Sam. xvi. 5, 1 Chron. viii. 3, 5 sq.)
+it has been thought that this notice is not genuine. The tribe
+of Benjamin rarely appears in the old history of the Hebrews
+before the time of Saul. See further <span class="sc"><a href="#artlinks">Benjamin</a></span>; <span class="sc"><a href="#artlinks">Judges</a></span>.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EIBENSTOCK<a name="ar2" id="ar2"></a></span>, a town of Germany, in the kingdom of Saxony,
+near the Mulde, on the borders of Bohemia, 17 m. by rail S.S.E.
+of Zwickau. Pop. (1905) 7460. It is a principal seat of the
+tambour embroidery which was introduced in 1775 by Clara
+Angermann. It possesses chemical and tobacco manufactories,
+and tin and iron works. It has also a large cattle market. Eibenstock,
+together with Schwarzenberg, was acquired by purchase
+in 1533 by Saxony and was granted municipal rights in the
+following year.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EICHBERG, JULIUS<a name="ar3" id="ar3"></a></span> (1824-1893), German musical composer,
+was born at Düsseldorf on the 13th of June 1824. When he was
+nineteen he entered the Brussels Conservatoire, where he took
+first prizes for violin-playing and composition. For eleven years
+he occupied the post of professor in the Conservatoire of Geneva.
+In 1857 he went to the United States, staying two years in New
+York and then proceeding to Boston, where he became director
+of the orchestra at the Boston Museum. In 1867 he founded the
+Boston Conservatory of Music. Eichberg published several
+educational works on music; and his four operettas, <i>The Doctor
+of Alcantara</i>, <i>The Rose of Tyrol</i>, <i>The Two Cadis</i> and <i>A Night in
+Rome</i>, were highly popular. He died in Boston on the 18th of
+January 1893.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EICHENDORFF, JOSEPH, FREIHERR VON<a name="ar4" id="ar4"></a></span> (1788-1857),
+German poet and romance-writer, was born at Lubowitz, near
+Ratibor, in Silesia, on the 10th of March 1788. He studied law
+at Halle and Heidelberg from 1805 to 1808. After a visit to
+Paris he went to Vienna, where he resided until 1813, when he
+joined the Prussian army as a volunteer in the famous Lützow
+corps. When peace was concluded in 1815, he left the army,
+and in the following year he was appointed to a judicial office
+at Breslau. He subsequently held similar offices at Danzig,
+Königsberg and Berlin. Retiring from public service in 1844,
+he lived successively in Danzig, Vienna, Dresden and Berlin.
+He died at Neisse on the 26th of November 1857. Eichendorff
+was one of the most distinguished of the later members of the
+German romantic school. His genius was essentially lyrical.
+Thus he is most successful in his shorter romances and dramas,
+where constructive power is least called for. His first work,
+written in 1811, was a romance, <i>Ahnung und Gegenwart</i> (1815).
+This was followed at short intervals by several others, among
+which the foremost place is by general consent assigned to <i>Aus
+dem Leben eines Taugenichts</i> (1826), which has often been reprinted.
+Of his dramas may be mentioned <i>Ezzelin von Romano</i>
+(1828); and <i>Der letzte Held von Marienburg</i> (1830), both tragedies;
+and a comedy, <i>Die Freier</i> (1833). He also translated several
+of Calderon&rsquo;s religious dramas (<i>Geistliche Schauspiele</i>, 1846).
+It is, however, through his lyrics (<i>Gedichte</i>, first collected 1837)
+that Eichendorff is best known; he is the greatest lyric poet of
+the romantic movement. No one has given more beautiful
+expression than he to the poetry of a wandering life; often, again,
+his lyrics are exquisite word pictures interpreting the mystic
+meaning of the moods of nature, as in <i>Nachts</i>, or the old-time
+mystery which yet haunts the twilight forests and feudal castles
+of Germany, as in the dramatic lyric <i>Waldesgespräch</i> or <i>Auf
+einer Burg</i>. Their language is simple and musical, which makes
+them very suitable for singing, and they have been often set,
+notably by Schubert and Schumann.</p>
+
+<p>In the later years of his life Eichendorff published several
+works on subjects in literary history and criticism such as <i>Über
+die ethische und religiöse Bedeutung der neuen romantischen
+Poesie in Deutschland</i> (1847), <i>Der deutsche Roman des 18.
+Jahrhunderts in seinem Verhältniss zum Christenthum</i> (1851),
+and <i>Geschichte der poetischen Litteratur Deutschlands</i> (1856),
+but the value of these works is impaired by the author&rsquo;s reactionary
+standpoint. An edition of his collected works in six
+volumes, appeared at Leipzig in 1870.</p>
+
+<div class="condensed">
+<p>Eichendorff&rsquo;s <i>Sämtliche Werke</i> appeared in 6 vols., 1864 (reprinted
+1869-1870); his <i>Sämtliche poetische Werke</i> in 4 vols. (1883). The
+latest edition is that edited by R. von Gottschall in 4 vols. (1901).
+A good selection edited by M. Kaoch will be found in vol. 145 of
+Kürschner&rsquo;s <i>Deutsche Nationalliteratur</i> (1893). Eichendorff&rsquo;s critical
+writings were collected in 1866 under the title <i>Vermischte Schriften</i>
+(5 vols.). Cp. H. von Eichendorff&rsquo;s biographical introduction to the
+<i>Sämtliche Werke</i>; also H. Keiter, <i>Joseph von Eichendorff</i> (Cologne,
+1887); H.A. Krüger, <i>Der junge Eichendorff</i> (Oppeln, 1898).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EICHHORN, JOHANN GOTTFRIED<a name="ar5" id="ar5"></a></span> (1752-1827), German
+theologian, was born at Dörrenzimmern, in the principality of
+Hohenlohe-Oehringen, on the 16th of October 1752. He was
+educated at the state school in Weikersheim, where his father
+was superintendent, at the gymnasium at Heilbronn and at the
+university of Göttingen (1770-1774), studying under J.D.
+Michaelis. In 1774 he received the rectorship of the gymnasium
+at Ohrdruf, in the duchy of Gotha, and in the following year was
+made professor of Oriental languages at Jena. On the death
+of Michaelis in 1788 he was elected professor <i>ordinarius</i> at
+Göttingen, where he lectured not only on Oriental languages and
+on the exegesis of the Old and New Testaments, but also on political
+history. His health was shattered in 1825, but he continued
+his lectures until attacked by fever on the 14th of June 1827.
+He died on the 27th of that month. Eichhorn has been called
+&ldquo;the founder of modern Old Testament criticism.&rdquo; He first
+properly recognized its scope and problems, and began many of
+its most important discussions. &ldquo;My greatest trouble,&rdquo; he
+says in the preface to the second edition of his <i>Einleitung</i>, &ldquo;I had
+to bestow on a hitherto unworked field&mdash;on the investigation of
+the inner nature of the Old Testament with the help of the Higher
+Criticism (not a new name to any humanist).&rdquo; His investigations
+led him to the conclusion that &ldquo;most of the writings of the
+Hebrews have passed through several hands.&rdquo; He took for
+granted that all the so-called supernatural facts relating to the
+Old and New Testaments were explicable on natural principles.
+He sought to judge them from the standpoint of the ancient
+world, and to account for them by the superstitious beliefs which
+were then generally in vogue. He did not perceive in the biblical
+books any religious ideas of much importance for modern times;
+they interested him merely historically and for the light they
+cast upon antiquity. He regarded many books of the Old
+Testament as spurious, questioned the genuineness of <i>2 Peter</i>
+and <i>Jude</i>, denied the Pauline authorship of <i>Timothy</i> and <i>Titus</i>,
+<span class="pagenum"><a name="page132" id="page132"></a>132</span>
+and suggested that the canonical gospels were based upon various
+translations and editions of a primary Aramaic gospel. He did
+not appreciate as sufficiently as David Strauss and the Tübingen
+critics the difficulties which a natural theory has to surmount,
+nor did he support his conclusions by such elaborate discussions
+as they deemed necessary.</p>
+
+<div class="condensed">
+<p>His principal works were&mdash;<i>Geschichte des Ostindischen Handels vor
+Mohammed</i> (Gotha, 1775); <i>Allgemeine Bibliothek der biblischen
+Literatur</i> (10 vols., Leipzig, 1787-1801); <i>Einleitung in das Alte Testament</i>
+(3 vols., Leipzig, 1780-1783); <i>Einleitung in das Neue Testament</i>
+(1804-1812); <i>Einleitung in die apokryphischen Bücher des Alten
+Testaments</i> (Gött., 1795); <i>Commentarius in apocalypsin Joannis</i>
+(2 vols., Gött., 1791); <i>Die Hebr. Propheten</i> (3 vols., Gött., 1816-1819);
+<i>Allgemeine Geschichte der Cultur und Literatur des neuern
+Europa</i> (2 vols., Gött., 1796-1799); <i>Literärgeschichte</i> (1st vol., Gött.,
+1799, 2nd ed. 1813, 2nd vol. 1814); <i>Geschichte der Literatur von
+ihrem Anfange bis auf die neuesten Zeiten</i> (5 vols., Gött., 1805-1812);
+<i>Übersicht der Französischen Revolution</i> (2 vols., Gött., 1797); <i>Weltgeschichte</i>
+(3rd ed., 5 vols., Gött., 1819-1820); <i>Geschichte der drei
+letzten Jahrhunderte</i> (3rd ed., 6 vols., Hanover, 1817-1818); <i>Urgeschichte
+des erlauchten Hauses der Welfen</i> (Hanover, 1817).</p>
+
+<p>See R.W. Mackay, <i>The Tübingen School and its Antecedents</i> (1863),
+pp. 103 ff.; Otto Pfleiderer, <i>Development of Theology</i> (1890), p. 209;
+T.K. Cheyne, <i>Founders of Old Testament Criticism</i> (1893), pp. 13 ff.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EICHHORN, KARL FRIEDRICH<a name="ar6" id="ar6"></a></span> (1781-1854), German jurist,
+son of the preceding, was born at Jena on the 20th of November
+1781. He entered the university of Göttingen in 1797. In 1805
+he obtained the professorship of law at Frankfort-on-Oder,
+holding it till 1811, when he accepted the same chair at Berlin.
+On the call to arms in 1813 he became a captain of horse, and
+received at the end of the war the decoration of the Iron Cross.
+In 1817 he was offered the chair of law at Göttingen, and, preferring
+it to the Berlin professorship, taught there with great
+success till ill-health compelled him to resign in 1828. His
+successor in the Berlin chair having died in 1832, he again entered
+on its duties, but resigned two years afterwards. In 1832 he also
+received an appointment in the ministry of foreign affairs, which,
+with his labours on many state committees and his legal researches
+and writings, occupied him till his death at Cologne
+on the 4th of July 1854. Eichhorn is regarded as one of the
+principal authorities on German constitutional law. His chief
+work is <i>Deutsche Staats- und Rechtsgeschichte</i> (Göttingen, 1808-1823,
+5th ed. 1843-1844). In company with Savigny and
+J.F.L. Göschen he founded the <i>Zeitschrift für geschichtliche
+Rechtswissenschaft</i>. He was the author besides of <i>Einleitung
+in das deutsche Privatrecht mit Einschluss des Lehnrechts</i> (Gött.,
+1823) and the <i>Grundsätze des Kirchenrechts der Katholischen und
+der Evangelischen Religionspartei in Deutschland</i>, 2 Bde. (<i>ib.</i>, 1831-1833).</p>
+
+<div class="condensed">
+<p>See Schulte, <i>Karl Friedrich Eichhorn, sein Leben und Wirken</i>
+(1884).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EICHSTÄTT,<a name="ar7" id="ar7"></a></span> a town and episcopal see of Germany, in the
+kingdom of Bavaria, in the deep and romantic valley of the
+Altmühl, 35 m. S. of Nuremberg, on the railway to Ingolstadt
+and Munich. Pop. (1905) 7701. The town, with its numerous
+spires and remains of medieval fortifications, is very picturesque.
+It has an Evangelical and seven Roman Catholic churches,
+among the latter the cathedral of St Wilibald (first bishop of
+Eichstätt),&mdash;with the tomb of the saint and numerous pictures
+and relics,&mdash;the church of St Walpurgis, sister of Wilibald,
+whose remains rest in the choir, and the Capuchin church, a copy
+of the Holy Sepulchre. Of its secular buildings the most noticeable
+are the town hall and the Leuchtenberg palace, once the
+residence of the prince bishops and later of the dukes of Leuchtenberg
+(now occupied by the court of justice of the district), with
+beautiful grounds. The Wilibaldsburg, built on a neighbouring
+hill in the 14th century by Bishop Bertold of Hohenzollern, was
+long the residence of the prince bishops of Eichstätt, and now
+contains an historical museum. There are an episcopal lyceum,
+a clerical seminary, a classical and a modern school, and numerous
+religious houses. The industries of the town include bootmaking,
+brewing and the production of lithographic stones.</p>
+
+<p>Eichstätt (Lat. <i>Aureatum</i> or <i>Rubilocus</i>) was originally a Roman
+station which, after the foundation of the bishopric by Boniface
+in 745, developed into a considerable town, which was surrounded
+with walls in 908. The bishops of Eichstätt were princes of the
+Empire, subject to the spiritual jurisdiction of the archbishops
+of Mainz, and ruled over considerable territories in the Circle of
+Franconia. In 1802 the see was secularized and incorporated
+in Bavaria. In 1817 it was given, with the duchy of Leuchtenberg,
+as a mediatized domain under the Bavarian crown, by the
+king of Bavaria to his son-in-law Eugène de Beauharnais,
+ex-viceroy of Italy, henceforth styled duke of Leuchtenberg.
+In 1855 it reverted to the Bavarian crown.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EICHWALD, KARL EDUARD VON<a name="ar8" id="ar8"></a></span> (1795-1876), Russian
+geologist and physician, was born at Mitau in Courland on the
+4th of July 1795. He became doctor of medicine and professor
+of zoology in Kazañ in 1823; four years later professor of zoology
+and comparative anatomy at Vilna; in 1838 professor of
+zoology, mineralogy and medicine at St Petersburg; and finally
+professor of palaeontology in the institute of mines in that city.
+He travelled much in the Russian empire, and was a keen
+observer of its natural history and geology. He died at St
+Petersburg on the 10th of November 1876. His published works
+include <i>Reise auf dem Caspischen Meere und in den Caucasus</i>,
+2 vols. (Stuttgart and Tübingen, 1834-1838); <i>Die Urwelt Russlands</i>
+(St Petersburg, 1840-1845); <i>Lethaea Rossica, ou paléontologie
+de la Russie</i>, 3 vols. (Stuttgart, 1852-1868), with Atlases.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EIDER,<a name="ar9" id="ar9"></a></span> a river of Prussia, in the province of Schleswig-Holstein.
+It rises to the south of Kiel, in Lake Redder, flows
+first north, then west (with wide-sweeping curves), and after a
+course of 117 m. enters the North Sea at Tönning. It is navigable
+up to Rendsburg, and is embanked through the marshes across
+which it runs in its lower course. Since the reign of Charlemagne,
+the Eider (originally <i>Ägyr Dör</i>&mdash;Neptune&rsquo;s gate) was known
+as <i>Romani terminus imperii</i> and was recognized as the boundary
+of the Empire in 1027 by the emperor Conrad II., the founder
+of the Salian dynasty. In the controversy arising out of the
+Schleswig-Holstein Question, which culminated in the war of
+Austria and Prussia against Denmark in 1864, the Eider gave
+its name to the &ldquo;Eider Danes,&rdquo; the <i>intransigeant</i> Danish party
+which maintained that Schleswig (Sonderjylland, South Jutland)
+was by nature and historical tradition an integral part of Denmark.
+The Eider Canal (<i>Eider-Kanal</i>), which was constructed
+between 1777 and 1784, leaves the Eider at the point where the
+river turns to the west and enters the Bay of Kiel at Holtenau. It
+was hampered by six sluices, but was used annually by some
+4000 vessels, and until its conversion in 1887-1895 into the
+Kaiser Wilhelm Canal afforded the only direct connexion between
+the North Sea and the Baltic.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EIDER<a name="ar10" id="ar10"></a></span> (Icelandic, <i>Ædur</i>), a large marine duck, the <i>Somateria
+mollissima</i> of ornithologists, famous for its down, which, from
+its extreme lightness and elasticity, is in great request for filling
+bed-coverlets. This bird generally frequents low rocky islets
+near the coast, and in Iceland and Norway has long been afforded
+every encouragement and protection, a fine being inflicted for
+killing it during the breeding-season, or even for firing a gun near
+its haunts, while artificial nesting-places are in many localities
+contrived for its further accommodation. From the care thus
+taken of it in those countries it has become exceedingly tame at
+its chief resorts, which are strictly regarded as property, and the
+taking of eggs or down from them, except by authorized persons,
+is severely punished by law. In appearance the eider is somewhat
+clumsy, though it flies fast and dives admirably. The
+female is of a dark reddish-brown colour barred with brownish-black.
+The adult male in spring is conspicuous by his pied
+plumage of velvet-black beneath, and white above: a patch
+of shining sea-green on his head is only seen on close inspection.
+This plumage he is considered not to acquire until his third
+year, being when young almost exactly like the female, and
+it is certain that the birds which have not attained their full
+dress remain in flocks by themselves without going to the
+breeding-stations. The nest is generally in some convenient
+corner among large stones, hollowed in the soil, and furnished
+with a few bits of dry grass, seaweed or heather. By the time
+that the full number of eggs (which rarely if ever exceeds five)
+is laid the down is added. Generally the eggs and down are
+<span class="pagenum"><a name="page133" id="page133"></a>133</span>
+taken at intervals of a few days by the owners of the &ldquo;eider-fold,&rdquo;
+and the birds are thus kept depositing both during the
+whole season; but some experience is needed to ensure the
+greatest profit from each commodity. Every duck is ultimately
+allowed to hatch an egg or two to keep up the stock, and the
+down of the last nest is gathered after the birds have left the spot.
+The story of the drake&rsquo;s furnishing down, after the duck&rsquo;s
+supply is exhausted is a fiction. He never goes near the nest.
+The eggs have a strong flavour, but are much relished by both
+Icelanders and Norwegians. In the Old World the eider breeds
+in suitable localities from Spitsbergen to the Farne Islands off
+the coast of Northumberland&mdash;where it is known as St Cuthbert&rsquo;s
+duck. Its food consists of marine animals (molluscs and crustaceans),
+and hence the young are not easily reared in captivity.
+The eider of the New World differs somewhat, and has been
+described as a distinct species (<i>S. dresseri</i>). Though much
+diminished in numbers by persecution, it is still abundant on
+the coast of Newfoundland and thence northward. In Greenland
+also eiders are very plentiful, and it is supposed that three-fourths
+of the supply of down sent to Copenhagen comes from
+that country. The limits of the eider&rsquo;s northern range are not
+known, but the Arctic expedition of 1875 did not meet with it
+after leaving the Danish settlements, and its place was taken
+by an allied species, the king-duck (<i>S. spectabilis</i>), a very beautiful
+bird which sometimes appears on the British coast. The female
+greatly resembles that of the eider, but the male has a black
+chevron on his chin and a bright orange prominence on his
+forehead, which last seems to have given the species its English
+name. On the west coast of North America the eider is represented
+by a species (<i>S. v-nigrum</i>) with a like chevron, but otherwise
+resembling the Atlantic bird. In the same waters two
+other fine species are also found (<i>S. fischeri</i> and <i>S. stelleri</i>), one
+of which (the latter) also inhabits the Arctic coast of Russia
+and East Finmark and has twice reached England. The Labrador
+duck (<i>S. labradoria</i>), now extinct, also belongs to this
+group.</p>
+<div class="author">(A. N.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">EIFEL,<a name="ar11" id="ar11"></a></span> a district of Germany, in the Prussian Rhine Province,
+between the Rhine, the Moselle and the frontier of the grand
+duchy of Luxemburg. It is a hilly region, most elevated in the
+eastern part (Hohe Eifel), where there are several points from
+2000 up to 2410 ft. above sea-level. In the west is the Schneifels
+or Schnee-Eifel; and the southern part, where the most picturesque
+scenery and chief geological interest is found, is called
+the Vorder Eifel.</p>
+
+<p>The Eifel is an ancient massif of folded Devonian rocks
+upon the margins of which, near Hillesheim and towards Bitburg
+and Trier, rest unconformably the nearly undisturbed sandstones,
+marls and limestones of the Trias. On the southern border,
+at Wittlich, the terrestrial deposits of the Permian Rothliegende
+are also met with. The slates and sandstones of the Lower
+Devonian form by far the greater part of the region; but folded
+amongst these, in a series of troughs running from south-west
+to north-east lie the fossiliferous limestones of the Middle
+Devonian, and occasionally, as for example near Büdesheim,
+a few small patches of the Upper Devonian. Upon the ancient
+floor of folded Devonian strata stand numerous small volcanic
+cones, many of which, though long extinct, are still very perfect
+in form. The precise age of the eruptions is uncertain. The
+only sign of any remaining volcanic activity is the emission in
+many places of carbon dioxide and of heated waters. There is no
+historic or legendary record of any eruption, but nevertheless the
+eruptions must have continued to a very recent geological period.
+The lavas of Papenkaule are clearly posterior to the excavation
+of the valley of the Kyll, and an outflow of basalt has forced
+the Uess to seek a new course. The volcanic rocks occur both
+as tuffs and as lava-flows. They are chiefly leucite and nepheline
+rocks, such as leucitite, leucitophyre and nephelinite, but basalt
+and trachyte also occur. The leucite lavas of Niedermendig contain
+haüyne in abundance. The most extensive and continuous
+area of volcanic rocks is that surrounding the Laacher See and
+extending eastwards to Neuwied and Coblenz and even beyond
+the Rhine.</p>
+
+<p>The numerous so-called crater-lakes or <i>maare</i> of the Eifel
+present several features of interest. They do not, as a rule,
+lie in true craters at the summit of volcanic cones, but rather
+in hollows which have been formed by explosions. The most
+remarkable group is that of Daun, where the three depressions
+of Gemünd, Weinfeld and Schalkenmehren have been hollowed
+out in the Lower Devonian strata. The first of these shows no
+sign of either lavas or scoriae, but volcanic rocks occur on the
+margins of the other two. The two largest lakes in the Eifel
+region, however, are the Laacher See in the hills west of Andernach
+on the Rhine, and the Pulvermaar S.E. of the Daun group,
+with its shores of peculiar volcanic sand, which also appears in
+its waters as a black powder (<i>pulver</i>).</p>
+
+
+<hr class="art" />
+<p><span class="bold">EIFFEL TOWER.<a name="ar12" id="ar12"></a></span> Erected for the exposition of 1889, the
+Eiffel Tower, in the Champ de Mars, Paris, is by far the highest
+artificial structure in the world, and its height of 300 metres
+(984 ft.) surpasses that of the obelisk at Washington by 429 ft.,
+and that of St Paul&rsquo;s cathedral by 580 ft. Its framework is
+composed essentially of four uprights, which rise from the
+corners of a square measuring 100 metres on the side; thus the
+area it covers at its base is nearly 2½ acres. These uprights
+are supported on huge piers of masonry and concrete, the
+foundations for which were carried down, by the aid of iron
+caissons and compressed air, to a depth of about 15 metres on
+the side next the Seine, and about 9 metres on the other side.
+At first they curve upwards at an angle of 54°; then they
+gradually become straighter, until they unite in a single shaft
+rather more than half-way up. The first platform, at a height
+of 57 metres, has an area of 5860 sq. yds., and is reached either
+by staircases or lifts. The next, accessible by lifts only, is 115
+metres up, and has an area of 32 sq. yds; while the third, at
+276, supports a pavilion capable of holding 800 persons. Nearly
+25 metres higher up still is the lantern, with a gallery 5 metres
+in diameter. The work of building this structure, which is
+mainly composed of iron lattice-work, was begun on the 28th
+of January 1887, and the full height was reached on the 13th of
+March 1889. Besides being one of the sights of Paris, to which
+visitors resort in order to enjoy the extensive view that can be
+had from its higher galleries on a clear day, the tower is used to
+some extent for scientific and semi-scientific purposes; thus
+meteorological observations are carried on. The engineer under
+whose direction the tower was constructed was Alexandre
+Gustave Eiffel (born at Dijon on the 15th of December 1832),
+who had already had a wide experience in the construction of
+large metal bridges, and who designed the huge sluices for the
+Panama Canal, when it was under the French company.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EILDON HILLS,<a name="ar13" id="ar13"></a></span> a group of three conical hills, of volcanic
+origin, in Roxburghshire, Scotland, 1 m. S. by E. of Melrose,
+about equidistant from Melrose and St Boswells stations on the
+North British railway. They were once known as Eldune&mdash;the
+<i>Eldunum</i> of Simeon of Durham (fl. 1130)&mdash;probably derived from
+the Gaelic <i>aill</i>, &ldquo;rock,&rdquo; and <i>dun</i>, &ldquo;hill&rdquo;; but the name is also
+said to be a corruption of the Cymric <i>moeldun</i>, &ldquo;bald hill.&rdquo;
+The northern peak is 1327 ft. high, the central 1385 ft. and the
+southern 1216 ft. Whether or not the Roman station of <i>Trimontium</i>
+was situated here is matter of controversy. According
+to General William Roy (1726-1790) Trimontium&mdash;so called,
+according to this theory, from the triple Eildon heights&mdash;was
+Old Melrose; other authorities incline to place the station on the
+northern shore of the Solway Firth. The Eildons have been the
+subject of much legendary lore. Michael Scot (1175-1234),
+acting as a confederate of the Evil One (so the fable runs) cleft
+Eildon Hill, then a single cone, into the three existing peaks.
+Another legend states that Arthur and his knights sleep in a
+vault beneath the Eildons. A third legend centres in Thomas
+of Erceldoune. The Eildon Tree Stone, a large moss-covered
+boulder, lying on the high road as it bends towards the west
+within 2 m. of Melrose, marks the spot where the Fairy Queen
+led him into her realms in the heart of the hills. Other places
+associated with this legend may still be identified. Huntly
+Banks, where &ldquo;true Thomas&rdquo; lay and watched the queen&rsquo;s
+approach, is half a mile west of the Eildon Tree Stone, and on the
+<span class="pagenum"><a name="page134" id="page134"></a>134</span>
+west side of the hills is Bogle Burn, a streamlet that feeds the
+Tweed and probably derives its name from his ghostly visitor.
+Here, too, is Rhymer&rsquo;s glen, although the name was invented
+by Sir Walter Scott, who added the dell to his Abbotsford estate.
+Bowden, to the south of the hills, was the birthplace of the poets
+Thomas Aird (1802-1876) and James Thomson, and its parish
+church contains the burial-place of the dukes of Roxburghe.
+Eildon Hall is a seat of the duke of Buccleuch.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EILENBURG,<a name="ar14" id="ar14"></a></span> a town of Germany, in the Prussian province
+of Saxony, on an island formed by the Mulde, 31 m. E. from
+Halle, at the junction of the railways Halle-Cottbus and Leipzig-Eilenburg.
+Pop. (1905) 15,145. There are three churches, two
+Evangelical and one Roman Catholic. The industries of the
+town include the manufacture of chemicals, cloth, quilting,
+calico, cigars and agricultural implements, bleaching, dyeing,
+basket-making, carriage-building and trade in cattle. In the
+neighbourhood is the iron foundry of Erwinhof. Opposite the
+town, on the steep left bank of the Mulde, is the castle from
+which it derives its name, the original seat of the noble family
+of Eulenburg. This castle (Ilburg) is mentioned in records of
+the reigns of Henry the Fowler as an important outpost against
+the Sorbs and Wends. The town itself, originally called
+Mildenau, is of great antiquity. It is first mentioned as a town
+in 981, when it belonged to the house of Wettin and was the
+chief town of the East Mark. In 1386 it was incorporated in
+the margraviate of Meissen. In 1815 it passed to Prussia.</p>
+
+<div class="condensed">
+<p>See Gundermann, <i>Chronik der Stadt Eilenburg</i> (Eilenburg, 1879).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EINBECK,<a name="ar15" id="ar15"></a></span> or <span class="sc">Eimbeck</span>, a town of Germany, in the Prussian
+province of Hanover, on the Ilm, 50 m. by rail S. of Hanover.
+Pop. (1905) 8709. It is an old-fashioned town with many quaint
+wooden houses, notable among them the &ldquo;Northeimhaus,&rdquo; a
+beautiful specimen of medieval architecture. There are several
+churches, among them the Alexanderkirche, containing the
+tombs of the princes of Grubenhagen, and a synagogue. The
+schools include a <i>Realgymnasium</i> (<i>i.e.</i> predominantly for
+&ldquo;modern&rdquo; subjects), technical schools for the advanced study
+of machine-making, for weaving and for the textile industries,
+a preparatory training-college and a police school. The industries
+include brewing, weaving and the manufacture of
+cloth, carpets, tobacco, sugar, leather-grease, toys and roofing-felt.</p>
+
+<p>Einbeck grew up originally round the monastery of St
+Alexander (founded 1080), famous for its relic of the True Blood.
+It is first recorded as a town in 1274, and in the 14th century
+was the seat of the princes of Grubenhagen, a branch of the
+ducal house of Brunswick. The town subsequently joined the
+Hanseatic League. In the 15th century it became famous for
+its beer (&ldquo;Eimbecker,&rdquo; whence the familiar &ldquo;Bock&rdquo;). In 1540
+the Reformation was introduced by Duke Philip of Brunswick-Saltzderhelden
+(d. 1551), with the death of whose son Philip II.
+(1596) the Grubenhagen line became extinct. In 1626, during
+the Thirty Years&rsquo; War, Einbeck was taken by Pappenheim and
+in October 1641 by Piccolomini. In 1643 it was evacuated by the
+Imperialists. In 1761 its walls were razed by the French.</p>
+
+<div class="condensed">
+<p>See H.L. Harland, <i>Gesch. der Stadt Einbeck</i>, 2 Bde. (Einbeck,
+1854-1859; abridgment, <i>ib.</i> 1881).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EINDHOVEN,<a name="ar16" id="ar16"></a></span> a town in the province of North Brabant,
+Holland, and a railway junction 8 m. by rail W. by S. of
+Helmond. Pop. (1900) 4730. Like Tilburg and Helmond it
+has developed in modern times into a flourishing industrial
+centre, having linen, woollen, cotton, tobacco and cigar,
+matches, &amp;c., factories and several breweries.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EINHARD<a name="ar17" id="ar17"></a></span> (<i>c.</i> 770-840), the friend and biographer of Charlemagne;
+he is also called Einhartus, Ainhardus or Heinhardus,
+in some of the early manuscripts. About the 10th century
+the name was altered into Agenardus, and then to Eginhardus,
+or Eginhartus, but, although these variations were largely used
+in the English and French languages, the form Einhardus, or
+Einhartus, is unquestionably the right one.</p>
+
+<p>According to the statement of Walafrid Strabo, Einhard was
+born in the district which is watered by the river Main, and his
+birth has been fixed at about 770. His parents were of noble
+birth, and were probably named Einhart and Engilfrit; and
+their son was educated in the monastery of Fulda, where he
+was certainly residing in 788 and in 791. Owing to his intelligence
+and ability he was transferred, not later than 796, from Fulda
+to the palace of Charlemagne by abbot Baugulf; and he soon
+became very intimate with the king and his family, and undertook
+various important duties, one writer calling him <i>domesticus
+palatii regalis</i>. He was a member of the group of scholars who
+gathered around Charlemagne and was entrusted with the
+charge of the public buildings, receiving, according to a fashion
+then prevalent, the scriptural name of Bezaleel (Exodus xxxi. 2
+and xxxv. 30-35) owing to his artistic skill. It has been supposed
+that he was responsible for the erection of the basilica at Aix-la-Chapelle,
+where he resided with the emperor, and the other
+buildings mentioned in chapter xvii. of his <i>Vita Karoli Magni</i>,
+but there is no express statement to this effect. In 806 Charlemagne
+sent him to Rome to obtain the signature of Pope Leo III.
+to a will which he had made concerning the division of his
+empire; and it was possibly owing to Einhard&rsquo;s influence that
+in 813, after the death of his two elder sons, the emperor made
+his remaining son, Louis, a partner with himself in the imperial
+dignity. When Louis became sole emperor in 814 he retained
+his father&rsquo;s minister in his former position; then in 817 made
+him tutor to his son, Lothair, afterwards the emperor Lothair I.;
+and showed him many other marks of favour. Einhard married
+Emma, or Imma, a sister of Bernharius, bishop of Worms, and
+a tradition of the 12th century represented this lady as a daughter
+of Charlemagne, and invented a romantic story with regard to
+the courtship which deserves to be noticed as it frequently
+appears in literature. Einhard is said to have visited the
+emperor&rsquo;s daughter regularly and secretly, and on one occasion
+a fall of snow made it impossible for him to walk away without
+leaving footprints, which would lead to his detection. This risk,
+however, was obviated by the foresight of Emma, who carried
+her lover across the courtyard of the palace; a scene which was
+witnessed by Charlemagne, who next morning narrated the
+occurrence to his counsellors, and asked for their advice. Very
+severe punishments were suggested for the clandestine lover,
+but the emperor rewarded the devotion of the pair by consenting
+to their marriage. This story is, of course, improbable, and is
+further discredited by the fact that Einhard does not mention
+Emma among the number of Charlemagne&rsquo;s children. Moreover,
+a similar story has been told of a daughter of the emperor
+Henry III. It is uncertain whether Einhard had any children.
+He addressed a letter to a person named Vussin, whom he calls
+<i>fili</i> and <i>mi nate</i>, but, as Vussin is not mentioned in documents
+in which his interests as Einhard&rsquo;s son would have been
+concerned, it is possible that he was only a young man in whom
+he took a special interest. In January 815 the emperor Louis I.
+bestowed on Einhard and his wife the domains of Michelstadt
+and Mulinheim in the Odenwald, and in the charter conveying
+these lands he is called simply Einhardus, but, in a document
+dated the 2nd of June of the same year, he is referred to as abbot.
+After this time he is mentioned as head of several monasteries:
+St Peter, Mount Blandin and St Bavon at Ghent, St Servais
+at Maastricht, St Cloud near Paris, and Fontenelle near Rouen,
+and he also had charge of the church of St John the Baptist
+at Pavia.</p>
+
+<p>During the quarrels which took place between Louis I. and
+his sons, in consequence of the emperor&rsquo;s second marriage,
+Einhard&rsquo;s efforts were directed to making peace, but after a time
+he grew tired of the troubles and intrigues of court life. In 818
+he had given his estate at Michelstadt to the abbey of Lorsch,
+but he retained Mulinheim, where about 827 he founded an
+abbey and erected a church, to which he transported some relics
+of St Peter and St Marcellinus, which he had procured from
+Rome. To Mulinheim, which was afterwards called Seligenstadt,
+he finally retired in 830. His wife, who had been his constant
+helper, and whom he had not put away on becoming an abbot,
+died in 836, and after receiving a visit from the emperor, Einhard
+died on the 14th of March 840. He was buried at Seligenstadt,
+and his epitaph was written by Hrabanus Maurus. Einhard
+<span class="pagenum"><a name="page135" id="page135"></a>135</span>
+was a man of very short stature, a feature on which Alcuin wrote
+an epigram. Consequently he was called <i>Nardulus</i>, a diminutive
+form of Einhardus, and his great industry and activity caused
+him to be likened to an ant. He was also a man of learning and
+culture. Reaping the benefits of the revival of learning brought
+about by Charlemagne, he was on intimate terms with Alcuin,
+was well versed in Latin literature, and knew some Greek. His
+most famous work is his <i>Vita Karoli Magni</i>, to which a prologue
+was added by Walafrid Strabo. Written in imitation of the
+<i>De vitis Caesarum</i> of Suetonius, this is the best contemporary
+account of the life of Charlemagne, and could only have been
+written by one who was very intimate with the emperor and his
+court. It is, moreover, a work of some artistic merit, although
+not free from inaccuracies. It was written before 821, and having
+been very popular during the middle ages, was first printed
+at Cologne in 1521. G.H. Pertz collated more than sixty
+manuscripts for his edition of 1829, and others have since come
+to light. Other works by Einhard are: <i>Epistolae</i>, which are of
+considerable importance for the history of the times; <i>Historia
+translationis beatorum Christi martyrum Marcellini et Petri</i>,
+which gives a curious account of how the bones of these martyrs
+were stolen and conveyed to Seligenstadt, and what miracles
+they wrought; and <i>De adoranda cruce</i>, a treatise which has only
+recently come to light, and which has been published by E.
+Dümmler in the <i>Neues Archiv der Gesellschaft für ältere deutsche
+Geschichtskunde</i>, Band xi. (Hanover, 1886). It has been asserted
+that Einhard was the author of some of the Frankish annals,
+and especially of part of the annals of Lorsch (<i>Annales Laurissenses
+majores</i>), and part of the annals of Fulda (<i>Annales
+Fuldenses</i>). Much discussion has taken place on this question,
+and several of the most eminent of German historians, Ranke
+among them, have taken part therein, but no certain decision
+has been reached.</p>
+
+<div class="condensed">
+<p>The literature on Einhard is very extensive, as nearly all those
+who deal with Charlemagne, early German and early French literature,
+treat of him. Editions of his works are by A. Teulet, <i>Einhardi
+omnia quae extant opera</i> (Paris, 1840-1843), with a French translation;
+P. Jaffé, in the <i>Bibliotheca rerum Germanicarum</i>, Band iv. (Berlin,
+1867); G.H. Pertz in the <i>Monumenta Germaniae historica</i>, Bände
+i. and ii. (Hanover, 1826-1829), and J.P. Migne in the <i>Patrologia
+Latina</i>, tomes 97 and 104 (Paris, 1866). The <i>Vita Karoli Magni</i>,
+edited by G.H. Pertz and G. Waitz, has been published separately
+(Hanover, 1880). Among the various translations of the <i>Vita</i> may
+be mentioned an English one by W. Glaister (London, 1877) and a
+German one by O. Abel (Leipzig, 1893). For a complete bibliography
+of Einhard, see A. Potthast, <i>Bibliotheca historica</i>, pp. 394-397
+(Berlin, 1896), and W. Wattenbach, <i>Deutschlands Geschichtsquellen</i>,
+Band i. (Berlin, 1904).</p>
+</div>
+<div class="author">(A. W. H.*)</div>
+
+
+<hr class="art" />
+<p><span class="bold">EINHORN, DAVID<a name="ar18" id="ar18"></a></span> (1809-1879), leader of the Jewish reform
+movement in the United States of America, was born in Bavaria.
+He was a supporter of the principles of Abraham Geiger (<i>q.v.</i>),
+and while still in Germany advocated the introduction of prayers
+in the vernacular, the exclusion of nationalistic hopes from the
+synagogue service, and other ritual modifications. In 1855 he
+migrated to America, where he became the acknowledged leader
+of reform, and laid the foundation of the régime under which the
+mass of American Jews (excepting the newly arrived Russians)
+now worship. In 1858 he published his revised prayer book,
+which has formed the model for all subsequent revisions. In 1861
+he strongly supported the anti-slavery party, and was forced
+to leave Baltimore where he then ministered. He continued his
+work first in Philadelphia and later in New York.</p>
+<div class="author">(I. A.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">EINSIEDELN,<a name="ar19" id="ar19"></a></span> the most populous town in the Swiss canton of
+Schwyz. It is built on the right bank of the Alpbach (an affluent
+of the Sihl), at a height of 2908 ft. above the sea-level on a rather
+bare moorland, and by rail is 25 m. S.E. of Zürich, or by a round-about
+railway route about 38 m. north of Schwyz, with which
+it communicates directly over the Hacken Pass (4649 ft.) or the
+Holzegg Pass (4616 ft.). In 1900 the population was 8496, all
+(save 75) Romanists and all (save 111) German-speaking. The
+town is entirely dependent on the great Benedictine abbey that
+rises slightly above it to the east. Close to its present site
+Meinrad, a hermit, was murdered in 861 by two robbers, whose
+crime was made known by Meinrad&rsquo;s two pet ravens. Early
+in the 10th century Benno, a hermit, rebuilt the holy man&rsquo;s cell,
+but the abbey proper was not founded till about 934, the church
+having been consecrated (it is said by Christ Himself) in 948.
+In 1274 the dignity of a prince of the Holy Roman Empire was
+confirmed by the emperor to the reigning abbot. Originally
+under the protection of the counts of Rapperswil (to which town
+on the lake of Zürich the old pilgrims&rsquo; way still leads over the
+Etzel Pass, 3146 ft., with its chapel and inn), this position passed
+by marriage with their heiress in 1295 to the Laufenburg or
+cadet line of the Habsburgs, but from 1386 was permanently
+occupied by Schwyz. A black wooden image of the Virgin and
+the fame of St Meinrad caused the throngs of pilgrims to resort
+to Einsiedeln in the middle ages, and even now it is much
+frequented, particularly about the 14th of September. The
+existing buildings date from the 18th century only, while the
+treasury and the library still contain many precious objects,
+despite the sack by the French in 1798. There are now about
+100 fully professed monks, who direct several educational
+institutions. The Black Virgin has a special chapel in the stately
+church. Zwingli was the parish priest of Einsiedeln 1516-1518
+(before he became a Protestant), while near the town Paracelsus
+(1493-1541), the celebrated philosopher, was born.</p>
+
+<div class="condensed">
+<p>See Father O. Ringholz, <i>Geschichte d. fürstl. Benediktinerstiftes
+Einsiedeln</i>, vol. i. (to 1526), (Einsiedeln, 1904).</p>
+</div>
+<div class="author">(W. A. B. C.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">EISENACH,<a name="ar20" id="ar20"></a></span> a town of Germany, second capital of the grand-duchy
+of Saxe-Weimar-Eisenach, lies at the north-west foot
+of the Thuringian forest, at the confluence of the Nesse and
+Hörsel, 32 m. by rail W. from Erfurt. Pop. (1905) 35,123.
+The town mainly consists of a long street, running from east to
+west. Off this are the market square, containing the grand-ducal
+palace, built in 1742, where the duchess Hélène of Orleans
+long resided, the town-hall, and the late Gothic St Georgenkirche;
+and the square on which stands the Nikolaikirche, a
+fine Romanesque building, built about 1150 and restored in 1887.
+Noteworthy are also the Klemda, a small castle dating from
+1260; the Lutherhaus, in which the reformer stayed with the
+Cotta family in 1498; the house in which Sebastian Bach was
+born, and that (now a museum) in which Fritz Reuter lived
+(1863-1874). There are monuments to the two former in the
+town, while the resting-place of the latter in the cemetery is
+marked by a less pretentious memorial. Eisenach has a school
+of forestry, a school of design, a classical school (<i>Gymnasium</i>)
+and modern school (<i>Realgymnasium</i>), a deaf and dumb school, a
+teachers&rsquo; seminary, a theatre and a Wagner museum. The
+most important industries of the town are worsted-spinning,
+carriage and wagon building, and the making of colours and
+pottery. Among others are the manufacture of cigars, cement
+pipes, iron-ware and machines, alabaster ware, shoes, leather,
+&amp;c., cabinet-making, brewing, granite quarrying and working,
+tile-making, and saw- and corn-milling.</p>
+
+<p>The natural beauty of its surroundings and the extensive
+forests of the district have of late years attracted many summer
+residents. Magnificently situated on a precipitous hill, 600 ft.
+above the town to the south, is the historic Wartburg (<i>q.v.</i>), the
+ancient castle of the landgraves of Thuringia, famous as the
+scene of the contest of Minnesingers immortalized in Wagner&rsquo;s
+Tannhäuser, and as the place where Luther, on his return from
+the diet of Worms in 1521, was kept in hiding and made his
+translation of the Bible. On a high rock adjacent to the Wartburg
+are the ruins of the castle of Mädelstein.</p>
+
+<p>Eisenach (<i>Isenacum</i>) was founded in 1070 by Louis II. the
+Springer, landgrave of Thuringia, and its history during the
+middle ages was closely bound up with that of the Wartburg,
+the seat of the landgraves. The Klemda, mentioned above,
+was built by Sophia (d. 1284), daughter of the landgrave Louis
+IV., and wife of Duke Henry II. of Brabant, to defend the town
+against Henry III., margrave of Meissen, during the succession
+contest that followed the extinction of the male line of the
+Thuringian landgraves in 1247. The principality of Eisenach
+fell to the Saxon house of Wettin in 1440, and in the partition of
+1485 formed part of the territories given to the Ernestine line.
+It was a separate Saxon duchy from 1596 to 1638, from 1640
+<span class="pagenum"><a name="page136" id="page136"></a>136</span>
+to 1644, and again from 1662 to 1741, when it finally fell to Saxe-Weimar.
+The town of Eisenach, by reason of its associations,
+has been a favourite centre for the religious propaganda of
+Evangelical Germany, and since 1852 it has been the scene of
+the annual conference of the German Evangelical Church, known
+as the Eisenach conference.</p>
+
+<div class="condensed">
+<p>See Trinius, <i>Eisenach und Umgebung</i> (Minden, 1900); and H.A.
+Daniel, <i>Deutschland</i> (Leipzig, 1895), and further references in U.
+Chevalier, &ldquo;Répertoire des sources,&rdquo; &amp;c., <i>Topo-bibliogr.</i> (Montbéliard,
+1894-1899), s.v.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EISENBERG<a name="ar21" id="ar21"></a></span> (<i>Isenberg</i>), a town of Germany, in the duchy of
+Saxe-Altenburg, on a plateau between the rivers Saale and
+Elster, 20 m. S.W. from Zeitz, and connected with the railway
+Leipzig-Gera by a branch to Crossen. Pop. (1905) 8824. It
+possesses an old castle, several churches and monuments to
+Duke Christian of Saxe-Eisenberg (d. 1707), Bismarck, and the
+philosopher Karl Christian Friedrich Krause (<i>q.v.</i>). Its principal
+industries are weaving, and the manufacture of machines,
+ovens, furniture, pianos, porcelain and sausages.</p>
+
+<div class="condensed">
+<p>See Back, <i>Chronik der Sladt und des Amtes Eisenberg</i> (Eisenb., 1843).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EISENERZ<a name="ar22" id="ar22"></a></span> (&ldquo;Iron ore&rdquo;), a market-place and old mining
+town in Styria, Austria, 68 m. N.W. of Graz by rail. Pop.
+(1900) 6494. It is situated in a deep valley, dominated on the
+east by the Pfaffenstein (6140 ft.), on the west by the Kaiserschild
+(6830 ft.), and on the south by the Erzberg (5030 ft.). It
+has an interesting example of a medieval fortified church, a
+Gothic edifice founded by Rudolph of Habsburg in the 13th
+century and rebuilt in the 16th. The Erzberg or Ore Mountain
+furnishes such rich ore that it is quarried in the open air like
+stone, in the summer months. There is documentary evidence
+of the mines having been worked as far back as the 12th century.
+They afford employment to two or three thousand hands in
+summer and about half as many in winter, and yield some
+800,000 tons of iron per annum. Eisenerz is connected with the
+mines by the Erzberg railway, a bold piece of engineering work,
+14 m. long, constructed on the Abt&rsquo;s rack-and-pinion system.
+It passes through some beautiful scenery, and descends to
+Vordernberg (pop. 3111), an important centre of the iron trade
+situated on the south side of the Erzberg. Eisenerz possesses,
+in addition, twenty-five furnaces, which produce iron, and
+particularly steel, of exceptional excellence. A few miles to the
+N.W. of Eisenerz lies the castle of Leopoldstein, and near it the
+beautiful Leopoldsteiner Lake. This lake, with its dark-green
+water, situated at an altitude of 2028 ft., and surrounded on all
+sides by high peaks, is not big, but is very deep, having a depth
+of 520 ft.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EISLEBEN<a name="ar23" id="ar23"></a></span> (Lat. <i>Islebia</i>), a town of Germany, in the Prussian
+province of Saxony, 24 m. W. by N. from Halle, on the railway
+to Nordhausen and Cassel. Pop. (1905) 23,898. It is divided
+into an old and a new town (Altstadt and Neustadt). Among
+its principal buildings are the church of St Andrew (Andreaskirche),
+which contains numerous monuments of the counts of
+Mansfeld; the church of St Peter and St Paul (Peter-Paulkirche),
+containing the font in which Luther was baptized; the royal
+gymnasium (classical school), founded by Luther shortly before
+his death in 1546; and the hospital. Eisleben is celebrated
+as the place where Luther was born and died. The house in
+which he was born was burned in 1689, but was rebuilt in 1693
+as a free school for orphans. This school fell into decay under
+the régime of the kingdom of Westphalia, but was restored in
+1817 by King Frederick William III. of Prussia, who, in 1819,
+transferred it to a new building behind the old house. The
+house in which Luther died was restored towards the end of the
+19th century, and his death chamber is still preserved. A
+bronze statue of Luther by Rudolf Siemering (1835-1905) was
+unveiled in 1883. Eisleben has long been the centre of an
+important mining district (Luther was a miner&rsquo;s son), the
+principal products being silver and copper. It possesses smelting
+works and a school of mining.</p>
+
+<p>The earliest record of Eisleben is dated 974. In 1045, at
+which time it belonged to the counts of Mansfeld, it received
+the right to hold markets, coin money, and levy tolls. From
+1531 to 1710 it was the seat of the cadet line of the counts of
+Mansfeld-Eisleben. After the extinction of the main line of
+the counts of Mansfeld, Eisleben fell to Saxony, and, in the
+partition of Saxony by the congress of Vienna in 1815, was
+assigned to Prussia.</p>
+
+<div class="condensed">
+<p>See G. Grössler, <i>Urkundliche Gesch. Eislebens bis zum Ende des 12.
+Jahrhunderts</i> (Halle, 1875); <i>Chronicon Islebiense; Eisleben Stadtchronik
+aus den Jahren</i> 1520-1738, edited from the original, with
+notes by Grössler and Sommer (Eisleben, 1882).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EISTEDDFOD<a name="ar24" id="ar24"></a></span> (plural Eisteddfodau), the national bardic congress
+of Wales, the objects of which are to encourage bardism
+and music and the general literature of the Welsh, to maintain
+the Welsh language and customs of the country, and to foster and
+cultivate a patriotic spirit amongst the people. This institution,
+so peculiar to Wales, is of very ancient origin.<a name="fa1a" id="fa1a" href="#ft1a"><span class="sp">1</span></a> The term
+<i>Eisteddfod</i>, however, which means &ldquo;a session&rdquo; or &ldquo;sitting,&rdquo;
+was probably not applied to bardic congresses before the 12th
+century.</p>
+
+<p>The Eisteddfod in its present character appears to have
+originated in the time of Owain ap Maxen Wledig, who at the
+close of the 4th century was elected to the chief sovereignty
+of the Britons on the departure of the Romans. It was at this
+time, or soon afterwards, that the laws and usages of the Gorsedd
+were codified and remodelled, and its motto of &ldquo;Y gwir yn erbyn
+y byd&rdquo; (The truth against the world) given to it. &ldquo;Chairs&rdquo;
+(with which the Eisteddfod as a national institution is now
+inseparably connected) were also established, or rather perhaps
+resuscitated, about the same time. The chair was a kind of
+convention where disciples were trained, and bardic matters
+discussed preparatory to the great Gorsedd, each chair having a
+distinctive motto. There are now existing four chairs in Wales,&mdash;namely,
+the &ldquo;royal&rdquo; chair of Powys, whose motto is &ldquo;A laddo
+a leddir&rdquo; (He that slayeth shall be slain); that of Gwent and
+Glamorgan, whose motto is &ldquo;Duw a phob daioni&rdquo; (God and all
+goodness); that of Dyfed, whose motto is &ldquo;Calon wrth galon&rdquo;
+(Heart with heart); and that of Gwynedd, or North Wales, whose
+motto is &ldquo;Iesu,&rdquo; or &ldquo;O Iesu! na&rsquo;d gamwaith&rdquo; (Jesus, or Oh
+Jesus! suffer not iniquity).</p>
+
+<p>The first Eisteddfod of which any account seems to have
+descended to us was one held on the banks of the Conway in
+the 6th century, under the auspices of Maelgwn Gwynedd, prince
+of North Wales. Maelgwn on this occasion, in order to prove
+the superiority of vocal song over instrumental music, is recorded
+to have offered a reward to such bards and minstrels as should
+swim over the Conway. There were several competitors, but on
+their arrival on the opposite shore the harpers found themselves
+unable to play owing to the injury their harps had sustained
+from the water, while the bards were in as good tune as ever.
+King Cadwaladr also presided at an Eisteddfod about the
+middle of the 7th century.</p>
+
+<p>Griffith ap Cynan, prince of North Wales, who had been born
+in Ireland, brought with him from that country many Irish
+musicians, who greatly improved the music of Wales. During
+his long reign of 56 years he offered great encouragement to
+bards, harpers and minstrels, and framed a code of laws for their
+better regulation. He held an Eisteddfod about the beginning
+of the 12th century at Caerwys in Flintshire, &ldquo;to which there
+repaired all the musicians of Wales, and some also from England
+and Scotland.&rdquo; For many years afterwards the Eisteddfod
+appears to have been held triennially, and to have enforced the
+rigid observance of the enactments of Griffith ap Cynan. The
+places at which it was generally held were Aberffraw, formerly
+the royal seat of the princes of North Wales; Dynevor, the
+royal castle of the princes of South Wales; and Mathrafal,
+the royal palace of the princes of Powys: and in later times
+<span class="pagenum"><a name="page137" id="page137"></a>137</span>
+Caerwys in Flintshire received that honourable distinction, it
+having been the princely residence of Llewelyn the Last. Some
+of these Eisteddfodau were conducted in a style of great magnificence,
+under the patronage of the native princes. At Christmas
+1107 Cadwgan, the son of Bleddyn ap Cynfyn, prince of Powys,
+held an Eisteddfod in Cardigan Castle, to which he invited the
+bards, harpers and minstrels, &ldquo;the best to be found in all Wales&rdquo;;
+and &ldquo;he gave them chairs and subjects of emulation according
+to the custom of the feasts of King Arthur.&rdquo; In 1176 Rhys ab
+Gruffydd, prince of South Wales, held an Eisteddfod in the same
+castle on a scale of still greater magnificence, it having been
+proclaimed, we are told, a year before it took place, &ldquo;over Wales,
+England, Scotland, Ireland and many other countries.&rdquo;</p>
+
+<p>On the annexation of Wales to England, Edward I. deemed it
+politic to sanction the bardic Eisteddfod by his famous statute of
+Rhuddlan. In the reign of Edward III. Ifor Hael, a South Wales
+chieftain, held one at his mansion. Another was held in 1451,
+with the permission of the king, by Griffith ab Nicholas at
+Carmarthen, in princely style, where Dafydd ab Edmund, an
+eminent poet, signalized himself by his wonderful powers of
+versification in the Welsh metres, and whence &ldquo;he carried home
+on his shoulders the silver chair&rdquo; which he had fairly won.
+Several Eisteddfodau, were held, one at least by royal mandate,
+in the reign of Henry VII. In 1523 one was held at Caerwys
+before the chamberlain of North Wales and others, by virtue of
+a commission issued by Henry VIII. In the course of time,
+through relaxation of bardic discipline, the profession was
+assumed by unqualified persons, to the great detriment of the
+regular bards. Accordingly in 1567 Queen Elizabeth issued
+a commission for holding an Eisteddfod at Caerwys in the
+following year, which was duly held, when degrees were conferred
+on 55 candidates, including 20 harpers. From the terms of the
+royal proclamation we find that it was then customary to bestow
+&ldquo;a silver harp&rdquo; on the chief of the faculty of musicians, as it had
+been usual to reward the chief bard with &ldquo;a silver chair.&rdquo; This
+was the last Eisteddfod appointed by royal commission, but
+several others of some importance were held during the 16th
+and 17th centuries, under the patronage of the earl of Pembroke,
+Sir Richard Neville, and other influential persons. Amongst
+these the last of any particular note was one held in Bewper
+Castle, Glamorgan, by Sir Richard Basset in 1681.</p>
+
+<p>During the succeeding 130 years Welsh nationality was at its
+lowest ebb, and no general Eisteddfod on a large scale appears
+to have been held until 1819, though several small ones were
+held under the auspices of the Gwyneddigion Society, established
+in 1771,&mdash;the most important being those at Corwen (1789),
+St Asaph (1790) and Caerwys (1798).</p>
+
+<p>At the close of the Napoleonic wars, however, there was a
+general revival of Welsh nationality, and numerous Welsh
+literary societies were established throughout Wales, and in
+the principal English towns. A large Eisteddfod was held under
+distinguished patronage at Carmarthen in 1819, and from that
+time to the present they have been held (together with numerous
+local Eisteddfodau), almost without intermission, annually.
+The Eisteddfod at Llangollen in 1858 is memorable for its archaic
+character, and the attempts then made to revive the ancient
+ceremonies, and restore the ancient vestments of druids, bards
+and ovates.</p>
+
+<p>To constitute a provincial Eisteddfod it is necessary that
+it should be proclaimed by a graduated bard of a Gorsedd a
+year and a day before it takes place. A local one may be held
+without such a proclamation. A provincial Eisteddfod generally
+lasts three, sometimes four days. A president and a conductor
+are appointed for each day. The proceedings commence with a
+Gorsedd meeting, opened with sound of trumpet and other
+ceremonies, at which candidates come forward and receive
+bardic degrees after satisfying the presiding bard as to their
+fitness. At the subsequent meetings the president gives a brief
+address; the bards follow with poetical addresses; adjudications
+are made, and prizes and medals with suitable devices are given
+to the successful competitors for poetical, musical and prose
+compositions, for the best choral and solo singing, and singing with
+the harp or &ldquo;Pennillion singing&rdquo;<a name="fa2a" id="fa2a" href="#ft2a"><span class="sp">2</span></a> as it is called, for the best playing
+on the harp or stringed or wind instruments, as well as
+occasionally for the best specimens of handicraft and art. In the
+evening of each day a concert is given, generally attended by very
+large numbers. The great day of the Eisteddfod is the &ldquo;chair&rdquo; day&mdash;usually
+the third or last day&mdash;the grand event of the Eisteddfod
+being the adjudication on the chair subject, and the chairing and
+investiture of the fortunate winner. This is the highest object
+of a Welsh bard&rsquo;s ambition. The ceremony is an imposing one,
+and is performed with sound of trumpet. (See also the articles
+<span class="sc"><a href="#artlinks">Bard</a></span>, <span class="sc"><a href="#artlinks">Celt</a></span>: <i>Celtic Literature</i>, and <span class="sc"><a href="#artlinks">Wales</a></span>.)</p>
+<div class="author">(R. W.*)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1a" id="ft1a" href="#fa1a"><span class="fn">1</span></a> According to the Welsh Triads and other historical records, the
+<i>Gorsedd</i> or assembly (an essential part of the modern Eisteddfod,
+from which indeed the latter sprung) is as old at least as the time of
+Prydain the son of Ædd the Great, who lived many centuries before
+the Christian era. Upon the destruction of the political ascendancy
+of the Druids, the Gorsedd lost its political importance, though it
+seems to have long afterwards retained its institutional character as
+the medium for preserving the laws, doctrines and traditions of
+bardism.</p>
+
+<p><a name="ft2a" id="ft2a" href="#fa2a"><span class="fn">2</span></a> According to Jones&rsquo;s <i>Bardic Remains</i>, &ldquo;To sing &lsquo;Pennillion&rsquo;
+with a Welsh harp is not so easily accomplished as may be imagined.
+The singer is obliged to follow the harper, who may change the tune,
+or perform variations <i>ad libitum</i>, whilst the vocalist must keep time,
+and end precisely with the strain. The singer does not commence
+with the harper, but takes the strain up at the second, third or
+fourth bar, as best suits the &lsquo;pennill&rsquo; he intends to sing....
+Those are considered the best singers who can adapt stanzas of various
+metres to one melody, and who are acquainted with the twenty-four
+measures according to the bardic laws and rules of composition.&rdquo;</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EJECTMENT<a name="ar25" id="ar25"></a></span> (Lat. e, out, and <i>jacere</i>, to throw), in English law,
+an action for the recovery of the possession of land, together
+with damages for the wrongful withholding thereof. In the old
+classifications of actions, as real or personal, this was known
+as a mixed action, because its object was twofold, viz. to recover
+both the realty and personal damages. It should be noted that
+the term &ldquo;ejectment&rdquo; applies in law to distinct classes of
+proceedings&mdash;ejectments as between rival claimants to land,
+and ejectments as between those who hold, or have held, the
+relation of landlord and tenant. Under the Rules of the Supreme
+Court, actions in England for the recovery of land are commenced
+and proceed in the same manner as ordinary actions. But the
+historical interest attaching to the action of ejectment is so
+great as to render some account of it necessary.</p>
+
+<p>The form of the action as it prevailed in the English courts
+down to the Common Law Procedure Act 1852 was a series of
+fictions, among the most remarkable to be found in the entire
+body of English law. A, the person claiming title to land,
+delivered to B, the person in possession, a declaration in ejectment
+in which C and D, fictitious persons, were plaintiff and
+defendant. C stated that A had devised the land to him for a
+term of years, and that he had been ousted by D. A notice
+signed by D informed B of the proceedings, and advised him to
+apply to be made defendant in D&rsquo;s place, as he, D, having no
+title, did not intend to defend the suit. If B did not so apply,
+judgment was given against D, and possession of the lands was
+given to A. But if B did apply, the Court allowed him to
+defend the action only on condition that he admitted the three
+fictitious averments&mdash;the lease, the entry and the ouster&mdash;which,
+together with title, were the four things necessary to maintain
+an action of ejectment. This having been arranged the action
+proceeded, B being made defendant instead of D. The names
+used for the fictitious parties were John Doe, plaintiff, and
+Richard Roe, defendant, who was called &ldquo;the casual ejector.&rdquo;
+The explanation of these mysterious fictions is this. The writ
+<i>de ejectione firmae</i> was invented about the beginning of the reign
+of Edward III. as a remedy to a lessee for years who had been
+ousted of his term. It was a writ of trespass, and carried damages,
+but in the time of Henry VII., if not before that date, the courts
+of common law added thereto a species of remedy neither
+warranted by the original writ nor demanded by the declaration,
+viz. a judgment to recover so much of the term as was still to
+run, and a writ of possession thereupon. The next step was to
+extend the remedy&mdash;limited originally to leaseholds&mdash;to cases
+of disputed title to freeholds. This was done indirectly by the
+claimant entering on the land and there making a lease for a
+term of years to another person; for it was only a term that
+could be recovered by the action, and to create a term required
+actual possession in the granter. The lessee remained on the land,
+and the next person who entered even by chance was accounted
+an ejector of the lessee, who then served upon him a writ of
+trespass and ejectment. The case then went to trial as on a
+<span class="pagenum"><a name="page138" id="page138"></a>138</span>
+common action of trespass; and the claimant&rsquo;s title, being the
+real foundation of the lessee&rsquo;s right, was thus indirectly determined.
+These proceedings might take place without the knowledge
+of the person really in possession; and to prevent the
+abuse of the action a rule was laid down that the plaintiff in
+ejectment must give notice to the party in possession, who
+might then come in and defend the action. When the action
+came into general use as a mode of trying the title to freeholds,
+the actual entry, lease and ouster which were necessary to found
+the action were attended with much inconvenience, and accordingly
+Lord Chief Justice Rolle during the Protectorate (<i>c.</i> 1657)
+substituted for them the fictitious averments already described.
+The action of ejectment is now only a curiosity of legal history.
+Its fictitious suitors were swept away by the Common Law
+Procedure Act of 1852. A form of writ was prescribed, in which
+the person in possession of the disputed premises by name and
+all persons entitled to defend the possession were informed that
+the plaintiff claimed to be entitled to possession, and required
+to appear in court to defend the possession of the property or
+such part of it as they should think fit. In the form of the writ
+and in some other respects ejectment still differed from other
+actions. But, as already mentioned, it has now been assimilated
+(under the name of action for the recovery of lands) to ordinary
+actions by the Rules of the Supreme Court. It is commenced
+by writ of summons, and&mdash;subject to the rules as to summary
+judgments (<i>v. inf.</i>)&mdash;proceeds along the usual course of pleadings
+and trial to judgment; but is subject to one special rule, viz:
+that except by leave of the Court or a judge the only claims
+which may be joined with one for recovery of land are claims
+in respect of arrears of rent or double value for holding over,
+or mesne profits (<i>i.e.</i> the value of the land during the period
+of illegal possession), or damages for breach of a contract under
+which the premises are held or for any wrong or injury to the
+premises claimed (R.S.C., O. xviii. r. 2). These claims were
+formerly recoverable by an independent action.</p>
+
+<p>With regard to actions for the recovery of land&mdash;apart from
+the relationship of landlord and tenant&mdash;the only point that
+need be noted is the presumption of law in favour of the actual
+possessor of the land in dispute. Where the action is brought
+by a landlord against his tenant, there is of course no presumption
+against the landlord&rsquo;s title arising from the tenant&rsquo;s possession.
+By the Common Law Procedure Act 1852 (ss. 210-212) special
+provision was made for the prompt recovery of demised premises
+where half a year&rsquo;s rent was in arrear and the landlord was
+entitled to re-enter for non-payment. These provisions are
+still in force, but advantage is now more generally taken of the
+summary judgment procedure introduced by the Rules of the
+Supreme Court (Order 3, r. 6.). This procedure may be adopted
+when (<i>a</i>) the tenant&rsquo;s term has expired, (<i>b</i>) or has been duly
+determined by notice to quit, or (<i>c</i>) has become liable to forfeiture
+for non-payment of rent, and applies not only to the tenant
+but to persons claiming under him. The writ is specially endorsed
+with the plaintiff&rsquo;s claim to recover the land with or
+without rent or mesne profits, and summary judgment obtained
+if no substantial defence is disclosed. Where an action to
+recover land is brought against the tenant by a person claiming
+adversely to the landlord, the tenant is bound, under penalty
+of forfeiting the value of three years&rsquo; improved or rack rent of the
+premises, to give notice to the landlord in order that he may
+appear and defend his title. Actions for the recovery of land,
+other than land belonging to spiritual corporations and to the
+crown, are barred in 12 years (Real Property Limitation Acts
+1833 (s. 29) and 1874 (s. 1). A landlord can recover possession
+in the county court (i.) by an action for the recovery of possession,
+where neither the value of the premises nor the rent exceeds
+£100 a year, and the tenant is holding over (County Courts Acts
+of 1888, s. 138, and 1903, s. 3); (ii.) by &ldquo;an action of ejectment,&rdquo;
+where (<i>a</i>) the value or rent of the premises does not exceed
+£100, (<i>b</i>) half a year&rsquo;s rent is in arrear, and (<i>c</i>) no sufficient
+distress (see <span class="sc"><a href="#artlinks">Rent</a></span>) is to be found on the premises (Act of 1888,
+s. 139; Act of 1903, s. 3; County Court Rules 1903, Ord. v. rule 3).
+Where a tenant at a rent not exceeding £20 a year of premises
+at will, or for a term not exceeding 7 years, refuses nor neglects,
+on the determination or expiration of his interest, to deliver up
+possession, such possession may be recovered by proceedings
+before justices under the Small Tenements Recovery Act 1838,
+an enactment which has been extended to the recovery of allotments.
+Under the Distress for Rent Act 1737, and the Deserted
+Tenements Act 1817, a landlord can have himself put by the order
+of two justices into premises deserted by the tenant where half
+a year&rsquo;s rent is owing and no sufficient distress can be found.</p>
+
+<p>In <i>Ireland</i>, the practice with regard to the recovery of land is
+regulated by the Rules of the Supreme Court 1891, made under
+the Judicature (Ireland) Act 1877; and resembles that of
+England. Possession may be recovered summarily by a special
+indorsement of the writ, as in England; and there are analogous
+provisions with regard to the recovery of small tenements
+(see Land Act, 1860 ss. 84 and 89). The law with regard to
+the ejectment or eviction of tenants is consolidated by the Land
+Act 1860. (See ss. 52-66, 68-71, and further under <span class="sc"><a href="#artlinks">Landlord
+and Tenant</a></span>.)</p>
+
+<p>In <i>Scotland</i>, the recovery of land is effected by an action of
+&ldquo;removing&rdquo; or summary ejection. In the case of a tenant
+&ldquo;warning&rdquo; is necessary unless he is bound by his lease to
+remove without warning. In the case of possessors without
+title, or a title merely precarious, no warning is needed. A
+summary process of removing from small holdings is provided
+for by Sheriff Courts (Scotland) Acts of 1838 and 1851.</p>
+
+<p>In the United States, the old English action of ejectment was
+adopted to a very limited extent, and where it was so adopted
+has often been superseded, as in Connecticut, by a single action
+for all cases of ouster, disseisin or ejectment. In this action,
+known as an action of disseisin or ejectment, both possession of
+the land and damages may be recovered. In some of the states
+a tenant against whom an action of ejectment is brought by a
+stranger is bound under a penalty, as in England, to give notice
+of the claim to the landlord in order that he may appear and
+defend his title.</p>
+
+<p>In <i>French law</i> the landlord&rsquo;s claim for rent is fairly secured
+by the hypothec, and by summary powers which exist for the
+seizure of the effects of defaulting tenants. Eviction or annulment
+of a lease can only be obtained through the judicial
+tribunals. The Civil Code deals with the position of a tenant
+in case of the sale of the property leased. If the lease is by
+authentic act (<i>acte authentique</i>) or has an ascertained date, the
+purchaser cannot evict the tenant unless a right to do so was
+reserved on the lease (art. 1743), and then only on payment of an
+indemnity (arts. 1744-1747). If the lease is not by authentic
+act, or has not an ascertained date, the purchaser is not liable
+for indemnity (art. 1750). The tenant of rural lands is bound
+to give the landlord notice of acts of usurpation (art. 1768).
+There are analogous provisions in the Civil Codes of Belgium
+(arts. 1743 et seq.), Holland (arts. 1613, 1614), Portugal (art.
+1572); and see the German Civil Code (arts. 535 et seq.). In
+many of the colonies there are statutory provisions for the
+recovery of land or premises on the lines of English law (cf.
+Ontario, Rev. Stats. 1897, c. 170. ss. 19 et seq.; Manitoba, Rev.
+Stats. 1902, <i>c.</i> 1903). In others (<i>e.g.</i> New Zealand, Act. No. 55
+of 1893, ss. 175-187; British Columbia, Revised Statutes, 1897,
+c. 182: Cyprus, Ord. 15 of 1895) there has been legislation similar
+to the Small Tenements Recovery Act 1838.</p>
+
+<div class="condensed">
+<p><span class="sc">Authorities.</span>&mdash;<i>English Law</i>: Cole on <i>Ejectment</i>; Digby, <i>History
+of Real Property</i> (3rd ed., London, 1884); Pollock and Maitland,
+<i>History of English Law</i> (Cambridge, 1895); Foa, <i>Landlord and
+Tenant</i> (4th ed., London, 1907); Fawcett, <i>Landlord and Tenant</i>
+(London, 1905). <i>Irish Law</i>: Nolan and Kane&rsquo;s <i>Statutes relating
+to the Law of Landlord and Tenant</i> (5th ed., Dublin, 1898); Wylie&rsquo;s
+<i>Judicature Acts</i> (Dublin, 1900). <i>Scots Law</i>: Hunter on <i>Landlord
+and Tenant</i> (4th ed., Edin., 1878); Erskine&rsquo;s <i>Principles</i> (20th ed.,
+Edin., 1903). <i>American Law: Two Centuries&rsquo; Growth of American
+Law</i> (New York and London, 1901); Bouvier&rsquo;s <i>Law Dictionary</i>
+(Boston and London, 1897); Stimson, <i>American Statute Law</i>
+(Boston, 1886).</p>
+</div>
+<div class="author">(A. W. R.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">EKATERINBURG,<a name="ar26" id="ar26"></a></span> a town of Russia, in the government of
+Perm, 311 m. by rail S.E. of the town of Perm, on the Iset river,
+near the E. foot of the Ural Mountains, in 56° 49&prime; N. and
+<span class="pagenum"><a name="page139" id="page139"></a>139</span>
+60° 35&prime; E., at an altitude of 870 ft. above sea-level. It is the
+most important town of the Urals. Pop. (1860) 19,830; (1897)
+55,488. The streets are broad and regular, and several of the
+houses of palatial proportions. In 1834 Ekaterinburg was made
+the see of a suffragan bishop of the Orthodox Greek Church.
+There are two cathedrals&mdash;St Catherine&rsquo;s, founded in 1758, and
+that of the Epiphany, in 1774&mdash;and a museum of natural history,
+opened in 1853. Ekaterinburg is the seat of the central mining
+administration of the Ural region, and has a chemical laboratory
+for the assay of gold, a mining school, the Ural Society of
+Naturalists, and a magnetic and meteorological observatory.
+Besides the government mint for copper coinage, which dates
+from 1735, the government engineering works, and the
+imperial factory for the cutting and polishing of malachite,
+jasper, marble, porphyry and other ornamental stones, the
+industrial establishments comprise candle, paper, soap and
+machinery works, flour and woollen mills, and tanneries. There is
+a lively trade in cattle, cereals, iron, woollen and silk goods,
+and colonial products; and two important fairs are held annually.
+Nearly forty gold and platinum mines, over thirty iron-works,
+and numerous other factories are scattered over the district,
+while wheels, travelling boxes, hardware, boots and so forth
+are extensively made in the villages. Ekaterinburg took its
+origin from the mining establishments founded by Peter the
+Great in 1721, and received its name in honour of his wife,
+Catherine I. Its development was greatly promoted in 1763
+by the diversion of the Siberian highway from Verkhoturye to
+this place.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EKATERINODAR,<a name="ar27" id="ar27"></a></span> a town of South Russia, chief town of the
+province of Kubañ, on the right bank of the river Kubañ, 85 m.
+E.N.E. of Novo-rossiysk on the railway to Rostov-on-Don,
+and in 45° 3&prime; N. and 38° 50&prime; E. It is badly built, on a swampy
+site exposed to the inundations of the river; and its houses,
+with few exceptions, are slight structures of wood and plaster.
+Founded by Catherine II. in 1794 on the site of an old town
+called Tmutarakan, as a small fort and Cossack settlement, its
+population grew from 9620 in 1860 to 65,697 in 1897. It has
+various technical schools, an experimental fruit-farm, a military
+hospital, and a natural history museum. A considerable trade is
+carried on, especially in cereals.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EKATERINOSLAV,<a name="ar28" id="ar28"></a></span> a government of south Russia, having the
+governments of Poltava and Kharkov on the N., the territory
+of the Don Cossacks on the E., the Sea of Azov and Taurida on
+the S., and Kherson on the W. Area, 24,478 sq. m. Its surface
+is undulating steppe, sloping gently south and north, with a few
+hills reaching 1200 ft. in the N.E., where a slight swelling (the
+Don Hills) compels the Don to make a great curve eastwards.
+Another chain of hills, to which the eastward bend of the Dnieper
+is due, rises in the west. These hills have a crystalline core
+(granites, syenites and diorites), while the surface strata belong
+to the Carboniferous, Permian, Cretaceous and Tertiary formations.
+The government is rich in minerals, especially in coal&mdash;the
+mines lie in the middle of the Donets coalfield&mdash;iron ores,
+fireclay and rock-salt, and every year the mining output increases
+in quantity, especially of coal and iron. Granite, limestone,
+grindstone, slate, with graphite, manganese and mercury are
+found. The government is drained by the Dnieper, the Don and
+their tributaries (<i>e.g.</i> the Donets and Volchya) and by several
+affluents (<i>e.g.</i> the Kalmius) of the Sea of Azov. The soil is the
+fertile black earth, but the crops occasionally suffer from drought,
+the average annual rainfall being only 15 in. Forests are scarce.
+Pop. (1860) 1,138,750; (1897) 2,118,946, chiefly Little Russians,
+with Great Russians, Greeks (48,740), Germans (80,979),
+Rumanians and a few gypsies. Jews constitute 4.7% of the
+population. The estimated population in 1906 was 2,708,700.</p>
+
+<p>Wheat and other cereals are extensively grown; other noteworthy
+crops are potatoes, tobacco and grapes. Nearly 40,000
+persons find occupation in factories, the most <span class="correction" title="amended from imporant">important</span> being
+iron-works and agricultural machinery works, though there are
+also tobacco, glass, soap and candle factories, potteries, tanneries
+and breweries. In the districts of Mariupol the making of
+agricultural implements and machinery is carried on extensively
+as a domestic industry in the villages. Bees are kept in very considerable
+numbers. Fishing employs many persons in the Don
+and the Dnieper. Cereals are exported in large quantities via
+the Dnieper, the Sevastopol railway, and the port of Mariupol.
+The chief towns of the eight districts, with their populations in
+1897, are Ekaterinoslav (135,552 inhabitants in 1900), Alexandrovsk
+(28,434), Bakhmut (30,585), Mariupol (31,772),
+Novomoskovsk (12,862), Pavlograd (17,188), Slavyanoserbsk
+(3120), and Verkhne-dnyeprovsk (11,607).</p>
+
+
+<hr class="art" />
+<p><span class="bold">EKATERINOSLAV,<a name="ar29" id="ar29"></a></span> a town of Russia, capital of the government
+of the same name, on the right bank of the Dnieper above
+the rapids, 673 m. by rail S.S.W. of Moscow, in 48° 21&prime; N. and
+35° 4&prime; E., at an altitude of 210 ft. Pop. (1861) 18,881, without
+suburbs; (1900) 135,552. If the suburb of Novyikoindak be
+included, the town extends for upwards of 4 m. along the river.
+The oldest part lies very low and is much exposed to floods. Contiguous
+to the towns on the N.W. is the royal village of Novyimaidani
+or the New Factories. The bishop&rsquo;s palace, mining
+academy, archaeological museum and library are the principal
+public buildings. The house now occupied by the Nobles Club
+was formerly inhabited by the author and statesman Potemkin.
+Ekaterinoslav is a rapidly growing city, with a number of technical
+schools, and is an important depot for timber floated down the
+Dnieper, and also for cereals. Its iron-works, flour-mills and
+agricultural machinery works give occupation to over 5000
+persons. In fact since 1895 the city has become the centre of
+numerous Franco-Belgian industrial undertakings. In addition
+to the branches just mentioned, there are tobacco factories and
+breweries. Considerable trade is carried on in cattle, cereals,
+horses and wool, there being three annual fairs. On the site of
+the city there formerly stood the Polish castle of Koindak, built
+in 1635, and destroyed by the Cossacks. The existing city was
+founded by Potemkin in 1786, and in the following year Catherine
+II. laid the foundation-stone of the cathedral, though it was not
+actually built until 1830-1835. On the south side of it is a bronze
+statue of the empress, put up in 1846. Paul I. changed the name
+of the city to Novo-rossiysk, but the original name was restored
+in 1802.</p>
+
+
+<hr class="art" />
+<p><span class="bold">EKHOF, KONRAD<a name="ar30" id="ar30"></a></span> (1720-1778), German actor, was born in
+Hamburg on the 12th of August 1720. In 1739 he became a
+member of Johann Friedrich Schönemann&rsquo;s (1704-1782) company
+in Lüneburg, and made his first appearance there on the 15th
+of January 1740 as Xiphares in Racine&rsquo;s <i>Mithridate</i>. From
+1751 the Schönemann company performed mainly in Hamburg
+and at Schwerin, where Duke Christian Louis II. of Mecklenburg-Schwerin
+made them comedians to the court. During this
+period Ekhof founded a theatrical academy, which, though
+short-lived, was of great importance in helping to raise the
+standard of German acting and the status of German actors.
+In 1757 Ekhof left Schönemann to join Franz Schuch&rsquo;s company
+at Danzig; but he soon returned to Hamburg, where, in conjunction
+with two other actors, he succeeded Schönemann in
+the direction of the company. He resigned this position, however,
+in favour of H.G. Koch, with whom he acted until 1764, when
+he joined K.E. Ackermann&rsquo;s company. In 1767 was founded
+the National Theatre at Hamburg, made famous by Lessing&rsquo;s
+<i>Hamburgische Dramaturgie</i>, and Ekhof was the leading member
+of the company. After the failure of the enterprise Ekhof was
+for a time in Weimar, and ultimately became co-director of the
+new court theatre at Gotha. This, the first permanently established
+theatre in Germany, was opened on the 2nd of October
+1775. Ekhof&rsquo;s reputation was now at its height; Goethe called
+him the only German tragic actor; and in 1777 he acted with
+Goethe and Duke Charles Augustus at a private performance
+at Weimar, dining afterwards with the poet at the ducal table.
+He died on the 16th of June 1778. His versatility may be
+judged from the fact that in the comedies of Goldoni and Molière
+he was no less successful than in the tragedies of Lessing and
+Shakespeare. He was regarded by his contemporaries as an
+unsurpassed exponent of naturalness on the stage; and in this
+respect he has been not unfairly compared with Garrick. His
+fame, however, was rapidly eclipsed by that of Friedrich U.L.
+<span class="pagenum"><a name="page140" id="page140"></a>140</span>
+Schröder. His literary efforts were chiefly confined to translations
+from French authors.</p>
+
+<div class="condensed">
+<p>See H. Uhde, biography of Ekhof in vol. iv. of <i>Der neue Plutarch</i>
+(1876), and J. Rüschner, <i>K. Ekhofs Leben und Wirken</i> (1872). Also
+H. Devrient, <i>J.F. Schönemann und seine Schauspielergesellschaft</i>
+(1895).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EKRON<a name="ar31" id="ar31"></a></span> (better, as in the Septuagint and Josephus, <span class="sc">Accaron</span>,
+<span class="grk" title="Akkarôn">&#7944;&#954;&#954;&#945;&#961;&#974;&#957;</span>), a royal city of the Philistines commonly identified
+with the modern Syrian village of &lsquo;A&#7731;ir, 5 m. from Ramleh,
+on the southern slope of a low ridge separating the plain of
+Philistia from Sharon. It lay inland and off the main line of
+traffic. Though included by the Israelites within the limits of
+the tribe of Judah, and mentioned in Judges xix. as one of the
+cities of Dan, it was in Philistine possession in the days of
+Samuel, and apparently maintained its independence. According
+to the narrative of the Hebrew text, here differing from the
+Greek text and Josephus (which read Askelon), it was the last
+town to which the ark was transferred before its restoration to
+the Israelites. Its maintenance of a sanctuary of Baal Zebub
+is mentioned in 2 Kings i. From Assyrian inscriptions it has
+been gathered that Padi, king of Ekron, was for a time the
+vassal of Hezekiah of Judah, but regained his independence
+when the latter was hard pressed by Sennacherib. A notice of
+its history in 147 <span class="scs">B.C.</span> is found in 1 Macc. x. 89; after the fall of
+Jerusalem <span class="scs">A.D.</span> 70 it was settled by Jews. At the time of the
+crusades it was still a large village. Recently a Jewish agricultural
+colony has been settled there. The houses are built of
+mud, and in the absence of visible remains of antiquity, the
+identification of the site is questionable. The neighbourhood
+is fertile.</p>
+<div class="author">(R. A. S. M.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELABUGA,<a name="ar32" id="ar32"></a></span> a town of Russia, in the government of Vyatka,
+on the Kama river, 201 m. by steamboat down the Volga from
+Kazan and then up the Kama. It has flour-mills, and carries
+on a brisk trade in exporting corn. Pop. (1897) 9776.</p>
+
+<p>The famous <i>Ananiynskiy Mogilnik</i> (burial-place) is on the
+right bank of the Kama, 3 m. above the town. It was discovered
+in 1858, was excavated by Alabin, Lerch and Nevostruyev,
+and has since supplied extremely valuable collections belonging
+to the Stone, Bronze and Iron Ages. It consisted of a mound,
+about 500 ft. in circumference, adorned with decorated stones
+(which have disappeared), and contained an inner wall, 65 ft.
+in circumference, made of uncemented stone flags. Nearly
+fifty skeletons were discovered, mostly lying upon charred logs,
+surrounded with cinerary urns filled with partially burned
+bones. A great variety of bronze decorations and glazed clay
+pearls were strewn round the skeletons. The knives, daggers
+and arrowpoints are of slate, bronze and iron, the last two being
+very rough imitations of stone implements. One of the flags
+bore the image of a man, without moustaches or beard, dressed
+in a costume and helmet recalling those of the Circassians.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELAM,<a name="ar33" id="ar33"></a></span> the name given in the Bible to the province of Persia
+called Susiana by the classical geographers, from Susa or Shushan
+its capital. In one passage, however (Ezra iv. 9), it is confined
+to Elymais, the north-western part of the province, and its
+inhabitants distinguished from those of Shushan, which elsewhere
+(Dan. viii. 2) is placed in Elam. Strabo (xv. 3. 12, &amp;c.)
+makes Susiana a part of Persia proper, but a comparison of his
+account with those of Ptolemy (vi. 3. 1, &amp;c.) and other writers
+would limit it to the mountainous district to the east of Babylonia,
+lying between the Oroatis and the Tigris, and stretching
+from India to the Persian Gulf. Along with this mountainous
+district went a fertile low tract of country on the western side,
+which also included the marshes at the mouths of the Euphrates
+and Tigris and the north-eastern coast land of the Gulf. This low
+tract, though producing large quantities of grain, was intensely
+hot in summer; the high regions, however, were cool and well
+watered.</p>
+
+<p>The whole country was occupied by a variety of tribes, speaking
+agglutinative dialects for the most part, though the western
+districts were occupied by Semites. Strabo (xi. 13. 3, 6), quoting
+from Nearchus, seems to include the Susians under the Elymaeans,
+whom he associates with the Uxii, and places on the frontiers
+of Persia and Susa; but Pliny more correctly makes the Eulaeus
+the boundary between Susiana and Elymais (<i>N.H.</i> vi. 29-31).
+The Uxii are described as a robber tribe in the mountains
+adjacent to Media, and their name is apparently to be identified
+with the title given to the whole of Susiana in the Persian
+cuneiform inscriptions, <i>Uwaja</i>, <i>i.e.</i> &ldquo;Aborigines.&rdquo; Uwaja is
+probably the origin of the modern Khuzistan, though Mordtmann
+would derive the latter from <img style="width:25px; height:15px" src="images/img140.jpg" alt="" /> &ldquo;a sugar-reed.&rdquo; Immediately
+bordering on the Persians were the Amardians or Mardians,
+as well as the people of Khapirti (Khatamti, according to Scheil),
+the name given to Susiana in the Neo-Susian texts. Khapirti
+appears as Apir in the inscriptions of Mal-Amir, which fix the
+locality of the district. Passing over the Messabatae, who
+inhabited a valley which may perhaps be the modern M&#257;h-Sabadan,
+as well as the level district of Yamutbal or Yatbur
+which separated Elam from Babylonia, and the smaller districts
+of Characene, Cabandene, Corbiana and Gabiene mentioned
+by classical authors, we come to the fourth principal tribe of
+Susiana, the Cissii (Aesch. <i>Pers.</i> 16; Strabo xv. 3. 2) or Cossaei
+(Strabo xi. 5. 6, xvi. 11. 17; Arr. <i>Ind.</i> 40; Polyb. v. 54, &amp;c.),
+the Kassi of the cuneiform inscriptions. So important were they,
+that the whole of Susiana was sometimes called Cissia after
+them, as by Herodotus (iii. 91, v. 49, &amp;c.). In fact Susiana
+was only a late name for the country, dating from the time
+when Susa had been made a capital of the Persian empire. In
+the Sumerian texts of Babylonia it was called Numma, &ldquo;the
+Highlands,&rdquo; of which Elamtu or Elamu, &ldquo;Elam,&rdquo; was the
+Semitic translation. Apart from Susa, the most important
+part of the country was Anzan (Anshan, contracted Assan),
+where the native population maintained itself unaffected by
+Semitic intrusion. The exact position of Anzan is still disputed,
+but it probably included originally the site of Susa and was
+distinguished from it only when Susa became the seat of a
+Semitic government. In the lexical tablets Anzan is given
+as the equivalent of Elamtu, and the native kings entitle themselves
+kings of &ldquo;Anzan and Susa,&rdquo; as well as &ldquo;princes of the
+Khapirti.&rdquo;</p>
+
+<p>The principal mountains of Elam were on the north, called
+Charbanus and Cambalidus by Pliny (vi. 27, 31), and belonging
+to the Parachoathras chain. There were numerous rivers
+flowing into either the Tigris or the Persian Gulf. The most
+important were the Ulai or Eulaeus (<i>K&#363;ran</i>) with its tributary
+the Pasitigris, the Choaspes (<i>Kerkhah</i>), the Coprates (river of
+<i>Diz</i> called Itit&#275; in the inscriptions), the Hedyphon or Hedypnus
+(<i>Jerr&#257;hi</i>), and the Croatis (<i>Hindyan</i>), besides the monumental
+Surappi and Ukni, perhaps to be identified with the Hedyphon
+and Oroatis, which fell into the sea in the marshy region at the
+mouth of the Tigris. Shushan or Susa, the capital now marked
+by the mounds of <i>Shush</i>, stood near the junction of the Choaspes
+and Eulaeus (see <span class="sc"><a href="#artlinks">Susa</a></span>); and Badaca, Madaktu in the inscriptions,
+lay between the <i>Shapur</i> and the river of <i>Diz</i>. Among the
+other chief cities mentioned in the inscriptions may be named
+Naditu, Khaltemas, Din-sar, Bubilu, Bit-imbi, Khidalu and
+Nagitu on the sea-coast. Here, in fact, lay some of the oldest
+and wealthiest towns, the sites of which have, however, been
+removed inland by the silting up of the shore. J. de Morgan&rsquo;s
+excavations at Susa have thrown a flood of light on the early
+history of Elam and its relations to Babylon. The earliest settlement
+there goes back to neolithic times, but it was already a
+fortified city when Elam was conquered by Sargon of Akkad
+(3800 <span class="scs">B.C.</span>) and Susa became the seat of a Babylonian viceroy.
+From this time onward for many centuries it continued under
+Semitic suzerainty, its high-priests, also called &ldquo;Chief Envoys
+of Elam, Sippara and Susa,&rdquo; bearing sometimes Semitic, sometimes
+native &ldquo;Anzanite&rdquo; names. One of the kings of the dynasty
+of Ur built at Susa. Before the rise of the First Dynasty of
+Babylon, however, Elam had recovered its independence, and
+in 2280 <span class="scs">B.C.</span> the Elamite king Kutur-Nakhkhunte made a raid
+in Babylonia and carried away from Erech the image of the
+goddess Nan&#257;. The monuments of many of his successors have
+been discovered by de Morgan and their inscriptions deciphered
+by v. Scheil. One of them was defeated by Ammi-zadoq
+<span class="pagenum"><a name="page141" id="page141"></a>141</span>
+of Babylonia (<i>c.</i> 2100 <span class="scs">B.C.</span>); another would have been the
+Chedor-laomer (Kutur-Lagamar) of Genesis xiv. One of the
+greatest builders among them was Untas-<span class="sc">Gal</span> (the pronunciation
+of the second element in the name is uncertain). About 1330
+<span class="scs">B.C.</span> Khurba-tila was captured by Kuri-galzu III., the Kassite
+king of Babylonia, but a later prince Kidin-Khutrutas avenged
+his defeat, and Sutruk-Nakhkhunte (1220 <span class="scs">B.C.</span>) carried fire and
+sword through Babylonia, slew its king Zamama-sum-iddin and
+carried away a stela of Naram-Sin and the famous code of laws
+of Khammurabi from Sippara, as well as a stela of Manistusu
+from Akkuttum or Akkad. He also conquered the land of
+Asnunnak and carried off from Padan a stela belonging to a
+refugee from Malatia. He was succeeded by his son who was
+followed on the throne by his brother, one of the great builders of
+Elam. In 750 <span class="scs">B.C.</span> Umbadara was king of Elam; Khumban-igas
+was his successor in 742 <span class="scs">B.C.</span> In 720 <span class="scs">B.C.</span> the latter prince
+met the Assyrians under Sargon at Dur-ili in Yamutbal, and
+though Sargon claims a victory the result was that Babylonia
+recovered its independence under Merodach-baladan and the
+Assyrian forces were driven north. From this time forward it
+was against Assyria instead of Babylonia that Elam found
+itself compelled to exert its strength, and Elamite policy was
+directed towards fomenting revolt in Babylonia and assisting the
+Babylonians in their struggle with Assyria. In 716 <span class="scs">B.C.</span> Khumban-igas
+died and was followed by his nephew, Sutruk-Nakhkhunte.
+He failed to make head against the Assyrians; the frontier cities
+were taken by Sargon and Merodach-baladan was left to his
+fate. A few years later (704 <span class="scs">B.C.</span>) the combined forces of Elam
+and Babylonia were overthrown at Kis, and in the following
+year the Kassites were reduced to subjection. The Elamite king
+was dethroned and imprisoned in 700 <span class="scs">B.C.</span> by his brother Khallusu,
+who six years later marched into Babylonia, captured the son of
+Sennacherib, whom his father had placed there as king, and raised
+a nominee of his own, Nergal-yusezib, to the throne. Khallusu
+was murdered in 694 <span class="scs">B.C.</span>, after seeing the maritime part of his
+dominions invaded by the Assyrians. His successor Kudur-Nakhkhunte
+invaded Babylonia; he was repulsed, however,
+by Sennacherib, 34 of his cities were destroyed, and he himself
+fled from Madaktu to Khidalu. The result was a revolt in which
+he was killed after a reign of ten months. His brother Umman-menan
+at once collected allies and prepared for resistance to the
+Assyrians. But the terrible defeat at Khalul&#275; broke his power;
+he was attacked by paralysis shortly afterwards, and Khumba-Khaldas
+II. followed him on the throne (689 <span class="scs">B.C.</span>). The new king
+endeavoured to gain Assyrian favour by putting to death the
+son of Merodach-baladan, but was himself murdered by his
+brothers Urtaki and Teumman (681 <span class="scs">B.C.</span>), the first of whom
+seized the crown. On his death Teumman succeeded and almost
+immediately provoked a quarrel with Assur-bani-pal by demanding
+the surrender of his nephews who had taken refuge at the
+Assyrian court. The Assyrians pursued the Elamite army to
+Susa, where a battle was fought on the banks of the Eulaeus, in
+which the Elamites were defeated, Teumman captured and slain,
+and Umman-igas, the son of Urtaki, made king, his younger
+brother Tammaritu being given the district of Khidalu. Umman-igas
+afterwards assisted in the revolt of Babylonia under Samas-sum-yukin,
+but his nephew, a second Tammaritu, raised a
+rebellion against him, defeated him in battle, cut off his head
+and seized the crown. Tammaritu marched to Babylonia;
+while there, his officer Inda-bigas made himself master of Susa
+and drove Tammaritu to the coast whence he fled to Assur-bani-pal.
+Inda-bigas was himself overthrown and slain by a new
+pretender, Khumba-Khaldas III., who was opposed, however,
+by three other rivals, two of whom maintained themselves in
+the mountains until the Assyrian conquest of the country, when
+Tammaritu was first restored and then imprisoned, Elam being
+utterly devastated. The return of Khumba-Khaldas led to a
+fresh Assyrian invasion; the Elamite king fled from Madaktu
+to Dur-undasi; Susa and other cities were taken, and the
+Elamite army almost exterminated on the banks of the Itit&#275;.
+The whole country was reduced to a desert, Susa was plundered
+and razed to the ground, the royal sepulchres were desecrated,
+and the images of the gods and of 32 kings &ldquo;in silver, gold,
+bronze and alabaster,&rdquo; were carried away. All this must have
+happened about 640 <span class="scs">B.C.</span> After the fall of the Assyrian empire
+Elam was occupied by the Persian Teispes, the forefather of
+Cyrus, who, accordingly, like his immediate successors, is called
+in the inscriptions &ldquo;king of Anzan.&rdquo; Susa once more became
+a capital, and on the establishment of the Persian empire remained
+one of the three seats of government, its language,
+the Neo-Susian, ranking with the Persian of Persepolis and the
+Semitic of Babylon as an official tongue. In the reign of Darius,
+however, the Susianians attempted to revolt, first under Assina
+or Atrina, the son of Umbadara, and later under Martiya, the son
+of Issainsakria, who called himself Immanes; but they gradually
+became completely Aryanized, and their agglutinative dialects
+were supplanted by the Aryan Persian from the south-east.</p>
+
+<p>Elam, &ldquo;the land of the cedar-forest,&rdquo; with its enchanted
+trees, figured largely in Babylonian mythology, and one of the
+adventures of the hero Gilgamesh was the destruction of the
+tyrant Khumbaba who dwelt in the midst of it. A list of the
+Elamite deities is given by Assur-bani-pal; at the head of them
+was In-Susinak, &ldquo;the lord of the Susians,&rdquo;&mdash;a title which went
+back to the age of Babylonian suzerainty,&mdash;whose image and
+oracle were hidden from the eyes of the profane. Nakhkhunte,
+according to Scheil, was the Sun-goddess, and Lagamar, whose
+name enters into that of Chedor-laomer, was borrowed from
+Semitic Babylonia.</p>
+
+<div class="condensed">
+<p>See W.K. Loftus, <i>Chaldaea and Susiana</i> (1857); A. Billerbeck,
+<i>Susa</i> (1893); J. de Morgan, <i>Mémoires de la Délégation en Perse</i>
+(9 vols., 1899-1906).</p>
+</div>
+<div class="author">(A. H. S.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELAND<a name="ar34" id="ar34"></a></span> (= elk), the Dutch name for the largest of the South
+African antelopes (<i>Taurotragus oryx</i>), a species near akin to the
+kudu, but with horns present in both sexes, and their spiral
+much closer, being in fact screw-like instead of corkscrew-like.
+There is also a large dewlap, while old bulls have a thick forelock.
+In the typical southern form the body-colour is wholly pale
+fawn, but north of the Orange river the body is marked by
+narrow vertical white lines, this race being known as <i>T. oryx
+livingstonei</i>. In Senegambia the genus is represented by <i>T.
+derbianus</i>, a much larger animal, with a dark neck; while in the
+Bahr-el-Ghazal district there is a gigantic local race of this species
+(<i>T. derbianus giganteus</i>).</p>
+<div class="author">(R. L.*)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELASTICITY.<a name="ar35" id="ar35"></a></span> 1. Elasticity is the property of recovery of
+an original size or shape. A body of which the size, or shape,
+or both size and shape, have been altered by the application of
+forces may, and generally does, tend to return to its previous
+size and shape when the forces cease to act. Bodies which
+exhibit this tendency are said to be <i>elastic</i> (from Greek, <span class="grk" title="elaunein">&#7952;&#955;&#945;&#973;&#957;&#949;&#953;&#957;</span>,
+to drive). All bodies are more or less elastic as regards size;
+and all solid bodies are more or less elastic as regards shape.
+For example: gas contained in a vessel, which is closed by a
+piston, can be compressed by additional pressure applied to the
+piston; but, when the additional pressure is removed, the gas
+expands and drives the piston outwards. For a second example:
+a steel bar hanging vertically, and loaded with one ton for each
+square inch of its sectional area, will have its length increased by
+about seven one-hundred-thousandths of itself, and its sectional
+area diminished by about half as much; and it will spring back
+to its original length and sectional area when the load is gradually
+removed. Such changes of size and shape in bodies subjected
+to forces, and the recovery of the original size and shape when
+the forces cease to act, become conspicuous when the bodies
+have the forms of thin wires or planks; and these properties
+of bodies in such forms are utilized in the construction of spring
+balances, carriage springs, buffers and so on.</p>
+
+<p>It is a familiar fact that the hair-spring of a watch can be
+coiled and uncoiled millions of times a year for several years
+without losing its elasticity; yet the same spring can have its
+shape permanently altered by forces which are much greater
+than those to which it is subjected in the motion of the watch.
+The incompleteness of the recovery from the effects of great
+forces is as important a fact as the practical completeness of
+the recovery from the effects of comparatively small forces.
+<span class="pagenum"><a name="page142" id="page142"></a>142</span>
+The fact is referred to in the distinction between &ldquo;perfect&rdquo;
+and &ldquo;imperfect&rdquo; elasticity; and the limitation which must
+be imposed upon the forces in order that the elasticity may be
+perfect leads to the investigation of &ldquo;limits of elasticity&rdquo;
+(see §§ 31, 32 below). Steel pianoforte wire is perfectly elastic
+within rather wide limits, glass within rather narrow limits;
+building stone, cement and cast iron appear not to be perfectly
+elastic within any limits, however narrow. When the limits of
+elasticity are not exceeded no injury is done to a material or
+structure by the action of the forces. The strength or weakness
+of a material, and the safety or insecurity of a structure, are thus
+closely related to the elasticity of the material and to the change
+of size or shape of the structure when subjected to forces. The
+&ldquo;science of elasticity&rdquo; is occupied with the more abstract side
+of this relation, viz. with the effects that are produced in a body
+of definite size, shape and constitution by definite forces; the
+&ldquo;science of the strength of materials&rdquo; is occupied with the
+more concrete side, viz. with the application of the results
+obtained in the science of elasticity to practical questions of
+strength and safety (see <span class="sc"><a href="#artlinks">Strength of Materials</a></span>).</p>
+
+<p>2. <i>Stress.</i>&mdash;Every body that we know anything about is
+always under the action of forces. Every body upon which
+we can experiment is subject to the force of gravity, and must,
+for the purpose of experiment, be supported by other forces.
+Such forces are usually applied by way of pressure upon a
+portion of the surface of the body; and such pressure is exerted
+by another body in contact with the first. The supported body
+exerts an equal and opposite pressure upon the supporting body
+across the portion of surface which is common to the two. The
+same thing is true of two portions of the same body. If, for
+example, we consider the two portions into which a body is
+divided by a (geometrical) horizontal plane, we conclude that
+the lower portion supports the upper portion by pressure across
+the plane, and the upper portion presses downwards upon the
+lower portion with an equal pressure. The pressure is still
+exerted when the plane is not horizontal, and its direction may
+be obliquely inclined to, or tangential to, the plane. A more
+precise meaning is given to &ldquo;pressure&rdquo; below. It is important
+to distinguish between the two classes of forces: forces such as
+the force of gravity, which act all through a body, and forces
+such as pressure applied over a surface. The former are named
+&ldquo;body forces&rdquo; or &ldquo;volume forces,&rdquo; and the latter &ldquo;surface
+tractions.&rdquo; The action between two portions of a body separated
+by a geometrical surface is of the nature of surface traction.
+Body forces are ultimately, when the volumes upon which they
+act are small enough, proportional to the volumes; surface
+tractions, on the other hand, are ultimately, when the surfaces
+across which they act are small enough, proportional to these
+surfaces. Surface tractions are always exerted by one body
+upon another, or by one part of a body upon another part,
+across a surface of contact; and a surface traction is always
+to be regarded as one aspect of a &ldquo;stress,&rdquo; that is to say of a
+pair of equal and opposite forces; for an equal traction is always
+exerted by the second body, or part, upon the first across the
+surface.</p>
+
+<p>3. The proper method of estimating and specifying stress is
+a matter of importance, and its character is necessarily mathematical.
+The magnitudes of the surface tractions which compose
+a stress are estimated as so much force (in dynes or tons) per
+unit of area (per sq. cm. or per sq. in.). The traction across an
+assigned plane at an assigned point is measured by the mathematical
+limit of the fraction F/S, where F denotes the numerical
+measure of the force exerted across a small portion of the plane
+containing the point, and S denotes the numerical measure
+of the area of this portion, and the limit is taken by diminishing
+S indefinitely. The traction may act as &ldquo;tension,&rdquo; as it does
+in the case of a horizontal section of a bar supported at its
+upper end and hanging vertically, or as &ldquo;pressure,&rdquo; as it
+does in the case of a horizontal section of a block resting on
+a horizontal plane, or again it may act obliquely or even
+tangentially to the separating plane. Normal tractions are
+reckoned as positive when they are tensions, negative when
+they are pressures. Tangential tractions are often called
+&ldquo;shears&rdquo; (see § 7 below). Oblique tractions can always
+be resolved, by the vector law, into normal and tangential
+tractions. In a fluid at rest the traction across any plane at
+any point is normal to the plane, and acts as pressure. For the
+complete specification of the &ldquo;state of stress&rdquo; at any point of a
+body, we should require to know the normal and tangential
+components of the traction across every plane drawn through
+the point. Fortunately this requirement can be very much
+simplified (see §§ 6, 7 below).</p>
+
+<div class="condensed">
+<p>4. In general let &nu;  denote the direction of the normal drawn in a
+specified sense to a plane drawn through a point O of a body; and
+let T<span class="su">&nu;</span> denote the traction exerted across the plane, at the point O,
+by the portion of the body towards which &nu;  is drawn upon the
+remaining portion. Then T<span class="su">&nu;</span> is a vector quantity, which has a definite
+magnitude (estimated as above by the limit of a fraction of the form
+F/S) and a definite direction. It can be specified completely by its
+components X<span class="su">&nu;</span>, Y<span class="su">&nu;</span>, Z<span class="su">&nu;</span>, referred to fixed rectangular axes of x, y, z.
+When the direction of &nu;  is that of the axis of x, in the positive sense,
+the components are denoted by X<span class="su">x</span>, Y<span class="su">x</span>, Z<span class="su">x</span>; and a similar notation
+is used when the direction of &nu;  is that of y or z, the suffix x being
+replaced by y or z.</p>
+</div>
+
+<p>5. Every body about which we know anything is always in a
+state of stress, that is to say there are always internal forces
+acting between the parts of the body, and these forces are
+exerted as surface tractions across geometrical surfaces drawn in
+the body. The body, and each part of the body, moves under
+the action of all the forces (body forces and surface tractions)
+which are exerted upon it; or remains at rest if these forces are
+in equilibrium. This result is expressed analytically by means
+of certain equations&mdash;the &ldquo;equations of motion&rdquo; or &ldquo;equations
+of equilibrium&rdquo; of the body.</p>
+
+<div class="condensed">
+<p>Let &rho;  denote the density of the body at any point, X, Y, Z, the
+components parallel to the axes of x, y, z of the body forces, estimated
+as so much force per unit of mass; further let &fnof;<span class="su">x</span>, &fnof;<span class="su">y</span>, &fnof;<span class="su">z</span> denote
+the components, parallel to the same axes, of the acceleration of the
+particle which is momentarily at the point (x, y, z). The equations
+of motion express the result that the rates of change of the momentum,
+and of the moment of momentum, of any portion of the body are
+those due to the action of all the forces exerted upon the portion
+by other bodies, or by other portions of the same body. For the
+changes of momentum, we have three equations of the type</p>
+
+<p class="center">&int; &int; &int; &rho; Xdx dy dz + &int; &int; X<span class="su">&nu;</span>dS = &int; &int; &int; &rho; &fnof;<span class="su">x</span>dx dy dz,</p>
+<div class="author">(1)</div>
+
+<p class="noind">in which the volume integrations are taken through the volume
+of the portion of the body, the surface integration is taken over its
+surface, and the notation X<span class="su">&nu;</span> is that of § 4, the direction of &nu;  being
+that of the normal to this surface drawn outwards. For the changes
+of moment of momentum, we have three equations of the type</p>
+
+<p class="center">&int; &int; &int; &rho; (yZ &minus; zY) dx dy dz + &int; &int; (yZ<span class="su">&nu;</span> &minus; zY<span class="su">&nu;</span>) dS =
+&int; &int; &int; &rho; (y&fnof;<span class="su">z</span> &minus; z&fnof;<span class="su">y</span>) dx dy dz.</p>
+<div class="author">(2)</div>
+
+<p class="noind">The equations (1) and (2) are the equations of motion of any kind of
+body. The equations of equilibrium are obtained by replacing the
+right-hand members of these equations by zero.</p>
+
+<p>6. These equations can be used to obtain relations between the
+values of X<span class="su">&nu;</span>, Y<span class="su">&nu;</span>, ... for different directions &nu;. When the equations
+are applied to a very small volume, it appears that the terms expressed
+by surface integrals would, unless they tend to zero limits
+in a higher order than the areas of the surfaces, be very great compared
+with the terms expressed by volume integrals. We conclude
+that the surface tractions on the portion of the body which is bounded
+by any very small closed surface, are ultimately in equilibrium.
+When this result is interpreted for a small portion in the shape of a
+tetrahedron, having three of its faces at right angles to the co-ordinate
+axes, it leads to three equations of the type</p>
+
+<p class="center">X<span class="su">&nu;</span> = X<span class="su">x</span> cos(x, &nu;) + X<span class="su">y</span> cos(y, &nu;) + X<span class="su">z</span> cos(z, &nu;),</p>
+<div class="author">(1)</div>
+
+<p class="noind">where &nu; is the direction of the normal (drawn outwards) to the
+remaining face of the tetrahedron, and (x, &nu;) ... denote the angles
+which this normal makes with the axes. Hence X<span class="su">&nu;</span>, ... for any
+direction &nu; are expressed in terms of X<span class="su">x</span>,.... When the above
+result is interpreted for a very small portion in the shape of a cube,
+having its edges parallel to the co-ordinate axes, it leads to the
+equations</p>
+
+<p class="center">Y<span class="su">z</span> = Z<span class="su">y</span>, &emsp;&emsp; Z<span class="su">x</span> = X<span class="su">z</span>, &emsp;&emsp; X<span class="su">y</span> = Y<span class="su">x</span>.</p>
+<div class="author">(2)</div>
+
+<p class="noind">When we substitute in the general equations the particular results
+which are thus obtained, we find that the equations of motion take
+such forms as</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&rho;X +</td> <td>&part;X<span class="su">x</span></td>
+<td rowspan="2">+</td> <td>&part;X<span class="su">y</span></td>
+<td rowspan="2">+</td> <td>&part;Z<span class="su">x</span></td>
+<td rowspan="2">= &rho;&fnof;<span class="su">x</span>,</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td> <td class="denom">&part;z</td></tr></table>
+<div class="author">(3)</div>
+
+<p class="noind">and the equations of moments are satisfied identically. The equations
+of equilibrium are obtained by replacing the right-hand
+members by zero.</p>
+</div>
+
+<p><span class="pagenum"><a name="page143" id="page143"></a>143</span></p>
+
+<table class="flt" style="float: right; width: 340px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:286px; height:161px" src="images/img143a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span></td></tr>
+<tr><td class="figright1"><img style="width:269px; height:263px" src="images/img143b.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p>7. A state of stress in which the traction across any plane of
+a set of parallel planes is normal to the plane, and that across
+any perpendicular plane vanishes, is described as a state of
+&ldquo;simple tension&rdquo; (&ldquo;simple pressure&rdquo; if the traction is negative).
+A state of stress in which the traction across any plane is normal
+to the plane, and the traction is the same for all planes passing
+through any point, is described
+as a state of &ldquo;uniform
+tension&rdquo; (&ldquo;uniform
+pressure&rdquo; if the traction
+is negative). Sometimes
+the phrases &ldquo;isotropic
+tension&rdquo; and &ldquo;hydrostatic
+pressure&rdquo; are used
+instead of &ldquo;uniform&rdquo;
+tension or pressure. The
+distinction between the two states, simple tension and uniform
+tension, is illustrated in fig. 1.</p>
+
+<p>A state of stress in which there is purely tangential traction
+on a plane, and no normal traction on any perpendicular plane,
+is described as a state of &ldquo;shearing stress.&rdquo; The result (2) of
+§ 6 shows that tangential tractions occur in pairs. If, at any
+point, there is tangential traction, in any direction, on a plane
+parallel to this direction,
+and if we draw through
+the point a plane at right
+angles to the direction of
+this traction, and therefore
+containing the normal to
+the first plane, then there
+is equal tangential traction
+on this second plane in the
+direction of the normal to
+the first plane. The result
+is illustrated in fig. 2, where
+a rectangular block is subjected
+on two opposite faces
+to opposing tangential tractions,
+and is held in equilibrium by equal tangential tractions
+applied to two other faces.</p>
+
+<p>Through any point there always pass three planes, at
+right angles to each other, across which there is no tangential
+traction. These planes are called the &ldquo;principal planes of
+stress,&rdquo; and the (normal) tractions across them the &ldquo;principal
+stresses.&rdquo; Lines, usually curved, which have at every point the
+direction of a principal stress at the point, are called &ldquo;lines of
+stress.&rdquo;</p>
+
+<p>8. It appears that the stress at any point of a body is completely
+specified by six quantities, which can be taken to be the
+X<span class="su">x</span>, Y<span class="su">y</span>, Z<span class="su">z</span> and Y<span class="su">z</span>, Z<span class="su">x</span>, X<span class="su">y</span> of § 6. The first three are tensions
+(pressures if they are negative) across three planes parallel to
+fixed rectangular directions, and the remaining three are tangential
+tractions across the same three planes. These six quantities
+are called the &ldquo;components of stress.&rdquo; It appears also that the
+components of stress are connected with each other, and with the
+body forces and accelerations, by the three partial differential
+equations of the type (3) of § 6. These equations are available
+for the purpose of determining the state of stress which exists
+in a body of definite form subjected to definite forces, but they
+are not sufficient for the purpose (see § 38 below). In order
+to effect the determination it is necessary to have information
+concerning the constitution of the body, and to introduce subsidiary
+relations founded upon this information.</p>
+
+<p>9. The definite mathematical relations which have been found
+to connect the components of stress with each other, and with
+other quantities, result necessarily from the formation of a clear
+conception of the nature of stress. They do not admit of experimental
+verification, because the stress within a body does not
+admit of direct measurement. Results which are deduced by
+the aid of these relations can be compared with experimental
+results. If any discrepancy were observed it would not be interpreted
+as requiring a modification of the concept of stress, but
+as affecting some one or other of the subsidiary relations which
+must be introduced for the purpose of obtaining the theoretical
+result.</p>
+
+<p>10. <i>Strain.</i>&mdash;For the specification of the changes of size and
+shape which are produced in a body by any forces, we begin by
+defining the &ldquo;average extension&rdquo; of any linear element or
+&ldquo;filament&rdquo; of the body. Let l<span class="su">0</span> be the length of the filament
+before the forces are applied, l its length when the body is subjected
+to the forces. The average extension of the filament is measured
+by the fraction (l &minus; l<span class="su">0</span>)/l<span class="su">0</span>. If this fraction is negative there is
+&ldquo;contraction.&rdquo; The &ldquo;extension at a point&rdquo; of a body in any
+assigned direction is the mathematical limit of this fraction when
+one end of the filament is at the point, the filament has the
+assigned direction, and its length is diminished indefinitely. It
+is clear that all the changes of size and shape of the body are
+known when the extension at every point in every direction
+is known.</p>
+
+<div class="condensed">
+<p>The relations between the extensions in different directions
+around the same point are most simply expressed by introducing the
+extensions in the directions of the co-ordinate axes and the angles
+between filaments of the body which are initially parallel to these
+axes. Let e<span class="su">xx</span>, e<span class="su">yy</span>, e<span class="su">zz</span> denote the extensions parallel to the axes of
+x, y, z, and let e<span class="su">yz</span>, e<span class="su">zx</span>, e<span class="su">xy</span> denote the cosines of the angles between
+the pairs of filaments which are initially parallel to the axes of y
+and z, z and x, x and y. Also let e denote the extension in the
+direction of a line the direction cosines of which are l, m, n. Then,
+if the changes of size and shape are slight, we have the relation</p>
+
+<p class="center">e = e<span class="su">xx</span>l² + e<span class="su">yy</span>m² + e<span class="su">zz</span>n² + e<span class="su">yz</span>mn + e<span class="su">zx</span>nl + e<span class="su">xy</span>lm.</p>
+</div>
+
+<p>The body which undergoes the change of size or shape is said
+to be &ldquo;strained,&rdquo; and the &ldquo;strain&rdquo; is determined when the
+quantities e<span class="su">xx</span>, e<span class="su">yy</span>, e<span class="su">zz</span> and e<span class="su">yz</span>, e<span class="su">zx</span>, e<span class="su">xy</span> defined above are known
+at every point of it. These quantities are called &ldquo;components
+of strain.&rdquo; The three of the type e<span class="su">xx</span> are extensions, and the
+three of the type e<span class="su">yz</span> are called &ldquo;shearing strains&rdquo; (see § 12
+below).</p>
+
+<p>11. All the changes of relative position of particles of the body
+are known when the strain is known, and conversely the strain
+can be determined when the changes of relative position are
+given. These changes can be expressed most simply by the
+introduction of a vector quantity to represent the displacement
+of any particle.</p>
+
+<div class="condensed">
+<p>When the body is deformed by the action of any forces its particles
+pass from the positions which they occupied before the action of the
+forces into new positions. If x, y, z are the co-ordinates of the
+position of a particle in the first state, its co-ordinates in the second
+state may be denoted by x + u, y + v, z + w. The quantities, u, v, w
+are the &ldquo;components of displacement.&rdquo; When these quantities are
+small, the strain is connected with them by the equations</p>
+
+<p class="center">e<span class="su">xx</span> = &part;u / &part;x, &emsp;&emsp; e<span class="su">yy</span> = &part;v / &part;y, &emsp;&emsp; e<span class="su">zz</span> = &part;w / &part;z,</p>
+<div class="author">(1)</div>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">e<span class="su">yz</span> =</td> <td>&part;w</td>
+<td rowspan="2">+</td> <td>&part;v</td>
+<td rowspan="2">, &emsp;&emsp; e<span class="su">zx</span> =</td> <td>&part;u</td>
+<td rowspan="2">+</td> <td>&part;w</td>
+<td rowspan="2">, &emsp;&emsp; e<span class="su">xy</span> =</td> <td>&part;v</td>
+<td rowspan="2">+</td> <td>&part;u</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">&part;y</td> <td class="denom">&part;z</td>
+<td class="denom">&part;z</td> <td class="denom">&part;x</td>
+<td class="denom">&part;x</td> <td class="denom">&part;y</td></tr></table>
+</div>
+
+<p>12. These equations enable us to determine more exactly the
+nature of the &ldquo;shearing strains&rdquo; such as e<span class="su">xy</span>. Let u, for example,
+be of the form sy, where s is constant, and let v and w vanish.
+Then e<span class="su">xy</span> = s, and the remaining components of strain vanish.
+The nature of the strain (called &ldquo;simple shear&rdquo;) is simply
+appreciated by imagining the body to consist of a series of thin
+sheets, like the leaves of a book, which lie one over another and
+are all parallel to a plane (that of x, z); and the displacement
+is seen to consist in the shifting of each sheet relative to the sheet
+below in a direction (that of x) which is the same for all the
+sheets. The displacement of any sheet is proportional to its
+distance y from a particular sheet, which remains undisplaced.
+The shearing strain has the effect of distorting the shape of any
+portion of the body without altering its volume. This is shown
+in fig. 3, where a square ABCD is distorted by simple shear
+(each point moving parallel to the line marked xx) into a rhombus
+A&prime;B&prime;C&prime;D&prime;, as if by an extension of the diagonal BD and a contraction
+of the diagonal AC, which extension and contraction
+are adjusted so as to leave the area unaltered. In the general
+case, where u is not of the form sy and v and w do not vanish,
+the shearing strains such as e<span class="su">xy</span> result from the composition
+of pairs of simple shears of the type which has just been
+explained.</p>
+
+<p><span class="pagenum"><a name="page144" id="page144"></a>144</span></p>
+
+<div class="condensed">
+<p>13. Besides enabling us to express the extension in any direction
+and the changes of relative direction of any filaments of the body,
+the components of strain also express the changes of size of volumes
+and areas. In particular, the &ldquo;cubical dilatation,&rdquo; that is to say,
+the increase of volume per unit of volume, is expressed by the
+quantity e<span class="su">xx</span> + e<span class="su">yy</span> + e<span class="su">zz</span> or
+&part;u / &part;x + &part;v / &part;y + &part;w / &part;z. When this quantity is negative
+there is &ldquo;compression.&rdquo;</p>
+</div>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:366px; height:411px" src="images/img144.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span></td></tr></table>
+
+<p>14. It is important to distinguish between two types of
+strain: the &ldquo;rotational&rdquo; type and the &ldquo;irrotational&rdquo; type.
+The distinction is illustrated in fig. 3, where the figure
+A&Prime;B&Prime;C&Prime;D&Prime; is obtained from the figure ABCD by contraction
+parallel to AC and extension parallel to BD, and the figure
+A&prime;B&prime;C&prime;D&prime; can be obtained from ABCD by the same contraction
+and extension followed by a rotation through the
+angle A&Prime;OA&prime;. In strains of the irrotational type there are at
+any point three filaments at right angles to each other, which are
+such that the particles which lie in them before strain continue
+to lie in them after strain. A small spherical element of the body
+with its centre at the point becomes a small ellipsoid with its
+axes in the directions of these three filaments. In the case
+illustrated in the figure, the lines of the filaments in question,
+when the figure ABCD is strained into the figure A&Prime;B&Prime;C&Prime;D&Prime;,
+are OA, OB and a line through O at right angles to their plane. In
+strains of the rotational type, on the other hand, the single existing
+set of three filaments (issuing from a point) which cut each other
+at right angles both before and after strain do not retain their
+directions after strain, though one of them may do so in certain
+cases. In the figure, the lines of the filaments in question, when
+the figure ABCD is strained into A&prime;B&prime;C&prime;D&prime;, are OA, OB and a
+line at right angles to their plane before strain, and after strain
+they are OA&prime;, OB&prime;, and the same third line. A rotational
+strain can always be analysed into an irrotational strain (or
+&ldquo;pure&rdquo; strain) followed by a rotation.</p>
+
+<div class="condensed">
+<p>Analytically, a strain is irrotational if the three quantities</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;w</td> <td rowspan="2">&minus;</td> <td>&part;v</td>
+<td rowspan="2">, &emsp;</td> <td>&part;u</td>
+<td rowspan="2">&minus;</td> <td>&part;w</td>
+<td rowspan="2">, &emsp;</td> <td>&part;v</td>
+<td rowspan="2">&minus;</td> <td>&part;u</td></tr>
+<tr><td class="denom">&part;y</td> <td class="denom">&part;z</td>
+<td class="denom">&part;z</td> <td class="denom">&part;x</td>
+<td class="denom">&part;x</td> <td class="denom">&part;y</td></tr></table>
+
+<p class="noind">vanish, rotational if any one of them is different from zero. The
+halves of these three quantities are the components of a vector
+quantity called the &ldquo;rotation.&rdquo;</p>
+
+<p>15. Whether the strain is rotational or not, there is always one
+set of three linear elements issuing from any point which cut each
+other at right angles both before and after strain. If these directions
+are chosen as axes of x, y, z, the shearing strains e<span class="su">yz</span>, e<span class="su">zx</span>, e<span class="su">xy</span> vanish
+at this point. These directions are called the &ldquo;principal axes of
+strain,&rdquo; and the extensions in the directions of these axes the
+&ldquo;principal extensions.&rdquo;</p>
+</div>
+
+<p>16. It is very important to observe that the relations between
+components of strain and components of displacement imply
+relations between the components of strain themselves. If
+by any process of reasoning we arrive at the conclusion that
+the state of strain in a body is such and such a state, we have a
+test of the possibility or impossibility of our conclusion. The
+test is that, if the state of strain is a possible one, then there
+must be a displacement which can be associated with it in accordance
+with the equations (1) of § 11.</p>
+
+<div class="condensed">
+<p>We may eliminate u, v, w from these equations. When this is
+done we find that the quantities e<span class="su">xx</span>, ... e<span class="su">yz</span> are connected by the
+two sets of equations</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;²e<span class="su">yy</span></td>
+<td rowspan="2">+</td> <td>&part;²e<span class="su">zz</span></td>
+<td rowspan="2">=</td> <td>&part;²e<span class="su">yz</span></td></tr>
+<tr><td class="denom">&part;z²</td> <td class="denom">&part;y²</td>
+<td class="denom">&part;y&part;z</td></tr></table>
+<div class="author">(1)</div>
+
+<table class="math0" summary="math">
+<tr><td>&part;²e<span class="su">zz</span></td>
+<td rowspan="2">+</td> <td>&part;²e<span class="su">xx</span></td>
+<td rowspan="2">=</td> <td>&part;²e<span class="su">zx</span></td></tr>
+<tr><td class="denom">&part;x²</td> <td class="denom">&part;z²</td>
+<td class="denom">&part;z&part;x</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td>&part;²e<span class="su">xx</span></td>
+<td rowspan="2">+</td> <td>&part;²e<span class="su">yy</span></td>
+<td rowspan="2">=</td> <td>&part;²e<span class="su">xy</span></td></tr>
+<tr><td class="denom">&part;y²</td> <td class="denom">&part;x²</td>
+<td class="denom">&part;x&part;y</td></tr></table>
+
+<p class="noind">and</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">2</td> <td>&part;²e<span class="su">xx</span></td>
+<td rowspan="2">=</td> <td>&part;</td>
+<td rowspan="2"><span class="f150">(</span> &minus;</td> <td>&part;e<span class="su">yz</span></td>
+<td rowspan="2">+</td> <td>&part;e<span class="su">zx</span></td>
+<td rowspan="2">+</td> <td>&part;e<span class="su">xy</span></td>
+<td rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td class="denom">&part;y&part;z</td> <td class="denom">&part;x</td>
+<td class="denom">&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;z</td></tr></table>
+<div class="author">(2)</div>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">2</td> <td>&part;²e<span class="su">yy</span></td>
+<td rowspan="2">=</td> <td>&part;</td>
+<td rowspan="2"><span class="f150">(</span> &ensp;</td> <td>&part;e<span class="su">yz</span></td>
+<td rowspan="2">&minus;</td> <td>&part;e<span class="su">zx</span></td>
+<td rowspan="2">+</td> <td>&part;e<span class="su">xy</span></td>
+<td rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td class="denom">&part;z&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;z</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">2</td> <td>&part;²e<span class="su">zz</span></td>
+<td rowspan="2">=</td> <td>&part;</td>
+<td rowspan="2"><span class="f150">(</span> &ensp;</td> <td>&part;e<span class="su">yz</span></td>
+<td rowspan="2">+</td> <td>&part;e<span class="su">zx</span></td>
+<td rowspan="2">&minus;</td> <td>&part;e<span class="su">xy</span></td>
+<td rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td class="denom">&part;x&part;y</td> <td class="denom">&part;z</td>
+<td class="denom">&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;z</td></tr></table>
+
+</div>
+
+<p>These equations are known as the <i>conditions of compatibility
+of strain-components</i>. The components of strain which specify
+any possible strain satisfy them. Quantities arrived at in any
+way, and intended to be components of strain, if they fail to
+satisfy these equations, are not the components of any possible
+strain; and the theory or speculation by which they are reached
+must be modified or abandoned.</p>
+
+<div class="condensed">
+<p>When the components of strain have been found in accordance
+with these and other necessary equations, the displacement is
+to be found by solving the equations (1) of § 11, considered as
+differential equations to determine u, v, w. The most general
+possible solution will differ from any other solution by terms which
+contain arbitrary constants, and these terms represent a possible
+displacement. This &ldquo;complementary displacement&rdquo; involves no
+strain, and would be a possible displacement of an ideal perfectly
+rigid body.</p>
+</div>
+
+<p>17. The relations which connect the strains with each other
+and with the displacement are geometrical relations resulting
+from the definitions of the quantities and not requiring any
+experimental verification. They do not admit of such verification,
+because the strain within a body cannot be measured.
+The quantities (belonging to the same category) which can be
+measured are displacements of points on the surface of a body.
+For example, on the surface of a bar subjected to tension we may
+make two fine transverse scratches, and measure the distance
+between them before and after the bar is stretched. For such
+measurements very refined instruments are required. Instruments
+for this purpose are called barbarously &ldquo;extensometers,&rdquo;
+and many different kinds have been devised. From measurements
+of displacement by an extensometer we may deduce the
+average extension of a filament of the bar terminated by the
+two scratches. In general, when we attempt to measure a
+strain, we really measure some displacements, and deduce the
+values, not of the strain at a point, but of the average extensions
+of some particular linear filaments of a body containing the point;
+and these filaments are, from the nature of the case, nearly
+always superficial filaments.</p>
+
+<p>18. In the case of transparent materials such as glass there is
+available a method of studying experimentally the state of strain
+within a body. This method is founded upon the result that a
+piece of glass when strained becomes doubly refracting, with its
+optical principal axes at any point in the directions of the
+principal axes of strain (§ 15) at the point. When the piece has
+two parallel plane faces, and two of the principal axes of strain
+at any point are parallel to these faces, polarized light transmitted
+through the piece in a direction normal to the faces can be used
+to determine the directions of the principal axes of the strain
+at any point. If the directions of these axes are known theoretically
+the comparison of the experimental and theoretical results
+yields a test of the theory.</p>
+
+<p>19. <i>Relations between Stresses and Strains.</i>&mdash;The problem
+of the extension of a bar subjected to tension is the one which
+has been most studied experimentally, and as a result of this
+study it is found that for most materials, including all metals
+except cast metals, the measurable extension is proportional
+<span class="pagenum"><a name="page145" id="page145"></a>145</span>
+to the applied tension, provided that this tension is not too great.
+In interpreting this result it is assumed that the tension is uniform
+over the cross-section of the bar, and that the extension
+of longitudinal filaments is uniform throughout the bar; and
+then the result takes the form of a law of proportionality connecting
+stress and strain: The tension is proportional to the extension.
+Similar results are found for the same materials when other
+methods of experimenting are adopted, for example, when a
+bar is supported at the ends and bent by an attached load and the
+deflexion is measured, or when a bar is twisted by an axial couple
+and the relative angular displacement of two sections is measured.
+We have thus very numerous experimental verifications of the
+famous law first enunciated by Robert Hooke in 1678 in the words
+&ldquo;<i>Ut Tensio sic vis</i>&rdquo;; that is, &ldquo;the Power of any spring is in the
+same proportion as the Tension (&mdash;stretching) thereof.&rdquo; The
+most general statement of Hooke&rsquo;s Law in modern language
+would be:&mdash;<i>Each of the six components of stress at any point of
+a body is a linear function of the six components of strain at the
+point.</i> It is evident from what has been said above as to the
+nature of the measurement of stresses and strains that this law
+in all its generality does not admit of complete experimental
+verification, and that the evidence for it consists largely in the
+agreement of the results which are deduced from it in a theoretical
+fashion with the results of experiments. Of such results one of
+a general character may be noted here. If the law is assumed
+to be true, and the equations of motion of the body (§ 5) are
+transformed by means of it into differential equations for
+determining the components of displacement, these differential
+equations admit of solutions which represent periodic vibratory
+displacements (see § 85 below). The fact that solid bodies can
+be thrown into states of isochronous vibration has been
+emphasized by G.G. Stokes as a peremptory proof of the truth
+of Hooke&rsquo;s Law.</p>
+
+<p>20. According to the statement of the generalized Hooke&rsquo;s
+Law the stress-components vanish when the strain-components
+vanish. The strain-components contemplated in experiments
+upon which the law is founded are measured from a zero of
+reckoning which corresponds to the state of the body subjected
+to experiment before the experiment is made, and the stress-components
+referred to in the statement of the law are those
+which are called into action by the forces applied to the body
+in the course of the experiment. No account is taken of the stress
+which must already exist in the body owing to the force of gravity
+and the forces by which the body is supported. When it is
+desired to take account of this stress it is usual to suppose that the
+strains which would be produced in the body if it could be freed
+from the action of gravity and from the pressures of supports are
+so small that the strains produced by the forces which are
+applied in the course of the experiment can be compounded with
+them by simple superposition. This supposition comes to the
+same thing as measuring the strain in the body, not from the
+state in which it was before the experiment, but from an ideal
+state (the &ldquo;unstressed&rdquo; state) in which it would be entirely free
+from internal stress, and allowing for the strain which would
+be produced by gravity and the supporting forces if these forces
+were applied to the body when free from stress. In most practical
+cases the initial strain to be allowed for is unimportant
+(see §§ 91-93 below).</p>
+
+<p>21. Hooke&rsquo;s law of proportionality of stress and strain leads
+to the introduction of important physical constants: the
+<i>moduluses of elasticity</i> of a body. Let a bar of uniform section
+(of area &omega;) be stretched with tension T, which is distributed
+uniformly over the section, so that the stretching force is Tw&omega;,
+and let the bar be unsupported at the sides. The bar will undergo
+a longitudinal extension of magnitude T/E, where E is a constant
+quantity depending upon the material. This constant is called
+<i>Young&rsquo;s modulus</i> after Thomas Young, who introduced it into
+the science in 1807. The quantity E is of the same nature as a
+traction, that is to say, it is measured as a force estimated per
+unit of area. For steel it is about 2.04 × 10<span class="sp">12</span> dynes per square
+centimetre, or about 13,000 tons per sq. in.</p>
+
+<p>22. The longitudinal extension of the bar under tension is
+not the only strain in the bar. It is accompanied by a lateral
+contraction by which all the transverse filaments of the bar
+are shortened. The amount of this contraction is &sigma;T/E, where
+&sigma; is a certain number called <i>Poisson&rsquo;s ratio</i>, because its importance
+was at first noted by S.D. Poisson in 1828. Poisson arrived
+at the existence of this contraction, and the corresponding
+number &sigma;, from theoretical considerations, and his theory led
+him to assign to &sigma; the value ¼. Many experiments have been
+made with the view of determining &sigma;, with the result that it
+has been found to be different for different materials, although
+for very many it does not differ much from ¼. For steel the
+best value (Amagat&rsquo;s) is 0.268. Poisson&rsquo;s theory admits of
+being modified so as to agree with the results of experiment.</p>
+
+<p>23. The behaviour of an elastic solid body, strained within
+the limits of its elasticity, is entirely determined by the constants
+E and &sigma; if the body is <i>isotropic</i>, that is to say, if it has the same
+quality in all directions around any point. Nevertheless it is
+convenient to introduce other constants which are related to the
+action of particular sorts of forces. The most important of these
+are the &ldquo;modulus of compression&rdquo; (or &ldquo;bulk modulus&rdquo;) and
+the &ldquo;rigidity&rdquo; (or &ldquo;modulus of shear&rdquo;). To define the <i>modulus
+of compression</i>, we suppose that a solid body of any form is
+subjected to uniform hydrostatic pressure of amount p. The
+state of stress within it will be one of uniform pressure, the same
+at all points, and the same in all directions round any point.
+There will be compression, the same at all points, and proportional
+to the pressure; and the amount of the compression can
+be expressed as p/k. The quantity k is the modulus of compression.
+In this case the linear contraction in any direction
+is p/3k; but in general the linear extension (or contraction)
+is not one-third of the cubical dilatation (or compression).</p>
+
+<p>24. To define the <i>rigidity</i>, we suppose that a solid body is
+subjected to forces in such a way that there is shearing stress
+within it. For example, a cubical block may be subjected to
+opposing tractions on opposite faces acting in directions which
+are parallel to an edge of the cube and to both the faces. Let
+S be the amount of the traction, and let it be uniformly distributed
+over the faces. As we have seen (§ 7), equal tractions
+must act upon two other faces in suitable directions in order
+to maintain equilibrium (see fig. 2 of § 7). The two directions
+involved may be chosen as axes of x, y as in that figure. Then
+the state of stress will be one in which the stress-component
+denoted by X<span class="su">y</span> is equal to S, and the remaining stress-components
+vanish; and the strain produced in the body is shearing strain of
+the type denoted by e<span class="su">xy</span>. The amount of the shearing strain
+is S/&mu;, and the quantity &mu; is the &ldquo;rigidity.&rdquo;</p>
+
+<p>25. The modulus of compression and the rigidity are quantities
+of the same kind as Young&rsquo;s modulus. The modulus of compression
+of steel is about 1.43 × 10<span class="sp">12</span> dynes per square centimetre,
+the rigidity is about 8.19 × 10<span class="sp">11</span> dynes per square centimetre.
+It must be understood that the values for different
+specimens of nominally the same material may differ considerably.</p>
+
+<div class="condensed">
+<p>The modulus of compression k and the rigidity &mu; of an isotropic
+material are connected with the Young&rsquo;s modulus E and Poisson&rsquo;s
+ratio &sigma; of the material by the equations</p>
+
+<p class="center">k = E / 3(1 &minus; 2&sigma;), &emsp; &mu; = E / 2(1 + &sigma;).</p>
+
+<p>26. Whatever the forces acting upon an isotropic solid body may
+be, provided that the body is strained within its limits of elasticity,
+the strain-components are expressed in terms of the stress-components
+by the equations</p>
+
+<p class="center">e<span class="su">xx</span> = (X<span class="su">x</span> &minus; &sigma;Y<span class="su">y</span> &minus; &sigma;Z<span class="su">z</span>) / E, &emsp; e<span class="su">yz</span> = Y<span class="su">z</span> / &mu;,</p>
+<p class="center">e<span class="su">yy</span> = (Y<span class="su">y</span> &minus; &sigma;Z<span class="su">z</span> &minus; &sigma;X<span class="su">x</span>) / E, &emsp; e<span class="su">zx</span> = Z<span class="su">x</span> / &mu;,</p>
+<p class="center">e<span class="su">zz</span> = (Z<span class="su">z</span> &minus; &sigma;X<span class="su">x</span> &minus; &sigma;Y<span class="su">y</span>) / E, &emsp; e<span class="su">xy</span> = X<span class="su">y</span> / &mu;.</p>
+<div class="author">(1)</div>
+
+<p class="noind">If we introduce a quantity &lambda;, of the same nature as E or &mu;, by the
+equation</p>
+
+<p class="center">&lambda; = E&sigma; / (1 + &sigma;)(1 &minus; 2&sigma;),</p>
+<div class="author">(2)</div>
+
+<p class="noind">we may express the stress-components in terms of the strain-components
+by the equations</p>
+
+<p class="center">X<span class="su">x</span> = &lambda;(e<span class="su">xx</span> + e<span class="su">yy</span> + e<span class="su">zz</span>) + 2&mu;e<span class="su">xx</span>, &emsp; Y<span class="su">z</span> = &mu;e<span class="su">yz</span>,</p>
+<p class="center">Y<span class="su">y</span> = &lambda;(e<span class="su">xx</span> + e<span class="su">yy</span> + e<span class="su">zz</span>) + 2&mu;e<span class="su">yy</span>, &emsp; Z<span class="su">x</span> = &mu;e<span class="su">zx</span>,</p>
+<p class="center">Z<span class="su">z</span> = &lambda;(e<span class="su">xx</span> + e<span class="su">yy</span> + e<span class="su">zz</span>) + 2&mu;e<span class="su">zz</span>, &emsp; X<span class="su">y</span> = &mu;e<span class="su">xy</span>;</p>
+<div class="author">(3)</div>
+
+<p class="noind">and then the behaviour of the body under the action of any forces
+<span class="pagenum"><a name="page146" id="page146"></a>146</span>
+depends upon the two constants &lambda; and &mu;. These two constants were
+introduced by G. Lamé in his treatise of 1852. The importance of
+the quantity &mu; had been previously emphasized by L.J. Vicat and
+G.G. Stokes.</p>
+
+<p>27. The potential energy per unit of volume (often called the
+&ldquo;resilience&rdquo;) stored up in the body by the strain is equal to</p>
+
+<p class="center">½ (&lambda; + 2&mu;) (e<span class="su">xx</span> + e<span class="su">yy</span> + e<span class="su">zz</span>)² + ½&mu; (e²<span class="su">yz</span> + e²<span class="su">zx</span> +  e²<span class="su">xy</span> &minus; 4e<span class="su">yy</span>e<span class="su">zz</span> &minus; 4e<span class="su">zz</span>e<span class="su">xx</span> &minus; 4e<span class="su">xx</span>e<span class="su">yy</span>),</p>
+
+<p class="noind">or the equivalent expression</p>
+
+<p class="center">½ [(X²<span class="su">x</span> + Y²<span class="su">y</span> + Z²<span class="su">z</span>) &minus; 2&sigma; (Y<span class="su">y</span>Z<span class="su">z</span> + Z<span class="su">z</span>X<span class="su">x</span> + X<span class="su">x</span>Y<span class="su">y</span>) + 2 (1 + &sigma;) (Y²<span class="su">z</span> + Z²<span class="su">x</span> + X²<span class="su">y</span>)] / E.</p>
+
+<p class="noind">The former of these expressions is called the &ldquo;strain-energy-function.&rdquo;</p>
+</div>
+
+<p>28. The Young&rsquo;s modulus E of a material is often determined
+experimentally by the direct method of the extensometer
+(§ 17), but more frequently it is determined indirectly by means
+of a result obtained in the theory of the flexure of a bar (see
+§§ 47, 53 below). The rigidity &mu; is usually determined indirectly
+by means of results obtained in the theory of the torsion of a
+bar (see §§ 41, 42 below). The modulus of compression k may
+be determined directly by means of the piezometer, as was
+done by E.H. Amagat, or it may be determined indirectly by
+means of a result obtained in the theory of a tube under pressure,
+as was done by A. Mallock (see § 78 below). The value of
+Poisson&rsquo;s ratio &sigma; is generally inferred from the relation connecting
+it with E and &mu; or with E and k, but it may also be determined
+indirectly by means of a result obtained in the theory of the
+flexure of a bar (§ 47 below), as was done by M.A. Cornu and
+A. Mallock, or directly by a modification of the extensometer
+method, as has been done recently by J. Morrow.</p>
+
+<p>29. The <i>elasticity of a fluid</i> is always expressed by means of a
+single quantity of the same kind as the <i>modulus of compression</i>
+of a solid body. To any increment of pressure, which is not too
+great, there corresponds a proportional cubical compression,
+and the amount of this compression for an increment &delta;p of
+pressure can be expressed as &delta;p/k. The quantity that is usually
+tabulated is the reciprocal of k, and it is called the <i>coefficient
+of compressibility</i>. It is the amount of compression per unit
+increase of pressure. As a physical quantity it is of the same
+dimensions as the reciprocal of a pressure (or of a force per unit
+of area). The pressures concerned are usually measured in
+atmospheres (1 atmosphere = 1.014 × 10<span class="sp">6</span> dynes per sq. cm.).
+For water the coefficient of compressibility, or the compression
+per atmosphere, is about 4.5 × 10<span class="sp">-5</span>. This gives for k the value
+2.22 × 10<span class="sp">10</span> dynes per sq. cm. The Young&rsquo;s modulus and the
+rigidity of a fluid are always zero.</p>
+
+<p>30. The relations between stress and strain in a material
+which is not isotropic are much more complicated. In such a
+material the Young&rsquo;s modulus depends upon the direction of
+the tension, and its variations about a point are expressed
+by means of a surface of the fourth degree. The Poisson&rsquo;s
+ratio depends upon the direction of the contracted lateral
+filaments as well as upon that of the longitudinal extended
+ones. The rigidity depends upon both the directions involved
+in the specification of the shearing stress. In general there is
+no simple relation between the Young&rsquo;s moduluses and Poisson&rsquo;s
+ratios and rigidities for assigned directions and the modulus
+of compression. Many materials in common use, all fibrous
+woods for example, are actually <i>aeolotropic</i> (that is to say, are not
+isotropic), but the materials which are aeolotropic in the most
+regular fashion are natural crystals. The elastic behaviour
+of crystals has been studied exhaustively by many physicists,
+and in particular by W. Voigt. The strain-energy-function is a
+homogeneous quadratic function of the six strain-components,
+and this function may have as many as 21 independent coefficients,
+taking the place in the general case of the 2 coefficients
+&lambda;, &mu; which occur when the material is isotropic&mdash;a result first
+obtained by George Green in 1837. The best experimental
+determinations of the coefficients have been made indirectly
+by Voigt by means of results obtained in the theories of the
+torsion and flexure of aeolotropic bars.</p>
+
+<p>31. <i>Limits of Elasticity.</i>&mdash;A solid body which has been strained
+by considerable forces does not in general recover its original
+size and shape completely after the forces cease to act. The
+strain that is left is called <i>set</i>. If set occurs the elasticity is
+said to be &ldquo;imperfect,&rdquo; and the greatest strain (or the greatest
+load) of any specified type, for which no set occurs, defines the
+&ldquo;limit of perfect elasticity&rdquo; corresponding to the specified
+type of strain, or of stress. All fluids and many solid bodies,
+such as glasses and crystals, as well as some metals (copper,
+lead, silver) appear to be perfectly elastic as regards change of
+volume within wide limits; but malleable metals and alloys
+can have their densities permanently increased by considerable
+pressures. The limits of perfect elasticity as regards change
+of shape, on the other hand, are very low, if they exist at all,
+for glasses and other hard, brittle solids; but a class of metals
+including copper, brass, steel, <span class="correction" title="missing 'and'">and</span> platinum are very perfectly
+elastic as regards distortion, provided that the distortion is not
+too great. The question can be tested by observation of the
+torsional elasticity of thin fibres or wires. The limits of perfect
+elasticity are somewhat ill-defined, because an experiment
+cannot warrant us in asserting that there is no set, but only
+that, if there is any set, it is too small to be observed.</p>
+
+<p>32. A different meaning may be, and often is, attached to
+the phrase &ldquo;limits of elasticity&rdquo; in consequence of the following
+experimental result:&mdash;Let a bar be held stretched under a
+moderate tension, and let the extension be measured; let the
+tension be slightly increased and the extension again measured;
+let this process be continued, the tension being increased by
+equal increments. It is found that when the tension is not too
+great the extension increases by equal increments (as nearly as
+experiment can decide), but that, as the tension increases, a
+stage is reached in which the extension increases faster than
+it would do if it continued to be proportional to the tension.
+The beginning of this stage is tolerably well marked. Some
+time before this stage is reached the limit of perfect elasticity
+is passed; that is to say, if the load is removed it is found that
+there is some permanent set. The limiting tension beyond
+which the above law of proportionality fails is often called the
+&ldquo;limit of <i>linear</i> elasticity.&rdquo; It is higher than the limit of perfect
+elasticity. For steel bars of various qualities J. Bauschinger
+found for this limit values varying from 10 to 17 tons per square
+inch. The result indicates that, when forces which produce
+any kind of strain are applied to a solid body and are gradually
+increased, the strain at any instant increases proportionally
+to the forces up to a stage beyond that at which, if the forces
+were removed, the body would completely recover its original
+size and shape, but that the increase of strain ceases to be
+proportional to the increase of load when the load surpasses
+a certain limit. There would thus be, for any type of strain, a
+<i>limit of linear elasticity</i>, which exceeds the limit of perfect
+elasticity.</p>
+
+<p>33. A body which has been strained beyond the limit of
+linear elasticity is often said to have suffered an &ldquo;over-strain.&rdquo;
+When the load is removed, the <i>set</i> which can be observed is not
+entirely permanent; but it gradually diminishes with lapse of
+time. This phenomenon is named &ldquo;elastic after-working.&rdquo;
+If, on the other hand, the load is maintained constant, the
+strain is gradually increased. This effect indicates a gradual
+flowing of solid bodies under great stress; and a similar effect
+was observed in the experiments of H. Tresca on the punching
+and crushing of metals. It appears that all solid bodies under
+sufficiently great loads become &ldquo;plastic,&rdquo; that is to say, they
+take a set which gradually increases with the lapse of time.
+No plasticity is observed when the limit of linear elasticity is
+not exceeded.</p>
+
+<p>34. The values of the elastic limits are affected by overstrain.
+If the load is maintained for some time, and then removed,
+the limit of linear elasticity is found to be higher than before.
+If the load is not maintained, but is removed and then reapplied,
+the limit is found to be lower than before. During a period of
+rest a test piece recovers its elasticity after overstrain.</p>
+
+<p>35. The effects of repeated loading have been studied by
+A. Wöhler, J. Bauschinger, O. Reynolds and others. It has
+been found that, after many repetitions of rather rapidly alternating
+stress, pieces are fractured by loads which they have
+many times withstood. It is not certain whether the fracture
+<span class="pagenum"><a name="page147" id="page147"></a>147</span>
+is in every case caused by the gradual growth of minute flaws
+from the beginning of the series of tests, or whether the elastic
+quality of the material suffers deterioration apart from such
+flaws. It appears, however, to be an ascertained result that,
+so long as the limit of linear elasticity is not exceeded, repeated
+loads and rapidly alternating loads do not produce failure of
+the material.</p>
+
+<p>36. The question of the conditions of safety, or of the conditions
+in which rupture is produced, is one upon which there has
+been much speculation, but no completely satisfactory result
+has been obtained. It has been variously held that rupture
+occurs when the numerically greatest principal stress exceeds
+a certain limit, or when this stress is tension and exceeds a
+certain limit, or when the greatest difference of two principal
+stresses (called the &ldquo;stress-difference&rdquo;) exceeds a certain
+limit, or when the greatest extension or the greatest shearing
+strain or the greatest strain of any type exceeds a certain limit.
+Some of these hypotheses appear to have been disproved. It
+was held by G.F. Fitzgerald (<i>Nature</i>, Nov. 5, 1896) that rupture
+is not produced by pressure symmetrically applied all round a
+body, and this opinion has been confirmed by the recent experiments
+of A. Föppl. This result disposes of the greatest stress
+hypothesis and also of the greatest strain hypothesis. The
+fact that short pillars can be crushed by longitudinal pressure
+disposes of the greatest tension hypothesis, for there is no
+tension in the pillar. The greatest extension hypothesis failed
+to satisfy some tests imposed by H. Wehage, who experimented
+with blocks of wrought iron subjected to equal pressures in two
+directions at right angles to each other. The greatest stress-difference
+hypothesis and the greatest shearing strain hypothesis
+would lead to practically identical results, and these results
+have been held by J.J. Guest to accord well with his experiments
+on metal tubes subjected to various systems of combined
+stress; but these experiments and Guest&rsquo;s conclusion have been
+criticized adversely by O. Mohr, and the question cannot be
+regarded as settled. The fact seems to be that the conditions
+of rupture depend largely upon the nature of the test (tensional,
+torsional, flexural, or whatever it may be) that is applied to
+a specimen, and that no general formula holds for all kinds
+of tests. The best modern technical writings emphasize the
+importance of the limits of linear elasticity and of tests of
+dynamical resistance (§ 87 below) as well as of statical resistance.</p>
+
+<p>37. The question of the conditions of rupture belongs rather
+to the science of the strength of materials than to the science
+of elasticity (§ 1); but it has been necessary to refer to it briefly
+here, because there is no method except the methods of the
+theory of elasticity for determining the state of stress or strain
+in a body subjected to forces. Whatever view may ultimately
+be adopted as to the relation between the conditions of safety
+of a structure and the state of stress or strain in it, the calculation
+of this state by means of the theory or by experimental means
+(as in § 18) cannot be dispensed with.</p>
+
+<div class="condensed">
+<p>38. <i>Methods of determining the Stress in a Body subjected to given
+Forces.</i>&mdash;To determine the state of stress, or the state of strain,
+in an isotropic solid body strained within its limits of elasticity by
+given forces, we have to use (i.) the equations of equilibrium, (ii.)
+the conditions which hold at the bounding surface, (iii.) the relations
+between stress-components and strain-components, (iv.) the relations
+between strain-components and displacement. The equations
+of equilibrium are (with notation already used) three partial differential
+equations of the type</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;X<span class="su">x</span></td> <td rowspan="2">+</td> <td>&part;X<span class="su">y</span></td>
+<td rowspan="2">+</td> <td>&part;Z<span class="su">z</span></td>
+<td rowspan="2">+ &rho;X = 0.</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td> <td class="denom">&part;z</td></tr></table>
+<div class="author">(1)</div>
+
+<p class="noind">The conditions which hold at the bounding surface are three equations
+of the type</p>
+
+<p class="center">X<span class="su">x</span> cos (x, &nu;) + X<span class="su">y</span> cos (y, &nu;) + Z<span class="su">x</span> cos (z, &nu;) = <span class="ov">X</span><span class="su">&nu;</span>,</p>
+<div class="author">(2)</div>
+
+<p class="noind">where &nu; denotes the direction of the outward-drawn normal to the
+bounding surface, and <span class="ov">X</span><span class="su">&nu;</span> denotes the x-component of the applied
+surface traction. The relations between stress-components and
+strain-components are expressed by either of the sets of equations
+(1) or (3) of § 26. The relations between strain-components and
+displacement are the equations (1) of § 11, or the equivalent conditions
+of compatibility expressed in equations (1) and (2) of § 16.</p>
+
+<p>39. We may proceed by either of two methods. In one method
+we eliminate the stress-components and the strain-components and
+retain only the components of displacement. This method leads
+(with notation already used) to three partial differential equations
+of the type</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">(&lambda; + &mu;)</td> <td>&part;</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>&part;u</td>
+<td rowspan="2">+</td> <td>&part;v</td>
+<td rowspan="2">+</td> <td>&part;w</td>
+<td rowspan="2"><span class="f150">)</span> + &mu; <span class="f150">(</span></td> <td>&part;²u</td>
+<td rowspan="2">+</td> <td>&part;²u</td>
+<td rowspan="2">+</td> <td>&part;²u</td>
+<td rowspan="2"><span class="f150">)</span> + &rho;X = 0,</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;x</td>
+<td class="denom">&part;y</td> <td class="denom">&part;z</td>
+<td class="denom">&part;x²</td> <td class="denom">&part;y²</td>
+<td class="denom">&part;z²</td></tr></table>
+<div class="author">(3)</div>
+
+<p class="noind">and three boundary conditions of the type</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&lambda; cos (x, &nu;) <span class="f150">(</span></td> <td>&part;u</td>
+<td rowspan="2">+</td> <td>&part;v</td>
+<td rowspan="2">+</td> <td>&part;w</td>
+<td rowspan="2"><span class="f150">)</span> + &mu; <span class="f150">{</span> 2 cos (x, &nu;)</td> <td>&part;u</td>
+<td rowspan="2">+ cos (y, &nu;) <span class="f150">(</span></td> <td>&part;v</td>
+<td rowspan="2">+</td> <td>&part;u</td>
+<td rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;z</td> <td class="denom">&part;x</td>
+<td class="denom">&part;x</td> <td class="denom">&part;y</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">+ cos (z, &nu;) <span class="f150">(</span></td> <td>&part;u</td>
+<td rowspan="2">+</td> <td>&part;w</td>
+<td rowspan="2"><span class="f150">) }</span> = <span class="ov">X</span><span class="su">&nu;</span>.</td></tr>
+<tr><td class="denom">&part;z</td> <td class="denom">&part;x</td></tr></table>
+<div class="author">(4)</div>
+
+<p class="noind">In the alternative method we eliminate the strain-components and
+the displacements. This method leads to a system of partial differential
+equations to be satisfied by the stress-components. In this
+system there are three equations of the type</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;X<span class="su">x</span></td> <td rowspan="2">+</td> <td>&part;X<span class="su">y</span></td>
+<td rowspan="2">+</td> <td>&part;X<span class="su">z</span></td>
+<td rowspan="2">+ &rho;X = 0,</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;z</td></tr></table>
+<div class="author1">(1 <i>bis</i>)</div>
+
+<p class="noind">three of the type</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;²X<span class="su">x</span></td>
+<td rowspan="2">+</td> <td>&part;²X<span class="su">x</span></td>
+<td rowspan="2">+</td> <td>&part;²X<span class="su">x</span></td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">&nbsp;</td> <td>&part;²</td>
+<td rowspan="2">(X<span class="su">x</span> + Y<span class="su">y</span> + Z<span class="su">z</span>) =</td></tr>
+<tr><td class="denom">&part;x²</td> <td class="denom">&part;y²</td>
+<td class="denom">&part;z²</td> <td class="denom">1 + &sigma;</td>
+<td class="denom">&part;x²</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&minus;</td> <td>&sigma;</td>
+<td rowspan="2">&rho; <span class="f150">(</span></td> <td>&part;X</td>
+<td rowspan="2">+</td> <td>&part;Y</td>
+<td rowspan="2">+</td> <td>&part;Z</td>
+<td rowspan="2"><span class="f150">)</span> &minus; 2&rho;</td> <td>&part;X</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">1 &minus; &sigma;</td> <td class="denom">&part;x</td>
+<td class="denom">&part;y</td> <td class="denom">&part;z</td>
+<td class="denom">&part;x</td></tr></table>
+<div class="author">(5)</div>
+
+<p class="noind">and three of the type</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;²Y<span class="su">z</span></td>
+<td rowspan="2">+</td> <td>&part;²Y<span class="su">z</span></td>
+<td rowspan="2">+</td> <td>&part;²Y<span class="su">z</span></td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">&nbsp;</td> <td>&part;²</td>
+<td rowspan="2">(X<span class="su">x</span> + Y<span class="su">y</span> + Z<span class="su">z</span>) = &minus; &rho; <span class="f150">(</span></td> <td>&part;Z</td>
+<td rowspan="2">+</td> <td>&part;Y</td>
+<td rowspan="2"><span class="f150">)</span>,</td></tr>
+<tr><td class="denom">&part;x²</td> <td class="denom">&part;y²</td>
+<td class="denom">&part;z²</td> <td class="denom">1 + &sigma;</td>
+<td class="denom">&part;y&part;z</td> <td class="denom">&part;y</td>
+<td class="denom">&part;z</td></tr></table>
+<div class="author">(6)</div>
+
+<p class="noind">the equations of the two latter types being necessitated by the
+conditions of compatibility of strain-components. The solutions of
+these equations have to be adjusted so that the boundary conditions
+of the type (2) may be satisfied.</p>
+
+<p>40. It is evident that whichever method is adopted the mathematical
+problem is in general very complicated. It is also evident
+that, if we attempt to proceed by help of some intuition as to the
+nature of the stress or strain, our intuition ought to satisfy the
+tests provided by the above systems of equations. Neglect of this
+precaution has led to many errors. Another source of frequent error
+lies in the neglect of the conditions in which the above systems of
+equations are correct. They are obtained by help of the supposition
+that the relative displacements of the parts of the strained body
+are small. The solutions of them must therefore satisfy the test of
+smallness of the relative displacements.</p>
+</div>
+
+<p>41. Torsion.&mdash;As a first example of the application of the
+theory we take the problem of the torsion of prisms. This
+problem, considered first by C.A. Coulomb in 1784, was finally
+solved by B. de Saint-Venant in 1855. The problem is this:&mdash;A
+cylindrical or prismatic bar is held twisted by terminal
+couples; it is required to determine the state of stress and
+strain in the interior. When the bar is a circular cylinder
+the problem is easy. Any section is displaced by rotation about
+the central-line through a small angle, which is proportional
+to the distance z of the section from a fixed plane at right angles
+to this line. This plane is a terminal section if one of the two
+terminal sections is not displaced. The angle through which
+the section z rotates is &tau;z, where &tau; is a constant, called the
+amount of the twist; and this constant &tau; is equal to G/&mu;I,
+where G is the twisting couple, and I is the moment of inertia
+of the cross-section about the central-line. This result is often
+called &ldquo;Coulomb&rsquo;s law.&rdquo; The stress within the bar is shearing
+stress, consisting, as it must, of two sets of equal tangential
+tractions on two sets of planes which are at right angles to each
+other. These planes are the cross-sections and the axial planes
+of the bar. The tangential traction at any point of the cross-section
+is directed at right angles to the axial plane through
+the point, and the tangential traction on the axial plane is
+directed parallel to the length of the bar. The amount of
+either at a distance r from the axis is &mu;&tau;r or Gr/I. The result
+that G = &mu;&tau;I can be used to determine &mu; experimentally, for &tau;
+may be measured and G and I are known.</p>
+
+<p>42. When the cross-section of the bar is not circular it is
+clear that this solution fails; for the existence of tangential
+traction, near the prismatic bounding surface, on any plane
+which does not cut this surface at right angles, implies the
+existence of traction applied to this surface. We may attempt
+to modify the theory by retaining the supposition that the
+stress consists of shearing stress, involving tangential traction
+distributed in some way over the cross-sections. Such traction
+is obviously a necessary constituent of any stress-system
+which could be produced by terminal couples around the axis.
+<span class="pagenum"><a name="page148" id="page148"></a>148</span>
+We should then know that there must be equal tangential
+traction directed along the length of the bar, and exerted across
+some planes or other which are parallel to this direction. We
+should also know that, at the bounding surface, these planes
+must cut this surface at right angles. The corresponding strain
+would be shearing strain which could involve (i.) a sliding
+of elements of one cross-section relative to another, (ii.) a relative
+sliding of elements of the above mentioned planes in the direction
+of the length of the bar. We could conclude that there may
+be a longitudinal displacement of the elements of the cross-sections.
+We should then attempt to satisfy the conditions
+of the problem by supposing that this is the character of the
+strain, and that the corresponding displacement consists of
+(i.) a rotation of the cross-sections in their planes such as we
+found in the case of the circle, (ii.) a distortion of the cross-sections
+into curved surfaces by a displacement (w) which is
+directed normally to their planes and varies in some manner
+from point to point of these planes. We could show that all
+the conditions of the problem are satisfied by this assumption,
+provided that the longitudinal displacement (w), considered as
+a function of the position of a point (x, y) in the cross-section,
+satisfies the equation</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;²w</td>
+<td rowspan="2">+</td> <td>&part;²w</td>
+<td rowspan="2">= 0,</td></tr>
+<tr><td class="denom">&part;x²</td> <td class="denom">&part;y²</td></tr></table>
+<div class="author">(1)</div>
+
+<p class="noind">and the boundary condition</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">(</span></td> <td>&part;w</td>
+<td rowspan="2">&minus; &tau;y <span class="f150">)</span> cos(x, &nu;) + <span class="f150">(</span></td> <td>&part;w</td>
+<td rowspan="2">+ &tau;x <span class="f150">)</span> cos(y, &nu;) = 0,</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td></tr></table>
+<div class="author">(2)</div>
+
+<p class="noind">where &tau; denotes the amount of the twist, and &nu; the direction
+of the normal to the boundary. The solution is known for a
+great many forms of section. (In the particular case of a circular
+section w vanishes.) The tangential traction at any point of
+the cross-section is directed along the tangent to that curve
+of the family &psi; = const. which passes through the point, &psi; being
+the function determined by the equations</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;w</td>
+<td rowspan="2">= &tau; <span class="f150">(</span></td> <td>&part;&psi;</td>
+<td rowspan="2">+ y <span class="f150">)</span>, &emsp;</td> <td>&part;w</td>
+<td rowspan="2">= &minus; &tau; <span class="f150">(</span></td> <td>&part;&psi;</td>
+<td rowspan="2">+ x <span class="f150">)</span>.</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td>
+<td class="denom">&part;y</td> <td class="denom">&part;x</td></tr></table>
+
+<p class="noind">The amount of the twist &tau; produced by terminal couples of
+magnitude G is G/C, where C is a constant, called the &ldquo;torsional
+rigidity&rdquo; of the prism, and expressed by the formula</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">C = &mu; <span class="f150">&int;&int; {(</span></td> <td>&part;&psi;</td>
+<td rowspan="2"><span class="f150">)</span></td> <td>²</td>
+<td rowspan="2">+ <span class="f150">(</span></td> <td>&part;&psi;</td>
+<td rowspan="2"><span class="f150">)</span></td> <td>²</td>
+<td rowspan="2"><span class="f150">}</span> dxdy,</td></tr>
+<tr><td class="denom">&part;x</td> <td>&nbsp;</td> <td class="denom">&part;y</td> <td>&nbsp;</td></tr></table>
+
+<p class="noind">the integration being taken over the cross-section. When
+the coefficient of &mu; in the expression for C is known for any
+section, &mu; can be determined by experiment with a bar of that
+form of section.</p>
+
+<table class="flt" style="float: right; width: 350px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:299px; height:190px" src="images/img148a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 4.</span></td></tr>
+<tr><td class="figright1"><img style="width:285px; height:272px" src="images/img148b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span></td></tr></table>
+
+<p>43. The distortion of the cross-sections into curved surfaces
+is shown graphically by drawing the contour lines (w = const.).
+In general the section is divided into a number of compartments,
+and the portions that lie within two adjacent compartments
+are respectively concave
+and convex. This result
+is illustrated in the
+accompanying figures
+(fig. 4 for the ellipse,
+given by x²/b² + y²/c² = 1;
+fig. 5 for the equilateral
+triangle, given by (x + <span class="spp">1</span>&frasl;<span class="suu">3</span>a)
+(x² &minus; 3y² &minus; <span class="spp">4</span>&frasl;<span class="suu">3</span>ax + <span class="spp">4</span>&frasl;<span class="suu">9</span>a²) = 0;
+fig. 6 for the square).</p>
+
+<p>44. The distribution of
+the shearing stress over
+the cross-section is determined
+by the function &psi;, already introduced. If we
+draw the curves &psi; = const., corresponding to any form of
+section, for equidifferent values of the constant, the tangential
+traction at any point on the cross-section is directed along the
+tangent to that curve of the family which passes through the
+point, and the magnitude of it is inversely proportional to the
+distance between consecutive curves of the family. Fig. 7
+illustrates the result in the case of the <i>equilateral</i> triangle. The
+boundary is, of course, one of the lines. The &ldquo;lines of shearing
+stress&rdquo; which can thus be drawn are in every case identical
+with the lines of flow of frictionless liquid filling a cylindrical
+vessel of the same cross-section as the bar, when the liquid
+circulates in the plane of the section with uniform spin. They
+are also the same as the contour lines of a flexible and slightly
+extensible membrane, of
+which the edge has the
+same form as the bounding
+curve of the cross-section
+of the bar, when the membrane
+is fixed at the edge
+and slightly deformed by
+uniform pressure.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:361px; height:365px" src="images/img148c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span></td></tr></table>
+
+<table class="flt" style="float: right; width: 240px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:187px; height:167px" src="images/img148d.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 7.</span></td></tr></table>
+
+<p>45. Saint-Venant&rsquo;s theory
+shows that the true torsional
+rigidity is in general
+less than that which would
+be obtained by extending
+Coulomb&rsquo;s law (G = &mu;&tau;I)
+to sections which are not
+circular. For an elliptic
+cylinder of sectional area &omega; and moment of inertia I about
+its central-line the torsional rigidity is &mu;&omega;<span class="sp">4</span> / 4&pi;²I, and this
+formula is not far from being correct for a very large
+number of sections. For a bar of square section of side a
+centimetres, the torsional rigidity in C.G.S. units is (0.1406) &mu;a<span class="sp">4</span>
+approximately, &mu; being expressed in dynes per square centimetre.
+How great the defect of the true value from that
+given by extending Coulomb&rsquo;s law may be in the case of
+sections with projecting corners is shown by the diagrams (fig. 8
+especially no. 4). In these diagrams the upper of the two
+numbers under each figure indicates the fraction which the true
+torsional rigidity corresponding to the section is of that value
+which would be obtained by extending Coulomb&rsquo;s law; and the
+lower of the two numbers indicates the
+ratio which the torsional rigidity for a
+bar of the corresponding section bears
+to that of a bar of circular section of
+the same material and of equal sectional
+area. These results have an
+important practical application, inasmuch
+as they show that strengthening
+ribs and projections, such as are introduced
+in engineering to give stiffness
+to beams, have the reverse of
+a good effect when torsional stiffness is an object, although
+they are of great value in increasing the resistance to
+bending. The theory shows further that the resistance to
+torsion is very seriously diminished when there is in the
+surface any dent approaching to a re-entrant angle. At such
+a place the shearing strain tends to become infinite, and some
+<span class="pagenum"><a name="page149" id="page149"></a>149</span>
+permanent set is produced by torsion. In the case of a section
+of any form, the strain and stress are greatest at points on the
+contour, and these points are in many cases the points of the
+contour which are nearest to the centroid of the section. The
+theory has also been applied to show that a longitudinal flaw
+near the axis of a shaft transmitting a torsional couple has
+little influence on the strength of the shaft, but that in the
+neighbourhood of a similar flaw which is much nearer to the
+surface than to the axis the shearing strain may be nearly
+doubled, and thus the possibility of such flaws is a source of
+weakness against which special provision ought to be made.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:455px; height:196px" src="images/img149a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 8.</span>&mdash;Diagrams showing Torsional Rigidities.</td></tr></table>
+
+<table class="flt" style="float: right; width: 230px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:184px; height:147px" src="images/img149b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 9.</span></td></tr></table>
+
+<p>46. <i>Bending of Beams.</i>&mdash;As a second example of the application
+of the general theory we take the problem of the flexure
+of a beam. In this case also we begin by forming a simple
+intuition as to the nature of the strain and the stress. On the
+side of the beam towards the centre of curvature the longitudinal
+filaments must be contracted, and on the other side
+they must be extended. If we assume that the cross-sections
+remain plane, and that the central-line is unaltered in length,
+we see (at once from fig. 9) that the extensions (or contractions)
+are given by the formula y/R, where y
+denotes the distance of a longitudinal
+filament from the plane drawn through
+the unstrained central-line at right-angles
+to the plane of bending, and
+R is the radius of curvature of the
+curve into which this line is bent
+(shown by the dotted line in the figure).
+Corresponding to this strain there must
+be traction acting across the cross-sections.
+If we assume that there is no other stress, then the
+magnitude of the traction in question is Ey/R, where E is Young&rsquo;s
+modulus, and it is tension on the side where the filaments are
+extended and pressure on the side where they are contracted.
+If the plane of bending contains a set of principal axes of the
+cross-sections at their centroids, these tractions for the whole
+cross-section are equivalent to a couple of moment EI/R, where
+I now denotes the moment of inertia of the cross-section about
+an axis through its centroid at right angles to the plane of
+bending, and the plane of the couple is the plane of bending.
+Thus a beam of any form of section can be held bent in a
+&ldquo;principal plane&rdquo; by terminal couples of moment M, that is
+to say by a &ldquo;bending moment&rdquo; M; the central-line will take
+a curvature M/EI, so that it becomes an arc of a circle of radius
+EI/M; and the stress at any point will be tension of amount
+My/I, where y denotes distance (reckoned positive towards the
+side remote from the centre of curvature) from that plane which
+initially contains the central-line and is at right angles to the
+plane of the couple. This plane is called the &ldquo;neutral plane.&rdquo;
+The restriction that the beam is bent in a principal plane means
+that the plane of bending contains one set of principal axes of the
+cross-sections at their centroids; in the case of a beam of rectangular
+section the plane would bisect two opposite edges at
+right angles. In order that the theory may hold good the
+radius of curvature must be very large.</p>
+
+<table class="flt" style="float: right; width: 360px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:301px; height:158px" src="images/img149c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 10.</span></td></tr>
+<tr><td class="figright1"><img style="width:310px; height:156px" src="images/img149d.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 11.</span></td></tr></table>
+
+<p>47. In this problem of the bending of a beam by terminal
+couples the stress is tension, determined as above, and the
+corresponding strain consists therefore of longitudinal extension
+of amount My/EI or y/R (contraction if y is negative), accompanied
+by lateral contraction of amount &sigma;My/EI or &sigma;y/R (extension
+if y is negative), &sigma; being Poisson&rsquo;s ratio for the material.
+Our intuition of the nature of the strain was imperfect, inasmuch
+as it took no account of these lateral strains. The necessity
+for introducing them was pointed out by Saint-Venant. The
+effect of them is a change
+of shape of the cross-sections
+in their own
+planes. This is shown in
+an exaggerated way in fig.
+10, where the rectangle
+ABCD represents the
+cross-section of the unstrained
+beam, or a rectangular
+portion of this
+cross-section, and the curvilinear figure A&prime;B&prime;C&prime;D&prime; represents in an
+exaggerated fashion the cross-section (or the corresponding portion
+of the cross-section) of the same beam, when bent so that the
+centre of curvature of the central-line (which is at right angles
+to the plane of the figure) is on the line EF produced beyond F.
+The lines A&prime;B&prime; and C&prime;D&prime; are approximately circles of radii R/&sigma;,
+when the central-line is a circle of radius R, and their centres
+are on the line FE produced beyond E. Thus the neutral plane,
+and each of the faces that is parallel to it, becomes strained
+into an <i>anticlastic surface</i>, whose principal curvatures are in the
+ratio &sigma; : 1. The general appearance of the bent beam is shown
+in an exaggerated fashion in fig. 11, where the traces of the surface
+into which the neutral plane is bent are dotted. The result
+that the ratio of the
+principal curvatures of
+the anticlastic surfaces,
+into which the top and
+bottom planes of the
+beam (of rectangular
+section) are bent, is
+Poisson&rsquo;s ratio &sigma;, has
+been used for the experimental
+determination
+of &sigma;. The result that the radius of curvature of the bent
+central-line is EI/M is used in the experimental determination
+of E. The quantity EI is often called the &ldquo;flexural rigidity&rdquo;
+of the beam. There are two principal flexural rigidities corresponding
+to bending in the two principal planes (cf. § 62 below).</p>
+
+<table class="flt" style="float: left; width: 390px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:342px; height:280px" src="images/img149e.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 12.</span></td></tr></table>
+
+<p>48. That this theory requires modification, when the load
+does not consist simply of terminal couples, can be seen most
+easily by considering the problem of a beam loaded at one end
+with a weight W, and supported in a horizontal position at its
+other end. The forces that are exerted at any section p, to
+balance the weight W, must reduce statically to a vertical
+force W and a couple, and these forces arise from the action of
+the part Ap on the part Bp (see fig. 12), <i>i.e.</i> from the stresses
+across the section at p. The couple is equal to the moment of
+the applied load W
+about an axis drawn
+through the centroid
+of the section
+p at right angles to
+the plane of bending.
+This moment
+is called the &ldquo;bending
+moment&rdquo; at
+the section, it is the
+product of the load
+W and the distance
+of the section from
+the loaded end, so
+that it varies uniformly
+along the
+length of the beam. The stress that suffices in the simpler problem
+gives rise to no vertical force, and it is clear that in addition to
+longitudinal tensions and pressures there must be tangential
+tractions on the cross-sections. The resultant of these tangential
+tractions must be a force equal to W, and directed vertically;
+<span class="pagenum"><a name="page150" id="page150"></a>150</span>
+but the direction of the traction at a point of the cross-section
+need not in general be vertical. The existence of tangential
+traction on the cross-sections implies the existence of equal
+tangential traction, directed parallel to the central-line, on
+some planes or other which are parallel to this line, the two sets
+of tractions forming a shearing stress. We conclude that such
+shearing stress is a necessary constituent of the stress-system
+in the beam bent by terminal transverse load. We can develop
+a theory of this stress-system from the assumptions (i.) that the
+tension at any point of the cross-section is related to the bending
+moment at the section by the same law as in the case of uniform
+bending by terminal couples; (ii.) that, in addition to this
+tension, there is at any point shearing stress, involving tangential
+tractions acting in appropriate directions upon the elements
+of the cross-sections. When these assumptions are made it
+appears that there is one and only one distribution of shearing
+stress by which the conditions of the problem can be satisfied.
+The determination of the amount and direction of this shearing
+stress, and of the corresponding strains and displacements, was
+effected by Saint-Venant and R.F.A. Clebsch for a number of
+forms of section by means of an analysis of the same kind as that
+employed in the solution of the torsion problem.</p>
+
+<table class="flt" style="float: right; width: 290px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:250px; height:353px" src="images/img150a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 13.</span></td></tr></table>
+
+<div class="condensed">
+<p>49. Let l be the length of the beam, x the distance of the section
+p from the fixed end A, y the distance of any point below the horizontal
+plane through the centroid of the
+section at A, then the bending moment at
+p is W (l &minus; x), and the longitudinal tension P
+or X<span class="su">x</span> at any point on the cross-section is
+&minus;W (l &minus; x)y/I, and this is related to the
+bending moment exactly as in the
+simpler problem.</p>
+
+<p>50. The expressions for the
+shearing stresses depend on the
+shape of the cross-section. Taking
+the beam to be of isotropic
+material and the cross-section to
+be an ellipse of semiaxes a and b
+(fig. 13), the a axis being vertical
+in the unstrained state, and drawing the axis
+z at right angles to the plane of flexure, we
+find that the vertical shearing stress U or X<span class="su">y</span>
+at any point (y, z) on any cross-section is</p>
+
+<table class="math0" summary="math">
+<tr><td>2W [(a² &minus; y²) {2a² (1 + &sigma;) + b²} &minus; z²a² (1 &minus; 2&sigma;)]</td> <td rowspan="2">.</td></tr>
+<tr><td class="denom">&pi;a³b (1 + &sigma;) (3a² + b²)</td></tr></table>
+
+<p class="noind">The resultant of these stresses is W, but the
+amount at the centroid, which is the maximum
+amount, exceeds the average amount,
+W/&pi;ab, in the ratio</p>
+
+<p class="center">{4a² (1 + &sigma;) + 2b²} / (3a² + b²) (1 + &sigma;).</p>
+
+<p class="noind">If &sigma; = ¼, this ratio is <span class="spp">7</span>&frasl;<span class="suu">5</span> for a circle, nearly <span class="spp">4</span>&frasl;<span class="suu">3</span> for a flat elliptic bar
+with the longest diameter vertical, nearly <span class="spp">8</span>&frasl;<span class="suu">5</span> for a flat elliptic bar with
+the longest diameter horizontal.</p>
+
+<p>In the same problem the horizontal shearing stress T or Z<span class="su">x</span> at any
+point on any cross-section is of amount</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&minus;</td> <td>4Wyz {a² (1 + &sigma;) + b²&sigma;}</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">&pi;a³b (1 + &sigma;) (3a² + b²)</td></tr></table>
+
+<p class="noind">The resultant of these stresses vanishes; but, taking as before &sigma; = ¼,
+and putting for the three cases above a = b, a = 10b, b = 10a, we find
+that the ratio of the maximum of this stress to the average vertical
+shearing stress has the values <span class="spp">3</span>&frasl;<span class="suu">5</span>, nearly <span class="spp">1</span>&frasl;<span class="suu">15</span>, and nearly 4. Thus the
+stress T is of considerable importance when the beam is a plank.</p>
+
+<p>As another example we may consider a circular tube of external
+radius r<span class="su">0</span> and internal radius r<span class="su">1</span>. Writing P, U, T for X<span class="su">x</span>, X<span class="su">y</span>, Z<span class="su">x</span>, we find</p>
+
+<table class="math0l" summary="math">
+<tr><td rowspan="2">P = &minus;</td> <td>4W</td>
+<td rowspan="2">(l &minus; x)y,</td></tr>
+<tr><td class="denom">&pi; (r<span class="su">0</span><span class="sp">4</span> &minus; r<span class="su">1</span><span class="sp">4</span>)</td></tr></table>
+
+<table class="math0l" summary="math">
+<tr><td rowspan="2">U =</td> <td>W</td>
+<td rowspan="2"><span class="f150">[</span> (3 + 2&sigma;) <span class="f150">{</span> r<span class="su">0</span>² + r<span class="su">1</span>² &minus; y² &minus;</td> <td>r<span class="su">0</span>² r<span class="su">1</span>²</td>
+<td rowspan="2">(y² &minus; z²) <span class="f150">}</span> &minus; (1 &minus; 2&sigma;) z² <span class="f150">]</span></td></tr>
+<tr><td class="denom">2(1 + &sigma;) &pi; (r<span class="su">0</span><span class="sp">4</span> &minus; r<span class="su">1</span><span class="sp">4</span>)</td>
+ <td class="denom">(y² + z²)²</td></tr></table>
+
+<table class="math0l" summary="math">
+<tr><td rowspan="2">T = &minus;</td> <td>W</td>
+<td rowspan="2"><span class="f150">{</span> 1 + 2&sigma; + (3 + 2&sigma;)</td> <td>r<span class="su">0</span>² r<span class="su">1</span>²</td>
+<td rowspan="2"><span class="f150">}</span> yz;</td></tr>
+<tr><td class="denom">(1 + &sigma;) &pi; (r<span class="su">0</span><span class="sp">4</span> &minus; r<span class="su">1</span><span class="sp">4</span>)</td>
+ <td class="denom">(y² + z²)²</td></tr></table>
+
+<p class="noind">and for a tube of radius r and small thickness t the value of P and
+the maximum values of U and T reduce approximately to</p>
+
+<p class="center">P = &minus; W (l &minus; x)y / &pi;r³t</p>
+
+<p class="center">U<span class="su">max.</span> = W / &pi;rt, &emsp; T<span class="su">max.</span> = W / 2&pi;rt.</p>
+
+<p class="noind">The greatest value of U is in this case approximately twice its
+average value, but it is possible that these results for the bending
+of very thin tubes may be seriously at fault if the tube is not plugged,
+and if the load is not applied in the manner contemplated in the
+theory (cf. § 55). In such cases the extensions and contractions of
+the longitudinal filaments may be practically confined to a small
+part of the material near the ends of the tube, while the rest of the
+tube is deformed without stretching.</p>
+</div>
+
+<p>51. The tangential tractions U, T on the cross-sections are
+necessarily accompanied by tangential tractions on the longitudinal
+sections, and on each such section the tangential traction
+is parallel to the central line; on a vertical section z = const.
+its amount at any point is T, and on a horizontal section y =
+const. its amount at any point is U.</p>
+
+<p>The internal stress at any point is completely determined
+by the components P, U, T, but these are not principal stresses
+(§ 7). Clebsch has given an elegant geometrical construction
+for determining the principal stresses at any point when the
+values of P, U, T are known.</p>
+
+<table class="flt" style="float: right; width: 300px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:262px; height:197px" src="images/img150b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 14.</span></td></tr></table>
+
+<div class="condensed">
+<p>From the point O (fig. 14) draw lines OP, OU, OT, to represent
+the stresses P, U, T at O, on the cross-section through O, in magnitude,
+direction and sense, and
+compound U and T into a
+resultant represented by OE;
+the plane EOP is a principal
+plane of stress at O, and the
+principal stress at right angles
+to this plane vanishes. Take
+M the middle point of OP, and
+with centre M and radius ME
+describe a circle cutting the
+line OP in A and B; then OA
+and OB represent the magnitudes
+of the two remaining
+principal stresses. On AB
+describe a rectangle ABDC so
+that DC passes through E; then OC is the direction of the principal
+stress represented in magnitude by OA, and OD is the direction
+of the principal stress represented in magnitude by OB.</p>
+</div>
+
+<table class="flt" style="float: left; width: 230px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:191px; height:181px" src="images/img150c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 15.</span></td></tr></table>
+
+<p>52. As regards the strain in the beam, the longitudinal and
+lateral extensions and contractions depend on the bending
+moment in the same way as in the simpler problem; but, the
+bending moment being variable, the anticlastic curvature
+produced is also variable. In addition to these extensions
+and contractions there are shearing strains corresponding to the
+shearing stresses T, U. The shearing strain corresponding to
+T consists of a relative sliding parallel to the central-line of
+different longitudinal linear elements combined with a relative
+sliding in a transverse horizontal direction of elements of different
+cross-sections; the latter of these is concerned in the production
+of those displacements by which the variable anticlastic curvature
+is brought about; to see the effect of the former we may most
+suitably consider, for the case of an elliptic cross-section, the
+distortion of the shape of a rectangular portion of a plane of the
+material which in the natural state
+was horizontal; all the boundaries
+of such a portion become parabolas of
+small curvature, which is variable along
+the length of the beam, and the particular
+effect under consideration is
+the change of the transverse horizontal
+linear elements from straight lines
+such as HK to parabolas such as H&rsquo;K&rsquo;
+(fig. 15); the lines HL and KM are
+parallel to the central-line, and the
+figure is drawn for a plane above the neutral plane. When the
+cross-section is not an ellipse the character of the strain is the
+same, but the curves are only approximately parabolic.</p>
+
+<p>The shearing strain corresponding to U is a distortion which
+has the effect that the straight vertical filaments become curved
+lines which cut the longitudinal filaments obliquely, and thus
+the cross-sections do not remain plane, but become curved
+surfaces, and the tangent plane to any one of these surfaces
+at the centroid cuts the central line obliquely (fig. 16). The
+angle between these tangent planes and the central-line is the
+same at all points of the line; and, if it is denoted by ½&pi; + s<span class="su">0</span>,
+the value of s<span class="su">0</span> is expressible as</p>
+
+<table class="math0" summary="math">
+<tr> <td>shearing stress at centroid</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">rigidity of material</td></tr></table>
+
+<p><span class="pagenum"><a name="page151" id="page151"></a>151</span></p>
+
+<p class="noind">and it thus depends on the shape of the cross-section; for the
+elliptic section of § 50 its value is</p>
+
+<table class="math0" summary="math">
+<tr><td>4W</td> <td rowspan="2">&nbsp;</td> <td>2a² (1 + &sigma;) + b²</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">E&pi;ab</td> <td class="denom">3a² + b²</td></tr></table>
+
+<p class="noind">for a circle (with &sigma; = ¼) this becomes 7W / 2E&pi;a². The vertical
+filament through the centroid of any cross-section becomes
+a cubical parabola, as shown in fig. 16, and the contour lines
+of the curved surface into which any cross-section is distorted
+are shown in fig. 17 for a circular section.</p>
+
+<table class="flt" style="float: right; width: 340px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:299px; height:262px" src="images/img151a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 16.</span></td></tr>
+<tr><td class="figright1"><img style="width:304px; height:306px" src="images/img151b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 17.</span></td></tr></table>
+
+<p>53. The deflection of the beam is determined from the equation</p>
+
+<p class="center">curvature of central line = bending moment ÷ flexural rigidity,</p>
+
+<p class="noind">and the special conditions at the supported end; there is no
+alteration of this statement on account of the shears. As regards
+the special condition at
+an end which is <i>encastrée</i>,
+or built in, Saint-Venant
+proposed to assume that
+the central tangent plane
+of the cross-section at
+the end is vertical; with
+this assumption the tangent
+to the central line
+at the end is inclined
+downwards and makes an
+angle s<span class="su">0</span> with the horizontal
+(see fig. 18); it is,
+however, improbable that
+this condition is exactly
+realized in practice. In the application of the theory to the
+experimental determination of Young&rsquo;s modulus, the small
+angle which the central-line at the support makes with the
+horizontal is an unknown quantity, to be eliminated by observation
+of the deflection at two or more points.</p>
+
+<p>54. We may suppose the displacement in a bent beam to be
+produced by the following operations: (1) the central-line is
+deflected into its curved form, (2) the cross-sections are rotated
+about axes through their centroids at right angles to the plane
+of flexure so as to make angles equal to ½&pi; + s<span class="su">0</span> with the central-line,
+(3) each cross-section is distorted in its own plane in such
+a way that the appropriate variable anticlastic curvature is
+produced, (4) the cross-sections are further distorted into curved
+surfaces. The contour lines of fig. 17 show the disturbance
+from the central tangent plane, not from the original vertical
+plane.</p>
+
+<p>55. <i>Practical Application of Saint-Venant&rsquo;s Theory.</i>&mdash;The
+theory above described is exact provided the forces applied to
+the loaded end, which
+have W for resultant,
+are distributed over the
+terminal section in a particular
+way, not likely to
+be realized in practice;
+and the application to
+practical problems depends
+on a principle due
+to Saint-Venant, to the
+effect that, except for
+comparatively small portions
+of the beam near
+to the loaded and fixed
+ends, the resultant only
+is effective, and its mode
+of distribution does not
+seriously affect the internal
+strain and stress. In fact, the actual stress is that due
+to forces with the required resultant distributed in the manner
+contemplated in the theory, superposed upon that due to a
+certain distribution of forces on each terminal section which, if
+applied to a rigid body, would keep it in equilibrium; according
+to Saint-Venant&rsquo;s principle, the stresses and strains due to such
+distributions of force are unimportant except near the ends. For
+this principle to be exactly applicable it is necessary that the
+length of the beam should be very great compared with any
+linear dimension of its cross-section; for the practical application
+it is sufficient that the length should be about ten times the
+greatest diameter.</p>
+
+<p>56. In recent years the problem of the bending of a beam by
+loads distributed along its length has been much advanced.
+It is now practically solved for the case of a load distributed
+uniformly, or according to any rational algebraic law, and it is
+also solved for the case where the thickness is small compared
+with the length and depth, as in a plate girder, and the load is
+distributed in any way. These solutions are rather complicated
+and difficult to interpret. The case which has been worked
+out most fully is that of a transverse load distributed uniformly
+along the length of the beam. In this case two noteworthy
+results have been obtained. The first of these is that the central-line
+in general suffers extension. This result had been found
+experimentally many years before. In the case of the plate
+girder loaded uniformly along the top, this extension is just
+half as great as the extension of the central-line of the same
+girder when free at the ends, supported along the base, and
+carrying the same load along the top. The second noteworthy
+result is that the curvature of the strained central-line
+is not proportional to the bending moment. Over and
+above the curvature which would be found from the ordinary
+relation&mdash;</p>
+
+<p class="center">curvature of central-line = bending moment ÷ flexural rigidity,</p>
+
+<table class="flt" style="float: right; width: 280px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:235px; height:236px" src="images/img151c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 18.</span></td></tr></table>
+
+<p class="noind">there is an additional curvature which is the same at all the
+cross-sections. In ordinary cases, provided the length is large
+compared with any linear dimension of the cross-section, this
+additional curvature is small compared with that calculated
+from the ordinary formula, but it may become important in
+cases like that of suspension
+bridges, where a load carried
+along the middle of the roadway
+is supported by tensions in rods
+attached at the sides.</p>
+
+<p>57. When the ordinary relation
+between the curvature and the
+bending moment is applied to the
+calculation of the deflection of <i>continuous
+beams</i> it must not be
+forgotten that a correction of the
+kind just mentioned may possibly
+be requisite. In the usual method
+of treating the problem such corrections
+are not considered, and the ordinary relation is made
+the basis of the theory. In order to apply this relation to the
+calculation of the deflection, it is necessary to know the bending
+moment at every point; and, since the pressures of the supports
+are not among the data of the problem, we require a method
+of determining the bending moments at the supports either
+by calculation or in some other way. The calculation of the
+bending moment can be replaced by a method of graphical
+construction, due to Mohr, and depending on the two following
+theorems:&mdash;</p>
+
+<p>(i.) The curve of the central-line of each span of a beam, when
+the bending moment M is given,<a name="fa1b" id="fa1b" href="#ft1b"><span class="sp">1</span></a> is identical with the catenary
+or funicular curve passing through the ends of the span under a
+(fictitious) load per unit length of the span equal to M/EI, the
+horizontal tension in the funicular being unity.</p>
+
+<p>(ii.) The directions of the tangents to this funicular curve
+at the ends of the span are the same for all statically equivalent
+systems of (fictitious) load.</p>
+
+<p>When M is known, the magnitude of the resultant shearing
+stress at any section is dM/dx, where x is measured along the
+beam.</p>
+
+<p><span class="pagenum"><a name="page152" id="page152"></a>152</span></p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:323px; height:53px" src="images/img152a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 20.</span></td></tr></table>
+
+<div class="condensed">
+<p>58. Let l be the length of a span of a loaded beam (fig. 19), M<span class="su">1</span>
+and M<span class="su">2</span> the bending moments at the ends, M the bending moment
+at a section distant x from the end (M<span class="su">1</span>), M&prime; the bending moment at
+the same section when the same span with the same load is simply
+supported; then M is given by the formula</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">M = M&prime; + M<span class="su">1</span></td> <td>l &minus; x</td>
+<td rowspan="2">+ M<span class="su">2</span></td> <td>x</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">l</td> <td class="denom">l</td></tr></table>
+
+<table class="flt" style="float: right; width: 330px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:299px; height:181px" src="images/img152b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 19.</span></td></tr></table>
+
+<p>and thus a fictitious load statically equivalent to M/EI can be
+easily found when M&prime; has been found. If we draw a curve (fig. 20)
+to pass through the ends of the span, so that its ordinate represents
+the value of M&prime;/EI, the corresponding fictitious loads are statically
+equivalent to a single load, of amount represented by the area of the
+curve, placed at the point of the span vertically above the centre of
+gravity of this area. If PN is the ordinate of this curve, and if at
+the ends of the span we erect ordinates in the proper sense to represent
+M<span class="su">1</span>/EI and M<span class="su">2</span>/EI, the bending moment at any point is represented
+by the length PQ.<a name="fa2b" id="fa2b" href="#ft2b"><span class="sp">2</span></a> For
+a uniformly distributed
+load the curve of M&rsquo; is a
+parabola M&prime; = ½wx (l &minus; x),
+where w is the load per
+unit of length; and the
+statically equivalent fictitious
+load is <span class="spp">1</span>&frasl;<span class="suu">12</span>wl³ / EI
+placed at the middle point
+G of the span; also the
+loads statically equivalent
+to the fictitious loads
+M<span class="su">1</span> (l &minus; x) / lEI and M<span class="su">2</span>x / lEI
+are ½M<span class="su">1</span>l / EI and ½M<span class="su">2</span>l / EI
+placed at the points g, g&prime; of trisection of the span. The funicular
+polygon for the fictitious loads can thus be drawn, and the
+direction of the central-line at the supports is determined when the
+bending moments at the supports are known.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:418px; height:313px" src="images/img152c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 21.</span></td></tr></table>
+
+<table class="flt" style="float: right; width: 280px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:232px; height:165px" src="images/img152f.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 22.</span></td></tr>
+<tr><td class="figright1"><img style="width:148px; height:308px" src="images/img152d.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 23.</span></td></tr></table>
+
+<p>59. When there is more than one span the funiculars in question
+may be drawn for each of the spans, and, if the bending moments
+at the ends of the extreme spans are known, the intermediate ones
+can be determined. This determination depends on two considerations:
+(1) the fictitious loads corresponding to the bending moment
+at any support are proportional to the lengths of the spans which
+abut on that support; (2) the sides of two funiculars that end at
+any support coincide in direction. Fig. 21 illustrates the method
+for the case of a uniform beam on three supports A, B, C, the ends
+A and C being freely supported. There will be an unknown bending
+moment M<span class="su">0</span> at B, and the system<a name="fa3b" id="fa3b" href="#ft3b"><span class="sp">3</span></a> of fictitious loads is <span class="spp">1</span>&frasl;<span class="suu">12</span>wAB³/EI
+at G the middle point of AB, <span class="spp">1</span>&frasl;<span class="suu">12</span>wBC³ / EI at G&prime; the middle point of
+BC, &minus;½M<span class="su">0</span>AB / EI at g and &minus;½M<span class="su">0</span>BC / EI at g&prime;, where g and g&prime; are the
+points of trisection nearer to B of the spans AB, BC. The centre of
+gravity of the two latter is a fixed point independent of M<span class="su">0</span>, and the
+line VK of the figure is the vertical through this point. We draw
+AD and CE to represent the loads at G and G&rsquo; in magnitude; then
+D and E are fixed points. We construct any triangle UVW whose
+sides UV, UW pass through D, B, and whose vertices lie on the
+verticals gU, VK, g&prime;W; the point F where VW meets DB is a fixed
+point, and the lines EF, DK are the two sides (2, 4) of the required
+funiculars which do not pass through A, B or C. The remaining
+sides (1, 3, 5) can then be drawn, and the side 3 necessarily passes
+through B; for the triangle UVW
+and the triangle whose sides are
+2, 3, 4 are in perspective.</p>
+
+<p>The bending moment M<span class="su">0</span> is represented
+in the figure by the vertical
+line BH where H is on the continuation
+of the side 4, the scale
+being given by</p>
+
+<table class="math0" summary="math">
+<tr><td>BH</td> <td rowspan="2">=</td> <td>½M<span class="su">0</span>BC</td>
+<td rowspan="2">;</td></tr>
+<tr><td class="denom">CE</td> <td class="denom"><span class="spp">1</span>&frasl;<span class="suu">12</span>wBC³</td></tr></table>
+
+<p class="noind">this appears from the diagrams of
+forces, fig. 22, in which the oblique
+lines are marked to correspond to the sides of the funiculars to
+which they are parallel.</p>
+
+<p>In the application of the method to more complicated cases there
+are two systems of fixed points corresponding to F, by means of
+which the sides of the funiculars are drawn.</p>
+</div>
+
+<p>60. <i>Finite Bending of Thin Rod.</i>&mdash;The equation</p>
+
+<p class="center">curvature = bending moment ÷ flexural rigidity</p>
+
+<p class="noind">may also be applied to the problem of the flexure in a principal
+plane of a very thin rod or wire, for which the curvature need
+not be small. When the forces that produce
+the flexure are applied at the ends
+only, the curve into which the central-line
+is bent is one of a definite family of curves,
+to which the name <i>elastica</i> has been given,
+and there is a division of the family into two
+species according as the external forces are
+applied directly to the ends or are applied
+to rigid arms attached to the ends; the
+curves of the former species are characterized
+by the presence of inflections at all the points
+at which they cut the line of action of the
+applied forces.</p>
+
+<div class="condensed">
+<p>We select this case for consideration. The
+problem of determining the form of the curve
+(cf. fig. 23) is mathematically identical with
+the problem of determining the motion of a
+simple circular pendulum oscillating through a
+finite angle, as is seen by comparing the differential equation of the
+curve</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">EI</td> <td>d²&phi;</td>
+<td rowspan="2">+ W sin &phi; = 0</td></tr>
+<tr><td class="denom">ds²</td></tr></table>
+
+<p class="noind">with the equation of motion of the pendulum</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">l</td> <td>d²&phi;</td>
+<td rowspan="2">+ g sin &phi; = 0.</td></tr>
+<tr><td class="denom">dt²</td></tr></table>
+
+<p class="noind">The length L of the curve between two inflections corresponds to the
+time of oscillation of the pendulum from rest to rest, and we thus
+have</p>
+
+<p class="center">L &radic;(W / EI) = 2K,</p>
+
+<table class="flt" style="float: right; width: 300px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:248px; height:293px" src="images/img152e.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 24.</span></td></tr></table>
+
+<p class="noind">where K is the real quarter period of elliptic functions of modulus
+sin ½&alpha;, and &alpha; is the angle at which the curve cuts the line of action
+of the applied forces. Unless
+the length of the rod exceeds
+&pi;&radic;(EI / W) it will not bend under
+the force, but when the length is
+great enough there may be more
+than two points of inflection and
+more than one bay of the curve;
+for n bays (n + 1 inflections) the
+length must exceed n&pi; &radic;(EI / W).
+Some of the forms of the curve
+are shown in fig. 24.</p>
+
+<p>For the form d, in which two
+bays make a figure of eight, we
+have</p>
+
+<p class="center">L&radic;(W / EI) = 4.6, &emsp; &alpha; = 130°</p>
+
+<p class="noind">approximately. It is noteworthy
+that whenever the length and force
+admit of a sinuous form, such as
+&alpha; or b, with more than two inflections,
+there is also possible a
+crossed form, like e, with two inflections only; the latter form is
+stable and the former unstable.</p>
+</div>
+
+<table class="flt" style="float: left; width: 310px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:272px; height:275px" src="images/img153a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 25.</span></td></tr></table>
+
+<p>61. The particular case of the above for which &alpha; is very
+small is a curve of sines of small amplitude, and the result
+in this case has been applied to the problem of the buckling
+of struts under thrust. When the strut, of length L&prime;, is
+<span class="pagenum"><a name="page153" id="page153"></a>153</span>
+maintained upright at its lower end, and loaded at its upper
+end, it is simply contracted, unless L&prime;²W &gt; ¼&pi;²EI, for the
+lower end corresponds to a point at which the tangent is
+vertical on an elastica for which the line of inflections is also
+vertical, and thus the length must be half of one bay (fig. 25, a).
+For greater lengths or loads
+the strut tends to bend or
+buckle under the load. For
+a very slight excess of L&prime;²W
+above ¼&pi;²EI, the theory on
+which the above discussion
+is founded, is not quite
+adequate, as it assumes the
+central-line of the strut to be
+free from extension or contraction,
+and it is probable
+that bending without extension
+does not take place
+when the length or the force
+exceeds the critical value but
+slightly. It should be noted
+also that the formula has no application to short struts, as the
+theory from which it is derived is founded on the assumption
+that the length is great compared with the diameter
+(cf. § 56).</p>
+
+<p>The condition of buckling, corresponding to the above, for a
+long strut, of length L&prime;, when both ends are free to turn is
+L&prime;²W &gt; &pi;²EI; for the central-line forms a complete bay (fig. 25,
+b); if both ends are maintained in the same vertical line, the
+condition is L&prime;²W &gt; 4&pi;²EI, the central-line forming a complete
+bay and two half bays (fig. 25, <i>c</i>).</p>
+
+<p>62. In our consideration of flexure it has so far been supposed
+that the bending takes place in a principal plane. We may remove
+this restriction by resolving the forces that tend to produce
+bending into systems of forces acting in the two principal planes.
+To each plane there corresponds a particular flexural rigidity,
+and the systems of forces in the two planes give rise to independent
+systems of stress, strain and displacement, which
+must be superposed in order to obtain the actual state. Applying
+this process to the problem of §§ 48-54, and supposing that
+one principal axis of a cross-section at its centroid makes an
+angle &theta; with the vertical, then for any shape of section the
+neutral surface or locus of unextended fibres cuts the section
+in a line DD&prime;, which is conjugate to the vertical diameter CP
+with respect to any ellipse of inertia of the section. The central-line
+is bent into a plane curve which is not in a vertical plane,
+but is in a plane through the line CY which is perpendicular
+to DD&prime; (fig. 26).</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:460px; height:456px" src="images/img153b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 26.</span></td></tr></table>
+
+<p>63. <i>Bending and Twisting of Thin Rods.</i>&mdash;When a very thin
+rod or wire is bent and twisted by applied forces, the forces on
+any part of it limited by a normal section are balanced by the
+tractions across the section, and these tractions are statically
+equivalent to certain forces and couples at the centroid of the
+section; we shall call them the <i>stress-resultants</i> and the <i>stress-couples</i>.
+The stress-couples consist of two flexural couples in
+the two principal planes, and the torsional couple about the
+tangent to the central-line. The torsional couple is the product
+of the torsional rigidity and the twist produced; the torsional
+rigidity is exactly the same as for a straight rod of the same
+material and section twisted without bending, as in Saint-Venant&rsquo;s
+torsion problem (§ 42). The twist &tau; is connected with
+the deformation of the wire in this way: if we suppose a very
+small ring which fits the cross-section of the wire to be provided
+with a pointer in the direction of one principal axis of the section
+at its centroid, and to move along the wire with velocity v, the
+pointer will rotate about the central-line with angular velocity &tau;v.
+The amount of the flexural couple for either principal plane at
+any section is the product of the flexural rigidity for that plane,
+and the resolved part in that plane of the curvature of the central
+line at the centroid of the section; the resolved part of the
+curvature along the normal to any plane is obtained by treating
+the curvature as a vector directed along the normal to the osculating
+plane and projecting this vector. The flexural couples
+reduce to a single couple in the osculating plane proportional
+to the curvature when the two flexural rigidities are equal, and
+in this case only.</p>
+
+<p>The stress-resultants across any section are tangential forces
+in the two principal planes, and a tension or thrust along the
+central-line; when the stress-couples and the applied forces are
+known these stress-resultants are determinate. The existence,
+in particular, of the resultant tension or thrust parallel to the
+central-line does not imply sensible extension or contraction of
+the central filament, and the tension per unit area of the cross-section
+to which it would be equivalent is small compared
+with the tensions and pressures in longitudinal filaments not
+passing through the centroid of the section; the moments
+of the latter tensions and pressures constitute the flexural
+couples.</p>
+
+<table class="flt" style="float: right; width: 200px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:160px; height:350px" src="images/img153c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 27.</span></td></tr></table>
+
+<p>64. We consider, in particular, the case of a naturally straight
+spring or rod of circular section, radius c, and of homogeneous
+isotropic material. The torsional rigidity is ¼E&pi;c<span class="sp">4</span> / (1 + &sigma;);
+and the flexural rigidity, which is the same for all planes through
+the central-line, is ¼E&pi;c<span class="sp">4</span>; we shall denote these by C and A
+respectively. The rod may be held bent by suitable forces into
+a curve of double curvature with an amount of twist &tau;, and then
+the torsional couple is C&tau;, and the flexural couple in the osculating
+plane is A/&rho;, where &rho; is the radius of circular
+curvature. Among the curves in which
+the rod can be held by forces and couples
+applied at its ends only, one is a circular
+helix; and then the applied forces and
+couples are equivalent to a wrench about
+the axis of the helix.</p>
+
+<div class="condensed">
+<p>Let &alpha; be the angle and r the radius of the
+helix, so that &rho; is r sec²&alpha;; and let R and K be
+the force and couple of the wrench (fig. 27).</p>
+
+<p>Then the couple formed by R and an equal
+and opposite force at any section and the
+couple K are equivalent to the torsional and
+flexural couples at the section, and this gives
+the equations for R and K</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">R = A</td> <td>sin &alpha; cos³ &alpha;</td>
+<td rowspan="2">&minus;</td> <td>cos &alpha;</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">r²</td> <td class="denom">r</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">K = A</td> <td>cos³ &alpha;</td>
+<td rowspan="2">+ C&tau; sin &alpha;.</td></tr>
+<tr><td class="denom">r</td></tr></table>
+
+<p class="noind">The thrust across any section is R sin &alpha;
+parallel to the tangent to the helix, and
+the shearing stress-resultant is R cos &alpha; at right angles to the
+osculating plane.</p>
+
+<p>When the twist is such that, if the rod were simply unbent, it
+<span class="pagenum"><a name="page154" id="page154"></a>154</span>
+would also be untwisted, &tau; is (sin &alpha; cos &alpha;) / r, and then, restoring the
+values of A and C, we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">R =</td> <td>E&pi;c<span class="sp">4</span></td>
+<td rowspan="2">&nbsp;</td> <td>&sigma;</td>
+<td rowspan="2">sin &alpha; cos² &alpha;,</td></tr>
+<tr><td class="denom">4r²</td> <td class="denom">1 + &sigma;</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">K =</td> <td>E&pi;c<span class="sp">4</span></td>
+<td rowspan="2">&nbsp;</td> <td>1 + &sigma; cos² &alpha;</td>
+<td rowspan="2">cos &alpha;.</td></tr>
+<tr><td class="denom">4r</td> <td class="denom">1 + &sigma;</td></tr></table>
+
+<p>65. The theory of spiral springs affords an application of these
+results. The stress-couples called into play when a naturally helical
+spring (&alpha;, r) is held in the form of a helix (&alpha;&prime;, r&prime;), are equal to the
+differences between those called into play when a straight rod of the
+same material and section is held in the first form, and those called
+into play when it is held in the second form.</p>
+
+<p>Thus the torsional couple is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">C <span class="f150">(</span></td> <td>sin &alpha;&prime; cos &alpha;&prime;</td>
+<td rowspan="2">&minus;</td> <td>sin &alpha; cos &alpha;</td>
+<td rowspan="2"><span class="f150">)</span>.</td></tr>
+<tr><td class="denom">r&prime;</td> <td class="denom">r</td></tr></table>
+
+<p class="noind">and the flexural couple is</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">A <span class="f150">(</span></td> <td>cos² &alpha;&prime;</td>
+<td rowspan="2">&minus;</td> <td>cos² &alpha;</td>
+<td rowspan="2"><span class="f150">)</span>.</td></tr>
+<tr><td class="denom">r&prime;</td> <td class="denom">r</td></tr></table>
+
+<p class="noind">The wrench (R, K) along the axis by which the spring can be held
+in the form (&alpha;&prime;, r&prime;) is given by the equations</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">R = A</td> <td>sin &alpha;&prime;</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>cos² &alpha;&prime;</td>
+<td rowspan="2">&minus;</td> <td>cos² &alpha;</td>
+<td rowspan="2"><span class="f150">)</span> &minus; C</td> <td>cos &alpha;&prime;</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>sin &alpha;&prime; cos &alpha;&prime;</td>
+<td rowspan="2">&minus;</td> <td>sin &alpha; cos &alpha;</td>
+<td rowspan="2"><span class="f150">)</span>,</td></tr>
+<tr><td class="denom">r&prime;</td> <td class="denom">r&prime;</td>
+<td class="denom">r</td> <td class="denom">r&prime;</td>
+<td class="denom">r&prime;</td> <td class="denom">r</td></tr></table>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">K = A cos &alpha;&prime; <span class="f150">(</span></td> <td>cos² &alpha;&prime;</td>
+<td rowspan="2">&minus;</td> <td>cos² &alpha;</td>
+<td rowspan="2"><span class="f150">)</span> + sin &alpha;&prime; <span class="f150">(</span></td> <td>sin &alpha;&prime; cos &alpha;&prime;</td>
+<td rowspan="2">&minus;</td> <td>sin &alpha; cos &alpha;</td>
+<td rowspan="2"><span class="f150">)</span>.</td></tr>
+<tr><td class="denom">r&prime;</td> <td class="denom">r</td>
+<td class="denom">r&prime;</td> <td class="denom">r</td></tr></table>
+
+<p class="noind">When the spring is slightly extended by an axial force F, = &minus;R,
+and there is no couple, so that K vanishes, and &alpha;&prime;, r&prime; differ very
+little from &alpha;, r, it follows from these equations that the axial elongation,
+&delta;x, is connected with the axial length x and the force F by the
+equation</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">F =</td> <td>E&pi;c<span class="sp">4</span></td>
+<td rowspan="2">&nbsp;</td> <td>sin &alpha;</td>
+<td rowspan="2">&nbsp;</td> <td>&delta;x</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">4r²</td> <td class="denom">1 + &sigma; cos² &alpha;</td>
+ <td class="denom">x</td></tr></table>
+
+<p class="noind">and that the loaded end is rotated about the axis of the helix through
+a small angle</p>
+
+<table class="math0" summary="math">
+<tr><td>4&sigma;Fxr cos &alpha;</td> <td rowspan="2">,</td></tr>
+<tr><td class="denom">E&pi;c<span class="sp">4</span></td></tr></table>
+
+<p class="noind">the sense of the rotation being such that the spring becomes more
+tightly coiled.</p>
+</div>
+
+<p>66. A horizontal pointer attached to a vertical spiral spring
+would be made to rotate by loading the spring, and the angle
+through which it turns might be used to measure the load, at
+any rate, when the load is not too great; but a much more
+sensitive contrivance is the twisted strip devised by W.E.
+Ayrton and J. Perry. A very thin, narrow rectangular strip
+of metal is given a permanent twist about its longitudinal
+middle line, and a pointer is attached to it at right angles to
+this line. When the strip is subjected to longitudinal tension
+the pointer rotates through a considerable angle. G.H. Bryan
+(<i>Phil. Mag.</i>, December 1890) has succeeded in constructing a
+theory of the action of the strip, according to which it is regarded
+as a strip of <i>plating</i> in the form of a right helicoid, which,
+after extension of the middle line, becomes a portion of a slightly
+different helicoid; on account of the thinness of the strip, the
+change of curvature of the surface is considerable, even when
+the extension is small, and the pointer turns with the generators
+of the helicoid.</p>
+
+<div class="condensed">
+<p>If b stands for the breadth and t for the thickness of the strip,
+and &tau; for the permanent twist, the approximate formula for the
+angle &theta; through which the strip is untwisted on the application of
+a load W was found to be</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&theta; =</td> <td colspan="5">Wb&tau; (1 + &sigma;)</td> <td rowspan="2">.</td></tr>
+<tr><td class="denom" rowspan="2">2Et<span class="sp">3</span> <span class="f150">(</span> 1 +</td>
+ <td class="denom">(1 + &sigma;)</td> <td class="denom" rowspan="2">&nbsp;</td>
+ <td class="denom">b<span class="sp">4</span>&tau;<span class="sp">2</span></td>
+ <td class="denom" rowspan="2"><span class="f150">)</span></td></tr>
+<tr><td>&nbsp;</td>
+ <td class="denom">30</td> <td class="denom">t²</td></tr></table>
+
+<p class="noind">The quantity b&tau; which occurs in the formula is the total twist in a
+length of the strip equal to its breadth, and this will generally be
+very small; if it is small of the same order as t/b, or a higher order,
+the formula becomes ½Wb&tau; (1+&sigma;) / Et<span class="sp">3</span>, with sufficient approximation,
+and this result appears to be in agreement with observations of the
+behaviour of such strips.</p>
+</div>
+
+<p>67. <i>Thin Plate under Pressure.</i>&mdash;The theory of the deformation
+of plates, whether plane or curved, is very intricate, partly
+because of the complexity of the kinematical relations involved.
+We shall here indicate the nature of the effects produced in a
+thin plane plate, of isotropic material, which is slightly bent by
+pressure. This theory should have an application to the stress
+produced in a ship&rsquo;s plates. In the problem of the cylinder
+under internal pressure (§ 77 below) the most important stress
+is the circumferential tension, counteracting the tendency of
+the circular filaments to expand under the pressure; but in the
+problem of a plane plate some of the filaments parallel to the
+plane of the plate are extended and others are contracted,
+so that the tensions and pressures along them give rise to resultant
+couples but not always to resultant forces. Whatever
+forces are applied to bend the plate, these couples are always
+expressible, at least approximately in terms of the principal
+curvatures produced in the surface which, before strain, was the
+middle plane of the plate. The simplest case is that of a rectangular
+plate, bent by a distribution of couples applied to its
+edges, so that the middle surface becomes a cylinder of large
+radius R; the requisite couple per unit of length of the straight
+edges is of amount C/R, where C is a certain constant; and the
+requisite couple per unit of length of the circular edges is of
+amount C&sigma;/R, the latter being required to resist the tendency
+to anticlastic curvature (cf. § 47). If normal sections of the
+plate are supposed drawn through the generators and circular
+sections of the cylinder, the action of the neighbouring portions
+on any portion so bounded involves flexural couples of the
+above amounts. When the plate is bent in any manner, the
+curvature produced at each section of the middle surface may
+be regarded as arising from the superposition of two cylindrical
+curvatures; and the flexural couples across normal sections
+through the lines of curvature, estimated per unit of length
+of those lines, are C (1/R<span class="su">1</span> + &sigma;/R<span class="su">2</span>) and C (1/R<span class="su">2</span> + &sigma;/R<span class="su">1</span>), where
+R<span class="su">1</span> and R<span class="su">2</span> are the principal radii of curvature. The value of
+C for a plate of small thickness 2h is <span class="spp">2</span>&frasl;<span class="suu">3</span>Eh<span class="sp">3</span> / (1 &minus; &sigma;²). Exactly as
+in the problem of the beam (§§ 48, 56), the action between
+neighbouring portions of the plate generally involves shearing
+stresses across normal sections as well as flexural couples; and
+the resultants of these stresses are determined by the conditions
+that, with the flexural couples, they balance the forces applied
+to bend the plate.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:374px; height:362px" src="images/img154.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 28.</span></td></tr></table>
+
+<div class="condensed">
+<p>68. To express this theory analytically, let the middle plane of
+the plate in the unstrained position be taken as the plane of (x, y),
+and let normal sections at right angles to the axes of x and y be
+drawn through any point. After strain let w be the displacement
+of this point in the direction perpendicular to the plane, marked
+p in fig. 28. If the axes of x and y were parallel to the lines of
+curvature at the point, the flexural couple acting across the section
+normal to x (or y) would have the axis of y (or x) for its axis; but
+when the lines of curvature are inclined to the axes of co-ordinates,
+the flexural couple across a section normal to either axis has a
+component about that axis as well as a component about the perpendicular
+axis. Consider an element ABCD of the section at
+right angles to the axis of x, contained between two lines near
+together and perpendicular to the middle plane. The action of the
+portion of the plate to the right upon the portion to the left,
+across the element, gives rise to a couple about the middle line
+(y) of amount, estimated per unit of length of that line, equal
+to C [&part;²w/&part;x² + &sigma; (&part;²w/&part;y²)], = G<span class="su">1</span>, say, and to a couple, similarly estimated,
+about the normal (x) of amount &minus;C (1 &minus; &sigma;) (&part;²w/&part;x&part;y), H, say. The
+<span class="pagenum"><a name="page155" id="page155"></a>155</span>
+corresponding couples on an element of a section at right angles
+to the axis of y, estimated per unit of length of the axis of x, are
+of amounts &minus;C [&part;²w/&part;y² + &sigma; (&part;²w/&part;x²)],  = G<span class="su">2</span> say, and &minus;H. The resultant
+S<span class="su">1</span> of the shearing stresses on the element ABCD, estimated as
+before, is given by the equation S<span class="su">1</span> = &part;G<span class="su">1</span>/&part;x &minus; &part;H/&part;y (cf. § 57), and the
+corresponding resultant S<span class="su">2</span> for an element perpendicular to the
+axis of y is given by the equation S<span class="su">2</span>= &minus;&part;H/&part;x &minus; &part;G<span class="su">2</span>/&part;y. If the plate
+is bent by a pressure p per unit of area, the equation of equilibrium
+is &part;S<span class="su">1</span>/&part;x + &part;S<span class="su">2</span>/&part;y = p, or, in terms of w,</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;<span class="sp">4</span>w</td>
+<td rowspan="2">+</td> <td>&part;<span class="sp">4</span>w</td>
+<td rowspan="2">+ 2</td> <td>&part;<span class="sp">4</span>w</td>
+<td rowspan="2">=</td> <td>p</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">&part;x<span class="sp">4</span></td> <td class="denom">&part;y<span class="sp">4</span></td>
+<td class="denom">&part;x<span class="sp">2</span>&part;y<span class="sp">2</span></td> <td class="denom">C</td></tr></table>
+
+<p class="noind">This equation, together with the special conditions at the rim,
+suffices for the determination of w, and then all the quantities
+here introduced are determined. Further, the most important
+of the stress-components are those which act across elements of
+normal sections: the tension in direction x, at a distance z from
+the middle plane measured in the direction of p, is of amount
+&minus;3Cz/2h<span class="sp">3</span> [&part;²w/&part;x² + &sigma; (&part;²w/&part;y²)], and there is a corresponding tension in direction
+y; the shearing stress consisting of traction parallel to y on
+planes x = const., and traction parallel to x on planes y = const., is of
+amount [3C(1 &minus; &sigma;)z/2h<span class="sp">3</span>] · (&part;²w/&part;x&part;y); these tensions and shearing stresses are
+equivalent to two principal tensions, in the directions of the lines of
+curvature of the surface into which the middle plane is bent, and
+they give rise to the flexural couples.</p>
+
+<p>69. In the special example of a circular plate, of radius a, supported
+at the rim, and held bent by a uniform pressure p, the value
+of w at a point distant r from the axis is</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&nbsp;</td> <td>p</td>
+<td rowspan="2">(a² &minus; r²) <span class="f150">(</span></td> <td>5 + &sigma;</td>
+<td rowspan="2">a² &minus; r² <span class="f150">)</span>,</td></tr>
+<tr><td class="denom">64</td> <td class="denom">C</td>
+<td class="denom">1 + &sigma;</td></tr></table>
+
+<p class="noind">and the most important of the stress components is the radial
+tension, of which the amount at any point is <span class="spp">3</span>&frasl;<span class="suu">32</span>(3 + &sigma;) pz (a² &minus; r)/h³;
+the maximum radial tension is about <span class="spp">1</span>&frasl;<span class="suu">3</span>(a/h)²p, and, when the thickness
+is small compared with the diameter, this is a large multiple of p.</p>
+</div>
+
+<p>70. <i>General Theorems.</i>&mdash;Passing now from these questions
+of flexure and torsion, we consider some results that can be
+deduced from the general equations of equilibrium of an elastic
+solid body.</p>
+
+<table class="flt" style="float: right; width: 260px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:220px; height:253px" src="images/img155a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 29.</span></td></tr></table>
+
+<p>The form of the general expression for the potential energy
+(§ 27) stored up in the strained body leads, by a general property
+of quadratic functions, to a reciprocal theorem relating to the
+effects produced in the body by two different systems of forces,
+viz.: The whole work done by the forces of the first system,
+acting over the displacements produced by the forces of the
+second system, is equal to the whole work done by the forces
+of the second system, acting over the displacements produced
+by the forces of the first system. By a suitable choice of the
+second system of forces, the average values of the component
+stresses and strains produced by given forces, considered as
+constituting the first system, can
+be obtained, even when the distribution
+of the stress and strain
+cannot be determined.</p>
+
+<div class="condensed">
+<p>Taking for example the problem
+presented by an isotropic body of
+any form<a name="fa4b" id="fa4b" href="#ft4b"><span class="sp">4</span></a> pressed between two
+parallel planes distant l apart (fig.
+29), and denoting the resultant pressure
+by p, we find that the diminution
+of volume -&delta;v is given by the
+equation</p>
+
+<p class="center">&minus;&delta;v = lp / 3k,</p>
+
+<p class="noind">where k is the modulus of compression,
+equal to <span class="spp">1</span>&frasl;<span class="suu">3</span>E / (1 &minus; 2&sigma;). Again,
+take the problem of the changes
+produced in a heavy body by different
+ways of supporting it; when the body is suspended from
+one or more points in a horizontal plane its volume is increased by</p>
+
+<p class="center">&delta;v = Wh / 3k,</p>
+
+<p class="noind">where W is the weight of the body, and h the depth of its centre
+of gravity below the plane; when the body is supported by upward
+vertical pressures at one or more points in a horizontal plane the
+volume is diminished by</p>
+
+<p class="center">&minus;&delta;v = Wh&prime; / 3k,</p>
+
+<p class="noind">where h&prime; is the height of the centre of gravity above the plane; if
+the body is a cylinder, of length l and section A, standing with
+its base on a smooth horizontal plane, its length is shortened by
+an amount</p>
+
+<p class="center">&minus;&delta;l = Wl / 2EA;</p>
+
+<p class="noind">if the same cylinder lies on the plane with its generators horizontal,
+its length is increased by an amount</p>
+
+<p class="center">&delta;l = &sigma;Wh&prime; / EA.</p>
+</div>
+
+<p>71. In recent years important results have been found by
+considering the effects produced in an elastic solid by forces
+applied at isolated points.</p>
+
+<div class="condensed">
+<p>Taking the case of a single force F applied at a point in the interior,
+we may show that the stress at a distance r from the point consists of</p>
+
+<p>(1) a radial pressure of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>2 &minus; &sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>F</td>
+<td rowspan="2">&nbsp;</td> <td>cos &theta;</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">1 &minus; &sigma;</td> <td class="denom">4&pi;</td>
+<td class="denom">r²</td></tr></table>
+
+<p>(2) tension in all directions at right angles to the radius of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 &minus; 2&sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>F</td>
+<td rowspan="2">&nbsp;</td> <td>cos &theta;</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2(1 &minus; &sigma;)</td> <td class="denom">4&pi;</td>
+<td class="denom">r²</td></tr></table>
+
+<p>(3) shearing stress consisting of traction acting along the radius <i>dr</i>
+on the surface of the cone &theta; = const. and traction acting along the
+meridian d&theta; on the surface of the sphere r = const. of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 &minus; 2&sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>F</td>
+<td rowspan="2">&nbsp;</td> <td>sin &theta;</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2(1 &minus; &sigma;)</td> <td class="denom">4&pi;</td>
+<td class="denom">r²</td></tr></table>
+
+<p class="noind">where &theta; is the angle between the radius vector r and the line of
+action of F. The line marked T in fig. 30 shows the direction of
+the tangential traction on the spherical surface.</p>
+
+<table class="flt" style="float: right; width: 300px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:268px; height:275px" src="images/img155b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 30.</span></td></tr>
+<tr><td class="figright1"><img style="width:272px; height:182px" src="images/img155c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 31.</span></td></tr></table>
+
+<p>Thus the lines of stress are in and perpendicular to the
+meridian plane, and the direction
+of one of those in the
+meridian plane is inclined to
+the radius vector r at an angle</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">½ tan<span class="sp">&minus;1</span> <span class="f150">(</span></td> <td>2 &minus; 4&sigma;</td>
+<td rowspan="2">tan &theta; <span class="f150">)</span>.</td></tr>
+<tr><td class="denom">5 &minus; 4&sigma;</td></tr></table>
+
+<p class="noind">The corresponding displacement
+at any point is compounded
+of a radial displacement
+of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 + &sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>F</td>
+<td rowspan="2">&nbsp;</td> <td>cos &theta;</td></tr>
+<tr><td class="denom">2(1 &minus; &sigma;)</td> <td class="denom">4&pi;E</td>
+<td class="denom">r</td></tr></table>
+
+<p class="noind">and a displacement parallel to
+the line of action of F of
+amount</p>
+
+<table class="math0" summary="math">
+<tr><td>(3 &minus; 4&sigma;) (1 + &sigma;)</td>
+<td rowspan="2">&nbsp;</td> <td>F</td>
+<td rowspan="2">&nbsp;</td> <td>1</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">2(1 &minus; &sigma;)</td> <td class="denom">4&pi;E</td>
+<td class="denom">r</td></tr></table>
+
+<p class="noind">The effects of forces applied
+at different points and in different directions can be obtained by
+summation, and the effect of continuously distributed forces can
+be obtained by integration.</p>
+</div>
+
+<p>72. The stress system considered in § 71 is equivalent, on the
+plane through the origin at right angles to the line of action of
+F, to a resultant pressure of magnitude ½F at the origin and a
+[1 &minus; 2&sigma;/2(1 &minus; &sigma;)] · F/4&pi;r², and, by the application
+of this system of tractions to a solid bounded by a plane, the
+displacement just described would be produced. There is also
+another stress system for a solid so bounded which is equivalent,
+on the same plane, to a resultant pressure at the origin, and a
+radial traction proportional to
+1/r², but these are in the ratio
+2&pi; : r<span class="sp">&minus;2</span>, instead of being in
+the ratio 4&pi;(1 &minus; &sigma;) : (1 &minus; 2&sigma;)r<span class="sp">&minus;2</span>.</p>
+
+<div class="condensed">
+<p>The second stress system (see
+fig. 31) consists of:</p>
+
+<p>(1) radial pressure F&prime;r<span class="sp">&minus;2</span>,</p>
+
+<p>(2) tension in the meridian
+plane across the radius vector
+of amount</p>
+
+<p class="center">F&prime;r<span class="sp">&minus;2 </span>cos &theta; / (1 + cos &theta;),</p>
+
+<p>(3) tension across the meridian
+plane of amount</p>
+
+<p class="center">F&prime;r<span class="sp">&minus;2</span> / (l + cos &theta;),</p>
+
+<p>(4) shearing stress as in § 71 of amount</p>
+
+<p class="center">F&prime;r<span class="sp">&minus;2</span> sin &theta; / (1 + cos &theta;),</p>
+
+<p class="noind">and the stress across the plane boundary consists of a resultant
+pressure of magnitude 2&pi;F&prime; and a radial traction of amount F&prime;r<span class="sp">&minus;2</span>. If
+<span class="pagenum"><a name="page156" id="page156"></a>156</span>
+then we superpose the component stresses of the last section multiplied
+by 4(1 &minus; &sigma;)W/F, and the component stresses here written down
+multiplied by &minus;(1 &minus; 2&sigma;)W/2&pi;F&prime;, the stress on the plane boundary
+will reduce to a single pressure W at the origin. We shall thus
+obtain the stress system at any point due to such a force applied
+at one point of the boundary.</p>
+
+<p>In the stress system thus arrived at the traction across any plane
+parallel to the boundary is directed away from the place where W
+is supported, and its amount is 3W cos²&theta; / 2&pi;r². The corresponding
+displacement consists of</p>
+
+<p>(1) a horizontal displacement radially outwards from the vertical
+through the origin of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>W (1 + &sigma;) sin &theta;</td>
+<td rowspan="2"><span class="f150">(</span> cos &theta; &minus;</td> <td>1 &minus; 2&sigma;</td>
+<td rowspan="2"><span class="f150">)</span>,</td></tr>
+<tr><td class="denom">2&pi;Er</td> <td class="denom">1 + cos &theta;</td></tr></table>
+
+<p>(2) a vertical displacement downwards of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>W (1 + &sigma;)</td>
+<td rowspan="2">{2 (1 &minus; &sigma;) + cos²&theta; }.</td></tr>
+<tr><td class="denom">2&pi;Er</td></tr></table>
+
+<p class="noind">The effects produced by a system of loads on a solid bounded by a
+plane can be deduced.</p>
+</div>
+
+<p>The results for a solid body bounded by an infinite plane
+may be interpreted as giving the local effects of forces applied
+to a small part of the surface of a body. The results show
+that pressure is transmitted into a body from the boundary
+in such a way that the traction at a point on a section parallel
+to the boundary is the same at all points of any sphere which
+touches the boundary at the point of pressure, and that its
+amount at any point is inversely proportional to the square of
+the radius of this sphere, while its direction is that of a line
+drawn from the point of pressure to the point at which the
+traction is estimated. The transmission of force through a
+solid body indicated by this result was strikingly demonstrated
+in an attempt that was made to measure the lunar deflexion
+of gravity; it was found that the weight of the observer on the
+floor of the laboratory produced a disturbance of the instrument
+sufficient to disguise completely the effect which the instrument
+had been designed to measure (see G.H. Darwin, <i>The Tides
+and Kindred Phenomena in the Solar System</i>, London, 1898).</p>
+
+<p>73. There is a corresponding theory of two-dimensional
+systems, that is to say, systems in which either the displacement
+is parallel to a fixed plane, or there is no traction across any
+plane of a system of parallel planes. This theory shows that,
+when pressure is applied at a point of the edge of a plate in any
+direction in the plane of the plate, the stress developed in the
+plate consists exclusively of radial pressure across any circle
+having the point of pressure as centre, and the magnitude of
+this pressure is the same at all points of any circle which touches
+the edge at the point of pressure, and its amount at any point
+is inversely proportional to the radius of this circle. This result
+leads to a number of interesting solutions of problems relating
+to plane systems; among these may be mentioned the problem
+of a circular plate strained by any forces applied at its edge.</p>
+
+<p>74. The results stated in § 72 have been applied to give an
+account of the nature of the actions concerned in the impact
+of two solid bodies. The dissipation of energy involved in the
+impact is neglected, and the resultant pressure between the
+bodies at any instant during the impact is equal to the rate of
+destruction of momentum of either along the normal to the
+plane of contact drawn towards the interior of the other. It
+has been shown that in general the bodies come into contact
+over a small area bounded by an ellipse, and remain in contact
+for a time which varies inversely as the fifth root of the initial
+relative velocity.</p>
+
+<div class="condensed">
+<p>For equal spheres of the same material, with &sigma; = ¼, impinging
+directly with relative velocity v, the patches that come into contact
+are circles of radius</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2"><span class="f150">(</span></td> <td>45&pi;</td>
+<td rowspan="2"><span class="f150">)</span></td> <td><span class="spp">1</span>&frasl;<span class="suu">5</span></td>
+<td rowspan="2"><span class="f150">(</span></td> <td>v</td>
+<td rowspan="2"><span class="f150">)</span></td> <td><span class="spp">2</span>&frasl;<span class="suu">5</span></td>
+<td rowspan="2">r,</td></tr>
+<tr><td class="denom">256</td> <td>&nbsp;</td>
+<td class="denom">V</td> <td>&nbsp;</td></tr></table>
+
+<p class="noind">where r is the radius of either, and V the velocity of longitudinal
+waves in a thin bar of the material. The duration of the impact is
+approximately</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">(2.9432) <span class="f150">(</span></td> <td>2025&pi;²</td>
+<td rowspan="2"><span class="f150">)</span></td> <td><span class="spp">1</span>&frasl;<span class="suu">5</span></td>
+<td>r</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">512</td> <td>&nbsp;</td>
+<td class="denom">v<span class="sp">1/5</span>V<span class="sp">4/5</span></td></tr></table>
+
+<p class="noind">For two steel spheres of the size of the earth impinging with a
+velocity of 1 cm. per second the duration of the impact would be
+about twenty-seven hours. The fact that the duration of impact
+is, for moderate velocities, a considerable multiple of the time
+taken by a wave of compression to travel through either of two
+impinging bodies has been ascertained experimentally, and constitutes
+the reason for the adequacy of the statical theory here
+described.</p>
+</div>
+
+<p>75. <i>Spheres and Cylinders.</i>&mdash;Simple results can be found for
+spherical and cylindrical bodies strained by radial forces.</p>
+
+<div class="condensed">
+<p>For a sphere of radius a, and of homogeneous isotropic material
+of density &rho;, strained by the mutual gravitation of its parts, the
+stress at a distance r from the centre consists of</p>
+
+<p>(1) uniform hydrostatic pressure of amount <span class="spp">1</span>&frasl;<span class="suu">10</span> g&rho;a (3 &minus; &sigma;) / (1 &minus; &sigma;),</p>
+
+<p>(2) radial tension of amount <span class="spp">1</span>&frasl;<span class="suu">10</span> g&rho; (r²/a) (3 &minus; &sigma;) / (1 &minus; &sigma;),</p>
+
+<p>(3) uniform tension at right angles to the radius vector of amount</p>
+
+<p class="center"><span class="spp">1</span>&frasl;<span class="suu">10</span> g&rho; (r²/a) (1 + 3&sigma;) / (1 &minus; &sigma;),</p>
+
+<p class="noind">where g is the value of gravity at the surface. The corresponding
+strains consist of</p>
+
+<p>(1) uniform contraction of all lines of the body of amount</p>
+
+<p class="center"><span class="spp">1</span>&frasl;<span class="suu">30</span> k<span class="sp">&minus;1</span>g&rho;a (3 &minus; &sigma;) / (1 &minus; &sigma;),</p>
+
+<p>(2) radial extension of amount <span class="spp">1</span>&frasl;<span class="suu">10</span> k<span class="sp">&minus;1</span>g&rho; (r²/a) (1 + &sigma;) / (1 &minus; &sigma;),</p>
+
+<p>(3) extension in any direction at right angles to the radius vector
+of amount</p>
+
+<p class="center"><span class="spp">1</span>&frasl;<span class="suu">30</span> k<span class="sp">&minus;1</span>g&rho; (r²/a) (1 + &sigma;) / (1 &minus; &sigma;),</p>
+
+<p class="noind">where k is the modulus of compression. The volume is diminished
+by the fraction g&rho;a/5k of itself. The parts of the radii <span class="correction" title="amended from vectores">vectors</span> within
+the sphere r = a {(3 &minus; &sigma;) / (3 + 3&sigma;)}<span class="sp">1/2</span> are contracted, and the parts
+without this sphere are extended. The application of the above
+results to the state of the interior of the earth involves a neglect of
+the caution emphasized in § 40, viz. that the strain determined by
+the solution must be small if the solution is to be accepted. In a
+body of the size and mass of the earth, and having a resistance to
+compression and a rigidity equal to those of steel, the radial contraction
+at the centre, as given by the above solution, would be
+nearly <span class="spp">1</span>&frasl;<span class="suu">3</span>, and the radial extension at the surface nearly <span class="spp">1</span>&frasl;<span class="suu">6</span>, and these
+fractions can by no means be regarded as &ldquo;small.&rdquo;</p>
+
+<p>76. In a spherical shell of homogeneous isotropic material, of
+internal radius r<span class="su">1</span> and external radius r<span class="su">0</span>, subjected to pressure p<span class="su">0</span>
+on the outer surface, and p<span class="su">1</span> on the inner surface, the stress at any
+point distant r from the centre consists of</p>
+
+<p>(1) uniform tension in all directions of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>p<span class="su">1</span>r<span class="su">1</span>³ &minus; p<span class="su">0</span>r<span class="su">0</span>³</td> <td rowspan="2">,</td></tr>
+<tr><td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td></tr></table>
+
+<p>(2) radial pressure of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>p<span class="su">1</span> &minus; p<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>³r<span class="su">1</span>³</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td> <td class="denom">r³</td></tr></table>
+
+<p>(3) tension in all directions at right angles to the radius vector
+of amount</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">½</td> <td>p<span class="su">1</span> &minus; p<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>³r<span class="su">1</span>³</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td> <td class="denom">r³</td></tr></table>
+
+<p class="noind">The corresponding strains consist of</p>
+
+<p>(1) uniform extension of all lines of the body of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&nbsp;</td> <td>p<span class="su">1</span>r<span class="su">1</span>³ &minus; p<span class="su">0</span>r<span class="su">0</span>³</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">3k</td> <td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td></tr></table>
+
+<p>(2) radial contraction of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&nbsp;</td> <td>p<span class="su">1</span> &minus; p<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>³r<span class="su">1</span>³</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2&mu;</td> <td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td>
+<td class="denom">r³</td></tr></table>
+
+<p>(3) extension in all directions at right angles to the radius vector
+of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td>
+<td rowspan="2">&nbsp;</td> <td>p<span class="su">1</span> &minus; p<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>³r<span class="su">1</span>³</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">4&mu;</td> <td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td>
+<td class="denom">r³</td></tr></table>
+
+<p class="noind">where &mu; is the modulus of rigidity of the material, = ½E / (1 + &sigma;).
+The volume included between the two surfaces of the body is increased
+by the fraction (p<span class="su">1</span>r<span class="su">1</span>³ &minus; p<span class="su">0</span>r<span class="su">0</span>³) / k(r<span class="su">0</span>³ &minus; r<span class="su">1</span>³) of itself, and the volume within
+the inner surface is increased by the fraction</p>
+
+<table class="math0" summary="math">
+<tr><td>3 (p<span class="su">1</span> &minus; p<span class="su">0</span>)</td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>³</td>
+<td rowspan="2">+</td> <td>p<span class="su">1</span>r<span class="su">1</span>³ &minus; p<span class="su">0</span>r<span class="su">0</span>³</td></tr>
+<tr><td class="denom">4&mu;</td> <td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td>
+<td class="denom">k (r<span class="su">0</span>³ &minus; r<span class="su">1</span>³)</td></tr></table>
+
+<p class="noind">of itself. For a shell subject only to internal pressure p the greatest
+extension is the extension at right angles to the radius at the inner
+surface, and its amount is</p>
+
+<table class="math0" summary="math">
+<tr><td>pr<span class="su">1</span>³</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>1</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>³</td>
+<td rowspan="2"><span class="f150">)</span>;</td></tr>
+<tr><td class="denom">r<span class="su">0</span>³ &minus; r<span class="su">1</span>³</td> <td class="denom">3k</td>
+<td class="denom">4&mu;</td> <td class="denom">r<span class="su">1</span>³</td></tr></table>
+
+<p class="noind">the greatest tension is the transverse tension at the inner surface,
+and its amount is p (½ r<span class="su">0</span>³ + r<span class="su">1</span>³) / (r<span class="su">0</span>³ &minus; r<span class="su">1</span>³).</p>
+
+<p>77. In the problem of a cylindrical shell under pressure a complication
+may arise from the effects of the ends; but when the
+ends are free from stress the solution is very simple. With notation
+similar to that in § 76 it can be shown that the stress at a distance r
+from the axis consists of</p>
+
+<p>(1) uniform tension in all directions at right angles to the axis
+of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>p<span class="su">1</span>r<span class="su">1</span>² &minus; p<span class="su">0</span>r<span class="su">0</span>²</td> <td rowspan="2">,</td></tr>
+<tr><td class="denom">r<span class="su">0</span>² &minus; r<span class="su">1</span>²</td></tr></table>
+
+<p>(2) radial pressure of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>p<span class="su">1</span> &minus; p<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>²r<span class="su">1</span>²</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">r<span class="su">0</span>² &minus; r<span class="su">1</span>²</td> <td class="denom">r²</td></tr></table>
+
+<p>(3) hoop tension numerically equal to this radial pressure.</p>
+
+<p><span class="pagenum"><a name="page157" id="page157"></a>157</span></p>
+
+<p>The corresponding strains consist of</p>
+
+<p>(1) uniform extension of all lines of the material at right angles
+to the axis of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 &minus; &sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>p<span class="su">1</span>r<span class="su">1</span>² &minus; p<span class="su">0</span>r<span class="su">0</span>²</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">E</td> <td class="denom">r<span class="su">0</span>² &minus; r<span class="su">1</span>²</td></tr></table>
+
+<p>(2) radial contraction of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 + &sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>p<span class="su">1</span> &minus; p<span class="su">0</span></td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>²r<span class="su">1</span>²</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">E</td> <td class="denom">r<span class="su">0</span>² &minus; r<span class="su">1</span>²</td>
+<td class="denom">r²</td></tr></table>
+
+<p>(3) extension along the circular filaments numerically equal to
+this radial contraction,</p>
+
+<p>(4) uniform contraction of the longitudinal filaments of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>2&sigma;</td>
+<td rowspan="2">&nbsp;</td> <td>p<span class="su">1</span>r<span class="su">1</span>² &minus; p<span class="su">0</span>r<span class="su">0</span>²</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">E</td> <td class="denom">r<span class="su">0</span>² &minus; r<span class="su">1</span>²</td></tr></table>
+
+<p class="noind">For a shell subject only to internal pressure p the greatest extension
+is the circumferential extension at the inner surface, and its amount is</p>
+
+<table class="math0" summary="math">
+<tr><td>p</td>
+<td rowspan="2"><span class="f150">(</span></td> <td>r<span class="su">0</span>² + r<span class="su">1</span>²</td>
+<td rowspan="2">+ &sigma; <span class="f150">)</span>;</td></tr>
+<tr><td class="denom">E</td> <td class="denom">r<span class="su">0</span>² &minus; r<span class="su">1</span>²</td></tr></table>
+
+<p class="noind">the greatest tension is the hoop tension at the inner surface, and
+its amount is p (r<span class="su">0</span>² + r<span class="su">1</span>²) / (r<span class="su">0</span>² &minus; r<span class="su">1</span>²).</p>
+
+<p>78. When the ends of the tube, instead of being free, are closed by
+disks, so that the tube becomes a closed cylindrical vessel, the
+longitudinal extension is determined by the condition that the
+resultant longitudinal tension in the walls balances the resultant
+normal pressure on either end. This condition gives the value of the
+extension of the longitudinal filaments as</p>
+
+<p class="center">(p<span class="su">1</span>r<span class="su">1</span>² &minus; p<span class="su">0</span>r<span class="su">0</span>²) / 3k (r<span class="su">0</span>² &minus; r<span class="su">1</span>²),</p>
+
+<p class="noind">where k is the modulus of compression of the material. The result
+may be applied to the experimental determination of k, by measuring
+the increase of length of a tube subjected to internal pressure
+(A. Mallock, <i>Proc. R. Soc. London</i>, lxxiv., 1904, and C. Chree, <i>ibid.</i>).</p>
+</div>
+
+<p>79. The results obtained in § 77 have been applied to gun
+construction; we may consider that one cylinder is heated
+so as to slip over another upon which it shrinks by cooling,
+so that the two form a single body in a condition of initial stress.</p>
+
+<div class="condensed">
+<p>We take P as the measure of the pressure between the two, and
+p for the pressure within the inner cylinder by which the system
+is afterwards strained, and denote by r&prime; the radius of the common
+surface. To obtain the stress at any point we superpose the
+system consisting of radial pressure p (r<span class="su">1</span>²/r²) · (r<span class="su">0</span>² &minus; r²) / (r<span class="su">0</span>² &minus; r<span class="su">1</span>²) and hoop tension
+p (r<span class="su">1</span>²/r²) · (r<span class="su">0</span>² + r²) / (r<span class="su">0</span>² &minus; r<span class="su">1</span>²) upon a system which, for the outer cylinder, consists
+of radial pressure P (r&prime;²/r²) · (r<span class="su">0</span>² &minus; r²) / (r<span class="su">0</span>² &minus; r&prime;²)
+and hoop tension P (r&prime;²/r²) · (r<span class="su">0</span>² + r²) / (r<span class="su">0</span>² &minus; r&prime;²), and
+for the inner cylinder consists of radial pressure
+P (r&prime;²/r²) · (r² &minus; r<span class="su">1</span>²) / (r&prime;² &minus; r<span class="su">1</span>²) and
+hoop tension P (r&prime;²/r²) · (r² + r<span class="su">1</span>²) / (r&prime;² &minus; r<span class="su">1</span>²). The hoop tension at the inner surface
+is less than it would be for a tube of equal thickness without initial
+stress in the ratio</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">1 &minus;</td> <td>P</td>
+<td rowspan="2">&nbsp;</td> <td>2r&prime;²</td>
+<td rowspan="2">&nbsp;</td> <td>r<span class="su">0</span>² + r<span class="su">1</span>²</td>
+<td rowspan="2">: 1.</td></tr>
+<tr><td class="denom">p</td> <td class="denom">r<span class="su">0</span>² + r<span class="su">1</span>²</td>
+<td class="denom">r&prime;² &minus; r<span class="su">1</span>²</td></tr></table>
+
+<p class="noind">This shows how the strength of the tube is increased by the initial
+stress. When the initial stress is produced by tightly wound wire,
+a similar gain of strength accrues.</p>
+</div>
+
+<p>80. In the problem of determining the distribution of stress
+and strain in a circular cylinder, rotating about its axis, simple
+solutions have been obtained which are sufficiently exact for
+the two special cases of a thin disk and a long shaft.</p>
+
+<div class="condensed">
+<p>Suppose that a circular disk of radius a and thickness 2l, and of
+density &rho;, rotates about its axis with angular velocity &omega;, and consider
+the following systems of superposed stresses at any point distant r
+from the axis and z from the middle plane:</p>
+
+<p>(1) uniform tension in all directions at right angles to the axis
+of amount <span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;a² (3 + &sigma;),</p>
+
+<p>(2) radial pressure of amount <span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;r² (3 + &sigma;),</p>
+
+<p>(3) pressure along the circular filaments of amount <span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;r² (1 + 3&sigma;),</p>
+
+<p>(4) uniform tension in all directions at right angles to the axis
+of amount <span class="spp">1</span>&frasl;<span class="suu">6</span> &omega;²&rho; (l² &minus; 3z²) &sigma; (1 + &sigma;) / (1 &minus; &sigma;).</p>
+
+<p>The corresponding strains may be expressed as</p>
+
+<p>(1) uniform extension of all filaments at right angles to the axis
+of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 &minus; &sigma;</td> <td rowspan="2"><span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;a² (3 + &sigma;),</td></tr>
+<tr><td class="denom">E</td></tr></table>
+
+<p>(2) radial contraction of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 &minus; &sigma;²</td> <td rowspan="2"><span class="spp">3</span>&frasl;<span class="suu">8</span> &omega;²&rho;r²,</td></tr>
+<tr><td class="denom">E</td></tr></table>
+
+<p>(3) contraction along the circular filaments of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1 &minus; &sigma;²</td> <td rowspan="2"><span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;r²,</td></tr>
+<tr><td class="denom">E</td></tr></table>
+
+<p>(4) extension of all filaments at right angles to the axis of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>1</td> <td rowspan="2"><span class="spp">1</span>&frasl;<span class="suu">6</span> &omega;²&rho; (l² &minus; 3<span class="su">z</span>²) &sigma; (1 + &sigma;),</td></tr>
+<tr><td class="denom">E</td></tr></table>
+
+<p>(5) contraction of the filaments normal to the plane of the disk
+of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>2&sigma;</td>
+<td rowspan="2"><span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;a² (3 + &sigma;) &minus;</td> <td>&sigma;</td>
+<td rowspan="2"><span class="spp">1</span>&frasl;<span class="suu">2</span> &omega;²&rho;r² (1 + &sigma;) +</td> <td>2&sigma;</td>
+<td rowspan="2"><span class="spp">1</span>&frasl;<span class="suu">6</span> &omega;²&rho; (l² &minus; 3z²) &sigma;</td> <td>(1 + &sigma;)</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">E</td> <td class="denom">E</td>
+<td class="denom">E</td> <td class="denom">(1 &minus; &sigma;)</td></tr></table>
+
+<p>The greatest extension is the circumferential extension near the
+centre, and its amount is</p>
+
+<table class="math0" summary="math">
+<tr><td>(3 + &sigma;) (1 &minus; &sigma;)</td>
+<td rowspan="2">&omega;²&rho;a² +</td> <td>&sigma; (1 + &sigma;)</td>
+<td rowspan="2">&omega;²&rho;l².</td></tr>
+<tr><td class="denom">8E</td> <td class="denom">6E</td></tr></table>
+
+<table class="flt" style="float: right; width: 270px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:236px; height:252px" src="images/img157.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 32.</span></td></tr></table>
+
+<p>The longitudinal contraction is required to make the plane faces
+of the disk free from pressure, and the terms in l and z enable
+us to avoid tangential traction on any cylindrical surface. The
+system of stresses and strains thus expressed satisfies all the conditions,
+except that there is a small
+radial tension on the bounding
+surface of amount per unit area
+<span class="spp">1</span>&frasl;<span class="suu">6</span> &omega;²&rho; (l² &minus; 3z²) &sigma; (1 + &sigma;) / (1 &minus; &sigma;). The resultant
+of these tensions on any
+part of the edge of the disk
+vanishes, and the stress in question
+is very small in comparison with
+the other stresses involved when
+the disk is thin; we may conclude
+that, for a thin disk, the expressions
+given represent the actual
+condition at all points which are
+not very close to the edge (cf. § 55).
+The effect to the longitudinal contraction
+is that the plane faces
+become slightly concave (fig. 32).</p>
+
+<p>81. The corresponding solution
+for a disk with a circular axle-hole
+(radius b) will be obtained from that given in the last section by
+superposing the following system of additional stresses:</p>
+
+<p>(1) radial tension of amount <span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;b² (1 &minus; a²/r²) (3 + &sigma;),</p>
+
+<p>(2) tension along the circular filaments of amount</p>
+
+<p class="center"><span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;b² (1 + a²/r²) (3 + &sigma;).</p>
+
+<p>The corresponding additional strains are</p>
+
+<p>(1) radial contraction of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>3 + &sigma;</td>
+<td rowspan="2"><span class="f150">{</span> (1 + &sigma;)</td> <td>a²</td>
+<td rowspan="2">&minus; (1 &minus; &sigma;) <span class="f150">}</span> &omega;²&rho;b²,</td></tr>
+<tr><td class="denom">8E</td> <td class="denom">r²</td></tr></table>
+
+<p>(2) extension along the circular filaments of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>3 + &sigma;</td>
+<td rowspan="2"><span class="f150">{</span> (1 + &sigma;)</td> <td>a²</td>
+<td rowspan="2">+ (1 &minus; &sigma;) <span class="f150">}</span> &omega;²&rho;b².</td></tr>
+<tr><td class="denom">8E</td> <td class="denom">r²</td></tr></table>
+
+<p>(3) contraction of the filaments parallel to the axis of amount</p>
+
+<table class="math0" summary="math">
+<tr><td>&sigma; (3 + &sigma;)</td> <td rowspan="2">&omega;²&rho;b².</td></tr>
+<tr><td class="denom">4E</td></tr></table>
+
+<p class="noind">Again, the greatest extension is the circumferential extension at
+the inner surface, and, when the hole is very small, its amount is
+nearly double what it would be for a complete disk.</p>
+
+<p>82. In the problem of the rotating shaft we have the following
+stress-system:</p>
+
+<p>(1) radial tension of amount <span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho; (a² &minus; r²) (3 &minus; 2&sigma;) / (1 &minus; &sigma;),</p>
+
+<p>(2) circumferential tension of amount</p>
+
+<p class="center"><span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho; {a² (3 &minus; 2&sigma;) / (1 &minus; &sigma;) &minus; r² (1 + 2&sigma;) / (1 &minus; &sigma;)},</p>
+
+<p>(3) longitudinal tension of amount ¼ &omega;²&rho; (a² &minus; 2r²) &sigma; / (1 &minus; &sigma;).</p>
+
+<p>The resultant longitudinal tension at any normal section vanishes,
+and the radial tension vanishes at the bounding surface; and
+thus the expressions here given may be taken to represent the
+actual condition at all points which are not very close to the ends
+of the shaft. The contraction of the longitudinal filaments is
+uniform and equal to ½ &omega;²&rho;a²&sigma; / E. The greatest extension in the
+rotating shaft is the circumferential extension close to the axis,
+and its amount is <span class="spp">1</span>&frasl;<span class="suu">8</span> &omega;²&rho;a² (3 &minus; 5&sigma;) / E (1 &minus; &sigma;).</p>
+
+<p>The value of any theory of the strength of long rotating shafts
+founded on these formulae is diminished by the circumstance that
+at sufficiently high speeds the shaft may tend to take up a curved
+form, the straight form being unstable. The shaft is then said to
+<i>whirl</i>. This occurs when the period of rotation of the shaft is very
+nearly coincident with one of its periods of lateral vibration. The
+lowest speed at which whirling can take place in a shaft of length l,
+freely supported at its ends, is given by the formula</p>
+
+<p class="center">&omega;²&rho; = ¼ Ea² (&pi;/l)<span class="sp">4</span>.</p>
+
+<p class="noind">As in § 61, this formula should not be applied unless the length of
+the shaft is a considerable multiple of its diameter. It implies that
+whirling is to be expected whenever &omega; approaches this critical value.</p>
+</div>
+
+<p>83. When the forces acting upon a spherical or cylindrical body
+are not radial, the problem becomes more complicated. In the
+case of the sphere deformed by any forces it has been completely
+solved, and the solution has been applied by Lord Kelvin and
+<span class="pagenum"><a name="page158" id="page158"></a>158</span>
+Sir G.H. Darwin to many interesting questions of cosmical
+physics. The nature of the stress produced in the interior of
+the earth by the weight of continents and mountains, the spheroidal
+figure of a rotating solid planet, the rigidity of the earth,
+are among the questions which have in this way been attacked.
+Darwin concluded from his investigation that, to support the
+weight of the existing continents and mountain ranges, the
+materials of which the earth is composed must, at great depths
+(1600 kilometres), have at least the strength of granite. Kelvin
+concluded from his investigation that the actual heights of the
+tides in the existing oceans can be accounted for only on the
+supposition that the interior of the earth is solid, and of rigidity
+nearly as great as, if not greater than, that of steel.</p>
+
+<div class="condensed">
+<p>84. Some interesting problems relating to the strains produced in a
+cylinder of finite length by forces distributed symmetrically round
+the axis have been solved. The most important is that of a cylinder
+crushed between parallel planes in contact with its plane ends.
+The solution was applied to explain the discrepancies that have been
+observed in different tests of crushing strength according as the
+ends of the test specimen are or are not prevented from spreading.
+It was applied also to explain the fact that in such tests small conical
+pieces are sometimes cut out at the ends subjected to pressure.</p>
+</div>
+
+<p>85. <i>Vibrations and Waves.</i>&mdash;When a solid body is struck, or
+otherwise suddenly disturbed, it is thrown into a state of vibration.
+There always exist dissipative forces which tend to
+destroy the vibratory motion, one cause of the subsidence of the
+motion being the communication of energy to surrounding
+bodies. When these dissipative forces are disregarded, it is
+found that an elastic solid body is capable of vibrating in such
+a way that the motion of any particle is simple harmonic motion,
+all the particles completing their oscillations in the same period
+and being at any instant in the same phase, and the displacement
+of any selected one in any particular direction bearing a definite
+ratio to the displacement of an assigned one in an assigned
+direction. When a body is moving in this way it is said to be
+<i>vibrating in a normal mode</i>. For example, when a tightly
+stretched string of negligible flexural rigidity, such as a violin
+string may be taken to be, is fixed at the ends, and vibrates
+transversely in a normal mode, the displacements of all the
+particles have the same direction, and their magnitudes are
+proportional at any instant to the ordinates of a curve of sines.
+Every body possesses an infinite number of normal modes of
+vibration, and the <i>frequencies</i> (or numbers of vibrations per
+second) that belong to the different modes form a sequence
+of increasing numbers. For the string, above referred to, the
+fundamental tone and the various overtones form an harmonic
+scale, that is to say, the frequencies of the normal modes of
+vibration are proportional to the integers 1, 2, 3, .... In all
+these modes except the first the string vibrates as if it were
+divided into a number of equal pieces, each having fixed ends;
+this number is in each case the integer defining the frequency.
+In general the normal modes of vibration of a body are distinguished
+one from another by the number and situation of the
+surfaces (or other <i>loci</i>) at which some characteristic displacement
+or traction vanishes. The problem of determining the normal
+modes and frequencies of free vibration of a body of definite
+size, shape and constitution, is a mathematical problem of a
+similar character to the problem of determining the state of
+stress in the body when subjected to given forces. The bodies
+which have been most studied are strings and thin bars, membranes,
+thin plates and shells, including bells, spheres and
+cylinders. Most of the results are of special importance in their
+bearing upon the theory of sound.</p>
+
+<div class="condensed">
+<p>86. The most complete success has attended the efforts of mathematicians
+to solve the problem of free vibrations for an isotropic
+sphere. It appears that the modes of vibration fall into two classes:
+one characterized by the absence of a radial component of displacement,
+and the other by the absence of a radial component of rotation
+(§ 14). In each class there is a doubly infinite number of modes.
+The displacement in any mode is determined in terms of a single
+spherical harmonic function, so that there are modes of each class
+corresponding to spherical harmonics of every integral degree;
+and for each degree there is an infinite number of modes, differing
+from one another in the number and position of the concentric
+spherical surfaces at which some characteristic displacement vanishes.
+The most interesting modes are those in which the sphere becomes
+slightly spheroidal, being alternately prolate and oblate during the
+course of a vibration; for these vibrations tend to be set up in a
+spherical planet by tide-generating forces. In a sphere of the size
+of the earth, supposed to be incompressible and as rigid as steel,
+the period of these vibrations is 66 minutes.</p>
+</div>
+
+<p>87. The theory of free vibrations has an important bearing
+upon the question of the strength of structures subjected to
+sudden blows or shocks. The stress and strain developed in a
+body by sudden applications of force may exceed considerably
+those which would be produced by a gradual application of the
+same forces. Hence there arises the general question of <i>dynamical
+resistance</i>, or of the resistance of a body to forces applied
+so quickly that the inertia of the body comes sensibly into play.
+In regard to this question we have two chief theoretical results.
+The first is that the strain produced by a force suddenly applied
+may be as much as twice the statical strain, that is to say, as the
+strain which would be produced by the same force when the
+body is held in equilibrium under its action; the second is that
+the sudden reversal of the force may produce a strain three
+times as great as the statical strain. These results point to the
+importance of specially strengthening the parts of any machine
+(<i>e.g.</i> screw propeller shafts) which are subject to sudden applications
+or reversals of load. The theoretical limits of twice, or
+three times, the statical strain are not in general attained. For
+example, if a thin bar hanging vertically from its upper end is
+suddenly loaded at its lower end with a weight equal to its own
+weight, the greatest dynamical strain bears to the greatest
+statical strain the ratio 1.63 : 1; when the attached weight is
+four times the weight of the bar the ratio becomes 1.84 : 1. The
+method by which the result just mentioned is reached has
+recently been applied to the question of the breaking of winding
+ropes used in mines. It appeared that, in order to bring the
+results into harmony with the observed facts, the strain in the
+supports must be taken into account as well as the strain in the
+rope (J. Perry, <i>Phil. Mag.</i>, 1906 (vi.), vol. ii.).</p>
+
+<p>88. The immediate effect of a blow or shock, locally applied
+to a body, is the generation of a wave which travels through
+the body from the locality first affected. The question of the
+propagation of waves through an elastic solid body is historically
+of very great importance; for the first really successful efforts
+to construct a theory of elasticity (those of S.D. Poisson, A.L.
+Cauchy and G. Green) were prompted, at least in part, by
+Fresnel&rsquo;s theory of the propagation of light by transverse
+vibrations. For many years the luminiferous medium was
+identified with the isotropic solid of the theory of elasticity.
+Poisson showed that a disturbance communicated to the body
+gives rise to two waves which are propagated through it with
+different velocities; and Sir G.G. Stokes afterwards showed
+that the quicker wave is a wave of irrotational dilatation, and
+the slower wave is a wave of rotational distortion accompanied
+by no change of volume. The velocities of the two waves in a
+solid of density &rho; are &radic; {(&lambda; + 2&mu;)/&rho;} and &radic; (&mu;/&rho;), &lambda; and &mu; being
+the constants so denoted in § 26. When the surface of the body
+is free from traction, the waves on reaching the surface are
+reflected; and thus after a little time the body would, if there
+were no dissipative forces, be in a very complex state of motion
+due to multitudes of waves passing to and fro through it. This
+state can be expressed as a state of vibration, in which the motions
+belonging to the various normal modes (§ 85) are superposed,
+each with an appropriate amplitude and phase. The waves of
+dilatation and distortion do not, however, give rise to different
+modes of vibration, as was at one time supposed, but any mode
+of vibration in general involves both dilatation and rotation.
+There are exceptional results for solids of revolution; such
+solids possess normal modes of vibration which involve no
+dilatation. The existence of a boundary to the solid body
+has another effect, besides reflexion, upon the propagation of
+waves. Lord Rayleigh has shown that any disturbance originating
+at the surface gives rise to waves which travel away over
+the surface as well as to waves which travel through the interior;
+and any internal disturbance, on reaching the surface, also
+gives rise to such superficial waves. The velocity of the superficial
+waves is a little less than that of the waves of distortion:
+<span class="pagenum"><a name="page159" id="page159"></a>159</span>
+0.9554 &radic; (&mu;/&rho;) when the material is incompressible 0.9194 &radic; (&mu;/&rho;)
+when the Poisson&rsquo;s ratio belonging to the material is ¼.</p>
+
+<p>89. These results have an application to the propagation of
+earthquake shocks (see also <span class="sc"><a href="#artlinks">Earthquake</a></span>). An internal disturbance
+should, if the earth can be regarded as solid, give rise
+to three wave-motions: two propagated through the interior
+of the earth with different velocities, and a third propagated
+over the surface. The results of seismographic observations
+have independently led to the recognition of three phases of
+the recorded vibrations: a set of &ldquo;preliminary tremors&rdquo;
+which are received at different stations at such times as to show
+that they are transmitted directly through the interior of the
+earth with a velocity of about 10 km. per second, a second
+set of preliminary tremors which are received at different
+stations at such times as to show that they are transmitted
+directly through the earth with a velocity of about 5 km. per
+second, and a &ldquo;main shock,&rdquo; or set of large vibrations, which
+becomes sensible at different stations at such times as to show
+that a wave is transmitted over the surface of the earth with
+a velocity of about 3 km. per second. These results can be
+interpreted if we assume that the earth is a solid body the
+greater part of which is practically homogeneous, with high
+values for the rigidity and the resistance to compression, while
+the superficial portions have lower values for these quantities.
+The rigidity of the central portion would be about (1.4)10<span class="sp">12</span>
+dynes per square cm., which is considerably greater than that
+of steel, and the resistance to compression would be about
+(3.8)10<span class="sp">12</span> dynes per square cm. which is much greater than that
+of any known material. The high value of the resistance to
+compression is not surprising when account is taken of the great
+pressures, due to gravitation, which must exist in the interior
+of the earth. The high value of the rigidity can be regarded as
+a confirmation of Lord Kelvin&rsquo;s estimate founded on tidal
+observations (§ 83).</p>
+
+<p>90. <i>Strain produced by Heat.</i>&mdash;The mathematical theory
+of elasticity as at present developed takes no account of the
+strain which is produced in a body by unequal heating. It
+appears to be impossible in the present state of knowledge
+to form as in § 39 a system of differential equations to determine
+both the stress and the temperature at any point of a solid body
+the temperature of which is liable to variation. In the cases
+of isothermal and adiabatic changes, that is to say, when the
+body is slowly strained without variation of temperature, and
+also when the changes are effected so rapidly that there is no
+gain or loss of heat by any element, the internal energy of the
+body is sufficiently expressed by the strain-energy-function
+(§§ 27, 30). Thus states of equilibrium and of rapid vibration
+can be determined by the theory that has been explained above.
+In regard to thermal effects we can obtain some indications
+from general thermodynamic theory. The following passages
+extracted from the article &ldquo;Elasticity&rdquo; contributed to the 9th
+edition of the <i>Encyclopaedia Britannica</i> by Sir W. Thomson
+(Lord Kelvin) illustrate the nature of these indications:&mdash;&ldquo;From
+thermodynamic theory it is concluded that cold is produced
+whenever a solid is strained by opposing, and heat when
+it is strained by yielding to, any elastic force of its own, the
+strength of which would diminish if the temperature were raised;
+but that, on the contrary, heat is produced when a solid is
+strained against, and cold when it is strained by yielding to, any
+elastic force of its own, the strength of which would increase
+if the temperature were raised. When the strain is a condensation
+or dilatation, uniform in all directions, a fluid may be
+included in the statement. Hence the following propositions:&mdash;</p>
+
+<p>&ldquo;(1) A cubical compression of any elastic fluid or solid in an
+ordinary condition causes an evolution of heat; but, on the
+contrary, a cubical compression produces cold in any substance,
+solid or fluid, in such an abnormal state that it would contract
+if heated while kept under constant pressure. Water below its
+temperature (3.9° Cent.) of maximum density is a familiar instance.</p>
+
+<p>&ldquo;(2) If a wire already twisted be suddenly twisted further,
+always, however, within its limits of elasticity, cold will be
+produced; and if it be allowed suddenly to untwist, heat will
+be evolved from itself (besides heat generated externally by any
+work allowed to be wasted, which it does in untwisting). It is
+assumed that the torsional rigidity of the wire is diminished
+by an elevation of temperature, as the writer of this article
+had found it to be for copper, iron, platinum and other metals.</p>
+
+<p>&ldquo;(3) A spiral spring suddenly drawn out will become lower
+in temperature, and will rise in temperature when suddenly
+allowed to draw in. [This result has been experimentally
+verified by Joule (&rsquo;Thermodynamic Properties of Solids,&rsquo;
+<i>Phil. Trans.</i>, 1858) and the amount of the effect found to agree
+with that calculated, according to the preceding thermodynamic
+theory, from the amount of the weakening of the spring which
+he found by experiment.]</p>
+
+<p>&ldquo;(4) A bar or rod or wire of any substance with or without
+a weight hung on it, or experiencing any degree of end thrust,
+to begin with, becomes cooled if suddenly elongated by end pull
+or by diminution of end thrust, and warmed if suddenly shortened
+by end thrust or by diminution of end pull; except abnormal
+cases in which with constant end pull or end thrust elevation
+of temperature produces shortening; in every such case pull
+or diminished thrust produces elevation of temperature, thrust
+or diminished pull lowering of temperature.</p>
+
+<p>&ldquo;(5) An india-rubber band suddenly drawn out (within its
+limits of elasticity) becomes warmer; and when allowed to
+contract, it becomes colder. Any one may easily verify this
+curious property by placing an india-rubber band in slight
+contact with the edges of the lips, then suddenly extending it&mdash;it
+becomes very perceptibly warmer: hold it for some time
+stretched nearly to breaking, and then suddenly allow it to
+shrink&mdash;it becomes quite startlingly colder, the cooling effect
+being sensible not merely to the lips but to the fingers holding
+the band. The first published statement of this curious observation
+is due to J. Gough (<i>Mem. Lit. Phil. Soc. Manchester</i>, 2nd
+series, vol. i. p. 288), quoted by Joule in his paper on &lsquo;Thermodynamic
+Properties of Solids&rsquo; (cited above). The thermodynamic
+conclusion from it is that an india-rubber band, stretched
+by a constant weight of sufficient amount hung on it, must,
+when heated, pull up the weight, and, when cooled, allow the
+weight to descend: this Gough, independently of thermodynamic
+theory, had found to be actually the case. The experiment
+any one can make with the greatest ease by hanging
+a few pounds weight on a common india-rubber band, and
+taking a red-hot coal in a pair of tongs, or a red-hot poker, and
+moving it up and down close to the band. The way in which
+the weight rises when the red-hot body is near, and falls when
+it is removed, is quite startling. Joule experimented on the
+amount of shrinking per degree of elevation of temperature,
+with different weights hung on a band of vulcanized india-rubber,
+and found that they closely agreed with the amounts calculated
+by Thomson&rsquo;s theory from the heating effects of pull, and cooling
+effects of ceasing to pull, which he had observed in the same
+piece of india-rubber.&rdquo;</p>
+
+<p>91. <i>Initial Stress.</i>&mdash;It has been pointed out above (§ 20)
+that the &ldquo;unstressed&rdquo; state, which serves as a zero of reckoning
+for strains and stresses is never actually attained, although
+the strain (measured from this state), which exists in a body
+to be subjected to experiment, may be very slight. This is the
+case when the &ldquo;initial stress,&rdquo; or the stress existing before the
+experiment, is small in comparison with the stress developed
+during the experiment, and the limit of linear elasticity (§ 32)
+is not exceeded. The existence of initial stress has been correlated
+above with the existence of body forces such as the force
+of gravity, but it is not necessarily dependent upon such forces.
+A sheet of metal rolled into a cylinder, and soldered to maintain
+the tubular shape, must be in a state of considerable initial
+stress quite apart from the action of gravity. Initial stress is
+utilized in many manufacturing processes, as, for example, in
+the construction of ordnance, referred to in § 79, in the winding
+of golf balls by means of india-rubber in a state of high tension
+(see the report of the case <i>The Haskell Golf Ball Company</i> v.
+<i>Hutchinson &amp; Main</i> in <i>The Times</i> of March 1, 1906). In the
+case of a body of ordinary dimensions it is such internal stress
+<span class="pagenum"><a name="page160" id="page160"></a>160</span>
+as this which is especially meant by the phrase &ldquo;initial stress.&rdquo;
+Such a body, when in such a state of internal stress, is sometimes
+described as &ldquo;self-strained.&rdquo; It would be better described as
+&ldquo;self-stressed.&rdquo; The somewhat anomalous behaviour of cast
+iron has been supposed to be due to the existence within the
+metal of initial stress. As the metal cools, the outer layers cool
+more rapidly than the inner, and thus the state of initial stress
+is produced. When cast iron is tested for tensile strength, it
+shows at first no sensible range either of perfect elasticity or of
+linear elasticity; but after it has been loaded and unloaded
+several times its behaviour begins to be more nearly like that
+of wrought iron or steel. The first tests probably diminish the
+initial stress.</p>
+
+<div class="condensed">
+<p>92. From a mathematical point of view the existence of initial
+stress in a body which is &ldquo;self-stressed&rdquo; arises from the fact that
+the equations of equilibrium of a body free from body forces or surface
+tractions, viz. the equations of the type</p>
+
+<table class="math0" summary="math">
+<tr><td>&part;X<span class="su">x</span></td>
+<td rowspan="2">+</td> <td>&part;X<span class="su">y</span></td>
+<td rowspan="2">+</td> <td>&part;Z<span class="su">x</span></td>
+<td rowspan="2">= 0,</td></tr>
+<tr><td class="denom">&part;x</td> <td class="denom">&part;y</td> <td class="denom">&part;z</td></tr></table>
+
+<p class="noind">possess solutions which differ from zero. If, in fact, &phi;<span class="su">1</span>, &phi;<span class="su">2</span>, &phi;<span class="su">3</span> denote
+any arbitrary functions of <i>x, y, z</i>, the equations are satisfied by
+putting</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">X<span class="su">x</span> =</td> <td>&part;²&phi;<span class="su">3</span></td>
+<td rowspan="2">+</td> <td>&part;²&phi;<span class="su">2</span></td>
+<td rowspan="2">, ..., Y<span class="su">z</span> = &minus;</td> <td>&part;²&phi;<span class="su">1</span></td>
+<td rowspan="2">, ... ;</td></tr>
+<tr><td class="denom">&part;y²</td> <td class="denom">&part;z</td>
+<td class="denom">&part;y&part;z</td></tr></table>
+
+<p class="noind">and it is clear that the functions &phi;<span class="su">1</span>, &phi;<span class="su">2</span>, &phi;<span class="su">3</span> can be adjusted in an
+infinite number of ways so that the bounding surface of the body
+may be free from traction.</p>
+</div>
+
+<p>93. Initial stress due to body forces becomes most important
+in the case of a gravitating planet. Within the earth the stress
+that arises from the mutual gravitation of the parts is very great.
+If we assumed the earth to be an elastic solid body with moduluses
+of elasticity no greater than those of steel, the strain (measured
+from the unstressed state) which would correspond to the stress
+would be much too great to be calculated by the ordinary methods
+of the theory of elasticity (§ 75). We require therefore some
+other method of taking account of the initial stress. In many
+investigations, for example those of Lord Kelvin and Sir G.H.
+Darwin referred to in § 83, the difficulty is turned by assuming
+that the material may be treated as practically incompressible;
+but such investigations are to some extent incomplete, so long
+as the corrections due to a finite, even though high, resistance to
+compression remain unknown. In other investigations, such as
+those relating to the propagation of earthquake shocks and to
+gravitational instability, the possibility of compression is an
+essential element of the problem. By gravitational instability
+is meant the tendency of gravitating matter to condense into
+nuclei when slightly disturbed from a state of uniform diffusion;
+this tendency has been shown by J.H. Jeans (<i>Phil. Trans</i>.
+A. 201, 1903) to have exerted an important influence upon the
+course of evolution of the solar system. For the treatment of
+such questions Lord Rayleigh (<i>Proc. R. Soc. London</i>, A. 77,
+1906) has advocated a method which amounts to assuming that
+the initial stress is hydrostatic pressure, and that the actual
+state of stress is to be obtained by superposing upon this initial
+stress a stress related to the state of strain (measured from the
+initial state) by the same formulae as hold for an elastic solid
+body free from initial stress. The development of this method
+is likely to lead to results of great interest.</p>
+
+<div class="condensed">
+<p><span class="sc">Authorities</span>.&mdash;In regard to the analysis requisite to prove the
+results set forth above, reference may be made to A.E.H. Love,
+<i>Treatise on the Mathematical Theory of Elasticity</i> (2nd ed., Cambridge,
+1906), where citations of the original authorities will also be found.
+The following treatises may be mentioned: Navier, <i>Résumé des
+leçons sur l&rsquo;application de la mécanique</i> (3rd ed., with notes by Saint-Venant,
+Paris, 1864); G. Lamé, <i>Leçons sur la théorie mathématique
+de l&rsquo;élasticité des corps solides</i> (Paris, 1852); A. Clebsch, <i>Theorie der
+Elasticität fester Körper</i> (Leipzig, 1862; French translation with
+notes by Saint-Venant, Paris, 1883); F. Neumann, <i>Vorlesungen
+über die Theorie der Elasticität</i> (Leipzig, 1885); Thomson and Tait,
+<i>Natural Philosophy</i> (Cambridge, 1879, 1883); Todhunter and
+Pearson, <i>History of the Elasticity and Strength of Materials</i> (Cambridge,
+1886-1893). The article &ldquo;Elasticity&rdquo; by Sir W. Thomson (Lord
+Kelvin) in 9th ed. of <i>Encyc. Brit</i>. (reprinted in his <i>Mathematical
+and Physical Papers</i>, iii., Cambridge, 1890) is especially valuable,
+not only for the exposition of the theory and its practical
+applications, but also for the tables of physical constants which
+are there given.</p>
+</div>
+<div class="author">(A. E. H. L.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1b" id="ft1b" href="#fa1b"><span class="fn">1</span></a> The sign of M is shown by the arrow-heads in fig. 19, for which,
+with y downwards,</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">EI</td> <td>d²y</td>
+<td rowspan="2">+ M = 0.</td></tr>
+<tr><td class="denom">dx²</td></tr></table>
+
+<p><a name="ft2b" id="ft2b" href="#fa2b"><span class="fn">2</span></a> The figure is drawn for a case where the bending moment has the
+same sign throughout.</p>
+
+<p><a name="ft3b" id="ft3b" href="#fa3b"><span class="fn">3</span></a> M<span class="su">0</span> is taken to have, as it obviously has, the opposite sense to that
+shown in fig. 19.</p>
+
+<p><a name="ft4b" id="ft4b" href="#fa4b"><span class="fn">4</span></a> The line joining the points of contact must be normal to the
+planes.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELATERITE,<a name="ar36" id="ar36"></a></span> also termed <span class="sc">Elastic Bitumen</span> and <span class="sc">Mineral
+Caoutchouc</span>, a mineral hydrocarbon, which occurs at Castleton
+in Derbyshire, in the lead mines of Odin and elsewhere. It
+varies somewhat in consistency, being sometimes soft, elastic
+and sticky; often closely resembling india-rubber; and occasionally
+hard and brittle. It is usually dark brown in colour and
+slightly translucent. A substance of similar physical character
+is found in the Coorong district of South Australia, and is hence
+termed coorongite, but Prof. Ralph Tate considers this to be a
+vegetable product.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELATERIUM,<a name="ar37" id="ar37"></a></span> a drug consisting of a sediment deposited
+by the juice of the fruit of <i>Ecballium Elaterium</i>, the squirting
+cucumber, a native of the Mediterranean region. The plant,
+which is a member of the natural order Cucurbitaceae, resembles
+the vegetable marrow in its growth. The fruit resembles a
+small cucumber, and when ripe is highly turgid, and separates
+almost at a touch from the fruit stalk. The end of the stalk
+forms a stopper, on the removal of which the fluid contents of
+the fruit, together with the seeds, are squirted through the
+aperture by the sudden contraction of the wall of the fruit.
+To prepare the drug the fruit is sliced lengthwise and slightly
+pressed; the greenish and slightly turbid juice thus obtained
+is strained and set aside; and the deposit of elaterium formed
+after a few hours is collected on a linen filter, rapidly drained,
+and dried on porous tiles at a gentle heat. Elaterium is met
+with in commerce in light, thin, friable, flat or slightly incurved
+opaque cakes, of a greyish-green colour, bitter taste and tea-like
+smell.</p>
+
+<p>The drug is soluble in alcohol, but insoluble in water and ether.
+The official dose is <span class="spp">1</span>&frasl;<span class="suu">10</span>-<span class="spp">1</span>&frasl;<span class="suu">2</span> grain, and the British pharmacopeia
+directs that the drug is to contain from 20 to 25% of the active
+principle elaterinum or elaterin. A resin in the natural product
+aids its action. Elaterin is extracted from elaterium by chloroform
+and then precipitated by ether. It has the formula
+C<span class="su">20</span>H<span class="su">28</span>O<span class="su">5</span>. It forms colourless scales which have a bitter taste,
+but it is highly inadvisable to taste either this substance or
+elaterium. Its dose is <span class="spp">1</span>&frasl;<span class="suu">40</span>-<span class="spp">1</span>&frasl;<span class="suu">10</span> grain, and the British pharmacopeia
+contains a useful preparation, the Pulvis Elaterini Compositus,
+which contains one part of the active principle in forty.</p>
+
+<p>The action of this drug resembles that of the saline aperients,
+but is much more powerful. It is the most active hydragogue
+purgative known, causing also much depression and violent
+griping. When injected subcutaneously it is inert, as its action
+is entirely dependent upon its admixture with the bile. The
+drug is undoubtedly valuable in cases of dropsy and Bright&rsquo;s
+disease, and also in cases of cerebral haemorrhage, threatened or
+present. It must not be used except in urgent cases, and must
+invariably be employed with the utmost care, especially if the
+state of the heart be unsatisfactory.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELBA<a name="ar38" id="ar38"></a></span> (Gr. <span class="grk" title="Aithalia">&#913;&#7984;&#952;&#945;&#955;&#943;&#945;</span>; Lat. <i>Ilva</i>), an island off the W. coast
+of Italy, belonging to the province of Leghorn, from which
+it is 45 m. S., and 7 m. S.W. of Piombino, the nearest point of
+the mainland. Pop. (1901) 25,043 (including Pianosa). It is
+about 19 m. long, 6½ m. broad, and 140 sq. m. in area; and its
+highest point is 3340 ft. (Monte Capanne). It forms, like Giglio
+and Monte Cristo, part of a sunken mountain range extending
+towards Corsica and Sardinia.</p>
+
+<p>The oldest rocks of Elba consist of schist and serpentine which
+in the eastern part of the island are overlaid by beds containing
+Silurian and Devonian fossils. The Permian may be represented,
+but the Trias is absent, and in general the older Palaeozoic rocks
+are overlaid directly by the Rhaetic and Lias. The Liassic beds
+are often metamorphosed and the limestones contain garnet
+and wollastonite. The next geological formation which is
+represented is the Eocene, consisting of nummulitic limestone,
+sandstone and schist. The Miocene and Pliocene are absent.
+The most remarkable feature in the geology of Elba is the extent
+of the granitic and ophiolitic eruptions of the Tertiary period.
+Serpentines, peridotites and diabases are interstratified with the
+Eocene deposits. The granite, which is intruded through the
+Eocene beds, is associated with a pegmatite containing tourmaline
+and cassiterite. The celebrated iron ore of Elba is of
+<span class="pagenum"><a name="page161" id="page161"></a>161</span>
+Tertiary age and occurs indifferently in all the older rocks. The
+deposits are superficial, resulting from the opening out of veins
+at the surface, and consist chiefly of haematite. These ores were
+worked by the ancients, but so inefficiently that their spoil-heaps
+can be smelted again with profit. This process is now
+gone through on the island itself. The granite was also quarried
+by the Romans, but is not now much worked.</p>
+
+<p>Parts of the island are fertile, and the cultivation of vines,
+and the tunny and sardine fishery, also give employment to a part
+of the population. The capital of the island is Portoferraio&mdash;pop.
+(1901) 5987&mdash;in the centre of the N. coast, enclosed by an
+amphitheatre of lofty mountains, the slopes of which are covered
+with villas and gardens. This is the best harbour, the ancient
+<i>Portus Argous</i>. The town was built and fortified by Cosimo I.
+in 1548, who called it Cosmopolis. Above the harbour, between
+the forts Stella and Falcone, is the palace of Napoleon I., and
+4 m. to the S.W. is his villa; while on the N. slope of Monte
+Capanne is another of his country houses. The other villages
+in the island are Campo nell&rsquo; Elba, on the S. near the W. end,
+Marciana and Marciana Marina on the N. of the island near the
+W. extremity, Porto Longone, on the E. coast, with picturesque
+Spanish fortifications, constructed in 1602 by Philip III.; Rio
+dell&rsquo; Elba and Rio Marina, both on the E. side of the island, in
+the mining district. At Le Grotte, between Portoferraio and Rio
+dell&rsquo; Elba, and at Capo Castello, on the N.E. of the island, are
+ruins of Roman date.</p>
+
+<p>Elba was famous for its mines in early times, and the smelting
+furnaces gave it its Greek name of <span class="grk" title="A' thalia">&#913;&#8125; &#952;&#945;&#955;&#943;&#945;</span> (&ldquo;soot island&rdquo;).
+In Roman times, and until 1900, however, owing to lack of fuel,
+the smelting was done on the mainland. In 453 <span class="scs">B.C.</span> Elba was
+devastated by a Syracusan squadron. From the 11th to the
+14th century it belonged to Pisa, and in 1399 came under the
+dukes of Piombino. In 1548 it was ceded by them to Cosimo I.
+of Florence. In 1596 Porto Longone was taken by Philip III.
+of Spain, and retained until 1709, when it was ceded to Naples.
+In 1802 the island was given to France by the peace of Amiens.
+On Napoleon&rsquo;s deposition, the island was ceded to him with full
+sovereign rights, and he resided there from the 5th of May 1814
+to the 26th of February 1815. After his fall it was restored
+to Tuscany, and passed with it to Italy in 1860.</p>
+
+<div class="condensed">
+<p>See Sir R. Colt Hoare, <i>A Tour through the Island of Elba</i> (London,
+1814).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELBE<a name="ar39" id="ar39"></a></span> (the <i>Albis</i> of the Romans and the <i>Labe</i> of the Czechs),
+a river of Germany, which rises in Bohemia not far from the
+frontiers of Silesia, on the southern side of the Riesengebirge,
+at an altitude of about 4600 ft. Of the numerous small streams
+(Seifen or Flessen as they are named in the district) whose confluent
+waters compose the infant river, the most important are
+the Weisswasser, or White Water, and the Elbseifen, which is
+formed in the same neighbourhood, but at a little lower elevation.
+After plunging down the 140 ft. of the Elbfall, the latter stream
+unites with the steep torrential Weisswasser at Mädelstegbaude,
+at an altitude of 2230 ft., and thereafter the united stream of
+the Elbe pursues a southerly course, emerging from the mountain
+glens at Hohenelbe (1495 ft.), and continuing on at a soberer pace
+to Pardubitz, where it turns sharply to the west, and at Kolin
+(730 ft.), some 27 m. farther on, bends gradually towards the
+north-west. A little above Brandeis it picks up the Iser, which,
+like itself, comes down from the Riesengebirge, and at Melnik
+it has its stream more than doubled in volume by the Moldau,
+a river which winds northwards through the heart of Bohemia
+in a sinuous, trough-like channel carved through the plateaux.
+Some miles lower down, at Leitmeritz (433 ft.), the waters of
+the Elbe are tinted by the reddish Eger, a stream which drains
+the southern slopes of the Erzgebirge. Thus augmented, and
+swollen into a stream 140 yds. wide, the Elbe carves a path
+through the basaltic mass of the Mittelgebirge, churning its
+way through a deep, narrow rocky gorge. Then the river winds
+through the fantastically sculptured sandstone mountains of the
+&ldquo;Saxon Switzerland,&rdquo; washing successively the feet of the lofty
+Lilienstein (932 ft. above the Elbe), the scene of one of Frederick
+the Great&rsquo;s military exploits in the Seven Years&rsquo; War, Königstein
+(797 ft. above the Elbe), where in times of war Saxony has more
+than once stored her national purse for security, and the pinnacled
+rocky wall of the Bastei, towering 650 ft. above the surface of
+the stream. Shortly after crossing the Bohemian-Saxon frontier,
+and whilst still struggling through the sandstone defiles, the
+stream assumes a north-westerly direction, which on the whole
+it preserves right away to the North Sea. At Pirna the Elbe
+leaves behind it the stress and turmoil of the Saxon Switzerland,
+rolls through Dresden, with its noble river terraces, and finally,
+beyond Meissen, enters on its long journey across the North
+German plain, touching Torgau, Wittenberg, Magdeburg,
+Wittenberge, Hamburg, Harburg and Altona on the way, and
+gathering into itself the waters of the Mulde and Saale from the
+left, and those of the Schwarze Elster, Havel and Elde from the
+right. Eight miles above Hamburg the stream divides into the
+Norder (or Hamburg) Elbe and the Süder (or Harburg) Elbe,
+which are linked together by several cross-channels, and embrace
+in their arms the large island of Wilhelmsburg and some smaller
+ones. But by the time the river reaches Blankenese, 7 m. below
+Hamburg, all these anastomosing branches have been reunited,
+and the Elbe, with a width of 4 to 9 m. between bank and bank,
+travels on between the green marshes of Holstein and Hanover
+until it becomes merged in the North Sea off Cuxhaven. At
+Kolin the width is about 100 ft., at the mouth of the Moldau
+about 300, at Dresden 960, and at Magdeburg over 1000. From
+Dresden to the sea the river has a total fall of only 280 ft., although
+the distance is about 430 m. For the 75 m. between Hamburg
+and the sea the fall is only 3¼ ft. One consequence of this is that
+the bed of the river just below Hamburg is obstructed by a bar,
+and still lower down is choked with sandbanks, so that navigation
+is confined to a relatively narrow channel down the middle of
+the stream. But unremitting efforts have been made to maintain
+a sufficient fairway up to Hamburg (<i>q.v.</i>). The tide advances
+as far as Geesthacht, a little more than 100 m. from the sea.
+The river is navigable as far as Melnik, that is, the confluence of
+the Moldau, a distance of 525 m., of which 67 are in Bohemia.
+<span class="correction" title="amended from it">Its</span> total length is 725 m., of which 190 are in Bohemia, 77 in the
+kingdom of Saxony, and 350 in Prussia, the remaining 108 being
+in Hamburg and other states of Germany. The area of the drainage
+basin is estimated at 56,000 sq. m.</p>
+
+<p><i>Navigation.</i>&mdash;Since 1842, but more especially since 1871, improvements
+have been made in the navigability of the Elbe by
+all the states which border upon its banks. As a result of these
+labours there is now in the Bohemian portion of the river a
+minimum depth of 2 ft. 8 in., whilst from the Bohemian frontier
+down to Magdeburg the minimum depth is 3 ft., and from
+Magdeburg to Hamburg, 3 ft. 10 in. In 1896 and 1897 Prussia
+and Hamburg signed covenants whereby two channels are to be
+kept open to a depth of 9¾ ft., a width of 656 ft., and a length
+of 550 yds. between Bunthaus and Ortkathen, just above the
+bifurcation of the Norder Elbe and the Süder Elbe. In 1869 the
+maximum burden of the vessels which were able to ply on the
+upper Elbe was 250 tons; but in 1899 it was increased to 800 tons.
+The large towns through which the river flows have vied with one
+another in building harbours, providing shipping accommodation,
+and furnishing other facilities for the efficient navigation of the
+Elbe. In this respect the greatest efforts have naturally been
+made by Hamburg; but Magdeburg, Dresden, Meissen, Riesa,
+Tetschen, Aussig and other places have all done their relative
+shares, Magdeburg, for instance, providing a commercial
+harbour and a winter harbour. In spite, however, of all that has
+been done, the Elbe remains subject to serious inundations at
+periodic intervals. Among the worst floods were those of the
+years 1774, 1799, 1815, 1830, 1845, 1862, 1890 and 1909. The
+growth of traffic up and down the Elbe has of late years become
+very considerable. A towing chain, laid in the bed of the river,
+extends from Hamburg to Aussig, and by this means, as by
+paddle-tug haulage, large barges are brought from the port of
+Hamburg into the heart of Bohemia. The fleet of steamers and
+barges navigating the Elbe is in point of fact greater than on
+any other German river. In addition to goods thus conveyed,
+enormous quantities of timber are floated down the Elbe; the
+<span class="pagenum"><a name="page162" id="page162"></a>162</span>
+weight of the rafts passing the station of Schandau on the Saxon
+Bohemian frontier amounting in 1901 to 333,000 tons.</p>
+
+<p>A vast amount of traffic is directed to Berlin, by means of the
+Havel-Spree system of canals, to the Thuringian states and the
+Prussian province of Saxony, to the kingdom of Saxony and
+Bohemia, and to the various riverine states and provinces of the
+lower and middle Elbe. The passenger traffic, which is in the
+hands of the Sächsisch-Böhmische Dampfschifffahrtsgesellschaft
+is limited to Bohemia and Saxony, steamers plying up and down
+the stream from Dresden to Melnik, occasionally continuing the
+journey up the Moldau to Prague, and down the river as far as
+Riesa, near the northern frontier of Saxony, and on the average
+1½ million passengers are conveyed.</p>
+
+<p>In 1877-1879, and again in 1888-1895, some 100 m. of canal
+were dug, 5 to 6½ ft. deep and of various widths, for the purpose of
+connecting the Elbe, through the Havel and the Spree, with the
+system of the Oder. The most noteworthy of these connexions
+are the Elbe Canal (14¼ m. long), the Reek Canal (9½ m.), the
+Rüdersdorfer Gewässer (11½ m.), the Rheinsberger Canal (11¼ m.),
+and the Sacrow-Paretzer Canal (10 m.), besides which the Spree
+has been canalized for a distance of 28 m., and the Elbe for a
+distance of 70 m. Since 1896 great improvements have been
+made in the Moldau and the Bohemian Elbe, with the view of
+facilitating communication between Prague and the middle of
+Bohemia generally on the one hand, and the middle and lower
+reaches of the Elbe on the other. In the year named a special
+commission was appointed for the regulation of the Moldau and
+Elbe between Prague and Aussig, at a cost estimated at about
+£1,000,000, of which sum two-thirds were to be borne by the
+Austrian empire and one-third by the kingdom of Bohemia.
+The regulation is effected by locks and movable dams, the latter
+so designed that in times of flood or frost they can be dropped flat
+on the bottom of the river. In 1901 the Austrian government laid
+before the Reichsrat a canal bill, with proposals for works
+estimated to take twenty years to complete, and including the
+construction of a canal between the Oder, starting at Prerau, and
+the upper Elbe at Pardubitz, and for the canalization of the Elbe
+from Pardubitz to Melnik (see <span class="sc"><a href="#artlinks">Austria</a></span>: <i>Waterways</i>). In 1900
+Lübeck was put into direct communication with the Elbe at
+Lauenburg by the opening of the Elbe-Trave Canal, 42 m. in
+length, and constructed at a cost of £1,177,700, of which the state
+of Lübeck contributed £802,700, and the kingdom of Prussia
+£375,000. The canal has been made 72 ft. wide at the bottom,
+105 to 126 ft. wide at the top, has a minimum depth of 8<span class="spp">1</span>&frasl;<span class="suu">6</span> ft., and
+is equipped with seven locks, each 262½ ft. long and 39¼ ft. wide.
+It is thus able to accommodate vessels up to 800 tons burden;
+and the passage from Lübeck to Lauenburg occupies 18 to 21
+hours. In the first year of its being open (June 1900 to June
+1901) a total of 115,000 tons passed through the canal.<a name="fa1c" id="fa1c" href="#ft1c"><span class="sp">1</span></a> A
+gigantic project has also been put forward for providing water
+communication between the Rhine and the Elbe, and so with the
+Oder, through the heart of Germany. This scheme is known as
+the Midland Canal. Another canal has been projected for connecting
+Kiel with the Elbe by means of a canal trained through
+the Plön Lakes.</p>
+
+<p><i>Bridges.</i>&mdash;The Elbe is crossed by numerous bridges, as at
+Königgrätz, Pardubitz, Kolin, Leitmeritz, Tetschen, Schandau,
+Pirna, Dresden, Meissen, Torgau, Wittenberg, Rosslau, Barby,
+Magdeburg, Rathenow, Wittenberge, Dömitz, Lauenburg, and
+Hamburg and Harburg. At all these places there are railway
+bridges, and nearly all, but more especially those in Bohemia,
+Saxony and the middle course of the river&mdash;these last on the main
+lines between Berlin and the west and south-west of the empire&mdash;possess
+a greater or less strategic value. At Leitmeritz there is an
+iron trellis bridge, 600 yds long. Dresden has four bridges, and
+there is a fifth bridge at Loschwitz, about 3 m. above the city.
+Meissen has a railway bridge, in addition to an old road bridge.
+Magdeburg is one of the most important railway centres in
+northern Germany; and the Elbe, besides being bridged&mdash;it
+divides there into three arms&mdash;several times for vehicular traffic,
+is also spanned by two fine railway bridges. At both Hamburg
+and Harburg, again, there are handsome railway bridges, the one
+(1868-1873 and 1894) crossing the northern Elbe, and the other
+(1900) the southern Elbe; and the former arm is also crossed by a
+fine triple-arched bridge (1888) for vehicular traffic.</p>
+
+<p><i>Fish.</i>&mdash;The river is well stocked with fish, both salt-water and
+fresh-water species being found in its waters, and several varieties
+of fresh-water fish in its tributaries. The kinds of greatest
+economic value are sturgeon, shad, salmon, lampreys, eels, pike
+and whiting.</p>
+
+<p><i>Tolls.</i>&mdash;In the days of the old German empire no fewer than
+thirty-five different tolls were levied between Melnik and Hamburg,
+to say nothing of the special dues and privileged exactions of
+various riparian owners and political authorities. After these had
+been <i>de facto</i>, though not <i>de jure</i>, in abeyance during the period of
+the Napoleonic wars, a commission of the various Elbe states met
+and drew up a scheme for their regulation, and the scheme,
+embodied in the Elbe Navigation Acts, came into force in 1822.
+By this a definite number of tolls, at fixed rates, was substituted
+for the often arbitrary tolls which had been exacted previously.
+Still further relief was afforded in 1844 and in 1850, on the latter
+occasion by the abolition of all tolls between Melnik and the
+Saxon frontier. But the number of tolls was only reduced to one,
+levied at Wittenberge, in 1863, about one year after Hanover was
+induced to give up the Stade or Brunsbüttel toll in return for a
+compensation of 2,857,340 thalers. Finally, in 1870, 1,000,000
+thalers were paid to Mecklenburg and 85,000 thalers to <span class="correction" title="amended from Anhal">Anhalt</span>,
+which thereupon abandoned all claims to levy tolls upon the
+Elbe shipping, and thus navigation on the river became at last
+entirely free.</p>
+
+<p><i>History.</i>&mdash;The Elbe cannot rival the Rhine in the picturesqueness
+of the scenery it travels through, nor in the glamour which
+its romantic and legendary associations exercise over the imagination.
+But it possesses much to charm the eye in the deep
+glens of the Riesengebirge, amid which its sources spring, and
+in the bizarre rock-carving of the Saxon Switzerland. It has
+been indirectly or directly associated with many stirring events
+in the history of the German peoples. In its lower course, whatever
+is worthy of record clusters round the historical vicissitudes
+of Hamburg&mdash;its early prominence as a missionary centre
+(Ansgar) and as a bulwark against Slav and marauding Northman,
+its commercial prosperity as a leading member of the Hanseatic
+League, and its sufferings during the Napoleonic wars, especially
+at the hands of the ruthless Davoût. The bridge over the river
+at Dessau recalls the hot assaults of the <i>condottiere</i> Ernst von
+Mansfeld in April 1626, and his repulse by the crafty generalship
+of Wallenstein. But three years later this imperious leader was
+checked by the heroic resistance of the &ldquo;Maiden&rdquo; fortress of
+Magdeburg; though two years later still she lost her reputation,
+and suffered unspeakable horrors at the hands of Tilly&rsquo;s lawless
+and unlicensed soldiery. Mühlberg, just outside the Saxon
+frontier, is the place where Charles V. asserted his imperial
+authority over the Protestant elector of Saxony, John Frederick,
+the Magnanimous or Unfortunate, in 1547. Dresden, Aussig
+and Leitmeritz are all reminiscent of the fierce battles of the
+Hussite wars, and the last named of the Thirty Years&rsquo; War.
+But the chief historical associations of the upper (<i>i.e.</i> the Saxon
+and Bohemian) Elbe are those which belong to the Seven Years&rsquo;
+War, and the struggle of the great Frederick of Prussia against
+the power of Austria and her allies. At Pirna (and Lilienstein) in
+1756 he caught the entire Saxon army in his fowler&rsquo;s net, after
+driving back at Lobositz the Austrian forces which were hastening
+to their <span class="correction" title="amended from asistance">assistance</span>; but only nine months later he lost his
+reputation for &ldquo;invincibility&rdquo; by his crushing defeat at Kolin,
+where the great highway from Vienna to Dresden crosses the
+Elbe. Not many miles distant, higher up the stream, another
+decisive battle was fought between the same national antagonists,
+but with a contrary result, on the memorable 3rd of July
+1866.</p>
+
+<div class="condensed">
+<p>See M. Buchheister, &ldquo;Die Elbe u. der Hafen von Hamburg,&rdquo;
+in <i>Mitteil. d. Geog. Gesellsch. in Hamburg</i> (1899), vol. xv. pp. 131-188;
+V. Kurs, &ldquo;Die künstlichen Wasserstrassen des deutschen
+<span class="pagenum"><a name="page163" id="page163"></a>163</span>
+Reichs,&rdquo; in <i>Geog. Zeitschrift</i> (1898), pp. 601-617; and (the official)
+<i>Der Elbstrom</i> (1900); B. Weissenborn, <i>Die Elbzölle und Elbstapelplätze
+im Mittelalter</i> (Halle, 1900); Daniel, <i>Deutschland</i>; and A.
+Supan, <i>Wasserstrassen und Binnenschifffahrt</i> (Berlin, 1902).</p>
+</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1c" id="ft1c" href="#fa1c"><span class="fn">1</span></a> See <i>Der Bau des Elbe-Trave Canals und seine Vorgeschichte</i>
+(Lübeck, 1900).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELBERFELD,<a name="ar40" id="ar40"></a></span> a manufacturing town of Germany, in the
+Prussian Rhine province, on the Wupper, and immediately west
+of and contiguous to Barmen (<i>q.v.</i>). Pop. (1816) 21,710; (1840)
+31,514; (1885) 109,218; (1905) 167,382. Elberfeld-Barmen,
+although administratively separate, practically form a single
+whole. It winds, a continuous strip of houses and factories,
+for 9 m. along the deep valley, on both banks of the Wupper,
+which is crossed by numerous bridges, the engirdling hills
+crowned with woods. Local intercommunication is provided
+by an electric tramway line and a novel hanging railway&mdash;on
+the Langen mono-rail system&mdash;suspended over the bed of the
+river, with frequent stations. In the centre of the town are a
+number of irregular and narrow streets, and the river, polluted
+by the refuse of dye-works and factories, constitutes a constant
+eyesore. Yet within recent years great alterations have been
+effected; in the newer quarters are several handsome streets
+and public buildings; in the centre many insanitary dwellings
+have been swept away, and their place occupied by imposing
+blocks of shops and business premises, and a magnificent new
+town-hall, erected in a dominant position. Among the most
+recent improvements must be mentioned the Brausenwerther
+Platz, flanked by the theatre, the public baths, and the railway
+station and administrative offices. There are eleven Evangelical
+and five Roman Catholic churches (noticeable among the latter
+the Suitbertuskirche), a synagogue, and chapels of various other
+sects. Among other public buildings may be enumerated the
+civic hall, the law courts and the old town-hall.</p>
+
+<p>The town is particularly rich in educational, industrial, philanthropic
+and religious institutions. The schools include the
+Gymnasium (founded in 1592 by the Protestant community
+as a Latin school), the Realgymnasium (founded in 1830, for
+&ldquo;modern&rdquo; subjects and Latin), the Oberrealschule and Realschule
+(founded 1893, the latter wholly &ldquo;modern&rdquo;), two girls&rsquo;
+high schools, a girls&rsquo; middle-class school, a large number of
+popular schools, a mechanics&rsquo; and polytechnic school, a school
+of mechanics, an industrial drawing school, a commercial school,
+and a school for the deaf and dumb. There are also a theatre,
+an institute of music, a library, a museum, a zoological garden,
+and numerous scientific societies. The town is the seat of the
+Berg Bible Society. The majority of the inhabitants are
+Protestant, with a strong tendency towards Pietism; but the
+Roman Catholics number upwards of 40,000, forming about
+one-fourth of the total population. The industries of Elberfeld
+are on a scale of great magnitude. It is the chief centre in
+Germany of the cotton, wool, silk and velvet manufactures, and
+of upholstery, drapery and haberdashery of all descriptions, of
+printed calicoes, of Turkey-red and other dyes, and of fine
+chemicals. Leather and rubber goods, gold, silver and aluminium
+wares, machinery, wall-paper, and stained glass are also among
+other of its staple products. Commerce is lively and the exports
+to foreign countries are very considerable. The railway system
+is well devised to meet the requirements of its rapidly increasing
+trade. Two main lines of railway traverse the valley; that on
+the south is the main line from Aix-la-Chapelle, Cologne and
+Düsseldorf to central Germany and Berlin, that on the north
+feeds the important towns of the Ruhr valley.</p>
+
+<p>The surroundings of Elberfeld are attractive, and public
+grounds and walks have been recently opened on the hills around
+with results eminently beneficial to the health of the population.</p>
+
+<p>In the 12th century the site of Elberfeld was occupied by the
+castle of the lords of Elverfeld, feudatories of the archbishops of
+Cologne. The fief passed later into the possession of the counts
+of Berg. The industrial development of the place started with
+a colony of bleachers, attracted by the clear waters of the Wupper,
+who in 1532 were granted the exclusive privilege of bleaching
+yarn. It was not, however, until 1610 that Elberfeld was raised
+to the status of a town, and in 1640 was surrounded with walls.
+In 1760 the manufacture of silk was introduced, and dyeing with
+Turkey-red in 1780; but it was not till the end of the century
+that its industries developed into importance under the influence
+of Napoleon&rsquo;s continental system, which barred out British
+competition. In 1815 Elberfeld was assigned by the congress
+of Vienna, with the grand-duchy of Berg, to Prussia, and its
+prosperity rapidly developed under the Prussian Zollverein.</p>
+
+<div class="condensed">
+<p>See Coutelle, <i>Elberfeld, topographisch-statistische Darstellung</i> (Elberfeld,
+1853); Schell, <i>Geschichte der Stadt Elberfeld</i> (1900); A. Shadwell,
+<i>Industrial Efficiency</i> (London, 1906); and Jorde, <i>Führer durch Elberfeld
+und seine Umgebung</i> (1902).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELBEUF,<a name="ar41" id="ar41"></a></span> a town of northern France in the department of
+Seine-Inférieure, 14 m. S.S.W. of Rouen by the western railway.
+Pop. (1906) 17,800. Elbeuf, a town of wide, clean streets, with
+handsome houses and factories, stands on the left bank of the
+Seine at the foot of hills over which extends the forest of Elbeuf.
+A tribunal and chamber of commerce, a board of trade-arbitrators,
+a lycée, a branch of the Bank of France, a school of industry,
+a school of cloth manufacture and a museum of natural history
+are among its institutions. The churches of St Étienne and St
+Jean, both of the Renaissance period with later additions,
+preserve stained glass of the 16th century. The hôtel-de-ville
+and the Cercle du Commerce are the chief modern buildings.
+The town with its suburbs, Orival, Caudebec-lès-Elbeuf,
+St Aubin and St Pierre, is one of the principal and most ancient
+seats of the woollen manufacture in France; more than half the
+inhabitants are directly maintained by the staple industry and
+numbers more by the auxiliary crafts. As a river-port it has a
+brisk trade in the produce of the surrounding district as well as in
+the raw materials of its manufactures, especially in wool from
+La Plata, Australia and Germany. Two bridges, one of them a
+suspension-bridge, communicate with St Aubin on the opposite
+bank of the Seine, and steamboats ply regularly to Rouen.</p>
+
+<p>Elbeuf was, in the 13th century, the centre of an important
+fief held by the house of Harcourt, but its previous
+history goes back at least to the early years of the Norman
+occupation, when it appears under the name of Hollebof. It
+passed into the hands of the houses of Rieux and Lorraine, and
+was raised to the rank of a duchy in the peerage of France by
+Henry III. in favour of Charles of Lorraine (d. 1605), grandson
+of Claude, duke of Guise, master of the hounds and master of
+the horse of France. The last duke of Elbeuf was Charles Eugène
+of Lorraine, prince de Lambesc, who distinguished himself in
+1789 by his energy in repressing risings of the people at Paris.
+He fought in the army of the Bourbons, and later in the service
+of Austria, and died in 1825.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELBING,<a name="ar42" id="ar42"></a></span> a seaport town of Germany, in the kingdom of
+Prussia, 49 m. by rail E.S.E. of Danzig, on the Elbing, a small
+river which flows into the Frische Haff about 5 m. from the
+town, and is united with the Nogat or eastern arm of the Vistula
+by means of the Kraffohl canal. Pop. (1905) 55,627. By the
+Elbing-Oberländischer canal, 110 m. long, constructed in 1845-1860,
+Lakes Geserich and Drewenz are connected with Lake
+Drausen, and consequently with the port of Elbing. The old
+town was formerly surrounded by fortifications, but of these only
+a few fragments remain. There are several churches, among
+them the Marienkirche (dating from the 15th century and restored
+in 1887), a classical school (Gymnasium) founded in 1536, a
+modern school (Realschule), a public library of over 28,000
+volumes, and several charitable institutions. The town-hall
+(1894) contains a historical museum.</p>
+
+<p>Elbing is a place of rapidly growing industries. At the great
+Schichau iron-works, which employ thousands of workmen, are
+built most of the torpedo-boats and destroyers for the German
+navy, as well as larger craft, locomotives and machinery. In
+addition to this there are at Elbing important iron foundries, and
+manufactories of machinery, cigars, lacquer and metal ware, flax
+and hemp yarn, cotton, linen, organs, &amp;c. There is a considerable
+trade also in agricultural produce.</p>
+
+<p>The origin of Elbing was a colony of traders from Lübeck and
+Bremen, which established itself under the protection of a castle
+of the Teutonic Knights, built in 1237. In 1246 the town acquired
+&ldquo;Lübeck rights,&rdquo; <i>i.e.</i> the full autonomy conceded by the charter
+<span class="pagenum"><a name="page164" id="page164"></a>164</span>
+of the emperor Frederick II. in 1226 (see <span class="sc"><a href="#artlinks">Lübeck</a></span>), and it was
+early admitted to the Hanseatic League. In 1454 the town
+repudiated the overlordship of the Teutonic Order, and placed
+itself under the protection of the king of Poland, becoming the
+seat of a Polish voivode. From this event dates a decline in its
+prosperity, a decline hastened by the wars of the early 18th
+century. In 1698, and again in 1703, it was seized by the elector
+of Brandenburg as security for a debt due to him by the
+Polish king. It was taken and held to ransom by Charles XII. of
+Sweden, and in 1710 was captured by the Russians. In 1772,
+when it fell to Prussia through the first partition of Poland, it was
+utterly decayed.</p>
+
+<div class="condensed">
+<p>See Fuchs, <i>Gesch. der Stadt Elbing</i> (Elbing, 1818-1852); Rhode,
+<i>Der Elbinger Kreis in topographischer, historischer, und statistischer
+Hinsicht</i> (Danzig, 1871); Wernick, <i>Elbing</i> (Elbing, 1888).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELBOW<a name="ar43" id="ar43"></a></span>, in anatomy, the articulation of the <i>humerus</i>, the bone
+of the upper arm, and the <i>ulna</i> and <i>radius</i>, the bones of the forearm
+(see <span class="sc"><a href="#artlinks">Joints</a></span>). The word is thus applied to things which are
+like this joint in shape, such as a sharp bend of a stream or river,
+an angle in a tube, &amp;c. The word is derived from the O. Eng.
+<i>elnboga</i>, a combination of <i>eln</i>, the forearm, and <i>boga</i>, a bow or
+bend. This combination is common to many Teutonic languages,
+cf. Ger. <i>Ellbogen</i>. <i>Eln</i> still survives in the name of a linear
+measure, the &ldquo;ell,&rdquo; and is derived from the O. Teut. <i>alina</i>,
+cognate with Lat. <i>ulna</i> and Gr. <span class="grk" title="ôlenê">&#8032;&#955;&#941;&#957;&#951;</span>, the forearm. The use of
+the arm as a measure of length is illustrated by the uses of <i>ulna</i>,
+in Latin, cubit, and fathom.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELBURZ,<a name="ar44" id="ar44"></a></span> or <span class="sc">Alburz</span> (from O. Pers. <i>Hara-bere-zaiti</i>, the
+&ldquo;High Mountain&rdquo;), a great chain of mountains in northern
+Persia, separating the Caspian depression from the Persian
+highlands, and extending without any break for 650 m. from the
+western shore of the Caspian Sea to north-eastern Khorasan.
+According to the direction, or strike, of its principal ranges the
+Elburz may be divided into three sections: the first 120 m. in
+length with a direction nearly N. to S., the second 240 m. in length
+with a direction N.W. to S.E., and the third 290 m. in length striking
+S.W. to N.E. The first section, which is connected with the
+system of the Caucasus, and begins west of Lenkoran in 39° N. and
+45° E., is known as the Talish range and has several peaks 9000 to
+10,000 ft. in height. It runs almost parallel to the western shore
+of the Caspian, and west of Astara is only 10 or 12 m. distant from
+the sea. At the point west of Resht, where the direction of the
+principal range changes to one of N.W. to S.E., the second section
+of the Elburz begins, and extends from there to beyond Mount
+Demavend, east of Teheran. South of Resht this section is broken
+through at almost a right angle by the Safid Rud (White river), and
+along it runs the principal commercial road between the Caspian
+and inner Persia, Resht-Kazvin-Teheran. The Elburz then
+splits into three principal ranges running parallel to one another
+and connected at many places by secondary ranges and spurs.
+Many peaks of the ranges in this section have an altitude of
+11,000 to 13,000 ft., and the elevation of the passes leading over
+the ranges varies between 7000 and 10,000 ft. The highest peaks
+are situated in the still unexplored district of Talikan, N.W. of
+Teheran, and thence eastwards to beyond Mount Demavend.
+The part of the Elburz immediately north of Teheran is known as
+the Kuh i Shimran (mountain of Shimran, from the name of the
+Shimran district on its southern slopes) and culminates in the
+Sar i Tochal (12,600 ft.). Beyond it, and between the border of
+Talikan in the N.W. and Mount Demavend in the N.E., are the
+ranges Azadbur, Kasil, Kachang, Kendevan, Shahzad, Varzeh,
+Derbend i Sar and others, with elevations of 12,000 to 13,500 ft.,
+while Demavend towers above them all with its altitude of
+19,400 ft. The eastern foot of Demavend is washed by the river
+Herhaz (called Lar river in its upper course), which there breaks
+through the Elburz in a S.-N. direction in its course to the Caspian,
+past the city of Amol. The third section of the Elburz, with its
+principal ranges striking S.W. to N.E., has a length of about 290
+m., and ends some distance beyond Bujnurd in northern Khorasan,
+where it joins the Ala Dagh range, which has a direction to
+the S.E., and, continuing with various appellations to northern
+Afghanistan, unites with the Paropamisus. For about two-thirds
+of its length&mdash;from its beginning to Khush Yailak&mdash;the
+third section consists of three principal ranges connected by
+lateral ranges and spurs. It also has many peaks over 10,000 ft.
+in height, and the Nizva mountain on the southern border of the
+unexplored district of Hazarjirib, north of Semnan, and the
+Shahkuh, between Shahrud and Astarabad, have an elevation
+exceeding 13,000 ft. Beyond Khush Yailak (meaning &ldquo;pleasant
+summer quarters&rdquo;), with an elevation of 10,000 ft., are the
+Kuh i Buhar (8000) and Kuh i Suluk (8000), which latter joins
+the Ala Dagh (11,000).</p>
+
+<p>The northern slopes of the Elburz and the lowlands which lie
+between them and the Caspian, and together form the provinces of
+Gilan, Mazandaran and Astarabad, are covered with dense forest
+and traversed by hundreds (Persian writers say 1362) of perennial
+rivers and streams. The breadth of the lowlands between the
+foot of the hills and the sea is from 2 to 25 m., the greatest breadth
+being in the meridian of Resht in Gilan, and in the districts of
+Amol, Sari and Barfurush in Mazandaran. The inner slopes and
+ranges of the Elburz south of the principal watershed, generally
+the central one of the three principal ranges which are outside of
+the fertilizing influence of the moisture brought from the sea,
+have little or no natural vegetation, and those farthest south are,
+excepting a few stunted cypresses, completely arid and bare.</p>
+
+<p>&ldquo;North of the principal watershed forest trees and general
+verdure refresh the eye. Gurgling water, strips of sward and tall
+forest trees, backed by green hills, make a scene completely unlike
+the usual monotony of Persian landscape. The forest scenery
+much resembles that of England, with fine oaks and greensward.
+South of the watershed the whole aspect of the landscape is as
+hideous and disappointing as scenery in Afghanistan. Ridge after
+ridge of bare hill and curtain behind curtain of serrated mountain,
+certainly sometimes of charming greys and blues, but still all bare
+and naked, rugged and arid&rdquo; (&ldquo;Beresford Lovett, <i>Proc. R.G.S.</i>,
+Feb. 1883).</p>
+
+<p>The higher ranges of the Elburz are snow-capped for the
+greater part of the year, and some, which are not exposed to the
+refracted heat from the arid districts of inner Persia, are rarely
+without snow. Water is plentiful in the Elburz, and situated in
+well-watered valleys and gorges are innumerable flourishing
+villages, embosomed in gardens and orchards, with extensive
+cultivated fields and meadows, and at higher altitudes small
+plateaus, under snow until March or April, afford cool camping
+grounds to the nomads of the plains, and luxuriant grazing to
+their sheep and cattle during the summer.</p>
+<div class="author">(A. H.-S.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELCHE,<a name="ar45" id="ar45"></a></span> a town of eastern Spain, in the province of Alicante,
+on the river Vinalapo. Pop. (1900) 27,308. Elche is the meeting-place
+of three railways, from Novelda, Alicante and Murcia.
+It contains no building of high architectural merit, except,
+perhaps, the collegiate church of Santa Maria, with its lofty
+blue-tiled dome and fine west doorway. But the costume and
+physiognomy of the inhabitants, the narrow streets and flat-roofed,
+whitewashed houses, and more than all, the thousands
+of palm-trees in its gardens and fields, give the place a strikingly
+Oriental aspect, and render it unique among the cities of Spain.
+The cultivation of the palm is indeed the principal occupation;
+and though the dates are inferior to those of the Barbary States,
+upwards of 22,500 tons are annually exported. The blanched
+fronds are also sold in large quantities for the processions of
+Palm Sunday, and after they have received the blessing of the
+priest they are regarded throughout Spain as certain defences
+against lightning. Other thriving local industries include the
+manufacture of oil, soap, flour, leather, alcohol and esparto
+grass rugs. The harbour of Elche is Santa Pola (pop. 4100),
+situated 6 m. E.S.E., where the Vinalapo enters the Mediterranean,
+after forming the wide lagoon known as the Albufera de Elche.</p>
+
+<p>Elche is usually identified with the Iberian <i>Helike</i>, afterwards
+the Roman colony of <i>Ilici</i> or <i>Illici</i>. From the 8th century to
+the 13th it was held by the Moors, who finally failed to recapture
+it from the Spaniards in 1332.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELCHINGEN,<a name="ar46" id="ar46"></a></span> a village of Germany, in the kingdom of Bavaria,
+not far from the Danube, 5 m. N.E. from Ulm. Here, on the
+14th of October 1805, the Austrians under Laudon were
+<span class="pagenum"><a name="page165" id="page165"></a>165</span>
+defeated by the French under Ney, who by taking the bridge
+decided the day and gained for himself the title of duke of
+Elchingen.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELDAD BEN MA&#7716;LI,<a name="ar47" id="ar47"></a></span> also surnamed had-Dani, Abu-Dani,
+David-had-Dani, or the Danite, Jewish traveller, was the supposed
+author of a Jewish travel-narrative of the 9th century
+<span class="scs">A.D.</span>, which enjoyed great authority in the middle ages, especially
+on the question of the Lost Ten Tribes. Eldad first set out to
+visit his Hebrew brethren in Africa and Asia. His vessel was
+wrecked, and he fell into the hands of cannibals; but he was
+saved by his leanness, and by the opportune invasion of a neighbouring
+tribe. After spending four years with his new captors,
+he was ransomed by a fellow-countryman, a merchant of the
+tribe of Issachar. He then (according to his highly fabulous
+narrative) visited the territory of Issachar, in the mountains
+of Media and Persia; he also describes the abodes of Zabulon,
+on the &ldquo;other side&rdquo; of the Paran Mountains, extending to
+Armenia and the Euphrates; of Reuben, on another side of the
+same mountains; of Ephraim and Half Manasseh, in Arabia,
+not far from Mecca; and of Simeon and the other Half of
+Manasseh, in Chorazin, six months&rsquo; journey from Jerusalem.
+Dan, he declares, sooner than join in Jeroboam&rsquo;s scheme of an
+Israelite war against Judah, had migrated to Cush, and finally,
+with the help of Naphthali, Asher and Gad, had founded an
+independent Jewish kingdom in the Gold Land of Havila, beyond
+Abyssinia. The tribe of Levi had also been miraculously guided,
+from near Babylon, to Havila, where they were enclosed and
+protected by the mystic river Sambation or Sabbation, which
+on the Sabbath, though calm, was veiled in impenetrable mist,
+while on other days it ran with a fierce untraversable current of
+stones and sand.</p>
+
+<p>Apart from these tales, we have the genuine Eldad, a celebrated
+Jewish traveller and philologist; who flourished <i>c.</i> <span class="scs">A.D.</span> 830-890;
+to whom the work above noticed is ascribed; who was a native
+either of S. Arabia, Palestine or Media; who journeyed in Egypt,
+Mesopotamia, North Africa, and Spain; who spent several
+years at Kairawan in Tunis; who died on a visit to Cordova,
+and whose authority, as to the lost tribes, is supported by a
+great Hebrew doctor of his own time, &#7826;ema&#7717; Gaon, the rector
+of the Academy at Sura (<span class="scs">A.D.</span> 889-898). It is possible that a
+certain relationship exists (as suggested by Epstein and supported
+by D.H. Müller) between the famous apocryphal <i>Letter of
+Prester John</i> (of <i>c.</i> <span class="scs">A.D.</span> 1165) and the narrative of Eldad; but
+the affinity is not close. Eldad is quoted as an authority on
+linguistic difficulties by the leading medieval Jewish grammarians
+and lexicographers.</p>
+
+<div class="condensed">
+<p>The work ascribed to Eldad is in Hebrew, divided into six chapters,
+probably abbreviated from the original text. The first edition
+appeared at Mantua about 1480; the second at Constantinople in
+1516; this was reprinted at Venice in 1544 and 1605, and at Jessnitz
+in 1722. A Latin version by Gilb. Génébrard was published at Paris
+in 1563, under the title of <i>Eldad Danius ... de Judaeis clausis
+eorumque in Aethiopia ... imperio</i>, and was afterwards incorporated
+in the translator&rsquo;s <i>Chronologia Hebraeorum</i> of 1584; a German version
+appeared at Prague in 1695, and another at Jessnitz in 1723.
+In 1838 E. Carmoly edited and translated a fuller recension which
+he had found in a MS. from the library of Eliezer Ben Hasan, forwarded
+to him by David Zabach of Morocco (see <i>Relation d&rsquo;Eldad le
+Danite</i>, Paris, 1838). Both forms are printed by Dr Jellinek in his
+<i>Bet-ha-Midrasch</i>, vols. ii. p. 102, &amp;c., and iii. p. 6, &amp;c. (Leipzig, 1853-1855).
+See also Bartolocci, <i>Bibliotheca magna Rabbinica</i>, i. 101-130;
+Fürst, <i>Bibliotheca Judaica</i>, i. 30, &amp;c.; Hirsch Graetz, <i>Geschichte der
+Juden</i> (3rd ed., Leipzig, 1895), v. 239-244; Rossi, <i>Dizionario degli
+Ebrei</i>; Steinschneider, <i>Cat. librorum Hebraeorum in bibliotheca
+Bodleiana</i>, cols. 923-925; Kitto&rsquo;s <i>Biblical Cyclopaedia</i> (3rd edition,
+<i>sub nomine</i>); Abr. Epstein, <i>Eldad ha-Dani</i> (Pressburg, 1891);
+D.H. Müller, &ldquo;Die Recensionen und Versionen des Eldad had-Dani,&rdquo;
+in <i>Denkschriften d. Wiener Akad.</i> (Phil.-Hist. Cl.), vol. xli. (1892),
+pp. 1-80.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELDER<a name="ar48" id="ar48"></a></span> (Gr. <span class="grk" title="presbuteros">&#960;&#961;&#949;&#963;&#946;&#973;&#964;&#949;&#961;&#959;&#962;</span>), the name given at different times
+to a ruler or officer in certain political and ecclesiastical systems
+of government.</p>
+
+<p>1. The office of elder is in its origin political and is a relic of
+the old patriarchal system. The unit of primitive society is
+always the family; the only tie that binds men together is that
+of kinship. &ldquo;The eldest male parent,&rdquo; to quote Sir Henry
+Maine,<a name="fa1d" id="fa1d" href="#ft1d"><span class="sp">1</span></a> &ldquo;is absolutely supreme in his household. His dominion
+extends to life and death and is as unqualified over his children
+and their houses as over his slaves.&rdquo; The tribe, which is a later
+development, is always an aggregate of families or clans, not a
+collection of individuals. &ldquo;The union of several clans for common
+political action,&rdquo; as Robertson Smith says, &ldquo;was produced by
+the pressure of practical necessity, and always tended towards
+dissolution when this practical pressure was withdrawn. The
+only organization for common action was that the leading men
+of the clans consulted together in time of need, and their influence
+led the masses with them. Out of these conferences arose the
+senates of elders found in the ancient states of Semitic and Aryan
+antiquity alike.&rdquo;<a name="fa2d" id="fa2d" href="#ft2d"><span class="sp">2</span></a> With the development of civilization there
+came a time when age ceased to be an indispensable condition
+of leadership. The old title was, however, generally retained,
+<i>e.g.</i> the <span class="grk" title="gerontes">&#947;&#941;&#961;&#959;&#957;&#964;&#949;&#962;</span> so often mentioned in Homer, the <span class="grk" title="gerousia">&#947;&#949;&#961;&#959;&#965;&#963;&#943;&#945;</span> of
+the Dorian states, the <i>senatus</i> and the <i>patres conscripti</i> of Rome,
+the sheikh or elder of Arabia, the alderman of an English borough,
+the seigneur (Lat. <i>senior</i>) of feudal France.</p>
+
+<p>2. It was through the influence of Judaism that the originally
+political office of elder passed over into the Christian Church
+and became ecclesiastical. The Israelites inherited the office
+from their Semitic ancestors (just as did the Moabites and the
+Midianites, of whose elders we read in Numbers xxii. 7), and traces
+of it are found throughout their history. Mention is made in
+Judges viii. 14 of the elders of Succoth whom &ldquo;Gideon taught
+with thorns of the wilderness and with briers.&rdquo; It was to the
+elders of Israel in Egypt that Moses communicated the plan of
+Yahweh for the redemption of the people (Exodus iii. 16).
+During the sojourn in the wilderness the elders were the intermediaries
+between Moses and the people, and it was out of the
+ranks of these elders that Moses chose a council of seventy &ldquo;to
+bear with him the burden of the people&rdquo; (Numbers xi. 16).
+The elders were the governors of the people and the administrators
+of justice. There are frequent references to their work in the
+latter capacity in the book of Deuteronomy, especially in
+relation to the following crimes&mdash;the disobedience of sons;
+slander against a wife; the refusal of levirate marriage; manslaughter;
+and blood-revenge. Their powers were gradually
+curtailed by (<i>a</i>) the development of the monarchy, to which of
+course they were in subjection, and which became the court of
+appeal in questions of law;<a name="fa3d" id="fa3d" href="#ft3d"><span class="sp">3</span></a> (<i>b</i>) the appointment of special
+judges, probably chosen from amongst the elders themselves,
+though their appointment meant the loss of privilege to the
+general body; (<i>c</i>) the rise of the priestly orders, which usurped
+many of the prerogatives that originally belonged to the elders.
+But in spite of the rise of new authorities, the elders still retained
+a large amount of influence. We hear of them frequently in the
+Persian, Greek and Roman periods. In the New Testament
+the members of the Sanhedrin in Jerusalem are very frequently
+termed &ldquo;elders&rdquo; or <span class="grk" title="presbyteroi">&#960;&#961;&#949;&#963;&#946;&#973;&#964;&#949;&#961;&#959;&#953;</span>, and from them the name was
+taken over by the Church.</p>
+
+<p>3. The name &ldquo;elder&rdquo; was probably the first title bestowed
+upon the officers of the Christian Church&mdash;since the word deacon
+does not occur in connexion with the appointment of the Seven
+in Acts vi. Its universal adoption is due not only to its currency
+amongst the Jews, but also to the fact that it was frequently
+used as the title of magistrates in the cities and villages of Asia
+Minor. For the history of the office of elder in the early Church
+and the relation between elders and bishops see <span class="sc"><a href="#artlinks">Presbyter</a></span>.</p>
+
+<p>4. In modern times the use of the term is almost entirely
+confined to the Presbyterian church, the officers of which are
+always called elders. According to the Presbyterian theory of
+church government there are two classes of elders&mdash;&ldquo;teaching
+elders,&rdquo; or those specially set apart to the pastoral office, and
+&ldquo;ruling elders,&rdquo; who are laymen, chosen generally by the congregation
+and set apart by ordination to be associated with the
+pastor in the oversight and government of the church. When
+<span class="pagenum"><a name="page166" id="page166"></a>166</span>
+the word is used without any qualification it is understood to
+apply to the latter class alone. For an account of the duties,
+qualifications and powers of elders in the Presbyterian Church
+see <span class="sc"><a href="#artlinks">Presbyterianism</a></span>.</p>
+
+<div class="condensed">
+<p>See W.R. Smith, <i>History of the Semites</i>; H. Maine, <i>Ancient Law</i>;
+E. Schürer, <i>The Jewish People in the Time of Christ</i>; J. Wellhausen,
+<i>History of Israel and Judah</i>; G.A. Deissmann, <i>Bible Studies</i>, p. 154.</p>
+</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1d" id="ft1d" href="#fa1d"><span class="fn">1</span></a> <i>Ancient Law</i>, p. 126.</p>
+
+<p><a name="ft2d" id="ft2d" href="#fa2d"><span class="fn">2</span></a> <i>Religion of the Semites</i>, p. 34.</p>
+
+<p><a name="ft3d" id="ft3d" href="#fa3d"><span class="fn">3</span></a> There is a hint at this even in the Pentateuch, &ldquo;every great
+matter they shall bring unto thee, but every small matter they shall
+judge themselves.&rdquo;</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELDER<a name="ar49" id="ar49"></a></span> (O. Eng. <i>ellarn</i>; Ger. <i>Holunder</i>; Fr. <i>sureau</i>), the
+popular designation of the deciduous shrubs and trees constituting
+the genus <i>Sambucus</i> of the natural order Caprifoliaceae.
+The Common Elder, <i>S. nigra</i>, the bourtree of Scotland, is found
+in Europe, the north of Africa, Western Asia, the Caucasus, and
+Southern Siberia; in sheltered spots it attains a height of over
+20 ft. The bark is smooth; the shoots are stout and angular,
+and the leaves glabrous, pinnate, with oval or elliptical leaflets.
+The flowers, which form dense flat-topped clusters (corymbose
+cymes), with five main branches, have a cream-coloured, gamopetalous,
+five-lobed corolla, five stamens, and three sessile
+stigmas; the berries are purplish-black, globular and three- or
+four-seeded, and ripen about September. The elder thrives best
+in moist, well-drained situations, but can be grown in a great
+diversity of soils. It grows readily from young shoots, which
+after a year are fit for transplantation. It is found useful for
+making screen-fences in bleak, exposed situations, and also as
+a shelter for other shrubs in the outskirts of plantations. By
+clipping two or three times a year, it may be made close and
+compact in growth. The young trees furnish a brittle wood,
+containing much pith; the wood of old trees is white, hard and
+close-grained, polishes well, and is employed for shoemakers&rsquo; pegs,
+combs, skewers, mathematical instruments and turned articles.
+Young elder twigs deprived of pith have from very early times
+been in request for making whistles, popguns and other toys.</p>
+
+<p>The elder was known to the ancients for its medicinal properties,
+and in England the inner bark was formerly administered as a
+cathartic. The flowers (<i>sambuci flores</i>) contain a volatile oil, and
+serve for the distillation of elder-flower water (<i>aqua sambuci</i>),
+used in confectionery, perfumes and lotions. The leaves of the
+elder are employed to impart a green colour to fat and oil (<i>unguentum
+sambuci foliorum</i> and <i>oleum viride</i>), and the berries for
+making wine, a common adulterant of port. The leaves and
+bark emit a sickly odour, believed to be repugnant to insects.
+Christopher Gullet (<i>Phil. Trans.</i>, 1772, lxii. p. 348) recommends
+that cabbages, turnips, wheat and fruit trees, to preserve them
+from caterpillars, flies and blight, should be whipped with twigs
+of young elder. According to German folklore, the hat must be
+doffed in the presence of the elder-tree; and in certain of the
+English midland counties a belief was once prevalent that the
+cross of Christ was made from its wood, which should therefore
+never be used as fuel, or treated with disrespect (see <i>Quart. Rev.</i>
+cxiv. 233). It was, however, a common medieval tradition,
+alluded to by Ben Jonson, Shakespeare and other writers, that the
+elder was the tree on which Judas hanged himself; and on this
+account, probably, to be crowned with elder was in olden times
+accounted a disgrace. In Cymbeline (act iv. s. 2) &ldquo;the stinking
+elder&rdquo; is mentioned as a symbol of grief. In Denmark the tree is
+supposed by the superstitious to be under the protection of the
+&ldquo;Elder-mother&rdquo;: its flowers may not be gathered without her
+leave; its wood must not be employed for any household
+furniture; and a child sleeping in an elder-wood cradle would
+certainly be strangled by the Elder-mother.</p>
+
+<p>Several varieties are known in cultivation: <i>aurea</i>, golden elder,
+has golden-yellow leaves; <i>laciniata</i>, parsley-leaved elder, has the
+leaflets cut into fine segments; <i>rotundifolia</i> has rounded leaflets;
+forms also occur with variegated white and yellow leaves, and
+<i>virescens</i> is a variety having white bark and green-coloured berries.
+The scarlet-berried elder, <i>S. racemosa</i>, is the handsomest species
+of the genus. It is a native of various parts of Europe, growing in
+Britain to a height of over 15 ft., but often producing no fruit.
+The dwarf elder or Danewort (supposed to have been introduced
+into Britain by the Danes), <i>S. Ebulus</i>, a common European
+species, reaches a height of about 6 ft. Its cyme is hairy, has
+three principal branches, and is smaller than that of <i>S. nigra</i>; the
+flowers are white tipped with pink. All parts of the plant are
+cathartic and emetic.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELDON, JOHN SCOTT,<a name="ar50" id="ar50"></a></span> 1st <span class="sc">Earl of</span> (1751-1838), lord high
+chancellor of England, was born at Newcastle on the 4th of June
+1751. His grandfather, William Scott of Sandgate, a suburb of
+Newcastle, was clerk to a &ldquo;fitter&rdquo;&mdash;a sort of water-carrier and
+broker of coals. His father, whose name also was William,
+began life as an apprentice to a fitter, in which service he obtained
+the freedom of Newcastle, becoming a member of the gild of
+Hoastmen (coal-fitters); later in life he became a principal in the
+business, and attained a respectable position as a merchant in
+Newcastle, accumulating property worth nearly £20,000.</p>
+
+<p>John Scott was educated at the grammar school of his native
+town. He was not remarkable at school for application to his
+studies, though his wonderful memory enabled him to make good
+progress in them; he frequently played truant and was whipped
+for it, robbed orchards, and indulged in other questionable schoolboy
+freaks; nor did he always come out of his scrapes with
+honour and a character for truthfulness. When he had finished
+his education at the grammar school, his father thought of
+apprenticing him to his own business, to which an elder brother
+Henry had already devoted himself; and it was only through
+the interference of his elder brother William (afterwards Lord
+Stowell, <i>q.v.</i>), who had already obtained a fellowship at University
+College, Oxford, that it was ultimately resolved that he should
+continue the prosecution of his studies. Accordingly, in 1766,
+John Scott entered University College with the view of taking
+holy orders and obtaining a college living. In the year following
+he obtained a fellowship, graduated B.A. in 1770, and in 1771 won
+the prize for the English essay, the only university prize open in
+his time for general competition.</p>
+
+<p>His wife was the eldest daughter of Aubone Surtees, a Newcastle
+banker. The Surtees family objected to the match, and
+attempted to prevent it; but a strong attachment had sprung
+up between them. On the 18th November 1772 Scott, with the
+aid of a ladder and an old friend, carried off the lady from her
+father&rsquo;s house in the Sandhill, across the border to Blackshiels,
+in Scotland, where they were married. The father of the bridegroom
+objected not to his son&rsquo;s choice, but to the time he chose to
+marry; for it was a blight on his son&rsquo;s prospects, depriving him
+of his fellowship and his chance of church preferment. But
+while the bride&rsquo;s family refused to hold intercourse with the pair,
+Mr Scott, like a prudent man and an affectionate father, set
+himself to make the best of a bad matter, and received them
+kindly, settling on his son £2000. John returned with his wife
+to Oxford, and continued to hold his fellowship for what is called
+the year of grace given after marriage, and added to his income
+by acting as a private tutor. After a time Mr Surtees was
+reconciled with his daughter, and made a liberal settlement
+on her.</p>
+
+<p>John Scott&rsquo;s year of grace closed without any college living
+falling vacant; and with his fellowship he gave up the church
+and turned to the study of law. He became a student at the
+Middle Temple in January 1773. In 1776 he was called to the
+bar, intending at first to establish himself as an advocate in his
+native town, a scheme which his early success led him to abandon,
+and he soon settled to the practice of his profession in London,
+and on the northern circuit. In the autumn of the year in which
+he was called to the bar his father died, leaving him a legacy of
+£1000 over and above the £2000 previously settled on him.</p>
+
+<p>In his second year at the bar his prospects began to brighten.
+His brother William, who by this time held the Camden professorship
+of ancient history, and enjoyed an extensive acquaintance
+with men of eminence in London, was in a position materially
+to advance his interests. Among his friends was the notorious
+Andrew Bowes of Gibside, to the patronage of whose house
+the rise of the Scott family was largely owing. Bowes having
+contested Newcastle and lost it, presented an election petition
+against the return of his opponent. Young Scott was retained as
+junior counsel in the case, and though he lost the petition he did
+not fail to improve the opportunity which it afforded for displaying
+his talents. This engagement, in the commencement of his
+<span class="pagenum"><a name="page167" id="page167"></a>167</span>
+second year at the bar, and the dropping in of occasional fees,
+must have raised his hopes; and he now abandoned the scheme
+of becoming a provincial barrister. A year or two of dull drudgery
+and few fees followed, and he began to be much depressed. But
+in 1780 we find his prospects suddenly improved, by his appearance
+in the case of <i>Ackroyd</i> v. <i>Smithson</i>, which became a leading
+case settling a rule of law; and young Scott, having lost his
+point in the inferior court, insisted on arguing it, on appeal,
+against the opinion of his clients, and carried it before Lord
+Thurlow, whose favourable consideration he won by his able
+argument. The same year Bowes again retained him in an
+election petition; and in the year following Scott greatly
+increased his reputation by his appearance as leading counsel in
+the Clitheroe election petition. From this time his success was
+certain. In 1782 he obtained a silk gown, and was so far cured
+of his early modesty that he declined accepting the king&rsquo;s
+counselship if precedence over him were given to his junior,
+Thomas (afterwards Lord) Erskine, though the latter was the son
+of a peer and a most accomplished orator. He was now on the
+high way to fortune. His health, which had hitherto been but
+indifferent, strengthened with the demands made upon it; his
+talents, his power of endurance, and his ambition all expanded
+together. He enjoyed a considerable practice in the northern
+part of his circuit, before parliamentary committees and at the
+chancery bar. By 1787 his practice at the equity bar had so far
+increased that he was obliged to give up the eastern half of his
+circuit (which embraced six counties) and attend it only at
+Lancaster.</p>
+
+<p>In 1782 he entered parliament for Lord Weymouth&rsquo;s close
+borough of Weobley, which Lord Thurlow obtained for him
+without solicitation. In parliament he gave a general and
+independent support to Pitt. His first parliamentary speeches
+were directed against Fox&rsquo;s India Bill. They were unsuccessful.
+In one he aimed at being brilliant; and becoming merely
+laboured and pedantic, he was covered with ridicule by Sheridan,
+from whom he received a lesson which he did not fail to turn
+to account. In 1788 he was appointed solicitor-general, and
+was knighted, and at the close of this year he attracted attention
+by his speeches in support of Pitt&rsquo;s resolutions on the state of
+the king (George III., who then laboured under a mental malady)
+and the delegation of his authority. It is said that he drew the
+Regency Bill, which was introduced in 1789. In 1793 Sir John
+Scott was promoted to the office of attorney-general, in which
+it fell to him to conduct the memorable prosecutions for high
+treason against British sympathizers with French republicanism,&mdash;amongst
+others, against the celebrated Horne Tooke. These
+prosecutions, in most cases, were no doubt instigated by Sir
+John Scott, and were the most important proceedings in which
+he was ever professionally engaged. He has left on record, in
+his <i>Anecdote Book</i>, a defence of his conduct in regard to them.
+A full account of the principal trials, and of the various legislative
+measures for repressing the expressions of popular opinion for
+which he was more or less responsible, will be found in Twiss&rsquo;s
+<i>Public and Private Life of the Lord Chancellor Eldon</i>, and in the
+<i>Lives of the Lord Chancellors</i>, by Lord Campbell.</p>
+
+<p>In 1799 the office of chief justice of the Court of Common
+Pleas falling vacant, Sir John Scott&rsquo;s claim to it was not overlooked;
+and after seventeen years&rsquo; service in the Lower House,
+he entered the House of Peers as Baron Eldon. In February
+1801 the ministry of Pitt was succeeded by that of Addington,
+and the chief justice now ascended the woolsack. The chancellorship
+was given to him professedly on account of his notorious
+anti-Catholic zeal. From the peace of Amiens (1802) till 1804
+Lord Eldon appears to have interfered little in politics. In the
+latter year we find him conducting the negotiations which
+resulted in the dismissal of Addington and the recall of Pitt to
+office as prime minister. Lord Eldon was continued in office
+as chancellor under Pitt; but the new administration was of
+short duration, for on the 23rd of January 1806 Pitt died, worn
+out with the anxieties of office, and his ministry was succeeded
+by a coalition, under Lord Grenville. The death of Fox, who
+became foreign secretary and leader of the House of Commons,
+soon, however, broke up the Grenville administration; and in
+the spring of 1807 Lord Eldon once more, under Lord Liverpool&rsquo;s
+administration, returned to the woolsack, which, from that
+time, he continued to occupy for about twenty years, swaying
+the cabinet, and being in all but name prime minister of England.
+It was not till April 1827, when the premiership, vacant through
+the paralysis of Lord Liverpool, fell to Canning, the chief advocate
+of Roman Catholic emancipation, that Lord Eldon, in the
+seventy-sixth year of his age, finally resigned the chancellorship.
+When, after the two short administrations of Canning and
+Goderich, it fell to the duke of Wellington to construct a cabinet,
+Lord Eldon expected to be included, if not as chancellor, at least
+in some important office, but he was overlooked, at which he
+was much chagrined. Notwithstanding his frequent protests
+that he did not covet power, but longed for retirement, we find
+him again, so late as 1835, within three years of his death, in
+hopes of office under Peel. He spoke in parliament for the last
+time in July 1834.</p>
+
+<p>In 1821 Lord Eldon had been created Viscount Encombe and
+earl of Eldon by George IV., whom he managed to conciliate,
+partly, no doubt, by espousing his cause against his wife, whose
+advocate he had formerly been, and partly through his reputation
+for zeal against the Roman Catholics. In the same year his
+brother William, who from 1798 had filled the office of judge
+of the High Court of Admiralty, was raised to the peerage under
+the title of Lord Stowell.</p>
+
+<p>Lord Eldon&rsquo;s wife, his dear &ldquo;Bessy,&rdquo; his love for whom is a
+beautiful feature in his life, died before him, on the 28th of June
+1831. By nature she was of simple character, and by habits
+acquired during the early portion of her husband&rsquo;s career almost
+a recluse. Two of their sons reached maturity&mdash;John, who
+died in 1805, and William Henry John, who died unmarried
+in 1832. Lord Eldon himself survived almost all his immediate
+relations. His brother William died in 1836. He himself died
+in London on the 13th of January 1838, leaving behind him two
+daughters, Lady Frances Bankes and Lady Elizabeth Repton,
+and a grandson John (1805-1854), who succeeded him as second
+earl, the title subsequently passing to the latter&rsquo;s son John
+(b. 1846).</p>
+
+<p>Lord Eldon was no legislator&mdash;his one aim in politics was to
+keep in office, and maintain things as he found them; and almost
+the only laws he helped to pass were laws for popular coercion.
+For nearly forty years he fought against every improvement in
+law, or in the constitution&mdash;calling God to witness, on the smallest
+proposal of reform, that he foresaw from it the downfall of his
+country. Without any political principles, properly so called,
+and without interest in or knowledge of foreign affairs, he maintained
+himself and his party in power for an unprecedented
+period by his great tact, and in virtue of his two great political
+properties&mdash;of zeal against every species of reform, and zeal
+against the Roman Catholics. To pass from his political to his
+judicial character is to shift to ground on which his greatness
+is universally acknowledged. His judgments, which have
+received as much praise for their accuracy as abuse for their
+clumsiness and uncouthness, fill a small library. But though
+intimately acquainted with every nook and cranny of the English
+law, he never carried his studies into foreign fields, from which
+to enrich our legal literature; and it must be added that against
+the excellence of his judgments, in too many cases, must be set
+off the hardships, worse than injustice, that arose from his
+protracted delays in pronouncing them. A consummate judge
+and the narrowest of politicians, he was doubt on the bench,
+and promptness itself in the political arena. For literature, as
+for art, he had no feeling. What intervals of leisure he enjoyed
+from the cares of office he filled up with newspapers and the
+gossip of old cronies. Nor were his intimate associates men of
+refinement and taste; they were rather good fellows who quietly
+enjoyed a good bottle and a joke; he uniformly avoided encounters
+of wit with his equals. He is said to have been
+parsimonious, and certainly he was quicker to receive than to
+reciprocate hospitalities; but his mean establishment and mode
+of life are explained by the retired habits of his wife, and her
+<span class="pagenum"><a name="page168" id="page168"></a>168</span>
+dislike of company. His manners were very winning and courtly,
+and in the circle of his immediate relatives he is said to have
+always been lovable and beloved.</p>
+
+<p>&ldquo;In his person,&rdquo; says Lord Campbell, &ldquo;Lord Eldon was about
+the middle size, his figure light and athletic, his features regular
+and handsome, his eye bright and full, his smile remarkably
+benevolent, and his whole appearance prepossessing. The
+advance of years rather increased than detracted from these
+personal advantages. As he sat on the judgment-seat, &lsquo;the deep
+thought betrayed in his furrowed brow&mdash;the large eyebrows,
+overhanging eyes that seemed to regard more what was taking
+place within than around him&mdash;his calmness, that would have
+assumed a character of sternness but for its perfect placidity&mdash;his
+dignity, repose and venerable age, tended at once to win
+confidence and to inspire respect&rsquo; (Townsend). He had a voice
+both sweet and deep-toned, and its effect was not injured by his
+Northumbrian burr, which, though strong, was entirely free from
+harshness and vulgarity.&rdquo;</p>
+
+<div class="condensed">
+<p><span class="sc">Authorities.</span>&mdash;Horace Twiss, <i>Life of Lord Chancellor Eldon</i>
+(1844); W.E. Surtees, <i>Sketch of the Lives of Lords Stowell and
+Eldon</i> (1846); Lord Campbell, <i>Lives of the Chancellors</i>; W.C.
+Townsend, <i>Lives of Twelve Eminent Judges</i> (1846); <i>Greville Memoirs</i>.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">EL DORADO<a name="ar51" id="ar51"></a></span> (Span. &ldquo;the gilded one&rdquo;), a name applied, first,
+to the king or chief priest of a South American tribe who was said
+to cover himself with gold dust at a yearly religious festival held
+near Santa Fé de Bogotá; next, to a legendary city called Manoa
+or Omoa; and lastly, to a mythical country in which gold and
+precious stones were found in fabulous abundance. The legend,
+which has never been traced to its ultimate source, had many
+variants, especially as regards the situation attributed to Manoa.
+It induced many Spanish explorers to lead expeditions in search
+of treasure, but all failed. Among the most famous were the
+expedition undertaken by Diego de Ordaz, whose lieutenant
+Martinez claimed to have been rescued from shipwreck, conveyed
+inland, and entertained at Omoa by &ldquo;El Dorado&rdquo; himself (1531);
+and the journeys of Orellana (1540-1541), who passed down the
+Rio Napo to the valley of the Amazon; that of Philip von Hutten
+(1541-1545), who led an exploring party from Coro on the coast of
+Caracas; and of Gonzalo Ximenes de Quesada (1569), who started
+from Santa Fé de Bogotá. Sir Walter Raleigh, who resumed the
+search in 1595, described Manoa as a city on Lake Parimá in
+Guiana. This lake was marked on English and other maps until
+its existence was disproved by A. von Humboldt (1769-1859).
+Meanwhile the name of El Dorado came to be used metaphorically
+of any place where wealth could be rapidly acquired. It was
+given to a county in California, and to towns and cities in various
+states. In literature frequent allusion is made to the legend,
+perhaps the best-known references being those in Milton&rsquo;s
+<i>Paradise Lost</i> (vi. 411) and Voltaire&rsquo;s <i>Candide</i> (chs. 18, 19).</p>
+
+<div class="condensed">
+<p>See A.F.A. Bandelier, <i>The Gilded Man, El Dorado</i> (New York,
+1893).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELDUAYEN, JOSÉ DE,<a name="ar52" id="ar52"></a></span> 1st Marquis del Pazo de la Merced
+(1823-1898), Spanish politician, was born in Madrid on the
+22nd of June 1823. He was educated in the capital, took the
+degree of civil engineer, and as such directed important works
+in Asturias and Galicia, entered the Cortes in 1856 as deputy
+for Vigo, and sat in all the parliaments until 1867 as member of
+the Union Liberal with Marshal O&rsquo;Donnell. He attacked the
+Miraflores cabinet in 1864, and became under-secretary of the
+home office when Canovas was minister in 1865. He was made a
+councillor of state in 1866, and in 1868 assisted the other members
+of the Union Liberal in preparing the revolution. In the Cortes
+of 1872 he took much part in financial debates. He accepted
+office as member of the last Sagasta cabinet under King Amadeus.
+On the proclamation of the republic Elduayen very earnestly
+co-operated in the Alphonsist conspiracy, and endeavoured to
+induce the military and politicians to work together. He went
+abroad to meet and accompany the prince after the <i>pronunciamiento</i>
+of Marshal Campos, landed with him at Valencia, was made
+governor of Madrid, a marquis, grand cross of Charles III., and
+minister for the colonies in 1878. He accepted the portfolio of
+foreign affairs in the Canovas cabinet from 1883 to 1885, and was
+made a life senator. He always prided himself on having been
+one of the five members of the Cortes of 1870 who voted for
+Alphonso XII. when that parliament elected Amadeus of Savoy.
+He died at Madrid on the 24th of June 1898.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELEANOR OF AQUITAINE<a name="ar53" id="ar53"></a></span> (<i>c.</i> 1122-1204), wife of the English
+king Henry II., was the daughter and heiress of Duke William X.
+of Aquitaine, whom she succeeded in April 1137. In accordance
+with arrangements made by her father, she at once married
+Prince Louis, the heir to the French crown, and a month later her
+husband became king of France under the title of Louis VII.
+Eleanor bore Louis two daughters but no sons. This was probably
+the reason why their marriage was annulled by mutual consent
+in 1151, but contemporary scandal-mongers attributed the
+separation to the king&rsquo;s jealousy. It was alleged that, while
+accompanying her husband on the Second Crusade (1146-1149),
+Eleanor had been unduly familiar with her uncle, Raymond of
+Antioch. Chronology is against this hypothesis, since Louis and
+she lived on good terms together for two years after the Crusade.
+There is still less ground for the supposition that Henry of Anjou,
+whom she married immediately after the divorce, had been her
+lover before it. This second marriage, with a youth some years
+her junior, was purely political. The duchy of Aquitaine required
+a strong ruler, and the union with Anjou was eminently desirable.
+Louis, who had hoped that Aquitaine would descend to his
+daughters, was mortified and alarmed by the Angevin marriage;
+all the more so when Henry of Anjou succeeded to the English
+crown in 1154. From this event dates the beginning of the
+secular strife between England and France which runs like a red
+thread through medieval history.</p>
+
+<p>Eleanor bore to her second husband five sons and three
+daughters; John, the youngest of their children, was born in
+1167. But her relations with Henry passed gradually through
+indifference to hatred. Henry was an unfaithful husband, and
+Eleanor supported her sons in their great rebellion of 1173.
+Throughout the latter years of the reign she was kept in a sort of
+honourable confinement. It was during her captivity that Henry
+formed his connexion with Rosamond Clifford, the Fair Rosamond
+of romance. Eleanor, therefore, can hardly have been
+responsible for the death of this rival, and the romance of the
+poisoned bowl appears to be an invention of the next century.</p>
+
+<p>Under the rule of Richard and John the queen became a
+political personage of the highest importance. To both her sons
+the popularity which she enjoyed in Aquitaine was most valuable.
+But in other directions also she did good service. She helped to
+frustrate the conspiracy with France which John concocted
+during Richard&rsquo;s captivity. She afterwards reconciled the king
+and the prince, thus saving for John the succession which he had
+forfeited by his misconduct. In 1199 she crushed an Angevin
+rising in favour of John&rsquo;s nephew, Arthur of Brittany. In 1201
+she negotiated a marriage between her grand-daughter, Blanche
+of Castile, and Louis of France, the grandson of her first husband.
+It was through her staunch defence of Mirabeau in Poitou that
+John got possession of his nephew&rsquo;s person. She died on the 1st
+of April 1204, and was buried at Fontevrault. Although a woman
+of strong passions and great abilities she is, historically, less
+important as an individual than as the heiress of Aquitaine, a part
+of which was, through her second marriage, united to England for
+some four hundred years.</p>
+
+<div class="condensed">
+<p>See the chronicles cited for the reigns of Henry II., Richard I.
+and John. Also Sir J.H. Ramsay, <i>Angevin Empire</i> (London, 1903);
+K. Norgate, <i>England under the Angevin Kings</i> (London, 1887);
+and A. Strickland, <i>Lives of the Queens of England</i>, vol. i. (1841).</p>
+</div>
+<div class="author">(H. W. C. D.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELEATIC SCHOOL,<a name="ar54" id="ar54"></a></span> a Greek school of philosophy which came
+into existence towards the end of the 6th century <span class="scs">B.C.</span>, and
+ended with Melissus of Samos (fl. <i>c.</i> 450 <span class="scs">B.C.</span>). It took its
+name from Elea, a Greek city of lower Italy, the home of its
+chief exponents, Parmenides and Zeno. Its foundation is often
+attributed to Xenophanes of Colophon, but, although there is
+much in his speculations which formed part of the later Eleatic
+doctrine, it is probably more correct to regard Parmenides as
+the founder of the school. At all events, it was Parmenides who
+gave it its fullest development. The main doctrines of the
+Eleatics were evolved in opposition, on the one hand, to the
+<span class="pagenum"><a name="page169" id="page169"></a>169</span>
+physical theories of the early physical philosophers who explained
+all existence in terms of primary matter (see <span class="sc"><a href="#artlinks">Ionian School</a></span>),
+and, on the other hand, to the theory of Heraclitus that all
+existence may be summed up as perpetual change. As against
+these theories the Eleatics maintained that the true explanation
+of things lies in the conception of a universal unity of being.
+The senses with their changing and inconsistent reports cannot
+cognize this unity; it is by thought alone that we can pass
+beyond the false appearances of sense and arrive at the knowledge
+of being, at the fundamental truth that &ldquo;the All is One.&rdquo; There
+can be no creation, for being cannot come from not-being; a
+thing cannot arise from that which is different from it. The
+errors of common opinion arise to a great extent from the
+ambiguous use of the verb &ldquo;to be,&rdquo; which may imply existence
+or be merely the copula which connects subject and predicate.</p>
+
+<p>In these main contentions the Eleatic school achieved a real
+advance, and paved the way to the modern conception of metaphysics.
+Xenophanes in the middle of the 6th century had
+made the first great attack on the crude mythology of early Greece,
+including in his onslaught the whole anthropomorphic system
+enshrined in the poems of Homer and Hesiod. In the hands of
+Parmenides this spirit of free thought developed on metaphysical
+lines. Subsequently, whether from the fact that such bold
+speculations were obnoxious to the general sense of propriety
+in Elea, or from the inferiority of its leaders, the school degenerated
+into verbal disputes as to the possibility of motion,
+and similar academic trifling. The best work of the school was
+absorbed in the Platonic metaphysic (see E. Caird, <i>Evolution
+of Theology in the Greek Philosophers</i>, 1904).</p>
+
+<div class="condensed">
+<p>See further the articles on <span class="sc"><a href="#artlinks">Xenophanes</a></span>; <span class="sc"><a href="#artlinks">Parmenides</a></span>; <span class="sc"><a href="#artlinks">Zeno</a></span>
+(of Elea); <span class="sc"><a href="#artlinks">Melissus</a></span>, with the works there quoted; also the histories
+of philosophy by Zeller, Gomperz, Windelband, &amp;c.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECAMPANE<a name="ar55" id="ar55"></a></span> (Med. Lat. <i>Enula Campana</i>), a perennial
+composite plant, the <i>Inula Helenium</i> of botanists, which is
+common in many parts of Britain, and ranges throughout
+central and southern Europe, and in Asia as far eastwards as
+the Himalayas. It is a rather rigid herb, the stem of which
+attains a height of from 3 to 5 ft.; the leaves are large and
+toothed, the lower ones stalked, the rest embracing the stem; the
+flowers are yellow, 2 in. broad, and have many rays, each three-notched
+at the extremity. The root is thick, branching and
+mucilaginous, and has a warm, bitter taste and a camphoraceous
+odour. For medicinal purposes it should be procured from
+plants not more than two or three years old. Besides <i>inulin</i>,
+C<span class="su">12</span>H<span class="su">20</span>O<span class="su">10</span>, a body isomeric with starch, the root contains <i>helenin</i>,
+C<span class="su">6</span>H<span class="su">8</span>O, a stearoptene, which may be prepared in white acicular
+crystals, insoluble in water, but freely soluble in alcohol. When
+freed from the accompanying inula-camphor by repeated
+crystallization from alcohol, helenin melts at 110° C. By the
+ancients the root was employed both as a medicine and as a
+condiment, and in England it was formerly in great repute as
+an aromatic tonic and stimulant of the secretory organs. &ldquo;The
+fresh roots of elecampane preserved with sugar, or made into a
+syrup or conserve,&rdquo; are recommended by John Parkinson in
+his <i>Theatrum Botanicum</i> as &ldquo;very effectual to warm a cold and
+windy stomack, and the pricking and stitches therein or in the
+sides caused by the Spleene, and to helpe the cough, shortnesse
+of breath, and wheesing in the Lungs.&rdquo; As a drug, however,
+the root is now seldom resorted to except in veterinary practice,
+though it is undoubtedly possessed of antiseptic properties. In
+France and Switzerland it is used in the manufacture of absinthe.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTION<a name="ar56" id="ar56"></a></span> (from Lat. <i>eligere</i>, to pick out), the method by
+which a choice or selection is made by a constituent body (the
+electors or electorate) of some person to fill a certain office or
+dignity. The procedure itself is called an election. Election,
+as a special form of selection, is naturally a loose term covering
+many subjects; but except in the theological sense (the doctrine
+of election), as employed by Calvin and others, for the choice
+by God of His &ldquo;elect,&rdquo; the legal sense (see <span class="sc"><a href="#ar57">Election</a></span>, <i>in law</i>,
+below), and occasionally as a synonym for personal choice (one&rsquo;s
+own &ldquo;election&rdquo;), it is confined to the selection by the preponderating
+vote of some properly constituted body of electors
+of one of two or more candidates, sometimes for admission only
+to some private social position (as in a club), but more particularly
+in connexion with public representative positions in political
+government. It is thus distinguished from arbitrary methods
+of appointment, either where the right of nominating rests in an
+individual, or where pure chance (such as selection by lot)
+dictates the result. The part played by different forms of
+election in history is alluded to in numerous articles in this work,
+dealing with various countries and various subjects. It is only
+necessary here to consider certain important features in the
+elections, as ordinarily understood, namely, the exercise of the
+right of voting for political and municipal offices in the United
+Kingdom and America. See also the articles <span class="sc"><a href="#artlinks">Parliament</a></span>;
+<span class="sc"><a href="#artlinks">Representation</a></span>; <span class="sc"><a href="#artlinks">Voting</a></span>; <span class="sc"><a href="#artlinks">Ballot</a></span>, &amp;c., and <span class="sc"><a href="#artlinks">United
+States</a></span>: <i>Political Institutions</i>. For practical details as to the
+conduct of political elections in England reference must be made
+to the various text-books on the subject; the candidate and his
+election agent require to be on their guard against any false
+step which might invalidate his return.</p>
+
+<p><i>Law in the United Kingdom.</i>&mdash;Considerable alterations have
+been made in recent years in the law of Great Britain and Ireland
+relating to the procedure at parliamentary and municipal
+elections, and to election petitions.</p>
+
+<p>As regards parliamentary elections (which may be either the
+&ldquo;general election,&rdquo; after a dissolution of parliament, or &ldquo;by-elections,&rdquo;
+when casual vacancies occur during its continuance),
+the most important of the amending statutes is the Corrupt
+and Illegal Practices Act 1883. This act, and the Parliamentary
+Elections Act 1868, as amended by it, and other enactments
+dealing with corrupt practices, are temporary acts requiring
+annual renewal. As regards municipal elections, the Corrupt
+Practices (Municipal Elections) Act 1872 has been repealed by
+the Municipal Corporations Act 1882 for England, and by the
+Local Government (Ireland) Act 1898 for Ireland. The governing
+enactments for England are now the Municipal Corporations
+Act 1882, part iv., and the Municipal Elections (Corrupt and
+Illegal Practices) Act 1884, the latter annually renewable. The
+provisions of these enactments have been applied with necessary
+modifications to municipal and other local government elections
+in Ireland by orders of the Irish Local Government Board made
+under powers conferred by the Local Government (Ireland) Act
+1898. In Scotland the law regulating municipal and other
+local government elections is now to be found in the Elections
+(Scotland) (Corrupt and Illegal Practices) Act 1890.</p>
+
+<p>The alterations in the law have been in the direction of
+greater strictness in regard to the conduct of elections, and
+increased control in the public interest over the proceedings
+on election petitions. Various acts and payments which were
+previously lawful in the absence of any corrupt bargain or
+motive are now altogether forbidden under the name of &ldquo;illegal
+practices&rdquo; as distinguished from &ldquo;corrupt practices.&rdquo; Failure
+on the part of a parliamentary candidate or his election agent
+to comply with the requirements of the law in any particular
+is sufficient to invalidate the return (see the articles <span class="sc"><a href="#artlinks">Bribery</a></span>
+and <span class="sc"><a href="#artlinks">Corrupt Practices</a></span>). Certain relaxations are, however,
+allowed in consideration of the difficulty of absolutely avoiding
+all deviation from the strict rules laid down. Thus, where the
+judges who try an election petition report that there has been
+treating, undue influence, or any illegal practice by the candidate
+or his election agent, but that it was trivial, unimportant and
+of a limited character, and contrary to the orders and without
+the sanction or connivance of the candidate or his election agent,
+and that the candidate and his election agent took all reasonable
+means for preventing corrupt and illegal practices, and that the
+election was otherwise free from such practices on their part,
+the election will not be avoided. The court has also the power
+to relieve from the consequences of certain innocent contraventions
+of the law caused by inadvertence or miscalculation.</p>
+
+<p>The inquiry into a disputed parliamentary election was
+formerly conducted before a committee of the House of Commons,
+chosen as nearly as possible from both sides of the House for that
+particular business. The decisions of these tribunals laboured
+<span class="pagenum"><a name="page170" id="page170"></a>170</span>
+under the suspicion of being prompted by party feeling, and by an
+act of 1868 the jurisdiction was finally transferred to judges of
+the High Court, notwithstanding the general unwillingness of the
+bench to accept a class of business which they feared might bring
+their integrity into dispute. Section 11 of the act ordered, <i>inter
+alia</i>, that the trial of every election petition shall be conducted
+before a <i>puisne judge</i> of one of the common law courts at Westminster
+and Dublin; that the said courts shall each select a
+judge to be placed on the rota for the trial of election petitions;
+that the said judges shall try petitions standing for trial according
+to seniority or otherwise, as they may agree; that the trial shall
+take place in the county or borough to which the petition refers,
+unless the court should think it desirable to hold it elsewhere.
+The judge shall determine &ldquo;whether the member whose return
+is complained of, or any and what other person, was duly returned
+and elected, or whether the election was void,&rdquo; and shall certify
+his determination to the speaker. When corrupt practices have
+been charged the judge shall also report (1) whether any such
+practice has been committed by or with the knowledge or consent
+of any candidate, and the nature thereof; (2) the names of persons
+proved to have been guilty of any corrupt practice; and (3)
+whether corrupt practices have extensively prevailed at the
+election. Questions of law were to be referred to the decision of
+the court of common pleas. On the abolition of that court by the
+Judicature Act 1873, the jurisdiction was transferred to the
+common pleas division, and again on the abolition of that
+<span class="sidenote">Election petitions.</span>
+division was transferred to the king&rsquo;s bench division,
+in whom it is now vested. The rota of judges for
+the trial of election petitions is also supplied by the
+king&rsquo;s bench division. The trial now takes place before two
+judges instead of one; and, when necessary, the number of
+judges on the rota may be increased. Both the judges who try a
+petition are to sign the certificates to be made to the speaker. If
+they differ as to the validity of a return, they are to state such
+difference in their certificate, and the return is to be held good;
+if they differ as to a report on any other matter, they are to
+certify their difference and make no report on such matter.
+The director of public prosecutions attends the trial personally or
+by representative. It is his duty to watch the proceedings in the
+public interest, to issue summonses to witnesses whose evidence
+is desired by the court, and to prosecute before the election court
+or elsewhere those persons whom he thinks to have been guilty of
+corrupt or illegal practices at the election in question. If an
+application is made for leave to withdraw a petition, copies of the
+affidavits in support are to be delivered to him; and he is
+entitled to be heard and to call evidence in opposition to such
+application. Witnesses are not excused from answering criminating
+questions; but their evidence cannot be used against them in
+any proceedings except criminal proceedings for perjury in
+respect of that evidence. If a witness answers truly all questions
+which he is required by the court to answer, he is entitled to
+receive a certificate of indemnity, which will save him from all
+proceedings for any offence under the Corrupt Practices Acts
+committed by him before the date of the certificate at or in
+relation to the election, except proceedings to enforce any
+incapacity incurred by such offence. An application for leave to
+withdraw a petition must be supported by affidavits from all the
+parties to the petition and their solicitors, and by the election
+agents of all of the parties who were candidates at the election.
+Each of these affidavits is to state that to the best of the deponent&rsquo;s
+knowledge and belief there has been no agreement and
+no terms or undertaking made or entered into as to the withdrawal,
+or, if any agreement has been made, shall state its terms.
+The applicant and his solicitor are also to state in their affidavits
+the grounds on which the petition is sought to be withdrawn. If
+any person makes an agreement for the withdrawal of a petition
+in consideration of a money payment, or of the promise that the
+seat shall be vacated or another petition withdrawn, or omits to
+state in his affidavit that he has made an agreement, lawful or
+unlawful, for the withdrawal, he is guilty of an indictable
+misdemeanour. The report of the judges to the speaker is to
+contain particulars as to illegal practices similar to those
+previously required as to corrupt practices; and they are to
+report further whether any candidate has been guilty by his
+agents of an illegal practice, and whether certificates of indemnity
+have been given to persons reported guilty of corrupt or illegal
+practices.</p>
+
+<p>The Corrupt Practices Acts apply, with necessary variations
+in details, to parliamentary elections in Scotland and Ireland.</p>
+
+<p>The amendments in the law as to municipal elections are
+generally similar to those which have been made in parliamentary
+election law. The procedure on trial of petitions is substantially
+the same, and wherever no other provision is made by the acts or
+rules the procedure on the trial of parliamentary election petitions
+is to be followed. Petitions against municipal elections were
+dealt with in 35 &amp; 36 Vict. c. 60. The election judges appoint
+a number of barristers, not exceeding five, as commissioners to
+try such petitions. No barrister can be appointed who is of less
+than fifteen years&rsquo; standing, or a member of parliament, or holder
+of any office of profit (other than that of recorder) under the
+crown; nor can any barrister try a petition in any borough in
+which he is recorder or in which he resides, or which is included in
+his circuit. The barrister sits without a jury. The provisions are
+generally similar to those relating to parliamentary elections. The
+petition may allege that the election was avoided as to the
+borough or ward on the ground of general bribery, &amp;c., or that the
+election of the person petitioned against was avoided by corrupt
+practices, or by personal disqualification, or that he had not the
+majority of lawful votes. The commissioner who tries a petition
+sends to the High Court a certificate of the result, together with
+reports as to corrupt and illegal practices, &amp;c., similar to those
+made to the speaker by the judges who try a parliamentary
+election petition. The Municipal Elections (Corrupt and Illegal
+Practices) Act 1884 applied to school board elections subject to
+certain variations, and has been extended by the Local Government
+Act 1888 to county council elections, and by the Local
+Government Act 1894 to elections by parochial electors. The
+law in Scotland is on the same lines, and extends to all non-parliamentary
+elections, and, as has been stated, the English
+statutes have been applied with adaptations to all municipal
+and local government elections in Ireland.</p>
+
+<p><i>United States.</i>&mdash;Elections are much more frequent in the United
+States than they are in Great Britain, and they are also more
+complicated. The terms of elective officers are shorter; and as
+there are also more offices to be filled, the number of persons to
+be voted for is necessarily much greater. In the year of a
+presidential election the citizen may be called upon to vote at one
+time for all of the following: (1) National candidates&mdash;president
+and vice-president (indirectly through the electoral college) and
+members of the House of Representatives; (2) state candidates&mdash;governor,
+members of the state legislature, attorney-general,
+treasurer, &amp;c.; (3) county candidates&mdash;sheriff, county judges,
+district attorney, &amp;c.; (4) municipal or town candidates&mdash;mayor,
+aldermen, selectmen, &amp;c. The number of persons actually voted
+for may therefore be ten or a dozen, or it may be many more.
+In addition, the citizen is often called upon to vote yea or nay on
+questions such as amendments to the state constitutions, granting
+of licences, and approval or disapproval of new municipal
+undertakings. As there may be, and generally is, more than one
+candidate for each office, and as all elections are now, and have
+been for many years, conducted by ballot, the total number of
+names to appear on the ballot may be one hundred or may be
+several hundred. These names are arranged in different ways,
+according to the laws of the different states. Under the Massachusetts
+law, which is considered the best by reformers, the names
+of candidates for each office are arranged alphabetically on a
+&ldquo;blanket&rdquo; ballot, as it is called from its size, and the elector
+places a mark opposite the names of such candidates as he may
+wish to vote for. Other states, New York for example, have the
+blanket system, but the names of the candidates are arranged in
+party columns. Still other states allow the grouping on one
+ballot of all the candidates of a single party, and there would be
+therefore as many separate ballots in such states as there were
+parties in the field.</p>
+
+<p><span class="pagenum"><a name="page171" id="page171"></a>171</span></p>
+
+<p>The qualifications for voting, while varying in the different
+states in details, are in their main features the same throughout
+the Union. A residence in the state is required of from three
+months to two years. Residence is also necessary, but for a
+shorter period, in the county, city or town, or voting precinct.
+A few states require the payment of a poll tax. Some require
+that the voter shall be able to read and understand the Constitution.
+This latter qualification has been introduced into several
+of the Southern states, partly at least to disqualify the ignorant
+coloured voters. In all, or practically all, the states idiots,
+convicts and the insane are disqualified; in some states paupers;
+in some of the Western states the Chinese. In some states
+women are allowed to vote on certain questions, or for the
+candidates for certain offices, especially school officials; and in
+four of the Western states women have the same rights of
+suffrage as men. The number of those who are qualified to vote,
+but do not avail themselves of the right, varies greatly in the
+different states and according to the interest taken in the election.
+As a general rule, but subject to exceptions, the national elections
+call out the largest number, the state elections next, and the local
+elections the smallest number of voters. In an exciting national
+election between 80 and 90% of the qualified voters actually
+vote, a proportion considerably greater than in Great Britain or
+Germany.</p>
+
+<p>The tendency of recent years has been towards a decrease both
+in the number and in the frequency of elections. A president and
+vice-president are voted for every fourth year, in the years
+divisible by four, on the first Tuesday following the first Monday
+of November. Members of the national House of Representatives
+are chosen for two years on the even-numbered years.
+State and local elections take place in accordance with state laws,
+and may or may not be on the same day as the national elections.
+Originally the rule was for the states to hold annual elections; in
+fact, so strongly did the feeling prevail of the need in a democratic
+country for frequent elections, that the maxim &ldquo;where annual
+elections end, tyranny begins,&rdquo; became a political proverb. But
+opinion gradually changed even in the older or Eastern states,
+and in 1909 Massachusetts and Rhode Island were the only states
+in the Union holding annual elections for governor and both
+houses of the state legislature. In the Western states especially
+state officers are chosen for longer terms&mdash;in the case of the
+governor often for four years&mdash;and the number of elections has
+correspondingly decreased. Another cause of the decrease in the
+number of elections is the growing practice of holding all the
+elections of any year on one and the same day. Before the Civil
+War Pennsylvania held its state elections several months before
+the national elections. Ohio and Indiana, until 1885 and 1881
+respectively, held their state elections early in October. Maine,
+Vermont and Arkansas keep to September. The selection of one
+day in the year for all elections held in that year has resulted
+in a considerable decrease in the total number.</p>
+
+<p>Another tendency of recent years, but not so pronounced, is to
+hold local elections in what is known as the &ldquo;off&rdquo; year; that is,
+on the odd-numbered year, when no national election is held.
+The object of this reform is to encourage independent voting.
+The average American citizen is only too prone to carry his
+national political predilections into local elections, and to vote for
+the local nominees of his party, without regard to the question of
+fitness of candidates and the fundamental difference of issues
+involved. This tendency to vote the entire party ticket is the
+more pronounced because under the system of voting in use in
+many of the states all the candidates of the party are arranged on
+one ticket, and it is much easier to vote a straight or unaltered
+ticket than to change or &ldquo;scratch&rdquo; it. Again, the voter,
+especially the ignorant one, refrains from scratching his ticket,
+lest in some way he should fail to comply with the technicalities
+of the law and his vote be lost. On the other hand, if local
+elections are held on the &ldquo;off&rdquo; or odd year, and there be no
+national or state candidates, the voter feels much more free to
+select only those candidates whom he considers best qualified for
+the various offices.</p>
+
+<p>On the important question of the purity of elections it is
+difficult to speak with precision. In many of the states, especially
+those with an enlightened public spirit, such as most of the
+New England states and many of the North-Western, the elections
+are fairly conducted, there being no intimidation at all, little or no
+bribery, and an honest count. It can safely be said that through
+the Union as a whole the tendency of recent years has been
+decidedly towards greater honesty of elections. This is owing to
+a number of causes: (1) The selection of a single day for all
+elections, and the consequent immense number voting on that
+day. Some years ago, when for instance the Ohio and Indiana
+elections were held a few weeks before the general election, each
+party strained every nerve to carry them, for the sake of prestige
+and the influence on other states. In fact, presidential elections
+were often felt to turn on the result in these early voting states,
+and the party managers were none too scrupulous in the means
+employed to carry them. Bribery has decreased in such states
+since the change of election day to that of the rest of the country.
+(2) The enactment in most of the states of the Australian or
+secret ballot (<i>q.v.</i>) laws. These have led to the secrecy of the
+ballot, and hence to a greater or less extent have prevented
+intimidation and bribery. (3) Educational or other such test,
+more particularly in the Southern states, the object of which is to
+exclude the coloured, and especially the ignorant coloured, voters
+from the polls. In those southern states in which the coloured
+vote was large, and still more in those in which it was the majority,
+it was felt among the whites that intimidation or ballot-box
+stuffing was justified by the necessity of white supremacy. With
+the elimination of the coloured vote by educational or other tests
+the honesty of elections has increased. (4) The enactment of new
+and more stringent registration laws. Under these laws only
+those persons are allowed to vote whose names have been placed
+on the rolls a certain number of days or months before election.
+These rolls are open to public inspection, and the names may be
+challenged at the polls, and &ldquo;colonization&rdquo; or repeating is
+therefore almost impossible. (5) The reform of the civil service
+and the gradual elimination of the vicious principle of &ldquo;to the
+victors belong the spoils.&rdquo; With the reform of the civil service
+elections become less a scramble for office and more a contest of
+political or economic principle. They bring into the field,
+therefore, a better class of candidates. (6) The enactment in a
+number of states of various other laws for the prevention of corrupt
+practices, for the publication of campaign expenses, and for the
+prohibition of party workers from coming within a certain
+specified distance of the polls. In the state of Massachusetts, for
+instance, an act passed in 1892, and subsequently amended,
+provides that political committees shall file a full statement, duly
+sworn to, of all campaign expenditures made by them. The act
+applies to all public elections except that of town officers, and also
+covers nominations by caucuses and conventions as well. Apart
+from his personal expenses such as postage, travelling expenses,
+&amp;c., a candidate is prohibited from spending anything himself to
+promote either his nomination or his election, but he is allowed
+to contribute to the treasury of the political committee. The law
+places no limit on the amount that these committees may spend.
+The reform sought by the law is thorough publicity, and not only
+are details of receipts and expenditures to be published, but the
+names of contributors and the amount of their contributions. In
+the state of New York the act which seeks to prevent corrupt
+practices relies in like manner on the efficacy of publicity, but
+it is less effective than the Massachusetts law in that it provides
+simply for the filing by the candidates themselves of sworn
+statements of their own expenses. There is nothing to prevent
+their contributing to political committees, and the financial
+methods and the amounts expended by such committees are not
+made public. But behind all these causes that have led to more
+honest elections lies the still greater one of a healthier public
+spirit. In the reaction following the Civil War all reforms halted.
+In recent years, however, a new and healthier interest has sprung
+up in things political; and one result of this improved civic
+spirit is seen in the various laws for purification of elections. It
+may now be safely affirmed that in the majority of states the
+elections are honestly conducted; that intimidation, bribery,
+<span class="pagenum"><a name="page172" id="page172"></a>172</span>
+stuffing of the ballot boxes or other forms of corruption, when
+they exist, are owing in large measure to temporary or local
+causes; and that the tendency of recent years has been towards
+a decrease in all forms of corruption.</p>
+
+<p>The expenses connected with elections, such as the renting and
+preparing of the polling-places, the payment of the clerks and
+other officers who conduct the elections and count the vote, are
+borne by the community. A candidate therefore is not, as far
+as the law is concerned, liable to any expense whatever. As a
+matter of fact he does commonly contribute to the party treasury,
+though in the case of certain candidates, particularly those for the
+presidency and for judicial offices, financial contributions are not
+general. The amount of a candidate&rsquo;s contribution varies
+greatly, according to the office sought, the state in which he lives,
+and his private wealth. On one occasion, in a district in New
+York, a candidate for Congress is credibly believed to have spent
+at one election $50,000. On the other hand, in a Congressional
+election in a certain district in Massachusetts, the only expenditure
+of one of the candidates was for the two-cent stamp
+placed on his letter of acceptance. No estimate of the average
+amount expended can be made. It is, however, the conclusion of
+Mr Bryce, in his <i>American Commonwealth</i>, that as a rule a seat in
+Congress costs the candidate less than a seat for a county
+division in the House of Commons. (See also <span class="sc"><a href="#artlinks">Ballot</a></span>.)</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTION,<a name="ar57" id="ar57"></a></span> in English law, the obligation imposed upon a
+party by courts of equity to choose between two inconsistent
+or alternative rights or claims in cases where there is a clear
+intention of the person from whom he derives one that he should
+not enjoy both. Thus a testator died seized of property in fee
+simple and in fee tail&mdash;he had two daughters, and devised the
+fee simple property to one and the entailed property to the other;
+the first one claimed to have her share of the entailed property
+as coparcener and also to retain the benefit she took under the
+will. It was held that she was put to her election whether she
+would take under the will and renounce her claim to the entailed
+property or take against the will, in which case she must renounce
+the benefits she took under the will in so far as was necessary
+to compensate her sister. As the essence of the doctrine is
+compensation, a person electing against a document does not
+lose all his rights under it, but the court will sequester so much
+only of the benefit intended for him as will compensate the persons
+disappointed by his election. For the same reason it is necessary
+that there should be a free and disposable fund passing by the
+instrument from which compensation can be made in the event
+of election against the will. If, therefore, a man having a special
+power of appointment appoint the fund equally between two
+persons, one being an object of the power and the other not an
+object, no question of election arises, but the appointment to
+the person not an object is bad.</p>
+
+<p>Election, though generally arising in cases of wills, may also
+arise in the case of a deed. There is, however, a distinction to
+be observed. In the case of a will a clear intention on the part
+of the testator that he meant to dispose of property not his own
+must be shown, and parol evidence is not admissible as to this.
+In the case of a deed, however, no such intention need be shown,
+for if a deed confers a benefit and imposes a liability on the same
+person he cannot be allowed to accept the one and reject the other,
+but this must be distinguished from cases where two separate
+gifts are given to a person, one beneficial and the other onerous.
+In such a case no question of election arises and he may take
+the one and reject the other, unless, indeed, there are words
+used which make the one conditional on the acceptance of the
+other.</p>
+
+<p>Election is either express, <i>e.g.</i> by deed, or implied; in the
+latter case it is often a question of considerable difficulty
+whether there has in fact been an election or not; each case
+must depend upon the particular circumstances, but quite
+generally it may be said that the person who has elected must
+have been capable of electing, aware of the existence of the
+doctrine of election, and have had the opportunity of satisfying
+himself of the relative value of the properties between which
+he has elected. In the case of infants the court will sometimes
+elect after an inquiry as to which course is the most advantageous,
+or if there is no immediate urgency, will allow the matter to stand
+over till the infant attains his majority. In the cases of married
+women and lunatics the courts will exercise the right for them.
+It sometimes happens that the parties have so dealt with
+the property that it would be inequitable to disturb it; in
+such cases the court will not interfere in order to allow of
+election.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTORAL COMMISSION,<a name="ar58" id="ar58"></a></span> in United States history, a
+commission created to settle the disputed presidential election
+of 1876. In this election Samuel J. Tilden, the Democratic
+candidate, received 184 uncontested electoral votes, and Rutherford
+B. Hayes, the Republican candidate, 163.<a name="fa1e" id="fa1e" href="#ft1e"><span class="sp">1</span></a> The states of
+Florida, Louisiana, Oregon and South Carolina, with a total
+of 22 votes, each sent in two sets of electoral ballots,<a name="fa2e" id="fa2e" href="#ft2e"><span class="sp">2</span></a> and from
+each of these states except Oregon one set gave the whole vote
+to Tilden and the other gave the whole vote to Hayes. From
+Oregon one set of ballots gave the three electoral votes of the
+state to Hayes; the other gave two votes to Hayes and one to
+Tilden.</p>
+
+<p>The election of a president is a complex proceeding, the method
+being indicated partly in the Constitution, and being partly left
+to Congress and partly to the states. The manner of selecting
+the electors is left to state law; the electoral ballots are sent
+to the president of the Senate, who &ldquo;shall, in the presence of
+the Senate and House of Representatives, open all certificates,
+and the votes shall then be counted.&rdquo; Concerning this provision
+many questions of vital importance arose in 1876: Did the president
+of the Senate count the votes, the houses being mere
+witnesses; or did the houses count them, the president&rsquo;s duties
+being merely ministerial? Did counting imply the determination
+of what should be counted, or was it a mere arithmetical process;
+that is, did the Constitution itself afford a method of settling
+disputed returns, or was this left to legislation by Congress?
+Might Congress or an officer of the Senate go behind a state&rsquo;s
+certificate and review the acts of its certifying officials? Might
+it go further and examine into the choice of electors? And if
+it had such powers, might it delegate them to a commission?
+As regards the procedure of Congress, it seems that, although
+in early years the president of the Senate not only performed or
+overlooked the electoral count but also exercised discretion in
+some matters very important in 1876, Congress early began to
+assert power, and, at least from 1821 onward, controlled the
+count, claiming complete power. The fact, however, that the
+Senate in 1876 was controlled by the Republicans and the House
+by the Democrats, lessened the chances of any harmonious
+settlement of these questions by Congress. The country seemed
+on the verge of civil war. Hence it was that by an act of the
+29th of January 1877, Congress created the Electoral Commission
+to pass upon the contested returns, giving it &ldquo;the same powers,
+if any&rdquo; possessed by itself in the premises, the decisions to stand
+unless rejected by the two houses separately. The commission
+was composed of five Democratic and five Republican Congressmen,
+two justices of the Supreme Court of either party, and a
+fifth justice chosen by these four. As its members of the commission
+the Senate chose G.F. Edmunds of Vermont, O.P.
+Morton of Indiana, and F.T. Frelinghuysen of New Jersey
+(Republicans); and A.G. Thurman of Ohio and T.F. Bayard
+of Delaware (Democrats). The House chose Henry B. Payne
+of Ohio, Eppa Hunton of Virginia, and Josiah G. Abbott of
+Massachusetts (Democrats); and George F. Hoar of Massachusetts
+and James A. Garfield of Ohio (Republicans). The
+Republican judges were William Strong and Samuel F. Miller;
+the Democratic, Nathan Clifford and Stephen J. Field. These
+four chose as the fifteenth member Justice Joseph P. Bradley,
+<span class="pagenum"><a name="page173" id="page173"></a>173</span>
+a Republican but the only member not selected avowedly as a
+partisan. As counsel for the Democratic candidate there appeared
+before the commission at different times Charles O&rsquo;Conor
+of New York, Jeremiah S. Black of Pennsylvania, Lyman
+Trumbull of Illinois, R.T. Merrick of the District of Columbia,
+Ashbel Green of New Jersey, Matthew H. Carpenter of Wisconsin,
+George Hoadley of Ohio, and W.C. Whitney of New York.
+W.M. Evarts and E.W. Stoughton of New York and Samuel
+Shellabarger and Stanley Matthews of Ohio appeared regularly
+in behalf of Mr Hayes.</p>
+
+<p>The popular vote seemed to indicate that Hayes had carried
+South Carolina and Oregon, and Tilden Florida and Louisiana.
+It was evident, however, that Hayes could secure the 185 votes
+necessary to elect only by gaining every disputed ballot. As
+the choice of Republican electors in Louisiana had been accomplished
+by the rejection of several thousand Democratic votes
+by a Republican returning board, the Democrats insisted that
+the commission should go behind the returns and correct injustice;
+the Republicans declared that the state&rsquo;s action was
+final, and that to go behind the returns would be invading its
+sovereignty. When this matter came before the commission
+it virtually accepted the Republican contention, ruling that it
+could not go behind the returns except on the superficial issues
+of manifest fraud therein or the eligibility of electors to their
+office under the Constitution; that is, it could not investigate
+antecedents of fraud or misconduct of state officials in the results
+certified. All vital questions were settled by the votes of eight
+Republicans and seven Democrats; and as the Republican
+Senate would never concur with the Democratic House in overriding
+the decisions, all the disputed votes were awarded to Mr
+Hayes, who therefore was declared elected.</p>
+
+<p>The strictly partisan votes of the commission and the adoption
+by prominent Democrats and Republicans, both within and
+without the commission, of an attitude toward states-rights
+principles quite inconsistent with party tenets and tendencies,
+have given rise to much severe criticism. The Democrats and
+the country, however, quietly accepted the decision. The
+judgments underlying it were two: (1) That Congress rightly
+claimed the power to settle such contests within the limits set;
+(2) that, as Justice Miller said regarding these limits, the people
+had never at any time intended to give to Congress the power,
+by naming the electors, to &ldquo;decide who are to be the president
+and vice-president of the United States.&rdquo;</p>
+
+<p>There is no doubt that Mr Tilden was morally entitled to the
+presidency, and the correction of the Louisiana frauds would
+certainly have given satisfaction then and increasing satisfaction
+later, in the retrospect, to the country. The commission might
+probably have corrected the frauds without exceeding its Congressional
+precedents. Nevertheless, the principles of its
+decisions must be recognized by all save ultra-nationalists as
+truer to the spirit of the Constitution and promising more for
+the good of the country than would have been the principles
+necessary to a contrary decision.</p>
+
+<p>By an act of the 3rd of February 1887 the electoral procedure
+is regulated in great detail. Under this act determination by a
+state of electoral disputes is conclusive, subject to certain
+formalities that guarantee definite action and accurate certification.
+These formalities constitute &ldquo;regularity,&rdquo; and are in all
+cases judgable by Congress. When Congress is forced by the
+lack or evident inconclusiveness of state action, or by conflicting
+state action, to decide disputes, votes are lost unless both
+houses concur.</p>
+
+<div class="condensed">
+<p><span class="sc">Authorities.</span>&mdash;J.F. Rhodes, <i>History of the United States</i>, vol. 7,
+covering 1872-1877 (New York, 1906); P.L. Haworth, <i>The Hayes-Tilden
+disputed Presidential Election of 1876</i> (Cleveland, 1906);
+J.W. Burgess, <i>Political Science Quarterly</i>, vol. 3 (1888), pp. 633-653,
+&ldquo;The Law of the Electoral Count&rdquo;; and for the sources. Senate
+Miscellaneous Document No. 5 (vol. 1), and House Miscel. Doc.
+No. 13 (vol. 2), 44 Congress, 2 Session,&mdash;<i>Count of the Electoral Vote.
+Proceedings of Congress and Electoral Commission</i>,&mdash;the latter
+identical with <i>Congressional Record</i>, vol. 5, pt. 4, 44 Cong., 2 Session;
+also about twenty volumes of evidence on the state elections involved.
+The volume called <i>The Presidential Counts</i> (New York,
+1877) was compiled by Mr. Tilden and his secretary.</p>
+</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1e" id="ft1e" href="#fa1e"><span class="fn">1</span></a> The election of a vice-president was, of course, involved also.
+William A. Wheeler was the Republican candidate, and Thomas A.
+Hendricks the Democratic.</p>
+
+<p><a name="ft2e" id="ft2e" href="#fa2e"><span class="fn">2</span></a> A second set of electoral ballots had also been sent in from
+Vermont, where Hayes had received a popular majority vote of
+24,000. As these ballots had been transmitted in an irregular
+manner, the president of the Senate refused to receive them, and
+was sustained in this action by the upper House.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTORS<a name="ar59" id="ar59"></a></span> (Ger. <i>Kurfürsten</i>, from <i>Küren</i>, O.H.G. <i>kiosan</i>,
+choose, elect, and <i>Fürst</i>, prince), a body of German princes,
+originally seven in number, with whom rested the election of
+the German king, from the 13th until the beginning of the 19th
+century. The German kings, from the time of Henry the
+Fowler (919-936) till the middle of the 13th century, succeeded
+to their position partly by heredity, and partly by election.
+Primitive Germanic practice had emphasized the element of
+heredity. <i>Reges ex nobilitate sumunt</i>: the man whom a German
+tribe recognized as its king must be in the line of hereditary
+descent from Woden; and therefore the genealogical trees of
+early Teutonic kings (as, for instance, in England those of the
+Kentish and West Saxon sovereigns) are carefully constructed
+to prove that descent from the god which alone will constitute
+a proper title for his descendants. Even from the first, however,
+there had been some opening for election; for the principle of
+primogeniture was not observed, and there might be several
+competing candidates, all of the true Woden stock. One of
+these competing candidates would have to be recognized (as
+the Anglo-Saxons said, <i>geceosan</i>); and to this limited extent
+Teutonic kings may be termed elective from the very first. In
+the other nations of western Europe this element of election
+dwindled, and the principle of heredity alone received legal
+recognition; in medieval Germany, on the contrary, the principle
+of heredity, while still exercising an inevitable natural force,
+sank formally into the background, and legal recognition was
+finally given to the elective principle. <i>De facto</i>, therefore, the
+principle of heredity exercises in Germany a great influence,
+an influence never more striking than in the period which follows
+on the formal recognition of the elective principle, when the
+Habsburgs (like the Metelli at Rome) <i>fato imperatores fiunt:
+de jure</i>, each monarch owes his accession simply and solely to
+the vote of an electoral college.</p>
+
+<p>This difference between the German monarchy and the other
+monarchies of western Europe may be explained by various
+considerations. Not the least important of these is what seems
+a pure accident. Whereas the Capetian monarchs, during the
+three hundred years that followed on the election of Hugh Capet
+in 987, always left an heir male, and an heir male of full age,
+the German kings again and again, during the same period,
+either left a minor to succeed to their throne, or left no issue
+at all. The principle of heredity began to fail because there
+were no heirs. Again the strength of tribal feeling in Germany
+made the monarchy into a prize, which must not be the apanage
+of any single tribe, but must circulate, as it were, from Franconian
+to Saxon, from Saxon to Bavarian, from Bavarian to Franconian,
+from Franconian to Swabian; while the growing power of the
+baronage, and its habit of erecting anti-kings to emphasize its
+opposition to the crown (as, for instance, in the reign of Henry
+IV.), coalesced with and gave new force to the action of tribal
+feeling. Lastly, the fact that the German kings were also
+Roman emperors finally and irretrievably consolidated the growing
+tendency towards the elective principle. The principle of
+heredity had never held any great sway under the ancient Roman
+Empire (see under <span class="sc"><a href="#artlinks">Emperor</a></span>); and the medieval Empire,
+instituted as it was by the papacy, came definitely under the
+influence of ecclesiastical prepossessions in favour of election.
+The church had substituted for that descent from Woden, which
+had elevated the old pagan kings to their thrones, the conception
+that the monarch derived his crown from the choice of God,
+after the manner of Saul; and the theoretical choice of God
+was readily turned into the actual choice of the church, or, at
+any rate, of the general body of churchmen. If an ordinary
+king is thus regarded by the church as essentially elected, much
+more will the emperor, connected as he is with the church as
+one of its officers, be held to be also elected; and as a bishop
+is chosen by the chapter of his diocese, so, it will be thought,
+must the emperor be chosen by some corresponding body in his
+empire. Heredity might be tolerated in a mere matter of kingship:
+the precious trust of imperial power could not be allowed
+to descend according to the accidents of family succession. To
+Otto of Freising (<i>Gesta Frid.</i> ii. 1) it is already a point of right
+<span class="pagenum"><a name="page174" id="page174"></a>174</span>
+vindicated for itself by the excellency of the Roman Empire,
+as a matter of singular prerogative, that it should not descend
+<i>per sanguinis propaginem, sed per principum electionem</i>.</p>
+
+<p>The accessions of Conrad II. (see Wipo, <i>Vita Cuonradi</i>, c. 1-2),
+of Lothair II. (see <i>Narratio de electione Lotharii</i>, M.G.H. <i>Scriptt.</i>
+xii. p. 510), of Conrad III. (see Otto of Freising, <i>Chronicon</i>, vii.
+22) and of Frederick I. (see Otto of Freising, <i>Gesta Frid.</i> ii. 1)
+had all been marked by an element, more or less pronounced,
+of election. That element is perhaps most considerable in the
+case of Lothair, who had no rights of heredity to urge. Here
+we read of ten princes being selected from the princes of the
+various duchies, to whose choice the rest promise to assent, and
+of these ten selecting three candidates, one of whom, Lothair,
+is finally chosen (apparently by the whole assembly) in a somewhat
+tumultuary fashion. In this case the electoral assembly
+would seem to be, in the last resort, the whole diet of all the
+princes. But a <i>de facto</i> pre-eminence in the act of election is
+already, during the 12th century, enjoyed by the three Rhenish
+archbishops, probably because of the part they afterwards
+played at the coronation, and also by the dukes of the great
+duchies&mdash;possibly because of the part they too played, as vested
+for the time with the great offices of the household, at the coronation
+feast.<a name="fa1f" id="fa1f" href="#ft1f"><span class="sp">1</span></a> Thus at the election of Lothair it is the archbishop
+of Mainz who conducts the proceedings; and the election is
+not held to be final until the duke of Bavaria has given his assent.
+The fact is that, votes being weighed by quality as well as by
+quantity (see <span class="sc"><a href="#artlinks">Diet</a></span>), the votes of the archbishops and dukes,
+which would first be taken, would of themselves, if unanimous,
+decide the election. To prevent tumultuary elections, it was
+well that the election should be left exclusively with these great
+dignitaries; and this is what, by the middle of the 13th century,
+had eventually been done.</p>
+
+<p>The chaos of the interregnum from 1198 to 1212 showed the
+way for the new departure; the chaos of the great interregnum
+(1250-1273) led to its being finally taken. The decay of the great
+duchies, and the narrowing of the class of princes into a close
+corporation, some of whose members were the equals of the old
+dukes in power, introduced difficulties and doubts into the
+practice of election which had been used in the 12th century.
+The contested election of the interregnum of 1198-1212 brought
+these difficulties and doubts into strong relief. The famous
+bull of Innocent III. (<i>Venerabilem</i>), in which he decided for
+Otto IV. against Philip of Swabia, on the ground that, though
+he had fewer votes than Philip, he had a majority of the votes
+of those <i>ad quos principaliter spectat electio</i>, made it almost
+imperative that there should be some definition of these principal
+electors. The most famous attempt at such a definition is that
+of the <i>Sachsenspiegel</i>, which was followed, or combated, by
+many other writers in the first half of the 13th century.
+Eventually the contested election of 1257 brought light and
+definition. Here we find seven potentates acting&mdash;the same
+seven whom the Golden Bull recognizes in 1356; and we find
+these seven described in an official letter to the pope, as <i>principes
+vocem in hujusmodi electione habentes, qui sunt septem numero</i>.
+The doctrine thus enunciated was at once received. The pope
+acknowledged it in two bulls (1263); a cardinal, in a commentary
+on the bull <i>Venerabilem</i> of Innocent III., recognized it about
+the same time; and the erection of statues of the seven electors
+at Aix-la-Chapelle gave the doctrine a visible and outward
+expression.</p>
+
+<p>By the date of the election of Rudolph of Habsburg (1273)
+the seven electors may be regarded as a definite body, with an
+acknowledged right. But the definition and the acknowledgment
+were still imperfect. (1) The composition of the electoral body
+was uncertain in two respects. The duke of Bavaria claimed
+as his right the electoral vote of the king of Bohemia; and the
+practice of <i>partitio</i> in electoral families tended to raise further
+difficulties about the exercise of the vote. The Golden Bull of
+1356 settled both these questions. Bohemia (of which Charles
+IV., the author of the Golden Bull, was himself the king) was
+assigned the electoral vote in preference to Bavaria; and a
+provision annexing the electoral vote to a definite territory,
+declaring that territory indivisible, and regulating its descent
+by the rule of primogeniture instead of partition, swept away the
+old difficulties which the custom of partition had raised. After
+1356 the seven electors are regularly the three Rhenish archbishops,
+Mainz, Cologne and Trier, and four lay magnates, the
+palatine of the Rhine, the duke of Saxony, the margrave of
+Brandenburg, and the king of Bohemia; the three former
+being vested with the three archchancellorships, and the four
+latter with the four offices of the royal household (see <span class="sc"><a href="#artlinks">Household</a></span>).
+(2) The rights of the seven electors, in their collective
+capacity as an electoral college, were a matter of dispute with the
+papacy. The result of the election, whether made, as at first,
+by the princes generally or, as after 1257, by the seven electors
+exclusively, was in itself simply the creation of a German king&mdash;an
+<i>electio in regem</i>. But since 962 the German king was also,
+after coronation by the pope, Roman emperor. Therefore the
+election had a double result: the man elected was not only
+<i>electus in regem</i>, but also <i>promovendus ad imperium</i>. The
+difficulty was to define the meaning of the term <i>promovendus</i>.
+Was the king elect <i>inevitably</i> to become emperor? or did the
+<i>promotio</i> only follow at the discretion of the pope, if he thought
+the king elect fit for promotion? and if so, to what extent, and
+according to what standard, did the pope judge of such fitness?
+Innocent III. had already claimed, in the bull <i>Venerabilem</i>,
+(1) that the electors derived their power of election, so far as it
+made an emperor, from the Holy See (which had originally &ldquo;translated&rdquo;
+the Empire from the East to the West), and (2) that the
+papacy had a <i>jus et auctoritas examinandi personam electam in
+regem et promovendam ad imperium</i>. The latter claim he had
+based on the fact that he anointed, consecrated and crowned
+the emperor&mdash;in other words, that he gave a spiritual office
+according to spiritual methods, which entitled him to inquire
+into the fitness of the recipient of that office, as a bishop inquires
+into the fitness of a candidate for ordination. Innocent had put
+forward this claim as a ground for deciding between competing
+candidates: Boniface VIII. pressed the claim against Albert I.
+in 1298, even though his election was unanimous; while John
+XXII. exercised it in its harshest form, when in 1324 he ex-communicated
+Louis IV. for using the title and exerting the
+rights even of king without previous papal confirmation. This
+action ultimately led to a protest from the electors themselves,
+whose right of election would have become practically meaningless,
+if such assumptions had been tolerated. A meeting of the
+electors (<i>Kurverein</i>) at Rense in 1338 declared (and the declaration
+was reaffirmed by a diet at Frankfort in the same year)
+that <i>postquam aliquis eligitur in Imperatorem sive Regem ab
+Electoribus Imperii concorditer, vel majori parte eorundem, statim
+ex sola electione est Rex verus et Imperator Romanus censendus
+... nec Papae sive Sedis Apostolicae ... approbatione ...
+indiget</i>. The doctrine thus positively affirmed at Rense is
+negatively reaffirmed in the Golden Bull, in which a significant
+silence is maintained in regard to papal rights. But the doctrine
+was not in practice followed: Sigismund himself did not venture
+to dispense with papal approbation.</p>
+
+<p>By the end of the 14th century the position of the electors,
+both individually and as a corporate body, had become definite
+and precise. Individually, they were distinguished from all
+other princes, as we have seen, by the indivisibility of their
+territories and by the custom of primogeniture which secured
+that indivisibility; and they were still further distinguished by
+the fact that their person, like that of the emperor himself, was
+protected by the law of treason, while their territories were only
+subject to the jurisdiction of their own courts. They were
+independent territorial sovereigns; and their position was at
+once the envy and the ideal of the other princes of Germany.
+Such had been the policy of Charles IV.; and thus had he, in the
+Golden Bull, sought to magnify the seven electors, and himself
+<span class="pagenum"><a name="page175" id="page175"></a>175</span>
+as one of the seven, in his capacity of king of Bohemia, even at
+the expense of the Empire, and of himself in his capacity of
+emperor. Powerful as they were, however, in their individual
+capacity, the electors showed themselves no less powerful as a
+corporate body. As such a corporate body, they may be considered
+from three different points of view, and as acting in
+three different capacities. They are an electoral body, choosing
+each successive emperor; they are one of the three colleges of
+the imperial diet (see <span class="sc"><a href="#artlinks">Diet</a></span>); and they are also an electoral
+union (<i>Kurfürstenverein</i>), acting as a separate and independent
+political organ even after the election, and during the reign, of
+the monarch. It was in this last capacity that they had met at
+Rense in 1338; and in the same capacity they acted repeatedly
+during the 15th century. According to the Golden Bull, such
+meetings were to be annual, and their deliberations were to
+concern &ldquo;the safety of the Empire and the world.&rdquo; Annual
+they never were; but occasionally they became of great importance.
+In 1424, during the attempt at reform occasioned by
+the failure of German arms against the Hussites, the <i>Kurfürstenverein</i>
+acted, or at least it claimed to act, as the predominant
+partner in a duumvirate, in which the unsuccessful Sigismund
+was relegated to a secondary position. During the long reign
+of Frederick III.&mdash;a reign in which the interests of Austria
+were cherished, and the welfare of the Empire neglected, by
+that apathetic yet tenacious emperor&mdash;the electors once more
+attempted, in the year 1453, to erect a new central government
+in place of the emperor, a government which, if not conducted
+by themselves directly in their capacity of a <i>Kurfürstenverein</i>,
+should at any rate be under their influence and control. So,
+they hoped, Germany might be able to make head against that
+papal aggression, to which Frederick had yielded, and to take
+a leading part in that crusade against the Turks, which he had
+neglected. Like the previous attempt at reform during the
+Hussite wars, the scheme came to nothing; the forces of disunion
+in Germany were too strong for any central government, whether
+monarchical and controlled by the emperor, or oligarchical and
+controlled by the electors. But a final attempt, the most
+strenuous of all, was made in the reign of Maximilian I., and
+under the influence of Bertold, elector and archbishop of Mainz.
+The council of 1500, in which the electors (with the exception
+of the king of Bohemia) were to have sat, and which would have
+been under their control, represents the last effective attempt
+at a real <i>Reichsregiment</i>. Inevitably, however, it shipwrecked
+on the opposition of Maximilian; and though the attempt was
+again made between 1521 and 1530, the idea of a real central
+government under the control of the electors perished, and the
+development of local administration by the circle took its place.</p>
+
+<p>In the course of the 16th century a new right came to be
+exercised by the electors. As an electoral body (that is to say,
+in the first of the three capacities distinguished above), they
+claimed, at the election of Charles V. in 1519 and at subsequent
+elections, to impose conditions on the elected monarch, and to
+determine the terms on which he should exercise his office in
+the course of his reign. This <i>Wahlcapitulation</i>, similar to the
+<i>Pacta Conventa</i> which limited the elected kings of Poland, was
+left by the diet to the discretion of the electors, though after
+the treaty of Westphalia an attempt was made, with some little
+success,<a name="fa2f" id="fa2f" href="#ft2f"><span class="sp">2</span></a> to turn the capitulation into a matter of legislative
+enactment by the diet. From this time onwards the only fact of
+importance in the history of the electors is the change which
+took place in the composition of their body during the 17th
+and 18th centuries. From the Golden Bull to the treaty of
+Westphalia (1356-1648) the composition of the electoral body
+had remained unchanged. In 1623, however, in the course
+of the Thirty Years&rsquo; War, the vote of the count palatine of the
+Rhine had been transferred to the duke of Bavaria; and at the
+treaty of Westphalia the vote, with the office of imperial butler
+which it carried, was left to Bavaria, while an eighth vote, along
+with the new office of imperial treasurer, was created for the
+count palatine. In 1708 a ninth vote, along with the office of
+imperial standard-bearer, was created for Hanover; while
+finally, in 1778, the vote of Bavaria and the office of imperial
+butler returned to the counts palatine, as heirs of the duchy,
+on the extinction of the ducal line, while the new vote created
+for the Palatinate in 1648, with the office of imperial treasurer,
+was transferred to Brunswick-Lüneburg (Hanover) in lieu of the
+one which this house already held. In 1806, on the dissolution
+of the Holy Roman Empire, the electors ceased to exist.</p>
+
+<div class="condensed">
+<p><span class="sc">Literature.</span>&mdash;T. Lindner, <i>Die deutschen Königswahlen und die
+Entstehung des Kurfürstentums</i> (1893), and <i>Der Hergang bei den
+deutschen Königswahlen</i> (1899); R. Kirchhöfer, <i>Zur Entstehung des
+Kurkollegiums</i> (1893); W. Maurenbrecher, <i>Geschichte der deutschen
+Königswahlen</i> (1889); and G. Blondel, <i>Étude sur Frédéric II</i>,
+p. 27 sqq. See also J. Bryce, <i>Holy Roman Empire</i> (edition of 1904),
+c. ix.; and R. Schröder, <i>Lehrbuch der deutschen Rechtsgeschichte</i>,
+pp. 471-481 and 819-820.</p>
+</div>
+<div class="author">(E. Br.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1f" id="ft1f" href="#fa1f"><span class="fn">1</span></a> This is the view of the <i>Sachsenspiegel</i>, and also of Albert of Stade
+(quoted in Schröder, p. 476, n. 27): &ldquo;Palatinus eligit, quia dapifer est;
+dux Saxoniae, quia marescalcus,&rdquo; &amp;c. Schröder points out (p. 479,
+n. 45) that &ldquo;participation in the coronation feast is an express
+recognition of the king&rdquo;; and those who are to discharge their office
+in the one must have had a prominent voice in the other.</p>
+
+<p><a name="ft2f" id="ft2f" href="#fa2f"><span class="fn">2</span></a> See Schröder&rsquo;s <i>Lehrbuch der deutschen Rechtsgeschichte</i>, p. 820.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRA<a name="ar60" id="ar60"></a></span> (<span class="grk" title="Elektra">&#7976;&#955;&#941;&#954;&#964;&#961;&#945;</span>), &ldquo;the bright one,&rdquo; in Greek mythology.
+(1) One of the seven Pleiades, daughter of Atlas and Pleïone.
+She is closely connected with the old constellation worship and
+the religion of Samothrace, the chief seat of the Cabeiri (<i>q.v.</i>),
+where she was generally supposed to dwell. By Zeus she was the
+mother of Dardanus, Iasion (or Eëtion), and Harmonia; but in
+the Italian tradition, which represented Italy as the original
+home of the Trojans, Dardanus was her son by a king of Italy
+named Corythus. After her amour with Zeus, Electra fled to the
+Palladium as a suppliant, but Athena, enraged that it had been
+touched by one who was no longer a maiden, flung Electra and
+the image from heaven to earth, where it was found by Ilus, and
+taken by him to Ilium; according to another tradition, Electra
+herself took it to Ilium, and gave it to her son Dardanus (Schol.
+Eurip. <i>Phoen.</i> 1136). In her grief at the destruction of the city
+she plucked out her hair and was changed into a comet; in
+another version Electra and her six sisters had been placed among
+the stars as the Pleiades, and the star which she represented lost
+its brilliancy after the fall of Troy. Electra&rsquo;s connexion with
+Samothrace (where she was also called Electryone and Strategis)
+is shown by the localization of the carrying off of her reputed
+daughter Harmonia by Cadmus, and by the fact that, according
+to Athenicon (the author of a work on Samothrace quoted by the
+scholiast on Apollonius Rhodius i. 917), the Cabeiri were
+Dardanus and Iasion. The gate Electra at Thebes and the
+fabulous island Electris were said to have been called after her
+(Apollodorus iii. 10. 12; Servius on <i>Aen.</i> iii. 167, vii. 207, x. 272,
+<i>Georg.</i> i. 138).</p>
+
+<p>(2) Daughter of Agamemnon and Clytaemnestra, sister of
+Orestes and Iphigeneia. She does not appear in Homer, although
+according to Xanthus (regarded by some as a fictitious personage),
+to whom Stesichorus was indebted for much in his <i>Oresteia</i>, she
+was identical with the Homeric Laodice, and was called Electra
+because she remained so long unmarried (<span class="grk" title="&rsquo;A-lektra">&#7944;-&#955;&#941;&#954;&#964;&#961;&#945;</span>). She was
+said to have played an important part in the poem of Stesichorus,
+and subsequently became a favourite figure in tragedy. After
+the murder of her father on his return from Troy by her mother
+and Aegisthus, she saved the life of her brother Orestes by
+sending him out of the country to Strophius, king of Phanote in
+Phocis, who had him brought up with his own son Pylades.
+Electra, cruelly ill-treated by Clytaemnestra and her paramour,
+never loses hope that her brother will return to avenge his father.
+When grown up, Orestes, in response to frequent messages from
+his sister, secretly repairs with Pylades to Argos, where he
+pretends to be a messenger from Strophius bringing the news
+of the death of Orestes. Being admitted to the palace, he slays
+both Aegisthus and Clytaemnestra. According to another story
+(Hyginus, <i>Fab.</i> 122), Electra, having received a false report that
+Orestes and Pylades had been sacrificed to Artemis in Tauris,
+went to consult the oracle at Delphi. In the meantime Aletes,
+the son of Aegisthus, seized the throne of Mycenae. Her arrival
+at Delphi coincided with that of Orestes and Iphigeneia. The
+same messenger, who had already communicated the false report
+of the death of Orestes, informed her that he had been slain by
+Iphigeneia. Electra in her rage seized a burning brand from
+the altar, intending to blind her sister; but at the critical
+moment Orestes appeared, recognition took place, and the brother
+and sister returned to Mycenae. Aletes was slain by Orestes, and
+<span class="pagenum"><a name="page176" id="page176"></a>176</span>
+Electra became the wife of Pylades. The story of Electra is the
+subject of the <i>Choëphori</i> of Aeschylus, the <i>Electra</i> of Sophocles
+and the <i>Electra</i> of Euripides. It is in the Sophoclean play that
+Electra is most prominent.</p>
+
+<div class="condensed">
+<p>There are many variations in the treatment of the legend, for
+which, as also for a discussion of the modern plays on the subject
+by Voltaire and Alfieri, see Jebb&rsquo;s Introduction to his edition of the
+<i>Electra</i> of Sophocles.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRICAL<a name="ar61" id="ar61"></a></span> (or <span class="sc">Electrostatic</span>) <b>MACHINE,</b> a machine
+operating by manual or other power for transforming mechanical
+work into electric energy in the form of electrostatic charges of
+opposite sign delivered to separate conductors. Electrostatic
+machines are of two kinds: (1) Frictional, and (2) Influence
+machines.</p>
+
+<table class="flt" style="float: right; width: 340px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:290px; height:445px" src="images/img176a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 1.</span>&mdash;Ramsden&rsquo;s electrical machine.</td></tr></table>
+
+<p><i>Frictional Machines.</i>&mdash;A primitive form of frictional electrical
+machine was constructed about 1663 by Otto von Guericke
+(1602-1686). It consisted of a globe of sulphur fixed on an axis
+and rotated by a winch, and it was electrically excited by the
+friction of warm hands held against it. Sir Isaac Newton
+appears to have been the first to use a glass globe instead of
+sulphur (<i>Optics</i>, 8th Query). F. Hawksbee in 1709 also used a
+revolving glass globe. A metal chain resting on the globe served
+to collect the charge. Later G.M. Bose (1710-1761), of Wittenberg,
+added the prime conductor, an insulated tube or cylinder
+supported on silk strings, and J.H. Winkler (1703-1770),
+professor of physics at Leipzig, substituted a leather cushion for
+the hand. Andreas Gordon (1712-1751) of Erfurt, a Scotch
+Benedictine monk, first used a glass cylinder in place of a sphere.
+Jesse Ramsden (1735-1800) in 1768 constructed his well-known
+form of plate electrical machine (fig. 1). A glass plate fixed to a
+wooden or metal shaft is rotated by a winch. It passes between
+two rubbers made of leather, and is partly covered with two silk
+aprons which extend over quadrants of its surface. Just below
+the places where the aprons terminate, the glass is embraced by
+two insulated metal forks having the sharp points projecting
+towards the glass, but not quite touching it. The glass is
+excited positively by friction with the rubbers, and the charge is
+drawn off by the action of the points which, when acted upon
+inductively, discharge negative electricity against it. The
+insulated conductor to which the points are connected therefore
+becomes positively electrified.
+The cushions must
+be connected to earth to
+remove the negative electricity
+which accumulates
+on them. It was found
+that the machine acted
+better if the rubbers were
+covered with bisulphide of
+tin or with F. von Kienmayer&rsquo;s
+amalgam, consisting
+of one part of zinc, one
+of tin and two of mercury.
+The cushions were
+greased and the amalgam
+in a state of powder
+spread over them. Edward
+Nairne&rsquo;s electrical machine
+(1787) consisted of a glass
+cylinder with two insulated
+conductors, called
+prime conductors, on glass
+legs placed near it. One
+of these carried the leather
+exacting cushions and the
+other the collecting metal points, a silk apron extending over the
+cylinder from the cushion almost to the points. The rubber was
+smeared with amalgam. The function of the apron is to prevent
+the escape of electrification from the glass during its passage
+from the rubber to the collecting points. Nairne&rsquo;s machine could
+give either positive or negative electricity, the first named being
+collected from the prime conductor carrying the collecting
+points and the second from the prime conductor carrying the
+cushion.</p>
+
+<table class="flt" style="float: left; width: 350px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:315px; height:222px" src="images/img176b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p><i>Influence Machines.</i>&mdash;Frictional machines are, however, now
+quite superseded by the second class of instrument mentioned
+above, namely, influence machines. These operate by electrostatic
+induction and convert mechanical work into electrostatic
+energy by the aid of a small initial charge which is continually
+being replenished
+or reinforced. The
+general principle of
+all the machines described
+below will be
+best understood by
+considering a simple
+ideal case. Imagine
+two Leyden jars with
+large brass knobs, A
+and B, to stand on the
+ground (fig. 2). Let
+one jar be initially
+charged with positive electricity on its inner coating and
+the other with negative, and let both have their outsides
+connected to earth. Imagine two insulated balls A&prime; and B&prime;
+so held that A&prime; is near A and B&prime; is near B. Then the positive
+charge on A induces two charges on A&prime;, viz.: a negative
+on the side nearest and a positive on the side most removed.
+Likewise the negative charge on B induces a positive charge
+on the side of B&prime; nearest to it and repels negative electricity to
+the far side. Next let the balls A&prime; and B&prime; be connected together
+for a moment by a wire N called a neutralizing conductor which
+is subsequently removed. Then A&prime; will be left negatively
+electrified and B&prime; will be left positively electrified. Suppose
+that A&prime; and B&prime; are then made to change places. To do this we
+shall have to exert energy to remove A&prime; against the attraction
+of A and B&prime; against the attraction of B. Finally let A&prime; be
+brought in contact with B and B&prime; with A. The ball A&prime; will give
+up its charge of negative electricity to the Leyden jar B, and the
+ball B&prime; will give up its positive charge to the Leyden jar A.
+This transfer will take place because the inner coatings of the
+Leyden jars have greater capacity with respect to the earth than
+the balls. Hence the charges of the jars will be increased. The
+balls A&prime; and B&prime; are then practically discharged, and the above
+cycle of operations may be repeated. Hence, however small
+may be the initial charges of the Leyden jars, by a principle of
+accumulation resembling that of compound interest, they can
+be increased as above shown to any degree. If this series of
+operations be made to depend upon the continuous rotation of
+a winch or handle, the arrangement constitutes an electrostatic
+influence machine. The principle therefore somewhat resembles
+that of the self-exciting dynamo.</p>
+
+<p>The first suggestion for a machine of the above kind seems
+to have grown out of the invention of Volta&rsquo;s electrophorus.
+<span class="sidenote">Bennet&rsquo;s Doubler.</span>
+Abraham Bennet, the inventor of the gold leaf electroscope,
+described a doubler or machine for multiplying
+electric charges (<i>Phil. Trans.</i>, 1787).</p>
+
+<div class="condensed">
+<p>The principle of this apparatus may be explained thus. Let A and
+C be two fixed disks, and B a disk which can be brought at will within
+a very short distance of either A or C. Let us suppose all the plates
+to be equal, and let the capacities of A and C in presence of B be
+each equal to p, and the coefficient of induction between A and B,
+or C and B, be q. Let us also suppose that the plates A and C are so
+distant from each other that there is no mutual influence, and that p&rsquo;
+is the capacity of one of the disks when it stands alone. A small
+charge Q is communicated to A, and A is insulated, and B, uninsulated,
+is brought up to it; the charge on B will be&mdash;(q/p)Q.
+B is now uninsulated and brought to face C, which is uninsulated;
+the charge on C will be (q/p)²Q. C is now insulated and connected
+with A, which is always insulated. B is then brought to face A and
+uninsulated, so that the charge on A becomes rQ, where</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">r =</td> <td>p</td>
+<td rowspan="2"><span class="f150">(</span> 1 +</td> <td>q²</td>
+<td rowspan="2"><span class="f150">)</span>.</td></tr>
+<tr><td class="denom">p + p&prime;</td> <td class="denom">p²</td></tr></table>
+
+<p class="noind">A is now disconnected from C, and here the first operation ends.
+It is obvious that at the end of n such operations the charge on
+A will be r<span class="sp">n</span>Q, so that the charge goes on increasing in geometrical
+progression. If the distance between the disks could be made
+<span class="pagenum"><a name="page177" id="page177"></a>177</span>
+infinitely small each time, then the multiplier r would be 2, and
+the charge would be doubled each time. Hence the name of the
+apparatus.</p>
+</div>
+
+<table class="flt" style="float: right; width: 390px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:353px; height:280px" src="images/img177a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 3.</span>&mdash;Nicholson&rsquo;s Revolving Doubler.</td></tr></table>
+
+<p>Erasmus Darwin, B. Wilson, G.C. Bohnenberger and J.C.E.
+Peclet devised various modifications of Bennet&rsquo;s instrument
+(see S.P. Thompson, &ldquo;The Influence Machine from
+1788 to 1888,&rdquo; <i>Journ. Soc. Tel. Eng.</i>, 1888, 17, p. 569).
+<span class="sidenote">Nicholson&rsquo;s doubler.</span>
+Bennet&rsquo;s doubler appears to have given a suggestion
+to William Nicholson (<i>Phil. Trans.</i>, 1788, p. 403) of
+&ldquo;an instrument which by turning a winch produced the two
+states of electricity without friction or communication with the
+earth.&rdquo; This &ldquo;revolving doubler,&rdquo; according to the description
+of Professor S.P. Thompson (<i>loc. cit.</i>), consists of two fixed
+plates of brass A and C (fig. 3), each two inches in diameter and
+separately supported on insulating arms in the same plane, so
+that a third revolving plate B may pass very near them without
+touching. A brass ball D two inches in diameter is fixed on
+the end of the axis that carries the plate B, and is loaded within
+at one side, so as to act as a counterpoise to the revolving plate
+B. The axis P N is made of varnished glass, and so are the axes
+that join the three plates with the brass axis N O. The axis N O
+passes through the brass piece M, which stands on an insulating
+pillar of glass, and supports the plates A and C. At one extremity
+of this axis is the ball D, and the other is connected with a rod
+of glass, N P, upon which is fixed the handle L, and also the piece
+G H, which is separately insulated. The pins E, F rise out of the
+back of the fixed plates A and C, at unequal distances from the
+axis. The piece K is parallel to G H, and both of them are
+furnished at their ends with small pieces of flexible wire that they
+may touch the pins E, F in certain points of their revolution.
+From the brass
+piece M there
+stands out a pin
+I, to touch against
+a small flexible
+wire or spring
+which projects
+sideways from the
+rotating plate B
+when it comes opposite
+A. The
+wires are so adjusted
+by bending
+that B, at the
+moment when it
+is opposite A, communicates
+with the ball D, and A communicates with C
+through GH; and half a revolution later C, when B comes
+opposite to it, communicates with the ball D through the contact
+of K with F. In all other positions A, B, C and D are completely
+disconnected from each other. Nicholson thus described the
+operation of his machine:&mdash;</p>
+
+<div class="condensed">
+<p>&ldquo;When the plates A and B are opposite each other, the two fixed
+plates A and C may be considered as one mass, and the revolving
+plate B, together with the ball D, will constitute another mass.
+All the experiments yet made concur to prove that these two masses
+will not possess the same electric state.... The redundant electricities
+in the masses under consideration will be unequally distributed;
+the plate A will have about ninety-nine parts, and the plate
+C one; and, for the same reason, the revolving plate B will have
+ninety-nine parts of the opposite electricity, and the ball D one.
+The rotation, by destroying the contacts, preserves this unequal
+distribution, and carries B from A to C at the same time that the tail
+K connects the ball with the plate C. In this situation, the electricity
+in B acts upon that in C, and produces the contrary state,
+by virtue of the communication between C and the ball; which
+last must therefore acquire an electricity of the same kind with that
+of the revolving plate. But the rotation again destroys the contact
+and restores B to its first situation opposite A. Here, if we attend
+to the effect of the whole revolution, we shall find that the electric
+states of the respective masses have been greatly increased; for the
+ninety-nine parts in A and B remain, and the one part of electricity
+in C has been increased so as nearly to compensate ninety-nine parts
+of the opposite electricity in the revolving plate B, while the communication
+produced an opposite mutation in the electricity of the
+ball. A second rotation will, of course, produce a proportional
+augmentation of these increased quantities; and a continuance of
+turning will soon bring the intensities to their maximum, which is
+limited by an explosion between the plates&rdquo; (<i>Phil. Trans.</i>, 1788, p. 405).</p>
+</div>
+
+<table class="flt" style="float: right; width: 320px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:279px; height:249px" src="images/img177b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 4.</span>&mdash;Belli&rsquo;s Doubler.</td></tr></table>
+
+<p>Nicholson described also another apparatus, the &ldquo;spinning
+condenser,&rdquo; which worked on the same principle. Bennet and
+Nicholson were followed by T. Cavallo, John Read,
+Bohnenberger, C.B. Désormes and J.N.P. Hachette
+<span class="sidenote">Belli&rsquo;s doubler.</span>
+and others in the invention of various forms of rotating
+doubler. A simple and typical form of doubler, devised in 1831
+by G. Belli (fig. 4), consisted of two curved metal plates between
+which revolved a pair of
+balls carried on an insulating
+stem. Following the
+nomenclature usual in connexion
+with dynamos we
+may speak of the conductors
+which carry the initial
+charges as the field plates,
+and of the moving conductors
+on which are induced
+the charges which are subsequently
+added to those on
+the field plates, as the
+carriers. The wire which
+connects two armature
+plates for a moment is the neutralizing conductor. The
+two curved metal plates constitute the field plates and must
+have original charges imparted to them of opposite sign. The
+rotating balls are the carriers, and are connected together for a
+moment by a wire when in a position to be acted upon inductively
+by the field plates, thus acquiring charges of opposite sign. The
+moment after they are separated again. The rotation continuing
+the ball thus negatively charged is made to give up this
+charge to that negatively electrified field plate, and the ball
+positively charged its charge to the positively electrified field
+plate, by touching little contact springs. In this manner the
+field plates accumulate charges of opposite sign.</p>
+
+<table class="flt" style="float: right; width: 250px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:210px; height:219px" src="images/img177c.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 5.</span>&mdash;Varley&rsquo;s Machine.</td></tr></table>
+
+<p>Modern types of influence machine may be said to date from
+1860 when C.F. Varley patented a type of influence machine
+which has been the parent of numerous subsequent
+forms (<i>Brit. Pat. Spec.</i> No. 206 of 1860). In it the
+<span class="sidenote">Varley&rsquo;s machine.</span>
+field plates were sheets of tin-foil attached to a glass
+plate (fig. 5). In front of them a disk of ebonite or glass, having
+carriers of metal fixed to its edge, was rotated by a winch. In
+the course of their rotation two diametrically opposite carriers
+touched against the ends of a neutralizing conductor so as to form
+for a moment one conductor, and the moment afterwards these
+two carriers were insulated, one carrying away a positive charge
+and the other a negative. Continuing their rotation, the positively
+charged carrier gave up its positive charge by touching a little
+knob attached to the positive field plate, and similarly for the
+negative charge carrier. In this way the charges on the field
+plates were continually replenished
+and reinforced. Varley also constructed
+a multiple form of influence
+machine having six rotating disks,
+each having a number of carriers
+and rotating between field plates.
+With this apparatus he obtained
+sparks 6 in. long, the initial source
+of electrification being a single
+Daniell cell.</p>
+
+<p>Varley was followed by A.J.I.
+Toepler, who in 1865 constructed
+an influence machine consisting of
+two disks fixed on the same shaft and rotating in the same
+direction. Each disk carried two strips of tin-foil extending
+<span class="sidenote">Toepler machine.</span>
+nearly over a semi-circle, and there were two field
+plates, one behind each disk; one of the plates was
+positively and the other negatively electrified. The
+carriers which were touched under the influence of the positive
+field plate passed on and gave up a portion of their negative
+charge to increase that of the negative field plate; in the same
+<span class="pagenum"><a name="page178" id="page178"></a>178</span>
+way the carriers which were touched under the influence of the
+negative field plate sent a part of their charge to augment that
+of the positive field plate. In this apparatus one of the charging
+rods communicated with one of the field plates, but the other
+with the neutralizing brush opposite to the other field plate.
+Hence one of the field plates would always remain charged
+when a spark was taken at the transmitting terminals.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:429px; height:347px" src="images/img178a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span>&mdash;Holtz&rsquo;s Machine.</td></tr></table>
+
+<p>Between 1864 and 1880, W.T.B. Holtz constructed and
+described a large number of influence machines which were for a
+long time considered the most advanced development
+of this type of electrostatic machine. In one form the
+<span class="sidenote">Holtz machine.</span>
+Holtz machine consisted of a glass disk mounted on a
+horizontal axis F (fig. 6) which could be made to rotate at a
+considerable speed by a multiplying gear, part of which is seen at
+X. Close behind this disk was fixed another vertical disk of glass
+in which were cut two windows B, B. On the side of the fixed
+disk next the rotating disk were pasted two sectors of paper A, A,
+with short blunt points attached to them which projected out
+into the windows on the side away from the rotating disk. On
+the other side of the rotating disk were placed two metal combs
+C, C, which consisted of sharp points set in metal rods and were
+each connected to one of a pair of discharge balls E, D, the
+distance between which could be varied. To start the machine the
+balls were brought in contact, one of the paper armatures
+electrified, say, with positive electricity, and the disk set in
+motion. Thereupon very shortly a hissing sound was heard
+and the machine became harder to turn as if the disk were moving
+through a resisting medium. After that the discharge balls
+might be separated a little and a continuous series of sparks or
+brush discharges would take place between them. If two Leyden
+jars L, L were hung upon the conductors which supported the
+combs, with their outer coatings put in connexion with one
+another by M, a series of strong spark discharges passed between
+the discharge balls. The action of the machine is as follows:
+Suppose one paper armature to be charged positively, it acts by
+induction on the right hand comb, causing negative electricity to
+issue from the comb points upon the glass revolving disk; at the
+same time the positive electricity passes through the closed
+discharge circuit to the left comb and issues from its teeth upon
+the part of the glass disk at the opposite end of the diameter.
+This positive electricity electrifies the left paper armature by
+induction, positive electricity issuing from the blunt point upon
+the side farthest from the rotating disk. The charges thus
+deposited on the glass disk are carried round so that the upper
+half is electrified negatively on both sides and the lower half
+positively on both sides, the sign of the electrification being
+reversed as the disk passes between the combs and the armature
+by discharges issuing from them respectively. If it were not for
+leakage in various ways, the electrification would go on everywhere
+increasing, but in practice a stationary state is soon
+attained. Holtz&rsquo;s machine is very uncertain in its action in a
+moist climate, and has generally to be enclosed in a chamber in
+which the air is kept artificially dry.</p>
+
+<p>Robert Voss, a Berlin instrument maker, in 1880 devised a form
+of machine in which he claimed that the principles of Toepler and
+Holtz were combined. On a rotating glass or ebonite
+disk were placed carriers of tin-foil or metal buttons
+<span class="sidenote">Voss&rsquo;s machine.</span>
+against which neutralizing brushes touched. This
+armature plate revolved in front of a field plate carrying two
+pieces of tin-foil backed up by larger pieces of varnished paper.
+The studs on the armature plate were charged inductively by
+being connected for a moment by a neutralizing wire as they
+passed in front of the field plates, and then gave up their charges
+partly to renew the field charges and partly to collecting combs
+connected to discharge balls. In general design and construction,
+the manner of moving the rotating plate and in the use of the two
+Leyden jars in connexion with the discharge balls, Voss borrowed
+his ideas from Holtz.</p>
+
+<p>All the above described machines, however, have been thrown
+into the shade by the invention of a greatly improved type of influence
+machine first constructed by James Wimshurst
+about 1878. Two glass disks are mounted on two shafts
+<span class="sidenote">Wimshurst machine.</span>
+in such a manner that, by means of two belts and pulleys
+worked from a winch shaft, the disks can be rotated
+rapidly in opposite directions close to each other (fig. 7). These
+glass disks carry on them a certain number (not less than 16 or
+20) tin-foil carriers which may or may not have brass buttons
+upon them. The glass plates are well varnished, and the carriers
+are placed on the outer sides of the two glass plates. As therefore
+the disks revolve, these carriers travel in opposite directions,
+coming at intervals in opposition to each other. Each upright
+bearing carrying the shafts of the revolving disks also carries a
+neutralizing conductor or wire ending in a little brush of gilt
+thread. The neutralizing conductors for each disk are placed at
+right angles to each other. In addition there are collecting
+combs which occupy an intermediate position and have sharp
+points projecting inwards, and coming near to but not touching
+the carriers. These combs on opposite sides are connected
+respectively to the inner coatings of two Leyden jars whose outer
+coatings are in connexion with one another.</p>
+
+<table class="flt" style="float: right; width: 330px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:308px; height:328px" src="images/img178b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 7.</span>&mdash;Wimshurst&rsquo;s Machine.</td></tr>
+<tr><td class="figright1"><img style="width:216px; height:239px" src="images/img179a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 8.</span>&mdash;Action of the
+Wimshurst Machine.</td></tr></table>
+
+<p>The operation of the machine is as follows: Let us suppose
+that one of the studs on the back plate is positively electrified
+and one at the opposite end of a diameter is negatively electrified,
+and that at that moment two corresponding studs on the front
+plate passing opposite to these back studs are momentarily
+connected together by
+the neutralizing wire
+belonging to the front
+plate. The positive stud
+on the back plate will
+act inductively on the
+front stud and charge it
+negatively, and similarly
+for the other stud, and
+as the rotation continues
+these charged studs will
+pass round and give up
+most of their charge
+through the combs to
+the Leyden jars. The
+moment, however, a pair
+of studs on the front
+plate are charged, they
+act as field plates to
+studs on the back plate which are passing at the moment,
+provided these last are connected by the back neutralizing wire.
+After a few revolutions of the disks half the studs on the front
+plate at any moment are charged negatively and half positively
+and the same on the back plate, the neutralizing wires forming the
+boundary between the positively and negatively charged studs.
+The diagram in fig. 8, taken by permission from S.P. Thompson&rsquo;s
+paper (<i>loc. cit.</i>), represents a view of the distribution of these
+charges on the front and back plates respectively. It will be
+<span class="pagenum"><a name="page179" id="page179"></a>179</span>
+seen that each stud is in turn both a field plate and a carrier
+having a charge induced on it, and then passing on in turn
+induces further charges on other studs. Wimshurst constructed
+numerous very powerful machines
+of this type, some of them with
+multiple plates, which operate in
+almost any climate, and rarely fail
+to charge themselves and deliver a
+torrent of sparks between the discharge
+balls whenever the winch is
+turned. He also devised an alternating
+current electrical machine
+in which the discharge balls were
+alternately positive and negative.
+Large Wimshurst multiple plate
+influence machines are often used
+instead of induction coils for exciting
+Röntgen ray tubes in medical
+work. They give very steady illumination on fluorescent
+screens.</p>
+
+<p>In 1900 it was found by F. Tudsbury that if an influence
+machine is enclosed in a metallic chamber containing compressed
+air, or better, carbon dioxide, the insulating properties of compressed
+gases enable a greatly improved effect to be obtained
+owing to the diminution of the leakage across the plates and from
+the supports. Hence sparks can be obtained of more than
+double the length at ordinary atmospheric pressure. In one
+case a machine with plates 8 in. in diameter which could give
+sparks 2.5 in. at ordinary pressure gave sparks of 5, 7, and 8 in.
+as the pressure was raised to 15, 30 and 45 &#8468; above the normal
+atmosphere.</p>
+
+<p>The action of Lord Kelvin&rsquo;s replenisher (fig. 9) used by him
+in connexion with his electrometers for maintaining their
+charge, closely resembles that of Belli&rsquo;s doubler and will be
+understood from fig. 9. Lord Kelvin also devised an influence
+machine, commonly called a &ldquo;mouse mill,&rdquo; for electrifying the
+ink in connexion with his siphon recorder. It was an electrostatic
+and electromagnetic machine combined, driven by an electric
+current and producing in turn electrostatic charges of electricity.
+In connexion with this subject mention must also be made of the
+water dropping influence machine of the same inventor.<a name="fa1g" id="fa1g" href="#ft1g"><span class="sp">1</span></a></p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:516px; height:236px" src="images/img179b.jpg" alt="" /></td></tr>
+<tr><td class="caption" colspan="2"><span class="sc">Fig. 9.</span>&mdash;Lord Kelvin&rsquo;s Replenisher.</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;"><p>C, C, Metal carriers fixed to ebonite cross-arm.</p>
+<p>F, F, Brass field-plates or conductors.</p></td>
+<td class="f90" style="width: 50%; vertical-align: top;"><p><i>a</i>, <i>a</i>, Receiving springs.</p>
+<p><i>n</i>, <i>n</i>, Connecting springs or neutralizing brushes.</p></td></tr></table>
+
+<p class="pt2">The action and efficiency of influence machines have been
+investigated by F. Rossetti, A. Righi and F.W.G. Kohlrausch.
+The electromotive force is practically constant no matter what the
+velocity of the disks, but according to some observers the internal
+resistance decreases as the velocity increases. Kohlrausch,
+using a Holtz machine with a plate 16 in. in diameter, found
+that the current given by it could only electrolyse acidulated
+water in 40 hours sufficient to liberate one cubic centimetre of
+mixed gases. E.E.N. Mascart, A. Roiti, and E. Bouchotte have
+also examined the efficiency and current producing power of
+influence machines.</p>
+
+<div class="condensed">
+<p><span class="sc">Bibliography.</span>&mdash;In addition to S.P. Thompson&rsquo;s valuable paper
+on influence machines (to which this article is much indebted) and
+other references given, see J. Clerk Maxwell, <i>Treatise on Electricity
+and Magnetism</i> (2nd ed., Oxford, 1881), vol. i. p. 294; J.D. Everett,
+<i>Electricity</i> (expansion of part iii. of Deschanel&rsquo;s <i>Natural Philosophy</i>)
+(London, 1901), ch. iv. p. 20; A. Winkelmann, <i>Handbuch der Physik</i>
+(Breslau, 1905), vol. iv. pp. 50-58 (contains a large number of
+references to original papers); J. Gray, <i>Electrical Influence Machines,
+their Development and Modern Forms</i> (London, 1903).</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1g" id="ft1g" href="#fa1g"><span class="fn">1</span></a> See Lord Kelvin, <i>Reprint of Papers on Electrostatics and Magnetism</i>
+(1872); &ldquo;Electrophoric Apparatus and Illustrations of Voltaic
+Theory,&rdquo; p. 319; &ldquo;On Electric Machines Founded on Induction
+and Convection,&rdquo; p. 330; &ldquo;The Reciprocal Electrophorus,&rdquo;
+p. 337.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRIC EEL<a name="ar62" id="ar62"></a></span> (<i>Gymnotus electricus</i>), a member of the
+family of fishes known as <i>Gymnotidae</i>. In spite of their external
+similarity the <i>Gymnotidae</i> have nothing to do with the eels
+(<i>Anguilla</i>). They resemble the latter in the elongation of the
+body, the large number of vertebrae (240 in <i>Gymnotus</i>), and the
+absence of pelvic fins; but they differ in all the more important
+characters of internal structure. They are in fact allied to the
+carps or <i>Cyprinidae</i> and the cat-fishes or <i>Siluridae</i>. In common
+with these two families and the <i>Characinidae</i> of Africa and South
+America, the <i>Gymnotidae</i> possess the peculiar structures called
+<i>ossicula auditus</i> or Weberian ossicles. These are a chain of
+small bones belonging to the first four vertebrae, which are
+much modified, and connecting the air-bladder with the auditory
+organs. Such an agreement in the structure of so complicated
+and specialized an apparatus can only be the result of a community
+of descent of the families possessing it. Accordingly
+these families are now placed together in a distinct sub-order,
+the Ostariophysi. The <i>Gymnotidae</i> are strongly modified and
+degraded <i>Characinidae</i>. In them the dorsal and caudal fins are
+very rudimentary or absent, and the anal is very long, extending
+from the anus, which is under the head or throat, to the end of
+the body.</p>
+
+<p><i>Gymnotus</i> is the only genus of the family which possesses
+electric organs. These extend the whole length of the tail, which
+is four-fifths of the body. They are modifications of the lateral
+muscles and are supplied with numerous branches of the spinal
+nerves. They consist of longitudinal columns, each composed
+of an immense number of &ldquo;electric plates.&rdquo; The posterior end
+of the organ is positive, the anterior negative, and the current
+passes from the tail to the head. The maximum shock is given
+when the head and tail of the <i>Gymnotus</i> are in contact with
+different points in the surface of some other animal. <i>Gymnotus
+electricus</i> attains a length of 3 ft. and the thickness of a man&rsquo;s
+thigh, and frequents the marshes of Brazil and the Guianas,
+where it is regarded with terror, owing to the formidable electrical
+apparatus with which it is provided. When this natural battery
+is discharged in a favourable position, it is sufficiently powerful
+to stun the largest animal; and according to A. von Humboldt,
+it has been found necessary to change the line of certain roads
+passing through the pools frequented by the electric eels. These
+fish are eaten by the Indians, who, before attempting to capture
+them, seek to exhaust their electrical power by driving horses
+into the ponds. By repeated discharges upon these they
+gradually expend this marvellous force; after which, being
+defenceless, they become timid, and approach the edge for
+shelter, when they fall an easy prey to the harpoon. It is only
+after long rest and abundance of food that the fish is able to
+resume the use of its subtle weapon. Humboldt&rsquo;s description of
+this method of capturing the fish has not, however, been verified
+by recent travellers.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRICITY.<a name="ar63" id="ar63"></a></span> This article is devoted to a general sketch of
+the history of the development of electrical knowledge on both
+the theoretical and the practical sides. The two great branches
+of electrical theory which concern the phenomena of electricity
+at rest, or &ldquo;frictional&rdquo; or &ldquo;static&rdquo; electricity, and of electricity
+in motion, or electric currents, are treated in two separate
+articles, <span class="sc"><a href="#artlinks">Electrostatics</a></span> and <span class="sc"><a href="#ar68">Electrokinetics</a></span>. The phenomena
+attendant on the passage of electricity through solids,
+through liquids and through gases, are described in the article
+<span class="sc"><a href="#artlinks">Conduction, Electric</a></span>, and also <span class="sc"><a href="#ar70">Electrolysis</a></span>, and the propagation
+of electrical vibrations in <span class="sc"><a href="#ar65">Electric Waves</a></span>. The interconnexion
+of magnetism (which has an article to itself) and
+<span class="pagenum"><a name="page180" id="page180"></a>180</span>
+electricity is discussed in <span class="sc"><a href="#ar71">Electromagnetism</a></span>, and these manifestations
+in nature in <span class="sc"><a href="#artlinks">Atmospheric Electricity</a></span>; <span class="sc"><a href="#artlinks">Aurora
+Polaris</a></span> and <span class="sc"><a href="#artlinks">Magnetism, Terrestrial</a></span>. The general principles
+of electrical engineering will be found in <span class="sc"><a href="#ar64">Electricity Supply</a></span>,
+and further details respecting the generation and use of electrical
+power are given in such articles as <span class="sc"><a href="#artlinks">Dynamo</a></span>; <span class="sc"><a href="#artlinks">Motors, Electric</a></span>;
+<span class="sc"><a href="#artlinks">Transformers</a></span>; <span class="sc"><a href="#artlinks">Accumulator</a></span>; <span class="sc"><a href="#artlinks">Power Transmission</a></span>:
+<i>Electric</i>; <span class="sc"><a href="#artlinks">Traction</a></span>; <span class="sc"><a href="#artlinks">Lighting</a></span>: <i>Electric</i>; <span class="sc"><a href="#ar66">Electrochemistry</a></span>
+and <span class="sc"><a href="#ar72">Electrometallurgy</a></span>. The principles of telegraphy (land,
+submarine and wireless) and of telephony are discussed in the
+articles <span class="sc"><a href="#artlinks">Telegraph</a></span> and <span class="sc"><a href="#artlinks">Telephone</a></span>, and various electrical
+instruments are treated in separate articles such as <span class="sc"><a href="#artlinks">Amperemeter</a></span>;
+<span class="sc"><a href="#ar73">Electrometer</a></span>; <span class="sc"><a href="#artlinks">Galvanometer</a></span>; <span class="sc"><a href="#artlinks">Voltmeter</a></span>;
+<span class="sc"><a href="#artlinks">Wheatstone&rsquo;s Bridge</a></span>; <span class="sc"><a href="#artlinks">Potentiometer</a></span>; <span class="sc"><a href="#artlinks">Meter, Electric</a></span>;
+<span class="sc"><a href="#ar75">Electrophorus</a></span>; <span class="sc"><a href="#artlinks">Leyden Jar</a></span>; &amp;c.</p>
+
+<p>The term &ldquo;electricity&rdquo; is applied to denote the physical
+agency which exhibits itself by effects of attraction and repulsion
+when particular substances are rubbed or heated, also in certain
+chemical and physiological actions and in connexion with moving
+magnets and metallic circuits. The name is derived from the
+word <i>electrica</i>, first used by William Gilbert (1544-1603) in his
+epoch-making treatise <i>De magnete, magneticisque corporibus,
+et de magno magnete tellure</i>, published in 1600,<a name="fa1h" id="fa1h" href="#ft1h"><span class="sp">1</span></a> to denote
+substances which possess a similar property to amber (= <i>electrum</i>,
+from <span class="grk" title="êlektron">&#7972;&#955;&#949;&#954;&#964;&#961;&#959;&#957;</span>) of attracting light objects when rubbed. Hence
+the phenomena came to be collectively called electrical, a term
+first used by William Barlowe, archdeacon of Salisbury, in 1618,
+and the study of them, electrical science.</p>
+
+<p class="pt2 center"><i>Historical Sketch.</i></p>
+
+<p>Gilbert was the first to conduct systematic scientific experiments
+on electrical phenomena. Prior to his date the scanty
+knowledge possessed by the ancients and enjoyed in the middle
+ages began and ended with facts said to have been familiar to
+Thales of Miletus (600 <span class="scs">B.C.</span>) and mentioned by Theophrastus
+(321 <span class="scs">B.C.</span>) and Pliny (<span class="scs">A.D.</span> 70), namely, that amber, jet and one
+or two other substances possessed the power, when rubbed, of
+attracting fragments of straw, leaves or feathers. Starting with
+careful and accurate observations on facts concerning the
+mysterious properties of amber and the lodestone, Gilbert laid
+the foundations of modern electric and magnetic science on the
+true experimental and inductive basis. The subsequent history
+of electricity may be divided into four well-marked periods.
+The first extends from the date of publication of Gilbert&rsquo;s great
+treatise in 1600 to the invention by Volta of the voltaic pile and
+the first production of the electric current in 1799. The second
+dates from Volta&rsquo;s discovery to the discovery by Faraday in
+1831 of the induction of electric currents and the creation of
+currents by the motion of conductors in magnetic fields, which
+initiated the era of modern electrotechnics. The third covers
+the period between 1831 and Clerk Maxwell&rsquo;s enunciation of the
+electromagnetic theory of light in 1865 and the invention of the
+self-exciting dynamo, which marks another great epoch in the
+development of the subject; and the fourth comprises the modern
+development of electric theory and of absolute quantitative
+measurements, and above all, of the applications of this knowledge
+in electrical engineering. We shall sketch briefly the historical
+progress during these various stages, and also the growth of
+electrical theories of electricity during that time.</p>
+
+<p><span class="sc">First Period.</span>&mdash;Gilbert was probably led to study the
+phenomena of the attraction of iron by the lodestone in consequence
+of his conversion to the Copernican theory of the earth&rsquo;s
+motion, and thence proceeded to study the attractions produced
+by amber. An account of his electrical discoveries is given in
+the <i>De magnete</i>, lib. ii. cap. 2.<a name="fa2h" id="fa2h" href="#ft2h"><span class="sp">2</span></a> He invented the <i>versorium</i> or
+electrical needle and proved that innumerable bodies he called
+<i>electrica</i>, when rubbed, can attract the needle of the versorium
+(see <span class="sc"><a href="#ar77">Electroscope</a></span>). Robert Boyle added many new facts and
+gave an account of them in his book, <i>The Origin of Electricity</i>.
+He showed that the attraction between the rubbed body and
+the test object is mutual. Otto von Guericke (1602-1686) constructed
+the first electrical machine with a revolving ball of
+sulphur (see <span class="sc"><a href="#ar61">Electrical Machine</a></span>), and noticed that light
+objects were repelled after being attracted by excited electrics.
+Sir Isaac Newton substituted a ball of glass for sulphur in the
+electrical machine and made other not unimportant additions
+to electrical knowledge. Francis Hawksbee (d. 1713) published
+in his book <i>Physico-Mechanical Experiments</i> (1709), and in several
+Memoirs in the <i>Phil. Trans.</i> about 1707, the results of his electrical
+inquiries. He showed that light was produced when mercury
+was shaken up in a glass tube exhausted of its air. Dr Wall
+observed the spark and crackling sound when warm amber was
+rubbed, and compared them with thunder and lightning (<i>Phil.
+Trans.</i>, 1708, 26, p. 69). Stephen Gray (1696-1736) noticed in
+1720 that electricity could be excited by the friction of hair, silk,
+wool, paper and other bodies. In 1729 Gray made the important
+discovery that some bodies were conductors and others non-conductors
+of electricity. In conjunction with his friend
+Granville Wheeler (d. 1770), he conveyed the electricity from
+rubbed glass, a distance of 886 ft., along a string supported on
+silk threads (<i>Phil. Trans.</i>, 1735-1736, 39, pp. 16, 166 and 400).
+Jean Théophile Desaguliers (1683-1744) announced soon after
+that electrics were non-conductors, and conductors were non-electrics.
+C.F. de C. du Fay (1699-1739) made the great discovery
+that electricity is of two kinds, vitreous and resinous
+(<i>Phil. Trans.</i>, 1733, 38, p. 263), the first being produced when
+glass, crystal, &amp;c. are rubbed with silk, and the second when
+resin, amber, silk or paper, &amp;c. are excited by friction with
+flannel. He also discovered that a body charged with positive
+or negative electricity repels a body free to move when the
+latter is charged with electricity of like sign, but attracts it if
+it is charged with electricity of opposite sign, <i>i.e.</i> positive repels
+positive and negative repels negative, but positive attracts
+negative. It is to du Fay also that we owe the abolition of the
+distinction between electrics and non-electrics. He showed
+that all substances could be electrified by friction, but that
+to electrify conductors they must be insulated or supported
+on non-conductors. Various improvements were made in the
+electrical machine, and thereby experimentalists were provided
+with the means of generating strong electrification; C.F.
+Ludolff (1707-1763) of Berlin in 1744 succeeded in igniting ether
+with the electric spark (<i>Phil. Trans.</i>, 1744, 43, p. 167).</p>
+
+<div class="condensed">
+<p>For a very full list of the papers and works of these early electrical
+philosophers, the reader is referred to the bibliography on Electricity
+in Dr Thomas Young&rsquo;s <i>Natural Philosophy</i>, vol. ii. p. 415.</p>
+</div>
+
+<p>In 1745 the important invention of the Leyden jar or condenser
+was made by E.G. von Kleist of Kammin, and almost simultaneously
+by Cunaeus and Pieter van Musschenbroek (1692-1761)
+of Leiden (see <span class="sc"><a href="#artlinks">Leyden Jar</a></span>). Sir William Watson (1715-1787)
+in England first observed the flash of light when a Leyden jar
+is discharged, and he and Dr John Bevis (1695-1771) suggested
+coating the jar inside and outside with tinfoil. Watson carried
+out elaborate experiments to discover how far the electric
+discharge of the jar could be conveyed along metallic wires and
+was able to accomplish it for a distance of 2 m., making
+the important observation that the electricity appeared to be
+transmitted instantaneously.</p>
+
+<p><i>Franklin&rsquo;s Researches.</i>&mdash;Benjamin Franklin (1706-1790) was
+one of the great pioneers of electrical science, and made the ever-memorable
+experimental identification of lightning and electric
+spark. He argued that electricity is not created by friction, but
+merely collected from its state of diffusion through other matter
+by which it is attracted. He asserted that the glass globe, when
+rubbed, attracted the electrical fire, and took it from the rubber,
+the same globe being disposed, when the friction ceases, to give
+out its electricity to any body which has less. In the case of the
+charged Leyden jar, he asserted that the inner coating of tinfoil
+<span class="pagenum"><a name="page181" id="page181"></a>181</span>
+had received more than its ordinary quantity of electricity, and
+was therefore electrified positively, or plus, while the outer
+coating of tinfoil having had its ordinary quantity of electricity
+diminished, was electrified negatively, or minus. Hence the
+cause of the shock and spark when the jar is discharged, or
+when the superabundant or plus electricity of the inside is
+transferred by a conducting body to the defective or minus
+electricity of the outside. This theory of the Leyden phial
+Franklin supported very ingeniously by showing that the outside
+and the inside coating possessed electricities of opposite sign, and
+that, in charging it, exactly as much electricity is added on one
+side as is subtracted from the other. The abundant discharge of
+electricity by points was observed by Franklin is his earliest
+experiments, and also the power of points to conduct it copiously
+from an electrified body. Hence he was furnished with a simple
+method of collecting electricity from other bodies, and he was
+enabled to perform those remarkable experiments which are
+chiefly connected with his name. Hawksbee, Wall and J.A.
+Nollet (1700-1770) had successively suggested the identity of
+lightning and the electric spark, and of thunder and the snap
+of the spark. Previously to the year 1750, Franklin drew up a
+statement, in which he showed that all the general phenomena
+and effects which were produced by electricity had their counterparts
+in lightning. After waiting some time for the erection of
+a spire at Philadelphia, by means of which he hoped to bring
+down the electricity of a thunderstorm, he conceived the idea
+of sending up a kite among thunder-clouds. With this view he
+made a small cross of two small light strips of cedar, the arms
+being sufficiently long to reach to the four corners of a large
+thin silk handkerchief when extended. The corners of the
+handkerchief were tied to the extremities of the cross, and when
+the body of the kite was thus formed, a tail, loop and string were
+added to it. The body was made of silk to enable it to bear the
+violence and wet of a thunderstorm. A very sharp pointed wire
+was fixed at the top of the upright stick of the cross, so as to rise a
+foot or more above the wood. A silk ribbon was tied to the end
+of the twine next the hand, and a key suspended at the junction
+of the twine and silk. In company with his son, Franklin raised
+the kite like a common one, in the first thunderstorm, which
+happened in the month of June 1752. To keep the silk ribbon
+dry, he stood within a door, taking care that the twine did not
+touch the frame of the door; and when the thunder-clouds came
+over the kite he watched the state of the string. A cloud passed
+without any electrical indications, and he began to despair of
+success. At last, however, he saw the loose filaments of the twine
+standing out every way, and he found them to be attracted by
+the approach of his finger. The suspended key gave a spark on
+the application of his knuckle, and when the string had become
+wet with the rain the electricity became abundant. A Leyden
+jar was charged at the key, and by the electric fire thus obtained
+spirits were inflamed, and many other experiments performed
+which had been formerly made by excited electrics. In subsequent
+trials with another apparatus, he found that the clouds
+were sometimes positively and sometimes negatively electrified,
+and so demonstrated the perfect identity of lightning and
+electricity. Having thus succeeded in drawing the electric fire
+from the clouds, Franklin conceived the idea of protecting
+buildings from lightning by erecting on their highest parts pointed
+iron wires or conductors communicating with the ground. The
+electricity of a hovering or a passing cloud would thus be carried
+off slowly and silently; and if the cloud was highly charged, the
+lightning would strike in preference the elevated conductors.<a name="fa3h" id="fa3h" href="#ft3h"><span class="sp">3</span></a>
+The most important of Franklin&rsquo;s electrical writings are his
+<i>Experiments and Observations on Electricity made at Philadelphia</i>,
+1751-1754; his <i>Letters on Electricity</i>; and various memoirs and
+letters in the <i>Phil. Trans.</i> from 1756 to 1760.</p>
+
+<p>About the same time that Franklin was making his kite
+experiment in America, T.F. Dalibard (1703-1779) and others in
+France had erected a long iron rod at Marli, and obtained results
+agreeing with those of Franklin. Similar investigations were
+pursued by many others, among whom Father G.B. Beccaria
+(1716-1781) deserves especial mention. John Canton (1718-1772)
+made the important contribution to knowledge that
+electricity of either sign could be produced on nearly any body by
+friction with appropriate substances, and that a rod of glass
+roughened on one half was excited negatively in the rough part
+and positively in the smooth part by friction with the same rubber.
+Canton first suggested the use of an amalgam of mercury and tin
+for use with glass cylinder electrical machines to improve their
+action. His most important discovery, however, was that of
+electrostatic induction, the fact that one electrified body can
+produce charges of electricity upon another insulated body, and
+that when this last is touched it is left electrified with a charge of
+opposite sign to that of the inducing charge (<i>Phil. Trans.</i>, 1753-1754).
+We shall make mention lower down of Canton&rsquo;s contributions
+to electrical theory. Robert Symmer (d. 1763) showed that
+quite small differences determined the sign of the electrification
+that was generated by the friction of two bodies one against the
+other. Thus wearing a black and a white silk stocking one over the
+other, he found they were electrified oppositely when rubbed and
+drawn off, and that such a rubbed silk stocking when deposited in
+a Leyden jar gave up its electrification to the jar (<i>Phil. Trans.</i>,
+1759). Ebenezer Kinnersley (1711-1778) of Philadelphia made
+useful observations on the elongation and fusion of iron wires
+by electrical discharges (<i>Phil. Trans.</i>, 1763). A contemporary of
+Canton and co-discoverer with him of the facts of electrostatic
+induction was the Swede, Johann Karl Wilcke (1732-1796), then
+resident in Germany, who in 1762 published an account of
+experiments in which a metal plate held above the upper surface
+of a glass table was subjected to the action of a charge on an
+electrified metal plate held below the glass (<i>Kon. Schwedische
+Akad. Abhandl.</i>, 1762, 24, p. 213).</p>
+
+<p><i>Pyro-electricity.</i>&mdash;The subject of pyro-electricity, or the power
+possessed by some minerals of becoming electrified when merely
+heated, and of exhibiting positive and negative electricity, now
+began to attract notice. It is possible that the <i>lyncurium</i> of
+the ancients, which according to Theophrastus attracted light
+bodies, was tourmaline, a mineral found in Ceylon, which had
+been christened by the Dutch with the name of <i>aschentrikker</i>, or
+the attractor of ashes. In 1717 Louis Lémery exhibited to the
+Paris Academy of Sciences a stone from Ceylon which attracted
+light bodies; and Linnaeus in mentioning his experiments
+gives the stone the name of <i>lapis electricus</i>. Giovanni Caraffa,
+duca di Noja (1715-1768), was led in 1758 to purchase some of
+the stones called tourmaline in Holland, and, assisted by L.J.M.
+Daubenton and Michel Adanson, he made a series of experiments
+with them, a description of which he gave in a letter to G.L.L.
+Buffon in 1759. The subject, however, had already engaged the
+attention of the German philosopher, F.U.T. Aepinus, who
+published an account of them in 1756. Hitherto nothing had
+been said respecting the necessity of heat to excite the tourmaline;
+but it was shown by Aepinus that a temperature between 99½°
+and 212° Fahr. was requisite for the development of its attractive
+powers. Benjamin Wilson (<i>Phil. Trans.</i>, 1763, &amp;c.), J. Priestley,
+and Canton continued the investigation, but it was reserved for
+the Abbé Haüy to throw a clear light on this curious branch
+of the science (<i>Traité de minéralogie</i>, 1801). He found that the
+electricity of the tourmaline decreased rapidly from the summits
+or poles towards the middle of the crystal, where it was imperceptible;
+and he discovered that if a tourmaline is broken into
+any number of fragments, each fragment, when excited, has
+two opposite poles. Haüy discovered the same property in the
+Siberian and Brazilian topaz, borate of magnesia, mesotype,
+prehnite, sphene and calamine. He also found that the polarity
+which minerals receive from heat has a relation to the secondary
+forms of their crystals&mdash;the tourmaline, for example, having
+its resinous pole at the summit of the crystal which has three
+faces. In the other pyro-electric crystals above mentioned,
+Haüy detected the same deviation from the rules of symmetry
+<span class="pagenum"><a name="page182" id="page182"></a>182</span>
+in their secondary crystals which occurs in tourmaline. C.P.
+Brard (1788-1838) discovered that pyro-electricity was a
+property of axinite; and it was afterwards detected in other
+minerals. In repeating and extending the experiments of Haüy
+much later, Sir David Brewster discovered that various artificial
+salts were pyro-electric, and he mentions the tartrates of potash
+and soda and tartaric acid as exhibiting this property in a very
+strong degree. He also made many experiments with the
+tourmaline when cut into thin slices, and reduced to the finest
+powder, in which state each particle preserved its pyro-electricity;
+and he showed that scolezite and mesolite, even when deprived
+of their water of crystallization and reduced to powder, retain
+their property of becoming electrical by heat. When this white
+powder is heated and stirred about by any substance whatever,
+it collects in masses like new-fallen snow, and adheres to the
+body with which it is stirred.</p>
+
+<div class="condensed">
+<p>For Sir David Brewster&rsquo;s work on pyro-electricity, see <i>Trans. Roy.
+Soc. Edin.</i>, 1845, also <i>Phil. Mag.</i>, Dec. 1847. The reader will also
+find a full discussion on the subject in the <i>Treatise on Electricity</i>, by
+A. de la Rive, translated by C.V. Walker (London, 1856), vol. ii.
+part v. ch. i.</p>
+</div>
+
+<p><i>Animal electricity.</i>&mdash;The observation that certain animals
+could give shocks resembling the shock of a Leyden jar induced
+a closer examination of these powers. The ancients were
+acquainted with the benumbing power of the torpedo-fish, but
+it was not till 1676 that modern naturalists had their attention
+again drawn to the fact. E. Bancroft was the first person who
+distinctly suspected that the effects of the torpedo were electrical.
+In 1773 John Walsh (d. 1795) and Jan Ingenhousz (1730-1799)
+proved by many curious experiments that the shock of the
+torpedo was an electrical one (<i>Phil. Trans.</i>, 1773-1775); and
+John Hunter (id. 1773, 1775) examined and described the
+anatomical structure of its electrical organs. A. von Humboldt
+and Gay-Lussac (<i>Ann. Chim.</i>, 1805), and Etienne Geoffroy Saint-Hilaire
+(<i>Gilb. Ann.</i>, 1803) pursued the subject with success;
+and Henry Cavendish (<i>Phil. Trans.</i>, 1776) constructed an
+artificial torpedo, by which he imitated the actions of the living
+animal. The subject was also investigated (<i>Phil. Trans.</i>, 1812,
+1817) by Dr T.J. Todd (1789-1840), Sir Humphry Davy
+(id. 1829), John Davy (id. 1832, 1834, 1841) and Faraday
+(<i>Exp. Res.</i>, vol. ii.). The power of giving electric shocks has
+been discovered also in the <i>Gymnotus electricus</i> (electric eel),
+the <i>Malapterurus electricus</i>, the <i>Trichiurus electricus</i>, and the
+<i>Tetraodon electricus</i>. The most interesting and the best known
+of these singular fishes is the <i>Gymnotus</i> or Surinam eel. Humboldt
+gives a very graphic account of the combats which are
+carried on in South America between the gymnoti and the wild
+horses in the vicinity of Calabozo.</p>
+
+<p><i>Cavendish&rsquo;s Researches.</i>&mdash;The work of Henry Cavendish (1731-1810)
+entitles him to a high place in the list of electrical investigators.
+A considerable part of Cavendish&rsquo;s work was rescued
+from oblivion in 1879 and placed in an easily accessible form
+by Professor Clerk Maxwell, who edited the original manuscripts
+in the possession of the duke of Devonshire.<a name="fa4h" id="fa4h" href="#ft4h"><span class="sp">4</span></a> Amongst Cavendish&rsquo;s
+important contributions were his exact measurements of
+electrical capacity. The leading idea which distinguishes his
+work from that of his predecessors was his use of the phrase
+&ldquo;degree of electrification&rdquo; with a clear scientific definition
+which shows it to be equivalent in meaning to the modern term
+&ldquo;electric potential.&rdquo; Cavendish compared the capacity of
+different bodies with those of conducting spheres of known
+diameter and states these capacities in &ldquo;globular inches,&rdquo; a
+globular inch being the capacity of a sphere 1 in. in diameter.
+Hence his measurements are all directly comparable with modern
+electrostatic measurements in which the unit of capacity is that
+of a sphere 1 centimetre in radius. Cavendish measured the
+capacity of disks and condensers of various forms, and proved
+that the capacity of a Leyden pane is proportional to the surface
+of the tinfoil and inversely as the thickness of the glass. In
+connexion with this subject he anticipated one of Faraday&rsquo;s
+greatest discoveries, namely, the effect of the dielectric or insulator
+upon the capacity of a condenser formed with it, in other
+words, made the discovery of specific inductive capacity (see
+<i>Electrical Researches</i>, p. 183). He made many measurements
+of the electric conductivity of different solids and liquids, by
+comparing the intensity of the electric shock taken through his
+body and various conductors. He seems in this way to have
+educated in himself a very precise &ldquo;electrical sense,&rdquo; making
+use of his own nervous system as a kind of physiological galvanometer.
+One of the most important investigations he made in
+this way was to find out, as he expressed it, &ldquo;what power of the
+velocity the resistance is proportional to.&rdquo; Cavendish meant
+by the term &ldquo;velocity&rdquo; what we now call the current, and
+by &ldquo;resistance&rdquo; the electromotive force which maintains the
+current. By various experiments with liquids in tubes he found
+this power was nearly unity. This result thus obtained by
+Cavendish in January 1781, that the current varies in direct
+proportion to the electromotive force, was really an anticipation
+of the fundamental law of electric flow, discovered independently
+by G.S. Ohm in 1827, and since known as Ohm&rsquo;s Law. Cavendish
+also enunciated in 1776 all the laws of division of electric current
+between circuits in parallel, although they are generally supposed
+to have been first given by Sir C. Wheatstone. Another of his
+great investigations was the determination of the law according
+to which electric force varies with the distance. Starting from
+the fact that if an electrified globe, placed within two hemispheres
+which fit over it without touching, is brought in contact
+with these hemispheres, it gives up the whole of its charge to
+them&mdash;in other words, that the charge on an electrified body is
+wholly on the surface&mdash;he was able to deduce by most ingenious
+reasoning the law that electric force varies inversely as the
+square of the distance. The accuracy of his measurement, by
+which he established within 2% the above law, was only limited
+by the sensibility, or rather insensibility, of the pith ball electrometer,
+which was his only means of detecting the electric charge.<a name="fa5h" id="fa5h" href="#ft5h"><span class="sp">5</span></a>
+In the accuracy of his quantitative measurements and the range
+of his researches and his combination of mathematical and
+physical knowledge, Cavendish may not inaptly be described
+as the Kelvin of the 18th century. Nothing but his curious indifference
+to the publication of his work prevented him from
+securing earlier recognition for it.</p>
+
+<p><i>Coulomb&rsquo;s Work.</i>&mdash;Contemporary with Cavendish was C.A.
+Coulomb (1736-1806), who in France addressed himself to the
+same kind of exact quantitative work as Cavendish in England.
+Coulomb has made his name for ever famous by his invention
+and application of his torsion balance to the experimental
+verification of the fundamental law of electric attraction, in
+which, however, he was anticipated by Cavendish, namely,
+that the force of attraction between two small electrified spherical
+bodies varies as the product of their charges and inversely as the
+square of the distance of their centres. Coulomb&rsquo;s work received
+better publication than Cavendish&rsquo;s at the time of its accomplishment,
+and provided a basis on which mathematicians could
+operate. Accordingly the close of the 18th century drew into
+the arena of electrical investigation on its mathematical side
+P.S. Laplace, J.B. Biot, and above all, S.D. Poisson. Adopting
+the hypothesis of two fluids, Coulomb investigated experimentally
+and theoretically the distribution of electricity on the surface
+of bodies by means of his proof plane. He determined the law
+of distribution between two conducting bodies in contact; and
+measured with his proof plane the density of the electricity
+at different points of two spheres in contact, and enunciated
+an important law. He ascertained the distribution of electricity
+among several spheres (whether equal or unequal) placed in
+contact in a straight line; and he measured the distribution of
+<span class="pagenum"><a name="page183" id="page183"></a>183</span>
+electricity on the surface of a cylinder, and its distribution
+between a sphere and cylinder of different lengths but of the
+same diameter. His experiments on the dissipation of electricity
+possess also a high value. He found that the momentary
+dissipation was proportional to the degree of electrification at
+the time, and that, when the charge was moderate, its dissipation
+was not altered in bodies of different kinds or shapes. The
+temperature and pressure of the atmosphere did not produce
+any sensible change; but he concluded that the dissipation was
+nearly proportional to the cube of the quantity of moisture in
+the air.<a name="fa6h" id="fa6h" href="#ft6h"><span class="sp">6</span></a> In examining the dissipation which takes place along
+imperfectly insulating substances, he found that a thread of
+gum-lac was the most perfect of all insulators; that it insulated
+ten times as well as a dry silk thread; and that a silk thread
+covered with fine sealing-wax insulated as powerfully as gum-lac
+when it had four times its length. He found also that the
+dissipation of electricity along insulators was chiefly owing to
+adhering moisture, but in some measure also to a slight conducting
+power. For his memoirs see <i>Mém. de math. et phys. de
+l&rsquo;acad. de sc.</i>, 1785, &amp;c.</p>
+
+<p><span class="sc">Second Period.</span>&mdash;We now enter upon the second period of
+electrical research inaugurated by the epoch-making discovery
+of Alessandro Volta (1745-1827). L. Galvani had made in
+1790 his historic observations on the muscular contraction
+produced in the bodies of recently killed frogs when an electrical
+machine was being worked in the same room, and described
+them in 1791 (<i>De viribus electricitatis in motu musculari commentarius</i>,
+Bologna, 1791). Volta followed up these observations
+with rare philosophic insight and experimental skill. He showed
+that all conductors liquid and solid might be divided into two
+classes which he called respectively conductors of the first and
+of the second class, the first embracing metals and carbon in its
+conducting form, and the second class, water, aqueous solutions
+of various kinds, and generally those now called electrolytes.
+In the case of conductors of the first class he proved by the use
+of the condensing electroscope, aided probably by some form
+of multiplier or doubler, that a difference of potential (see
+<span class="sc"><a href="#artlinks">Electrostatics</a></span>) was created by the mere contact of two such
+conductors, one of them being positively electrified and the other
+negatively. Volta showed, however, that if a series of bodies of
+the first class, such as disks of various metals, are placed in
+contact, the potential difference between the first and the last
+is just the same as if they are immediately in contact. There
+is no accumulation of potential. If, however, pairs of metallic
+disks, made, say, of zinc and copper, are alternated with disks
+of cloth wetted with a conductor of the second class, such, for
+instance, as dilute acid or any electrolyte, then the effect of the
+feeble potential difference between one pair of copper and zinc
+disks is added to that of the potential difference between the
+next pair, and thus by a sufficiently long series of pairs any
+required difference of potential can be accumulated.</p>
+
+<p><i>The Voltaic Pile.</i>&mdash;This led him about 1799 to devise his famous
+voltaic pile consisting of disks of copper and zinc or other metals
+with wet cloth placed between the pairs. Numerous examples
+of Volta&rsquo;s original piles at one time existed in Italy, and were
+collected together for an exhibition held at Como in 1899, but
+were unfortunately destroyed by a disastrous fire on the 8th of
+July 1899. Volta&rsquo;s description of his pile was communicated
+in a letter to Sir Joseph Banks, president of the Royal Society
+of London, on the 20th of March 1800, and was printed in the
+<i>Phil. Trans.</i>, vol. 90, pt. 1, p. 405. It was then found that when
+the end plates of Volta&rsquo;s pile were connected to an electroscope
+the leaves diverged either with positive or negative electricity.
+Volta also gave his pile another form, the <i>couronne des tasses</i>
+(crown of cups), in which connected strips of copper and zinc
+were used to bridge between cups of water or dilute acid. Volta
+then proved that all metals could be arranged in an electromotive
+series such that each became positive when placed in contact
+with the one next below it in the series. The origin of the
+electromotive force in the pile has been much discussed, and
+Volta&rsquo;s discoveries gave rise to one of the historic controversies
+of science. Volta maintained that the mere contact
+of metals was sufficient to produce the electrical difference
+of the end plates of the pile. The discovery that chemical
+action was involved in the process led to the advancement of
+the chemical theory of the pile and this was strengthened by the
+growing insight into the principle of the conservation of energy.
+In 1851 Lord Kelvin (Sir W. Thomson), by the use of his then
+newly-invented electrometer, was able to confirm Volta&rsquo;s observations
+on contact electricity by irrefutable evidence, but the
+contact theory of the voltaic pile was then placed on a basis
+consistent with the principle of the conservation of energy.
+A.A. de la Rive and Faraday were ardent supporters of the
+chemical theory of the pile, and even at the present time opinions
+of physicists can hardly be said to be in entire accordance as to
+the source of the electromotive force in a voltaic couple or pile.<a name="fa7h" id="fa7h" href="#ft7h"><span class="sp">7</span></a></p>
+
+<p>Improvements in the form of the voltaic pile were almost
+immediately made by W. Cruickshank (1745-1800), Dr W.H.
+Wollaston and Sir H. Davy, and these, together with other
+eminent continental chemists, such as A.F. de Fourcroy, L.J.
+Thénard and J.W. Ritter (1776-1810), ardently prosecuted
+research with the new instrument. One of the first discoveries
+made with it was its power to electrolyse or chemically decompose
+certain solutions. William Nicholson (1753-1815) and Sir
+Anthony Carlisle (1768-1840) in 1800 constructed a pile of
+silver and zinc plates, and placing the terminal wires in water
+noticed the evolution from these wires of bubbles of gas, which
+they proved to be oxygen and hydrogen. These two gases, as
+Cavendish and James Watt had shown in 1784, were actually
+the constituents of water. From that date it was clearly recognized
+that a fresh implement of great power had been given
+to the chemist. Large voltaic piles were then constructed by
+Andrew Crosse (1784-1855) and Sir H. Davy, and improvements
+initiated by Wollaston and Robert Hare (1781-1858) of Philadelphia.
+In 1806 Davy communicated to the Royal Society
+of London a celebrated paper on some &ldquo;Chemical Agencies of
+Electricity,&rdquo; and after providing himself at the Royal Institution
+of London with a battery of several hundred cells, he announced
+in 1807 his great discovery of the electrolytic decomposition of
+the alkalis, potash and soda, obtaining therefrom the metals
+potassium and sodium. In July 1808 Davy laid a request
+before the managers of the Royal Institution that they would
+set on foot a subscription for the purchase of a specially large
+voltaic battery; as a result he was provided with one of 2000
+pairs of plates, and the first experiment performed with it was
+the production of the electric arc light between carbon poles.
+Davy followed up his initial work with a long and brilliant
+series of electrochemical investigations described for the most
+part in the <i>Phil. Trans.</i> of the Royal Society.</p>
+
+<p><i>Magnetic Action of Electric Current.</i>&mdash;Noticing an analogy
+between the polarity of the voltaic pile and that of the magnet,
+philosophers had long been anxious to discover a relation between
+the two, but twenty years elapsed after the invention of the pile
+before Hans Christian Oersted (1777-1851), professor of natural
+philosophy in the university of Copenhagen, made in 1819 the
+discovery which has immortalized his name. In the <i>Annals of
+Philosophy</i> (1820, 16, p. 273) is to be found an English translation
+of Oersted&rsquo;s original Latin essay (entitled &ldquo;Experiments on the
+Effect of a Current of Electricity on the Magnetic Needle&rdquo;),
+dated the 21st of July 1820, describing his discovery. In it
+Oersted describes the action he considers is taking place around
+<span class="pagenum"><a name="page184" id="page184"></a>184</span>
+the conductor joining the extremities of the pile; he speaks of
+it as the electric conflict, and says: &ldquo;It is sufficiently evident
+that the electric conflict is not confined to the conductor, but is
+dispersed pretty widely in the circumjacent space. We may
+likewise conclude that this conflict performs circles round the
+wire, for without this condition it seems impossible that one part
+of the wire when placed below the magnetic needle should drive
+its pole to the east, and when placed above it, to the west.&rdquo;
+Oersted&rsquo;s important discovery was the fact that when a wire
+joining the end plates of a voltaic pile is held near a pivoted
+magnet or compass needle, the latter is deflected and places itself
+more or less transversely to the wire, the direction depending
+upon whether the wire is above or below the needle, and on the
+manner in which the copper or zinc ends of the pile are connected
+to it. It is clear, moreover, that Oersted clearly recognized the
+existence of what is now called the magnetic field round the
+conductor. This discovery of Oersted, like that of Volta, stimulated
+philosophical investigation in a high degree.</p>
+
+<p><i>Electrodynamics.</i>&mdash;On the 2nd of October 1820, A.M. Ampère
+presented to the French Academy of Sciences an important
+memoir,<a name="fa8h" id="fa8h" href="#ft8h"><span class="sp">8</span></a> in which he summed up the results of his own and
+D.F.J. Arago&rsquo;s previous investigations in the new science of
+electromagnetism, and crowned that labour by the announcement
+of his great discovery of the dynamical action between conductors
+conveying the electric currents. Ampère in this paper gave an
+account of his discovery that conductors conveying electric
+currents exercise a mutual attraction or repulsion on one another,
+currents flowing in the same direction in parallel conductors
+attracting, and those in opposite directions repelling. Respecting
+this achievement when developed in its experimental and
+mathematical completeness, Clerk Maxwell says that it was
+&ldquo;perfect in form and unassailable in accuracy.&rdquo; By a series
+of well-chosen experiments Ampère established the laws of this
+mutual action, and not only explained observed facts by a
+brilliant train of mathematical analysis, but predicted others
+subsequently experimentally realized. These investigations led
+him to the announcement of the fundamental law of action
+between elements of current, or currents in infinitely short
+lengths of linear conductors, upon one another at a distance;
+summed up in compact expression this law states that the action
+is proportional to the product of the current strengths of the two
+elements, and the lengths of the two elements, and inversely
+proportional to the square of the distance between the two
+elements, and also directly proportional to a function of the angles
+which the line joining the elements makes with the directions
+of the two elements respectively. Nothing is more remarkable
+in the history of discovery than the manner in which Ampère
+seized upon the right clue which enabled him to disentangle the
+complicated phenomena of electrodynamics and to deduce them
+all as a consequence of one simple fundamental law, which
+occupies in electrodynamics the position of the Newtonian law
+of gravitation in physical astronomy.</p>
+
+<p>In 1821 Michael Faraday (1791-1867), who was destined
+later on to do so much for the science of electricity, discovered
+electromagnetic rotation, having succeeded in causing a wire
+conveying a voltaic current to rotate continuously round the pole
+of a permanent magnet.<a name="fa9h" id="fa9h" href="#ft9h"><span class="sp">9</span></a> This experiment was repeated in a
+variety of forms by A.A. De la Rive, Peter Barlow (1776-1862),
+William Ritchie (1790-1837), William Sturgeon (1783-1850),
+and others; and Davy (<i>Phil. Trans.</i>, 1823) showed that when two
+wires connected with the pole of a battery were dipped into a
+cup of mercury placed on the pole of a powerful magnet, the
+fluid rotated in opposite directions about the two electrodes.</p>
+
+<p><i>Electromagnetism.</i>&mdash;In 1820 Arago (<i>Ann. Chim. Phys.</i>, 1820,
+15, p. 94) and Davy (<i>Annals of Philosophy</i>, 1821) discovered
+independently the power of the electric current to magnetize
+iron and steel. Félix Savary (1797-1841) made some very
+curious observations in 1827 on the magnetization of steel
+needles placed at different distances from a wire conveying the
+discharge of a Leyden jar (<i>Ann. Chim. Phys.</i>, 1827, 34). W.
+Sturgeon in 1824 wound a copper wire round a bar of iron bent
+in the shape of a horseshoe, and passing a voltaic current through
+the wire showed that the iron became powerfully magnetized
+as long as the connexion with the pile was maintained (<i>Trans.
+Soc. Arts</i>, 1825). These researches gave us the electromagnet,
+almost as potent an instrument of research and invention as the
+pile itself (see <span class="sc"><a href="#ar71">Electromagnetism</a></span>).</p>
+
+<p>Ampère had already previously shown that a spiral conductor
+or solenoid when traversed by an electric current possesses
+magnetic polarity, and that two such solenoids act upon one
+another when traversed by electric currents as if they were
+magnets. Joseph Henry, in the United States, first suggested
+the construction of what were then called intensity electromagnets,
+by winding upon a horseshoe-shaped piece of soft
+iron many superimposed windings of copper wire, insulated by
+covering it with silk or cotton, and then sending through the
+coils the current from a voltaic battery. The dependence of
+the intensity of magnetization on the strength of the current was
+subsequently investigated (<i>Pogg. Ann. Phys.</i>, 1839, 47) by
+H.F.E. Lenz (1804-1865) and M.H. von Jacobi (1801-1874).
+J.P. Joule found that magnetization did not increase proportionately
+with the current, but reached a maximum (<i>Sturgeon&rsquo;s
+Annals of Electricity</i>, 1839, 4). Further investigations on this
+subject were carried on subsequently by W.E. Weber (1804-1891),
+J.H.J. Müller (1809-1875), C.J. Dub (1817-1873),
+G.H. Wiedemann (1826-1899), and others, and in modern times
+by H.A. Rowland (1848-1901), Shelford Bidwell (b. 1848),
+John Hopkinson (1849-1898), J.A. Ewing (b. 1855) and many
+others. Electric magnets of great power were soon constructed
+in this manner by Sturgeon, Joule, Henry, Faraday and Brewster.
+Oersted&rsquo;s discovery in 1819 was indeed epoch-making in the
+degree to which it stimulated other research. It led at once to
+the construction of the galvanometer as a means of detecting
+and measuring the electric current in a conductor. In 1820
+J.S.C. Schweigger (1779-1857) with his &ldquo;multiplier&rdquo; made
+an advance upon Oersted&rsquo;s discovery, by winding the wire
+conveying the electric current many times round the pivoted
+magnetic needle and thus increasing the deflection; and L.
+Nobili (1784-1835) in 1825 conceived the ingenious idea of
+neutralizing the directive effect of the earth&rsquo;s magnetism by
+employing a pair of magnetized steel needles fixed to one axis,
+but with their magnetic poles pointing in opposite directions.
+Hence followed the astatic multiplying galvanometer.</p>
+
+<p><i>Electrodynamic Rotation.</i>&mdash;The study of the relation between
+the magnet and the circuit conveying an electric current then
+led Arago to the discovery of the &ldquo;magnetism of rotation.&rdquo;
+He found that a vibrating magnetic compass needle came to
+rest sooner when placed over a plate of copper than otherwise,
+and also that a plate of copper rotating under a suspended
+magnet tended to drag the magnet in the same direction. The
+matter was investigated by Charles Babbage, Sir J.F.W.
+Herschel, Peter Barlow and others, but did not receive a final
+explanation until after the discovery of electromagnetic induction
+by Faraday in 1831. Ampère&rsquo;s investigations had led electricians
+to see that the force acting upon a magnetic pole due to a current
+in a neighbouring conductor was such as to tend to cause the
+pole to travel round the conductor. Much ingenuity had,
+however, to be expended before a method was found of exhibiting
+such a rotation. Faraday first succeeded by the simple but
+ingenious device of using a light magnetic needle tethered
+flexibly to the bottom of a cup containing mercury so that one
+pole of the magnet was just above the surface of the mercury.
+On bringing down on to the mercury surface a wire conveying
+an electric current, and allowing the current to pass through the
+mercury and out at the bottom, the magnetic pole at once began
+to rotate round the wire (<i>Exper. Res.</i>, 1822, 2, p. 148). Faraday
+and others then discovered, as already mentioned, means to
+make the conductor conveying the current rotate round a
+<span class="pagenum"><a name="page185" id="page185"></a>185</span>
+magnetic pole, and Ampère showed that a magnet could be made
+to rotate on its own axis when a current was passed through it.
+The difficulty in this case consisted in discovering means by
+which the current could be passed through one half of the magnet
+without passing it through the other half. This, however, was
+overcome by sending the current out at the centre of the magnet
+by means of a short length of wire dipping into an annular groove
+containing mercury. Barlow, Sturgeon and others then showed
+that a copper disk could be made to rotate between the poles
+of a horseshoe magnet when a current was passed through the
+disk from the centre to the circumference, the disk being rendered
+at the same time freely movable by making a contact with the
+circumference by means of a mercury trough. These experiments
+furnished the first elementary forms of electric motor, since it
+was then seen that rotatory motion could be produced in masses
+of metal by the mutual action of conductors conveying electric
+current and magnetic fields. By his discovery of thermo-electricity
+in 1822 (<i>Pogg. Ann. Phys.</i>, 6), T.J. Seebeck (1770-1831)
+opened up a new region of research (see <span class="sc"><a href="#artlinks">Thermo-electricity</a></span>).
+James Cumming (1777-1861) in 1823 (<i>Annals of
+Philosophy</i>, 1823) found that the thermo-electric series varied
+with the temperature, and J.C.A. Peltier (1785-1845) in 1834
+discovered that a current passed across the junction of two
+metals either generated or absorbed heat.</p>
+
+<p><i>Ohm&rsquo;s Law.</i>&mdash;In 1827 Dr G.S. Ohm (1787-1854) rendered a
+great service to electrical science by his mathematical investigation
+of the voltaic circuit, and publication of his paper, <i>Die
+galvanische Kette mathematisch bearbeitet</i>. Before his time,
+ideas on the measurable quantities with which we are concerned
+in an electric circuit were extremely vague. Ohm introduced
+the clear idea of current strength as an effect produced by
+electromotive force acting as a cause in a circuit having resistance
+as its quality, and showed that the current was directly proportional
+to the electromotive force and inversely as the resistance.
+Ohm&rsquo;s law, as it is called, was based upon an analogy with the
+flow of heat in a circuit, discussed by Fourier. Ohm introduced
+the definite conception of the distribution along the circuit of
+&ldquo;electroscopic force&rdquo; or tension (<i>Spannung</i>), corresponding to
+the modern term potential. Ohm verified his law by the aid of
+thermo-electric piles as sources of electromotive force, and Davy,
+C.S.M. Pouillet (1791-1868), A.C. Becquerel (1788-1878),
+G.T. Fechner (1801-1887), R.H.A. Kohlrausch (1809-1858)
+and others laboured at its confirmation. In more recent times,
+1876, it was rigorously tested by G. Chrystal (b. 1851) at Clerk
+Maxwell&rsquo;s instigation (see <i>Brit. Assoc. Report</i>, 1876, p. 36), and
+although at its original enunciation its meaning was not at first
+fully apprehended, it soon took its place as the expression of the
+fundamental law of electrokinetics.</p>
+
+<p><i>Induction of Electric Currents.</i>&mdash;In 1831 Faraday began the
+investigations on electromagnetic induction which proved more
+fertile in far-reaching practical consequences than any of those
+which even his genius gave to the world. These advances all
+centre round his supreme discovery of the induction of electric
+currents. Fully familiar with the fact that an electric charge
+upon one conductor could produce a charge of opposite sign
+upon a neighbouring conductor, Faraday asked himself whether
+an electric current passing through a conductor could not in any
+like manner induce an electric current in some neighbouring
+conductor. His first experiments on this subject were made in
+the month of November 1825, but it was not until the 29th of
+August 1831 that he attained success. On that date he had
+provided himself with an iron ring, over which he had wound
+two coils of insulated copper wire. One of these coils was connected
+with the voltaic battery and the other with the galvanometer.
+He found that at the moment the current in the battery
+circuit was started or stopped, transitory currents appeared
+in the galvanometer circuit in opposite directions. In ten days
+of brilliant investigation, guided by clear insight from the very
+first into the meaning of the phenomena concerned, he established
+experimentally the fact that a current may be induced in a
+conducting circuit simply by the variation in a magnetic field,
+the lines of force of which are linked with that circuit. The
+whole of Faraday&rsquo;s investigations on this subject can be summed
+up in the single statement that if a conducting circuit is placed
+in a magnetic field, and if either by variation of the field or by
+movement or variation of the form of the circuit the total
+magnetic flux linked with the circuit is varied, an electromotive
+force is set up in that circuit which at any instant is measured
+by the rate at which the total flux linked with the circuit is
+changing.</p>
+
+<p>Amongst the memorable achievements of the ten days which
+Faraday devoted to this investigation was the discovery that
+a current could be induced in a conducting wire simply by moving
+it in the neighbourhood of a magnet. One form which this
+experiment took was that of rotating a copper disk between the
+poles of a powerful electric magnet. He then found that a conductor,
+the ends of which were connected respectively with the
+centre and edge of the disk, was traversed by an electric current.
+This important fact laid the foundation for all subsequent
+inventions which finally led to the production of electromagnetic
+or dynamo-electric machines.</p>
+
+<p><span class="sc">Third Period.</span>&mdash;With this supremely important discovery
+of Faraday&rsquo;s we enter upon the third period of electrical research,
+in which that philosopher himself was the leading figure. He
+not only collected the facts concerning electromagnetic induction
+so industriously that nothing of importance remained for future
+discovery, and embraced them all in one law of exquisite simplicity,
+but he introduced his famous conception of lines of
+force which changed entirely the mode of regarding electrical
+phenomena. The French mathematicians, Coulomb, Biot,
+Poisson and Ampère, had been content to accept the fact that
+electric charges or currents in conductors could exert forces on
+other charges or conductors at a distance without inquiring
+into the means by which this action at a distance was produced.
+Faraday&rsquo;s mind, however, revolted against this notion; he felt
+intuitively that these distance actions must be the result of
+unseen operations in the interposed medium. Accordingly
+when he sprinkled iron filings on a card held over a magnet and
+revealed the curvilinear system of lines of force (see <span class="sc"><a href="#artlinks">Magnetism</a></span>),
+he regarded these fragments of iron as simple indicators of a
+physical state in the space already in existence round the magnet.
+To him a magnet was not simply a bar of steel; it was the
+core and origin of a system of lines of magnetic force attached
+to it and moving with it. Similarly he came to see an electrified
+body as a centre of a system of lines of electrostatic force. All
+the space round magnets, currents and electric charges was
+therefore to Faraday the seat of corresponding lines of magnetic
+or electric force. He proved by systematic experiments that the
+electromotive forces set up in conductors by their motions in
+magnetic fields or by the induction of other currents in the
+field were due to the secondary conductor <i>cutting</i> lines of magnetic
+force. He invented the term &ldquo;electrotonic state&rdquo; to signify
+the total magnetic flux due to a conductor conveying a current,
+which was linked with any secondary circuit in the field or even
+with itself.</p>
+
+<p><i>Faraday&rsquo;s Researches.</i>&mdash;Space compels us to limit our account
+of the scientific work done by Faraday in the succeeding twenty
+years, in elucidating electrical phenomena and adding to the
+knowledge thereon, to the very briefest mention. We must
+refer the reader for further information to his monumental work
+entitled <i>Experimental Researches on Electricity</i>, in three volumes,
+reprinted from the <i>Phil. Trans.</i> between 1831 and 1851. Faraday
+divided these researches into various series. The 1st and 2nd
+concern the discovery of magneto-electric induction already
+mentioned. The 3rd series (1833) he devoted to discussion of
+the identity of electricity derived from various sources, frictional,
+voltaic, animal and thermal, and he proved by rigorous experiments
+the identity and similarity in properties of the electricity
+generated by these various methods. The 5th series (1833) is
+occupied with his electrochemical researches. In the 7th series
+(1834) he defines a number of new terms, such as electrolyte,
+electrolysis, anode and cathode, &amp;c., in connexion with electrolytic
+phenomena, which were immediately adopted into the
+vocabulary of science. His most important contribution at
+<span class="pagenum"><a name="page186" id="page186"></a>186</span>
+this date was the invention of the voltameter and his enunciation
+of the laws of electrolysis. The voltameter provided a means
+of measuring quantity of electricity, and in the hands of Faraday
+and his successors became an appliance of fundamental importance.
+The 8th series is occupied with a discussion of the
+theory of the voltaic pile, in which Faraday accumulates evidence
+to prove that the source of the energy of the pile must be chemical.
+He returns also to this subject in the 16th series. In the 9th
+series (1834) he announced the discovery of the important
+property of electric conductors, since called their self-induction
+or inductance, a discovery in which, however, he was anticipated
+by Joseph Henry in the United States. The 11th series (1837)
+deals with electrostatic induction and the statement of the
+important fact of the specific inductive capacity of insulators
+or dielectrics. This discovery was made in November 1837
+when Faraday had no knowledge of Cavendish&rsquo;s previous
+researches into this matter. The 19th series (1845) contains
+an account of his brilliant discovery of the rotation of the plane
+of polarized light by transparent dielectrics placed in a magnetic
+field, a relation which established for the first time a practical
+connexion between the phenomena of electricity and light. The
+20th series (1845) contains an account of his researches on the
+universal action of magnetism and diamagnetic bodies. The
+22nd series (1848) is occupied with the discussion of magneto-crystallic
+force and the abnormal behaviour of various crystals
+in a magnetic field. In the 25th series (1850) he made known
+his discovery of the magnetic character of oxygen gas, and the
+important principle that the terms paramagnetic and diamagnetic
+are relative. In the 26th series (1850) he returned
+to a discussion of magnetic lines of force, and illuminated the
+whole subject of the magnetic circuit by his transcendent insight
+into the intricate phenomena concerned. In 1855 he brought
+these researches to a conclusion by a general article on magnetic
+philosophy, having placed the whole subject of magnetism and
+electromagnetism on an entirely novel and solid basis. In
+addition to this he provided the means for studying the phenomena
+not only qualitatively, but also quantitatively, by the profoundly
+ingenious instruments he invented for that purpose.</p>
+
+<p><i>Electrical Measurement.</i>&mdash;Faraday&rsquo;s ideas thus pressed upon
+electricians the necessity for the quantitative measurement of
+electrical phenomena.<a name="fa10h" id="fa10h" href="#ft10h"><span class="sp">10</span></a> It has been already mentioned that
+Schweigger invented in 1820 the &ldquo;multiplier,&rdquo; and Nobili in
+1825 the astatic galvanometer. C.S.M. Pouillet in 1837 contributed
+the sine and tangent compass, and W.E. Weber effected
+great improvements in them and in the construction and use
+of galvanometers. In 1849 H. von Helmholtz devised a tangent
+galvanometer with two coils. The measurement of electric
+resistance then engaged the attention of electricians. By his
+Memoirs in the <i>Phil. Trans.</i> in 1843, Sir Charles Wheatstone gave
+a great impulse to this study. He invented the rheostat and
+improved the resistance balance, invented by S.H. Christie
+(1784-1865) in 1833, and subsequently called the Wheatstone
+Bridge. (See his <i>Scientific Papers</i>, published by the Physical
+Society of London, p. 129.) Weber about this date invented
+the electrodynamometer, and applied the mirror and scale
+method of reading deflections, and in co-operation with C.F.
+Gauss introduced a system of absolute measurement of electric
+and magnetic phenomena. In 1846 Weber proceeded with
+improved apparatus to test Ampère&rsquo;s laws of electrodynamics.
+In 1845 H.G. Grassmann (1809-1877) published (<i>Pogg. Ann.</i>
+vol. 64) his &ldquo;Neue Theorie der Electrodynamik,&rdquo; in which he
+gave an elementary law differing from that of Ampère but leading
+to the same results for closed circuits. In the same year F.E.
+Neumann published another law. In 1846 Weber announced
+his famous hypothesis concerning the connexion of electrostatic
+and electrodynamic phenomena. The work of Neumann and
+Weber had been stimulated by that of H.F.E. Lenz (1804-1865),
+whose researches (<i>Pogg. Ann.</i>, 1834, 31; 1835, 34) among other
+results led him to the statement of the law by means of which
+the direction of the induced current can be predicted from the
+theory of Ampère, the rule being that the direction of the induced
+current is always such that its electrodynamic action tends to
+oppose the motion which produces it.</p>
+
+<p>Neumann in 1845 did for electromagnetic induction what
+Ampère did for electrodynamics, basing his researches upon the
+experimental laws of Lenz. He discovered a function, which
+has been called the potential of one circuit on another, from
+which he deduced a theory of induction completely in accordance
+with experiment. Weber at the same time deduced the mathematical
+laws of induction from his elementary law of electrical
+action, and with his improved instruments arrived at accurate
+verifications of the law of induction, which by this time had been
+developed mathematically by Neumann and himself. In 1849
+G.R. Kirchhoff determined experimentally in a certain case
+the absolute value of the current induced by one circuit in
+another, and in the same year Erik Edland (1819-1888) made
+a series of careful experiments on the induction of electric
+currents which further established received theories. These
+labours laid the foundation on which was subsequently erected
+a complete system for the absolute measurement of electric
+and magnetic quantities, referring them all to the fundamental
+units of mass, length and time. Helmholtz gave at the same
+time a mathematical theory of induced currents and a valuable
+series of experiments in support of them (<i>Pogg. Ann.</i>, 1851).
+This great investigator and luminous expositor just before that
+time had published his celebrated essay, <i>Die Erhaltung der
+Kraft</i> (&ldquo;The Conservation of Energy&rdquo;), which brought to a
+focus ideas which had been accumulating in consequence of the
+work of J.P. Joule, J.R. von Mayer and others, on the transformation
+of various forms of physical energy, and in particular
+the mechanical equivalent of heat. Helmholtz brought to bear
+upon the subject not only the most profound mathematical
+attainments, but immense experimental skill, and his work in
+connexion with this subject is classical.</p>
+
+<p><i>Lord Kelvin&rsquo;s Work.</i>&mdash;About 1842 Lord Kelvin (then William
+Thomson) began that long career of theoretical and practical
+discovery and invention in electrical science which revolutionized
+every department of pure and applied electricity. His early
+contributions to electrostatics and electrometry are to be found
+described in his <i>Reprint of Papers on Electrostatics and Magnetism</i>
+(1872), and his later work in his collected <i>Mathematical and
+Physical Papers</i>. By his studies in electrostatics, his elegant
+method of electrical images, his development of the theory of
+potential and application of the principle of conservation of
+energy, as well as by his inventions in connexion with electrometry,
+he laid the foundations of our modern knowledge of
+electrostatics. His work on the electrodynamic qualities of
+metals, thermo-electricity, and his contributions to galvanometry,
+were not less massive and profound. From 1842 onwards to the
+end of the 19th century, he was one of the great master workers
+in the field of electrical discovery and research.<a name="fa11h" id="fa11h" href="#ft11h"><span class="sp">11</span></a> In 1853 he
+published a paper &ldquo;On Transient Electric Currents&rdquo; (<i>Phil.
+Mag.</i>, 1853 [4], 5, p. 393), in which he applied the principle of
+the conservation of energy to the discharge of a Leyden jar.
+He added definiteness to the idea of the self-induction or inductance
+of an electric circuit, and gave a mathematical expression
+for the current flowing out of a Leyden jar during its discharge.
+He confirmed an opinion already previously expressed by
+Helmholtz and by Henry, that in some circumstances this discharge
+is oscillatory in nature, consisting of an alternating electric
+current of high frequency. These theoretical predictions were
+confirmed and others, subsequently, by the work of B.W.
+Feddersen (b. 1832), C.A. Paalzow (b. 1823), and it was then
+seen that the familiar phenomena of the discharge of a Leyden
+<span class="pagenum"><a name="page187" id="page187"></a>187</span>
+jar provided the means of generating electric oscillations of very
+high frequency.</p>
+
+<p><i>Telegraphy.</i>&mdash;Turning to practical applications of electricity,
+we may note that electric telegraphy took its rise in 1820,
+beginning with a suggestion of Ampère immediately after
+Oersted&rsquo;s discovery. It was established by the work of Weber
+and Gauss at Göttingen in 1836, and that of C.A. Steinheil
+(1801-1870) of Munich, Sir W.F. Cooke (1806-1879) and Sir
+C. Wheatstone in England, Joseph Henry and S.F.B. Morse
+(1791-1872) in the United States in 1837. In 1845 submarine
+telegraphy was inaugurated by the laying of an insulated conductor
+across the English Channel by the brothers Brett, and
+their temporary success was followed by the laying in 1851
+of a permanent Dover-Calais cable by T.R. Crampton. In
+1856 the project for an Atlantic submarine cable took shape
+and the Atlantic Telegraph Company was formed with a capital
+of £350,000, with Sir Charles Bright as engineer-in-chief and
+E.O.W. Whitehouse as electrician. The phenomena connected
+with the propagation of electric signals by underground insulated
+wires had already engaged the attention of Faraday in 1854,
+who pointed out the Leyden-jar-like action of an insulated
+subterranean wire. Scientific and practical questions connected
+with the possibility of laying an Atlantic submarine cable then
+began to be discussed, and Lord Kelvin was foremost in developing
+true scientific knowledge on this subject, and in the invention
+of appliances for utilizing it. One of his earliest and most useful
+contributions (in 1858) was the invention of the mirror galvanometer.
+Abandoning the long and somewhat heavy magnetic
+needles that had been used up to that date in galvanometers,
+he attached to the back of a very small mirror made of microscopic
+glass a fragment of magnetized watch-spring, and suspended
+the mirror and needle by means of a cocoon fibre in the
+centre of a coil of insulated wire. By this simple device he
+provided a means of measuring small electric currents far in
+advance of anything yet accomplished, and this instrument
+proved not only most useful in pure scientific researches, but at
+the same time was of the utmost value in connexion with submarine
+telegraphy. The history of the initial failures and final
+success in laying the Atlantic cable has been well told by Mr.
+Charles Bright (see <i>The Story of the Atlantic Cable</i>, London, 1903).<a name="fa12h" id="fa12h" href="#ft12h"><span class="sp">12</span></a>
+The first cable laid in 1857 broke on the 11th of August during
+laying. The second attempt in 1858 was successful, but the
+cable completed on the 5th of August 1858 broke down on the
+20th of October 1858, after 732 messages had passed through it.
+The third cable laid in 1865 was lost on the 2nd of August 1865,
+but in 1866 a final success was attained and the 1865 cable also
+recovered and completed. Lord Kelvin&rsquo;s mirror galvanometer
+was first used in receiving signals through the short-lived 1858
+cable. In 1867 he invented his beautiful siphon-recorder for
+receiving and recording the signals through long cables. Later,
+in conjunction with Prof. Fleeming Jenkin, he devised his automatic
+curb sender, an appliance for sending signals by means
+of punched telegraphic paper tape. Lord Kelvin&rsquo;s contributions
+to the science of exact electric measurement<a name="fa13h" id="fa13h" href="#ft13h"><span class="sp">13</span></a> were enormous.
+His ampere-balances, voltmeters and electrometers, and double
+bridge, are elsewhere described in detail (see <span class="sc"><a href="#artlinks">Amperemeter</a></span>;
+<span class="sc"><a href="#ar73">Electrometer</a></span>, and <span class="sc"><a href="#artlinks">Wheatstone&rsquo;s Bridge</a></span>).</p>
+
+<p><i>Dynamo.</i>&mdash;The work of Faraday from 1831 to 1851 stimulated
+and originated an immense mass of scientific research, but at
+the same time practical inventors had not been slow to perceive
+that it was capable of purely technical application. Faraday&rsquo;s
+copper disk rotated between the poles of a magnet, and producing
+thereby an electric current, became the parent of
+innumerable machines in which mechanical energy was directly
+converted into the energy of electric currents. Of these
+machines, originally called magneto-electric machines, one of
+the first was devised in 1832 by H. Pixii. It consisted of a fixed
+horseshoe armature wound over with insulated copper wire in
+front of which revolved about a vertical axis a horseshoe magnet.
+Pixii, who invented the split tube commutator for converting
+the alternating current so produced into a continuous current
+in the external circuit, was followed by J. Saxton, E.M. Clarke,
+and many others in the development of the above-described
+magneto-electric machine. In 1857 E.W. Siemens effected a
+great improvement by inventing a shuttle armature and improving
+the shape of the field magnet. Subsequently similar machines
+with electromagnets were introduced by Henry Wilde (b. 1833),
+Siemens, Wheatstone, W. Ladd and others, and the principle
+of self-excitation was suggested by Wilde, C.F. Varley (1828-1883),
+Siemens and Wheatstone (see <span class="sc"><a href="#artlinks">Dynamo</a></span>). These machines
+about 1866 and 1867 began to be constructed on a commercial
+scale and were employed in the production of the electric light.
+The discovery of electric-current induction also led to the production
+of the induction coil (<i>q.v.</i>), improved and brought to its
+present perfection by W. Sturgeon, E.R. Ritchie, N.J. Callan,
+H.D. Rühmkorff (1803-1877), A.H.L. Fizeau, and more recently
+by A. Apps and modern inventors. About the same time
+Fizeau and J.B.L. Foucault devoted attention to the invention
+of automatic apparatus for the production of Davy&rsquo;s electric
+arc (see <span class="sc"><a href="#artlinks">Lighting</a></span>: <i>Electric</i>), and these appliances in conjunction
+with magneto-electric machines were soon employed in lighthouse
+work. With the advent of large magneto-electric machines the
+era of electrotechnics was fairly entered, and this period, which
+may be said to terminate about 1867 to 1869, was consummated
+by the theoretical work of Clerk Maxwell.</p>
+
+<p><i>Maxwell&rsquo;s Researches.</i>&mdash;James Clerk Maxwell (1831-1879)
+entered on his electrical studies with a desire to ascertain if the
+ideas of Faraday, so different from those of Poisson and the
+French mathematicians, could be made the foundation of a
+mathematical method and brought under the power of analysis.<a name="fa14h" id="fa14h" href="#ft14h"><span class="sp">14</span></a>
+Maxwell started with the conception that all electric and magnetic
+phenomena are due to effects taking place in the dielectric or in
+the ether if the space be vacuous. The phenomena of light had
+compelled physicists to postulate a space-filling medium, to which
+the name ether had been given, and Henry and Faraday had long
+previously suggested the idea of an electromagnetic medium.
+The vibrations of this medium constitute the agency called
+light. Maxwell saw that it was unphilosophical to assume a
+multiplicity of ethers or media until it had been proved that one
+would not fulfil all the requirements. He formulated the conception,
+therefore, of electric charge as consisting in a displacement
+taking place in the dielectric or electromagnetic medium
+(see <span class="sc"><a href="#artlinks">Electrostatics</a></span>). Maxwell never committed himself to a
+precise definition of the physical nature of electric displacement,
+but considered it as defining that which Faraday had called the
+polarization in the insulator, or, what is equivalent, the number
+of lines of electrostatic force passing normally through a unit of
+area in the dielectric. A second fundamental conception of
+Maxwell was that the electric displacement whilst it is changing
+is in effect an electric current, and creates, therefore, magnetic
+force. The total current at any point in a dielectric must be
+considered as made up of two parts: first, the true conduction
+current, if it exists; and second, the rate of change of dielectric
+displacement. The fundamental fact connecting electric currents
+and magnetic fields is that the line integral of magnetic
+force taken once round a conductor conveying an electric current
+is equal to 4 &pi;-times the surface integral of the current density,
+or to 4 &pi;-times the total current flowing through the closed
+line round which the integral is taken (see <span class="sc"><a href="#ar68">Electrokinetics</a></span>).
+A second relation connecting magnetic and electric force is
+<span class="pagenum"><a name="page188" id="page188"></a>188</span>
+based upon Faraday&rsquo;s fundamental law of induction, that the
+rate of change of the total magnetic flux linked with a conductor
+is a measure of the electromotive force created in it (see <span class="sc"><a href="#ar68">Electrokinetics</a></span>).
+Maxwell also introduced in this connexion the
+notion of the vector potential. Coupling together these ideas
+he was finally enabled to prove that the propagation of electric
+and magnetic force takes place through space with a certain
+velocity determined by the dielectric constant and the magnetic
+permeability of the medium. To take a simple instance, if we
+consider an electric current as flowing in a conductor it is, as
+Oersted discovered, surrounded by closed lines of magnetic
+force. If we imagine the current in the conductor to be instantaneously
+reversed in direction, the magnetic force surrounding
+it would not be instantly reversed everywhere in direction,
+but the reversal would be propagated outwards through space
+with a certain velocity which Maxwell showed was inversely
+as the square root of the product of the magnetic permeability
+and the dielectric constant or specific inductive capacity of the
+medium.</p>
+
+<p>These great results were announced by him for the first time
+in a paper presented in 1864 to the Royal Society of London
+and printed in the <i>Phil. Trans.</i> for 1865, entitled &ldquo;A Dynamical
+Theory of the Electromagnetic Field.&rdquo; Maxwell showed in this
+paper that the velocity of propagation of an electromagnetic
+impulse through space could also be determined by certain experimental
+methods which consisted in measuring the same electric
+quantity, capacity, resistance or potential in two ways. W.E.
+Weber had already laid the foundations of the absolute system
+of electric and magnetic measurement, and proved that a
+quantity of electricity could be measured either by the force
+it exercises upon another static or stationary quantity of electricity,
+or magnetically by the force this quantity of electricity
+exercises upon a magnetic pole when flowing through a neighbouring
+conductor. The two systems of measurement were called
+respectively the electrostatic and the electromagnetic systems
+(see <span class="sc"><a href="#artlinks">Units, Physical</a></span>). Maxwell suggested new methods for
+the determination of this ratio of the electrostatic to the electromagnetic
+units, and by experiments of great ingenuity was able
+to show that this ratio, which is also that of the velocity of the
+propagation of an electromagnetic impulse through space, is
+identical with that of light. This great fact once ascertained,
+it became clear that the notion that electric phenomena are
+affections of the luminiferous ether was no longer a mere speculation
+but a scientific theory capable of verification. An immediate
+deduction from Maxwell&rsquo;s theory was that in transparent dielectrics,
+the dielectric constant or specific inductive capacity should
+be numerically equal to the square of the refractive index for very
+long electric waves. At the time when Maxwell developed his
+theory the dielectric constants of only a few transparent insulators
+were known and these were for the most part measured with
+steady or unidirectional electromotive force. The only refractive
+indices which had been measured were the optical refractive
+indices of a number of transparent substances. Maxwell made
+a comparison between the optical refractive index and the
+dielectric constant of paraffin wax, and the approximation
+between the numerical values of the square of the first and that
+of the last was sufficient to show that there was a basis for further
+work. Maxwell&rsquo;s electric and magnetic ideas were gathered
+together in a great mathematical treatise on electricity and
+magnetism which was published in 1873.<a name="fa15h" id="fa15h" href="#ft15h"><span class="sp">15</span></a> This book stimulated
+in a most remarkable degree theoretical and practical research
+into the phenomena of electricity and magnetism. Experimental
+methods were devised for the further exact measurements
+of the electromagnetic velocity and numerous determinations
+of the dielectric constants of various solids, liquids and gases,
+and comparisons of these with the corresponding optical refractive
+indices were conducted. This early work indicated
+that whilst there were a number of cases in which the square
+of optical refractive index for long waves and the dielectric
+constant of the same substance were sufficiently close to afford
+an apparent confirmation of Maxwell&rsquo;s theory, yet in other
+cases there were considerable divergencies. L. Boltzmann
+(1844-1907) made a large number of determinations for solids
+and for gases, and the dielectric constants of many solid and
+liquid substances were determined by N.N. Schiller (b. 1848),
+P.A. Silow (b. 1850), J. Hopkinson and others. The accumulating
+determinations of the numerical value of the electromagnetic
+velocity (<i>v</i>) from the earliest made by Lord Kelvin
+(Sir W. Thomson) with the aid of King and M<span class="sp">c</span>Kichan, or those
+of Clerk Maxwell, W.E. Ayrton and J. Perry, to more recent
+ones by J.J. Thomson, F. Himstedt, H.A. Rowland, E.B. Rosa,
+J.S.H. Pellat and H.A. Abraham, showed it to be very close
+to the best determinations of the velocity of light (see <span class="sc"><a href="#artlinks">Units,
+Physical</a></span>). On the other hand, the divergence in some cases
+between the square of the optical refractive index and the
+dielectric constant was very marked. Hence although Maxwell&rsquo;s
+theory of electrical action when first propounded found many
+adherents in Great Britain, it did not so much dominate opinion
+on the continent of Europe.</p>
+
+<p><span class="sc">Fourth Period.</span>&mdash;With the publication of Clerk Maxwell&rsquo;s
+treatise in 1873, we enter fully upon the fourth and modern
+period of electrical research. On the technical side the invention
+of a new form of armature for dynamo electric machines by
+Z.T. Gramme (1826-1901) inaugurated a departure from which
+we may date modern electrical engineering. It will be convenient
+to deal with technical development first.</p>
+
+<p><i>Technical Development.</i>&mdash;As far back as 1841 large magneto-electric
+machines driven by steam power had been constructed,
+and in 1856 F.H. Holmes had made a magneto machine with
+multiple permanent magnets which was installed in 1862 in
+Dungeness lighthouse. Further progress was made in 1867
+when H. Wilde introduced the use of electromagnets for the field
+magnets. In 1860 Dr Antonio Pacinotti invented what is now
+called the toothed ring winding for armatures and described it
+in an Italian journal, but it attracted little notice until reinvented
+in 1870 by Gramme. In this new form of bobbin, the armature
+consisted of a ring of iron wire wound over with an endless coil
+of wire and connected to a commutator consisting of copper bars
+insulated from one another. Gramme dynamos were then soon
+made on the self-exciting principle. In 1873 at Vienna the fact
+was discovered that a dynamo machine of the Gramme type
+could also act as an electric motor and was set in rotation when
+a current was passed into it from another similar machine.
+Henceforth the electric transmission of power came within the
+possibilities of engineering.</p>
+
+<p><i>Electric Lighting.</i>&mdash;In 1876, Paul Jablochkov (1847-1894),
+a Russian officer, passing through Paris, invented his famous
+electric candle, consisting of two rods of carbon placed side by
+side and separated from one another by an insulating material.
+This invention in conjunction with an alternating current
+dynamo provided a new and simple form of electric arc lighting.
+Two years afterwards C.F. Brush, in the United States, produced
+another efficient form of dynamo and electric arc lamp suitable
+for working in series (see <span class="sc"><a href="#artlinks">Lighting</a></span>: <i>Electric</i>), and these inventions
+of Brush and Jablochkov inaugurated commercial arc
+lighting. The so-called subdivision of electric light by incandescent
+lighting lamps then engaged attention. E.A. King in
+1845 and W.E. Staite in 1848 had made incandescent electric
+lamps of an elementary form, and T.A. Edison in 1878 again
+attacked the problem of producing light by the incandescence of
+platinum. It had by that time become clear that the most
+suitable material for an incandescent lamp was carbon contained
+in a good vacuum, and St G. Lane Fox and Sir J.W. Swan in
+England, and T.A. Edison in the United States, were engaged
+in struggling with the difficulties of producing a suitable carbon
+incandescence electric lamp. Edison constructed in 1879 a
+successful lamp of this type consisting of a vessel wholly of glass
+containing a carbon filament made by carbonizing paper or
+some other carbonizable material, the vessel being exhausted
+and the current led into the filament through platinum wires.
+<span class="pagenum"><a name="page189" id="page189"></a>189</span>
+In 1879 and 1880, Edison in the United States, and Swan in
+conjunction with C.H. Stearn in England, succeeded in completely
+solving the practical problems. From and after that date
+incandescent electric lighting became commercially possible,
+and was brought to public notice chiefly by an electrical exhibition
+held at the Crystal Palace, near London, in 1882. Edison,
+moreover, as well as Lane-Fox, had realized the idea of a public
+electric supply station, and the former proceeded to establish
+in Pearl Street, New York, in 1881, the first public electric supply
+station. A similar station in England was opened in the basement
+of a house in Holborn Viaduct, London, in March 1882. Edison,
+with copious ingenuity, devised electric meters, electric mains,
+lamp fittings and generators complete for the purpose. In 1881
+C.A. Faure made an important improvement in the lead
+secondary battery which G. Planté (1834-1889) had invented
+in 1859, and storage batteries then began to be developed as
+commercial appliances by Faure, Swan, J.S. Sellon and many
+others (see <span class="sc"><a href="#artlinks">Accumulator</a></span>). In 1882, numerous electric lighting
+companies were formed for the conduct of public and private
+lighting, but an electric lighting act passed in that year greatly
+hindered commercial progress in Great Britain. Nevertheless
+the delay was utilized in the completion of inventions necessary
+for the safe and economical distribution of electric current for
+the purpose of electric lighting.</p>
+
+<p><i>Telephone.</i>&mdash;Going back a few years we find the technical
+applications of electrical invention had developed themselves
+in other directions. Alexander Graham Bell in 1876 invented
+the speaking telephone (<i>q.v.</i>), and Edison and Elisha Gray in
+the United States followed almost immediately with other
+telephonic inventions for electrically transmitting speech.
+About the same time D.E. Hughes in England invented the
+microphone. In 1879 telephone exchanges began to be developed
+in the United States, Great Britain and other countries.</p>
+
+<p><i>Electric Power.</i>&mdash;Following on the discovery in 1873 of the
+reversible action of the dynamo and its use as a motor, efforts
+began to be made to apply this knowledge to transmission of
+power, and S.D. Field, T.A. Edison, Leo Daft, E.M. Bentley
+and W.H. Knight, F.J. Sprague, C.J. Van Depoele and others
+between 1880 and 1884 were the pioneers of electric traction. One
+of the earliest electric tram cars was exhibited by E.W. and W.
+Siemens in Paris in 1881. In 1883 Lucien Gaulard, following a
+line of thought opened by Jablochkov, proposed to employ high
+pressure alternating currents for electric distributions over wide
+areas by means of transformers. His ideas were improved by
+Carl Zipernowsky and O.T. Bláthy in Hungary and by S.Z.
+de Ferranti in England, and the alternating current transformer
+(see <span class="sc"><a href="#artlinks">Transformers</a></span>) came into existence. Polyphase alternators
+were first exhibited at the Frankfort electrical exhibition in 1891,
+developed as a consequence of scientific researches by Galileo
+Ferraris (1847-1897), Nikola Tesla, M.O. von Dolivo-Dobrowolsky
+and C.E.L. Brown, and long distance transmission of electrical
+power by polyphase electrical currents (see <span class="sc"><a href="#artlinks">Power Transmission</a></span>:
+<i>Electric</i>) was exhibited in operation at Frankfort in
+1891. Meanwhile the early continuous current dynamos devised
+by Gramme, Siemens and others had been vastly improved in
+scientific principle and practical construction by the labours of
+Siemens, J. Hopkinson, R.E.B. Crompton, Elihu Thomson,
+Rudolf Eickemeyer, Thomas Parker and others, and the theory
+of the action of the dynamo had been closely studied by J. and
+E. Hopkinson, G. Kapp, S.P. Thompson, C.P. Steinmetz and
+J. Swinburne, and great improvements made in the alternating
+current dynamo by W.M. Mordey, S.Z. de Ferranti and Messrs
+Ganz of Budapest. Thus in twenty years from the invention of
+the Gramme dynamo, electrical engineering had developed from
+small beginnings into a vast industry. The amendment, in 1888,
+of the Electric Lighting Act of 1882, before long caused a huge
+development of public electric lighting in Great Britain. By
+the end of the 19th century every large city in Europe and in
+North and South America was provided with a public electric
+supply for the purposes of electric lighting. The various improvements
+in electric illuminants, such as the Nernst oxide lamp, the
+tantalum and osmium incandescent lamps, and improved forms
+of arc lamp, enclosed, inverted and flame arcs, are described
+under <span class="sc"><a href="#artlinks">Lighting</a></span>: <i>Electric</i>.</p>
+
+<p>Between 1890 and 1900, electric traction advanced rapidly
+in the United States of America but more slowly in England.
+In 1902 the success of deep tube electric railways in Great
+Britain was assured, and in 1904 main line railways began to
+abandon, at least experimentally, the steam locomotive and substitute
+for it the electric transmission of power. Long distance
+electrical transmission had been before that time exemplified
+in the great scheme of utilizing the falls of Niagara. The first
+projects were discussed in 1891 and 1892 and completed practically
+some ten years later. In this scheme large turbines were
+placed at the bottom of hydraulic fall tubes 150 ft. deep, the
+turbines being coupled by long shafts with 5000 H.P. alternating
+current dynamos on the surface. By these electric current was
+generated and transmitted to towns and factories around, being
+sent overhead as far as Buffalo, a distance of 18 m. At the end
+of the 19th century electrochemical industries began to be
+developed which depended on the possession of cheap electric
+energy. The production of aluminium in Switzerland and
+Scotland, carborundum and calcium carbide in the United
+States, and soda by the Castner-Kellner process, began to be
+conducted on an immense scale. The early work of Sir W.
+Siemens on the electric furnace was continued and greatly
+extended by Henri Moissan and others on its scientific side, and
+electrochemistry took its place as one of the most promising
+departments of technical research and invention. It was
+stimulated and assisted by improvements in the construction
+of large dynamos and increased knowledge concerning the
+control of powerful electric currents.</p>
+
+<p>In the early part of the 20th century the distribution in bulk
+of electric energy for power purposes in Great Britain began to
+assume important proportions. It was seen to be uneconomical
+for each city and town to manufacture its own supply since,
+owing to the intermittent nature of the demand for current for
+lighting, the price had to be kept up to 4d. and 6d. per unit.
+It was found that by the manufacture in bulk, even by steam
+engines, at primary centres the cost could be considerably
+reduced, and in numerous districts in England large power
+stations began to be erected between 1903 and 1905 for the
+supply of current for power purposes. This involved almost a
+revolution in the nature of the tools used, and in the methods
+of working, and may ultimately even greatly affect the factory
+system and the concentration of population in large towns
+which was brought about in the early part of the 19th century
+by the invention of the steam engine.</p>
+
+<p class="pt2 center"><i>Development of Electric Theory.</i></p>
+
+<p>Turning now to the theory of electricity, we may note the
+equally remarkable progress made in 300 years in scientific
+insight into the nature of the agency which has so recast the
+face of human society. There is no need to dwell upon the
+early crude theories of the action of amber and lodestone. In
+a true scientific sense no hypothesis was possible, because few
+facts had been accumulated. The discoveries of Stephen Gray
+and C.F. de C. du Fay on the conductivity of some bodies for
+the electric agency and the dual character of electrification gave
+rise to the first notions of electricity as an imponderable fluid,
+or non-gravitative subtile matter, of a more refined and penetrating
+kind than ordinary liquids and gases. Its duplex character,
+and the fact that the electricity produced by rubbing
+glass and vitreous substances was different from that produced
+by rubbing sealing-wax and resinous substances, seemed to
+necessitate the assumption of two kinds of electric fluid; hence
+there arose the conception of <i>positive</i> and <i>negative</i> electricity,
+and the two-fluid theory came into existence.</p>
+
+<p><i>Single-fluid Theory.</i>&mdash;The study of the phenomena of the
+Leyden jar and of the fact that the inside and outside coatings
+possessed opposite electricities, so that in charging the jar as
+much positive electricity is added to one side as negative to the
+other, led Franklin about 1750 to suggest a modification called
+the single fluid theory, in which the two states of electrification
+<span class="pagenum"><a name="page190" id="page190"></a>190</span>
+were regarded as not the results of two entirely different fluids
+but of the addition or subtraction of one electric fluid from
+matter, so that positive electrification was to be looked upon
+as the result of increase or addition of something to ordinary
+matter and negative as a subtraction. The positive and negative
+electrifications of the two coatings of the Leyden jar were
+therefore to be regarded as the result of a transformation of
+something called electricity from one coating to the other, by
+which process a certain measurable quantity became so much
+less on one side by the same amount by which it became more
+on the other. A modification of this single fluid theory was put
+forward by F.U.T. Aepinus which was explained and illustrated
+in his <i>Tentamen theoriae electricitatis et magnetismi</i>, published
+in St Petersburg in 1759. This theory was founded on the
+following principles:&mdash;(1) the particles of the electric fluid
+repel each other with a force decreasing as the distance increases;
+(2) the particles of the electric fluid attract the atoms of all
+bodies and are attracted by them with a force obeying the same
+law; (3) the electric fluid exists in the pores of all bodies, and
+while it moves without any obstruction in conductors such as
+metals, water, &amp;c., it moves with extreme difficulty in so-called
+non-conductors such as glass, resin, &amp;c.; (4) electrical phenomena
+are produced either by the transference of the electric fluid of a
+body containing more to one containing less, or from its attraction
+and repulsion when no transference takes place. Electric
+attractions and repulsions were, however, regarded as differential
+actions in which the mutual repulsion of the particles of electricity
+operated, so to speak, in antagonism to the mutual attraction
+of particles of matter for one another and of particles of electricity
+for matter. Independently of Aepinus, Henry Cavendish
+put forward a single-fluid theory of electricity (<i>Phil. Trans.</i>,
+1771, 61, p. 584), in which he considered it in more precise
+detail.</p>
+
+<p><i>Two-fluid Theory.</i>&mdash;In the elucidation of electrical phenomena,
+however, towards the end of the 18th century, a modification of
+the two-fluid theory seems to have been generally preferred.
+The notion then formed of the nature of electrification was
+something as follows:&mdash;All bodies were assumed to contain a
+certain quantity of a so-called neutral fluid made up of equal
+quantities of positive and negative electricity, which when in
+this state of combination neutralized one another&rsquo;s properties.
+The neutral fluid could, however, be divided up or separated
+into its two constituents, and these could be accumulated on
+separate conductors or non-conductors. This view followed
+from the discovery of the facts of electric induction of J. Canton
+(1753, 1754). When, for instance, a positively electrified body
+was found to induce upon another insulated conductor a charge
+of negative electricity on the side nearest to it, and a charge of
+positive electricity on the side farthest from it, this was explained
+by saying that the particles of each of the two electric fluids
+repelled one another but attracted those of the positive fluid.
+Hence the operation of the positive charge upon the neutral
+fluid was to draw towards the positive the negative constituent
+of the neutral charge and repel to the distant parts of the conductor
+the positive constituent.</p>
+
+<p>C.A. Coulomb experimentally proved that the law of attraction
+and repulsion of simple electrified bodies was that the force
+between them varied inversely as the square of the distance
+and thus gave mathematical definiteness to the two-fluid hypothesis.
+It was then assumed that each of the two constituents
+of the neutral fluid had an atomic structure and that the so-called
+particles of one of the electric fluids, say positive, repelled
+similar particles with a force varying inversely as a square of the
+distance and attracted those of the opposite fluid according to
+the same law. This fact and hypothesis brought electrical
+phenomena within the domain of mathematical analysis and,
+as already mentioned, Laplace, Biot, Poisson, G.A.A. Plana
+(1781-1846), and later Robert Murphy (1806-1843), made them
+the subject of their investigations on the mode in which electricity
+distributes itself on conductors when in equilibrium.</p>
+
+<p><i>Faraday&rsquo;s Views.</i>&mdash;The two-fluid theory may be said to have
+held the field until the time when Faraday began his researches
+on electricity. After he had educated himself by the study of
+the phenomena of lines of magnetic force in his discoveries on
+electromagnetic induction, he applied the same conception to
+electrostatic phenomena, and thus created the notion of lines
+of electrostatic force and of the important function of the dielectric
+or non-conductor in sustaining them. Faraday&rsquo;s notion
+as to the nature of electrification, therefore, about the middle
+of the 19th century came to be something as follows:&mdash;He
+considered that the so-called charge of electricity on a conductor
+was in reality nothing on the conductor or in the conductor
+itself, but consisted in a state of strain or polarization, or a
+physical change of some kind in the particles of the dielectric
+surrounding the conductor, and that it was this physical state
+in the dielectric which constituted electrification. Since Faraday
+was well aware that even a good vacuum can act as a dielectric,
+he recognized that the state he called dielectric polarization
+could not be wholly dependent upon the presence of gravitative
+matter, but that there must be an electromagnetic medium of a
+supermaterial nature. In the 13th series of his <i>Experimental
+Researches on Electricity</i> he discussed the relation of a vacuum
+to electricity. Furthermore his electrochemical investigations,
+and particularly his discovery of the important law of electrolysis,
+that the movement of a certain quantity of electricity through an
+electrolyte is always accompanied by the transfer of a certain
+definite quantity of matter from one electrode to another and the
+liberation at these electrodes of an equivalent weight of the ions,
+gave foundation for the idea of a definite atomic charge of electricity.
+In fact, long previously to Faraday&rsquo;s electrochemical
+researches, Sir H. Davy and J.J. Berzelius early in the 19th
+century had advanced the hypothesis that chemical combination
+was due to electric attractions between the electric charges
+carried by chemical atoms. The notion, however, that electricity
+is atomic in structure was definitely put forward by Hermann
+von Helmholtz in a well-known Faraday lecture. Helmholtz
+says: &ldquo;If we accept the hypothesis that elementary substances
+are composed of atoms, we cannot well avoid concluding that
+electricity also is divided into elementary portions which behave
+like atoms of electricity.&rdquo;<a name="fa16h" id="fa16h" href="#ft16h"><span class="sp">16</span></a> Clerk Maxwell had already used in
+1873 the phrase, &ldquo;a molecule of electricity.&rdquo;<a name="fa17h" id="fa17h" href="#ft17h"><span class="sp">17</span></a> Towards the
+end of the third quarter of the 19th century it therefore became
+clear that electricity, whatever be its nature, was associated
+with atoms of matter in the form of exact multiples of an indivisible
+minimum electric charge which may be considered to be
+&ldquo;Nature&rsquo;s unit of electricity.&rdquo; This ultimate unit of electric
+quantity Professor Johnstone Stoney called an <i>electron</i>.<a name="fa18h" id="fa18h" href="#ft18h"><span class="sp">18</span></a> The
+formulation of electrical theory as far as regards operations in
+space free from matter was immensely assisted by Maxwell&rsquo;s
+mathematical theory. Oliver Heaviside after 1880 rendered
+much assistance by reducing Maxwell&rsquo;s mathematical analysis
+to more compact form and by introducing greater precision into
+terminology (see his <i>Electrical Papers</i>, 1892). This is perhaps
+the place to refer also to the great services of Lord Rayleigh
+to electrical science. Succeeding Maxwell as Cavendish professor
+of physics at Cambridge in 1880, he soon devoted himself especially
+to the exact redetermination of the practical electrical
+units in absolute measure. He followed up the early work of the
+British Association Committee on electrical units by a fresh
+determination of the ohm in absolute measure, and in conjunction
+with other work on the electrochemical equivalent of silver and
+the absolute electromotive force of the Clark cell may be said
+to have placed exact electrical measurement on a new basis.
+He also made great additions to the theory of alternating electric
+currents, and provided fresh appliances for other electrical
+measurements (see his <i>Collected Scientific Papers</i>, Cambridge,
+1900).</p>
+
+<p><i>Electro-optics.</i>&mdash;For a long time Faraday&rsquo;s observation on the
+rotation of the plane of polarized light by heavy glass in a
+<span class="pagenum"><a name="page191" id="page191"></a>191</span>
+magnetic field remained an isolated fact in electro-optics. Then
+M.E. Verdet (1824-1860) made a study of the subject and
+discovered that a solution of ferric perchloride in methyl alcohol
+rotated the plane of polarization in an opposite direction to heavy
+glass (<i>Ann. Chim. Phys.</i>, 1854, 41, p. 370; 1855, 43, p. 37;
+<i>Com. Rend.</i>, 1854, 39, p. 548). Later A.A.E.E. Kundt prepared
+metallic films of iron, nickel and cobalt, and obtained powerful
+negative optical rotation with them (<i>Wied. Ann.</i>, 1884, 23,
+p. 228; 1886, 27, p. 191). John Kerr (1824-1907) discovered
+that a similar effect was produced when plane polarized light was
+reflected from the pole of a powerful magnet (<i>Phil. Mag.</i>, 1877,
+[5], 3, p. 321, and 1878, 5, p. 161). Lord Kelvin showed that
+Faraday&rsquo;s discovery demonstrated that some form of rotation
+was taking place along lines of magnetic force when passing
+through a medium.<a name="fa19h" id="fa19h" href="#ft19h"><span class="sp">19</span></a> Many observers have given attention to
+the exact determination of Verdet&rsquo;s constant of rotation for
+standard substances, <i>e.g.</i> Lord Rayleigh for carbon bisulphide,<a name="fa20h" id="fa20h" href="#ft20h"><span class="sp">20</span></a>
+and Sir W.H. Perkin for an immense range of inorganic and
+organic bodies.<a name="fa21h" id="fa21h" href="#ft21h"><span class="sp">21</span></a> Kerr also discovered that when certain homogeneous
+dielectrics were submitted to electric strain, they
+became birefringent (<i>Phil. Mag.</i>, 1875, 50, pp. 337 and 446).
+The theory of electro-optics received great attention from
+Kelvin, Maxwell, Rayleigh, G.F. Fitzgerald, A. Righi and
+P.K.L. Drude, and experimental contributions from innumerable
+workers, such as F.T. Trouton, O.J. Lodge and J.L. Howard,
+and many others.</p>
+
+<p><i>Electric Waves.</i>&mdash;In the decade 1880-1890, the most important
+advance in electrical physics was, however, that which originated
+with the astonishing researches of Heinrich Rudolf Hertz (1857-1894).
+This illustrious investigator was stimulated, by a certain
+problem brought to his notice by H. von Helmholtz, to undertake
+investigations which had for their object a demonstration of the
+truth of Maxwell&rsquo;s principle that a variation in electric displacement
+was in fact an electric current and had magnetic effects.
+It is impossible to describe here the details of these elaborate
+experiments; the reader must be referred to Hertz&rsquo;s own papers,
+or the English translation of them by Prof. D.E. Jones. Hertz&rsquo;s
+great discovery was an experimental realization of a suggestion
+made by G.F. Fitzgerald (1851-1901) in 1883 as to a method of
+producing electric waves in space. He invented for this purpose
+a radiator consisting of two metal rods placed in one line, their
+inner ends being provided with poles nearly touching and their
+outer ends with metal plates. Such an arrangement constitutes
+in effect a condenser, and when the two plates respectively are
+connected to the secondary terminals of an induction coil in
+operation, the plates are rapidly and alternately charged, and
+discharged across the spark gap with electrical oscillations (see
+<span class="sc"><a href="#ar68">Electrokinetics</a></span>). Hertz then devised a wave detecting
+apparatus called a resonator. This in its simplest form consisted
+of a ring of wire nearly closed terminating in spark balls very
+close together, adjustable as to distance by a micrometer screw.
+He found that when the resonator was placed in certain positions
+with regard to the oscillator, small sparks were seen between the
+micrometer balls, and when the oscillator was placed at one end
+of a room having a sheet of zinc fixed against the wall at the
+other end, symmetrical positions could be found in the room at
+which, when the resonator was there placed, either no sparks
+or else very bright sparks occurred at the poles. These effects, as
+Hertz showed, indicated the establishment of stationary electric
+waves in space and the propagation of electric and magnetic
+force through space with a finite velocity. The other additional
+phenomena he observed finally contributed an all but conclusive
+proof of the truth of Maxwell&rsquo;s views. By profoundly ingenious
+methods Hertz showed that these invisible electric waves could
+be reflected and refracted like waves of light by mirrors and
+prisms, and that familiar experiments in optics could be repeated
+with electric waves which could not affect the eye. Hence
+there arose a new science of electro-optics, and in all parts of
+Europe and the United States innumerable investigators took
+possession of the novel field of research with the greatest delight.
+O.J. Lodge,<a name="fa22h" id="fa22h" href="#ft22h"><span class="sp">22</span></a> A. Righi,<a name="fa23h" id="fa23h" href="#ft23h"><span class="sp">23</span></a> J.H. Poincaré,<a name="fa24h" id="fa24h" href="#ft24h"><span class="sp">24</span></a> V.F.K. Bjerknes,
+P.K.L. Drude, J.J. Thomson,<a name="fa25h" id="fa25h" href="#ft25h"><span class="sp">25</span></a> John Trowbridge, Max Abraham,
+and many others, contributed to its elucidation.</p>
+
+<p>In 1892, E. Branly of Paris devised an appliance for detecting
+these waves which subsequently proved to be of immense
+importance. He discovered that they had the power of affecting
+the electric conductivity of materials when in a state of powder,
+the majority of metallic filings increasing in conductivity.
+Lodge devised a similar arrangement called a coherer, and E.
+Rutherford invented a magnetic detector depending on the
+power of electric oscillations to demagnetize iron or steel. The
+sum total of all these contributions to electrical knowledge
+had the effect of establishing Maxwell&rsquo;s principles on a firm basis,
+but they also led to technical inventions of the very greatest
+utility. In 1896 G. Marconi applied a modified and improved
+form of Branly&rsquo;s wave detector in conjunction with a novel
+form of radiator for the telegraphic transmission of intelligence
+through space without wires, and he and others developed this
+new form of telegraphy with the greatest rapidity and success
+into a startling and most useful means of communicating through
+space electrically without connecting wires.</p>
+
+<p><i>Electrolysis.</i>&mdash;The study of the transfer of electricity through
+liquids had meanwhile received much attention. The general
+facts and laws of electrolysis (<i>q.v.</i>) were determined experimentally
+by Davy and Faraday and confirmed by the researches of
+J.F. Daniell, R.W. Bunsen and Helmholtz. The modern
+theory of electrolysis grew up under the hands of R.J.E. Clausius,
+A.W. Williamson and F.W.G. Kohlrausch, and received a
+great impetus from the work of Svante Arrhenius, J.H. Van&rsquo;t
+Hoff, W. Ostwald, H.W. Nernst and many others. The theory
+of the ionization of salts in solution has raised much discussion
+amongst chemists, but the general fact is certain that electricity
+only moves through liquids in association with matter, and
+simultaneously involves chemical dissociation of molecular
+groups.</p>
+
+<p><i>Discharge through Gases.</i>&mdash;Many eminent physicists had an
+instinctive feeling that the study of the passage of electricity
+through gases would shed much light on the intrinsic nature
+of electricity. Faraday devoted to a careful examination of the
+phenomena the XIII<span class="sp">th</span> series of his <i>Experimental Researches</i>,
+and among the older workers in this field must be particularly
+mentioned J. Plücker, J.W. Hittorf, A.A. de la Rive, J.P.
+Gassiot, C.F. Varley, and W. Spottiswoode and J. Fletcher
+Moulton. It has long been known that air and other gases at
+the pressure of the atmosphere were very perfect insulators,
+but that when they were rarefied and contained in glass tubes
+with platinum electrodes sealed through the glass, electricity
+could be passed through them under sufficient electromotive
+force and produced a luminous appearance known as the electric
+glow discharge. The so-called vacuum tubes constructed by
+H. Geissler (1815-1879) containing air, carbonic acid, hydrogen,
+&amp;c., under a pressure of one or two millimetres, exhibit beautiful
+appearances when traversed by the high tension current produced
+by the secondary circuit of an induction coil. Faraday discovered
+the existence of a dark space round the negative electrode which
+is usually known as the &ldquo;Faraday dark space.&rdquo; De la Rive
+added much to our knowledge of the subject, and J. Plücker
+and his disciple J.W. Hittorf examined the phenomena exhibited
+in so-called high vacua, that is, in exceedingly rarefied gases.
+C.F. Varley discovered the interesting fact that no current
+could be sent through the rarefied gas unless a certain minimum
+potential difference of the electrodes was excited. Sir William
+Crookes took up in 1872 the study of electric discharge through
+<span class="pagenum"><a name="page192" id="page192"></a>192</span>
+high vacua, having been led to it by his researches on the radiometer.
+The particular details of the phenomena observed will
+be found described in the article <span class="sc"><a href="#artlinks">Conduction, Electric</a></span> (§ III.).
+The main fact discovered by researches of Plücker, Hittorf and
+Crookes was that in a vacuum tube containing extremely rarefied
+air or other gas, a luminous discharge takes place from the
+negative electrode which proceeds in lines normal to the surface
+of the negative electrode and renders phosphorescent both the
+glass envelope and other objects placed in the vacuum tube
+when it falls upon them. Hittorf made in 1869 the discovery
+that solid objects could cast shadows or intercept this cathode
+discharge. The cathode discharge henceforth engaged the
+attention of many physicists. Varley had advanced tentatively
+the hypothesis that it consisted in an actual projection of electrified
+matter from the cathode, and Crookes was led by his researches
+in 1870, 1871 and 1872 to embrace and confirm this
+hypothesis in a modified form and announce the existence of a
+fourth state of matter, which he called radiant matter, demonstrating
+by many beautiful and convincing experiments that
+there was an actual projection of material substance of some
+kind possessing inertia from the surface of the cathode. German
+physicists such as E. Goldstein were inclined to take another
+view. Sir J.J. Thomson, the successor of Maxwell and Lord
+Rayleigh in the Cavendish chair of physics in the university of
+Cambridge, began about the year 1899 a remarkable series of
+investigations on the cathode discharge, which finally enabled
+him to make a measurement of the ratio of the electric charge
+to the mass of the particles of matter projected from the cathode,
+and to show that this electric charge was identical with the
+atomic electric charge carried by a hydrogen ion in the act of
+electrolysis, but that the mass of the cathode particles, or
+&ldquo;corpuscles&rdquo; as he called them, was far less, viz. about <span class="spp">1</span>&frasl;<span class="suu">2000</span>th
+part of the mass of a hydrogen atom.<a name="fa26h" id="fa26h" href="#ft26h"><span class="sp">26</span></a> The subject was pursued
+by Thomson and the Cambridge physicists with great mathematical
+and experimental ability, and finally the conclusion
+was reached that in a high vacuum tube the electric charge is
+carried by particles which have a mass only a fraction, as above
+mentioned, of that of the hydrogen atom, but which carry a
+charge equal to the unit electric charge of the hydrogen ion as
+found by electrochemical researches.<a name="fa27h" id="fa27h" href="#ft27h"><span class="sp">27</span></a> P.E.A. Lenard made
+in 1894 (<i>Wied. Ann. Phys.</i>, 51, p. 225) the discovery that these
+cathode particles or corpuscles could pass through a window
+of thin sheet aluminium placed in the wall of the vacuum tube
+and give rise to a class of radiation called the Lenard rays.
+W.C. Röntgen of Munich made in 1896 his remarkable discovery
+of the so-called X or Röntgen rays, a class of radiation produced
+by the impact of the cathode particles against an impervious
+metallic screen or anticathode placed in the vacuum tube.
+The study of Röntgen rays was ardently pursued by the principal
+physicists in Europe during the years 1897 and 1898 and subsequently.
+The principal property of these Röntgen rays which
+attracted public attention was their power of passing through
+many solid bodies and affecting a photographic plate. Hence
+some substances were opaque to them and others transparent.
+The astonishing feat of photographing the bones of the living
+animal within the tissues soon rendered the Röntgen rays
+indispensable in surgery and directed an army of investigators
+to their study.</p>
+
+<p><i>Radioactivity.</i>&mdash;One outcome of all this was the discovery
+by H. Becquerel in 1896 that minerals containing uranium, and
+particularly the mineral known as pitchblende, had the power
+of affecting sensitive photographic plates enclosed in a black
+paper envelope when the mineral was placed on the outside, as
+well as of discharging a charged electroscope (<i>Com. Rend.</i>, 1896,
+122, p. 420). This research opened a way of approach to the
+phenomena of radioactivity, and the history of the steps by which
+P. Curie and Madame Curie were finally led to the discovery of
+radium is one of the most fascinating chapters in the history of
+science. The study of radium and radioactivity (see <span class="sc"><a href="#artlinks">Radioactivity</a></span>)
+led before long to the further remarkable knowledge
+that these so-called radioactive materials project into surrounding
+space particles or corpuscles, some of which are identical
+with those projected from the cathode in a high vacuum tube,
+together with others of a different nature. The study of radioactivity
+was pursued with great ability not only by the Curies
+and A. Debierne, who associated himself with them, in France,
+but by E. Rutherford and F. Soddy in Canada, and by J.J.
+Thomson, Sir William Crookes, Sir William Ramsay and others
+in England.</p>
+
+<p><i>Electronic Theory.</i>&mdash;The final outcome of these investigations
+was the hypothesis that Thomson&rsquo;s corpuscles or particles
+composing the cathode discharge in a high vacuum tube must
+be looked upon as the ultimate constituent of what we call
+negative electricity; in other words, they are atoms of negative
+electricity, possessing, however, inertia, and these negative
+electrons are components at any rate of the chemical atom.
+Each electron is a point-charge of negative electricity equal to
+3.9 × 10<span class="sp">&minus;10</span> of an electrostatic unit or to 1.3 × 10<span class="sp">&minus;20</span> of an electromagnetic
+unit, and the ratio of its charge to its mass is nearly
+2 × 10<span class="sp">7</span> using E.M. units. For the hydrogen atom the ratio of
+charge to mass as deduced from electrolysis is about 10<span class="sp">4</span>. Hence
+the mass of an electron is <span class="spp">1</span>&frasl;<span class="suu">2000</span>th of that of a hydrogen atom.
+No one has yet been able to isolate positive electrons, or to give
+a complete demonstration that the whole inertia of matter is
+only electric inertia due to what may be called the inductance
+of the electrons. Prof. Sir J. Larmor developed in a series of
+very able papers (<i>Phil. Trans.</i>, 1894, 185; 1895, 186; 1897,
+190), and subsequently in his book <i>Aether and Matter</i> (1900), a
+remarkable hypothesis of the structure of the electron or corpuscle,
+which he regards as simply a strain centre in the aether
+or electromagnetic medium, a chemical atom being a collection
+of positive and negative electrons or strain centres in stable
+orbital motion round their common centre of mass (see <span class="sc"><a href="#artlinks">Aether</a></span>).
+J.J. Thomson also developed this hypothesis in a profoundly
+interesting manner, and we may therefore summarize very
+briefly the views held on the nature of electricity and matter
+at the beginning of the 20th century by saying that the term
+electricity had come to be regarded, in part at least, as a collective
+name for electrons, which in turn must be considered as constituents
+of the chemical atom, furthermore as centres of certain
+lines of self-locked and permanent strain existing in the universal
+aether or electromagnetic medium. Atoms of matter are composed
+of congeries of electrons and the inertia of matter is probably
+therefore only the inertia of the electromagnetic medium.<a name="fa28h" id="fa28h" href="#ft28h"><span class="sp">28</span></a>
+Electric waves are produced wherever electrons are accelerated
+or retarded, that is, whenever the velocity of an electron is
+changed or accelerated positively or negatively. In every solid
+body there is a continual atomic dissociation, the result of which
+is that mixed up with the atoms of chemical matter composing
+them we have a greater or less percentage of free electrons.
+The operation called an electric current consists in a diffusion
+or movement of these electrons through matter, and this is
+controlled by laws of diffusion which are similar to those of the
+diffusion of liquids or gases. Electromotive force is due to a
+difference in the density of the electronic population in different
+or identical conducting bodies, and whilst the electrons can
+move freely through so-called conductors their motion is much
+more hindered or restricted in non-conductors. Electric charge
+consists, therefore, in an excess or deficit of negative electrons
+in a body. In the hands of H.A. Lorentz, P.K.L. Drude, J. J,
+Thomson, J. Larmor and many others, the electronic hypothesis
+of matter and of electricity has been developed in great detail
+and may be said to represent the outcome of modern researches
+upon electrical phenomena.</p>
+
+<p><span class="pagenum"><a name="page193" id="page193"></a>193</span></p>
+
+<p>The reader may be referred for an admirable summary of the
+theories of electricity prior to the advent of the electronic
+hypothesis to J.J. Thomson&rsquo;s &ldquo;Report on Electrical Theories&rdquo;
+(<i>Brit. Assoc. Report</i>, 1885), in which he divides electrical
+theories enunciated during the 19th century into four classes,
+and summarizes the opinions and theories of A.M. Ampère,
+H.G. Grassman, C.F. Gauss, W.E. Weber, G.F.B. Riemann,
+R.J.E. Clausius, F.E. Neumann and H. von Helmholtz.</p>
+
+<div class="condensed">
+<p><span class="sc">Bibliography.</span>&mdash;M. Faraday, <i>Experimental Researches in Electricity</i>
+(3 vols., London, 1839, 1844, 1855); A.A. De la Rive, <i>Treatise
+on Electricity</i> (3 vols., London, 1853, 1858); J. Clerk Maxwell, <i>A
+Treatise on Electricity and Magnetism</i> (2 vols., 3rd ed., 1892); id.,
+<i>Scientific Papers</i> (2 vols., edited by Sir W.J. Niven, Cambridge,
+1890); H.M. Noad, <i>A Manual of Electricity</i> (2 vols., London, 1855,
+1857); J.J. Thomson, <i>Recent Researches in Electricity and Magnetism</i>
+(Oxford, 1893); id., <i>Conduction of Electricity through Gases</i> (Cambridge,
+1903); id., <i>Electricity and Matter</i> (London, 1904); O.
+Heaviside, <i>Electromagnetic Theory</i> (London, 1893); O.J. Lodge,
+<i>Modern Views of Electricity</i> (London, 1889); E. Mascart and J.
+Joubert, <i>A Treatise on Electricity and Magnetism</i>, English trans. by
+E. Atkinson (2 vols., London, 1883); Park Benjamin, <i>The Intellectual
+Rise in Electricity</i> (London, 1895); G.C. Foster and A.W. Porter,
+<i>Electricity and Magnetism</i> (London, 1903); A. Gray, <i>A Treatise on
+Magnetism and Electricity</i> (London, 1898); H.W. Watson and S.H.
+Burbury, <i>The Mathematical Theory of Electricity and Magnetism</i>
+(2 vols., 1885); Lord Kelvin (Sir William Thomson), <i>Mathematical
+and Physical Papers</i> (3 vols., Cambridge, 1882); Lord Rayleigh,
+<i>Scientific Papers</i> (4 vols., Cambridge, 1903); A. Winkelmann,
+<i>Handbuch der Physik</i>, vols. iii. and iv. (Breslau, 1903 and 1905;
+a mine of wealth for references to original papers on electricity and
+magnetism from the earliest date up to modern times). For
+particular information on the modern Electronic theory the reader
+may consult W. Kaufmann, &ldquo;The Developments of the Electron
+Idea.&rdquo; <i>Physikalische Zeitschrift</i> (1st of Oct. 1901), or <i>The Electrician</i>
+(1901), 48, p. 95; H.A. Lorentz, <i>The Theory of Electrons</i> (1909);
+E.E. Fournier d&rsquo;Albe, <i>The Electron Theory</i> (London, 1906); H.
+Abraham and P. Langevin, <i>Ions, Electrons, Corpuscles</i> (Paris, 1905);
+J.A. Fleming, &ldquo;The Electronic Theory of Electricity,&rdquo; <i>Popular
+Science Monthly</i> (May 1902); Sir Oliver J. Lodge, <i>Electrons, or the
+Nature and Properties of Negative Electricity</i> (London, 1907).</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1h" id="ft1h" href="#fa1h"><span class="fn">1</span></a> Gilbert&rsquo;s work, <i>On the Magnet, Magnetic Bodies and the Great
+Magnet, the Earth</i>, has been translated from the rare folio Latin
+edition of 1600, but otherwise reproduced in its original form by the
+chief members of the Gilbert Club of England, with a series of valuable
+notes by Prof. S.P. Thompson (London, 1900). See also <i>The
+Electrician</i>, February 21, 1902.</p>
+
+<p><a name="ft2h" id="ft2h" href="#fa2h"><span class="fn">2</span></a> See <i>The Intellectual Rise in Electricity</i>, ch. x., by Park Benjamin
+(London, 1895).</p>
+
+<p><a name="ft3h" id="ft3h" href="#fa3h"><span class="fn">3</span></a> See Sir Oliver Lodge, &ldquo;Lightning, Lightning Conductors and
+Lightning Protectors,&rdquo; <i>Journ. Inst. Elec. Eng.</i> (1889), 18, p. 386, and
+the discussion on the subject in the same volume; also the book
+by the same author on <i>Lightning Conductors and Lightning Guards</i>
+(London, 1892).</p>
+
+<p><a name="ft4h" id="ft4h" href="#fa4h"><span class="fn">4</span></a> <i>The Electrical Researches of the Hon. Henry Cavendish 1771-1781</i>,
+edited from the original manuscripts by J. Clerk Maxwell,
+F.R.S. (Cambridge, 1879).</p>
+
+<p><a name="ft5h" id="ft5h" href="#fa5h"><span class="fn">5</span></a> In 1878 Clerk Maxwell repeated Cavendish&rsquo;s experiments with
+improved apparatus and the employment of a Kelvin quadrant
+electrometer as a means of detecting the absence of charge on the
+inner conductor after it had been connected to the outer case, and
+was thus able to show that if the law of electric attraction varies
+inversely as the nth power of the distance, then the exponent n
+must have a value of 2±<span class="spp">1</span>&frasl;<span class="suu">21600</span>. See Cavendish&rsquo;s <i>Electrical Researches</i>,
+p. 419.</p>
+
+<p><a name="ft6h" id="ft6h" href="#fa6h"><span class="fn">6</span></a> Modern researches have shown that the loss of charge is in fact
+dependent upon the ionization of the air, and that, provided the
+atmospheric moisture is prevented from condensing on the insulating
+supports, water vapour in the air does not <i>per se</i> bestow on it conductance
+for electricity.</p>
+
+<p><a name="ft7h" id="ft7h" href="#fa7h"><span class="fn">7</span></a> Faraday discussed the chemical theory of the pile and arguments
+in support of it in the 8th and 16th series of his <i>Experimental Researches
+on Electricity</i>. De la Rive reviews the subject in his large
+<i>Treatise on Electricity and <span class="correction" title="amended from Magnestism">Magnetism</span></i>, vol. ii. ch. iii. The writer
+made a contribution to the discussion in 1874 in a paper on &ldquo;The
+Contact Theory of the Galvanic Cell,&rdquo; <i>Phil. Mag.</i>, 1874, 47, p. 401.
+Sir Oliver Lodge reviewed the whole position in a paper in 1885,
+&ldquo;On the Seat of the Electromotive Force in a Voltaic Cell,&rdquo; <i>Journ.
+Inst. Elec. Eng.</i>, 1885, 14, p. 186.</p>
+
+<p><a name="ft8h" id="ft8h" href="#fa8h"><span class="fn">8</span></a> &ldquo;Mémoire sur la théorie mathématique des phénomènes électrodynamiques,&rdquo;
+<i>Mémoires de l&rsquo;institut</i>, 1820, 6; see also <i>Ann. de
+Chim.</i>, 1820, 15.</p>
+
+<p><a name="ft9h" id="ft9h" href="#fa9h"><span class="fn">9</span></a> See M. Faraday, &ldquo;On some new Electro-Magnetical Motions
+and on the Theory of Magnetism,&rdquo; <i>Quarterly Journal of Science</i>,
+1822, 12, p. 74; or <i>Experimental Researches on Electricity</i>, vol. ii.
+p. 127.</p>
+
+<p><a name="ft10h" id="ft10h" href="#fa10h"><span class="fn">10</span></a> Amongst the most important of Faraday&rsquo;s quantitative researches
+must be included the ingenious and convincing proofs he
+provided that the production of any quantity of electricity of one
+sign is always accompanied by the production of an equal quantity
+of electricity of the opposite sign. See <i>Experimental Researches on
+Electricity</i>, vol. i. § 1177.</p>
+
+<p><a name="ft11h" id="ft11h" href="#fa11h"><span class="fn">11</span></a> In this connexion the work of George Green (1793-1841) must
+not be forgotten. Green&rsquo;s <i>Essay on the Application of Mathematical
+Analysis to the Theories of Electricity and Magnetism</i>, published in
+1828, contains the first exposition of the theory of potential. An
+important theorem contained in it is known as Green&rsquo;s theorem,
+and is of great value.</p>
+
+<p><a name="ft12h" id="ft12h" href="#fa12h"><span class="fn">12</span></a> See also his <i>Submarine Telegraphs</i> (London, 1898).</p>
+
+<p><a name="ft13h" id="ft13h" href="#fa13h"><span class="fn">13</span></a> The quantitative study of electrical phenomena has been
+enormously assisted by the establishment of the absolute system of
+electrical measurement due originally to Gauss and Weber. The
+British Association for the advancement of science appointed in
+1861 a committee on electrical units, which made its first report in
+1862 and has existed ever since. In this work Lord Kelvin took a
+leading part. The popularization of the system was greatly assisted
+by the publication by Prof. J.D. Everett of <i>The C.G.S. System of
+Units</i> (London, 1891).</p>
+
+<p><a name="ft14h" id="ft14h" href="#fa14h"><span class="fn">14</span></a> The first paper in which Maxwell began to translate Faraday&rsquo;s
+conceptions into mathematical language was &ldquo;On Faraday&rsquo;s Lines
+of Force,&rdquo; read to the Cambridge Philosophical Society on the 10th
+of December 1855 and the 11th of February 1856. See Maxwell&rsquo;s
+<i>Collected Scientific Papers</i>, i. 155.</p>
+
+<p><a name="ft15h" id="ft15h" href="#fa15h"><span class="fn">15</span></a> <i>A Treatise on Electricity and Magnetism</i> (2 vols.), by James
+Clerk Maxwell, sometime professor of experimental physics in the
+university of Cambridge. A second edition was edited by Sir W.D.
+Niven in 1881 and a third by Prof. Sir J.J. Thomson in 1891.</p>
+
+<p><a name="ft16h" id="ft16h" href="#fa16h"><span class="fn">16</span></a> H. von Helmholtz, &ldquo;On the Modern Development of Faraday&rsquo;s
+Conception of Electricity,&rdquo; <i>Journ. Chem. Soc.</i>, 1881, 39, p. 277.</p>
+
+<p><a name="ft17h" id="ft17h" href="#fa17h"><span class="fn">17</span></a> See Maxwell&rsquo;s <i>Electricity and Magnetism</i>, vol. i. p. 350 (2nd ed.,
+1881).</p>
+
+<p><a name="ft18h" id="ft18h" href="#fa18h"><span class="fn">18</span></a> &ldquo;On the Physical Units of Nature,&rdquo; <i>Phil. Mag.</i>, 1881, [5], 11,
+p. 381. Also <i>Trans. Roy. Soc.</i> (Dublin, 1891), 4, p. 583.</p>
+
+<p><a name="ft19h" id="ft19h" href="#fa19h"><span class="fn">19</span></a> See Sir W. Thomson, <i>Proc. Roy. Soc. Lond.</i>, 1856, 8, p. 152; or
+Maxwell, <i>Elect. and Mag.</i>, vol. ii. p. 831.</p>
+
+<p><a name="ft20h" id="ft20h" href="#fa20h"><span class="fn">20</span></a> See Lord Rayleigh, <i>Proc. Roy. Soc. Lond.</i>, 1884, 37, p. 146;
+Gordon, <i>Phil. Trans.</i>, 1877, 167, p. 1; H. Becquerel, <i>Ann. Chim.
+Phys.</i>, 1882, [3], 27, p. 312.</p>
+
+<p><a name="ft21h" id="ft21h" href="#fa21h"><span class="fn">21</span></a> Perkin&rsquo;s Papers are to be found in the <i>Journ. Chem. Soc. Lond.</i>,
+1884, p. 421; 1886, p. 177; 1888, p. 561; 1889, p. 680; 1891,
+p. 981; 1892, p. 800; 1893, p. 75.</p>
+
+<p><a name="ft22h" id="ft22h" href="#fa22h"><span class="fn">22</span></a> <i>The Work of Hertz</i> (London, 1894).</p>
+
+<p><a name="ft23h" id="ft23h" href="#fa23h"><span class="fn">23</span></a> <i>L&rsquo;Ottica delle oscillazioni elettriche</i> (Bologna, 1897).</p>
+
+<p><a name="ft24h" id="ft24h" href="#fa24h"><span class="fn">24</span></a> <i>Les Oscillations électriques</i> (Paris, 1894).</p>
+
+<p><a name="ft25h" id="ft25h" href="#fa25h"><span class="fn">25</span></a> <i>Recent Researches in Electricity and Magnetism</i> (Oxford, 1892).</p>
+
+<p><a name="ft26h" id="ft26h" href="#fa26h"><span class="fn">26</span></a> See J.J. Thomson, <i>Proc. Roy. Inst. Lond.</i>, 1897, 15, p. 419;
+also <i>Phil. Mag.</i>, 1899, [5], 48, p. 547.</p>
+
+<p><a name="ft27h" id="ft27h" href="#fa27h"><span class="fn">27</span></a> Later results show that the mass of a hydrogen atom is not far
+from 1.3×10<span class="sp">-24</span> gramme and that the unit atomic charge or natural
+unit of electricity is 1.3 × 10<span class="sp">&minus;20</span> of an electromagnetic C.G.S. unit.
+The mass of the electron or corpuscle is 7.0 × 10<span class="sp">&minus;28</span> gramme and its
+diameter is 3 × 10<span class="sp">&minus;13</span> centimetre. The diameter of a chemical atom is
+of the order of 10<span class="sp">&minus;7</span> centimetre.</p>
+
+<p>See H.A. Lorentz, &ldquo;The Electron Theory,&rdquo; <i>Elektrotechnische
+Zeitschrift</i>, 1905, 26, p. 584; or <i>Science Abstracts</i>, 1905, 8, A, p. 603.</p>
+
+<p><a name="ft28h" id="ft28h" href="#fa28h"><span class="fn">28</span></a> See J.J. Thomson, <i>Electricity and Matter</i> (London, 1904).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRICITY SUPPLY.<a name="ar64" id="ar64"></a></span> I. <i>General Principles.</i>&mdash;The improvements
+made in the dynamo and electric motor between
+1870 and 1880 and also in the details of the arc and incandescent
+electric lamp towards the close of that decade, induced engineers
+to turn their attention to the question of the private and public
+supply of electric current for the purpose of lighting and power.
+T.A. Edison<a name="fa1i" id="fa1i" href="#ft1i"><span class="sp">1</span></a> and St G. Lane Fox<a name="fa2i" id="fa2i" href="#ft2i"><span class="sp">2</span></a> were among the first to see
+the possibilities and advantages of public electric supply, and
+to devise plans for its practical establishment. If a supply
+of electric current has to be furnished to a building the option
+exists in many cases of drawing from a public supply or of
+generating it by a private plant.</p>
+
+<p><i>Private Plants.</i>&mdash;In spite of a great amount of ingenuity
+devoted to the development of the primary battery and the
+thermopile, no means of generation of large currents can compete
+in economy with the dynamo. Hence a private electric generating
+plant involves the erection of a dynamo which may be driven
+either by a steam, gas or oil engine, or by power obtained by
+means of a turbine from a low or high fall of water. It may be
+either directly coupled to the motor, or driven by a belt; and
+it may be either a continuous-current machine or an alternator,
+and if the latter, either single-phase or polyphase. The convenience
+of being able to employ storage batteries in connexion
+with a private-supply system is so great that unless power has
+to be transmitted long distances, the invariable rule is to employ
+a continuous-current dynamo. Where space is valuable this
+is always coupled direct to the motor; and if a steam-engine
+is employed, an enclosed engine is most cleanly and compact.
+Where coal or heating gas is available, a gas-engine is exceedingly
+convenient, since it requires little attention. Where coal gas
+is not available, a Dowson gas-producer can be employed. The
+oil-engine has been so improved that it is extensively used in
+combination with a direct-coupled or belt-driven dynamo and
+thus forms a favourite and easily-managed plant for private
+electric lighting. Lead storage cells, however, as at present
+made, when charged by a steam-driven dynamo deteriorate less
+rapidly than when an oil-engine is employed, the reason being
+that the charging current is more irregular in the latter case,
+since the single cylinder oil-engine only makes an impulse every
+other revolution. In connexion with the generator, it is almost
+the invariable custom to put down a secondary battery of storage
+cells, to enable the supply to be given after the engine has stopped.
+This is necessary, not only as a security for the continuity of
+supply, but because otherwise the costs of labour in running
+the engine night and day become excessive. The storage battery
+gives its supply automatically, but the dynamo and engine
+require incessant skilled attendance. If the building to be
+lighted is at some distance from the engine-house the battery
+should be placed in the basement of the building, and underground
+or overhead conductors, to convey the charging current,
+brought to it from the dynamo.</p>
+
+<p>It is usual, in the case of electric lighting installations, to reckon
+all lamps in their equivalent number of 8 candle power (c.p.)
+incandescent lamps. In lighting a private house or building,
+the first thing to be done is to settle the total number of incandescent
+lamps and their size, whether 32 c.p., 16 c.p. or 8 c.p.
+Lamps of 5 c.p. can be used with advantage in small bedrooms
+and passages. Each candle-power in the case of a carbon filament
+lamp can be taken as equivalent to 3.5 watts, or the 8 c.p. lamp
+as equal to 30 watts, the 16 c.p. lamp to 60 watts, and so on.
+In the case of metallic filament lamps about 1.0 or 1.25 watts.
+Hence if the equivalent of 100 carbon filament 8 c.p. lamps is
+required in a building the maximum electric power-supply available
+must be 3000 watts or 3 kilowatts. The next matter to
+consider is the pressure of supply. If the battery can be in a
+position near the building to be lighted, it is best to use 100-volt
+incandescent lamps and enclosed arc lamps, which can be
+worked singly off the 100-volt circuit. If, however, the lamps
+are scattered over a wide area, or in separate buildings somewhat
+far apart, as in a college or hospital, it may be better to select 200
+volts as the supply pressure. Arc lamps can then be worked three
+in series with added resistance. The third step is to select the size
+of the dynamo unit and the amount of spare plant. It is desirable
+that there should be at least three dynamos, two of which
+are capable of taking the whole of the full load, the third being
+reserved to replace either of the others when required. The
+total power to be absorbed by the lamps and motors (if any)
+being given, together with an allowance for extensions, the size
+of the dynamos can be settled, and the power of the engines
+required to drive them determined. A good rule to follow is
+that the indicated horse-power (I.H.P.) of the engine should be
+double the dynamo full-load output in kilowatts; that is to
+say, for a 10-kilowatt dynamo an engine should be capable of
+giving 20 indicated (not nominal) H.P. From the I.H.P. of the
+engine, if a steam engine, the size of the boiler required for steam
+production becomes known. For small plants it is safe to reckon
+that, including water waste, boiler capacity should be provided
+equal to evaporating 40 &#8468; of water per hour for every
+I.H.P. of the engine. The locomotive boiler is a convenient
+form; but where large amounts of steam are required, some
+modification of the Lancashire boiler or the water-tube boiler
+is generally adopted. In settling the electromotive force of
+the dynamo to be employed, attention must be paid to the
+question of charging secondary cells, if these are used. If a
+secondary battery is employed in connexion with 100-volt lamps,
+it is usual to put in 53 or 54 cells. The electromotive force of
+these cells varies between 2.2 and 1.8 volts as they discharge;
+hence the above number of cells is sufficient for maintaining the
+necessary electromotive force. For charging, however, it is
+necessary to provide 2.5 volts per cell, and the dynamo must
+therefore have an electromotive force of 135 volts, <i>plus</i> any
+voltage required to overcome the fall of potential in the cable
+connecting the dynamo with the secondary battery. Supposing
+this to be 10 volts, it is safe to install dynamos having an electromotive
+force of 150 volts, since by means of resistance in the
+field circuits this electromotive force can be lowered to 110 or
+115 if it is required at any time to dispense with the battery.
+The size of the secondary cell will be determined by the nature
+<span class="pagenum"><a name="page194" id="page194"></a>194</span>
+of the supply to be given after the dynamos have been stopped.
+It is usual to provide sufficient storage capacity to run all the
+lamps for three or four hours without assistance from the dynamo.</p>
+
+<div class="condensed">
+<p>As an example taken from actual practice, the following figures
+give the capacity of the plant put down to supply 500 8 c.p. lamps
+in a hospital. The dynamos were 15-unit machines, having a full-load
+capacity of 100 amperes at 150 volts, each coupled direct to an
+engine of 25 H.P.; and a double plant of this description was supplied
+from two steel locomotive boilers, each capable of evaporating 800 &#8468;
+of water per hour. One dynamo during the day was used for charging
+the storage battery of 54 cells; and at night the discharge from the
+cells, together with the current from one of the dynamos, supplied
+the lamps until the heaviest part of the load had been taken; after
+that the current was drawn from the batteries alone. In working
+such a plant it is necessary to have the means of varying the electromotive
+force of the dynamo as the charging of the cells proceeds.
+When they are nearly exhausted, their electromotive force is less
+than 2 volts; but as the charging proceeds, a counter-electromotive
+force is gradually built up, and the engineer-in-charge has to raise
+the voltage of the dynamo in order to maintain a constant charging
+current. This is effected by having the dynamos designed to give
+normally the highest E.M.F. required, and then inserting resistance
+in their field circuits to reduce it as may be necessary. The space
+and attendance required for an oil-engine plant are much less than
+for a steam-engine.</p>
+</div>
+
+<p><i>Public Supply.</i>&mdash;The methods at present in successful operation
+for public electric supply fall into two broad divisions:&mdash;(1)
+continuous-current systems and (2) alternating-current systems.
+Continuous-current systems are either low- or high-pressure.
+In the former the current is generated by dynamos at some
+pressure less than 500 volts, generally about 460 volts, and is
+supplied to users at half this pressure by means of a three-wire
+system (see below) of distribution, with or without the addition
+of storage batteries.</p>
+
+<p>The general arrangements of a low-pressure continuous-current
+town supply station are as follows:&mdash;If steam is the motive
+power selected, it is generated under all the best
+conditions of economy by a battery of boilers, and
+<span class="sidenote">Low-pressure continuous supply.</span>
+supplied to engines which are now almost invariably
+coupled direct, each to its own dynamo, on one
+common bedplate; a multipolar dynamo is most
+usually employed, coupled direct to an enclosed engine. Parsons
+or Curtis steam turbines (see <span class="sc"><a href="#artlinks">Steam-Engine</a></span>) are frequently
+selected, since experience has shown that the costs of oil and
+attendance are far less for this type than for the reciprocating
+engine, whilst the floor space and, therefore, the building cost
+are greatly reduced. In choosing the size of unit to be adopted,
+the engineer has need of considerable experience and discretion,
+and also a full knowledge of the nature of the public demand
+for electric current. The rule is to choose as large units as possible,
+consistent with security, because they are proportionately
+more economical than small ones. The over-all efficiency of a
+steam dynamo&mdash;that is, the ratio between the electrical power
+output, reckoned say in kilowatts, and the I.H.P. of the
+engine, reckoned in the same units&mdash;is a number which falls
+rapidly as the load decreases, but at full load may reach some
+such value as 80 or 85%. It is common to specify the efficiency,
+as above defined, which must be attained by the plant at full-load,
+and also the efficiencies at quarter- and half-load which
+must be reached or exceeded. Hence in the selection of the size
+of the units the engineer is guided by the consideration that
+whatever units are in use shall be as nearly as possible fully
+loaded. If the demand on the station is chiefly for electric
+lighting, it varies during the hours of the day and night with
+tolerable regularity. If the output of the station, either in
+amperes or watts, is represented by the ordinates of a curve,
+the abscissae of which represent the hours of the day, this load
+diagram for a supply station with lighting load only, is a curve
+such as is shown in fig. 1, having a high peak somewhere between
+6 and 8 <span class="scs">P.M.</span> The area enclosed by this load-diagram compared
+with the area of the circumscribing rectangle is called the <i>load-factor</i>
+of the station. This varies from day to day during the
+year, but on the average for a simple lighting load is not generally
+above 10 or 12%, and may be lower. Thus the total output
+from the station is only some 10% on an average of that which
+it would be if the supply were at all times equal to the maximum
+demand. Roughly speaking, therefore, the total output of an
+electric supply station, furnishing current chiefly for electric
+lighting, is at best equal to about two hours&rsquo; supply during the
+day at full load. Hence during the greater part of the twenty-four
+hours a large part of the plant is lying idle. It is usual to
+provide certain small sets of steam dynamos, called the daylight
+machines, for supplying the demand during the day and later
+part of the evening, the remainder of the machines being called
+into requisition only for a short time. Provision must be made
+for sufficient reserve of plant, so that the breakdown of one or
+more sets will not cripple the output of the station.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:458px; height:287px" src="images/img194a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span></td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:520px; height:274px" src="images/img194b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p>Assuming current to be supplied at about 460 volts by different
+and separate steam dynamos, Dy<span class="su">1</span>, Dy<span class="su">2</span> (fig. 2), the machines are
+connected through proper amperemeters and voltmeters
+with <i>omnibus bars</i>, O<span class="su">1</span>, O<span class="su">2</span>, O<span class="su">3</span>, on a main switchboard,
+<span class="sidenote">Three-wire system.</span>
+so that any dynamo can be put in connexion
+or removed. The switchboard is generally divided
+into three parts&mdash;one panel for the connexions of the positive
+feeders, F<span class="su">1</span>, with the positive terminals of the generators; one for
+the negative feeders, F<span class="su">3</span>, and negative generator terminals;
+while from the third (or middle-wire panel) proceed an equal
+number of middle-wire feeders, F<span class="su">2</span>. These sets of conductors
+are led out into the district to be supplied with current, and are
+there connected into a distributing system, consisting of three
+separate insulated conductors, D<span class="su">1</span>, D<span class="su">2</span>, D<span class="su">3</span>, respectively called the
+positive, middle and negative distributing mains. The lamps
+in the houses, H<span class="su">1</span>, H<span class="su">2</span>, &amp;c., are connected between the middle and
+negative, and the middle and positive, mains by smaller supply
+and service wires. As far as possible the numbers of lamps
+installed on the two sides of the system are kept equal; but since
+it is not possible to control the consumption of current, it becomes
+necessary to provide at the station two small dynamos called
+the <i>balancing machines</i>, B<span class="su">1</span>, B<span class="su">2</span>, connected respectively between
+the middle and positive and the middle and negative omnibus
+bars. These machines may have their shafts connected together,
+or they may be driven by separate steam dynamos; their
+function is to supply the difference in the total current circulating
+through the whole of the lamps respectively on the two opposite
+sides of the middle wire. If storage batteries are employed in
+the station, it is usual to install two complete batteries, S<span class="su">1</span>, S<span class="su">2</span>,
+<span class="pagenum"><a name="page195" id="page195"></a>195</span>
+which are placed in a separate battery room and connected
+between the middle omnibus bar and the two outer omnibus
+bars. The extra electromotive force required to charge these
+batteries is supplied by two small dynamos b<span class="su">1</span>, b<span class="su">2</span>, called <i>boosters</i>.
+It is not unusual to join together the two balancing dynamos
+and the two boosters on one common bedplate, the shafts being
+coupled and in line, and to employ the balancing machines as
+electromotors to drive the boosters as required. By the use of
+<i>reversible boosters</i>, such as those made by the Lancashire Dynamo
+&amp; Motor Company under the patents of Turnbull &amp; M<span class="sp">c</span>Leod,
+having four field windings on the booster magnets (see <i>The
+Electrician</i>, 1904, p. 303), it is possible to adjust the relative duty
+of the dynamos and battery so that the load on the supply
+dynamos is always constant. Under these conditions the main
+engines can be worked all the time at their maximum steam
+economy and a smaller engine plant employed. If the load in
+the station rises above the fixed amount, the batteries discharge
+in parallel with the station dynamos; if it falls below, the
+batteries are charged and the station dynamos take the external
+load.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:1048px; height:1171px" src="images/img195.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Figs.</span> 3 and 4.&mdash;Low-pressure Supply Station.</td></tr></table>
+
+<p>The general arrangements of a low-pressure supply station
+are shown in figs. 3 and 4. It consists of a boiler-house containing
+a bank of boilers, either Lancashire or Babcock &amp; Wilcox being
+generally used (see <span class="sc"><a href="#artlinks">Boiler</a></span>), which furnish steam to the engines
+<span class="sidenote">Generating stations.</span>
+<span class="pagenum"><a name="page196" id="page196"></a>196</span>
+and dynamos, provision being made by duplicate steam-pipes
+or a ring main so that the failure of a single engine or dynamo
+does not cripple the whole supply. The furnace
+gases are taken through an economizer (generally
+Green&rsquo;s) so that they give up their heat to the cold
+feed water. If condensing water is available the engines
+are worked condensing, and this is an essential condition of
+economy when steam turbines are employed. Hence, either
+a condensing water pond or a cooling tower has to be provided
+to cool the condensing water and enable it to be used over and
+over again. Preferably the station should be situated near a
+river or canal and a railway siding. The steam dynamos are
+generally arranged in an engine-room so as to be overlooked
+from a switchboard gallery (fig. 3), from which all the control
+is carried out. The boiler furnaces are usually stoked by automatic
+stokers. Owing to the relatively small load factor (say
+8 or 10%) of a station giving electric supply for lighting only,
+the object of every station engineer is to cultivate a demand for
+electric current for power during the day-time by encouraging
+the use of electric motors for lifts and other purposes, but above
+all to create a demand for traction purposes. Hence most urban
+stations now supply current not only for electric lighting but
+for running the town tramway system, and this traction load
+being chiefly a daylight load serves to keep the plant employed
+and remunerative. It is usual to furnish a continuous current
+supply for traction at 500 or 600 volts, although some station
+engineers are advocating the use of higher voltages. In those
+stations which supply current for traction, but which have a
+widely scattered lighting load, <i>double current</i> dynamos are often
+employed, furnishing from one and the same armature a
+continuous current for traction purposes, and an alternating
+current for lighting purposes.</p>
+
+<p>In some places a high voltage system of electric supply by
+continuous current is adopted. In this case the current is
+generated at a pressure of 1000 or 2000 volts, and
+transmitted from the generating station by conductors,
+<span class="sidenote">High-pressure continuous supply.</span>
+called high-pressure feeders, to certain sub-centres
+or transformer centres, which are either buildings
+above ground or cellars or excavations under the ground. In
+these transformer centres are placed machines, called <i>continuous-current
+transformers</i>, which transform the electric energy and
+create a secondary electric current at a lower pressure, perhaps
+100 or 150 volts, to be supplied by distributing mains to users
+(see <span class="sc"><a href="#artlinks">Transformers</a></span>). From these sub-centres insulated conductors
+are run back to the generating station, by which the
+engineer can start or stop the continuous-current rotatory
+transformers, and at the same time inform himself as to their
+proper action and the electromotive force at the secondary
+terminals. This system was first put in practice in Oxford,
+England, and hence has been sometimes called by British
+engineers &ldquo;the Oxford system.&rdquo; It is now in operation in a
+number of places in England, such as Wolverhampton, Walsall,
+and Shoreditch in London. It has the advantage that in connexion
+with the low-pressure distributing system secondary
+batteries can be employed, so that a storage of electric energy
+is effected. Further, continuous-current arc lamps can be worked
+in series off the high-pressure mains, that is to say, sets of 20
+to 40 arc lamps can be operated for the purpose of street lighting
+by means of the high-pressure continuous current.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:517px; height:317px" src="images/img196.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span></td></tr></table>
+
+<p>The alternating current systems in operation at the present
+time are the <i>single-phase</i> system, with distributing transformers
+or transformer sub-centres, and the <i>polyphase</i> systems,
+in which the alternating current is transformed down
+<span class="sidenote">Alternating supply.</span>
+into an alternating current of low pressure, or, by means
+of rotatory transformers, into a continuous current.
+The general arrangement of a <i>single-phase</i> alternating-current
+system is as follows: The generating station contains a number
+of alternators, A<span class="su">1</span> A<span class="su">2</span> (fig. 5), producing single-phase alternating
+current, either at 1000, 2000, or sometimes, as at Deptford and
+other places, 10,000 volts. This current is distributed from the
+station either at the pressure at which it is generated, or after
+being transformed up to a higher pressure by the transformer T.
+The alternators are sometimes worked in parallel, that is to
+say, all furnish their current to two common omnibus bars on a
+high-pressure switchboard, and each is switched into circuit at
+the moment when it is brought into step with the other machines,
+as shown by some form of <i>phase-indicator</i>. In some cases,
+instead of the high-pressure feeders starting from omnibus bars,
+each alternator works independently and the feeders are grouped
+together on the various alternators as required. A number of
+high-pressure feeders are carried from the main switchboard to
+various transformer sub-centres or else run throughout the
+district to which current is to be furnished. If the system laid
+down is the transformer sub-centre system, then at each of these
+sub-centres is placed a battery of alternating-current transformers,
+T<span class="su">1</span> T<span class="su">2</span> T<span class="su">3</span>, having their primary circuits all joined in parallel to
+the terminals of the high-pressure feeders, and their secondary
+circuits all joined in parallel on a distributing main, suitable
+switches and cut-outs being interposed. The pressure of the
+current is then transformed down by these transformers to the
+required supply pressure. The secondary circuits of these
+transformers are generally provided with three terminals, so as
+to supply the low-pressure side on a three-wire system. It is
+not advisable to connect together directly the secondary circuits
+of all the different sub-centres, because then a fault or short
+circuit on one secondary system affects all the others. In banking
+together transformers in this manner in a sub-station it is
+necessary to take care that the transformation ratio and
+secondary drop (see <span class="sc"><a href="#artlinks">Transformers</a></span>) are exactly the same,
+otherwise one transformer will take more than its full share of
+the load and will become overheated. The transformer sub-station
+system can only be adopted where the area of supply
+is tolerably compact. Where the consumers lie scattered over
+a large area, it is necessary to carry the high-pressure mains
+throughout the area, and to place a separate transformer or
+transformers in each building. From a financial point of view,
+this &ldquo;house-to-house system&rdquo; of alternating-current supply,
+generally speaking, is less satisfactory in results than the transformer
+sub-centre system. In the latter some of the transformers
+can be switched off, either by hand or by automatic apparatus,
+during the time when the load is light, and then no power is
+expended in magnetizing their cores. But with the house-to-house
+system the whole of the transformers continually remain
+connected with the high-pressure circuits; hence in the case of
+supply stations which have only an ordinary electric lighting
+load, and therefore a load-factor not above 10%, the efficiency
+of distribution is considerably diminished.</p>
+
+<p>The single-phase alternating-current system is defective in
+that it cannot be readily combined with secondary batteries for
+the storage of electric energy. Hence in many places preference
+is now given to the <i>polyphase system</i>. In such a system a polyphase
+alternating current, either two- or three-phase, is transmitted
+from the generating station at a pressure of 5000 to
+10,000 volts, or sometimes higher, and at various sub-stations
+is transformed down, first by static transformers into an alternating
+current of lower pressure, say 500 volts, and then by
+<span class="pagenum"><a name="page197" id="page197"></a>197</span>
+means of rotatory transformers into a continuous current of
+500 volts or lower for use for lighting or traction.</p>
+
+<p>In the case of large cities such as London, New York, Chicago,
+Berlin and Paris the use of small supply stations situated in the
+interior of the city has gradually given way to the establishment
+of large supply stations outside the area; in these alternating
+current is generated on the single or polyphase system at a high
+voltage and transmitted by underground cables to sub-stations
+in the city, at which it is transformed down for distribution
+for private and public electric lighting and for urban electric
+traction.</p>
+
+<p>Owing to the high relative cost of electric power when generated
+in small amounts and the great advantages of generating it in
+proximity to coal mines and waterfalls, the supply of electric
+power in bulk to small towns and manufacturing districts has
+become a great feature in modern electrical engineering. In
+Great Britain, where there is little useful water power but
+abundance of coal, electric supply stations for supply in bulk
+have been built in the coal-producing districts of South Wales,
+the Midlands, the Clyde valley and Yorkshire. In these cases
+the current is a polyphase current generated at a high voltage,
+5000 to 10,000 volts, and sometimes raised again in pressure to
+20,000 or 40,000 volts and transmitted by overhead lines to the
+districts to be supplied. It is there reduced in voltage by transformers
+and employed as an alternating current, or is used to
+drive polyphase motors coupled to direct current generators to
+reproduce the power in continuous current form. It is then
+distributed for local lighting, street or railway traction, driving
+motors, and metallurgical or electrochemical applications.
+Experience has shown that it is quite feasible to distribute in all
+directions for 25 miles round a high-pressure generating station,
+which thus supplies an area of nearly 2000 sq. m. At such
+stations, employing large turbine engines and alternators,
+electric power may be generated at a works cost of 0.375d. per
+kilowatt (K.W.), the coal cost being less than 0.125d. per K.W.,
+and the selling price to large load-factor users not more than
+0.5d. per K.W. The average price of supply from the local
+generating stations in towns and cities is from 3d. to 4d. per unit,
+electric energy for power and heating being charged at a lower
+rate than that for lighting only.</p>
+
+<p>We have next to consider the structure and the arrangement
+of the conductors employed to convey the currents from their
+place of creation to that of utilization. The conductors
+themselves for the most part consist of copper having
+<span class="sidenote">Conductors.</span>
+a conductivity of not less than 98% according to
+Matthiessen&rsquo;s standard. They are distinguished as (1) <i>External
+conductors</i>, which are a part of the public supply and belong
+to the corporation or company supplying the electricity; (2)
+<i>Internal conductors</i>, or house wiring, forming a part of the structure
+of the house or building supplied and usually the property of its
+owner.</p>
+
+<p>The external conductors may be overhead or underground.
+<i>Overhead</i> conductors may consist of bare stranded copper cables
+carried on porcelain insulators mounted on stout iron
+or wooden poles. If the current is a high-pressure
+<span class="sidenote">External conductors.</span>
+one, these insulators must be carefully tested, and are
+preferably of the pattern known as oil insulators.
+In and near towns it is necessary to employ insulated overhead
+conductors, generally india-rubber-covered stranded copper
+cables, suspended by leather loops from steel bearer wires which
+take the weight. The British Board of Trade have issued
+elaborate rules for the construction of overhead lines to transmit
+large electric currents. Where telephone and telegraph wires
+pass over such overhead electric lighting wires, they have to be
+protected from falling on the latter by means of guard wires.</p>
+
+<p>By far the largest part, however, of the external electric
+distribution is now carried out by <i>underground conductors</i>, which
+are either bare or insulated. Bare copper conductors may be
+carried underground in culverts or chases, air being in this case
+the insulating material, as in the overhead system. A culvert
+and covered chase is constructed under the road or side-walk,
+and properly shaped oak crossbars are placed in it carrying
+glass or porcelain insulators, on which stranded copper cables,
+or, preferably, copper strips placed edgeways, are stretched
+and supported. The advantages of this method of construction
+are cheapness and the ease with which connexions can be made
+with service-lines for house supply; the disadvantages are the
+somewhat large space in which coal-gas leaking out of gas-pipes
+can accumulate, and the difficulty of keeping the culverts at all
+times free from rain-water. Moisture has a tendency to collect
+on the negative insulators, and hence to make a dead earth on
+the negative side of the main; while unless the culverts are
+well ventilated, explosions from mixtures of coal-gas and air
+are liable to occur. Insulated cables are insulated either with
+a material which is in itself waterproof, or with one which is
+only waterproof in so far as it is enclosed in a waterproof tube,
+<i>e.g.</i> of lead. Gutta-percha and india-rubber are examples of
+materials of the former kind. Gutta-percha, although practically
+everlasting when in darkness and laid under water, as in the
+case of submarine cables, has not been found satisfactory for
+use with large systems of electric distribution, although much
+employed for telephone and telegraph work. Insulated underground
+external conductors are of three types:&mdash;(<i>a</i>) <i>Insulated
+Cables drawn into Pipes.</i>&mdash;In this system of distribution cast-iron
+or stoneware pipes, or special stoneware conduits, or conduits
+made of a material called bitumen concrete, are first laid underground
+in the street. These contain a number of holes or &ldquo;ways,&rdquo;
+and at intervals drawing-in boxes are placed which consist of a
+brick or cast-iron box having a water-tight lid, by means of which
+access is gained to a certain section of the conduit. Wires are
+used to draw in the cables, which are covered with either india-rubber
+or lead, the copper being insulated by means of paper,
+impregnated jute, or other similar material. The advantages
+of a drawing-in system are that spare ways can be left when
+the conduits are put in, so that at a future time fresh cables can
+be added without breaking up the roadway. (<i>b</i>) <i>Cables in Bitumen.</i>&mdash;One
+of the earliest systems of distribution employed by T.A.
+Edison consisted in fixing two segment-shaped copper conductors
+in a steel tube, the interspace between the conductors and the
+tube being filled in with a bitumen compound. A later plan is
+to lay down an iron trough, in which the cables are supported by
+wooden bearers at proper distances, and fill in the whole with
+natural bitumen. This system has been carried out extensively
+by the Callendar Cable Company. Occasionally concentric lead-covered
+and armoured cables are laid in this way, and then
+form an expensive but highly efficient form of insulated conductor.
+In selecting a system of distribution regard must be paid to the
+nature of the soil in which the cables are laid. Lead is easily
+attacked by soft water, although under some conditions it is
+apparently exceedingly durable, and an atmosphere containing
+coal-gas is injurious to india-rubber. (<i>c</i>) <i>Armoured Cables.</i>&mdash;In
+a very extensively used system of distribution armoured cables
+are employed. In this case the copper conductors, two, three
+or more in number, may be twisted together or arranged concentrically,
+and insulated by means of specially prepared jute or
+paper insulation, overlaid with a continuous tube of lead. Over
+the lead, but separated by a hemp covering, is put a steel armour
+consisting of two layers of steel strip, wound in opposite directions
+and kept in place by an external covering. Such a cable can
+be laid directly in the ground without any preparation other
+than the excavation of a simple trench, junction-boxes being
+inserted at intervals to allow of branch cables being taken off.
+The armoured cable used is generally of the concentric pattern
+(fig. 6). It consists of a stranded copper cable composed of a
+number of wires twisted together and overlaid with an insulating
+material. Outside this a tubular arrangement of copper wires
+and a second layer of insulation, and finally a protective covering
+of lead and steel wires or armour are placed. In some cases
+three concentric cylindrical conductors are formed by twisting
+wires or copper strips with insulating material between. In
+others two or three cables of stranded copper are embedded in
+insulating material and included in a lead sheath. This last
+type of cable is usually called a <i>two-</i> or <i>three-core</i> pattern cable
+(fig. 7).</p>
+
+<p><span class="pagenum"><a name="page198" id="page198"></a>198</span></p>
+
+<table class="pic" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:508px; height:228px" src="images/img198.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span>&mdash;Armoured Concentric
+Cable (Section).</td>
+<td class="caption"><span class="sc">Fig. 7.</span>&mdash;Triple Conductor
+Armoured Cable (Section).</td></tr>
+
+<tr><td class="f90" style="width: 50%; vertical-align: top;"><p>IC, Inner conductor.</p>
+<p>OC, Outer conductor.</p>
+<p>I, Insulation.</p>
+<p>L, Lead sheath.</p>
+<p>S, Steel armour.</p>
+<p>H, Hemp covering.</p></td>
+
+<td class="f90" style="width: 50%; vertical-align: top;"><p>C, Copper conductor.</p>
+<p>I, Insulation.</p>
+<p>L, Lead sheath.</p>
+<p>H, Hemp covering.</p>
+<p>S, Steel armour.</p></td></tr></table>
+
+<p>The arrangement and nature of the external conductors
+depends on the system of electric supply in which they are used.
+In the case of continuous-current supply for incandescent
+electric lighting and motive power in small units, when the
+external conductors are laid down on the three-wire system,
+each main or branch cable in the street consists of a set of three
+conductors called the positive, middle and negative. Of these
+triple conductors some run from the supply station to various
+points in the area of supply without being tapped, and are called
+the <i>feeders</i>; others, called the <i>distributing mains</i>, are used for
+making connexions with the service lines of the consumers, one
+service line, as already explained, being connected to the middle
+conductor, and the other to either the positive or the negative
+one. Since the middle conductor serves to convey only the
+difference between the currents being used on the two sides of
+the system, it is smaller in section than the positive and negative
+ones. In laying out the system great judgment has to be exercised
+as to the selection of the points of attachment of the feeders
+to the distributing mains, the object being to keep a constant
+electric pressure or voltage between the two service-lines in all
+the houses independently of the varying demand for current.
+Legally the suppliers are under regulations to keep the supply
+voltage constant within 4% either way above or below the
+standard pressure. As a matter of fact very few stations do
+maintain such good regulation. Hence a considerable variation
+in the light given by the incandescent lamps is observed, since
+the candle-power of carbon glow lamps varies as the fifth or
+sixth power of the voltage of supply, <i>i.e.</i> a variation of only
+2% in the supply pressure affects the resulting candle-power
+of the lamps to the extent of 10 or 12%. This variation is, however,
+less in the case of metallic filament lamps (see <span class="sc"><a href="#artlinks">Lighting</a></span>:
+<i>Electric</i>). In the service-lines are inserted the meters for measuring
+the electric energy supplied to the customer (see <span class="sc"><a href="#artlinks">Meter,
+Electric</a></span>).</p>
+
+<p>In the interior of houses and buildings the conductors generally
+consist of india-rubber-covered cables laid in wood casing.
+The copper wire must be tinned and then covered,
+first with a layer of unvulcanized pure india-rubber,
+<span class="sidenote">Interior wiring.</span>
+then with a layer of vulcanized rubber, and lastly
+with one or more layers of protective cotton twist or tape. No
+conductor of this character employed for interior house-wiring
+should have a smaller insulation resistance than 300 megohms
+per mile when tested with a pressure of 600 volts after soaking
+24 hours in water. The wood casing should, if placed in damp
+positions or under plaster, be well varnished with waterproof
+varnish. As far as possible all joints in the run of the cable
+should be avoided by the use of the so-called looping-in system,
+and after the wiring is complete, careful tests for insulation
+should be made. The Institution of Electrical Engineers of
+Great Britain have drawn up rules to be followed in interior
+house-wiring, and the principal Fire Insurance offices, following
+the lead of the Phoenix Fire Office, of London, have made
+regulations which, if followed, are a safeguard against bad
+workmanship and resulting possibility of damage by fire. Where
+fires having an electric origin have taken place, they have invariably
+been traced to some breach of these rules. Opinions
+differ, however, as to the value and security of this method of
+laying interior conductors in buildings, and two or three alternative
+systems have been much employed. In one of these,
+called the <i>interior conduit</i> system, highly insulating waterproof
+and practically fireproof tubes or conduits replace the wooden
+casing; these, being either of plain insulating material, or
+covered with brass or steel armour, may be placed under plaster
+or against walls. They are connected by bends or joint-boxes.
+The insulated wires being drawn into them, any short circuit or
+heating of the wire cannot give rise to a fire, as it can only take
+place in the interior of a non-inflammable tube. A third system
+of electric light wiring is the safety concentric system, in which
+concentric conductors are used. The inner one, which is well
+insulated, consists of a copper-stranded cable. The outer may
+be a galvanized iron strand, a copper tape or braid, or a brass
+tube, and is therefore necessarily connected with the earth. A
+fourth system consists in the employment of twin insulated
+wires twisted together and sheathed with a lead tube; the
+conductor thus formed can be fastened by staples against walls,
+or laid under plaster or floors.</p>
+
+<p>The general arrangement for distributing current to the
+different portions of a building for the purpose of electric lighting
+is to run up one or more rising mains, from which branches are
+taken off to distributing boxes on each floor, and from these
+boxes to carry various branch circuits to the lamps. At the
+distributing boxes are collected the cut-outs and switches
+controlling the various circuits. When alternating currents
+are employed, it is usual to select as a type of conductor either
+twin-twisted conductor or concentric; and the employment
+of these types of cable, rather than two separate cables, is
+essential in any case where there are telephone or telegraph
+wires in proximity, for otherwise the alternating current would
+create inductive disturbances in the telephone circuit. The
+house-wiring also comprises the details of <i>switches</i> for controlling
+the lamps, <i>cut-outs</i> or fuses for preventing an excess of current
+passing, and fixtures or supports for lamps often of an ornamental
+character. For the details of these, special treatises on electric
+interior wiring must be consulted.</p>
+
+<div class="condensed">
+<p>For further information the reader may be referred to the following
+books:&mdash;C.H. Wordingham, <i>Central Electrical Stations</i> (London,
+1901); A. Gay and C.Y. Yeaman, <i>Central Station Electricity Supply</i>
+(London, 1906); S.P. Thompson, <i>Dynamo Electric Machinery</i> (2
+vols., London, 1905); E. Tremlett Carter and T. Davies, <i>Motive
+Power and Gearing</i> (London, 1906); W.C. Clinton, <i>Electric Wiring</i>
+(2nd ed., London, 1906); W. Perren Maycock, <i>Electric Wiring,
+Fitting, Switches and Lamps</i> (London, 1899); D. Salomons, <i>Electric
+Light Installations</i> (London, 1894); Stuart A. Russell, <i>Electric Light
+Cables</i> (London, 1901); F.A.C. Perrine, <i>Conductors for Electrical
+Distribution</i> (London, 1903); E. Rosenberg, W.W. Haldane Gee
+and C. Kinzbrunner, <i>Electrical Engineering</i> (London, 1903); E.C.
+Metcalfe, <i>Practical Electric Wiring for Lighting Installations</i> (London,
+1905); F.C. Raphael, <i>The Wireman&rsquo;s Pocket Book</i> (London,
+1903).</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<p>II. <i>Commercial Aspects.</i>&mdash;To enable the public supply enterprises
+referred to in the foregoing section to be carried out in
+England, statutory powers became necessary to break
+up the streets. In the early days a few small stations
+<span class="sidenote">History.</span>
+were established for the supply of electricity within &ldquo;block&rdquo;
+buildings, or by means of overhead wires within restricted areas,
+but the <span class="correction" title="amended from limitatons">limitations</span> proved uneconomical and the installations
+were for the most part merged into larger undertakings sanctioned
+by parliamentary powers. In the year 1879 the British
+government had its attention directed for the first time to electric
+lighting as a possible subject for legislation, and the consideration
+of the then existing state of electric lighting was referred to a
+select committee of the House of Commons. No legislative
+action, however, was taken at that time. In fact the invention
+of the incandescent lamp was incomplete&mdash;Edison&rsquo;s British
+master-patent was only filed in Great Britain in November
+1879. In 1881 and 1882 electrical exhibitions were held in Paris
+and at the Crystal Palace, London, where the improved electric
+<span class="pagenum"><a name="page199" id="page199"></a>199</span>
+incandescent lamp was brought before the general public. In
+1882 parliament passed the first Electric Lighting Act, and
+considerable speculation ensued. The aggregate capital of the
+companies registered in 1882-1883 to carry out the public
+supply of electricity in the United Kingdom amounted to
+£15,000,000, but the onerous conditions of the act deterred
+investors from proceeding with the enterprise. Not one of the
+sixty-two provisional orders granted to companies in 1883 under
+the act was carried out. In 1884 the Board of Trade received
+only four applications for provisional orders, and during the
+subsequent four years only one order was granted. Capitalists
+declined to go on with a business which if successful could be
+taken away from them by local authorities at the end of twenty-one
+years upon terms of paying only the then value of the plant,
+lands and buildings, without regard to past or future profits,
+goodwill or other considerations. The electrical industry in
+Great Britain ripened at a time when public opinion was averse
+to the creation of further monopolies, the general belief being
+that railway, water and gas companies had in the past received
+valuable concessions on terms which did not sufficiently safeguard
+the interests of the community. The great development
+of industries by means of private enterprise in the early part
+of the 19th century produced a reaction which in the latter part
+of the century had the effect of discouraging the creation by
+private enterprise of undertakings partaking of the nature of
+monopolies; and at the same time efforts were made to strengthen
+local and municipal institutions by investing them with wider
+functions. There were no fixed principles governing the relations
+between the state or municipal authorities and commercial
+companies rendering monopoly services. The new conditions
+imposed on private enterprise for the purpose of safeguarding
+the interests of the public were very tentative, and a former
+permanent secretary of the Board of Trade has stated that the
+efforts made by parliament in these directions have sometimes
+proved injurious alike to the public and to investors. One of
+these tentative measures was the Tramways Act 1870, and
+twelve years later it was followed by the first Electric Lighting
+Act.</p>
+
+<p>It was several years before parliament recognized the harm
+that had been done by the passing of the Electric Lighting Act
+1882. A select committee of the House of Lords sat in 1886
+to consider the question of reform, and as a result the Electric
+Lighting Act 1888 was passed. This amending act altered the
+period of purchase from twenty-one to forty-two years, but
+the terms of purchase were not materially altered in favour of
+investors. The act, while stipulating for the consent of local
+authorities to the granting of provisional orders, gives the
+Board of Trade power in exceptional cases to dispense with the
+consent, but this power has been used very sparingly. The
+right of vetoing an undertaking, conferred on local authorities
+by the Electric Lighting Acts and also by the Tramways Act
+1870, has frequently been made use of to exact unduly onerous
+conditions from promoters, and has been the subject of complaint
+for years. Although, in the opinion of ministers of the Crown,
+the exercise of the veto by local authorities has on several
+occasions led to considerable scandals, no government has so
+far been able, owing to the very great power possessed by local
+authorities, to modify the law in this respect. After 1888
+electric lighting went ahead in Great Britain for the first time,
+although other countries where legislation was different had
+long previously enjoyed its benefits. The developments proceeded
+along three well-defined lines. In London, where none
+of the gas undertakings was in the hands of local authorities,
+many of the districts were allotted to companies, and competition
+was permitted between two and sometimes three companies.
+In the provinces the cities and larger towns were held by the
+municipalities, while the smaller towns, in cases where consents
+could be obtained, were left to the enterprise of companies.
+Where consents could not be obtained these towns were for
+some time left without supply.</p>
+
+<div class="condensed">
+<p>Some statistics showing the position of the electricity supply
+business respectively in 1896 and 1906 are interesting as indicating
+the progress made and as a means of comparison between these two
+periods of the state of the industry as a whole. In 1896 thirty-eight
+companies were at work with an aggregate capital of about £6,000,000,
+and thirty-three municipalities with electric lighting loans of nearly
+£2,000,000. The figures for 1906, ten years later, show that 187
+electricity supply companies were in operation with a total investment
+of close on £32,000,000, and 277 municipalities with loans
+amounting to close on £36,000,000. The average return on the
+capital invested in the companies at the later period was 5.1% per
+annum. In 1896 the average capital expenditure was about £100
+per kilowatt of plant installed; and £50 per kilowatt was regarded
+as a very low record. For 1906 the average capital expenditure per
+kilowatt installed was about £81. The main divisions of the average
+expenditure are:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">&nbsp;</td> <td class="tcl">1896.</td> <td class="tcl">1906.</td></tr>
+<tr><td class="tcl cl">Land and buildings</td> <td class="tcl cl">22.3%</td> <td class="tcl cl">17.8%</td></tr>
+<tr><td class="tcl">Plant and machinery</td> <td class="tcl">36.7</td> <td class="tcl">36.5</td></tr>
+<tr><td class="tcl cl">Mains</td> <td class="tcl cl">32.2</td> <td class="tcl cl">35.5</td></tr>
+<tr><td class="tcl">Meters and instruments</td> <td class="tcl">&ensp;4.6</td> <td class="tcl">&nbsp;5.7</td></tr>
+<tr><td class="tcl cl">Provisional orders, &amp;c.</td> <td class="tcl cl">&ensp;3.2</td> <td class="tcl cl">&nbsp;2.8</td></tr>
+</table>
+
+<p class="noind">The load connected, expressed in equivalents of eight candle-power
+lamps, was 2,000,000 in 1896 and 24,000,000 in 1906. About one-third
+of this load would be for power purposes and about two-thirds
+for lighting. The Board of Trade units sold were 30,200,000 in 1896
+and 533,600,000 in 1906, and the average prices per unit obtained
+were 5.7d. and 2.7d. respectively, or a revenue of £717,250 in 1896
+and over £6,000,000 in 1906. The working expenses per Board of
+Trade unit sold, excluding depreciation, sinking fund and interest
+were as follows:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl">&nbsp;</td> <td class="tcl">1896.</td> <td class="tcl">1906.</td></tr>
+<tr><td class="tcl cl">Generation and distribution</td> <td class="tcl cl">2.81d.</td> <td class="tcl cl">.99d.</td></tr>
+<tr><td class="tcl">Rent, rates and taxes</td> <td class="tcl">&ensp;.35</td> <td class="tcl">.14</td></tr>
+<tr><td class="tcl cl">Management</td> <td class="tcl cl">&ensp;.81</td> <td class="tcl cl">.18</td></tr>
+<tr><td class="tcl">Sundries</td> <td class="tcl">&ensp;.10</td> <td class="tcl">.02</td></tr>
+<tr><td class="tcl">&nbsp;</td> <td class="tcl">&mdash;&mdash;&mdash;</td> <td class="tcl">&mdash;&mdash;&mdash;</td></tr>
+<tr><td class="tcc">Total</td> <td class="tcl">4.07d.</td> <td class="tcl">1.33d.</td></tr>
+</table>
+
+<p class="noind">In 1896 the greatest output at one station was about 5½ million
+units, while in 1906 the station at Manchester had the largest output
+of over 40 million units.</p>
+
+<p>The capacity of the plants installed in the United Kingdom in
+1906 was:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="bb1">&nbsp;</td> <td class="tcc bb1">K.W.</td> <td class="tcl bb1">&nbsp;</td> <td class="tcr bb1">&nbsp;</td></tr>
+
+<tr><td class="tclm bb1 cl" rowspan="2">Continuous current</td> <td class="tcrm bb1" rowspan="2">417,000</td> <td class="tcl">Provinces</td> <td class="tcr">333,000</td></tr>
+  <tr><td class="tcl bb1">London</td> <td class="tcr bb1">84,000</td></tr>
+
+<tr><td class="tclm bb1 cl" rowspan="2">Alternating current</td> <td class="tcrm bb1" rowspan="2">132,000</td> <td class="tcl">Provinces</td> <td class="tcr">83,000</td></tr>
+  <tr><td class="tcl bb1">London</td> <td class="tcr bb1">49,000</td></tr>
+
+<tr><td class="tclm bb1 cl" rowspan="2">Continuous current and<br />&emsp;alternating current combined
+      </td> <td class="tcrm bb1" rowspan="2">480,000</td> <td class="tcl">Provinces</td> <td class="tcr">366,000</td></tr>
+  <tr><td class="tcl bb1">London</td> <td class="tcr bb1">114,000</td></tr>
+
+<tr><td class="tcl">&nbsp;</td> <td class="tcr">&mdash;&mdash;&mdash;&mdash;</td> <td class="tcl">&nbsp;</td> <td class="tcr">&nbsp;</td></tr>
+<tr><td class="tcl">&nbsp;</td> <td class="tcr">1,029,000</td> <td class="tcl">k.w.</td> <td class="tcr">&nbsp;</td></tr>
+</table></div>
+
+<p>The economics of electric lighting were at first assumed to be
+similar to those of gas lighting. Experience, however, soon
+proved that there were important differences, one
+being that gas may be stored in gasometers without
+<span class="sidenote">Economics.</span>
+appreciable loss and the work of production carried
+on steadily without reference to fluctuations of demand. Electricity
+cannot be economically stored to the same extent, and for
+the most part it has to be used as it is generated. The demand
+for electric light is practically confined to the hours between
+sunset and midnight, and it rises sharply to a &ldquo;peak&rdquo; during
+this period. Consequently the generating station has to be
+equipped with plant of sufficient capacity to cope with the
+maximum load, although the peak does not persist for many
+minutes&mdash;a condition which is very uneconomical both as regards
+capital expenditure and working costs (see <span class="sc"><a href="#artlinks">Lighting</a></span>:
+<i>Electric</i>). In order to obviate the unproductiveness of the
+generating plant during the greater part of the day, electricity
+supply undertakings sought to develop the &ldquo;daylight&rdquo; load.
+This they did by supplying electricity for traction purposes, but
+more particularly for industrial power purposes. The difficulties
+in the way of this line of development, however, were that
+electric power could not be supplied cheaply enough to compete
+with steam, hydraulic, gas and other forms of power, unless
+it was generated on a very large scale, and this large demand
+could not be developed within the restricted areas for which
+provisional orders were granted and under the restrictive
+conditions of these orders in regard to situation of power-house
+and other matters.</p>
+
+<p>The leading factors which make for economy in electricity
+supply are the magnitude of the output, the load factor, and
+<span class="pagenum"><a name="page200" id="page200"></a>200</span>
+the diversity factor, also the situation of the power house, the
+means of distribution, and the provision of suitable, trustworthy
+and efficient plant. These factors become more favourable the
+larger the area and the greater and more varied the demand
+to be supplied. Generally speaking, as the output increases so
+the cost per unit diminishes, but the ratio (called the load factor)
+which the output during any given period bears to the <i>maximum</i>
+possible output during the same period has a very important
+influence on costs. The ideal condition would be when a power
+station is working at its normal <i>maximum</i> output continuously
+night and day. This would give a load-factor of 100%, and
+represents the ultimate ideal towards which the electrical
+engineer strives by increasing the area of his operations and
+consequently also the load and the variety of the overlapping
+demands. It is only by combining a large number of demands
+which fluctuate at different times&mdash;that is by achieving a high
+diversity factor&mdash;that the supplier of electricity can hope to
+approach the ideal of continuous and steady output. Owing
+to the dovetailing of miscellaneous demands the actual demand
+on a power station at any moment is never anything like the
+aggregate of all the maximum demands. One large station
+would require a plant of 36,000 k.w. capacity if all the demands
+came upon the station simultaneously, but the maximum demand
+on the generating plant is only 15,000 kilowatts. The difference
+between these two figures may be taken to represent the economy
+effected by combining a large number of demands on one station.
+In short, the keynote of progress in cheap electricity is increased
+and diversified demand combined with concentration of load.
+The average load-factor of all the British electricity stations in
+1907 was 14.5%&mdash;a figure which tends to improve.</p>
+
+<p>Several electric power supply companies have been established
+in the United Kingdom to give practical effect to these principles.
+The Electric Lighting Acts, however, do not provide
+for the establishment of large power companies, and
+<span class="sidenote">Power companies.</span>
+special acts of parliament have had to be promoted
+to authorize these undertakings. In 1898 several
+bills were introduced in parliament for these purposes. They
+were referred to a joint committee of both Houses of Parliament
+presided over by Lord Cross. The committee concluded that,
+where sufficient public advantages are shown, powers should be
+given for the supply of electricity over areas including the districts
+of several local authorities and involving the use of exceptional
+plant; that the usual conditions of purchase of the undertakings
+by the local authorities did not apply to such undertakings;
+that the period of forty-two years was &ldquo;none too long&rdquo; a
+tenure; and that the terms of purchase should be reconsidered.
+With regard to the provision of the Electric Lighting Acts which
+requires that the consent of the local authority should be obtained
+as a condition precedent to the granting of a provisional order,
+the committee was of opinion that the local authority should
+be entitled to be heard by the Board of Trade, but should not
+have the power of veto. No general legislation took place as a
+result of these recommendations, but the undermentioned special
+acts constituting power supply companies were passed.</p>
+
+<p>In 1902 the president of the Board of Trade stated that a bill
+had been drafted which he thought &ldquo;would go far to meet all
+the reasonable objections that had been urged against the present
+powers by the local authorities.&rdquo; In 1904 the government
+introduced the Supply of Electricity Bill, which provided for
+the removal of some of the minor anomalies in the law relating
+to electricity. The bill passed through all its stages in the
+House of Lords but was not proceeded with in the House of
+Commons. In 1905 the bill was again presented to parliament
+but allowed to lie on the table. In the words of the president
+of the Board of Trade, there was &ldquo;difficulty of dealing with this
+question so long as local authorities took so strong a view as to
+the power which ought to be reserved to them in connexion with
+this enterprise.&rdquo; In the official language of the council of the
+Institution of Electrical Engineers, the development of electrical
+science in the United Kingdom is in a backward condition as
+compared with other countries in respect of the practical application
+to the industrial and social requirements of the nation,
+notwithstanding that Englishmen have been among the first in
+inventive genius. The cause of such backwardness is largely
+due to the conditions under which the electrical industry has been
+carried on in the country, and especially to the restrictive
+character of the legislation governing the initiation and development
+of electrical power and traction undertakings, and to the
+powers of obstruction granted to local authorities. Eventually
+The Electric Lighting Act 1909 was passed. This Act provides:&mdash;(1)
+for the granting of provisional orders authorizing any local
+authority or company to supply electricity in bulk; (2) for the
+exercise of electric lighting powers by local authorities jointly
+under provisional order; (3) for the supply of electricity to
+railways, canals and tramways outside the area of supply with
+the consent of the Board of Trade; (4) for the compulsory
+acquisition of land for generating stations by provisional order;
+(5) for the exemption of agreements for the supply of electricity
+from stamp duty; and (6) for the amendment of regulations
+relating to July notices, revision of maximum price, certification
+of meters, transfer of powers of undertakers, auditors&rsquo; reports,
+and other matters.</p>
+
+<p>The first of the Power Bills was promoted in 1898, under which
+it was proposed to erect a large generating station in the Midlands
+from which an area of about two thousand square miles would
+be supplied. Vigorous opposition was organized against the
+bill by the local authorities and it did not pass. The bill was
+revived in 1899, but was finally crushed. In 1900 and following
+years several power bills were successfully promoted, and the
+following are the areas over which the powers of these acts extend:</p>
+
+<p>In Scotland, (1) the Clyde Valley, (2) the county of Fife,
+(3) the districts described as &ldquo;Scottish Central,&rdquo; comprising
+Linlithgow, Clackmannan, and portions of Dumbarton and
+Stirling, and (4) the Lothians, which include portions of Midlothian,
+East Lothian, Peebles and Lanark.</p>
+
+<p>In England there are companies operating in (1) Northumberland,
+(2) Durham county, (3) Lancashire, (4) South Wales and
+Carmarthenshire, (5) Derbyshire and Nottinghamshire, (6)
+Leicestershire and Warwickshire, (7) Yorkshire, (8) Shropshire,
+Worcestershire and Staffordshire, (9) Somerset, (10) Kent, (11)
+Cornwall, (12) portions of Gloucestershire, (13) North Wales,
+(14) North Staffordshire, Derbyshire, Denbighshire and Flintshire,
+(15) West Cumberland, (16) the Cleveland district,
+(17) the North Metropolitan district, and (18) the West Metropolitan
+area. An undertaking which may be included in this
+category, although it is not a Power Act company, is the Midland
+Electric Corporation in South Staffordshire. The systems of
+generation and distribution are generally 10,000 or 11,000 volts
+three-phase alternating current.</p>
+
+<p>The powers conferred by these acts were much restricted as a
+result of opposition offered to them. In many cases the larger
+towns were cut out of the areas of supply altogether, but the
+general rule was that the power company was prohibited from
+supplying direct to a power consumer in the area of an authorized
+distributor without the consent of the latter, subject to appeal
+to the Board of Trade. Even this restricted power of direct
+supply was not embodied in all the acts, the power of taking
+supply in bulk being left only to certain authorized distributors
+and to authorized users such as railways and tramways. Owing
+chiefly to the exclusion of large towns and industrial centres from
+their areas, these power supply companies did not all prove as
+successful as was expected.</p>
+
+<p>In the case of one of the power companies which has been in a
+favourable position for the development of its business, the
+theoretical conclusions in regard to the economy of large production
+above stated have been amply demonstrated in practice.
+In 1901, when this company was emerging from the stage of a
+simple electric lighting company, the total costs per unit were
+1.05d. with an output of about 2½ million units per annum.
+In 1905 the output rose to over 30 million units mostly for power
+and traction purposes, and the costs fell to 0.56d. per unit.</p>
+
+<p>An interesting phase of the power supply question has arisen
+in London. Under the general acts it was stipulated that the
+power-house should be erected within the area of supply, and
+<span class="pagenum"><a name="page201" id="page201"></a>201</span>
+amalgamation of undertakings was prohibited. After less than
+a decade of development several of the companies in London
+found themselves obliged to make considerable additions to their
+generating plants. But their existing buildings were full to their
+utmost capacity, and the difficulties of generating cheaply on
+crowded sites had increased instead of diminished during the
+interval. Several of the companies had to promote special acts
+of parliament to obtain relief, but the idea of a general combination
+was not considered to be within the range of practical
+politics until 1905, when the Administrative County of London
+Electric Power Bill was introduced. Compared with other
+large cities, the consumption of electricity in London is small.
+The output of electricity in New York for all purposes is 971
+million units per annum or 282 units per head of population.
+The output of electricity in London is only 42 units per head
+per annum. There are in London twelve local authorities and
+fourteen companies carrying on electricity supply undertakings.
+The capital expenditure is £3,127,000 by the local authorities
+and £12,530,000 by the companies, and their aggregate capacity
+of plant is 165,000 k.w. The total output is about 160,000,000
+units per annum, the total revenue is over £2,000,000, and the
+gross profit before providing for interest and sinking fund
+charges is £1,158,000. The general average cost of production
+is 1.55d. per unit, and the average price per unit sold is 3.16d.,
+but some of the undertakers have already supplied electricity
+to large power consumers at below 1d. per unit. By generating
+on a large scale for a wide variety of demands the promoters of
+the new scheme calculated to be able to offer electrical energy
+in bulk to electricity supply companies and local authorities
+at prices substantially below their costs of production at separate
+stations, and also to provide them and power users with electricity
+at rates which would compete with other forms of power. The
+authorized capital was fixed at £6,666,000, and the initial outlay
+on the first plant of 90,000 k.w., mains, &amp;c., was estimated at
+£2,000,000. The costs of generation were estimated at 0.15d.
+per unit, and the total cost at 0.52d. per unit sold. The output
+by the year 1911 was estimated at 133,500,000 units at an
+average selling price of 0.7d. per unit, to be reduced to 0.55d. by
+1916 when the output was estimated at 600,000,000 units. The
+bill underwent a searching examination before the House of
+Lords committee and was passed in an amended form. At the
+second reading in the House of Commons a strong effort was made
+to throw it out, but it was allowed to go to committee on the
+condition&mdash;contrary to the general recommendations of the
+parliamentary committee of 1898&mdash;that a purchase clause
+would be inserted; but amendments were proposed to such an
+extent that the bill was not reported for third reading until the
+eve of the prorogation of parliament. In the following year
+(1906) the Administrative Company&rsquo;s bill was again introduced
+in parliament, but the London County Council, which had
+previously adopted an attitude both hostile and negative, also
+brought forward a similar bill. Among other schemes, one known
+as the Additional Electric Power Supply Bill was to authorize
+the transmission of current from St Neots in Hunts. This bill
+was rejected by the House of Commons because the promoters
+declined to give precedence to the bill of the London County
+Council. The latter bill was referred to a hybrid committee with
+instructions to consider the whole question of London power
+supply, but it was ultimately rejected. The same result attended
+a second bill which was promoted by the London County Council
+in 1907. The question was settled by the London Electric
+Supply Act 1908, which constitutes the London County Council
+the purchasing authority (in the place of the local authorities)
+for the electric supply companies in London. This Act also
+enabled the Companies and other authorized undertakers to
+enter into agreements for the exchange of current and the
+linking-up of stations.</p>
+
+<p>The general supply of electricity is governed primarily by
+the two acts of parliament passed in 1882 and 1888, which apply
+to the whole of the United Kingdom. Until 1899 the other
+statutory provisions relating to electricity supply were incorporated
+<span class="sidenote">Legislation and regulations.</span>
+in provisional orders granted by the Board of Trade
+and confirmed by parliament in respect of each undertaking, but
+in that year an Electric Lighting Clauses Act was passed by
+which the clauses previously inserted in each order
+were standardized. Under these acts the Board of
+Trade made rules with respect to applications for
+licences and provisional orders, and regulations for
+the protection of the public, and of the electric lines and works
+of the post office, and others, and also drew up a model form
+for provisional orders.</p>
+
+<p>Until the passing of the Electric Lighting Acts, wires could be
+placed wherever permission for doing so could be obtained, but
+persons breaking up streets even with the consent of the local
+authority were liable to indictment for nuisance. With regard
+to overhead wires crossing the streets, the local authorities had
+no greater power than any member of the public, but a road
+authority having power to make a contract for lighting the road
+could authorize others to erect poles and wires for the purpose.
+A property owner, however, was able to prevent wires from being
+taken over his property. The act of 1888 made all electric lines
+or other works for the supply of electricity, not entirely enclosed
+within buildings or premises in the same occupation, subject to
+regulations of the Board of Trade. The postmaster-general
+may also impose conditions for the protection of the post office.
+Urban authorities, the London County Council, and some other
+corporations have now powers to make by-laws for prevention
+of obstruction from posts and overhead wires for telegraph,
+telephone, lighting or signalling purposes; and electric lighting
+stations are now subject to the provisions of the Factory Acts.</p>
+
+<p>Parliamentary powers to supply electricity can now be obtained
+by (A) Special Act, (B) Licence, or (C) Provisional order.</p>
+
+<p>A. <i>Special Act.</i>&mdash;Prior to the report of Lord Cross&rsquo;s joint
+committee of 1898 (referred to above), only one special act was
+passed. The provisions of the Electric Power Acts passed
+subsequently are not uniform, but the following are some of the
+usual provisions:&mdash;</p>
+
+<p>The company shall not supply electricity for lighting purposes
+except to authorized undertakers, provided that the energy
+supplied to any person for power may be used for lighting any
+premises on which the power is utilized. The company shall not
+supply energy (except to authorized undertakers) in any area
+which forms part of the area of supply of any authorized distributors
+without their consent, such consent not to be unreasonably
+withheld. The company is bound to supply authorized
+undertakers upon receiving notice and upon the applicants
+agreeing to pay for at least seven years an amount sufficient to
+yield 20% on the outlay (excluding generating plant or wires
+already installed). Other persons to whom the company is
+authorized to supply may require it upon terms to be settled,
+if not agreed, by the Board of Trade. Dividends are usually
+restricted to 8%, with a provision that the rate may be increased
+upon the average price charged being reduced. The maximum
+charges are usually limited to 3d. per unit for any quantity up
+to 400 hours&rsquo; supply, and 2d. per unit beyond. No preference is
+to be shown between consumers in like circumstances. Many provisions
+of the general Electric Lighting Acts are excluded from
+these special acts, in particular the clause giving the local
+authority the right to purchase the undertaking compulsorily.</p>
+
+<p>B. <i>Licence.</i>&mdash;The only advantages of proceeding by licence
+are that it can be expeditiously obtained and does not require
+confirmation by parliament; but some of the provisions usually
+inserted in provisional orders would be <i>ultra vires</i> in a licence,
+and the Electric Lighting Clauses Act 1899 does not extend to
+licences. The term of a licence does not exceed seven years,
+but is renewable. The consent of the local authority is necessary
+even to an application for a licence. None of the licences that
+have been granted is now in force.</p>
+
+<p>C. <i>Provisional Order.</i>&mdash;An intending applicant for a provisional
+order must serve notice of his intention on every local
+authority within the proposed area of supply on or before the 1st
+of July prior to the session in which application is to be made to
+the Board of Trade. This provision has given rise to much complaint,
+as it gives the local authorities a long time for bargaining
+<span class="pagenum"><a name="page202" id="page202"></a>202</span>
+and enables them to supersede the company&rsquo;s application by
+themselves applying for provisional orders. The Board of Trade
+generally give preference to the applications of local authorities.</p>
+
+<p>In 1905 the Board of Trade issued a memorandum stating
+that, in view of the revocation of a large number of provisional
+orders which had been obtained by local authorities, or in regard
+to which local authorities had entered into agreements with
+companies for carrying the orders into effect (which agreements
+were in many cases <i>ultra vires</i> or at least of doubtful validity), it
+appeared undesirable that a local authority should apply for a
+provisional order without having a definite intention of exercising
+the powers, and that in future the Board of Trade would not
+grant an order to a local authority unless the board were satisfied
+that the powers would be exercised within a specified period.</p>
+
+<p>Every undertaking authorized by provisional order is subject
+to the provision of the general act entitling the local authority
+to purchase compulsorily at the end of forty-two years (or
+shorter period), or after the expiration of every subsequent
+period of ten years (unless varied by agreement between the
+parties with the consent of the Board of Trade), so much of the
+undertaking as is within the jurisdiction of the purchasing
+authority upon the terms of paying the then value of all lands,
+buildings, works, materials and plant, suitable to and used for
+the purposes of the undertaking; provided that the value of
+such lands, &amp;c., shall be deemed to be their fair market value
+at the time of purchase, due regard being had to the nature and
+then condition and state of repair thereof, and to the circumstance
+that they are in such positions as to be ready for immediate
+working, and to the suitability of the same to the purposes of
+the undertaking, and where a part only of the undertaking is
+purchased, to any loss occasioned by severance, but without
+any addition in respect of compulsory purchase or of goodwill,
+or of any profits which may or might have been or be made from
+the undertaking or any similar consideration. Subject to this
+right of purchase by the local authority, a provisional order
+(but not a licence) may be for such period as the Board of Trade
+may think proper, but so far no limit has been imposed, and
+unless purchased by a local authority the powers are held in
+perpetuity. No monopoly is granted to undertakers, and since
+1889 the policy of the Board of Trade has been to sanction two
+undertakings in the same metropolitan area, preferably using
+different systems, but to discourage competing schemes within
+the same area in the provinces. Undertakers must within two
+years lay mains in certain specified streets. After the first
+eighteen months they may be required to lay mains in other
+streets upon conditions specified in the order, and any owner
+or occupier of premises within 50 yds. of a distributing main
+may require the undertakers to give a supply to his premises;
+but the consumer must pay the cost of the lines laid upon his
+property and of so much outside as exceeds 60 ft. from the
+main, and he must also contract for two and in some cases for
+three years&rsquo; supply. But undertakers are prohibited in making
+agreements for supply from showing any undue preference.
+The maximum price in London is 13s. 4d. per quarter for any
+quantity up to 20 units, and beyond that 8d. per unit, but 11s. 8d.
+per quarter up to 20 units and 7d. per unit beyond is the more
+general maximum. The &ldquo;Bermondsey clause&rdquo; requires the
+undertakers (local authority) so to fix their charges (not exceeding
+the specified maximum) that the revenue shall not be less than
+the expenditure.</p>
+
+<p>There is no statutory obligation on municipalities to provide
+for depreciation of electricity supply undertakings, but after
+providing for all expenses, interest on loans, and sinking fund
+instalments, the local authority may create a reserve fund until
+it amounts, with interest, to one-tenth of the aggregate capital
+expenditure. Any deficiency when not met out of reserve is
+payable out of the local rates.</p>
+
+<p>The principle on which the Local Government Board sanctions
+municipal loans for electric lighting undertakings is that the
+period of the loan shall not exceed the life of the works, and that
+future ratepayers shall not be unduly burdened. The periods
+of the loans vary from ten years for accumulators and arc lamps
+to sixty years for lands. Within the county of London the
+loans raised by the metropolitan borough councils for electrical
+purposes are sanctioned by the London County Council, and that
+body allows a minimum period of twenty years for repayment.
+Up to 1904-1905, 245 loans had been granted by the council
+amounting in the aggregate to £4,045,067.</p>
+
+<p>In 1901 the Institution of Civil Engineers appointed a committee
+to consider the advisability of standardizing various
+kinds of iron and steel sections. Subsequently the
+original reference was enlarged, and in 1902 the
+<span class="sidenote">Standardization.</span>
+Institution of Electrical Engineers was invited to
+co-operate. The treasury, as well as railway companies, manufacturers
+and others, have made grants to defray the expenses.
+The committee on electrical plant has ten sub-committees. In
+August 1904 an interim report was issued by the sub-committee
+on generators, motors and transformers, dealing with pressures
+and frequencies, rating of generators and motors, direct-current
+generators, alternating-current generators, and motors.</p>
+
+<p>In 1903 the specification for British standard tramway rails
+and fish-plates was issued, and in 1904 a standard specification
+for tubular tramway poles was issued. A sectional committee
+was formed in 1904 to correspond with foreign countries with
+regard to the formation of an electrical international commission
+to study the question of an international standardization of
+nomenclature and ratings of electrical apparatus and machinery.</p>
+
+<p>The electrical manufacturing branch, which is closely related
+to the electricity supply and other operating departments of the
+electrical industry, only dates from about 1880. Since
+that time it has undergone many vicissitudes. It
+<span class="sidenote">The electrical industry.</span>
+began with the manufacture of small arc lighting
+equipments for railway stations, streets and public
+buildings. When the incandescent lamp became a commercial
+article, ship-lighting sets and installations for theatres and
+mansions constituted the major portion of the electrical work.
+The next step was the organization of house-to-house distribution
+of electricity from small &ldquo;central stations,&rdquo; ultimately
+leading to the comprehensive public supply in large towns,
+which involved the manufacture of generating and distributing
+plants of considerable magnitude and complexity. With the
+advent of electric traction about 1896, special machinery had
+to be produced, and at a later stage the manufacturer had to
+solve problems in connexion with bulk supply in large areas and
+for power purposes. Each of these main departments involved
+changes in ancillary manufactures, such as cables, switches,
+transformers, meters, &amp;c., so that the electrical manufacturing
+industry has been in a constant state of transition. At the
+beginning of the period referred to Germany and America were
+following the lead of England in theoretical developments, and
+for some time Germany obtained electrical machinery from
+England. Now scarcely any electrical apparatus is exported
+to Germany, and considerable imports are received by England
+from that country and America. The explanation is to be found
+mainly in the fact that the adverse legislation of 1882 had the
+effect of restricting enterprise, and while British manufacturers
+were compulsorily inert during periods of impeded growth of
+the two most important branches of the industry&mdash;electric
+lighting and traction&mdash;manufacturers in America and on the
+continent of Europe, who were in many ways encouraged by
+their governments, devoted their resources to the establishment
+of factories and electrical undertakings, and to the development
+of efficient selling organizations at home and abroad. When
+after the amendment of the adverse legislation in 1888 a demand
+for electrical machinery arose in England, the foreign manufacturers
+were fully organized for trade on a large scale, and
+were further aided by fiscal conditions to undersell English
+manufacturers, not only in neutral markets, but even in their
+own country. Successful manufacture on a large scale is possible
+only by standardizing the methods of production. English
+manufacturers were not able to standardize because they had
+not the necessary output. There had been no repetitive demand,
+and there was no production on a large scale. Foreign manufacturers,
+however, were able to standardize by reason of the
+<span class="pagenum"><a name="page203" id="page203"></a>203</span>
+large uniform demand which existed for their manufactures.
+Statistics are available showing the extent to which the growth
+of the electrical manufacturing industry in Great Britain was
+delayed. Nearly twenty years after the inception of the industry
+there were only twenty-four manufacturing companies registered
+in the United Kingdom, having an aggregate subscribed capital
+of under £7,000,000. But in 1907 there were 292 companies
+with over £42,000,000 subscribed capital. The cable and incandescent
+lamp sections show that when the British manufacturers
+are allowed opportunities they are not slow to take
+advantage of them. The cable-making branch was established
+under the more encouraging conditions of the telegraph industry,
+and the lamp industry was in the early days protected by patents.
+Other departments not susceptible to foreign competition on
+account of freightage, such as the manufacture of storage
+batteries and rolling stock, are also fairly prosperous. In
+departments where special circumstances offer a prospect of
+success, the technical skill, commercial enterprise and general
+efficiency of British manufacturers manifest themselves by
+positive progress and not merely by the continuance of a struggle
+against adverse conditions. The normal posture of the British
+manufacturer of electrical machinery has been described as one
+of desperate defence of his home trade; that of the foreign
+manufacturer as one of vigorous attack upon British and other
+open markets. In considering the position of English manufacturers
+as compared with their foreign rivals, some regard
+should be had to the patent laws. One condition of a grant
+of a patent in most foreign countries is that the patent shall
+be worked in those countries within a specified period. But a
+foreign inventor was until 1907 able to secure patent protection
+in Great Britain without any obligation to manufacture there.
+The effect of this was to encourage the manufacture of patented
+apparatus in foreign countries, and to stimulate their exportation
+to Great Britain in competition with British products. With
+regard to the electrochemical industry the progress which has
+been achieved by other nations, notably Germany, is very
+marvellous by comparison with the advance made by England,
+but to state the reasons why this industry has had such extraordinary
+development in Germany, notwithstanding that many
+of the fundamental inventions were made in England, would
+require a statement of the marked differences in the methods
+by which industrial progress is promoted in the two countries.</p>
+
+<p>There has been very little solidarity among those interested
+in the commercial development of electricity, and except for
+the discussion of scientific subjects there has been very little
+organization with the object of protecting and promoting common
+interests.</p>
+<div class="author">(E. Ga.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1i" id="ft1i" href="#fa1i"><span class="fn">1</span></a> British Patent Specification, No. 5306 of 1878, and No. 602 of
+1880.</p>
+
+<p><a name="ft2i" id="ft2i" href="#fa2i"><span class="fn">2</span></a> <i>Ibid.</i> No. 3988 of 1878.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRIC WAVES.<a name="ar65" id="ar65"></a></span> § 1. Clerk Maxwell proved that on his
+theory electromagnetic disturbances are propagated as a wave
+motion through the dielectric, while Lord Kelvin in 1853 (<i>Phil.
+Mag.</i> [4] 5, p. 393) proved from electromagnetic theory that the
+discharge of a condenser is oscillatory, a result which Feddersen
+(<i>Pogg. Ann.</i> 103, p. 69, &amp;c.) verified by a beautiful series of
+experiments. The oscillating discharge of a condenser had been
+inferred by Henry as long ago as 1842 from his experiments on
+the magnetization produced in needles by the discharge of a
+condenser. From these two results it follows that electric waves
+must be passing through the dielectric surrounding a condenser
+in the act of discharging, but it was not until 1887 that the
+existence of such waves was demonstrated by direct experiment.
+This great step was made by Hertz (<i>Wied. Ann.</i> 34, pp. 155,
+551, 609; <i>Ausbreitung der elektrischen Kraft</i>, Leipzig, 1892),
+whose experiments on this subject form one of the greatest
+contributions ever made to experimental physics. The difficulty
+which had stood in the way of the observations of these waves
+was the absence of any method of detecting electrical and
+magnetic forces, reversed some millions of times per second, and
+only lasting for an exceedingly short time. This was removed
+by Hertz, who showed that such forces would produce small
+sparks between pieces of metal very nearly in contact, and that
+these sparks were sufficiently regular to be used to detect electric
+waves and to investigate their properties. Other and more
+delicate methods have subsequently been discovered, but the
+results obtained by Hertz with his detector were of such signal
+importance, that we shall begin our account of experiments on
+these waves by a description of some of Hertz&rsquo;s more fundamental
+experiments.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:430px; height:136px" src="images/img203a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span></td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:399px; height:227px" src="images/img203b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p>To produce the waves Hertz used two forms of vibrator. The
+first is represented in fig. 1. A and B are two zinc plates about
+40 cm. square; to these brass rods, C, D, each about 30 cm. long,
+are soldered, terminating in brass balls E and F. To get good
+results it is necessary that these balls should be very brightly
+polished, and as they get roughened by the sparks which pass
+between them it is necessary to repolish them at short intervals;
+they should be shaded from light and from sparks, or other
+source of ultra-violet light. In order to excite the waves, C and
+D are connected to the two poles of an induction coil; sparks
+cross the air-gap which becomes a conductor, and the charges on
+the plates oscillate backwards and forwards like the charges on
+the coatings of a Leyden jar when it is short-circuited. The
+object of polishing the balls and screening off light is to get a
+sudden and sharp discharge; if the balls are rough there will
+be sharp points from which the charge will gradually leak, and
+the discharge will not be abrupt enough to start electrical
+vibrations, as these have an exceedingly short period. From
+the open form of this vibrator we should expect the radiation
+to be very large and the rate of decay of the amplitude very
+rapid. Bjerknes (<i>Wied. Ann.</i> 44, p. 74) found that the amplitude
+fell to 1/e of the original value, after a time 4T where T was the
+period of the electrical vibrations. Thus after a few vibrations
+the amplitude becomes inappreciable. To detect the waves
+produced by this vibrator Hertz used a piece of copper wire bent
+into a circle, the ends being furnished with two balls, or a ball
+and a point connected by a screw, so that the distance between
+them admitted of very fine adjustment. The radius of the
+circle for use with the vibrator just described was 35 cm., and
+was so chosen that the free period of the detector might be the
+same as that of the vibrator, and the effects in it increased by
+resonance. It is evident, however, that with a primary system
+as greatly damped as the vibrator used by Hertz, we could not
+expect very marked resonance effects, and as a matter of fact
+the accurate timing of vibrator and detector in this case is not
+very important. With electrical vibrators which can maintain
+a large number of vibrations, resonance effects are very striking,
+as is beautifully shown by the following experiment due to
+Lodge (<i>Nature</i>, 41, p. 368), whose researches have greatly
+advanced our knowledge of electric waves. A and C (fig. 2) are
+two Leyden jars, whose inner and outer coatings are connected
+by wires, B and D, bent so as to include a considerable area.
+There is an air-break in the circuit connecting the inside and
+outside of one of the jars, A, and electrical oscillations are started
+in A by joining the inside and outside with the terminals of a
+coil or electrical machine. The circuit in the jar C is provided
+<span class="pagenum"><a name="page204" id="page204"></a>204</span>
+with a sliding piece, F, by means of which the self-induction of
+the discharging circuit, and, therefore, the time of an electrical
+oscillation of the jar, can be adjusted. The inside and outside
+of this jar are put almost, but not quite, into electrical contact
+by means of a piece of tin-foil, E, bent over the lip of the jar.
+The jars are placed face to face so that the circuits B and D
+are parallel to each other, and approximately at right angles to
+the line joining their centres. When the electrical machine is
+in action sparks pass across the air-break in the circuit in A,
+and by moving the slider F it is possible to find one position for
+it in which sparks pass from the inside to the outside of C across
+the tin-foil, while when the slider is moved a short distance on
+either side of this position the sparks cease.</p>
+
+<p>Hertz found that when he held his detector in the neighbourhood
+of the vibrator minute sparks passed between the balls.
+These sparks were not stopped when a large plate of non-conducting
+substance, such as the wall of a room, was interposed between
+the vibrator and detector, but a large plate of very thin metal
+stopped them completely.</p>
+
+<p>To illustrate the analogy between electric waves and waves
+of light Hertz found another form of apparatus more convenient.
+The vibrator consisted of two equal brass cylinders, 12 cm. long
+and 3 cm. in diameter, placed with their axes coincident, and in
+the focal line of a large zinc parabolic mirror about 2 m. high,
+with a focal length of 12.5 cm. The ends of the cylinders nearest
+each other, between which the sparks passed, were carefully
+polished. The detector, which was placed in the focal line of
+an equal parabolic mirror, consisted of two lengths of wire,
+each having a straight piece about 50 cm. long and a curved
+piece about 15 cm. long bent round at right angles so as to pass
+through the back of the mirror. The ends which came through
+the mirror were connected with a spark micrometer, the sparks
+being observed from behind the mirror. The mirrors are shown,
+in fig. 3.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:445px; height:285px" src="images/img204a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span></td></tr></table>
+
+<p>§ 2. <i>Reflection and Refraction.</i>&mdash;To show the reflection of the
+waves Hertz placed the mirrors side by side, so that their openings
+looked in the same direction, and their axes converged at a point
+about 3 m. from the mirrors. No sparks were then observed
+in the detector when the vibrator was in action. When, however,
+a large zinc plate about 2 m. square was placed at right angles
+to the line bisecting the angle between the axes of the mirrors
+sparks became visible, but disappeared again when the metal
+plate was twisted through an angle of about 15° to either side.
+This experiment showed that electric waves are reflected, and
+that, approximately at any rate, the angle of incidence is equal
+to the angle of reflection. To show refraction Hertz used a large
+prism made of hard pitch, about 1.5 m. high, with a slant side
+of 1.2 m. and an angle of 30°. When the waves from the vibrator
+passed through this the sparks in the detector were not excited
+when the axes of the two mirrors were parallel, but appeared
+when the axis of the mirror containing the detector made a
+certain angle with the axis of that containing the vibrator. When
+the system was adjusted for minimum deviation the sparks were
+most vigorous when the angle between the axes of the mirrors
+was 22°. This corresponds to an index of refraction of 1.69.</p>
+
+<p>§ 3. <i>Analogy to a Plate of Tourmaline.</i>&mdash;If a screen be made
+by winding wire round a large rectangular framework, so that
+the turns of the wire are parallel to one pair of sides of the frame,
+and if this screen be interposed between the parabolic mirrors
+when placed so as to face each other, there will be no sparks in
+the detector when the turns of the wire are parallel to the focal
+lines of the mirror; but if the frame is turned through a right
+angle so that the wires are perpendicular to the focal lines of the
+mirror the sparks will recommence. If the framework is substituted
+for the metal plate in the experiment on the reflection
+of electric waves, sparks will appear in the detector when the
+wires are parallel to the focal lines of the mirrors, and will disappear
+when the wires are at right angles to these lines. Thus
+the framework reflects but does not transmit the waves when the
+electric force in them is parallel to the wires, while it transmits
+but does not reflect waves in which the electric force is at right
+angles to the wires. The wire framework behaves towards the
+electric waves exactly as a plate of tourmaline does to waves
+of light. Du Bois and Rubens (<i>Wied. Ann.</i> 49, p. 593), by using
+a framework wound with very fine wire placed very close together,
+have succeeded in polarizing waves of radiant heat, whose wave
+length, although longer than that of ordinary light, is very small
+compared with that of electric waves.</p>
+
+<p>§ 4. <i>Angle of Polarization.</i>&mdash;When light polarized at right
+angles to the plane of incidence falls on a refracting substance
+at an angle tan<span class="sp">&minus;1</span>&mu;, where &mu; is the refractive index of the substance,
+all the light is refracted and none reflected; whereas
+when light is polarized in the plane of incidence, some of the
+light is always reflected whatever the angle of incidence.
+Trouton (<i>Nature</i>, 39, p. 391) showed that similar effects take
+place with electric waves. From a paraffin wall 3 ft. thick,
+reflection always took place when the electric force in the incident
+wave was at right angles to the plane of incidence, whereas
+at a certain angle of incidence there was no reflection when
+the vibrator was turned, so that the electric force was in the
+plane of incidence. This shows that on the electromagnetic
+theory of light the electric force is at right angles to the plane of
+polarization.</p>
+
+<table class="flt" style="float: right; width: 200px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:170px; height:227px" src="images/img204b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 4.</span></td></tr></table>
+
+<p>§ 5. <i>Stationary Electrical Vibrations.</i>&mdash;Hertz (<i>Wied. Ann.</i>
+34, p. 609) made his experiments on these in a large room about
+15 m. long. The vibrator, which was of the type first described,
+was placed at one end of the room, its plates being parallel to
+the wall, at the other end a piece of sheet zinc about 4 m. by
+2 m. was placed vertically against the wall. The detector&mdash;the
+circular ring previously described&mdash;was held so that its plane
+was parallel to the metal plates of the vibrator, its centre on the
+line at right angles to the metal plate bisecting at right angles
+the spark gap of the vibrator, and with the spark gap of the
+detector parallel to that of the vibrator. The following effects
+were observed when the detector was moved about. When it
+was close up to the zinc plate there were no sparks, but they
+began to pass feebly as soon as it was moved forward a little
+way from the plate, and increased rapidly in brightness until it
+was about 1.8 m. from the plate, when they attained their
+maximum. When its distance was still further increased they
+diminished in brightness, and vanished again at a distance of
+about 4 m. from the plate. When the distance was still further
+increased they reappeared, attained another maximum, and so
+on. They thus exhibited a remarkable
+periodicity similar to that which occurs
+when stationary vibrations are produced
+by the interference of direct waves with
+those reflected from a surface placed at
+right angles to the direction of propagation.
+Similar periodic alterations in the
+spark were observed by Hertz when the
+waves, instead of passing freely through
+the air and being reflected by a metal
+plate at the end of the room, were led
+along wires, as in the arrangement shown
+in fig. 4. L and K are metal plates
+placed parallel to the plates of the vibrator, long parallel
+wires being attached to act as guides to the waves which
+were reflected from the isolated end. (Hertz used only one
+<span class="pagenum"><a name="page205" id="page205"></a>205</span>
+plate and one wire, but the double set of plates and wires
+introduced by Sarasin and De la Rive make the results more
+definite.) In this case the detector is best placed so that its
+plane is at right angles to the wires, while the air space is parallel
+to the plane containing the wires. The sparks instead of vanishing
+when the detector is at the far end of the wire are a maximum
+in this position, but wax and wane periodically as the detector is
+moved along the wires. The most obvious interpretation of
+these experiments was the one given by Hertz&mdash;that there was
+interference between the direct waves given out by the vibrator
+and those reflected either from the plate or from the ends of the
+wire, this interference giving rise to stationary waves. The
+places where the electric force was a maximum were the
+places where the sparks were brightest, and the places
+where the electric force was zero were the places where
+the sparks vanished. On this explanation the distance between
+two consecutive places where the sparks vanished
+would be half the wave length of the waves given out by the
+vibrator.</p>
+
+<p>Some very interesting experiments made by Sarasin and De
+la Rive (<i>Comptes rendus</i>, 115, p. 489) showed that this explanation
+could not be the true one, since by using detectors of different
+sizes they found that the distance between two consecutive places
+where the sparks vanished depended mainly upon the size of
+the detector, and very little upon that of the vibrator. With
+small detectors they found the distance small, with large detectors,
+large; in fact it is directly proportional to the diameter
+of the detector. We can see that this result is a consequence
+of the large damping of the oscillations of the vibrator and the
+very small damping of those of the detector. Bjerknes showed
+that the time taken for the amplitude of the vibrations of the
+vibrator to sink to 1/e of their original value was only 4T, while
+for the detector it was 500T&prime;, when T and T&prime; are respectively
+the times of vibration of the vibrator and the detector. The
+rapid decay of the oscillations of the vibrator will stifle the
+interference between the direct and the reflected wave, as the
+amplitude of the direct wave will, since it is emitted later, be
+much smaller than that of the reflected one, and not able to
+annul its effects completely; while the well-maintained vibrations
+of the detector will interfere and produce the effects observed
+by Sarasin and De la Rive. To see this let us consider the extreme
+case in which the oscillations of the vibrator are absolutely dead-beat.
+Here an impulse, starting from the vibrator on its way
+to the reflector, strikes against the detector and sets it in vibration;
+it then travels up to the plate and is reflected, the electric
+force in the impulse being reversed by reflection. After reflection
+the impulse again strikes the detector, which is still vibrating
+from the effects of the first impact; if the phase of this vibration
+is such that the reflected impulse tends to produce a current
+round the detector in the same direction as that which is circulating
+from the effects of the first impact, the sparks will be increased,
+but if the reflected impulse tends to produce a current in the
+opposite direction the sparks will be diminished. Since the
+electric force is reversed by reflection, the greatest increase in the
+sparks will take place when the impulse finds, on its return, the
+detector in the opposite phase to that in which it left it; that
+is, if the time which has elapsed between the departure and return
+of the impulse is equal to an odd multiple of half the time of
+vibration of the detector. If d is the distance of the detector
+from the reflector when the sparks are brightest, and V the
+velocity of propagation of electromagnetic disturbance, then
+2d/V = (2n + 1) (T&prime;/2); where n is an integer and T&prime; the time of
+vibration of the detector, the distance between two spark
+maxima will be VT&prime;/2, and the places where the sparks are a
+minimum will be midway between the maxima. Sarasin and
+De la Rive found that when the same detector was used the
+distance between two spark maxima was the same with the
+waves through air reflected from a metal plate and with those
+guided by wires and reflected from the free ends of the wire, the
+inference being that the velocity of waves along wires is the
+same as that through the air. This result, which follows from
+Maxwell&rsquo;s theory, when the wires are not too fine, had been
+questioned by Hertz on account of some of his experiments on
+wires.</p>
+
+<p>§ 6. <i>Detectors.</i>&mdash;The use of a detector with a period of vibration
+of its own thus tends to make the experiments more complicated,
+and many other forms of detector have been employed by
+subsequent experimenters. For example, in place of the sparks
+in air the luminous discharge through a rarefied gas has been
+used by Dragoumis, Lecher (who used tubes without electrodes
+laid across the wires in an arrangement resembling that shown
+in fig. 7) and Arons. A tube containing neon at a low pressure
+is especially suitable for this purpose. Zehnder (<i>Wied. Ann.</i>
+47, p. 777) used an exhausted tube to which an external electromotive
+force almost but not quite sufficient of itself to produce
+a discharge was applied; here the additional electromotive
+force due to the waves was sufficient to start the discharge.
+Detectors depending on the heat produced by the rapidly
+alternating currents have been used by Paalzow and Rubens,
+Rubens and Ritter, and I. Klemen&#269;i&#269;. Rubens measured the
+heat produced by a bolometer arrangement, and Klemen&#269;i&#269;
+used a thermo-electric method for the same purpose; in consequence
+of the great increase in the sensitiveness of galvanometers
+these methods are now very frequently resorted to. Boltzmann
+used an electroscope as a detector. The spark gap consisted
+of a ball and a point, the ball being connected with the electroscope
+and the point with a battery of 200 dry cells. When the
+spark passed the cells charged up the electroscope. Ritter
+utilized the contraction of a frog&rsquo;s leg as a detector, Lucas and
+Garrett the explosion produced by the sparks in an explosive
+mixture of hydrogen and oxygen; while Bjerknes and Franke
+used the mechanical attraction between oppositely charged
+conductors. If the two sides of the spark gap are connected with
+the two pairs of quadrants of a very delicate electrometer, the
+needle of which is connected with one pair of quadrants, there
+will be a deflection of the electrometer when the detector is
+struck by electric waves. A very efficient detector is that invented
+by E. Rutherford (<i>Trans. Roy. Soc.</i> A. 1897, 189, p. 1);
+it consists of a bundle of fine iron wires magnetized to saturation
+and placed inside a small magnetizing coil, through which the
+electric waves cause rapidly alternating currents to pass which
+demagnetize the soft iron. If the instrument is used to detect
+waves in air, long straight wires are attached to the ends of the
+demagnetizing coil to collect the energy from the field; to
+investigate waves in wires it is sufficient to make a loop or two
+in the wire and place the magnetized piece of iron inside it.
+The amount of demagnetization which can be observed by the
+change in the deflection of a magnetometer placed near the iron,
+measures the intensity of the electric waves, and very accurate
+determinations can be made with ease with this apparatus.
+It is also very delicate, though in this respect it does not equal
+the detector to be next described, the coherer; Rutherford got
+indications in 1895 when the vibrator was ¾ of a mile away from
+the detector, and where the waves had to traverse a thickly
+populated part of Cambridge. It can also be used to measure
+the coefficient of damping of the electric waves, for since the
+wire is initially magnetized to saturation, if the direction of the
+current when it first begins to flow in the magnetizing coil is
+such as to tend to increase the magnetization of the wire, it will
+produce no effect, and it will not be until the current is
+reversed that the wire will lose some of its magnetization.
+The effect then gives the measure of the intensity half a period
+after the commencement of the waves. If the wire is put in the
+coil the opposite way, <i>i.e.</i> so that the magnetic force due to the
+current begins at once to demagnetize the wire, the demagnetization
+gives a measure of the initial intensity of the waves. Comparing
+this result with that obtained when the wires were
+reversed, we get the coefficient of damping. A very convenient
+detector of electric waves is the one discovered almost simultaneously
+by Fessenden (<i>Electrotech. Zeits.</i>, 1903, 24, p. 586) and
+Schlömilch (<i>ibid.</i> p. 959). This consists of an electrolytic cell in
+which one of the electrodes is an exceedingly fine point. The
+electromotive force in the circuit is small, and there is large
+polarization in the circuit with only a small current. When the
+<span class="pagenum"><a name="page206" id="page206"></a>206</span>
+circuit is struck by electric waves there is an increase in the
+currents due to the depolarization of the circuit. If a galvanometer
+is in the circuit, the increased deflection of the instrument
+will indicate the presence of the waves.</p>
+
+<p>§ 7. <i>Coherers.</i>&mdash;The most sensitive detector of electric waves
+is the &ldquo;coherer,&rdquo; although for metrical work it is not so suitable
+as that just described. It depends upon the fact discovered by
+Branly (<i>Comptes rendus</i>, 111, p. 785; 112, p. 90) that the resistance
+between loose metallic contacts, such as a pile of iron turnings,
+diminishes when they are struck by an electric wave. One of
+the forms made by Lodge (<i>The Work of Hertz and some of his
+Successors</i>, 1894) on this principle consists simply of a glass tube
+containing iron turnings, in contact with which are wires led
+into opposite ends of the tube. The arrangement is placed in
+series with a galvanometer (one of the simplest kind will do)
+and a battery; when the iron turnings are struck by electric
+waves their resistance is diminished and the deflection of the
+galvanometer is increased. Thus the deflection of the galvanometer
+can be used to indicate the arrival of electric waves. The
+tube must be tapped between each experiment, and the deflection
+of the galvanometer brought back to about its original value.
+This detector is marvellously delicate, but not metrical, the
+change produced in the resistance depending upon so many
+things besides the intensity of the waves that the magnitude of
+the galvanometer deflection is to some extent a matter of chance.
+Instead of the iron turnings we may use two iron wires, one
+resting on the other; the resistance of this contact will be altered
+by the incidence of the waves. To get greater regularity Bose
+uses, instead of the iron turnings, spiral springs, which are pushed
+against each other by means of a screw until the most sensitive
+state is attained. The sensitiveness of the coherer depends on
+the electromotive force put in the galvanometer circuit. Very
+sensitive ones can be made by using springs of very fine silver
+wire coated electrolytically with nickel. Though the impact
+of electric waves generally produces a diminution of resistance
+with these loose contacts, yet there are exceptions to the rule.
+Thus Branly showed that with lead peroxide, PbO<span class="su">2</span>, there is an
+increase in resistance. Aschkinass proved the same to be true
+with copper sulphide, CuS; and Bose showed that with potassium
+there is an increase of resistance and great power of self-recovery
+of the original resistance after the waves have ceased. Several
+theories of this action have been proposed. Branly (<i>Lumière
+électrique</i>, 40, p. 511) thought that the small sparks which
+certainly pass between adjacent portions of metal clear away
+layers of oxide or some other kind of non-conducting film, and
+in this way improve the contact. It would seem that if this
+theory is true the films must be of a much more refined kind than
+layers of oxide or dirt, for the coherer effect has been observed
+with clean non-oxidizable metals. Lodge explains the effect by
+supposing that the heat produced by the sparks fuses adjacent
+portions of metal into contact and hence diminishes the resistance;
+it is from this view of the action that the name coherer
+is applied to the detector. Auerbeck thought that the effect was
+a mechanical one due to the electrostatic attractions between
+the various small pieces of metal. It is probable that some
+or all of these causes are at work in some cases, but the
+effects of potassium make us hesitate to accept any of them
+as the complete explanation. Blanc (<i>Ann. chim. phys.</i>, 1905,
+[8] 6, p. 5), as the result of a long series of experiments,
+came to the conclusion that coherence is due to pressure. He
+regarded the outer layers as different from the mass of the metal
+and having a much greater specific resistance. He supposed
+that when two pieces of metal are pressed together the molecules
+diffuse across the surface, modifying the surface layers and increasing
+their conductivity.</p>
+
+<div class="condensed">
+<p>§ 8. <i>Generators of Electric Waves.</i>&mdash;Bose (<i>Phil. Mag.</i> 43, p. 55)
+designed an instrument which generates electric waves with a length
+of not more than a centimetre or so, and therefore allows their
+properties to be demonstrated with apparatus of moderate dimensions.
+The waves are excited by sparking between two platinum
+beads carried by jointed electrodes; a platinum sphere is placed
+between the beads, and the distance between the beads and the
+sphere can be adjusted by bending the electrodes. The diameter of
+the sphere is 8 mm., and the wave length of the shortest electrical
+waves generated is said to be about 6 mm. The beads are connected
+with the terminals of a small induction coil, which, with the battery
+to work it and the sparking arrangement, are enclosed in a metal
+box, the radiation passing out through a metal tube opposite to
+the spark gap. The ordinary vibrating break of the coil is not used,
+a single spark made by making and breaking the circuit by means of
+a button outside the box being employed instead. The detector is
+one of the spiral spring coherers previously described; it is shielded
+from external disturbance by being enclosed in a metal box provided
+with a funnel-shaped opening to admit the radiation. The wires
+leading from the coherers to the galvanometer are also surrounded
+by metal tubes to protect them from stray radiation. The radiating
+apparatus and the receiver are mounted on stands sliding in an
+optical bench. If a parallel beam of radiation is required, a cylindrical
+lens of ebonite or sulphur is mounted in a tube fitting on to
+the radiator tube and stopped by a guide when the spark is at the
+principal focal line of the lens. For experiments requiring angular
+measurements a spectrometer circle is mounted on one of the sliding
+stands, the receiver being carried on a radial arm and pointing to the
+centre of the circle. The arrangement is represented in fig. 5.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:514px; height:191px" src="images/img206a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span></td></tr></table>
+
+<p>With this apparatus the laws of reflection, refraction and polarization
+can readily be verified, and also the double refraction of crystals,
+and of bodies possessing a fibrous or laminated structure such as
+jute or books. (The double refraction of electric waves seems first
+to have been observed by Righi, and other researches on this subject
+have been made by Garbasso and Mack.) Bose showed the rotation
+of the plane of polarization by means of pieces of twisted jute rope;
+if the pieces were arranged so that their twists were all in one direction
+and placed in the path of the radiation, they rotated the plane of
+polarization in a direction depending upon the direction of twist;
+if they were mixed so that there were as many twisted in one direction
+as the other, there was no rotation.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:456px; height:200px" src="images/img206b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span></td></tr></table>
+
+<p>A series of experiments showing the complete analogy between
+electric and light waves is described by Righi in his book <i>L&rsquo;Ottica
+delle oscillazioni elettriche</i>. Righi&rsquo;s exciter, which is especially
+convenient when large statical electric machines are used instead
+of induction coils, is shown in fig. 6. E and F are balls connected
+with the terminals of the machine, and AB and CD are conductors
+insulated from each other, the ends B, C, between which the sparks
+pass, being immersed in vaseline oil. The period of the vibrations
+given out by the system is adjusted by means of metal plates M and
+N attached to AB and CD. When the waves are produced by induction
+coils or by electrical machines the intervals between the
+emission of different sets of waves occupy by far the largest part
+of the time. Simon (<i>Wied. Ann.</i>, 1898, 64, p. 293; <i>Phys. Zeit.</i>,
+1901, 2, p. 253), Duddell (<i>Electrician</i>, 1900, 46, p. 269) and Poulsen
+(<i>Electrotech. Zeits.</i>, 1906, 27, p. 1070) reduced these intervals very
+considerably by using the electric arc to excite the waves, and in this
+way produced electrical waves possessing great energy. In these
+methods the terminals between which the arc is passing are connected
+through coils with self-induction L to the plates of a condenser of
+capacity C. The arc is not steady, but is continually varying. This
+is especially the case when it passes through hydrogen. These
+variations excite vibrations with a period 2&pi;&radic;(LC) in the circuit
+containing the capacity of the self-induction. By this method
+Duddell produced waves with a frequency of 40,000. Poulsen, who
+cooled the terminals of the arc, produced waves with a frequency of
+1,000,000, while Stechodro (<i>Ann. der Phys.</i> 27, p. 225) claims to
+have produced waves with three hundred times this frequency, <i>i.e.</i>
+having a wave length of about a metre. When the self-induction
+<span class="pagenum"><a name="page207" id="page207"></a>207</span>
+and capacity are large so that the frequency comes within the limits
+of the frequency of audible notes, the system gives out a musical
+note, and the arrangement is often referred to as the singing arc.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:432px; height:223px" src="images/img207a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 7.</span></td></tr></table>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:485px; height:330px" src="images/img207b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 8.</span></td></tr></table>
+
+<p>§ <i>9. Waves in Wires.</i>&mdash;Many problems on electric waves along
+wires can readily be investigated by a method due to Lecher (<i>Wied.
+Ann.</i> 41, p. 850), and known as Lecher&rsquo;s bridge, which furnishes us
+with a means of dealing with waves of a definite and determinable
+wave-length. In this arrangement (fig. 7) two large plates A and
+B are, as in Hertz&rsquo;s exciter, connected with the terminals of an
+induction coil; opposite these and insulated from them are two
+smaller plates D, E, to which long parallel wires DFH, EGJ are
+attached. These wires are bridged across by a wire LM, and their
+farther ends H, J, may be insulated, or connected together, or with
+the plates of a condenser. To detect the waves in the circuit beyond
+the bridge, Lecher used an exhausted tube placed across the wires,
+and Rubens a bolometer, but Rutherford&rsquo;s detector is the most
+convenient and accurate. If this detector is placed in a fixed position
+at the end of the circuit, it is found that the deflections of this detector
+depend greatly upon the position of the bridge LM, rising rapidly
+to a maximum for some positions, and falling rapidly away when the
+bridge is displaced. As the bridge is moved from the coil end towards
+the detector the deflections show periodic variations, such as are
+represented in fig. 8 when the ordinates represent the deflections of
+the detector and the abscissae the distance of the bridge from the
+ends D, E. The maximum deflections of the detector correspond to
+the positions in which the two circuits DFLMGE, HLMJ (in which
+the vibrations are but slightly damped) are in resonance. For since
+the self-induction and resistance of the bridge LM is very small
+compared with that of the circuit beyond, it follows from the theory
+of circuits in parallel that only a small part of the current will in
+general flow round the longer circuit; it is only when the two circuits
+DFLMGE, HLMJ are in resonance that a considerable current will
+flow round the latter. Hence when we get a maximum effect in
+the detector we know that the waves we are dealing with are those
+corresponding to the free periods of the system HLMJ, so that if
+we know the free periods of this circuit we know the wave length
+of the electric waves under consideration. Thus if the ends of
+the wires H, J are free and have no capacity, the current along them
+must vanish at H and J, which must be in opposite electric condition.
+Hence half the wave length must be an odd submultiple of the length
+of the circuit HLMJ. If H and J are connected together the wave
+length must be a submultiple of the length of this circuit. When the
+capacity at the ends is appreciable the wave length of the circuit is
+determined by a somewhat complex expression. To facilitate the
+determination of the wave length in such cases, Lecher introduced a
+second bridge L&prime;M&prime;, and moved this about until the deflection of the
+detector was a maximum; when this occurs the wave length is one
+of those corresponding to the closed circuit LMM&prime;L&prime;, and must therefore
+be a submultiple of the length of the circuit. Lecher showed
+that if instead of using a single wire LM to form the bridge, he used
+two parallel wires PQ, LM, placed close together, the currents in the
+further circuit were hardly appreciably diminished when the main
+wires were cut between PL and QM. Blondlot used a modification of
+this apparatus better suited for the production of short waves. In his
+form (fig. 9) the exciter consists of two semicircular arms connected
+with the terminals of an induction coil, and the long wires, instead
+of being connected with the small plates, form a circuit round the
+exciter.</p>
+
+<table class="flt" style="float: right; width: 350px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:309px; height:297px" src="images/img207c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 9.</span></td></tr></table>
+
+<p>As an example of the use of Lecher&rsquo;s arrangement, we may quote
+Drude&rsquo;s application of the method to find the specific induction
+capacity of dielectrics under electric oscillations of varying frequency.
+In this application the ends of the wire are connected to the plates
+of a condenser, the space between whose plates can be filled
+with the liquid whose specific inductive capacity is required, and
+the bridge is moved until
+the detector at the end of
+the circuit gives the maximum
+deflection. Then if
+&lambda; is the wave length of
+the waves, &lambda; is the wave
+length of one of the free
+vibrations of the system
+HLMJ; hence if C is the
+capacity of the condenser
+at the end in electrostatic
+measure we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">cot</td> <td>2&pi;l</td> <td>&nbsp;</td> <td>&nbsp;</td></tr>
+<tr><td class="denom">&lambda;</td> <td rowspan="2">=</td> <td>C</td></tr>
+<tr><td class="denom un" colspan="2">2&pi;l</td> <td class="denom">C&prime;l</td></tr>
+<tr><td colspan="2">&lambda;</td> <td>&nbsp;</td> <td>&nbsp;</td></tr></table>
+
+<p class="noind">where l is the distance of
+the condenser from the
+bridge and C&prime; is the capacity of unit length of the wire. In the
+condenser part of the lines of force will pass through air and part
+through the dielectric; hence C will be of the form C<span class="su">0</span> + KC<span class="su">1</span> where
+K is the specific inductive capacity of the dielectric. Hence if l is
+the distance of maximum deflection when the dielectric is replaced
+by air, <i>l&prime;</i> when filled with a dielectric whose specific inductive
+capacity is known to be K&prime;, and l&Prime; the distance when filled with
+the dielectric whose specific inductive capacity is required, we easily
+see that&mdash;</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">cot</td> <td>2&pi;l</td> <td rowspan="2">&minus; cot</td> <td>2&pi;l&prime;</td> <td>&nbsp;</td> <td>&nbsp;</td></tr>
+<tr><td class="denom">&lambda;</td> <td class="denom">&lambda;</td> <td rowspan="2">=</td> <td>1 &minus; K&prime;</td></tr>
+<tr><td class="denom" rowspan="2">cot</td> <td class="denom">2&pi;l</td> <td class="denom" rowspan="2">&minus; cot</td> <td class="denom">2&pi;l&Prime;</td> <td class="denom">1 &minus; K</td></tr>
+<tr><td class="denom">&lambda;</td> <td class="denom">&lambda;</td> <td>&nbsp;</td> <td>&nbsp;</td></tr></table>
+
+<p class="noind">an equation by means of which K can be determined. It was in
+this way that Drude investigated the specific inductive capacity
+with varying frequency, and found a falling off in the specific inductive
+capacity with increase of frequency when the dielectrics
+contained the radicle OH. In another method used by him the
+wires were led through long tanks filled with the liquid whose specific
+inductive capacity was required; the velocity of propagation of the
+electric waves along the wires in the tank being the same as the
+velocity of propagation of an electromagnetic disturbance through
+the liquid filling the tank, if we find the wave length of the waves
+along the wires in the tank, due to a vibration of a given frequency,
+and compare this with the wave lengths corresponding to the same
+frequency when the wires are surrounded by air, we obtain the
+velocity of propagation of electromagnetic disturbance through the
+fluid, and hence the specific inductive capacity of the fluid.</p>
+
+<table class="flt" style="float: right; width: 320px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:285px; height:515px" src="images/img208.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 10.</span></td></tr></table>
+
+<p>§ 10. <i>Velocity of Propagation of Electromagnetic Effects through Air.</i>&mdash;The
+experiments of Sarasin and De la Rive already described
+(see § 5) have shown that, as theory requires, the velocity of propagation
+of electric effects through air is the same as along wires.
+The same result had been arrived at by J.J. Thomson, although
+from the method he used greater differences between the velocities
+might have escaped detection than was possible by Sarasin and De
+la Rive&rsquo;s method. The velocity of waves along wires has been
+directly determined by Blondlot by two different methods. In the
+first the detector consisted of two parallel plates about 6 cm. in
+diameter placed a fraction of a millimetre apart, and forming a
+condenser whose capacity C was determined in electromagnetic
+measure by Maxwell&rsquo;s method. The plates were connected by a
+rectangular circuit whose self-induction L was calculated from the
+dimensions of the rectangle and the size of the wire. The time of
+vibration T is equal to 2&pi;&radic;(LC). (The wave length corresponding
+to this time is long compared with the length of the circuit, so that
+the use of this formula is legitimate.) This detector is placed
+between two parallel wires, and the waves produced by the exciter
+are reflected from a movable bridge. When this bridge is placed just
+beyond the detector vigorous sparks are observed, but as the bridge
+is pushed away a place is reached where the sparks disappear; this
+place is distance 2/&lambda; from the detector, when &lambda; is the wave length
+of the vibration given out by the detector. The sparks again disappear
+when the distance of the bridge from the detector is 3&lambda;/4.
+Thus by measuring the distance between two consecutive positions
+of the bridge at which the sparks disappear &lambda; can be determined,
+<span class="pagenum"><a name="page208" id="page208"></a>208</span>
+and v, the velocity of propagation, is equal to &lambda;/T. As the means
+of a number of experiments Blondlot found v to be 3.02 × 10<span class="sp">10</span>
+cm./sec., which, within the errors of experiment, is equal to 3 × 10<span class="sp">10</span>
+cm./sec., the velocity of light. A second method used by Blondlot,
+and one which does not involve
+the calculation of the
+period, is as follows:&mdash;A and
+A&prime; (fig. 10) are two equal
+Leyden jars coated inside
+and outside with tin-foil.
+The outer coatings form two
+separate rings a, a<span class="su">1</span>; a&prime;, a&prime;<span class="su">1</span>,
+and the inner coatings are
+connected with the poles of
+the induction coil by means
+of the metal pieces b, b&prime;. The
+sharply pointed conductors p
+and p&prime;, the points of which
+are about ½ mm. apart, are
+connected with the rings of
+the tin-foil a and a&prime;, and two
+long copper wires pca<span class="su">1</span>, p&prime;c&prime;a&prime;<span class="su">1</span>,
+1029 cm. long, connect these
+points with the other rings
+a<span class="su">1</span>, a<span class="su">1</span>&prime;. The rings aa&prime;, a<span class="su">1</span>a<span class="su">1</span>&prime;,
+are connected by wet strings
+so as to charge up the jars.
+When a spark passes between
+b and b&prime;, a spark at once
+passes between pp&prime;, and this
+is followed by another spark
+when the waves travelling by
+the paths a<span class="su">1</span>cp, a&prime;<span class="su">1</span>c&prime;p&prime; reach
+p and p&prime;. The time between
+the passage of these sparks,
+which is the time taken by
+the waves to travel 1029 cm.,
+was observed by means of
+a rotating mirror, and the
+velocity measured in 15 experiments varied between 2.92 × 10<span class="sp">10</span> and
+3.03 × 10<span class="sp">10</span> cm./sec., thus agreeing well with that deduced by the
+preceding method. Other determinations of the velocity of electromagnetic
+propagation have been made by Lodge and Glazebrook,
+and by Saunders.</p>
+
+<p>On Maxwell&rsquo;s electromagnetic theory the velocity of propagation
+of electromagnetic disturbances should equal the velocity of light,
+and also the ratio of the electromagnetic unit of electricity to the
+electrostatic unit. A large number of determinations of this ratio
+have been made:&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc">Observer.</td> <td class="tcc">Date.</td> <td class="tcc">Ratio 10<span class="sp">10</span> ×.</td></tr>
+<tr><td class="tcl">Klemen&#269;i&#269;</td> <td class="tcc">1884</td> <td class="tcl">3.019 cm./sec.</td></tr>
+<tr><td class="tcl">Himstedt</td> <td class="tcc">1888</td> <td class="tcl">3.009 cm./sec.</td></tr>
+<tr><td class="tcl">Rowland</td> <td class="tcc">1889</td> <td class="tcl">2.9815 cm./sec.</td></tr>
+<tr><td class="tcl">Rosa</td> <td class="tcc">1889</td> <td class="tcl">2.9993 cm./sec.</td></tr>
+<tr><td class="tcl">J.J. Thomson and Searle</td> <td class="tcc">1890</td> <td class="tcl">2.9955 cm./sec.</td></tr>
+<tr><td class="tcl">Webster</td> <td class="tcc">1891</td> <td class="tcl">2.987 cm./sec.</td></tr>
+<tr><td class="tcl">Pellat</td> <td class="tcc">1891</td> <td class="tcl">3.009 cm./sec.</td></tr>
+<tr><td class="tcl">Abraham</td> <td class="tcc">1892</td> <td class="tcl">2.992 cm./sec.</td></tr>
+<tr><td class="tcl">Hurmuzescu</td> <td class="tcc">1895</td> <td class="tcl">3.002 cm./sec.</td></tr>
+<tr><td class="tcl">Rosa</td> <td class="tcc">1908</td> <td class="tcl">2.9963 cm./sec.</td></tr>
+</table>
+
+<p>The mean of these determinations is 3.001 × 10<span class="sp">10</span> cm./sec., while
+the mean of the last five determinations of the velocity of light in
+air is given by Himstedt as 3.002 × 10<span class="sp">10</span> cm./sec. From these experiments
+we conclude that the velocity of propagation of an electromagnetic
+disturbance is equal to the velocity of light, and to the
+velocity required by Maxwell&rsquo;s theory.</p>
+
+<p>In experimenting with electromagnetic waves it is in general
+more difficult to measure the period of the oscillations than their
+wave length. Rutherford used a method by which the period of
+the vibration can easily be determined; it is based upon the theory
+of the distribution of alternating currents in two circuits ACB, ADB
+in parallel. If A and B are respectively the maximum currents in
+the circuits ACB, ADB, then</p>
+
+<table class="math0" summary="math">
+<tr><td>A</td>
+<td rowspan="2">= <span style="font-size: 2em;">&radic;</span></td> <td class="ov">S² + (N &minus; M)²p²</td></tr>
+<tr><td class="denom">B</td> <td class="denom">R² + (L &minus; M)²p²</td></tr></table>
+
+<p class="noind">when R and S are the resistances, L and N the coefficients of self-induction
+of the circuits ACB, ADB respectively, M the coefficient
+of mutual induction between the circuits, and p the frequency of the
+currents. Rutherford detectors were placed in the two circuits, and
+the circuits adjusted until they showed that A = B; when this is
+the case</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">p² =</td> <td>R² &minus; S²</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">N² &minus; L² &minus; 2M (N &minus; L)</td></tr></table>
+
+<p class="noind">If we make one of the circuits, ADB, consist of a short length
+of a high liquid resistance, so that S is large and N small, and
+the other circuit ACB of a low metallic resistance bent to have
+considerable self-induction, the preceding equation becomes approximately
+p = S/L, so that when S and L are known p is readily
+determined.</p>
+</div>
+<div class="author">(J. J. T.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROCHEMISTRY.<a name="ar66" id="ar66"></a></span> The present article deals with
+processes that involve the electrolysis of aqueous solutions,
+whilst those in which electricity is used in the manufacture of
+chemical products at furnace temperatures are treated under
+<span class="sc"><a href="#ar72">Electrometallurgy</a></span>, although, strictly speaking, in some
+cases (<i>e.g.</i> calcium carbide and phosphorus manufacture) they
+are not truly metallurgical in character. For the theory and
+elemental laws of electro-deposition see <span class="sc"><a href="#ar70">Electrolysis</a></span>; and
+for the construction and use of electric generators see <span class="sc"><a href="#artlinks">Dynamo</a></span>
+and <span class="sc"><a href="#artlinks">Battery</a></span>: <i>Electric</i>. The importance of the subject may
+be gauged by the fact that all the aluminium, magnesium,
+sodium, potassium, calcium carbide, carborundum and artificial
+graphite, now placed on the market, is made by electrical processes,
+and that the use of such processes for the refining of copper
+and silver, and in the manufacture of phosphorus, potassium
+chlorate and bleach, already pressing very heavily on the older
+non-electrical systems, is every year extending. The convenience
+also with which the energy of waterfalls can be converted into
+electric energy has led to the introduction of chemical industries
+into countries and districts where, owing to the absence of coal,
+they were previously unknown. Norway and Switzerland have
+become important producers of chemicals, and pastoral districts
+such as those in which Niagara or Foyers are situated manufacturing
+centres. In this way the development of the electrochemical
+industry is in a marked degree altering the distribution
+of trade throughout the world.</p>
+
+<p><i>Electrolytic Refining of Metals.</i>&mdash;The principle usually followed
+in the electrolytic refining of metals is to cast the impure metal
+into plates, which are exposed as anodes in a suitable solvent,
+commonly a salt of the metal under treatment. On passing a
+current of electricity, of which the volume and pressure are
+adjusted to the conditions of the electrolyte and electrodes,
+the anode slowly dissolves, leaving the insoluble impurities in
+the form of a sponge, if the proportion be considerable, but
+otherwise as a mud or slime which becomes detached from the
+anode surface and must be prevented from coming into contact
+with the cathode. The metal to be refined passing into solution
+is concurrently deposited at the cathode. Soluble impurities
+which are more electro-negative than the metal under treatment
+must, if present, be removed by a preliminary process, and the
+voltage and other conditions must be so selected that none of
+the more electro-positive metals are co-deposited with the metal
+to be refined. From these and other considerations it is obvious
+that (1) the electrolyte must be such as will freely dissolve the
+metal to be refined; (2) the electrolyte must be able to dissolve
+the major portion of the anode, otherwise the mass of insoluble
+matter on the outer layer will prevent access of electrolyte to
+the core, which will thus escape refining; (3) the electrolyte
+should, if possible, be incapable of dissolving metals more
+electro-negative than that to be refined; (4) the proportion of
+soluble electro-positive impurities must not be excessive, or these
+substances will accumulate too rapidly in the solution and
+necessitate its frequent purification; (5) the current density
+must be so adjusted to the strength of the solution and to other
+conditions that no relatively electro-positive metal is deposited,
+and that the cathode deposit is physically suitable for subsequent
+treatment; (6) the current density should be as high as
+is consistent with the production of a pure and sound deposit,
+without undue expense of voltage, so that the operation may be
+rapid and the &ldquo;turnover&rdquo; large; (7) the electrolyte should
+be as good a conductor of electricity as possible, and should not,
+ordinarily, be altered chemically by exposure to air; and (8) the
+use of porous partitions should be avoided, as they increase the
+resistance and usually require frequent renewal. For details
+of the practical methods see <span class="sc"><a href="#artlinks">Gold</a></span>; <span class="sc"><a href="#artlinks">Silver</a></span>; <span class="sc"><a href="#artlinks">Copper</a></span> and headings
+for other metals.</p>
+
+<p><i>Electrolytic Manufacture of Chemical Products.</i>&mdash;When an
+aqueous solution of the salt of an alkali metal is electrolysed, the
+<span class="pagenum"><a name="page209" id="page209"></a>209</span>
+metal reacts with the water, as is well known, forming caustic
+alkali, which dissolves in the solution, and hydrogen, which comes
+off as a gas. So early as 1851 a patent was taken out by Cooke
+for the production of caustic alkali without the use of a separate
+current, by immersing iron and copper plates on opposite sides
+of a porous (biscuit-ware) partition in a suitable cell, containing
+a solution of the salt to be electrolysed, at 21°-65° C. (70°-150° F.).
+The solution of the iron anode was intended to afford the
+necessary energy. In the same year another patent was granted
+to C. Watt for a similar process, involving the employment of an
+externally generated current. When an alkaline chloride, say
+sodium chloride, is electrolysed with one electrode immersed
+in a porous cell, while caustic soda is formed at the cathode,
+chlorine is deposited at the anode. If the latter be insoluble,
+the gas diffuses into the solution and, when this becomes
+saturated, escapes into the air. If, however, no porous division
+be used to prevent the intermingling by diffusion of the anode
+and cathode solutions, a complicated set of subsidiary reactions
+takes place. The chlorine reacts with the caustic soda, forming
+sodium hypochlorite, and this in turn, with an excess of chlorine
+and at higher temperatures, becomes for the most part converted
+into chlorate, whilst any simultaneous electrolysis of a hydroxide
+or water and a chloride (so that hydroxyl and chlorine are simultaneously
+liberated at the anode) also produces oxygen-chlorine
+compounds direct. At the same time, the diffusion of these
+compounds into contact with the cathode leads to a partial
+reduction to chloride, by the removal of combined oxygen by the
+instrumentality of the hydrogen there evolved. In proportion as
+the original chloride is thus reproduced, the efficiency of the
+process is of course diminished. It is obvious that, with suitable
+methods and apparatus, the electrolysis of alkaline chlorides
+may be made to yield chlorine, hypochlorites (bleaching liquors),
+chlorates or caustic alkali, but that great care must be exercised
+if any of these products is to be obtained pure and with economy.
+Many patents have been taken out in this branch of electrochemistry,
+but it is to be remarked that that granted to C. Watt
+traversed the whole of the ground. In his process a current
+was passed through a tank divided into two or three cells by
+porous partitions, hoods and tubes were arranged to carry off
+chlorine and hydrogen respectively, and the whole was heated
+to 120° F. by a steam jacket when caustic alkali was being made.
+Hypochlorites were made, at ordinary temperatures, and
+chlorates at higher temperatures, in a cell without a partition in
+which the cathode was placed horizontally immediately above the
+anode, to favour the mixing of the ascending chlorine with the
+descending caustic solution.</p>
+
+<div class="condensed">
+<p>The relation between the composition of the electrolyte and the
+various conditions of current-density, temperature and the like
+has been studied by F. Oettel (<i>Zeitschrift f. Elektrochem.</i>, 1894, vol. i.
+pp. 354 and 474) in connexion with the production of hypochlorites
+and chlorates in tanks without diaphragms, by C. Häussermann and
+W. Naschold (<i>Chemiker Zeitung</i>, 1894, vol. xviii. p. 857) for their
+production in cells with porous diaphragms, and by F. Haber and
+S. Grinberg (<i>Zeitschrift f. anorgan. Chem.</i>, 1898, vol. xvi. pp. 198, 329,
+438) in connexion with the electrolysis of hydrochloric acid. Oettel,
+using a 20% solution of potassium chloride, obtained the best
+yield of hypochlorite with a high current-density, but as soon
+as 1¼% of bleaching chlorine (as hypochlorite) was present, the
+formation of chlorate commenced. The yield was at best very
+low as compared with that theoretically possible. The best yield
+of chlorate was obtained when from 1 to 4% of caustic potash
+was present. With high current-density, heating the solution tended
+to increase the proportion of chlorate to hypochlorite, but as the
+proportion of water decomposed is then higher, the amount of
+chlorine produced must be less and the total chlorine efficiency
+lower. He also traced a connexion between alkalinity, temperature
+and current-density, and showed that these conditions should be
+mutually adjusted. With a current-density of 130 to 140 amperes
+per sq. ft., at 3 volts, passing between platinum electrodes, he
+attained to a current-efficiency of 52%, and each (British) electrical
+horse-power hour was equivalent to a production of 1378.5 grains of
+potassium chlorate. In other words, each pound of chlorate would
+require an expenditure of nearly 5.1 e.h.p. hours. One of the
+earliest of the more modern processes was that of E. Hermite,
+which consisted in the production of bleach-liquors by the electrolysis
+(according to the 1st edition of the 1884 patent) of magnesium
+or calcium chloride between platinum anodes carried in wooden
+frames, and zinc cathodes. The solution, containing hypochlorites
+and chlorates, was then applied to the bleaching of linen, paper-pulp
+or the like, the solution being used over and over again. Many
+modifications have been patented by Hermite, that of 1895 specifying
+the use of platinum gauze anodes, held in ebonite or other
+frames. Rotating zinc cathodes were used, with scrapers to prevent
+the accumulation of a layer of insoluble magnesium compounds,
+which would otherwise increase the electrical resistance beyond
+reasonable limits. The same inventor has patented the application
+of electrolysed chlorides to the purification of starch by the oxidation
+of less stable organic bodies, to the bleaching of oils, and to the
+purification of coal gas, spirit and other substances. His system for
+the disinfection of sewage and similar matter by the electrolysis of
+chlorides, or of sea-water, has been tried, but for the most part abandoned
+on the score of expense. Reference may be made to papers
+written in the early days of the process by C.F. Cross and E.J. Bevan
+(<i>Journ. Soc. Chem. Industry</i>, 1887, vol. vi. p. 170, and 1888, vol. vii.
+p. 292), and to later papers by P. Schoop (<i>Zeitschrift f. Elektrochem.</i>,
+1895, vol. ii. pp. 68, 88, 107, 209, 289).</p>
+
+<p>E. Kellner, who in 1886 patented the use of cathode (caustic soda)
+and anode (chlorine) liquors in the manufacture of cellulose from
+wood-fibre, and has since evolved many similar processes, has produced
+an apparatus that has been largely used. It consists of a
+stoneware tank with a thin sheet of platinum-iridium alloy at
+either end forming the primary electrodes, and between them a
+number of glass plates reaching nearly to the bottom, each having
+a platinum gauze sheet on either side; the two sheets belonging to
+each plate are in metallic connexion, but insulated from all the
+others, and form intermediary or bi-polar electrodes. A 10-12%
+solution of sodium chloride is caused to flow upwards through the
+apparatus and to overflow into troughs, by which it is conveyed
+(if necessary through a cooling apparatus) back to the circulating
+pump. Such a plant has been reported as giving 0.229 gallon of a
+liquor containing 1% of available chlorine per kilowatt hour, or
+0.171 gallon per e.h.p. hour. Kellner has also patented a &ldquo;bleaching-block,&rdquo;
+as he terms it, consisting of a frame carrying parallel
+plates similar in principle to those last described. The block is
+immersed in the solution to be bleached, and may be lifted in or out
+as required. O. Knöfler and Gebauer have also a system of bi-polar
+electrodes, mounted in a frame in appearance resembling a filter-press.</p>
+</div>
+
+<p><i>Other Electrochemical Processes.</i>&mdash;It is obvious that electrolytic
+iodine and bromine, and oxygen compounds of these elements,
+may be produced by methods similar to those applied to chlorides
+(see <span class="sc"><a href="#artlinks">Alkali Manufacture</a></span> and <span class="sc"><a href="#artlinks">Chlorates</a></span>), and Kellner and
+others have patented processes with this end in view. <i>Hydrogen</i>
+and <i>oxygen</i> may also be produced electrolytically as gases, and
+their respective reducing and oxidizing powers at the moment
+of deposition on the electrode are frequently used in the
+laboratory, and to some extent industrially, chiefly in the field
+of organic chemistry. Similarly, the formation of organic
+halogen products may be effected by electrolytic chlorine, as,
+for example, in the production of <i>chloral</i> by the gradual introduction
+of alcohol into an anode cell in which the electrolyte is a
+strong solution of potassium chloride. Again, anode reactions,
+such as are observed in the electrolysis of the fatty acids, may be
+utilized, as, for example, when the radical CH<span class="su">3</span>CO<span class="su">2</span>&mdash;deposited
+at the anode in the electrolysis of acetic acid&mdash;is dissociated,
+two of the groups react to give one molecule of <i>ethane</i>, C<span class="su">2</span>H<span class="su">6</span>, and
+two of carbon dioxide. This, which has long been recognized
+as a class-reaction, is obviously capable of endless variation.
+Many electrolytic methods have been proposed for the purification
+of <i>sugar</i>; in some of them soluble anodes are used for a few
+minutes in weak alkaline solutions, so that the caustic alkali
+from the cathode reaction may precipitate chemically the
+hydroxide of the anode metal dissolved in the liquid, the precipitate
+carrying with it mechanically some of the impurities
+present, and thus clarifying the solution. In others the current
+is applied for a longer time to the original sugar-solution with
+insoluble (<i>e.g.</i> carbon) anodes. F. Peters has found that with
+these methods the best results are obtained when ozone is employed
+in addition to electrolytic oxygen. Use has been made
+of electrolysis in <i>tanning</i> operations, the current being passed
+through the tan-liquors containing the hides. The current,
+by endosmosis, favours the passage of the solution into the
+hide-substance, and at the same time appears to assist the chemical
+combinations there occurring; hence a great reduction in
+the time required for the completion of the process. Many
+patents have been taken out in this direction, one of the best
+known being that of Groth, experimented upon by S. Rideal
+and A.P. Trotter (<i>Journ. Soc. Chem. Indust.</i>, 1891, vol. x. p. 425),
+<span class="pagenum"><a name="page210" id="page210"></a>210</span>
+who employed copper anodes, 4 sq. ft. in area, with current-densities
+of 0.375 to 1 (ranging in some cases to 7.5) ampere per
+sq. ft., the best results being obtained with the smaller current-densities.
+Electrochemical processes are often indirectly used,
+as for example in the Villon process (<i>Elec. Rev.</i>, New York,
+1899, vol. xxxv. p. 375) applied in Russia to the manufacture of
+alcohol, by a series of chemical reactions starting from the production
+of acetylene by the action of water upon calcium carbide.
+The production of <i>ozone</i> in small quantities during electrolysis,
+and by the so-called silent discharge, has long been known, and
+the Siemens induction tube has been developed for use industrially.
+The Siemens and Halske ozonizer, in form somewhat
+resembling the old laboratory instrument, is largely used in
+Germany; working with an alternating current transformed
+up to 6500 volts, it has been found to give 280 grains or more
+of ozone per e.h.p. hour. E. Andreoli (whose first British
+ozone patent was No. 17,426 of 1891) uses flat aluminium plates
+and points, and working with an alternating current of 3000
+volts is said to have obtained 1440 grains per e.h.p. hour.
+Yarnold&rsquo;s process, using corrugated glass plates coated on one
+side with gold or other metal leaf, is stated to have yielded as
+much as 2700 grains per e.h.p. hour. The ozone so prepared
+has numerous uses, as, for example, in bleaching oils, waxes,
+fabrics, &amp;c., sterilizing drinking-water, maturing wines, cleansing
+foul beer-casks, oxidizing oil, and in the manufacture of vanillin.</p>
+
+<div class="condensed">
+<p>For further information the following books, among others, may
+be consulted:&mdash;Haber, <i>Grundriss der technischen Elektrochemie</i>
+(München, 1898); Borchers and M&rsquo;Millan, <i>Electric Smelting and
+Refining</i> (London, 1904); E.D. Peters, <i>Principles of Copper Smelting</i>
+(New York, 1907); F. Peters, <i>Angewandte Elektrochemie</i>, vols. ii.
+and iii. (Leipzig, 1900); Gore, <i>The Art of Electrolytic Separation of
+Metals</i> (London, 1890); Blount, <i>Practical Electro-Chemistry</i> (London,
+1906); G. Langbein, <i>Vollständiges Handbuch der galvanischen
+Metall-Niederschläge</i> (Leipzig, 1903), Eng. trans. by W.T. Brannt
+(1909); A. Watt, <i>Electro-Plating and Electro-Refining of Metals</i>
+(London, 1902); W.H. Wahl, <i>Practical Guide to the Gold and Silver
+Electroplater, &amp;c.</i> (Philadelphia, 1883); Wilson, <i>Stereotyping and
+Electrotyping</i> (London); Lunge, <i>Sulphuric Acid and Alkali</i>, vol. iii.
+(London, 1909). Also papers in various technical periodicals.
+The industrial aspect is treated in a Gartside Report, <i>Some Electro-Chemical
+Centres</i> (Manchester, 1908), by J.N. Pring.</p>
+</div>
+<div class="author">(W. G. M.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROCUTION<a name="ar67" id="ar67"></a></span> (an anomalous derivative from &ldquo;electro-execution&rdquo;;
+syn. &ldquo;electrothanasia&rdquo;), the popular name, invented
+in America, for the infliction of the death penalty on
+criminals (see <span class="sc"><a href="#artlinks">Capital Punishment</a></span>) by passing through the body
+of the condemned a sufficient current of electricity to cause
+death. The method was first adopted by the state of New York,
+a law making this method obligatory having been passed and
+approved by the governor on the 4th of June 1888. The law
+provides that there shall be present, in addition to the warden,
+two physicians, twelve reputable citizens of full age, seven deputy
+sheriffs, and such ministers, priests or clergymen, not exceeding
+two, as the criminal may request. A post-mortem examination
+of the body of the convict is required, and the body, unless
+claimed by relatives, is interred in the prison cemetery with a
+sufficient quantity of quicklime to consume it. The law became
+effective in New York on the 1st of January 1889. The first
+criminal to be executed by electricity was William Kemmler,
+on the 6th of August 1890, at Auburn prison. The validity of
+the New York law had previously been attacked in regard to
+this case (<i>Re Kemmler</i>, 1889; 136 U.S. 436), as providing &ldquo;a
+cruel and unusual punishment&rdquo; and therefore being contrary
+to the Constitution; but it was sustained in the state courts and
+finally in the Federal courts. By 1906 about one hundred and
+fifteen murderers had been successfully executed by electricity in
+New York state in Sing Sing, Auburn and Dannemora prisons.
+The method has also been adopted by the states of Ohio
+(1896), Massachusetts (1898), New Jersey (1906), Virginia
+(1908) and North Carolina (1910).</p>
+
+<p>The apparatus consists of a stationary engine, an alternating
+dynamo capable of generating a current at a pressure of 2000
+volts, a &ldquo;death-chair&rdquo; with adjustable head-rest, binding
+straps and adjustable electrodes devised by E.F. Davis, the
+state electrician of New York. The voltmeter, ammeter and
+switch-board controlling the current are located in the execution-room;
+the dynamo-room is communicated with by electric
+signals. Before each execution the entire apparatus is thoroughly
+tested. When everything is in readiness the criminal is brought
+in and seats himself in the death-chair. His head, chest, arms
+and legs are secured by broad straps; one electrode thoroughly
+moistened with salt-solution is affixed to the head, and another to
+the calf of one leg, both electrodes being moulded so as to secure
+good contact. The application of the current is usually as
+follows: the contact is made with a high voltage (1700-1800
+volts) for 5 to 7 seconds, reduced to 200 volts until a half-minute
+has elapsed; raised to high voltage for 3 to 5 seconds, again reduced
+to low voltage for 3 to 5 seconds, again reduced to a low
+voltage until one minute has elapsed, when it is again raised to
+the high voltage for a few seconds and the contact broken. The
+ammeter usually shows that from 7 to 10 amperes pass through
+the criminal&rsquo;s body. A second or even a third brief contact is
+sometimes made, partly as a precautionary measure, but rather
+the more completely to abolish reflexes in the dead body. Calculations
+have shown that by this method of execution from 7 to
+10 h. p. of energy are liberated in the criminal&rsquo;s body. The
+time consumed by the strapping-in process is usually about 45
+seconds, and the first contact is made about 70 seconds after the
+criminal has entered the death-chamber.</p>
+
+<p>When properly performed the effect is painless and instantaneous
+death. The mechanism of life, circulation and respiration
+cease with the first contact. Consciousness is blotted out
+instantly, and the prolonged application of the current ensures
+permanent derangement of the vital functions beyond recovery.
+Occasionally the drying of the sponges through undue generation
+of heat causes desquamation or superficial blistering of the skin
+at the site of the electrodes. Post-mortem discoloration, or
+post-mortem lividity, often appears during the first contact.
+The pupils of the eyes dilate instantly and remain dilated after
+death.</p>
+
+<p>The post-mortem examination of &ldquo;electrocuted&rdquo; criminals
+reveals a number of interesting phenomena. The temperature
+of the body rises promptly after death to a very high point.
+At the site of the leg electrode a temperature of over 128° F. was
+registered within fifteen minutes in many cases. After the removal
+of the brain the temperature recorded in the spinal canal was
+often over 120° F. The development of this high temperature is
+to be regarded as resulting from the active metabolism of tissues
+not (somatically) dead within a body where all vital mechanisms
+have been abolished, there being no circulation to carry off the
+generated heat. The heart, at first flaccid when exposed soon
+after death, gradually contracts and assumes a tetanized condition;
+it empties itself of all blood and takes the form of a heart
+in systole. The lungs are usually devoid of blood and weigh
+only 7 or 8 ounces (avoird.) each. The blood is profoundly
+altered biochemically; it is of a very dark colour and it rarely
+coagulates.</p>
+<div class="author">(E. A. S.*)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROKINETICS,<a name="ar68" id="ar68"></a></span> that part of electrical science which is
+concerned with the properties of electric currents.</p>
+
+<p><i>Classification of Electric Currents.</i>&mdash;Electric currents are
+classified into (<i>a</i>) conduction currents, (<i>b</i>) convection currents,
+(<i>c</i>) displacement or dielectric currents. In the case of conduction
+currents electricity flows or moves through a stationary
+material body called the conductor. In convection currents
+electricity is carried from place to place with and on moving
+material bodies or particles. In dielectric currents there is no
+continued movement of electricity, but merely a limited displacement
+through or in the mass of an insulator or dielectric. The
+path in which an electric current exists is called an electric
+circuit, and may consist wholly of a conducting body, or partly
+of a conductor and insulator or dielectric, or wholly of a dielectric.
+In cases in which the three classes of currents are present together
+the true current is the sum of each separately. In the case of
+conduction currents the circuit consists of a conductor immersed
+in a non-conductor, and may take the form of a thin wire or
+cylinder, a sheet, surface or solid. Electric conduction currents
+may take place in space of one, two or three dimensions, but for
+<span class="pagenum"><a name="page211" id="page211"></a>211</span>
+the most part the circuits we have to consider consist of thin
+cylindrical wires or tubes of conducting material surrounded
+with an insulator; hence the case which generally presents itself
+is that of electric flow in space of one dimension. Self-closed
+electric currents taking place in a sheet of conductor are called
+&ldquo;eddy currents.&rdquo;</p>
+
+<p>Although in ordinary language the current is said to flow in
+the conductor, yet according to modern views the real pathway
+of the energy transmitted is the surrounding dielectric, and the
+so-called conductor or wire merely guides the transmission of
+energy in a certain direction. The presence of an electric
+current is recognized by three qualities or powers: (1) by the
+production of a magnetic field, (2) in the case of conduction
+currents, by the production of heat in the conductor, and (3) if
+the conductor is an electrolyte and the current unidirectional,
+by the occurrence of chemical decomposition in it. An electric
+current may also be regarded as the result of a movement of
+electricity across each section of the circuit, and is then measured
+by the quantity conveyed per unit of time. Hence if dq is the
+quantity of electricity which flows across any section of the
+conductor in the element of time dt, the current i = dq/dt.</p>
+
+<p>Electric currents may be also classified as constant or variable
+and as unidirectional or &ldquo;direct,&rdquo; that is flowing always in the
+same direction, or &ldquo;alternating,&rdquo; that is reversing their direction
+at regular intervals. In the last case the variation of current
+may follow any particular law. It is called a &ldquo;periodic current&rdquo;
+if the cycle of current values is repeated during a certain time
+called the periodic time, during which the current reaches a
+certain maximum value, first in one direction and then in the
+opposite, and in the intervals between has a zero value at certain
+instants. The frequency of the periodic current is the number
+of periods or cycles in one second, and alternating currents are
+described as low frequency or high frequency, in the latter case
+having some thousands of periods per second. A periodic current
+may be represented either by a wave diagram, or by a polar
+diagram.<a name="fa1j" id="fa1j" href="#ft1j"><span class="sp">1</span></a> In the first case we take a straight line to represent
+the uniform flow of time, and at small equidistant intervals
+set up perpendiculars above or below the time axis, representing
+to scale the current at that instant in one direction or the other;
+the extremities of these ordinates then define a wavy curve
+which is called the wave form of the current (fig. 1). It is obvious
+that this curve can only be a single valued curve. In one particular
+and important case the form of the current curve is a
+simple harmonic curve or simple sine curve. If T represents
+the periodic time in which the cycle of current values takes
+place, whilst n is the frequency or number of periods per second
+and p stands for 2&pi;n, and i is the value of the current at any
+instant t, and I its maximum value, then in this case we have
+i = I sin pt. Such a current is called a &ldquo;sine current&rdquo; or simple
+periodic current.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:406px; height:160px" src="images/img211.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span></td>
+<td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p>In a polar diagram (fig. 2) a number of radial lines are drawn
+from a point at small equiangular intervals, and on these lines
+are set off lengths proportional to the current value of a periodic
+current at corresponding intervals during one complete period
+represented by four right angles. The extremities of these
+radii delineate a polar curve. The polar form of a simple sine
+current is obviously a circle drawn through the origin. As a
+consequence of Fourier&rsquo;s theorem it follows that any periodic
+curve having any wave form can be imitated by the superposition
+of simple sine currents differing in maximum value and
+in phase.</p>
+
+<p><i>Definitions of Unit Electric Current.</i>&mdash;In electrokinetic investigations
+we are most commonly limited to the cases of unidirectional
+continuous and constant currents (C.C. or D.C.), or of simple
+periodic currents, or alternating currents of sine form (A.C.).
+A continuous electric current is measured either by the magnetic
+effect it produces at some point outside its circuit, or by the
+amount of electrochemical decomposition it can perform in a
+given time on a selected standard electrolyte. Limiting our
+consideration to the case of linear currents or currents flowing
+in thin cylindrical wires, a definition may be given in the first
+place of the unit electric current in the centimetre, gramme,
+second (C.G.S.) of electromagnetic measurement (see <span class="sc"><a href="#artlinks">Units,
+Physical</a></span>). H.C. Oersted discovered in 1820 that a straight
+wire conveying an electric current is surrounded by a magnetic
+field the lines of which are self-closed lines embracing the electric
+circuit (see <span class="sc"><a href="#ar63">Electricity</a></span> and <span class="sc"><a href="#ar71">Electromagnetism</a></span>). The unit
+current in the electromagnetic system of measurement is defined
+as the current which, flowing in a thin wire bent into the form
+of a circle of one centimetre in radius, creates a magnetic field
+having a strength of 2&pi; units at the centre of the circle, and
+therefore would exert a mechanical force of 2&pi; dynes on a unit
+magnetic pole placed at that point (see <span class="sc"><a href="#artlinks">Magnetism</a></span>). Since
+the length of the circumference of the circle of unit radius is
+2&pi; units, this is equivalent to stating that the unit current on
+the electromagnetic C.G.S. system is a current such that unit
+length acts on unit magnetic pole with a unit force at a unit
+of distance. Another definition, called the electrostatic unit
+of current, is as follows: Let any conductor be charged with
+electricity and discharged through a thin wire at such a rate
+that one electrostatic unit of quantity (see <span class="sc"><a href="#artlinks">Electrostatics</a></span>)
+flows past any section of the wire in one unit of time. The
+electromagnetic unit of current defined as above is 3 × 10<span class="sp">10</span> times
+larger than the electrostatic unit.</p>
+
+<p>In the selection of a practical unit of current it was considered
+that the electromagnetic unit was too large for most purposes,
+whilst the electrostatic unit was too small; hence a practical
+unit of current called 1 ampere was selected, intended originally
+to be <span class="spp">1</span>&frasl;<span class="suu">10</span> of the absolute electromagnetic C.G.S. unit of current
+as above defined. The practical unit of current, called the
+international ampere, is, however, legally defined at the present
+time as the continuous unidirectional current which when
+flowing through a neutral solution of silver nitrate deposits in
+one second on the cathode or negative pole 0.001118 of a gramme
+of silver. There is reason to believe that the international unit
+is smaller by about one part in a thousand, or perhaps by one
+part in 800, than the theoretical ampere defined as <span class="spp">1</span>&frasl;<span class="suu">10</span> part of
+the absolute electromagnetic unit. A periodic or alternating
+current is said to have a value of 1 ampere if when passed through
+a fine wire it produces in the same time the same heat as a
+unidirectional continuous current of 1 ampere as above electrochemically
+defined. In the case of a simple periodic alternating
+current having a simple sine wave form, the maximum value
+is equal to that of the equiheating continuous current multiplied
+by &radic;2. This equiheating continuous current is called the effective
+or root-mean-square (R.M.S.) value of the alternating one.</p>
+
+<p><i>Resistance.</i>&mdash;A current flows in a circuit in virtue of an electromotive
+force (E.M.F.), and the numerical relation between the
+current and E.M.F. is determined by three qualities of the
+circuit called respectively, its resistance (R), inductance (L), and
+capacity (C). If we limit our consideration to the case of continuous
+unidirectional conduction currents, then the relation
+between current and E.M.F. is defined by Ohm&rsquo;s law, which states
+that the numerical value of the current is obtained as the quotient
+of the electromotive force by a certain constant of the circuit
+called its resistance, which is a function of the geometrical form
+of the circuit, of its nature, <i>i.e.</i> material, and of its temperature,
+but is independent of the electromotive force or current. The
+resistance (R) is measured in units called ohms and the electromotive
+force in volts (V); hence for a continuous current the
+value of the current in amperes (A) is obtained as the quotient
+<span class="pagenum"><a name="page212" id="page212"></a>212</span>
+of the electromotive force acting in the circuit reckoned in volts
+by the resistance in ohms, or A = V/R. Ohm established his law
+by a course of reasoning which was similar to that on which
+J.B.J. Fourier based his investigations on the uniform motion
+of heat in a conductor. As a matter of fact, however, Ohm&rsquo;s
+law merely states the direct proportionality of steady current
+to steady electromotive force in a circuit, and asserts that this
+ratio is governed by the numerical value of a quality of the conductor,
+called its resistance, which is independent of the current,
+provided that a correction is made for the change of temperature
+produced by the current. Our belief, however, in its universality
+and accuracy rests upon the close agreement between deductions
+made from it and observational results, and although it is not
+derivable from any more fundamental principle, it is yet one of
+the most certainly ascertained laws of electrokinetics.</p>
+
+<p>Ohm&rsquo;s law not only applies to the circuit as a whole but to any
+part of it, and provided the part selected does not contain a
+source of electromotive force it may be expressed as follows:&mdash;The
+difference of potential (P.D.) between any two points of a
+circuit including a resistance R, but not including any source of
+electromotive force, is proportional to the product of the resistance
+and the current i in the element, provided the conductor
+remains at the same temperature and the current is constant and
+unidirectional. If the current is varying we have, however, to take
+into account the electromotive force (E.M.F.) produced by this
+variation, and the product Ri is then equal to the difference
+between the observed P.D. and induced E.M.F.</p>
+
+<p>We may otherwise define the resistance of a circuit by saying
+that it is that physical quality of it in virtue of which energy is
+dissipated as heat in the circuit when a current flows through it.
+The power communicated to any electric circuit when a current
+i is created in it by a continuous unidirectional electromotive
+force E is equal to Ei, and the energy dissipated as heat in that
+circuit by the conductor in a small interval of time dt is measured
+by Ei dt. Since by Ohm&rsquo;s law E = Ri, where R is the resistance
+of the circuit, it follows that the energy dissipated as heat per
+unit of time in any circuit is numerically represented by Ri², and
+therefore the resistance is measured by the heat produced per
+unit of current, provided the current is unvarying.</p>
+
+<p><i>Inductance</i>.&mdash;As soon as we turn our attention, however, to
+alternating or periodic currents we find ourselves compelled to take
+into account another quality of the circuit, called its &ldquo;inductance.&rdquo;
+This may be defined as that quality in virtue of which energy is
+stored up in connexion with the circuit in a magnetic form.
+It can be experimentally shown that a current cannot be created
+instantaneously in a circuit by any finite electromotive force,
+and that when once created it cannot be annihilated instantaneously.
+The circuit possesses a quality analogous to the inertia
+of matter. If a current i is flowing in a circuit at any moment,
+the energy stored up in connexion with the circuit is measured
+by ½Li², where L, the inductance of the circuit, is related to the
+current in the same manner as the quantity called the mass of
+a body is related to its velocity in the expression for the ordinary
+kinetic energy, viz. ½Mv². The rate at which this conserved
+energy varies with the current is called the &ldquo;electrokinetic
+momentum&rdquo; of this circuit (= Li). Physically interpreted this
+quantity signifies the number of lines of magnetic flux due to
+the current itself which are self-linked with its own circuit.</p>
+
+<p><i>Magnetic Force and Electric Currents</i>.&mdash;In the case of every
+circuit conveying a current there is a certain magnetic force (see
+<span class="sc"><a href="#artlinks">Magnetism</a></span>) at external points which can in some instances be
+calculated. Laplace proved that the magnetic force due to an
+element of length dS of a circuit conveying a current I at a point
+P at a distance r from the element is expressed by IdS sin &theta;/r²,
+where &theta; is the angle between the direction of the current element
+and that drawn between the element and the point. This force
+is in a direction perpendicular to the radius vector and to the
+plane containing it and the element of current. Hence the
+determination of the magnetic force due to any circuit is reduced
+to a summation of the effects due to all the elements of length.
+For instance, the magnetic force at the centre of a circular
+circuit of radius r carrying a steady current I is 2&pi;I/r, since all
+elements are at the same distance from the centre. In the same
+manner, if we take a point in a line at right angles to the plane
+of the circle through its centre and at a distance d, the magnetic
+force along this line is expressed by 2&pi;r²I / (r² + d²)<span class="spp">3</span>&frasl;<span class="suu">2</span>. Another
+important case is that of an infinitely long straight current.
+By summing up the magnetic force due to each element at
+any point P outside the continuous straight current I, and at a
+distance d from it, we can show that it is equal to 2I/d or is
+inversely proportional to the distance of the point from the wire.
+In the above formula the current I is measured in absolute
+electromagnetic units. If we reckon the current in amperes
+A, then I = A/10.</p>
+
+<p>It is possible to make use of this last formula, coupled with an
+experimental fact, to prove that the magnetic force due to an
+element of current varies inversely as the square of the distance.
+If a flat circular disk is suspended so as to be free to rotate round
+a straight current which passes through its centre, and two
+bar magnets are placed on it with their axes in line with the
+current, it is found that the disk has no tendency to rotate round
+the current. This proves that the force on each magnetic pole
+is inversely as its distance from the current. But it can be shown
+that this law of action of the whole infinitely long straight current
+is a mathematical consequence of the fact that each element of
+the current exerts a magnetic force which varies inversely as
+the square of the distance. If the current flows N times round
+the circuit instead of once, we have to insert NA/10 in place of
+I in all the above formulae. The quantity NA is called the
+&ldquo;ampere-turns&rdquo; on the circuit, and it is seen that the magnetic
+field at any point outside a circuit is proportional to the ampere-turns
+on it and to a function of its geometrical form and the
+distance of the point.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:464px; height:230px" src="images/img212.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span></td>
+<td class="caption"><span class="sc">Fig. 4.</span></td></tr></table>
+
+<p>There is therefore a distribution of magnetic force in the field
+of every current-carrying conductor which can be delineated by
+lines of magnetic force and rendered visible to the eye by iron
+filings (see Magnetism). If a copper wire is passed vertically
+through a hole in a card on which iron filings are sprinkled, and
+a strong electric current is sent through the circuit, the filings
+arrange themselves in concentric circular lines making visible
+the paths of the lines of magnetic force (fig. 3). In the same
+manner, by passing a circular wire through a card and sending
+a strong current through the wire we can employ iron filings to
+delineate for us the form of the lines of magnetic force (fig. 4).
+In all cases a magnetic pole of strength M, placed in the field of an
+electric current, is urged along the lines of force with a mechanical
+force equal to MH, where H is the magnetic force. If then we
+carry a unit magnetic pole against the direction in which it would
+naturally move we do <i>work</i>. The lines of magnetic force embracing
+a current-carrying conductor are always loops or endless
+lines.</p>
+
+<div class="condensed">
+<p>The work done in carrying a unit magnetic pole once round a
+circuit conveying a current is called the &ldquo;line integral of magnetic
+force&rdquo; along that path. If, for instance, we carry a unit pole in a
+circular path of radius r once round an infinitely long straight
+filamentary current I, the line integral is 4&pi;I. It is easy to prove
+that this is a general law, and that if we have any currents flowing
+in a conductor the line integral of magnetic force taken once round
+a path linked with the current circuit is 4&pi; times the total current
+flowing through the circuit. Let us apply this to the case of an
+endless solenoid. If a copper wire insulated or covered with cotton
+or silk is twisted round a thin rod so as to make a close spiral, this
+<span class="pagenum"><a name="page213" id="page213"></a>213</span>
+forms a &ldquo;solenoid,&rdquo; and if the solenoid is bent round so that its two
+ends come together we have an endless solenoid. Consider such a
+solenoid of mean length l and N turns of wire. If it is made endless,
+the magnetic force H is the same everywhere along the central axis
+and the line integral along the axis is Hl. If the current is denoted
+by I, then NI is the total current, and accordingly 4&pi;NI = Hl, or
+H = 4&pi;NI/l. For a thin endless solenoid the axial magnetic force is
+therefore 4&pi; times the current-turns per unit of length. This holds
+good also for a long straight solenoid provided its length is large
+compared with its diameter. It can be shown that if insulated wire
+is wound round a sphere, the turns being all parallel to lines of
+latitude, the magnetic force in the interior is constant and the lines
+of force therefore parallel. The magnetic force at a point outside a
+conductor conveying a current can by various means be measured
+or compared with some other standard magnetic forces, and it
+becomes then a means of measuring the current. Instruments called
+galvanometers and ammeters for the most part operate on this
+principle.</p>
+</div>
+
+<p><i>Thermal Effects of Currents.</i>&mdash;J.P. Joule proved that the heat
+produced by a constant current in a given time in a wire having
+a constant resistance is proportional to the square of the strength
+of the current. This is known as Joule&rsquo;s law, and it follows,
+as already shown, as an immediate consequence of Ohm&rsquo;s law
+and the fact that the power dissipated electrically in a conductor,
+when an electromotive force E is applied to its extremities,
+producing thereby a current I in it, is equal to EI.</p>
+
+<div class="condensed">
+<p>If the current is alternating or periodic, the heat produced in
+any time T is obtained by taking the sum at equidistant intervals of
+time of all the values of the quantities Ri²dt, where dt represents a
+small interval of time and i is the current at that instant. The
+quantity T<span class="sp">&minus;1</span> <span class="f150">&int;</span>
+<span class="sp1">T</span><span class="su1">0</span> i²dt is called the mean-square-value of the variable
+current, i being the instantaneous value of the current, that is, its
+value at a particular instant or during a very small interval of time
+dt. The square root of the above quantity, or</p>
+
+<p class="center"><span class="f150">[</span> T<span class="sp">&minus;1</span>
+<span class="f150">&int;</span> <span class="sp1">T</span><span class="su1">0</span> i²dt
+<span class="f150">]</span><span class="sp1">1/2</span>,</p>
+
+<p class="noind">is called the root-mean-square-value, or the effective value of the
+current, and is denoted by the letters R.M.S.</p>
+</div>
+
+<p>Currents have equal heat-producing power in conductors of
+identical resistance when they have the same R.M.S. values.
+Hence periodic or alternating currents can be measured as regards
+their R.M.S. value by ascertaining the continuous current which
+produces in the same time the same heat in the same conductor
+as the periodic current considered. Current measuring instruments
+depending on this fact, called hot-wire ammeters, are
+in common use, especially for measuring alternating currents.
+The maximum value of the periodic current can only be determined
+from the R.M.S. value when we know the wave form of
+the current. The thermal effects of electric currents in conductors
+are dependent upon the production of a state of equilibrium
+between the heat produced electrically in the wire and the
+causes operative in removing it. If an ordinary round wire is
+heated by a current it loses heat, (1) by radiation, (2) by air
+convection or cooling, and (3) by conduction of heat out of the
+ends of the wire. Generally speaking, the greater part of the
+heat removal is effected by radiation and convection.</p>
+
+<div class="condensed">
+<p>If a round sectioned metallic wire of uniform diameter d and
+length l made of a material of resistivity &rho; has a current of A amperes
+passed through it, the heat in watts produced in any time t seconds
+is represented by the value of 4A²&rho;lt / 10<span class="sp">9</span>&pi;d², where d and l must be
+measured in centimetres and &rho; in absolute C.G.S. electromagnetic
+units. The factor 10<span class="sp">9</span> enters because one ohm is 10<span class="sp">9</span> absolute electromagnetic
+C.G.S. units (see <span class="sc"><a href="#artlinks">Units, Physical</a></span>). If the wire has an
+emissivity e, by which is meant that e units of heat reckoned in
+joules or watt-seconds are radiated per second from unit of surface,
+then the power removed by radiation in the time t is expressed
+by &pi;dlet. Hence when thermal equilibrium is established we have
+4A²&rho;lt / 10<span class="sp">9</span>&pi;d² = &pi;dlet, or A² =
+10<span class="sp">9</span>&pi;²ed³ / 4&rho;. If the diameter of the
+wire is reckoned in mils (1 mil = .001 in.), and if we take e to have
+a value 0.1, an emissivity which will generally bring the wire to
+about 60° C., we can put the above formula in the following forms
+for circular sectioned copper, iron or platinoid wires, viz.</p>
+
+<table class="reg" summary="poem"><tr><td> <div class="poemr">
+<p>A = &radic;<span class="ov">d³ / 500</span> for copper wires</p>
+<p>A = &radic;<span class="ov">d³ / 4000</span> for iron wires</p>
+<p>A = &radic;<span class="ov">d³ / 5000</span> for platinoid wires.</p>
+</div> </td></tr></table>
+
+<p>These expressions give the ampere value of the current which
+will bring bare, straight or loosely coiled wires of d mils in diameter
+to about 60° C. when the steady state of temperature is reached.
+Thus, for instance, a bare straight copper wire 50 mils in diameter
+(= 0.05 in.) will be brought to a steady temperature of about 60° C.
+if a current of &radic;50³/500 = &radic;250 = 16 amperes (nearly) is passed
+through it, whilst a current of &radic;25 = 5 amperes would bring a
+platinoid wire to about the same temperature.</p>
+</div>
+
+<p>A wire has therefore a certain safe current-carrying capacity
+which is determined by its specific resistance and emissivity,
+the latter being fixed by its form, surface and surroundings.
+The emissivity increases with the temperature, else no state of
+thermal equilibrium could be reached. It has been found
+experimentally that whilst for fairly thick wires from 8 to 60
+mils in diameter the safe current varies approximately as the
+1.5th power of the diameter, for fine wires of 1 to 3 mils it varies
+more nearly as the diameter.</p>
+
+<table class="flt" style="float: right; width: 380px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:339px; height:288px" src="images/img213.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span></td></tr></table>
+
+<p><i>Action of one Current on Another.</i>&mdash;The investigations of Ampère
+in connexion with electric currents are of fundamental importance
+in electrokinetics. Starting from the discovery of Oersted,
+Ampère made known the correlative fact that not only is there
+a mechanical action between a current and a magnet, but that
+two conductors conveying electric currents exert mechanical
+forces on each other. Ampère devised ingenious methods of
+making one portion of a circuit movable so that he might observe
+effects of attraction or repulsion between this circuit and some
+other fixed current. He employed for this purpose an astatic
+circuit B, consisting of a wire bent into a double rectangle
+round which a current flowed first in one and then in the opposite
+direction (fig. 5). In
+this way the circuit
+was removed from
+the action of the
+earth&rsquo;s magnetic
+field, and yet one
+portion of it could
+be submitted to the
+action of any other
+circuit C. The
+astatic circuit was
+pivoted by suspending
+it in mercury
+cups q, p, one of
+which was in electrical
+connexion
+with the tubular support A, and the other with a strong insulated
+wire passing up it.</p>
+
+<p>Ampère devised certain crucial experiments, and the theory
+deduced from them is based upon four facts and one assumption.<a name="fa2j" id="fa2j" href="#ft2j"><span class="sp">2</span></a>
+He showed (1) that wire conveying a current bent back on itself
+produced no action upon a proximate portion of a movable
+astatic circuit; (2) that if the return wire was bent zig-zag but
+close to the outgoing straight wire the circuit produced no action
+on the movable one, showing that the effect of an element of the
+circuit was proportional to its projected length; (3) that a closed
+circuit cannot cause motion in an element of another circuit free
+to move in the direction of its length; and (4) that the action
+of two circuits on one and the same movable circuit was null if
+one of the two fixed circuits was n times greater than the other
+but n times further removed from the movable circuit. From
+this last experiment by an ingenious line of reasoning he proved
+that the action of an element of current on another element of
+current varies inversely as a square of their distance. These
+experiments enabled him to construct a mathematical expression
+of the law of action between two elements of conductors conveying
+currents. They also enabled him to prove that an element of
+current may be resolved like a force into components in different
+directions, also that the force produced by any element of the
+circuit on an element of any other circuit was perpendicular
+to the line joining the elements and inversely as the square of
+their distance. Also he showed that this force was an attraction
+if the currents in the elements were in the same direction, but
+a repulsion if they were in opposite directions. From these
+experiments and deductions from them he built up a complete
+formula for the action of one element of a current of length dS
+<span class="pagenum"><a name="page214" id="page214"></a>214</span>
+of one conductor conveying a current I upon another element
+dS&prime; of another circuit conveying another current I&prime; the elements
+being at a distance apart equal to r.</p>
+
+<div class="condensed">
+<p>If &theta; and &theta;&rsquo; are the angles the elements make with the line joining
+them, and &phi; the angle they make with one another, then Ampère&rsquo;s
+expression for the mechanical force f the elements exert on one
+another is</p>
+
+<p class="center">f = 2II&prime;r<span class="sp">&minus;2</span> {cos &phi; &minus; <span class="spp">3</span>&frasl;<span class="suu">2</span> cos &theta; cos &theta;&prime;} dSdS&prime;.</p>
+
+<p class="noind">This law, together with that of Laplace already mentioned, viz. that
+the magnetic force due to an element of length dS of a current I at a
+distance r, the element making an angle &theta; with the radius vector o is
+IdS sin &theta;/r², constitute the fundamental laws of electrokinetics.</p>
+</div>
+
+<p>Ampère applied these with great mathematical skill to elucidate
+the mechanical actions of currents on each other, and experimentally
+confirmed the following deductions: (1) Currents in
+parallel circuits flowing in the same direction attract each
+other, but if in opposite directions repel each other. (2) Currents
+in wires meeting at an angle attract each other more into
+parallelism if both flow either to or from the angle, but repel
+each other more widely apart if they are in opposite directions.
+(3) A current in a small circular conductor exerts a magnetic
+force in its centre perpendicular to its plane and is in all respects
+equivalent to a magnetic shell or a thin circular disk of steel
+so magnetized that one face is a north pole and the other a south
+pole, the product of the area of the circuit and the current flowing
+in it determining the magnetic moment of the element. (4) A
+closely wound spiral current is equivalent as regards external
+magnetic force to a polar magnet, such a circuit being called a
+finite solenoid. (5) Two finite solenoid circuits act on each other
+like two polar magnets, exhibiting actions of attraction or
+repulsion between their ends.</p>
+
+<p>Ampère&rsquo;s theory was wholly built up on the assumption of
+action at a distance between elements of conductors conveying
+the electric currents. Faraday&rsquo;s researches and the discovery
+of the fact that the insulating medium is the real seat of the
+operations necessitates a change in the point of view from which
+we regard the facts discovered by Ampère. Maxwell showed
+that in any field of magnetic force there is a tension along the
+lines of force and a pressure at right angles to them; in other
+words, lines of magnetic force are like stretched elastic threads
+which tend to contract.<a name="fa3j" id="fa3j" href="#ft3j"><span class="sp">3</span></a> If, therefore, two conductors lie parallel
+and have currents in them in the same direction they are impressed
+by a certain number of lines of magnetic force which
+pass round the two conductors, and it is the tendency of these
+to contract which draws the circuits together. If, however, the
+currents are in opposite directions then the lateral pressure of the
+similarly contracted lines of force between them pushes the
+conductors apart. Practical application of Ampère&rsquo;s discoveries
+was made by W.E. Weber in inventing the electrodynamometer,
+and later Lord Kelvin devised ampere balances for the measurement
+of electric currents based on the attraction between coils
+conveying electric currents.</p>
+
+<p><i>Induction of Electric Currents</i>.&mdash;Faraday<a name="fa4j" id="fa4j" href="#ft4j"><span class="sp">4</span></a> in 1831 made the
+important discovery of the induction of electric currents (see
+<span class="sc"><a href="#ar63">Electricity</a></span>). If two conductors are placed parallel to each
+other, and a current in one of them, called the primary, started
+or stopped or changed in strength, every such alteration causes
+a transitory current to appear in the other circuit, called the
+secondary. This is due to the fact that as the primary current
+increases or decreases, its own embracing magnetic field alters,
+and lines of magnetic force are added to or subtracted from its
+fields. These lines do not appear instantly in their place at a
+distance, but are propagated out from the wire with a velocity
+equal to that of light; hence in their outward progress they
+cut through the secondary circuit, just as ripples made on the
+surface of water in a lake by throwing a stone on to it expand
+and cut through a stick held vertically in the water at a distance
+from the place of origin of the ripples. Faraday confirmed this
+view of the phenomena by proving that the mere motion of a
+wire transversely to the lines of magnetic force of a permanent
+magnet gave rise to an induced electromotive force in the wire.
+He embraced all the facts in the single statement that if there
+be any circuit which by movement in a magnetic field, or by the
+creation or change in magnetic fields round it, experiences a
+change in the number of lines of force linked with it, then an
+electromotive force is set up in that circuit which is proportional
+at any instant to the rate at which the total magnetic flux linked
+with it is changing. Hence if Z represents the total number of
+lines of magnetic force linked with a circuit of N turns, then
+&minus;N (dZ/dt) represents the electromotive force set up in that
+circuit. The operation of the induction coil (<i>q.v.</i>) and the
+transformer (<i>q.v.</i>) are based on this discovery. Faraday also
+found that if a copper disk A (fig. 6) is rotated between the poles
+of a magnet NO so that the disk moves with its plane perpendicular
+to the lines of magnetic force of the field, it has created in
+it an electromotive force directed from the centre to the edge
+or vice versa. The action of the dynamo (<i>q.v.</i>) depends on
+similar processes, viz. the cutting of the lines of magnetic force
+of a constant field produced by certain magnets by certain moving
+conductors called armature bars or coils in which an electromotive
+force is thereby created.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:356px; height:200px" src="images/img214.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig 6.</span></td></tr></table>
+
+<div class="condensed">
+<p>In 1834 H.F.E. Lenz enunciated a law which connects together
+the mechanical actions between electric circuits discovered by
+Ampère and the induction of electric currents discovered by Faraday.
+It is as follows: If a constant current flows in a primary circuit P,
+and if by motion of P a secondary current is created in a neighbouring
+circuit S, the direction of the secondary current will be such as to
+oppose the relative motion of the circuits. Starting from this, F.E.
+Neumann founded a mathematical theory of induced currents,
+discovering a quantity M, called the &ldquo;potential of one circuit on
+another,&rdquo; or generally their &ldquo;coefficient of mutual inductance.&rdquo;
+Mathematically M is obtained by taking the sum of all such quantities
+as &fnof;&fnof; dSdS&prime; cos &phi;/r, where dS and dS&prime; are the elements of length of the
+two circuits, r is their distance, and &phi; is the angle which they make
+with one another; the summation or integration must be extended
+over every possible pair of elements. If we take pairs of elements in
+the same circuit, then Neumann&rsquo;s formula gives us the coefficient
+of self-induction of the circuit or the potential of the circuit on itself.
+For the results of such calculations on various forms of circuit the
+reader must be referred to special treatises.</p>
+
+<p>H. von Helmholtz, and later on Lord Kelvin, showed that the
+facts of induction of electric currents discovered by Faraday could
+have been predicted from the electrodynamic actions discovered by
+Ampère assuming the principle of the conservation of energy.
+Helmholtz takes the case of a circuit of resistance R in which acts
+an electromotive force due to a battery or thermopile. Let a magnet
+be in the neighbourhood, and the potential of the magnet on the
+circuit be V, so that if a current I existed in the circuit the work done
+on the magnet in the time dt is I (dV/dt)dt. The source of electromotive
+force supplies in the time dt work equal to EIdt, and according
+to Joule&rsquo;s law energy is dissipated equal to RI²dt. Hence, by the
+conservation of energy,</p>
+
+<p class="center">EIdt = RI²dt + I (dV/dt) dt.</p>
+
+<p class="noind">If then E = 0, we have I = &minus;(dV/dt) / R, or there will be a current
+due to an induced electromotive force expressed by &minus;dV/dt. Hence
+if the magnet moves, it will create a current in the wire provided
+that such motion changes the potential of the magnet with respect
+to the circuit. This is the effect discovered by Faraday.<a name="fa5j" id="fa5j" href="#ft5j"><span class="sp">5</span></a></p>
+</div>
+
+<p><i>Oscillatory Currents.</i>&mdash;In considering the motion of electricity
+in conductors we find interesting phenomena connected with the
+discharge of a condenser or Leyden jar (<i>q.v.</i>). This problem was
+first mathematically treated by Lord Kelvin in 1853 (<i>Phil. Mag.</i>,
+1853, 5, p. 292).</p>
+
+<div class="condensed">
+<p>If a conductor of capacity C has its terminals connected by a wire
+of resistance R and inductance L, it becomes important to consider
+<span class="pagenum"><a name="page215" id="page215"></a>215</span>
+the subsequent motion of electricity in the wire. If Q is the quantity
+of electricity in the condenser initially, and q that at any time t
+after completing the circuit, then the energy stored up in the condenser
+at that instant is ½q² / C, and the energy associated with the
+circuit is ½L (dq/dt)², and the rate of dissipation of energy by resistance
+is R (dq/dt)², since dq/dt = i is the discharge current. Hence we can
+construct an equation of energy which expresses the fact that at
+any instant the power given out by the condenser is partly stored
+in the circuit and partly dissipated as heat in it. Mathematically
+this is expressed as follows:&mdash;</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&minus;</td> <td>d</td>
+<td rowspan="2"><span class="f150">[</span> ½</td> <td>q²</td>
+<td rowspan="2"><span class="f150">]</span> =</td> <td>d</td>
+<td rowspan="2"><span class="f150">[</span> ½L <span class="f150">(</span></td> <td>dq</td>
+<td rowspan="2"><span class="f150">)</span></td> <td>²</td>
+<td rowspan="2"><span class="f150">]</span> + R <span class="f150">(</span></td> <td>dq</td>
+<td rowspan="2"><span class="f150">)</span></td> <td>²</td></tr>
+<tr><td class="denom">dt</td> <td class="denom">C</td>
+<td class="denom">dt</td> <td class="denom">dt</td>
+<td>&nbsp;</td> <td class="denom">dt</td> <td>&nbsp;</td></tr></table>
+
+<p class="noind">or</p>
+
+<table class="math0" summary="math">
+<tr><td>d²q</td>
+<td rowspan="2">+</td> <td>R</td>
+<td rowspan="2">&nbsp;</td> <td>dq</td>
+<td rowspan="2">+</td> <td>1</td>
+<td rowspan="2">q = 0.</td></tr>
+<tr><td class="denom">dt²</td> <td class="denom">L</td>
+<td class="denom">dt</td> <td class="denom">LC</td></tr></table>
+
+<p class="noind">The above equation has two solutions according as R² / 4L² is greater
+or less than 1/LC. In the first case the current i in the circuit can
+be expressed by the equation</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">i = Q</td> <td>&alpha;² + &beta;²</td>
+<td rowspan="2">e<span class="sp">&minus;&alpha;t</span> (e<span class="sp">&beta;t</span> &minus; e<span class="sp">&minus;&beta;t</span>),</td></tr>
+<tr><td class="denom">2&beta;</td></tr></table>
+
+<p class="noind">where &alpha; = R/2L, &beta; = &radic;<span class="ov">(R²/4L² &minus; 1/LC)</span>, Q is the value of q when t = 0,
+and e is the base of Napierian logarithms; and in the second case
+by the equation</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">i = Q</td> <td>&alpha;²+&beta;²</td>
+<td rowspan="2">e<span class="sp">&minus;&alpha;t</span> sin &beta;t</td></tr>
+<tr><td class="denom">&beta;</td></tr></table>
+
+<p class="noind">where</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">&alpha; = R/2L, and &beta; = <span class="f200">&radic;</span></td> <td class="denom">1</td>
+<td class="denom" rowspan="2">&minus;</td> <td class="denom">R²</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">LC</td> <td class="denom">4L²</td></tr></table>
+
+<p class="noind">These expressions show that in the first case the discharge current
+of the jar is always in the same direction and is a transient unidirectional
+current. In the second case, however, the current is an
+oscillatory current gradually decreasing in amplitude, the frequency
+n of the oscillation being given by the expression</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">n =</td> <td>1</td>
+<td rowspan="2"><span class="f200">&radic;</span></td> <td class="denom">1</td>
+<td class="denom" rowspan="2">&minus;</td> <td class="denom">R²</td>
+<td rowspan="2">.</td></tr>
+<tr><td class="denom">2&pi;</td> <td class="denom">LC</td>
+<td class="denom">4L²</td></tr></table>
+
+<p class="noind">In those cases in which the resistance of the discharge circuit is
+very small, the expression for the frequency n and for the time
+period of oscillation R take the simple forms n = 1, 2&pi; &radic;<span class="ov">LC</span>, or
+T = 1/n = 2&pi; &radic;<span class="ov">LC</span>.</p>
+</div>
+
+<p>The above investigation shows that if we construct a circuit
+consisting of a condenser and inductance placed in series with
+one another, such circuit has a natural electrical time period of
+its own in which the electrical charge in it oscillates if disturbed.
+It may therefore be compared with a pendulum of any kind
+which when displaced oscillates with a time period depending
+on its inertia and on its restoring force.</p>
+
+<p>The study of these electrical oscillations received a great
+impetus after H.R. Hertz showed that when taking place in
+electric circuits of a certain kind they create electromagnetic
+waves (see <span class="sc"><a href="#ar65">Electric Waves</a></span>) in the dielectric surrounding the
+oscillator, and an additional interest was given to them by their
+application to telegraphy. If a Leyden jar and a circuit of low
+resistance but some inductance in series with it are connected
+across the secondary spark gap of an induction coil, then when
+the coil is set in action we have a series of bright noisy sparks,
+each of which consists of a train of oscillatory electric discharges
+from the jar. The condenser becomes charged as the secondary
+electromotive force of the coil is created at each break of the
+primary current, and when the potential difference of the
+condenser coatings reaches a certain value determined by the
+spark-ball distance a discharge happens. This discharge, however,
+is not a single movement of electricity in one direction but
+an oscillatory motion with gradually decreasing amplitude.
+If the oscillatory spark is photographed on a revolving plate or
+a rapidly moving film, we have evidence in the photograph that
+such a spark consists of numerous intermittent sparks gradually
+becoming feebler. As the coil continues to operate, these trains
+of electric discharges take place at regular intervals. We can
+cause a train of electric oscillations in one circuit to induce
+similar oscillations in a neighbouring circuit, and thus construct
+an oscillation transformer or high frequency induction coil.</p>
+
+<p><i>Alternating Currents</i>.&mdash;The study of alternating currents of
+electricity began to attract great attention towards the end of
+the 19th century by reason of their application in electrotechnics
+and especially to the transmission of power. A circuit in which
+a simple periodic alternating current flows is called a single phase
+circuit. The important difference between such a form of current
+flow and steady current flow arises from the fact that if the circuit
+has inductance then the periodic electric current in it is not in
+step with the terminal potential difference or electromotive force
+acting in the circuit, but the current lags behind the electromotive
+force by a certain fraction of the periodic time called the
+&ldquo;phase difference.&rdquo; If two alternating currents having a fixed
+difference in phase flow in two connected separate but related
+circuits, the two are called a two-phase current. If three or more
+single-phase currents preserving a fixed difference of phase flow
+in various parts of a connected circuit, the whole taken together
+is called a polyphase current. Since an electric current is a
+vector quantity, that is, has direction as well as magnitude,
+it can most conveniently be represented by a line denoting its
+maximum value, and if the alternating current is a simple
+periodic current then the root-mean-square or effective value
+of the current is obtained by dividing the maximum value by
+&radic;<span class="ov">2</span>. Accordingly when we have an electric circuit or circuits
+in which there are simple periodic currents we can draw a vector
+diagram, the lines of which represent the relative magnitudes and
+phase differences of these currents.</p>
+
+<div class="condensed">
+<p>A vector can most conveniently be represented by a symbol such
+as a + ib, where a stands for any length of a units measured horizontally
+and b for a length b units measured vertically, and the <span class="correction" title="amended from smybol">symbol</span> &iota;
+is a sign of perpendicularity, and equivalent analytically<a name="fa6j" id="fa6j" href="#ft6j"><span class="sp">6</span></a> to &radic;&minus;1.
+Accordingly if E represents the periodic electromotive force (maximum
+value) acting in a circuit of resistance R and inductance L and
+frequency n, and if the current considered as a vector is represented
+by I, it is easy to show that a vector equation exists between these
+quantities as follows:&mdash;</p>
+
+<p class="center">E = RI + &iota;2&pi;nLI.</p>
+
+<p class="noind">Since the absolute magnitude of a vector a + &iota;b is &radic;(a² + b²), it follows
+that considering merely magnitudes of current and electromotive
+force and denoting them by symbols (E) (I), we have the following
+equation connecting (I) and (E):&mdash;</p>
+
+<p class="center">(I) = (E) / &radic;<span class="ov">R² + p²L²</span>,</p>
+
+<p class="noind">where p stands for 2&pi;n. If the above equation is compared with the
+symbolic expression of Ohm&rsquo;s law, it will be seen that the quantity
+&radic;(R² + p²L²) takes the place of resistance R in the expression of
+Ohm. This quantity &radic;(R² + p²L²) is called the &ldquo;impedance&rdquo; of the
+alternating circuit. The quantity pL is called the &ldquo;reactance&rdquo; of
+the alternating circuit, and it is therefore obvious that the current
+in such a circuit lags behind the electromotive force by an angle,
+called the angle of lag, the tangent of which is pL/R.</p>
+
+<table class="flt" style="float: right; width: 250px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:211px; height:218px" src="images/img216.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 7.</span></td></tr></table>
+
+<p><i>Currents in Networks of Conductors</i>.&mdash;In dealing with problems
+connected with electric currents we have to consider the laws which
+govern the flow of currents in linear conductors (wires), in plane
+conductors (sheets), and throughout the mass of a material conductor.<a name="fa7j" id="fa7j" href="#ft7j"><span class="sp">7</span></a>
+In the first case consider the collocation of a number of
+linear conductors, such as rods or wires of metal, joined at their ends
+to form a network of conductors. The network consists of a number
+of conductors joining certain points and forming meshes. In each
+conductor a current may exist, and along each conductor there is a
+fall of potential, or an active electromotive force may be acting in it.
+Each conductor has a certain resistance. To find the current in each
+conductor when the individual resistances and electromotive forces
+are given, proceed as follows:&mdash;Consider any one mesh. The sum
+of all the electromotive forces which exist in the branches bounding
+that mesh must be equal to the sum of all the products of the resistances
+into the currents flowing along them, or &Sigma;(E) = &Sigma;(C.R.).
+Hence if we consider each mesh as traversed by imaginary currents
+all circulating in the same direction, the real currents are the sums
+or differences of these imaginary cyclic currents in each branch.
+Hence we may assign to each mesh a cycle symbol x, y, z, &amp;c., and
+form a cycle equation. Write down the cycle symbol for a mesh
+and prefix as coefficient the sum of all the resistances which bound
+that cycle, then subtract the cycle symbols of each adjacent cycle,
+each multiplied by the value of the bounding or common resistances,
+and equate this sum to the total electromotive force acting round the
+cycle. Thus if x y z are the cycle currents, and a b c the resistances
+bounding the mesh x, and b and c those separating it from the
+meshes y and z, and E an electromotive force in the branch a, then
+<span class="pagenum"><a name="page216" id="page216"></a>216</span>
+we have formed the cycle equation x(a + b + c) &minus; by &minus; cz = E. For
+each mesh a similar equation may be formed. Hence we have as
+many linear equations as there are meshes, and we can obtain the
+solution for each cycle symbol, and therefore for the current in
+each branch. The solution giving the current in such branch of
+the network is therefore always in the
+form of the quotient of two determinants.
+The solution of the well-known
+problem of finding the current
+in the galvanometer circuit of the
+arrangement of linear conductors called
+Wheatstone&rsquo;s Bridge is thus easily obtained.
+For if we call the cycles (see
+fig. 7) (x + y), y and z, and the resistances
+P, Q, R, S, G and B, and if E be
+the electromotive force in the battery
+circuit, we have the cycle equations</p>
+
+<table class="reg" summary="poem"><tr><td> <div class="poemr">
+<p>(P + G + R) (x + y) &minus; Gy &minus; Rz = 0,</p>
+<p>(Q + G + S)y &minus; G (x + y) &minus; Sz = 0,</p>
+<p>(R + S + B)z &minus; R (x + y) &minus; Sy = E.</p>
+</div> </td></tr></table>
+
+<p class="noind">From these we can easily obtain the
+solution for (x + y) &minus; y = x, which is the current through the galvanometer
+circuit in the form</p>
+
+<p class="center">x = E (PS &minus; RQ) &Delta;.</p>
+
+<p class="noind">where &Delta; is a certain function of P, Q, R, S, B and G.</p>
+
+<p><i>Currents in Sheets</i>.&mdash;In the case of current flow in plane sheets,
+we have to consider certain points called sources at which the current
+flows into the sheet, and certain points called sinks at which it leaves.
+We may investigate, first, the simple case of one source and one sink
+in an infinite plane sheet of thickness &delta; and conductivity k. Take
+any point P in the plane at distances R and r from the source and
+sink respectively. The potential V at P is obviously given by</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">V =</td> <td>Q</td>
+<td rowspan="2">log <span class="su">e</span></td> <td>r<span class="su">1</span></td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">2&pi;k&delta;</td> <td class="denom">r<span class="su">2</span></td></tr></table>
+
+<p class="noind">where Q is the quantity of electricity supplied by the source per
+second. Hence the equation to the equipotential curve is r<span class="su">1</span>r<span class="su">2</span> = a
+constant.</p>
+
+<p>If we take a point half-way between the sink and the source as
+the origin of a system of rectangular co-ordinates, and if the distance
+between sink and source is equal to p, and the line joining them is
+taken as the axis of x, then the equation to the equipotential line is</p>
+
+<table class="math0" summary="math">
+<tr><td>y² + (x + p)²</td> <td rowspan="2">= a constant.</td></tr>
+<tr><td class="denom">y² + (x &minus; p)²</td></tr></table>
+
+<p class="noind">This is the equation of a family of circles having the axis of y for
+a common radical axis, one set of circles surrounding the sink and
+another set of circles surrounding the source. In order to discover
+the form of the stream of current lines we have to determine the
+orthogonal trajectories to this family of coaxial circles. It is easy
+to show that the orthogonal trajectory of the system of circles is
+another system of circles all passing through the sink and the source,
+and as a corollary of this fact, that the electric resistance of a circular
+disk of uniform thickness is the same between any two points taken
+anywhere on its circumference as sink and source. These equipotential
+lines may be delineated experimentally by attaching the
+terminals of a battery or batteries to small wires which touch at
+various places a sheet of tinfoil. Two wires attached to a galvanometer
+may then be placed on the tinfoil, and one may be kept
+stationary and the other may be moved about, so that the galvanometer
+is not traversed by any current. The moving terminal then
+traces out an equipotential curve. If there are n sinks and sources
+in a plane conducting sheet, and if r, r&prime;, r&Prime; be the distances of any
+point from the sinks, and t, t&prime;, t&Prime; the distances of the sources, then</p>
+
+<table class="math0" summary="math">
+<tr><td>r r&prime; r&Prime; ...</td> <td rowspan="2">= a constant,</td></tr>
+<tr><td class="denom">t t&prime; t&Prime; ...</td></tr></table>
+
+<p class="noind">is the equation to the equipotential lines. The orthogonal trajectories
+or stream lines have the equation</p>
+
+<p class="center">&Sigma; (&theta; &minus; &theta;&prime;) = a constant,</p>
+
+<p class="noind">where &theta; and &theta;&prime; are the angles which the lines drawn from any point
+in the plane to the sink and corresponding source make with the line
+joining that sink and source. Generally it may be shown that if
+there are any number of sinks and sources in an infinite plane-conducting
+sheet, and if r, &theta; are the polar co-ordinates of any one,
+then the equation to the equipotential surfaces is given by the
+equation</p>
+
+<p class="center">&Sigma; (A log <span class="su">e</span> r) = a constant,</p>
+
+<p class="noind">where A is a constant; and the equation to the stream of current
+lines is</p>
+
+<p class="center">&Sigma; (&theta;) = a constant.</p>
+
+<p>In the case of electric flow in three dimensions the electric potential
+must satisfy Laplace&rsquo;s equation, and a solution is therefore found
+in the form &Sigma; (A/r) = a constant, as the equation to an equipotential
+surface, where r is the distance of any point on that surface from a
+source or sink.</p>
+</div>
+
+<p><i>Convection Currents.</i>&mdash;The subject of convection electric
+currents has risen to great importance in connexion with modern
+electrical investigations. The question whether a statically
+electrified body in motion creates a magnetic field is of fundamental
+importance. Experiments to settle it were first undertaken
+in the year 1876 by H.A. Rowland, at a suggestion of
+H. von Helmholtz.<a name="fa8j" id="fa8j" href="#ft8j"><span class="sp">8</span></a> After preliminary experiments, Rowland&rsquo;s
+first apparatus for testing this hypothesis was constructed, as
+follows:&mdash;An ebonite disk was covered with radial strips of gold-leaf
+and placed between two other metal plates which acted as
+screens. The disk was then charged with electricity and set in
+rapid rotation. It was found to affect a delicately suspended
+pair of astatic magnetic needles hung in proximity to the disk
+just as would, by Oersted&rsquo;s rule, a circular electric current
+coincident with the periphery of the disk. Hence the statically-charged
+but rotating disk becomes in effect a circular electric
+current.</p>
+
+<p>The experiments were repeated and confirmed by W.C.
+Röntgen (<i>Wied. Ann.</i>, 1888, 35, p. 264; 1890, 40, p. 93) and by
+F. Himstedt (<i>Wied. Ann.</i>, 1889, 38, p. 560). Later V. Crémieu
+again repeated them and obtained negative results (<i>Com. rend.</i>,
+1900, 130, p. 1544, and 131, pp. 578 and 797; 1901, 132, pp. 327 and
+1108). They were again very carefully reconducted by H. Pender
+(<i>Phil. Mag.</i>, 1901, 2, p. 179) and by E.P. Adams (id. <i>ib.</i>, 285).
+Pender&rsquo;s work showed beyond any doubt that electric convection
+does produce a magnetic effect. Adams employed charged
+copper spheres rotating at a high speed in place of a disk, and
+was able to prove that the rotation of such spheres produced a
+magnetic field similar to that due to a circular current and agreeing
+numerically with the theoretical value. It has been shown
+by J.J. Thomson (<i>Phil. Mag.</i>, 1881, 2, p. 236) and O. Heaviside
+(<i>Electrical Papers</i>, vol. ii. p. 205) that an electrified sphere,
+moving with a velocity v and carrying a quantity of electricity
+q, should produce a magnetic force H, at a point at a distance
+&rho; from the centre of the sphere, equal to qv sin &theta;/&rho;², where &theta;
+is the angle between the direction of &rho; and the motion of the
+sphere. Adams found the field produced by a known electric
+charge rotating at a known speed had a strength not very
+different from that predetermined by the above formula. An
+observation recorded by R.W. Wood (<i>Phil. Mag.</i>, 1902, 2, p. 659)
+provides a confirmatory fact. He noticed that if carbon-dioxide
+strongly compressed in a steel bottle is allowed to escape suddenly
+the cold produced solidifies some part of the gas, and the issuing
+jet is full of particles of carbon-dioxide snow. These by friction
+against the nozzle are electrified positively. Wood caused the
+jet of gas to pass through a glass tube 2.5 mm. in diameter,
+and found that these particles of electrified snow were blown
+through it with a velocity of 2000 ft. a second. Moreover, he
+found that a magnetic needle hung near the tube was deflected
+as if held near an electric current. Hence the positively electrified
+particles in motion in the tube create a magnetic field round it.</p>
+
+<p><i>Nature of an Electric Current.</i>&mdash;The question, What is an
+electric current? is involved in the larger question of the nature
+of electricity. Modern investigations have shown that negative
+electricity is identical with the electrons or corpuscles which are
+components of the chemical atom (see <span class="sc"><a href="#artlinks">Matter</a></span> and <span class="sc"><a href="#ar63">Electricity</a></span>).
+Certain lines of argument lead to the conclusion that a solid
+conductor is not only composed of chemical atoms, but that there
+is a certain proportion of free electrons present in it, the electronic
+density or number per unit of volume being determined by
+the material, its temperature and other physical conditions. If
+any cause operates to add or remove electrons at one point there
+is an immediate diffusion of electrons to re-establish equilibrium,
+and this electronic movement constitutes an electric current.
+This hypothesis explains the reason for the identity between the
+laws of diffusion of matter, of heat and of electricity. Electromotive
+force is then any cause making or tending to make an
+inequality of electronic density in conductors, and may arise
+from differences of temperature, <i>i.e.</i> thermoelectromotive force
+<span class="pagenum"><a name="page217" id="page217"></a>217</span>
+(see <span class="sc"><a href="#artlinks">Thermoelectricity</a></span>), or from chemical action when part
+of the circuit is an electrolytic conductor, or from the movement
+of lines of magnetic force across the conductor.</p>
+
+<div class="condensed">
+<p><span class="sc">Bibliography.</span>&mdash;For additional information the reader may be
+referred to the following books: M. Faraday, <i>Experimental Researches
+in Electricity</i> (3 vols., London, 1839, 1844, 1855); J. Clerk Maxwell,
+<i>Electricity and Magnetism</i> (2 vols., Oxford, 1892); W. Watson and
+S.H. Burbury, <i>Mathematical Theory of Electricity and Magnetism</i>,
+vol. ii. (Oxford, 1889); E. Mascart and J. Joubert, <i>A Treatise on
+Electricity and Magnetism</i> (2 vols., London, 1883); A. Hay, <i>Alternating
+Currents</i> (London, 1905); W.G. Rhodes, <i>An Elementary Treatise
+on Alternating Currents</i> (London, 1902); D.C. Jackson and J.P.
+Jackson, <i>Alternating Currents and Alternating Current Machinery</i>
+(1896, new ed. 1903); S.P. Thompson, <i>Polyphase Electric Currents</i>
+(London, 1900); <i>Dynamo-Electric Machinery</i>, vol. ii., &ldquo;Alternating
+Currents&rdquo; (London, 1905); E.E. Fournier d&rsquo;Albe, <i>The Electron
+Theory</i> (London, 1906).</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1j" id="ft1j" href="#fa1j"><span class="fn">1</span></a> See J.A. Fleming, <i>The Alternate Current Transformer</i>, vol. i.
+p. 519.</p>
+
+<p><a name="ft2j" id="ft2j" href="#fa2j"><span class="fn">2</span></a> See Maxwell, <i>Electricity and Magnetism</i>, vol. ii. chap. ii.</p>
+
+<p><a name="ft3j" id="ft3j" href="#fa3j"><span class="fn">3</span></a> See Maxwell, <i>Electricity and Magnetism</i>, vol. ii. 642.</p>
+
+<p><a name="ft4j" id="ft4j" href="#fa4j"><span class="fn">4</span></a> <i>Experimental Researches</i>, vol. i. ser. 1.</p>
+
+<p><a name="ft5j" id="ft5j" href="#fa5j"><span class="fn">5</span></a> See Maxwell, <i>Electricity and Magnetism</i>, vol. ii. § 542, p. 178.</p>
+
+<p><a name="ft6j" id="ft6j" href="#fa6j"><span class="fn">6</span></a> See W.G. Rhodes, <i>An Elementary Treatise on Alternating Currents</i>
+(London, 1902), chap. vii.</p>
+
+<p><a name="ft7j" id="ft7j" href="#fa7j"><span class="fn">7</span></a> See J.A. Fleming, &ldquo;Problems on the Distribution of Electric
+Currents in Networks of Conductors,&rdquo; <i>Phil. Mag</i>. (1885), or Proc.
+Phys. Soc. Lond. (1885), 7; also Maxwell, <i>Electricity and Magnetism</i>
+(2nd ed.), vol. i. p. 374, § 280, 282b.</p>
+
+<p><a name="ft8j" id="ft8j" href="#fa8j"><span class="fn">8</span></a> See <i>Berl. Acad. Ber.</i>, 1876, p. 211; also H.A. Rowland and C.T.
+Hutchinson, &ldquo;On the Electromagnetic Effect of Convection Currents,&rdquo;
+<i>Phil. Mag.</i>, 1889, 27, p. 445.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROLIER,<a name="ar69" id="ar69"></a></span> a fixture, usually pendent from the ceiling,
+for holding electric lamps. The word is analogous to chandelier,
+from which indeed it was formed.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROLYSIS<a name="ar70" id="ar70"></a></span> (formed from Gr. <span class="grk" title="lyein">&#955;&#973;&#949;&#953;&#957;</span>, to loosen). When
+the passage of an electric current through a substance is accompanied
+by definite chemical changes which are independent
+of the heating effects of the current, the process is known as
+<i>electrolysis</i>, and the substance is called an <i>electrolyte</i>. As an
+example we may take the case of a solution of a salt such as
+copper sulphate in water, through which an electric current is
+passed between copper plates. We shall then observe the following
+phenomena. (1) The bulk of the solution is unaltered,
+except that its temperature may be raised owing to the usual
+heating effect which is proportional to the square of the strength
+of the current. (2) The copper plate by which the current is
+said to enter the solution, <i>i.e.</i> the plate attached to the so-called
+positive terminal of the battery or other source of current, dissolves
+away, the copper going into solution as copper sulphate.
+(3) Copper is deposited on the surface of the other plate, being
+obtained from the solution. (4) Changes in concentration are
+produced in the neighbourhood of the two plates or electrodes.
+In the case we have chosen, the solution becomes stronger near
+the anode, or electrode at which the current enters, and weaker
+near the cathode, or electrode at which it leaves the solution.
+If, instead of using copper electrodes, we take plates of platinum,
+copper is still deposited on the cathode; but, instead of the
+anode dissolving, free sulphuric acid appears in the neighbouring
+solution, and oxygen gas is evolved at the surface of the platinum
+plate.</p>
+
+<p>With other electrolytes similar phenomena appear, though
+the primary chemical changes may be masked by secondary
+actions. Thus, with a dilute solution of sulphuric acid and
+platinum electrodes, hydrogen gas is evolved at the cathode,
+while, as the result of a secondary action on the anode, sulphuric
+acid is there re-formed, and oxygen gas evolved. Again, with
+the solution of a salt such as sodium chloride, the sodium, which
+is primarily liberated at the cathode, decomposes the water and
+evolves hydrogen, while the chlorine may be evolved as such,
+may dissolve the anode, or may liberate oxygen from the water,
+according to the nature of the plate and the concentration of
+the solution.</p>
+
+<p><i>Early History of Electrolysis.</i>&mdash;Alessandro Volta of Pavia
+discovered the electric battery in the year 1800, and thus placed
+the means of maintaining a steady electric current in the hands
+of investigators, who, before that date, had been restricted to
+the study of the isolated electric charges given by frictional
+electric machines. Volta&rsquo;s cell consists essentially of two plates
+of different metals, such as zinc and copper, connected by an
+electrolyte such as a solution of salt or acid. Immediately on
+its discovery intense interest was aroused in the new invention,
+and the chemical effects of electric currents were speedily
+detected. W. Nicholson and Sir A. Carlisle found that hydrogen
+and oxygen were evolved at the surfaces of gold and platinum
+wires connected with the terminals of a battery and dipped in
+water. The volume of the hydrogen was about double that of
+the oxygen, and, since this is the ratio in which these elements
+are combined in water, it was concluded that the process consisted
+essentially in the decomposition of water. They also
+noticed that a similar kind of chemical action went on in the
+battery itself. Soon afterwards, William Cruickshank decomposed
+the magnesium, sodium and ammonium chlorides, and
+precipitated silver and copper from their solutions&mdash;an observation
+which led to the process of electroplating. He also found
+that the liquid round the anode became acid, and that round
+the cathode alkaline. In 1804 W. Hisinger and J.J. Berzelius
+stated that neutral salt solutions could be decomposed by
+electricity, the acid appearing at one pole and the metal at the
+other. This observation showed that nascent hydrogen was
+not, as had been supposed, the primary cause of the separation
+of metals from their solutions, but that the action consisted
+in a direct decomposition into metal and acid. During the
+earliest investigation of the subject it was thought that, since
+hydrogen and oxygen were usually evolved, the electrolysis of
+solutions of acids and alkalis was to be regarded as a direct
+decomposition of water. In 1806 Sir Humphry Davy proved
+that the formation of acid and alkali when water was electrolysed
+was due to saline impurities in the water. He had shown
+previously that decomposition of water could be effected although
+the two poles were placed in separate vessels connected by
+moistened threads. In 1807 he decomposed potash and soda,
+previously considered to be elements, by passing the current
+from a powerful battery through the moistened solids, and thus
+isolated the metals potassium and sodium.</p>
+
+<p>The electromotive force of Volta&rsquo;s simple cell falls off rapidly
+when the cell is used, and this phenomenon was shown to be
+due to the accumulation at the metal plates of the products of
+chemical changes in the cell itself. This reverse electromotive
+force of polarization is produced in all electrolytes when the
+passage of the current changes the nature of the electrodes.
+In batteries which use acids as the electrolyte, a film of
+hydrogen tends to be deposited on the copper or platinum
+electrode; but, to obtain a constant electromotive force, several
+means were soon devised of preventing the formation of the film.
+Constant cells may be divided into two groups, according as
+their action is chemical (as in the bichromate cell, where the
+hydrogen is converted into water by an oxidizing agent placed
+in a porous pot round the carbon plate) or electrochemical (as
+in Daniell&rsquo;s cell, where a copper plate is surrounded by a solution
+of copper sulphate, and the hydrogen, instead of being liberated,
+replaces copper, which is deposited on the plate from the solution).</p>
+
+<table class="flt" style="float: right; width: +50px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:302px; height:197px" src="images/img217.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span></td></tr></table>
+
+<p><i>Faraday&rsquo;s Laws.</i>&mdash;The first exact quantitative study of electrolytic
+phenomena was made about 1830 by Michael Faraday
+(<i>Experimental Researches</i>, 1833). When an electric current flows
+round a circuit, there is no accumulation of electricity anywhere
+in the circuit, hence the current strength is everywhere
+the same, and we may picture the current as analogous
+to the flow of an incompressible fluid. Acting on this view,
+Faraday set himself to examine the relation between the flow
+of electricity round the circuit and the amount of chemical
+decomposition. He passed the current driven by a voltaic
+battery ZnPt (fig. 1) through two branches containing the two
+electrolytic cells A and
+B. The reunited current
+was then led
+through another cell C,
+in which the strength of
+the current must be the
+sum of those in the
+arms A and B. Faraday
+found that the mass of
+substance liberated at
+the electrodes in the cell
+C was equal to the sum
+of the masses liberated
+in the cells A and B. He also found that, for the same current,
+the amount of chemical action was independent of the size of
+the electrodes and proportional to the time that the current
+flowed. Regarding the current as the passage of a certain
+amount of electricity per second, it will be seen that the results
+<span class="pagenum"><a name="page218" id="page218"></a>218</span>
+of all these experiments may be summed up in the statement
+that the amount of chemical action is proportional to the
+quantity of electricity which passes through the cell.</p>
+
+<p>Faraday&rsquo;s next step was to pass the same current through
+different electrolytes in series. He found that the amounts of
+the substances liberated in each cell were proportional to the
+chemical equivalent weights of those substances. Thus, if the
+current be passed through dilute sulphuric acid between hydrogen
+electrodes, and through a solution of copper sulphate, it will
+be found that the mass of hydrogen evolved in the first cell is
+to the mass of copper deposited in the second as 1 is to 31.8.
+Now this ratio is the same as that which gives the relative
+chemical equivalents of hydrogen and copper, for 1 gramme of
+hydrogen and 31.8 grammes of copper unite chemically with
+the same weight of any acid radicle such as chlorine or the
+sulphuric group, SO<span class="su">4</span>. Faraday examined also the electrolysis
+of certain fused salts such as lead chloride and silver chloride.
+Similar relations were found to hold and the amounts of chemical
+change to be the same for the same electric transfer as in the
+case of solutions.</p>
+
+<p>We may sum up the chief results of Faraday&rsquo;s work in the
+statements known as Faraday&rsquo;s laws: The mass of substance
+liberated from an electrolyte by the passage of a current is
+proportional (1) to the total quantity of electricity which passes
+through the electrolyte, and (2) to the chemical equivalent
+weight of the substance liberated.</p>
+
+<p>Since Faraday&rsquo;s time his laws have been confirmed by modern
+research, and in favourable cases have been shown to hold good
+with an accuracy of at least one part in a thousand. The principal
+object of this more recent research has been the determination
+of the quantitative amount of chemical change associated with
+the passage for a given time of a current of strength known in
+electromagnetic units. It is found that the most accurate and
+convenient apparatus to use is a platinum bowl filled with a
+solution of silver nitrate containing about fifteen parts of the
+salt to one hundred of water. Into the solution dips a silver
+plate wrapped in filter paper, and the current is passed from the
+silver plate as anode to the bowl as cathode. The bowl is
+weighed before and after the passage of the current, and the
+increase gives the mass of silver deposited. The mean result
+of the best determinations shows that when a current of one
+ampere is passed for one second, a mass of silver is deposited
+equal to 0.001118 gramme. So accurate and convenient is
+this determination that it is now used conversely as a practical
+definition of the ampere, which (defined theoretically in terms
+of magnetic force) is defined practically as the current which in
+one second deposits 1.118 milligramme of silver.</p>
+
+<p>Taking the chemical equivalent weight of silver, as determined
+by chemical experiments, to be 107.92, the result described gives
+as the electrochemical equivalent of an ion of unit chemical
+equivalent the value 1.036 × 10<span class="sp">&minus;5</span>. If, as is now usual, we take
+the equivalent weight of oxygen as our standard and call it 16,
+the equivalent weight of hydrogen is 1.008, and its electrochemical
+equivalent is 1.044 × 10<span class="sp">&minus;5</span>. The electrochemical equivalent
+of any other substance, whether element or compound, may
+be found by multiplying its chemical equivalent by 1.036 × 10<span class="sp">&minus;5</span>.
+If, instead of the ampere, we take the C.G.S. electromagnetic
+unit of current, this number becomes 1.036 × 10<span class="sp">&minus;4</span>.</p>
+
+<p><i>Chemical Nature of the Ions.</i>&mdash;A study of the products of
+decomposition does not necessarily lead directly to a knowledge
+of the ions actually employed in carrying the current through
+the electrolyte. Since the electric forces are active throughout
+the whole solution, all the ions must come under its influence
+and therefore move, but their separation from the electrodes
+is determined by the electromotive force needed to liberate them.
+Thus, as long as every ion of the solution is present in the layer
+of liquid next the electrode, the one which responds to the least
+electromotive force will alone be set free. When the amount of
+this ion in the surface layer becomes too small to carry all the
+current across the junction, other ions must also be used, and
+either they or their secondary products will appear also at the
+electrode. In aqueous solutions, for instance, a few hydrogen
+(H) and hydroxyl (OH) ions derived from the water are always
+present, and will be liberated if the other ions require a higher
+decomposition voltage and the current be kept so small that
+hydrogen and hydroxyl ions can be formed fast enough to carry
+all the current across the junction between solution and electrode.</p>
+
+<p>The issue is also obscured in another way. When the ions are
+set free at the electrodes, they may unite with the substance
+of the electrode or with some constituent of the solution to
+form secondary products. Thus the hydroxyl mentioned above
+decomposes into water and oxygen, and the chlorine produced
+by the electrolysis of a chloride may attack the metal of the
+anode. This leads us to examine more closely the part played
+by water in the electrolysis of aqueous solutions. Distilled
+water is a very bad conductor, though, even when great care is
+taken to remove all dissolved bodies, there is evidence to show
+that some part of the trace of conductivity remaining is due to
+the water itself. By careful redistillation F. Kohlrausch has
+prepared water of which the conductivity compared with that
+of mercury was only 0.40 × 10<span class="sp">&minus;11</span> at 18° C. Even here some
+little impurity was present, and the conductivity of chemically
+pure water was estimated by thermodynamic reasoning as
+0.36 × 10<span class="sp">&minus;11</span> at 18° C. As we shall see later, the conductivity of
+very dilute salt solutions is proportional to the concentration, so
+that it is probable that, in most cases, practically all the current
+is carried by the salt. At the electrodes, however, the small
+quantity of hydrogen and hydroxyl ions from the water are
+liberated first in cases where the ions of the salt have a higher
+decomposition voltage. The water being present in excess, the
+hydrogen and hydroxyl are re-formed at once and therefore are
+set free continuously. If the current be so strong that new
+hydrogen and hydroxyl ions cannot be formed in time, other
+substances are liberated; in a solution of sulphuric acid a strong
+current will evolve sulphur dioxide, the more readily as the
+concentration of the solution is increased. Similar phenomena
+are seen in the case of a solution of hydrochloric acid. When
+the solution is weak, hydrogen and oxygen are evolved; but,
+as the concentration is increased, and the current raised, more
+and more chlorine is liberated.</p>
+
+<div class="condensed">
+<p>An interesting example of secondary action is shown by the
+common technical process of electroplating with silver from a bath
+of potassium silver cyanide. Here the ions are potassium and the
+group Ag(CN)<span class="su">2</span>.<a name="fa1k" id="fa1k" href="#ft1k"><span class="sp">1</span></a> Each potassium ion as it reaches the cathode
+precipitates silver by reacting with the solution in accordance with
+the chemical equation</p>
+
+<p class="center">K + KAg(CN)<span class="su">2</span> = 2KCN + Ag,</p>
+
+<p class="noind">while the anion Ag(CN)<span class="su">2</span> dissolves an atom of silver from the anode,
+and re-forms the complex cyanide KAg(CN)<span class="su">2</span> by combining with the
+2KCN produced in the reaction described in the equation. If the
+anode consist of platinum, cyanogen gas is evolved thereat from the
+anion Ag(CN)<span class="su">2</span>, and the platinum becomes covered with the insoluble
+silver cyanide, AgCN, which soon stops the current. The coating of
+silver obtained by this process is coherent and homogeneous, while
+that deposited from a solution of silver nitrate, as the result of the
+primary action of the current, is crystalline and easily detached.</p>
+
+<p>In the electrolysis of a concentrated solution of sodium acetate,
+hydrogen is evolved at the cathode and a mixture of ethane and
+carbon dioxide at the anode. According to H. Jahn,<a name="fa2k" id="fa2k" href="#ft2k"><span class="sp">2</span></a> the processes
+at the anode can be represented by the equations</p>
+
+<table class="reg" summary="poem"><tr><td> <div class="poemr">
+<p>2CH<span class="su">3</span>·COO + H<span class="su">2</span>O = 2CH<span class="su">3</span>·COOH + O</p>
+<p>2CH<span class="su">3</span>·COOH + O = C<span class="su">2</span>H<span class="su">6</span> + 2CO<span class="su">2</span> + H<span class="su">2</span>O.</p>
+</div> </td></tr></table>
+
+<p class="noind">The hydrogen at the cathode is developed by the secondary action</p>
+
+<p class="center">2Na + 2H<span class="su">2</span>O = 2NaOH + H<span class="su">2</span>.</p>
+
+<p>Many organic compounds can be prepared by taking advantage of
+secondary actions at the electrodes, such as reduction by the cathodic
+hydrogen, or oxidation at the anode (see <span class="sc"><a href="#ar66">Electrochemistry</a></span>).</p>
+
+<p>It is possible to distinguish between double salts and salts of
+compound acids. Thus J.W. Hittorf showed that when a current
+was passed through a solution of sodium platino-chloride, the
+platinum appeared at the anode. The salt must therefore be derived
+from an acid, chloroplatinic acid, H<span class="su">2</span>PtCl<span class="su">6</span>, and have the formula
+Na<span class="su">2</span>PtCl<span class="su">6</span>, the ions being Na and PtCl<span class="su">6</span>&rdquo;, for if it were a double salt
+it would decompose as a mixture of sodium chloride and platinum
+chloride and both metals would go to the cathode.</p>
+</div>
+
+<p><span class="pagenum"><a name="page219" id="page219"></a>219</span></p>
+
+<p><i>Early Theories of Electrolysis.</i>&mdash;The obvious phenomena to be
+explained by any theory of electrolysis are the liberation of the
+products of chemical decomposition at the two electrodes while
+the intervening liquid is unaltered. To explain these facts,
+Theodor Grotthus (1785-1822) in 1806 put forward an hypothesis
+which supposed that the opposite chemical constituents of an
+electrolyte interchanged partners all along the line between the
+electrodes when a current passed. Thus, if the molecule of a
+substance in solution is represented by AB, Grotthus considered
+a chain of AB molecules to exist from one electrode to the other.
+Under the influence of an applied electric force, he imagined that
+the B part of the first molecule was liberated at the anode, and
+that the A part thus isolated united with the B part of the second
+molecule, which, in its turn, passed on its A to the B of the
+third molecule. In this manner, the B part of the last molecule
+of the chain was seized by the A of the last molecule but one, and
+the A part of the last molecule liberated at the surface of the
+cathode.</p>
+
+<p>Chemical phenomena throw further light on this question.
+If two solutions containing the salts AB and CD be mixed,
+double decomposition is found to occur, the salts AD and CB
+being formed till a certain part of the first pair of substances
+is transformed into an equivalent amount of the second pair.
+The proportions between the four salts AB, CD, AD and CB,
+which exist finally in solution, are found to be the same whether
+we begin with the pair AB and CD or with the pair AD and CB.
+To explain this result, chemists suppose that both changes can
+occur simultaneously, and that equilibrium results when the rate
+at which AB and CD are transformed into AD and CB is the same
+as the rate at which the reverse change goes on. A freedom of
+interchange is thus indicated between the opposite parts of the
+molecules of salts in solution, and it follows reasonably that with
+the solution of a single salt, say sodium chloride, continual
+interchanges go on between the sodium and chlorine parts of the
+different molecules.</p>
+
+<p>These views were applied to the theory of electrolysis by
+R.J.E. Clausius. He pointed out that it followed that the
+electric forces did not cause the interchanges between the opposite
+parts of the dissolved molecules but only controlled their direction.
+Interchanges must be supposed to go on whether a current
+passes or not, the function of the electric forces in electrolysis
+being merely to determine in what direction the parts of the
+molecules shall work their way through the liquid and to effect
+actual separation of these parts (or their secondary products)
+at the electrodes. This conclusion is supported also by the
+evidence supplied by the phenomena of electrolytic conduction
+(see <span class="sc"><a href="#artlinks">Conduction, Electric</a></span>, § II.). If we eliminate the reverse
+electromotive forces of polarization at the two electrodes, the conduction
+of electricity through electrolytes is found to conform
+to Ohm&rsquo;s law; that is, once the polarization is overcome, the
+current is proportional to the electromotive force applied to
+the bulk of the liquid. Hence there can be no reverse forces of
+polarization inside the liquid itself, such forces being confined
+to the surface of the electrodes. No work is done in separating
+the parts of the molecules from each other. This result again
+indicates that the parts of the molecules are effectively separate
+from each other, the function of the electric forces being merely
+directive.</p>
+
+<table class="flt" style="float: right; width: 305px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:265px; height:68px" src="images/img219.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p><i>Migration of the Ions.</i>&mdash;The opposite parts of an electrolyte,
+which work their way through the liquid under the action of the
+electric forces, were named by Faraday the ions&mdash;the travellers.
+The changes of concentration which occur in the solution near
+the two electrodes were referred by W. Hittorf (1853) to the
+unequal speeds with which he supposed the two opposite ions
+to travel. It is clear that, when two opposite streams of ions
+move past each other, equivalent quantities are liberated at the
+two ends of the system. If the ions move at equal rates, the salt
+which is decomposed to supply the ions liberated must be taken
+equally from the neighbourhood of the two electrodes. But if
+one ion, say the anion, travels faster through the liquid than
+the other, the end of the solution from which it comes will be
+more exhausted of salt than the end towards which it goes.
+If we assume that no other cause is at work, it is easy to prove
+that, with non-dissolvable electrodes, the ratio of salt lost at
+the anode to the salt lost at the cathode must be equal to the
+ratio of the velocity of the cation to the velocity of the anion.
+This result may be illustrated by fig. 2. The black circles represent
+one ion and the white
+circles the other. If the black
+ions move twice as fast as the
+white ones, the state of things
+after the passage of a current
+will be represented by the
+lower part of the figure. Here the middle part of the solution is
+unaltered and the number of ions liberated is the same at either
+end, but the amount of salt left at one end is less than that at
+the other. On the right, towards which the faster ion travels,
+five molecules of salt are left, being a loss of two from the original
+seven. On the left, towards which the slower ion moves, only
+three molecules remain&mdash;a loss of four. Thus, the ratio of the
+losses at the two ends is two to one&mdash;the same as the ratio of
+the assumed ionic velocities. It should be noted, however, that
+another cause would be competent to explain the unequal
+dilution of the two solutions. If either ion carried with it some
+of the unaltered salt or some of the solvent, concentration or
+dilution of the liquid would be produced where the ion was
+liberated. There is reason to believe that in certain cases such
+complex ions do exist, and interfere with the results of the
+differing ionic velocities.</p>
+
+<p>Hittorf and many other observers have made experiments
+to determine the unequal dilution of a solution round the two
+electrodes when a current passes. Various forms of apparatus
+have been used, the principle of them all being to secure efficient
+separation of the two volumes of solution in which the changes
+occur. In some cases porous diaphragms have been employed;
+but such diaphragms introduce a new complication, for the liquid
+as a whole is pushed through them by the action of the current,
+the phenomenon being known as electric endosmose. Hence
+experiments without separating diaphragms are to be preferred,
+and the apparatus may be considered effective when a considerable
+bulk of intervening solution is left unaltered in composition.
+It is usual to express the results in terms of what is called the
+migration constant of the anion, that is, the ratio of the amount
+of salt lost by the anode vessel to the whole amount lost by both
+vessels. Thus the statement that the migration constant or
+transport number for a decinormal solution of copper sulphate
+is 0.632 implies that of every gramme of copper sulphate lost
+by a solution containing originally one-tenth of a gramme
+equivalent per litre when a current is passed through it between
+platinum electrodes, 0.632 gramme is taken from the cathode
+vessel and 0.368 gramme from the anode vessel. For certain
+concentrated solutions the transport number is found to be greater
+than unity; thus for a normal solution of cadmium iodide its
+value is 1.12. On the theory that the phenomena are wholly
+due to unequal ionic velocities this result would mean that the
+cation like the anion moved against the conventional direction
+of the current. That a body carrying a positive electric charge
+should move against the direction of the electric intensity is contrary
+to all our notions of electric forces, and we are compelled
+to seek some other explanation. An alternative hypothesis is
+given by the idea of complex ions. If some of the anions, instead
+of being simple iodine ions represented chemically by the symbol I,
+are complex structures formed by the union of iodine with unaltered
+cadmium iodide&mdash;structures represented by some such
+chemical formula as I(CdI<span class="su">2</span>), the concentration of the solution
+round the anode would be increased by the passage of an electric
+current, and the phenomena observed would be explained. It
+is found that, in such cases as this, where it seems necessary to
+imagine the existence of complex ions, the transport number
+changes rapidly as the concentration of the original solution is
+changed. Thus, diminishing the concentration of the cadmium
+iodine solution from normal to one-twentieth normal changes
+the transport number from 1.12 to 0.64. Hence it is probable
+that in cases where the transport number keeps constant with
+<span class="pagenum"><a name="page220" id="page220"></a>220</span>
+changing concentration the hypothesis of complex ions is unnecessary,
+and we may suppose that the transport number is a
+true migration constant from which the relative velocities of
+the two ions may be calculated in the matter suggested by
+Hittorf and illustrated in fig. 2. This conclusion is confirmed
+by the results of the direct visual determination of ionic velocities
+(see <span class="sc"><a href="#artlinks">Conduction, Electric</a></span>, § II.), which, in cases where the
+transport number remains constant, agree with the values
+calculated from those numbers. Many solutions in which the
+transport numbers vary at high concentration often become
+simple at greater dilution. For instance, to take the two solutions
+to which we have already referred, we have&mdash;</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcl lb rb tb">Concentration</td> <td class="tcl rb tb">2.0</td> <td class="tcl rb tb">1.5</td> <td class="tcl rb tb">1.0</td> <td class="tcl rb tb">0.5</td> <td class="tcl rb tb">0.2</td> <td class="tcl rb tb">0.1</td> <td class="tcl rb tb">0.05</td> <td class="tcl rb tb">0.02</td> <td class="tcl rb tb">0.01 normal</td></tr>
+<tr><td class="tcl lb rb">Copper sulphate transport numbers</td> <td class="tcl rb">0.72</td> <td class="tcl rb">0.714</td> <td class="tcl rb">0.696</td> <td class="tcl rb">0.668</td> <td class="tcl rb">0.643</td> <td class="tcl rb">0.632</td> <td class="tcl rb">0.626</td> <td class="tcl rb">0.62</td> <td class="tcc rb">· ·</td></tr>
+<tr><td class="tcl lb rb bb">Cadmium iodide &emsp; &rdquo;  &emsp;&emsp;&emsp; &rdquo;</td> <td class="tcl rb bb">1.22</td> <td class="tcl rb bb">1.18</td> <td class="tcl rb bb">1.12</td> <td class="tcl rb bb">1.00</td> <td class="tcl rb bb">0.83</td> <td class="tcl rb bb">0.71</td> <td class="tcl rb bb">0.64</td> <td class="tcl rb bb">0.59</td> <td class="tcl rb bb">0.56</td></tr>
+</table>
+
+<p class="noind">It is probable that in both these solutions complex ions exist at
+fairly high concentrations, but gradually gets less in number and
+finally disappear as the dilution is increased. In such salts as
+potassium chloride the ions seem to be simple throughout a wide
+range of concentration since the transport numbers for the same
+series of concentrations as those used above run&mdash;</p>
+
+<p class="center">Potassium chloride&mdash;<br />
+0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.507, 0.506.</p>
+
+<p>The next important step in the theory of the subject was made
+by F. Kohlrausch in 1879. Kohlrausch formulated a theory
+of electrolytic conduction based on the idea that, under the action
+of the electric forces, the oppositely charged ions moved in
+opposite directions through the liquid, carrying their charges
+with them. If we eliminate the polarization at the electrodes,
+it can be shown that an electrolyte possesses a definite electric
+resistance and therefore a definite conductivity. The conductivity
+gives us the amount of electricity conveyed per second
+under a definite electromotive force. On the view of the process
+of conduction described above, the amount of electricity conveyed
+per second is measured by the product of the number of ions,
+known from the concentration of the solution, the charge carried
+by each of them, and the velocity with which, on the average,
+they move through the liquid. The concentration is known,
+and the conductivity can be measured experimentally; thus
+the average velocity with which the ions move past each other
+under the existent electromotive force can be estimated. The
+velocity with which the ions move past each other is equal to
+the sum of their individual velocities, which can therefore be
+calculated. Now Hittorf&rsquo;s transport number, in the case of
+simple salts in moderately dilute solution, gives us the ratio
+between the two ionic velocities. Hence the absolute velocities
+of the two ions can be determined, and we can calculate the
+actual speed with which a certain ion moves through a given
+liquid under the action of a given potential gradient or electromotive
+force. The details of the calculation are given in the
+article <span class="sc"><a href="#artlinks">Conduction, Electric</a></span>, § II., where also will be found
+an account of the methods which have been used to measure
+the velocities of many ions by direct visual observation. The
+results go to show that, where the existence of complex ions is
+not indicated by varying transport numbers, the observed
+velocities agree with those calculated on Kohlrausch&rsquo;s theory.</p>
+
+<p><i>Dissociation Theory.</i>&mdash;The verification of Kohlrausch&rsquo;s theory
+of ionic velocity verifies also the view of electrolysis which regards
+the electric current as due to streams of ions moving in opposite
+directions through the liquid and carrying their opposite electric
+charges with them. There remains the question how the
+necessary migratory freedom of the ions is secured. As we have
+seen, Grotthus imagined that it was the electric forces which
+sheared the ions past each other and loosened the chemical
+bonds holding the opposite parts of each dissolved molecule
+together. Clausius extended to electrolysis the chemical ideas
+which looked on the opposite parts of the molecule as always
+changing partners independently of any electric force, and regarded
+the function of the current as merely directive. Still, the
+necessary freedom was supposed to be secured by interchanges
+of ions between molecules at the instants of molecular collision
+only; during the rest of the life of the ions they were regarded
+as linked to each other to form electrically neutral molecules.</p>
+
+<p>In 1887 Svante Arrhenius, professor of physics at Stockholm,
+put forward a new theory which supposed that the freedom
+of the opposite ions from each other was not a mere momentary
+freedom at the instants of molecular collision, but a more or less
+permanent freedom, the ions moving independently of each other
+through the liquid. The evidence which led Arrhenius to this
+conclusion was based on van &lsquo;t Hoff&rsquo;s work on the osmotic
+pressure of solutions (see <span class="sc"><a href="#artlinks">Solution</a></span>). If a solution, let us say
+of sugar, be confined in a closed vessel through the walls of
+which the solvent can pass but the solution cannot, the solvent
+will enter till a certain equilibrium pressure is reached. This
+equilibrium pressure is called the osmotic pressure of the solution,
+and thermodynamic theory shows that, in an ideal case of
+perfect separation between solvent and solute, it should have the
+same value as the pressure which a number of molecules equal
+to the number of solute molecules in the solution would exert if
+they could exist as a gas in a space equal to the volume of the solution,
+provided that the space was large enough (<i>i.e.</i> the solution
+dilute enough) for the intermolecular forces between the dissolved
+particles to be inappreciable. Van &lsquo;t Hoff pointed out that
+measurements of osmotic pressure confirmed this value in the
+case of dilute solutions of cane sugar.</p>
+
+<p>Thermodynamic theory also indicates a connexion between
+the osmotic pressure of a solution and the depression of its
+freezing point and its vapour pressure compared with those of the
+pure solvent. The freezing points and vapour pressures of solutions
+of sugar are also in conformity with the theoretical numbers.
+But when we pass to solutions of mineral salts and acids&mdash;to
+solutions of electrolytes in fact&mdash;we find that the observed values
+of the osmotic pressures and of the allied phenomena are greater
+than the normal values. Arrhenius pointed out that these
+exceptions would be brought into line if the ions of electrolytes
+were imagined to be separate entities each capable of producing
+its own pressure effects just as would an ordinary dissolved
+molecule.</p>
+
+<p>Two relations are suggested by Arrhenius&rsquo; theory. (1) In
+very dilute solutions of simple substances, where only one kind of
+dissociation is possible and the dissociation of the ions is complete,
+the number of pressure-producing particles necessary to produce
+the observed osmotic effects should be equal to the number of
+ions given by a molecule of the salt as shown by its electrical
+properties. Thus the osmotic pressure, or the depression of the
+freezing point of a solution of potassium chloride should, at
+extreme dilution, be twice the normal value, but of a solution
+of sulphuric acid three times that value, since the potassium
+salt contains two ions and the acid three. (2) As the concentration
+of the solutions increases, the ionization as measured
+electrically and the dissociation as measured osmotically might
+decrease more or less together, though, since the thermodynamic
+theory only holds when the solution is so dilute that the dissolved
+particles are beyond each other&rsquo;s sphere of action, there is much
+doubt whether this second relation is valid through any appreciable
+range of concentration.</p>
+
+<p>At present, measurements of freezing point are more convenient
+and accurate than those of osmotic pressure, and we may
+test the validity of Arrhenius&rsquo; relations by their means. The
+theoretical value for the depression of the freezing point of a
+dilute solution per gramme-equivalent of solute per litre is
+1.857° C. Completely ionized solutions of salts with two ions
+should give double this number or 3.714°, while electrolytes
+with three ions should have a value of 5.57°.</p>
+
+<p>The following results are given by H.B. Loomis for the
+concentration of 0.01 gramme-molecule of salt to one thousand
+grammes of water. The salts tabulated are those of which the
+<span class="pagenum"><a name="page221" id="page221"></a>221</span>
+equivalent conductivity reaches a limiting value indicating that
+complete ionization is reached as dilution is increased. With
+such salts alone is a valid comparison possible.</p>
+
+<table class="ws f90" summary="Contents">
+
+<tr><td class="tcc" colspan="4"><i>Molecular Depressions of the Freezing Point.</i></td></tr>
+<tr><td class="tcc pt1" colspan="4"><i>Electrolytes with two Ions.</i></td></tr>
+
+<tr><td class="tcl">Potassium chloride</td> <td class="tcc">3.60</td> <td class="tcl">Nitric acid</td> <td class="tcc">3.73</td></tr>
+<tr><td class="tcl">Sodium chloride</td> <td class="tcc">3.67</td> <td class="tcl">Potassium nitrate</td> <td class="tcc">3.46</td></tr>
+<tr><td class="tcl">Potassium hydrate</td> <td class="tcc">3.71</td> <td class="tcl">Sodium nitrate</td> <td class="tcc">3.55</td></tr>
+<tr><td class="tcl">Hydrochloric acid</td> <td class="tcc">3.61</td> <td class="tcl">Ammonium nitrate</td> <td class="tcc">3.58</td></tr>
+
+<tr><td class="tcc pt1" colspan="4"><i>Electrolytes with three Ions.</i></td></tr>
+
+<tr><td class="tcl">Sulphuric acid</td> <td class="tcc">4.49</td> <td class="tcl">Calcium chloride</td> <td class="tcc">5.04</td></tr>
+<tr><td class="tcl">Sodium sulphate</td> <td class="tcc">5.09</td> <td class="tcl">Magnesium chloride</td> <td class="tcc">5.08</td></tr>
+</table>
+
+<p>At the concentration used by Loomis the electrical conductivity
+indicates that the ionization is not complete, particularly
+in the case of the salts with divalent ions in the second list.
+Allowing for incomplete ionization the general concordance
+of these numbers with the theoretical ones is very striking.</p>
+
+<p>The measurements of freezing points of solutions at the extreme
+dilution necessary to secure complete ionization is a matter of
+great difficulty, and has been overcome only in a research
+initiated by E.H. Griffiths.<a name="fa3k" id="fa3k" href="#ft3k"><span class="sp">3</span></a> Results have been obtained for
+solutions of sugar, where the experimental number is 1.858,
+and for potassium chloride, which gives a depression of 3.720.
+These numbers agree with those indicated by theory, viz. 1.857
+and 3.714, with astonishing exactitude. We may take Arrhenius&rsquo;
+first relation as established for the case of potassium chloride.</p>
+
+<p>The second relation, as we have seen, is not a strict consequence
+of theory, and experiments to examine it must be treated as
+an investigation of the limits within which solutions are dilute
+within the thermodynamic sense of the word, rather than as a
+test of the soundness of the theory. It is found that divergence
+has begun before the concentration has become great enough
+to enable freezing points to be measured with any ordinary
+apparatus. The freezing point curve usually lies below the
+electrical one, but approaches it as dilution is increased.<a name="fa4k" id="fa4k" href="#ft4k"><span class="sp">4</span></a></p>
+
+<p>Returning once more to the consideration of the first relation,
+which deals with the comparison between the number of ions and
+the number of pressure-producing particles in dilute solution,
+one caution is necessary. In simple substances like potassium
+chloride it seems evident that one kind of dissociation only
+is possible. The electrical phenomena show that there are two
+ions to the molecule, and that these ions are electrically charged.
+Corresponding with this result we find that the freezing point of
+dilute solutions indicates that two pressure-producing particles
+per molecule are present. But the converse relation does not
+necessarily follow. It would be possible for a body in solution
+to be dissociated into non-electrical parts, which would give
+osmotic pressure effects twice or three times the normal value,
+but, being uncharged, would not act as ions and impart electrical
+conductivity to the solution. L. Kahlenberg (<i>Jour. Phys. Chem.</i>,
+1901, v. 344, 1902, vi. 43) has found that solutions of diphenylamine
+in methyl cyanide possess an excess of pressure-producing
+particles and yet are non-conductors of electricity. It is possible
+that in complicated organic substances we might have two
+kinds of dissociation, electrical and non-electrical, occurring
+simultaneously, while the possibility of the association of molecules
+accompanied by the electrical dissociation of some of them
+into new parts should not be overlooked. It should be pointed
+out that no measurements on osmotic pressures or freezing points
+can do more than tell us that an excess of particles is present;
+such experiments can throw no light on the question whether
+or not those particles are electrically charged. That question
+can only be answered by examining whether or not the particles
+move in an electric field.</p>
+
+<p>The dissociation theory was originally suggested by the
+osmotic pressure relations. But not only has it explained
+satisfactorily the electrical properties of solutions, but it seems
+to be the only known hypothesis which is consistent with the
+experimental relation between the concentration of a solution
+and its electrical conductivity (see <span class="sc"><a href="#artlinks">Conduction, Electric,</a></span>
+§ II., &ldquo;Nature of Electrolytes&rdquo;). It is probable that the
+electrical effects constitute the strongest arguments in favour
+of the theory. It is necessary to point out that the dissociated
+ions of such a body as potassium chloride are not in the same
+condition as potassium and chlorine in the free state. The ions
+are associated with very large electric charges, and, whatever
+their exact relations with those charges may be, it is certain that
+the energy of a system in such a state must be different from
+its energy when unelectrified. It is not unlikely, therefore,
+that even a compound as stable in the solid form as potassium
+chloride should be thus dissociated when dissolved. Again,
+water, the best electrolytic solvent known, is also the body of
+the highest specific inductive capacity (dielectric constant),
+and this property, to whatever cause it may be due, will reduce
+the forces between electric charges in the neighbourhood, and
+may therefore enable two ions to separate.</p>
+
+<p>This view of the nature of electrolytic solutions at once explains
+many well-known phenomena. Other physical properties of
+these solutions, such as density, colour, optical rotatory power,
+&amp;c., like the conductivities, are <i>additive</i>, <i>i.e.</i> can be calculated
+by adding together the corresponding properties of the parts.
+This again suggests that these parts are independent of each other.
+For instance, the colour of a salt solution is the colour obtained
+by the superposition of the colours of the ions and the colour
+of any undissociated salt that may be present. All copper salts
+in dilute solution are blue, which is therefore the colour of the
+copper ion. Solid copper chloride is brown or yellow, so that its
+concentrated solution, which contains both ions and undissociated
+molecules, is green, but changes to blue as water is added and
+the ionization becomes complete. A series of equivalent solutions
+all containing the same coloured ion have absorption spectra
+which, when photographed, show identical absorption bands
+of equal intensity.<a name="fa5k" id="fa5k" href="#ft5k"><span class="sp">5</span></a> The colour changes shown by many substances
+which are used as indicators (<i>q.v.</i>) of acids or alkalis can
+be explained in a similar way. Thus para-nitrophenol has colourless
+molecules, but an intensely yellow negative ion. In neutral,
+and still more in acid solutions, the dissociation of the indicator
+is practically nothing, and the liquid is colourless. If an alkali
+is added, however, a highly dissociated salt of para-nitrophenol
+is formed, and the yellow colour is at once evident. In other
+cases, such as that of litmus, both the ion and the undissociated
+molecule are coloured, but in different ways.</p>
+
+<p>Electrolytes possess the power of coagulating solutions of
+colloids such as albumen and arsenious sulphide. The mean
+values of the relative coagulative powers of sulphates of mono-,
+di-, and tri-valent metals have been shown experimentally to
+be approximately in the ratios 1 : 35 : 1023. The dissociation
+theory refers this to the action of electric charges carried by the
+free ions. If a certain minimum charge must be collected in
+order to start coagulation, it will need the conjunction of 6n
+monovalent, or 3n divalent, to equal the effect of 2n tri-valent
+ions. The ratios of the coagulative powers can thus be calculated
+to be 1 : x : x², and putting x = 32 we get 1 : 32 : 1024, a satisfactory
+agreement with the numbers observed.<a name="fa6k" id="fa6k" href="#ft6k"><span class="sp">6</span></a></p>
+
+<p>The question of the application of the dissociation theory to
+the case of fused salts remains. While it seems clear that the
+conduction in this case is carried on by ions similar to those of
+solutions, since Faraday&rsquo;s laws apply equally to both, it does
+not follow necessarily that semi-permanent dissociation is the
+only way to explain the phenomena. The evidence in favour
+of dissociation in the case of solutions does not apply to fused
+salts, and it is possible that, in their case, a series of molecular
+interchanges, somewhat like Grotthus&rsquo;s chain, may represent
+the mechanism of conduction.</p>
+
+<p>An interesting relation appears when the electrolytic conductivity
+of solutions is compared with their chemical activity.
+The readiness and speed with which electrolytes react are in
+<span class="pagenum"><a name="page222" id="page222"></a>222</span>
+sharp contrast with the difficulty experienced in the case of
+non-electrolytes. Moreover, a study of the chemical relations
+of electrolytes indicates that it is always the electrolytic ions
+that are concerned in their reactions. The tests for a salt,
+potassium nitrate, for example, are the tests not for KNO<span class="su">3</span>, but
+for its ions K and NO<span class="su">3</span>, and in cases of double decomposition
+it is always these ions that are exchanged for those of other
+substances. If an element be present in a compound otherwise
+than as an ion, it is not interchangeable, and cannot be recognized
+by the usual tests. Thus neither a chlorate, which contains the
+ion ClO<span class="su">3</span>, nor monochloracetic acid, shows the reactions of
+chlorine, though it is, of course, present in both substances;
+again, the sulphates do not answer to the usual tests which
+indicate the presence of sulphur as sulphide. The chemical
+activity of a substance is a quantity which may be measured
+by different methods. For some substances it has been shown
+to be independent of the particular reaction used. It is then
+possible to assign to each body a specific coefficient of affinity.
+Arrhenius has pointed out that the coefficient of affinity of an
+acid is proportional to its electrolytic ionization.</p>
+
+<div class="condensed">
+<p>The affinities of acids have been compared in several ways.
+W. Ostwald (<i>Lehrbuch der allg. Chemie</i>, vol. ii., Leipzig, 1893) investigated
+the relative affinities of acids for potash, soda and ammonia,
+and proved them to be independent of the base used. The method
+employed was to measure the changes in volume caused by the action.
+His results are given in column I. of the following table, the affinity
+of hydrochloric acid being taken as one hundred. Another method
+is to allow an acid to act on an insoluble salt, and to measure the
+quantity which goes into solution. Determinations have been made
+with calcium oxalate, CaC<span class="su">2</span>O<span class="su">4</span> + H<span class="su">2</span>O, which is easily decomposed by
+acids, oxalic acid and a soluble calcium salt being formed. The
+affinities of acids relative to that of oxalic acid are thus found, so
+that the acids can be compared among themselves (column II.).
+If an aqueous solution of methyl acetate be allowed to stand, a slow
+decomposition goes on. This is much quickened by the presence
+of a little dilute acid, though the acid itself remains unchanged. It
+is found that the influence of different acids on this action is proportional
+to their specific coefficients of affinity. The results of this
+method are given in column III. Finally, in column IV. the electrical
+conductivities of normal solutions of the acids have been tabulated.
+A better basis of comparison would be the ratio of the actual to the
+limiting conductivity, but since the conductivity of acids is chiefly
+due to the mobility of the hydrogen ions, its limiting value is nearly
+the same for all, and the general result of the comparison would be
+unchanged.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc allb">Acid.</td> <td class="tcc allb">I.</td> <td class="tcc allb">II.</td> <td class="tcc allb">III.</td> <td class="tcc allb">IV.</td></tr>
+
+<tr><td class="tcl lb rb">Hydrochloric</td> <td class="tcr rb">100&ensp;</td> <td class="tcr rb">100&ensp;</td> <td class="tcr rb">100&ensp;</td> <td class="tcr rb">100&ensp;</td></tr>
+<tr><td class="tcl lb rb">Nitric</td> <td class="tcr rb">102&ensp;</td> <td class="tcr rb">110&ensp;</td> <td class="tcr rb">92&ensp;</td> <td class="tcr rb">99.6</td></tr>
+<tr><td class="tcl lb rb">Sulphuric</td> <td class="tcr rb">68&ensp;</td> <td class="tcr rb">67&ensp;</td> <td class="tcr rb">74&ensp;</td> <td class="tcr rb">65.1</td></tr>
+<tr><td class="tcl lb rb">Formic</td> <td class="tcr rb">4.0</td> <td class="tcr rb">2.5</td> <td class="tcr rb">1.3</td> <td class="tcr rb">1.7</td></tr>
+<tr><td class="tcl lb rb">Acetic</td> <td class="tcr rb">1.2</td> <td class="tcr rb">1.0</td> <td class="tcr rb">0.3</td> <td class="tcr rb">0.4</td></tr>
+<tr><td class="tcl lb rb">Propionic</td> <td class="tcr rb">1.1</td> <td class="tcc rb">· ·</td> <td class="tcr rb">0.3</td> <td class="tcr rb">0.3</td></tr>
+<tr><td class="tcl lb rb">Monochloracetic</td> <td class="tcr rb">7.2</td> <td class="tcr rb">5.1</td> <td class="tcr rb">4.3</td> <td class="tcr rb">4.9</td></tr>
+<tr><td class="tcl lb rb">Dichloracetic</td> <td class="tcr rb">34&ensp;</td> <td class="tcr rb">18&ensp;</td> <td class="tcr rb">23.0</td> <td class="tcr rb">25.3</td></tr>
+<tr><td class="tcl lb rb">Trichloracetic</td> <td class="tcr rb">82&ensp;</td> <td class="tcr rb">63&ensp;</td> <td class="tcr rb">&ensp;68.2</td> <td class="tcr rb">62.3</td></tr>
+<tr><td class="tcl lb rb">Malic</td> <td class="tcr rb">3.0</td> <td class="tcr rb">5.0</td> <td class="tcr rb">1.2</td> <td class="tcr rb">1.3</td></tr>
+<tr><td class="tcl lb rb">Tartaric</td> <td class="tcr rb">5.3</td> <td class="tcr rb">6.3</td> <td class="tcr rb">2.3</td> <td class="tcr rb">2.3</td></tr>
+<tr><td class="tcl lb rb bb">Succinic</td> <td class="tcr rb bb">0.1</td> <td class="tcr rb bb">0.2</td> <td class="tcr rb bb">0.5</td> <td class="tcr rb bb">0.6</td></tr>
+</table>
+
+<p>It must be remembered that, the solutions not being of quite the
+same strength, these numbers are not strictly comparable, and that
+the experimental difficulties involved in the chemical measurements
+are considerable. Nevertheless, the remarkable general agreement
+of the numbers in the four columns is quite enough to show the
+intimate connexion between chemical activity and electrical conductivity.
+We may take it, then, that only that portion of these
+bodies is chemically active which is electrolytically active&mdash;that
+ionization is necessary for such chemical activity as we are dealing
+with here, just as it is necessary for electrolytic conductivity.</p>
+
+<p>The ordinary laws of chemical equilibrium have been applied to
+the case of the dissociation of a substance into its ions. Let x be
+the number of molecules which dissociate per second when the
+number of undissociated molecules in unit volume is unity, then
+in a dilute solution where the molecules do not interfere with each
+other, xp is the number when the concentration is p. Recombination
+can only occur when two ions meet, and since the frequency with
+which this will happen is, in dilute solution, proportional to the
+square of the ionic concentration, we shall get for the number of
+molecules re-formed in one second yq² where q is the number of dissociated
+molecules in one cubic centimetre. When there is equilibrium,
+xp = yq². If &mu; be the molecular conductivity, and &mu; <span class="su">&infin;</span> its value
+at infinite dilution, the fractional number of molecules dissociated is
+&mu; / &mu; <span class="su">&infin;</span>, which we may write as &alpha;. The number of undissociated molecules
+is then 1 &minus; &alpha;, so that if V be the volume of the solution containing
+1 gramme-molecule of the dissolved substance, we get</p>
+
+<p class="center">q = &alpha; / V and p = (1 &minus; &alpha;) / V,</p>
+
+<p class="noind">hence</p>
+
+<p class="center">x (1 &minus; &alpha;) V = ya² / V²,</p>
+
+<p class="noind">and</p>
+
+<table class="math0" summary="math">
+<tr><td>&alpha;²</td>
+<td rowspan="2">=</td> <td>x</td>
+<td rowspan="2">= constant = k.</td></tr>
+<tr><td class="denom">V (1 &minus; &alpha;)</td> <td class="denom">y</td></tr></table>
+
+<p class="noind">This constant k gives a numerical value for the chemical affinity,
+and the equation should represent the effect of dilution on the
+molecular conductivity of binary electrolytes.</p>
+
+<p>In the case of substances like ammonia and acetic acid, where the
+dissociation is very small, 1 &minus; &alpha; is nearly equal to unity, and only
+varies slowly with dilution. The equation then becomes &alpha;²/V = k, or
+&alpha; = &radic;<span class="ov">(Vk)</span>, so that the molecular conductivity is proportional to the
+square root of the dilution. Ostwald has confirmed the equation
+by observation on an enormous number of weak acids (<i>Zeits.
+physikal. Chemie</i>, 1888, ii. p. 278; 1889, iii. pp. 170, 241, 369).
+Thus in the case of cyanacetic acid, while the volume V changed by
+doubling from 16 to 1024 litres, the values of k were 0.00 (376, 373,
+374, 361, 362, 361, 368). The mean values of k for other common
+acids were&mdash;formic, 0.0000214; acetic, 0.0000180; monochloracetic,
+0.00155; dichloracetic, 0.051; trichloracetic, 1.21; propionic,
+0.0000134. From these numbers we can, by help of the
+equation, calculate the conductivity of the acids for any dilution.
+The value of k, however, does not keep constant so satisfactorily in the
+case of highly dissociated substances, and empirical formulae have
+been constructed to represent the effect of dilution on them. Thus
+the values of the expressions &alpha;² / (1 &minus; &alpha;&radic;<span class="ov">V</span>) (Rudolphi, <i>Zeits. physikal.
+Chemie</i>, 1895, vol. xvii. p. 385) and &alpha;³ / (1 &minus; &alpha;)²V (van &rsquo;t Hoff, ibid.,
+1895, vol. xviii. p. 300) are found to keep constant as V changes.
+Van &rsquo;t Hoff&rsquo;s formula is equivalent to taking the frequency of dissociation
+as proportional to the square of the concentration of the
+molecules, and the frequency of recombination as proportional to
+the cube of the concentration of the ions. An explanation of the
+failure of the usual dilution law in these cases may be given if we
+remember that, while the electric forces between bodies like undissociated
+molecules, each associated with equal and opposite
+charges, will vary inversely as the fourth power of the distance, the
+forces between dissociated ions, each carrying one charge only, will
+be inversely proportional to the square of the distance. The forces
+between the ions of a strongly dissociated solution will thus be considerable
+at a dilution which makes forces between undissociated
+molecules quite insensible, and at the concentrations necessary to
+test Ostwald&rsquo;s formula an electrolyte will be far from dilute in the
+thermodynamic sense of the term, which implies no appreciable
+intermolecular or interionic forces.</p>
+
+<p>When the solutions of two substances are mixed, similar considerations
+to those given above enable us to calculate the resultant
+changes in dissociation. (See Arrhenius, <i>loc. cit.</i>) The simplest
+and most important case is that of two electrolytes having one
+ion in common, such as two acids. It is evident that the undissociated
+part of each acid must eventually be in equilibrium with
+the free hydrogen ions, and, if the concentrations are not such as
+to secure this condition, readjustment must occur. In order that
+there should be no change in the states of dissociation on mixing,
+it is necessary, therefore, that the concentration of the hydrogen
+ions should be the same in each separate solution. Such solutions
+were called by Arrhenius &ldquo;isohydric.&rdquo; The two solutions, then,
+will so act on each other when mixed that they become isohydric.
+Let us suppose that we have one very active acid like hydrochloric,
+in which dissociation is nearly complete, another like acetic, in
+which it is very small. In order that the solutions of these should be
+isohydric and the concentrations of the hydrogen ions the same,
+we must have a very large quantity of the feebly dissociated acetic
+acid, and a very small quantity of the strongly dissociated hydrochloric,
+and in such proportions alone will equilibrium be possible.
+This explains the action of a strong acid on the salt of a weak acid.
+Let us allow dilute sodium acetate to react with dilute hydrochloric
+acid. Some acetic acid is formed, and this process will go on till
+the solutions of the two acids are isohydric: that is, till the dissociated
+hydrogen ions are in equilibrium with both. In order
+that this should hold, we have seen that a considerable quantity
+of acetic acid must be present, so that a corresponding amount of
+the salt will be decomposed, the quantity being greater the less
+the acid is dissociated. This &ldquo;replacement&rdquo; of a &ldquo;weak&rdquo; acid
+by a &ldquo;strong&rdquo; one is a matter of common observation in the chemical
+laboratory. Similar investigations applied to the general case of
+chemical equilibrium lead to an expression of exactly the same form
+as that given by C.M. Guldberg and P. Waage, which is universally
+accepted as an accurate representation of the facts.</p>
+</div>
+
+<p>The temperature coefficient of conductivity has approximately
+the same value for most aqueous salt solutions. It decreases
+both as the temperature is raised and as the concentration is
+increased, ranging from about 3.5% per degree for extremely
+dilute solutions (<i>i.e.</i> practically pure water) at 0° to about 1.5
+<span class="pagenum"><a name="page223" id="page223"></a>223</span>
+for concentrated solutions at 18°. For acids its value is usually
+rather less than for salts at equivalent concentrations. The
+influence of temperature on the conductivity of solutions depends
+on (1) the ionization, and (2) the frictional resistance of the
+liquid to the passage of the ions, the reciprocal of which is called
+the ionic fluidity. At extreme dilution, when the ionization is
+complete, a variation in temperature cannot change its amount.
+The rise of conductivity with temperature, therefore, shows
+that the fluidity becomes greater when the solution is heated.
+As the concentration is increased and un-ionized molecules are
+formed, a change in temperature begins to affect the ionization
+as well as the fluidity. But the temperature coefficient of
+conductivity is now generally less than before; thus the effect
+of temperature on ionization must be of opposite sign to its
+effect on fluidity. The ionization of a solution, then, is usually
+diminished by raising the temperature, the rise in conductivity
+being due to the greater increase in fluidity. Nevertheless, in
+certain cases, the temperature coefficient of conductivity becomes
+negative at high temperatures, a solution of phosphoric acid,
+for example, reaching a maximum conductivity at 75° C.</p>
+
+<p>The dissociation theory gives an immediate explanation of the
+fact that, in general, no heat-change occurs when two neutral
+salt solutions are mixed. Since the salts, both before and after
+mixture, exist mainly as dissociated ions, it is obvious that large
+thermal effects can only appear when the state of dissociation
+of the products is very different from that of the reagents. Let
+us consider the case of the neutralization of a base by an acid
+in the light of the dissociation theory. In dilute solution such
+substances as hydrochloric acid and potash are almost completely
+dissociated, so that, instead of representing the reaction as</p>
+
+<p class="center">HCl + KOH = KCl + H<span class="su">2</span>O,</p>
+
+<p class="noind">we must write</p>
+
+<table class="reg" summary="poem"><tr><td> <div class="poemr">
+<p>+ &emsp; &minus; &ensp; + &emsp; &minus; &emsp; + &emsp; &minus;</p>
+<p>H + Cl + K + OH = K + Cl + H<span class="su">2</span>O.</p>
+</div> </td></tr></table>
+
+<p class="noind">The ions K and Cl suffer no change, but the hydrogen of the acid
+and the hydroxyl (OH) of the potash unite to form water, which
+is only very slightly dissociated. The heat liberated, then, is
+almost exclusively that produced by the formation of water
+from its ions. An exactly similar process occurs when any
+strongly dissociated acid acts on any strongly dissociated base,
+so that in all such cases the heat evolution should be approximately
+the same. This is fully borne out by the experiments of
+Julius Thomsen, who found that the heat of neutralization of one
+gramme-molecule of a strong base by an equivalent quantity of a
+strong acid was nearly constant, and equal to 13,700 or 13,800
+calories. In the case of weaker acids, the dissociation of which
+is less complete, divergences from this constant value will occur,
+for some of the molecules have to be separated into their ions.
+For instance, sulphuric acid, which in the fairly strong solutions
+used by Thomsen is only about half dissociated, gives a higher
+value for the heat of neutralization, so that heat must be evolved
+when it is ionized. The heat of formation of a substance from
+its ions is, of course, very different from that evolved when it is
+formed from its elements in the usual way, since the energy
+associated with an ion is different from that possessed by the
+atoms of the element in their normal state. We can calculate
+the heat of formation from its ions for any substance dissolved
+in a given liquid, from a knowledge of the temperature coefficient
+of ionization, by means of an application of the well-known
+thermodynamical process, which also gives the latent heat of
+evaporation of a liquid when the temperature coefficient of its
+vapour pressure is known. The heats of formation thus obtained
+may be either positive or negative, and by using them to supplement
+the heat of formation of water, Arrhenius calculated the
+total heats of neutralization of soda by different acids, some of
+them only slightly dissociated, and found values agreeing well
+with observation (<i>Zeits. physikal. Chemie</i>, 1889, 4, p. 96; and
+1892, 9, p. 339).</p>
+
+<p><i>Voltaic Cells.</i>&mdash;When two metallic conductors are placed in
+an electrolyte, a current will flow through a wire connecting
+them provided that a difference of any kind exists between the
+two conductors in the nature either of the metals or of the
+portions of the electrolyte which surround them. A current
+can be obtained by the combination of two metals in the same
+electrolyte, of two metals in different electrolytes, of the same
+metal in different electrolytes, or of the same metal in solutions
+of the same electrolyte at different concentrations. In accordance
+with the principles of energetics (<i>q.v.</i>), any change which
+involves a decrease in the total available energy of the system
+will tend to occur, and thus the necessary and sufficient condition
+for the production of electromotive force is that the available
+energy of the system should decrease when the current flows.</p>
+
+<p>In order that the current should be maintained, and the
+electromotive force of the cell remain constant during action, it
+is necessary to ensure that the changes in the cell, chemical or
+other, which produce the current, should neither destroy the
+difference between the electrodes, nor coat either electrode
+with a non-conducting layer through which the current cannot
+pass. As an example of a fairly constant cell we may take that
+of Daniell, which consists of the electrical arrangement&mdash;zinc |
+zinc sulphate solution | copper sulphate solution | copper,&mdash;the
+two solutions being usually separated by a pot of porous earthenware.
+When the zinc and copper plates are connected through
+a wire, a current flows, the conventionally positive electricity
+passing from copper to zinc in the wire and from zinc to copper
+in the cell. Zinc dissolves at the anode, an equal amount of
+zinc replaces an equivalent amount of copper on the other side
+of the porous partition, and the same amount of copper is
+deposited on the cathode. This process involves a decrease in
+the available energy of the system, for the dissolution of zinc
+gives out more energy than the separation of copper absorbs.
+But the internal rearrangements which accompany the production
+of a current do not cause any change in the original nature
+of the electrodes, fresh zinc being exposed at the anode, and
+copper being deposited on copper at the cathode. Thus as long
+as a moderate current flows, the only variation in the cell is the
+appearance of zinc sulphate in the liquid on the copper side of the
+porous wall. In spite of this appearance, however, while the
+supply of copper is maintained, copper, being more easily
+separated from the solution than zinc, is deposited alone at the
+cathode, and the cell remains constant.</p>
+
+<p>It is necessary to observe that the condition for change in
+a system is that the total available energy of the whole system
+should be decreased by the change. We must consider what
+change is allowed by the mechanism of the system, and deal with
+the sum of all the alterations in energy. Thus in the Daniell cell
+the dissolution of copper as well as of zinc would increase the
+loss in available energy. But when zinc dissolves, the zinc
+ions carry their electric charges with them, and the liquid tends
+to become positively electrified. The electric forces then soon
+stop further action unless an equivalent quantity of positive
+ions are removed from the solution. Hence zinc can only dissolve
+when some more easily separable substance is present in solution
+to be removed pari passu with the dissolution of zinc. The
+mechanism of such systems is well illustrated by an experiment
+devised by W. Ostwald. Plates of platinum and pure or amalgamated
+zinc are separated by a porous pot, and each surrounded
+by some of the same solution of a salt of a metal
+more oxidizable than zinc, such as potassium. When the plates
+are connected together by means of a wire, no current flows,
+and no appreciable amount of zinc dissolves, for the dissolution
+of zinc would involve the separation of potassium and a gain
+in available energy. If sulphuric acid be added to the vessel
+containing the zinc, these conditions are unaltered and still no
+zinc is dissolved. But, on the other hand, if a few drops of acid
+be placed in the vessel with the platinum, bubbles of hydrogen
+appear, and a current flows, zinc dissolving at the anode, and
+hydrogen being liberated at the cathode. In order that positively
+electrified ions may enter a solution, an equivalent amount of
+other positive ions must be removed or negative ions be added,
+and, for the process to occur spontaneously, the possible action
+at the two electrodes must involve a decrease in the total available
+energy of the system.</p>
+
+<p>Considered thermodynamically, voltaic cells must be divided
+<span class="pagenum"><a name="page224" id="page224"></a>224</span>
+into reversible and non-reversible systems. If the slow processes
+of diffusion be ignored, the Daniell cell already described
+may be taken as a type of a reversible cell. Let an electromotive
+force exactly equal to that of the cell be applied to it in the reverse
+direction. When the applied electromotive force is diminished
+by an infinitesimal amount, the cell produces a current in the
+usual direction, and the ordinary chemical changes occur. If
+the external electromotive force exceed that of the cell by ever
+so little, a current flows in the opposite direction, and all the
+former chemical changes are reversed, copper dissolving from
+the copper plate, while zinc is deposited on the zinc plate. The
+cell, together with this balancing electromotive force, is thus
+a reversible system in true equilibrium, and the thermodynamical
+reasoning applicable to such systems can be used to examine its
+properties.</p>
+
+<p>Now a well-known relation connects the available energy of
+a reversible system with the corresponding change in its total
+internal energy.</p>
+
+<div class="condensed">
+<p>The available energy A is the amount of external work obtainable
+by an infinitesimal, reversible change in the system which occurs
+at a constant temperature T. If I be the change in the internal
+energy, the relation referred to gives us the equation</p>
+
+<p class="center">A = I + T (dA/dT),</p>
+
+<p class="noind">where dA/dT denotes the rate of change of the available energy
+of the system per degree change in temperature. During a small
+electric transfer through the cell, the external work done is Ee,
+where E is the electromotive force. If the chemical changes which
+occur in the cell were allowed to take place in a closed vessel without
+the performance of electrical or other work, the change in energy
+would be measured by the heat evolved. Since the final state of the
+system would be the same as in the actual processes of the cell,
+the same amount of heat must give a measure of the change in
+internal energy when the cell is in action. Thus, if L denote the heat
+corresponding with the chemical changes associated with unit
+electric transfer, Le will be the heat corresponding with an electric
+transfer e, and will also be equal to the change in internal energy
+of the cell. Hence we get the equation</p>
+
+<p class="center">Ee = Le + Te (dE/dT) or E = L + T (dE/dT),</p>
+
+<p class="noind">as a particular case of the general thermodynamic equation of
+available energy. This equation was obtained in different ways by
+J. Willard Gibbs and H. von Helmholtz.</p>
+
+<p>It will be noticed that when dE/dT is zero, that is, when the
+electromotive force of the cell does not change with temperature,
+the electromotive force is measured by the heat of reaction per unit of
+electrochemical change. The earliest formulation of the subject,
+due to Lord Kelvin, assumed that this relation was true in all cases,
+and, calculated in this way, the electromotive force of Daniell&rsquo;s
+cell, which happens to possess a very small temperature coefficient,
+was found to agree with observation.</p>
+
+<p>When one gramme of zinc is dissolved in dilute sulphuric acid,
+1670 thermal units or calories are evolved. Hence for the electrochemical
+unit of zinc or 0.003388 gramme, the thermal evolution is
+5.66 calories. Similarly, the heat which accompanies the dissolution
+of one electrochemical unit of copper is 3.00 calories. Thus, the
+thermal equivalent of the unit of resultant electrochemical change in
+Daniell&rsquo;s cell is 5.66 &minus; 3.00 = 2.66 calories. The dynamical equivalent
+of the calorie is 4.18 × 10<span class="sp">7</span> ergs or C.G.S. units of work, and therefore
+the electromotive force of the cell should be 1.112 × 10<span class="sp">8</span> C.G.S. units
+or 1.112 volts&mdash;a close agreement with the experimental result of
+about 1.08 volts. For cells in which the electromotive force varies
+with temperature, the full equation given by Gibbs and Helmholtz
+has also been confirmed experimentally.</p>
+</div>
+
+<p>As stated above, an electromotive force is set up whenever
+there is a difference of any kind at two electrodes immersed
+in electrolytes. In ordinary cells the difference is secured by
+using two dissimilar metals, but an electromotive force exists
+if two plates of the same metal are placed in solutions of different
+substances, or of the same substance at different concentrations.
+In the latter case, the tendency of the metal to dissolve in the
+more dilute solution is greater than its tendency to dissolve in
+the more concentrated solution, and thus there is a decrease in
+available energy when metal dissolves in the dilute solution and
+separates in equivalent quantity from the concentrated solution.
+An electromotive force is therefore set up in this direction, and,
+if we can calculate the change in available energy due to the
+processes of the cell, we can foretell the value of the electromotive
+force. Now the effective change produced by the action
+of the current is the concentration of the more dilute solution by
+the dissolution of metal in it, and the dilution of the originally
+stronger solution by the separation of metal from it. We may
+imagine these changes reversed in two ways. We may evaporate
+some of the solvent from the solution which has become weaker
+and thus reconcentrate it, condensing the vapour on the solution
+which had become stronger. By this reasoning Helmholtz
+showed how to obtain an expression for the work done. On the
+other hand, we may imagine the processes due to the electrical
+transfer to be reversed by an osmotic operation. Solvent may
+be supposed to be squeezed out from the solution which has
+become more dilute through a semi-permeable wall, and through
+another such wall allowed to mix with the solution which in
+the electrical operation had become more concentrated. Again,
+we may calculate the osmotic work done, and, if the whole cycle
+of operations be supposed to occur at the same temperature,
+the osmotic work must be equal and opposite to the electrical
+work of the first operation.</p>
+
+<div class="condensed">
+<p>The result of the investigation shows that the electrical work Ee
+is given by the equation</p>
+
+<p class="center">Ee = <span class="f150">&int;</span><span class="sp1">p2</span><span class="su1">p1</span> vdp,</p>
+
+<p class="noind">where v is the volume of the solution used and p its osmotic pressure.
+When the solutions may be taken as effectively dilute, so that the
+gas laws apply to the osmotic pressure, this relation reduces to</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">E =</td> <td>nrRT</td>
+<td rowspan="2">log<span class="su">&epsilon;</span></td> <td>c<span class="su">1</span></td></tr>
+<tr><td class="denom">ey</td> <td class="denom">c<span class="su">2</span></td></tr></table>
+
+<p class="noind">where n is the number of ions given by one molecule of the salt, r the
+transport ratio of the anion, R the gas constant, T the absolute
+temperature, y the total valency of the anions obtained from one
+molecule, and c<span class="su">1</span> and c<span class="su">2</span> the concentrations of the two solutions.</p>
+
+<p>If we take as an example a concentration cell in which silver plates
+are placed in solutions of silver nitrate, one of which is ten times as
+strong as the other, this equation gives</p>
+
+<table class="reg" summary="poem"><tr><td> <div class="poemr">
+<p>E = 0.060 × 10<span class="sp">8</span> C.G.S. units</p>
+<p class="i1">= 0.060 volts.</p>
+</div> </td></tr></table>
+
+<p class="noind">W. Nernst, to whom this theory is due, determined the electromotive
+force of this cell experimentally, and found the value 0.055 volt.</p>
+</div>
+
+<p>The logarithmic formulae for these concentration cells indicate
+that theoretically their electromotive force can be increased
+to any extent by diminishing without limit the concentration
+of the more dilute solution, log c<span class="su">1</span>/c<span class="su">2</span> then becoming very great.
+This condition may be realized to some extent in a manner that
+throws light on the general theory of the voltaic cell. Let us
+consider the arrangement&mdash;silver | silver chloride with potassium
+chloride solution | potassium nitrate solution | silver nitrate
+solution | silver. Silver chloride is a very insoluble substance,
+and here the amount in solution is still further reduced by the
+presence of excess of chlorine ions of the potassium salt. Thus
+silver, at one end of the cell in contact with many silver ions of the
+silver nitrate solution, at the other end is in contact with a
+liquid in which the concentration of those ions is very small
+indeed. The result is that a high electromotive force is set up,
+which has been calculated as 0.52 volt, and observed as 0.51 volt.
+Again, Hittorf has shown that the effect of a cyanide round a
+copper electrode is to combine with the copper ions. The concentration
+of the simple copper ions is then so much diminished
+that the copper plate becomes an anode with regard to zinc.
+Thus the cell&mdash;copper | potassium cyanide solution | potassium
+sulphate solution&mdash;zinc sulphate solution | zinc&mdash;gives a current
+which carries copper into solution and deposits zinc. In a similar
+way silver could be made to act as anode with respect to cadmium.</p>
+
+<p>It is now evident that the electromotive force of an ordinary
+chemical cell such as that of Daniell depends on the concentration
+of the solutions as well as on the nature of the metals. In
+ordinary cases possible changes in the concentrations only affect
+the electromotive force by a few parts in a hundred, but, by
+means such as those indicated above, it is possible to produce
+such immense differences in the concentrations that the electromotive
+force of the cell is not only changed appreciably but even
+reversed in direction. Once more we see that it is the total
+impending change in the available energy of the system which
+controls the electromotive force.</p>
+
+<p>Any reversible cell can theoretically be employed as an
+accumulator, though, in practice, conditions of general convenience
+are more sought after than thermodynamic efficiency.
+<span class="pagenum"><a name="page225" id="page225"></a>225</span>
+The effective electromotive force of the common lead accumulator
+(<i>q.v.</i>) is less than that required to charge it. This drop in
+the electromotive force has led to the belief that the cell is not
+reversible. F. Dolezalek, however, has attributed the difference
+to mechanical hindrances, which prevent the equalization of
+acid concentration in the neighbourhood of the electrodes,
+rather than to any essentially irreversible chemical action. The
+fact that the Gibbs-Helmholtz equation is found to apply also
+indicates that the lead accumulator is approximately reversible
+in the thermodynamic sense of the term.</p>
+
+<p><i>Polarization and Contact Difference of Potential.</i>&mdash;If we connect
+together in series a single Daniell&rsquo;s cell, a galvanometer, and two
+platinum electrodes dipping into acidulated water, no visible
+chemical decomposition ensues. At first a considerable current
+is indicated by the galvanometer; the deflexion soon diminishes,
+however, and finally becomes very small. If, instead of using
+a single Daniell&rsquo;s cell, we employ some source of electromotive
+force which can be varied as we please, and gradually raise its
+intensity, we shall find that, when it exceeds a certain value,
+about 1.7 volt, a permanent current of considerable strength
+flows through the solution, and, after the initial period, shows
+no signs of decrease. This current is accompanied by chemical
+decomposition. Now let us disconnect the platinum plates
+from the battery and join them directly with the galvanometer.
+A current will flow for a while in the reverse direction; the system
+of plates and acidulated water through which a current has been
+passed, acts as an accumulator, and will itself yield a current in
+return. These phenomena are explained by the existence of a
+reverse electromotive force at the surface of the platinum plates.
+Only when the applied electromotive force exceeds this reverse
+force of polarization, will a permanent steady current pass
+through the liquid, and visible chemical decomposition proceed.
+It seems that this reverse electromotive force of polarization is
+due to the deposit on the electrodes of minute quantities of the
+products of chemical decomposition. Differences between the
+two electrodes are thus set up, and, as we have seen above, an
+electromotive force will therefore exist between them. To pass
+a steady current in the direction opposite to this electromotive
+force of polarization, the applied electromotive force E must
+exceed that of polarization E&prime;, and the excess E &minus; E&prime; is the
+effective electromotive force of the circuit, the current being,
+in accordance with Ohm&rsquo;s law, proportional to the applied
+electromotive force and represented by (E &minus; E&prime;) / R, where R is
+a constant called the resistance of the circuit.</p>
+
+<p>When we use platinum electrodes in acidulated water, hydrogen
+and oxygen are evolved. The opposing force of polarization is
+about 1.7 volt, but, when the plates are disconnected and used
+as a source of current, the electromotive force they give is only
+about 1.07 volt. This irreversibility is due to the work required
+to evolve bubbles of gas at the surface of bright platinum
+plates. If the plates be covered with a deposit of platinum
+black, in which the gases are absorbed as fast as they are produced,
+the minimum decomposition point is 1.07 volt, and the
+process is reversible. If secondary effects are eliminated, the
+deposition of metals also is a reversible process; the decomposition
+voltage is equal to the electromotive force which the metal
+itself gives when going into solution. The phenomena of polarization
+are thus seen to be due to the changes of surface produced,
+and are correlated with the differences of potential which exist
+at any surface of separation between a metal and an electrolyte.</p>
+
+<p>Many experiments have been made with a view of separating
+the two potential-differences which must exist in any cell made
+of two metals and a liquid, and of determining each one individually.
+If we regard the thermal effect at each junction
+as a measure of the potential-difference there, as the total
+thermal effect in the cell undoubtedly is of the sum of its potential-differences,
+in cases where the temperature coefficient is negligible,
+the heat evolved on solution of a metal should give the electrical
+potential-difference at its surface. Hence, if we assume that,
+in the Daniell&rsquo;s cell, the temperature coefficients are negligible
+at the individual contacts as well as in the cell as a whole, the
+sign of the potential-difference ought to be the same at the surface
+of the zinc as it is at the surface of the copper. Since zinc goes
+into solution and copper comes out, the electromotive force of
+the cell will be the difference between the two effects. On the
+other hand, it is commonly thought that the single potential-differences
+at the surface of metals and electrolytes have been
+determined by methods based on the use of the capillary electrometer
+and on others depending on what is called a dropping
+electrode, that is, mercury dropping rapidly into an electrolyte
+and forming a cell with the mercury at rest in the bottom of
+the vessel. By both these methods the single potential-differences
+found at the surfaces of the zinc and copper have opposite signs,
+and the effective electromotive force of a Daniell&rsquo;s cell is the
+sum of the two effects. Which of these conflicting views represents
+the truth still remains uncertain.</p>
+
+<p><i>Diffusion of Electrolytes and Contact Difference of Potential
+between Liquids.</i>&mdash;An application of the theory of ionic velocity
+due to W. Nernst<a name="fa7k" id="fa7k" href="#ft7k"><span class="sp">7</span></a> and M. Planck<a name="fa8k" id="fa8k" href="#ft8k"><span class="sp">8</span></a> enables us to calculate the
+diffusion constant of dissolved electrolytes. According to the
+molecular theory, diffusion is due to the motion of the molecules
+of the dissolved substance through the liquid. When the dissolved
+molecules are uniformly distributed, the osmotic pressure will
+be the same everywhere throughout the solution, but, if the
+concentration vary from point to point, the pressure will vary
+also. There must, then, be a relation between the rate of change
+of the concentration and the osmotic pressure gradient, and thus
+we may consider the osmotic pressure gradient as a force driving
+the solute through a viscous medium. In the case of non-electrolytes
+and of all non-ionized molecules this analogy completely
+represents the facts, and the phenomena of diffusion can
+be deduced from it alone. But the ions of an electrolytic solution
+can move independently through the liquid, even when no current
+flows, as the consequences of Ohm&rsquo;s law indicate. The ions
+will therefore diffuse independently, and the faster ion will
+travel quicker into pure water in contact with a solution. The
+ions carry their charges with them, and, as a matter of fact, it is
+found that water in contact with a solution takes with respect
+to it a positive or negative potential, according as the positive
+or negative ion travels the faster. This process will go on until
+the simultaneous separation of electric charges produces an
+electrostatic force strong enough to prevent further separation
+of ions. We can therefore calculate the rate at which the salt
+as a whole will diffuse by examining the conditions for a steady
+transfer, in which the ions diffuse at an equal rate, the faster
+one being restrained and the slower one urged forward by the
+electric forces. In this manner the diffusion constant can
+be calculated in absolute units (HCl = 2.49, HNO<span class="su">3</span> = 2.27,
+NaCl = 1.12), the unit of time being the day. By experiments
+on diffusion this constant has been found by Scheffer, and the
+numbers observed agree with those calculated (HCl = 2.30,
+HNO<span class="su">3</span> = 2.22, NaCl = 1.11).</p>
+
+<p>As we have seen above, when a solution is placed in contact
+with water the water will take a positive or negative potential
+with regard to the solution, according as the cation or anion has
+the greater specific velocity, and therefore the greater initial
+rate of diffusion. The difference of potential between two
+solutions of a substance at different concentrations can be calculated
+from the equations used to give the diffusion constants.
+The results give equations of the same logarithmic form as those
+obtained in a somewhat different manner in the theory of concentration
+cells described above, and have been verified by
+experiment.</p>
+
+<p>The contact differences of potential at the interfaces of metals
+and electrolytes have been co-ordinated by Nernst with those
+at the surfaces of separation between different liquids. In
+contact with a solvent a metal is supposed to possess a definite
+solution pressure, analogous to the vapour pressure of a liquid.
+Metal goes into solution in the form of electrified ions. The
+liquid thus acquires a positive charge, and the metal a negative
+charge. The electric forces set up tend to prevent further
+separation, and finally a state of equilibrium is reached, when no
+<span class="pagenum"><a name="page226" id="page226"></a>226</span>
+more ions can go into solution unless an equivalent number are
+removed by voltaic action. On the analogy between this case
+and that of the interface between two solutions, Nernst has
+arrived at similar logarithmic expressions for the difference of
+potential, which becomes proportional to log (P<span class="su">1</span>/P<span class="su">2</span>) where P<span class="su">2</span>
+is taken to mean the osmotic pressure of the cations in the
+solution, and P<span class="su">1</span> the osmotic pressure of the cations in the substance
+of the metal itself. On these lines the equations of concentration
+cells, deduced above on less hypothetical grounds,
+may be regained.</p>
+
+<p><i>Theory of Electrons.</i>&mdash;Our views of the nature of the ions of
+electrolytes have been extended by the application of the ideas
+of the relations between matter and electricity obtained by the
+study of electric conduction through gases. The interpretation
+of the phenomena of gaseous conduction was rendered possible
+by the knowledge previously acquired of conduction through
+liquids; the newer subject is now reaching a position whence
+it can repay its debt to the older.</p>
+
+<p>Sir J.J. Thomson has shown (see <span class="sc"><a href="#artlinks">Conduction, Electric</a></span>,
+§ III.) that the negative ions in certain cases of gaseous conduction
+are much more mobile than the corresponding positive
+ions, and possess a mass of about the one-thousandth part of
+that of a hydrogen atom. These negative particles or corpuscles
+seem to be the ultimate units of negative electricity, and may be
+identified with the electrons required by the theories of H.A.
+Lorentz and Sir J. Larmor. A body containing an excess of these
+particles is negatively electrified, and is positively electrified if
+it has parted with some of its normal number. An electric
+current consists of a moving stream of electrons. In gases the
+electrons sometimes travel alone, but in liquids they are always
+attached to matter, and their motion involves the movement of
+chemical atoms or groups of atoms. An atom with an extra
+corpuscle is a univalent negative ion, an atom with one corpuscle
+detached is a univalent positive ion. In metals the electrons
+can slip from one atom to the next, since a current can pass
+without chemical action. When a current passes from an
+electrolyte to a metal, the electron must be detached from the
+atom it was accompanying and chemical action be manifested
+at the electrode.</p>
+
+<div class="condensed">
+<p><span class="sc">Bibliography.</span>&mdash;Michael Faraday, <i>Experimental Researches in
+Electricity</i> (London, 1844 and 1855); W. Ostwald, <i>Lehrbuch der
+allgemeinen Chemie</i>, 2te Aufl. (Leipzig, 1891); <i>Elektrochemie</i> (Leipzig,
+1896); W Nernst, <i>Theoretische Chemie</i>, 3te Aufl. (Stuttgart, 1900;
+English translation, London, 1904); F. Kohlrausch and L. Holborn,
+<i>Das Leitvermögen der Elektrolyte</i> (Leipzig, 1898); W.C.D. Whetham,
+<i>The Theory of Solution and Electrolysis</i> (Cambridge, 1902); M. Le
+Blanc, <i>Elements of Electrochemistry</i> (Eng. trans., London, 1896);
+S. Arrhenius, <i>Text-Book of Electrochemistry</i> (Eng. trans., London,
+1902); H.C. Jones, <i>The Theory of Electrolytic Dissociation</i> (New
+York, 1900); N. Munroe Hopkins, <i>Experimental Electrochemistry</i>
+(London, 1905); Lüphe, <i>Grundzüge der Elektrochemie</i> (Berlin, 1896).</p>
+
+<p>Some of the more important papers on the subject have been
+reprinted for Harper&rsquo;s <i>Series of Scientific Memoirs in Electrolytic
+Conduction</i> (1899) and the <i>Modern Theory of Solution</i> (1899). Several
+journals are published specially to deal with physical chemistry, of
+which electrochemistry forms an important part. Among them may
+be mentioned the <i>Zeitschrift für physikalische Chemie</i> (Leipzig);
+and the <i>Journal of Physical Chemistry</i> (Cornell University). In
+these periodicals will be found new work on the subject and
+abstracts of papers which appear in other physical and chemical
+publications.</p>
+</div>
+<div class="author">(W. C. D. W.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1k" id="ft1k" href="#fa1k"><span class="fn">1</span></a> See Hittorf, <i>Pogg. Ann.</i> cvi. 517 (1859).</p>
+
+<p><a name="ft2k" id="ft2k" href="#fa2k"><span class="fn">2</span></a> <i>Grundriss der Elektrochemie</i> (1895), p. 292; see also F. Kaufler
+and C. Herzog, <i>Ber.</i>, 1909, 42, p. 3858.</p>
+
+<p><a name="ft3k" id="ft3k" href="#fa3k"><span class="fn">3</span></a> <i>Brit. Ass. Rep.</i>, 1906, Section A, Presidential Address.</p>
+
+<p><a name="ft4k" id="ft4k" href="#fa4k"><span class="fn">4</span></a> See <i>Theory of Solution</i>, by W.C.D. Whetham (1902), p. 328.</p>
+
+<p><a name="ft5k" id="ft5k" href="#fa5k"><span class="fn">5</span></a> W. Ostwald, <i>Zeits. physikal. Chemie</i>, 1892, vol. IX. p. 579;
+T. Ewan, <i>Phil. Mag.</i> (5), 1892, vol. xxxiii. p. 317; G.D. Liveing,
+<i>Cambridge Phil. Trans.</i>, 1900, vol. xviii. p. 298.</p>
+
+<p><a name="ft6k" id="ft6k" href="#fa6k"><span class="fn">6</span></a> See W.B. Hardy, <i>Journal of Physiology</i>, 1899, vol. xxiv. p. 288;
+and W.C.D. Whetham, <i>Phil. Mag.</i>, November 1899.</p>
+
+<p><a name="ft7k" id="ft7k" href="#fa7k"><span class="fn">7</span></a> <i>Zeits. physikal. Chem.</i> 2, p. 613.</p>
+
+<p><a name="ft8k" id="ft8k" href="#fa8k"><span class="fn">8</span></a> <i>Wied. Ann.</i>, 1890, 40, p. 561.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROMAGNETISM<a name="ar71" id="ar71"></a></span>, that branch of physical science
+which is concerned with the interconnexion of electricity and
+magnetism, and with the production of magnetism by means of
+electric currents by devices called electromagnets.</p>
+
+<p><i>History.</i>&mdash;The foundation was laid by the observation first
+made by Hans Christian Oersted (1777-1851), professor of
+natural philosophy in Copenhagen, who discovered in 1820 that
+a wire uniting the poles or terminal plates of a voltaic pile has the
+property of affecting a magnetic needle<a name="fa1l" id="fa1l" href="#ft1l"><span class="sp">1</span></a> (see <span class="sc"><a href="#ar63">Electricity</a></span>).
+Oersted carefully ascertained that the nature of the wire itself
+did not influence the result but saw that it was due to the electric
+conflict, as he called it, round the wire; or in modern language,
+to the magnetic force or magnetic flux round the conductor.
+If a straight wire through which an electric current is flowing is
+placed above and parallel to a magnetic compass needle, it is
+found that if the current is flowing in the conductor in a direction
+from south to north, the north pole of the needle under the conductor
+deviates to the left hand, whereas if the conductor is
+placed under the needle, the north pole deviates to the right hand;
+if the conductor is doubled back over the needle, the effects of
+the two sides of the loop are added together and the deflection is
+increased. These results are summed up in the mnemonic rule:
+<i>Imagine yourself swimming in the conductor with the current, that
+is, moving in the direction of the positive electricity, with your face
+towards the magnetic needle; the north pole will then deviate to
+your left hand.</i> The deflection of the magnetic needle can therefore
+reveal the existence of an electric current in a neighbouring
+circuit, and this fact was soon utilized in the construction of
+instruments called galvanometers (<i>q.v.</i>).</p>
+
+<p>Immediately after Oersted&rsquo;s discovery was announced,
+D.F.J. Arago and A.M. Ampère began investigations on the
+subject of electromagnetism. On the 18th of September 1820,
+Ampère read a paper before the Academy of Sciences in Paris,
+in which he announced that the voltaic pile itself affected a
+magnetic needle as did the uniting wire, and he showed that the
+effects in both cases were consistent with the theory that electric
+current was a circulation round a circuit, and equivalent in
+magnetic effect to a very short magnet with axis placed at right
+angles to the plane of the circuit. He then propounded his
+brilliant hypothesis that the magnetization of iron was due to
+molecular electric currents. This suggested to Arago that wire
+wound into a helix carrying electric current should magnetize
+a steel needle placed in the interior. In the <i>Ann. Chim.</i> (1820,
+15, p. 94), Arago published a paper entitled &ldquo;Expériences relatives
+à l&rsquo;aimantation du fer et de l&rsquo;acier par l&rsquo;action du courant
+voltaïque,&rdquo; announcing that the wire conveying the current,
+even though of copper, could magnetize steel needles placed
+across it, and if plunged into iron filings it attracted them. About
+the same time Sir Humphry Davy sent a communication to Dr
+W.H. Wollaston, read at the Royal Society on the 16th of
+November 1820 (reproduced in the <i>Annals of Philosophy</i> for
+August 1821, p. 81), &ldquo;On the Magnetic Phenomena produced by
+Electricity,&rdquo; in which he announced his independent discovery
+of the same fact. With a large battery of 100 pairs of plates at
+the Royal Institution, he found in October 1820 that the uniting
+wire became strongly magnetic and that iron filings clung to it;
+also that steel needles placed across the wire were permanently
+magnetized. He placed a sheet of glass over the wire and
+sprinkling iron filings on it saw that they arranged themselves
+in straight lines at right angles to the wire. He then proved that
+Leyden jar discharges could produce the same effects. Ampère
+and Arago then seem to have experimented together and magnetized
+a steel needle wrapped in paper which was enclosed in a
+helical wire conveying a current. All these facts were rendered
+intelligible when it was seen that a wire when conveying an
+electric current becomes surrounded by a magnetic field. If
+the wire is a long straight one, the lines of magnetic force are
+circular and concentric with centres on the wire axis, and if the
+wire is bent into a circle the lines of magnetic force are endless
+loops surrounding and linked with the electric circuit. Since
+a magnetic pole tends to move along a line of magnetic force it
+was obvious that it should revolve round a wire conveying a
+current. To exhibit this fact involved, however, much ingenuity.
+It was first accomplished by Faraday in October 1821 (<i>Exper.
+Res.</i> ii. p. 127). Since the action is reciprocal a current free to
+move tends to revolve round a magnetic pole. The fact is most
+easily shown by a small piece of apparatus made as follows:
+In a glass cylinder (see fig. 1) like a lamp chimney are fitted two
+corks. Through the bottom one is passed the north end of a bar
+magnet which projects up above a little mercury lying in the
+cork. Through the top cork is passed one end of a wire from a
+<span class="pagenum"><a name="page227" id="page227"></a>227</span>
+battery, and a piece of wire in the cylinder is flexibly connected
+to it, the lower end of this last piece just touching the mercury.
+When a current is passed in at the top wire and out at the lower
+end of the bar magnet, the loose wire revolves round the magnet
+pole. All text-books on physics contain in their
+chapters on electromagnetism full accounts of
+various forms of this experiment.</p>
+
+<table class="flt" style="float: right; width: 170px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:128px; height:347px" src="images/img227a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span></td></tr></table>
+
+<p>In 1825 another important step forward was
+taken when William Sturgeon (1783-1850) of
+London produced the electromagnet. It consisted
+of a horseshoe-shaped bar of soft iron,
+coated with varnish, on which was wrapped a
+spiral coil of bare copper wire, the turns not
+touching each other. When a voltaic current
+was passed through the wire the iron became a
+powerful magnet, but on severing the connexion
+with the battery, the soft iron lost
+immediately nearly all its magnetism.<a name="fa2l" id="fa2l" href="#ft2l"><span class="sp">2</span></a></p>
+
+<p>At that date Ohm had not announced his
+law of the electric circuit, and it was a matter
+of some surprise to investigators to find that
+Sturgeon&rsquo;s electromagnet could not be operated
+at a distance through a long circuit of wire
+with such good results as when close to the
+battery. Peter Barlow, in January 1825, published in the
+<i>Edinburgh Philosophical Journal</i>, a description of such an
+experiment made with a view of applying Sturgeon&rsquo;s electromagnet
+to telegraphy, with results which were unfavourable.
+Sturgeon&rsquo;s experiments, however, stimulated Joseph Henry
+(<i>q.v.</i>) in the United States, and in 1831 he gave a description
+of a method of winding electromagnets which at once put a new
+face upon matters (<i>Silliman&rsquo;s Journal</i>, 1831, 19, p. 400). Instead
+of insulating the iron core, he wrapped the copper wire round
+with silk and wound in numerous turns and many layers upon
+the iron horseshoe in such fashion that the current went round
+the iron always in the same direction. He then found that such
+an electromagnet wound with a long fine wire, if worked with a
+battery consisting of a large number of cells in series, could be
+operated at a considerable distance, and he thus produced what
+were called at that time <i>intensity electromagnets</i>, and which
+subsequently rendered the electric telegraph a possibility. In
+fact, Henry established in 1831, in Albany, U.S.A., an electromagnetic
+telegraph, and in 1835 at Princeton even used an
+earth return, thereby anticipating the discovery (1838) of C.A.
+Steinheil (1801-1870) of Munich.</p>
+
+<table class="flt" style="float: left; width: 310px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:266px; height:120px" src="images/img227b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span></td></tr></table>
+
+<p>Inventors were then incited to construct powerful electromagnets
+as tested by the weight they could carry from their
+armatures. Joseph Henry made a magnet for Yale College,
+U.S.A., which lifted 3000 &#8468; (<i>Silliman&rsquo;s Journal</i>, 1831, 20, p. 201),
+and one for Princeton which lifted 3000 with a very small
+battery. Amongst others J.P. Joule, ever memorable for his
+investigations on the mechanical equivalent of heat, gave much
+attention about 1838-1840 to the construction of electromagnets
+and succeeded in devising some forms remarkable for their
+lifting power. One form was constructed by cutting a thick
+soft iron tube longitudinally
+into two equal parts. Insulated
+copper wire was then
+wound longitudinally over
+one of both parts (see fig. 2)
+and a current sent through
+the wire. In another form
+two iron disks with teeth at
+right angles to the disk had
+insulated wire wound zigzag between the teeth; when a current
+was sent through the wire, the teeth were so magnetized that
+they were alternately N. and S. poles. If two such similar disks
+were placed with teeth of opposite polarity in contact, a very
+large force was required to detach them, and with a magnet and
+armature weighing in all 11.575 &#8468; Joule found that a weight
+of 2718 was supported. Joule&rsquo;s papers on this subject will be
+found in his <i>Collected Papers</i> published by the Physical Society
+of London, and in <i>Sturgeon&rsquo;s Annals of Electricity</i>, 1838-1841,
+vols. 2-6.</p>
+
+<div class="condensed">
+<p><i>The Magnetic Circuit.</i>&mdash;The phenomena presented by the electromagnet
+are interpreted by the aid of the notion of the magnetic
+circuit. Let us consider a thin circular sectioned ring of iron wire
+wound over with a solenoid or spiral of insulated copper wire through
+which a current of electricity can be passed. If the solenoid or wire
+windings existed alone, a current having a strength A amperes
+passed through it would create in the interior of the solenoid a
+magnetic force H, numerically equal to 4&pi;/10 multiplied by the
+number of windings N on the solenoid, and by the current in amperes
+A, and divided by the mean length of the solenoid l, or H = 4&pi;AN/10l.
+The product AN is called the &ldquo;ampere-turns&rdquo; on the solenoid.
+The product Hl of the magnetic force H and the length l of the
+magnetic circuit is called the &ldquo;magnetomotive force&rdquo; in the magnetic
+circuit, and from the above formula it is seen that the magnetomotive
+force denoted by (M.M.F.) is equal to 4&pi;/10 (= 1.25 nearly) times
+the ampere-turns (A.N.) on the exciting coil or solenoid. Otherwise
+(A.N.) = 0.8(M.M.F.). The magnetomotive force is regarded as
+creating an effect called magnetic flux (Z) in the magnetic circuit,
+just as electromotive force E.M.F. produces electric current (A) in
+the electric circuit, and as by Ohm&rsquo;s law (see <span class="sc"><a href="#ar68">Electrokinetics</a></span>) the
+current varies as the E.M.F. and inversely as a quality of the electric
+circuit called its &ldquo;resistance,&rdquo; so in the magnetic circuit the magnetic
+flux varies as the magnetomotive force and inversely as a
+quality of the magnetic circuit called its &ldquo;reluctance.&rdquo; The great
+difference between the electric circuit and the magnetic circuit lies
+in the fact that whereas the electric resistance of a solid or liquid
+conductor is independent of the current and affected only by the
+temperature, the magnetic reluctance varies with the magnetic
+flux and cannot be defined except by means of a curve which shows
+its value for different flux densities. The quotient of the total
+magnetic flux, Z, in a circuit by the cross section, S, of the circuit is
+called the mean &ldquo;flux density,&rdquo; and the reluctance of a magnetic
+circuit one centimetre long and one square centimetre in cross
+section is called the &ldquo;reluctivity&rdquo; of the material. The relation
+between reluctivity &rho; = 1/&mu; magnetic force H, and flux density B,
+is defined by the equation H = &rho;B, from which we have Hl = Z (&rho;l/S) =
+M.M.F. acting on the circuit. Again, since the ampere-turns (AN)
+on the circuit are equal to 0.8 times the M.M.F., we have finally
+AN/l = 0.8(Z/&mu;S). This equation tells us the exciting force reckoned
+in ampere-turns, AN, which must be put on the ring core to create
+a total magnetic flux Z in it, the ring core having a mean perimeter l
+and cross section S and reluctivity &rho; = 1/&mu; corresponding to a flux
+density Z/S. Hence before we can make use of the equation for
+practical purposes we need to possess a curve for the particular
+material showing us the value of the reluctivity corresponding to
+various values of the possible flux density. The reciprocal of &rho; is
+usually called the &ldquo;permeability&rdquo; of the material and denoted by &mu;.
+Curves showing the relation of 1/&rho; and ZS or &mu; and B, are called
+&ldquo;permeability curves.&rdquo; For air and all other non-magnetic matter
+the permeability has the same value, taken arbitrarily as unity.
+On the other hand, for iron, nickel and cobalt the permeability may
+in some cases reach a value of 2000 or 2500 for a value of B = 5000 in
+C.G.S. measure (see <span class="sc"><a href="#artlinks">Units, Physical</a></span>). The process of taking these
+curves consists in sending a current of known strength through a
+solenoid of known number of turns wound on a circular iron ring of
+known dimensions, and observing the time-integral of the secondary
+current produced in a secondary circuit of known turns and resistance
+R wound over the iron core N times. The secondary electromotive
+force is by Faraday&rsquo;s law (see <span class="sc"><a href="#ar68">Electrokinetics</a></span>) equal to the time
+rate of change of the total flux, or E = NdZ/dt. But by Ohm&rsquo;s
+law E = Rdq/dt, where q is the quantity of electricity set flowing in
+the secondary circuit by a change dZ in the co-linked total flux.
+Hence if 2Q represents this total quantity of electricity set flowing
+in the secondary circuit by suddenly reversing the direction of the
+magnetic flux Z in the iron core we must have</p>
+
+<p class="center">RQ = NZ or Z = RQ/N.</p>
+
+<p class="noind">The measurement of the total quantity of electricity Q can be
+made by means of a ballistic galvanometer (<i>q.v.</i>), and the resistance
+R of the secondary circuit includes that of the coil wound on the
+iron core and the galvanometer as well. In this manner the value
+of the total flux Z and therefore of Z/S = B or the flux density, can be
+found for a given magnetizing force H, and this last quantity is
+determined when we know the magnetizing current in the solenoid
+and its turns and dimensions. The curve which delineates the relation
+of H and B is called the magnetization curve for the material in
+question. For examples of these curves see <span class="sc"><a href="#artlinks">Magnetism</a></span>.</p>
+
+<p>The fundamental law of the non-homogeneous magnetic circuit
+traversed by one and the same total magnetic flux Z is that the sum
+of all the magnetomotive forces acting in the circuit is numerically
+equal to the product of the factor 0.8, the total flux in the circuit,
+and the sum of all the reluctances of the various parts of the circuit.
+If then the circuit consists of materials of different permeability
+<span class="pagenum"><a name="page228" id="page228"></a>228</span>
+and it is desired to know the ampere-turns required to produce a given
+total of flux round the circuit, we have to calculate from the magnetization
+curves of the material of each part the necessary magnetomotive
+forces and add these forces together. The practical application
+of this principle to the predetermination of the field windings of
+dynamo magnets was first made by Drs J. and E. Hopkinson (<i>Phil.
+Trans.</i>, 1886, 177, p. 331).</p>
+
+<p>We may illustrate the principles of this predetermination by a
+simple example. Suppose a ring of iron has a mean diameter of
+10 cms. and a cross section of 2 sq. cms., and a transverse cut on air
+gap made in it 1 mm. wide. Let us inquire the ampere-turns to
+be put upon the ring to create in it a total flux of 24,000 C.G.S. units.
+The total length of the iron part of the circuit is (10&pi; &minus; 0.1) cms.,
+and its section is 2 sq. cms., and the flux density in it is to be 12,000.
+From Table II. below we see that the permeability of pure iron
+corresponding to a flux density of 12,000 is 2760. Hence the reluctance
+of the iron circuits is equal to</p>
+
+<table class="math0" summary="math">
+<tr><td>10&pi; &minus; 0.1</td>
+<td rowspan="2">=</td> <td>220</td>
+<td rowspan="2">C.G.S. units.</td></tr>
+<tr><td class="denom">2760 × 2</td> <td class="denom">38640</td></tr></table>
+
+<p>The length of the air gap is 0.1 cm., its section 2 sq. cms., and its
+permeability is unity. Hence the reluctance of the air gap is</p>
+
+<table class="math0" summary="math">
+<tr><td>0.1</td>
+<td rowspan="2">=</td> <td>1</td>
+<td rowspan="2">C.G.S. unit.</td></tr>
+<tr><td class="denom">1 × 2</td> <td class="denom">20</td></tr></table>
+
+<p>Accordingly the magnetomotive force in ampere-turns required to
+produce the required flux is equal to</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">0.8 (24,000) <span class="f150">(</span></td> <td>1</td>
+<td rowspan="2">+</td> <td>220</td>
+<td rowspan="2"><span class="f150">)</span> = 1070 nearly.</td></tr>
+<tr><td class="denom">20</td> <td class="denom">38640</td></tr></table>
+
+<p>It follows that the part of the magnetomotive force required to
+overcome the reluctance of the narrow air gap is about nine times
+that required for the iron alone.</p>
+
+<p>In the above example we have for simplicity assumed that the
+flux in passing across the air gap does not spread out at all. In
+dealing with electromagnet design in dynamo construction we have,
+however, to take into consideration the spreading as well as the
+leakage of flux across the circuit (see <span class="sc"><a href="#artlinks">Dynamo</a></span>). It will be seen,
+therefore, that in order that we may predict the effect of a certain
+kind of iron or steel when used as the core of an electromagnet,
+we must be provided with tables or curves showing the reluctivity
+or permeability corresponding to various flux densities or&mdash;which
+comes to the same thing&mdash;with (B, H) curves for the sample.</p>
+</div>
+
+<p><i>Iron and Steel for Electromagnetic Machinery.</i>&mdash;In connexion
+with the technical application of electromagnets such as those
+used in the field magnets of dynamos (<i>q.v.</i>), the testing of different
+kinds of iron and steel for magnetic permeability has therefore
+become very important. Various instruments called permeameters
+and hysteresis meters have been designed for this purpose,
+but much of the work has been done by means of a ballistic
+galvanometer and test ring as above described. The &ldquo;hysteresis&rdquo;
+of an iron or steel is that quality of it in virtue of which energy
+is dissipated as heat when the magnetization is reversed or
+carried through a cycle (see <span class="sc"><a href="#artlinks">Magnetism</a></span>), and it is generally
+measured either in ergs per cubic centimetre of metal per cycle
+of magnetization, or in watts per &#8468; per 50 or 100 cycles
+per second at or corresponding to a certain maximum flux
+density, say 2500 or 600 C.G.S. units. For the details of various
+forms of permeameter and hysteresis meter technical books
+must be consulted.<a name="fa3l" id="fa3l" href="#ft3l"><span class="sp">3</span></a></p>
+
+<p>An immense number of observations have been carried out
+on the magnetic permeability of different kinds of iron and
+steel, and in the following tables are given some typical results,
+mostly from experiments made by J.A. Ewing (see <i>Proc. Inst.
+C.E.</i>, 1896, 126, p. 185) in which the ballistic method was
+employed to determine the flux density corresponding to various
+magnetizing forces acting upon samples of iron and steel in the
+form of rings.</p>
+
+<div class="condensed">
+<p>The figures under heading I. are values given in a paper by A.W.S.
+Pocklington and F. Lydall (<i>Proc. Roy. Soc</i>., 1892-1893, 52, pp. 164
+and 228) as the results of a magnetic test of an exceptionally pure
+iron supplied for the purpose of experiment by Colonel Dyer, of the
+Elswick Works. The substances other than iron in this sample
+were stated to be: carbon, <i>trace</i>; silicon, <i>trace</i>; phosphorus,
+<i>none</i>; sulphur, 0.013%; manganese, 0.1%. The other five
+specimens, II. to VI., are samples of commercial iron or steel. No.
+II. is a sample of Low Moor bar iron forged into a ring, annealed and
+turned. No. III. is a steel forging furnished by Mr R. Jenkins as a
+sample of forged ingot-metal for dynamo magnets. No. IV. is a steel
+casting for dynamo magnets, unforged, made by Messrs Edgar Allen
+&amp; Company by a special pneumatic process under the patents of
+Mr A. Tropenas. No. V. is also an unforged steel casting for dynamo
+magnets, made by Messrs Samuel Osborne &amp; Company by the
+Siemens process. No. VI. is also an unforged steel casting for
+dynamo magnets, made by Messrs Fried. Krupp, of Essen.</p>
+
+<p class="pt1 center"><span class="sc">Table I.</span>&mdash;<i>Magnetic Flux Density corresponding to various Magnetizing
+Forces in the case of certain Samples of Iron and Steel</i>
+(<i>Ewing</i>).</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">Magnetizing<br />Force<br />H (C.G.S.<br />Units).</td>
+ <td class="tccm allb" colspan="6">Magnetic Flux Density B (C.G.S. Units).</td></tr>
+
+<tr><td class="tcr lb rb">&nbsp;</td> <td class="tcc rb">I.</td> <td class="tcc rb">II.</td> <td class="tcc rb">III.</td> <td class="tcc rb">IV.</td> <td class="tcc rb">V.</td> <td class="tcc rb">VI.</td></tr>
+
+<tr><td class="tcc lb rb">&ensp;5</td> <td class="tcc rb">12,700</td> <td class="tcr rb">10,900</td> <td class="tcr rb">12,300</td> <td class="tcr rb">4,700</td> <td class="tcr rb">9,600</td> <td class="tcr rb">10,900</td></tr>
+<tr><td class="tcc lb rb">10</td> <td class="tcc rb">14,980</td> <td class="tcr rb">13,120</td> <td class="tcr rb">14,920</td> <td class="tcr rb">12,250</td> <td class="tcr rb">13,050</td> <td class="tcr rb">13,320</td></tr>
+<tr><td class="tcc lb rb">15</td> <td class="tcc rb">15,800</td> <td class="tcr rb">14,010</td> <td class="tcr rb">15,800</td> <td class="tcr rb">14,000</td> <td class="tcr rb">14,600</td> <td class="tcr rb">14,350</td></tr>
+<tr><td class="tcc lb rb">20</td> <td class="tcc rb">16,300</td> <td class="tcr rb">14,580</td> <td class="tcr rb">16,280</td> <td class="tcr rb">15,050</td> <td class="tcr rb">15,310</td> <td class="tcr rb">14,950</td></tr>
+<tr><td class="tcc lb rb">30</td> <td class="tcc rb">16,950</td> <td class="tcr rb">15,280</td> <td class="tcr rb">16,810</td> <td class="tcr rb">16,200</td> <td class="tcr rb">16,000</td> <td class="tcr rb">15,660</td></tr>
+<tr><td class="tcc lb rb">40</td> <td class="tcc rb">17,350</td> <td class="tcr rb">15,760</td> <td class="tcr rb">17,190</td> <td class="tcr rb">16,800</td> <td class="tcr rb">16,510</td> <td class="tcr rb">16,150</td></tr>
+<tr><td class="tcc lb rb">50</td> <td class="tcc rb">· ·</td> <td class="tcr rb">16,060</td> <td class="tcr rb">17,500</td> <td class="tcr rb">17,140</td> <td class="tcr rb">16,900</td> <td class="tcr rb">16,480</td></tr>
+<tr><td class="tcc lb rb">60</td> <td class="tcc rb">· ·</td> <td class="tcr rb">16,340</td> <td class="tcr rb">17,750</td> <td class="tcr rb">17,450</td> <td class="tcr rb">17,180</td> <td class="tcr rb">16,780</td></tr>
+<tr><td class="tcc lb rb">70</td> <td class="tcc rb">· ·</td> <td class="tcr rb">16,580</td> <td class="tcr rb">17,970</td> <td class="tcr rb">17,750</td> <td class="tcr rb">17,400</td> <td class="tcr rb">17,000</td></tr>
+<tr><td class="tcc lb rb">80</td> <td class="tcc rb">· ·</td> <td class="tcr rb">16,800</td> <td class="tcr rb">18,180</td> <td class="tcr rb">18,040</td> <td class="tcr rb">17,620</td> <td class="tcr rb">17,200</td></tr>
+<tr><td class="tcc lb rb">90</td> <td class="tcc rb">· ·</td> <td class="tcr rb">17,000</td> <td class="tcr rb">18,390</td> <td class="tcr rb">18,230</td> <td class="tcr rb">17,830</td> <td class="tcr rb">17,400</td></tr>
+<tr><td class="tcc lb rb bb">100</td> <td class="tcc rb bb">· ·</td> <td class="tcr rb bb">17,200</td> <td class="tcr rb bb">18,600</td> <td class="tcr rb bb">18,420</td> <td class="tcr rb bb">18,030</td> <td class="tcr rb bb">17,600</td></tr>
+</table>
+
+<p>It will be seen from the figures and the description of the materials
+that the steel forgings and castings have a remarkably high permeability
+under small magnetizing force.</p>
+</div>
+
+<p>Table II. shows the magnetic qualities of some of these
+materials as found by Ewing when tested with small magnetizing
+forces.</p>
+
+<p class="pt1 center"><span class="sc">Table II.</span>&mdash;<i>Magnetic Permeability of Samples of Iron and Steel under
+Weak Magnetizing Forces.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">Magnetic Flux<br />Density B<br />(C.G.S. Units).</td>
+ <td class="tccm allb" colspan="2">I.<br />Pure Iron.</td> <td class="tccm allb" colspan="2">III.<br />Steel Forging.</td> <td class="tccm allb" colspan="2">VI.<br />Steel Casting.</td></tr>
+
+<tr><td class="tcc lb rb">&nbsp;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td></tr>
+<tr><td class="tcc lb rb">&ensp;2,000</td> <td class="tcc">0.90</td> <td class="tcc rb">2220</td> <td class="tcc">1.38</td> <td class="tcc rb">1450</td> <td class="tcc">1.18</td> <td class="tcc rb">1690</td></tr>
+<tr><td class="tcc lb rb">&ensp;4,000</td> <td class="tcc">1.40</td> <td class="tcc rb">2850</td> <td class="tcc">1.91</td> <td class="tcc rb">2090</td> <td class="tcc">1.66</td> <td class="tcc rb">2410</td></tr>
+<tr><td class="tcc lb rb">&ensp;6,000</td> <td class="tcc">1.85</td> <td class="tcc rb">3240</td> <td class="tcc">2.38</td> <td class="tcc rb">2520</td> <td class="tcc">2.15</td> <td class="tcc rb">2790</td></tr>
+<tr><td class="tcc lb rb">&ensp;8,000</td> <td class="tcc">2.30</td> <td class="tcc rb">3480</td> <td class="tcc">2.92</td> <td class="tcc rb">2740</td> <td class="tcc">2.83</td> <td class="tcc rb">2830</td></tr>
+<tr><td class="tcc lb rb">10,000</td> <td class="tcc">3.10</td> <td class="tcc rb">3220</td> <td class="tcc">3.62</td> <td class="tcc rb">2760</td> <td class="tcc">4.05</td> <td class="tcc rb">2470</td></tr>
+<tr><td class="tcc lb rb bb">12,000</td> <td class="tcc bb">4.40</td> <td class="tcc rb bb">2760</td> <td class="tcc bb">4.80</td> <td class="tcc rb bb">2500</td> <td class="tcc bb">6.65</td> <td class="tcc rb bb">1810</td></tr>
+</table>
+
+<p>The numbers I., III. and VI. in the above table refer to the samples
+mentioned in connexion with Table I.</p>
+
+<p>It is a remarkable fact that certain varieties of low carbon
+steel (commonly called mild steel) have a higher permeability
+than even annealed Swedish wrought iron under large magnetizing
+forces. The term <i>steel</i>, however, here used has reference
+rather to the mode of production than the final chemical nature
+of the material. In some of the mild-steel castings used for
+dynamo electromagnets it appears that the total foreign matter,
+including carbon, manganese and silicon, is not more than 0.3%
+of the whole, the material being 99.7% pure iron. This valuable
+magnetic property of steel capable of being cast is, however,
+of great utility in modern dynamo building, as it enables field
+magnets of very high permeability to be constructed, which can
+be fashioned into shape by casting instead of being built up as
+formerly out of masses of forged wrought iron. The curves in
+fig. 3 illustrate the manner in which the flux density or, as it is
+usually called, the magnetization curve of this mild cast steel
+crosses that of Swedish wrought iron, and enables us to obtain a
+higher flux density corresponding to a given magnetizing force
+with the steel than with the iron.</p>
+
+<p>From the same paper by Ewing we extract a number of results
+relating to permeability tests of thin sheet iron and sheet steel,
+such as is used in the construction of dynamo armatures and
+transformer cores.</p>
+
+<div class="condensed">
+<p>No. VII. is a specimen of good transformer-plate, 0.301 millimetre
+thick, rolled from Swedish iron by Messrs Sankey of Bilston. No.
+VIII. is a specimen of specially thin transformer-plate rolled from
+scrap iron. No. IX. is a specimen of transformer-plate rolled from
+<span class="pagenum"><a name="page229" id="page229"></a>229</span>
+ingot-steel. No. X. is a specimen of the wire which was used by
+J. Swinburne to form the core of his &ldquo;hedgehog&rdquo; transformers. Its
+diameter was 0.602 millimetre. All these samples were tested in the
+form of rings by the ballistic method, the rings of sheet-metal
+being stamped or turned in the flat. The wire ring No. X. was
+coiled and annealed after coiling.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:414px; height:424px" src="images/img229a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 3.</span></td></tr></table>
+
+<p class="pt1 center"><span class="sc">Table III.</span>&mdash;<i>Permeability Tests of Transformer Plate and Wire</i>.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">Magnetic<br />Flux<br />Density B<br />(C.G.S.<br />Units).</td> <td class="tccm allb" colspan="2">VII.<br />Transformer-<br />plate of<br />Swedish Iron.</td>
+  <td class="tccm allb" colspan="2">VIII.<br />Transformer-<br />plate of<br />Scrap Iron.</td> <td class="tccm allb" colspan="2">IX.<br />Transformer-<br />plate of<br />of Steel.</td>
+  <td class="tccm allb" colspan="2">X.<br />Transformer-<br />wire.</td></tr>
+
+<tr><td class="tcr lb rb">&nbsp;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td> <td class="tcc">H</td> <td class="tcc rb">&mu;</td></tr>
+<tr><td class="tcr lb rb">1,000</td> <td class="tcc">0.81</td> <td class="tcr rb">1230</td> <td class="tcc">1.08</td> <td class="tcr rb">920</td> <td class="tcc">0.60</td> <td class="tcr rb">1470</td> <td class="tcc">1.71</td> <td class="tcr rb">590</td></tr>
+<tr><td class="tcr lb rb">2,000</td> <td class="tcc">1.05</td> <td class="tcr rb">1900</td> <td class="tcc">1.46</td> <td class="tcr rb">1370</td> <td class="tcc">0.90</td> <td class="tcr rb">2230</td> <td class="tcc">2.10</td> <td class="tcr rb">950</td></tr>
+<tr><td class="tcr lb rb">3,000</td> <td class="tcc">1.26</td> <td class="tcr rb">2320</td> <td class="tcc">1.77</td> <td class="tcr rb">1690</td> <td class="tcc">1.04</td> <td class="tcr rb">2880</td> <td class="tcc">2.30</td> <td class="tcr rb">1300</td></tr>
+<tr><td class="tcr lb rb">4,000</td> <td class="tcc">1.54</td> <td class="tcr rb">2600</td> <td class="tcc">2.10</td> <td class="tcr rb">1900</td> <td class="tcc">1.19</td> <td class="tcr rb">3360</td> <td class="tcc">2.50</td> <td class="tcr rb">1600</td></tr>
+<tr><td class="tcr lb rb">5,000</td> <td class="tcc">1.82</td> <td class="tcr rb">2750</td> <td class="tcc">2.53</td> <td class="tcr rb">1980</td> <td class="tcc">1.38</td> <td class="tcr rb">3620</td> <td class="tcc">2.70</td> <td class="tcr rb">1850</td></tr>
+<tr><td class="tcr lb rb">6,000</td> <td class="tcc">2.14</td> <td class="tcr rb">2800</td> <td class="tcc">3.04</td> <td class="tcr rb">1970</td> <td class="tcc">1.59</td> <td class="tcr rb">3770</td> <td class="tcc">2.92</td> <td class="tcr rb">2070</td></tr>
+<tr><td class="tcr lb rb">7,000</td> <td class="tcc">2.54</td> <td class="tcr rb">2760</td> <td class="tcc">3.62</td> <td class="tcr rb">1930</td> <td class="tcc">1.89</td> <td class="tcr rb">3700</td> <td class="tcc">3.16</td> <td class="tcr rb">2210</td></tr>
+<tr><td class="tcr lb rb">8,000</td> <td class="tcc">3.09</td> <td class="tcr rb">2590</td> <td class="tcc">4.37</td> <td class="tcr rb">1830</td> <td class="tcc">2.25</td> <td class="tcr rb">3600</td> <td class="tcc">3.43</td> <td class="tcr rb">2330</td></tr>
+<tr><td class="tcr lb rb">9,000</td> <td class="tcc">3.77</td> <td class="tcr rb">2390</td> <td class="tcc">5.3&nbsp;</td> <td class="tcr rb">1700</td> <td class="tcc">2.72</td> <td class="tcr rb">3310</td> <td class="tcc">3.77</td> <td class="tcr rb">2390</td></tr>
+<tr><td class="tcr lb rb">10,000</td> <td class="tcc">4.6&nbsp;</td> <td class="tcr rb">2170</td> <td class="tcc">6.5&nbsp;</td> <td class="tcr rb">1540</td> <td class="tcc">3.33</td> <td class="tcr rb">3000</td> <td class="tcc">4.17</td> <td class="tcr rb">2400</td></tr>
+<tr><td class="tcr lb rb">11,000</td> <td class="tcc">5.7&nbsp;</td> <td class="tcr rb">1930</td> <td class="tcc">7.9&nbsp;</td> <td class="tcr rb">1390</td> <td class="tcc">4.15</td> <td class="tcr rb">2650</td> <td class="tcc">4.70</td> <td class="tcr rb">2340</td></tr>
+<tr><td class="tcr lb rb">12,000</td> <td class="tcc">7.0&nbsp;</td> <td class="tcr rb">1710</td> <td class="tcc">9.8&nbsp;</td> <td class="tcr rb">1220</td> <td class="tcc">5.40</td> <td class="tcr rb">2220</td> <td class="tcc">5.45</td> <td class="tcr rb">2200</td></tr>
+<tr><td class="tcr lb rb">13,000</td> <td class="tcc">8.5&nbsp;</td> <td class="tcr rb">1530</td> <td class="tcc">11.9</td> <td class="tcr rb">1190</td> <td class="tcc">7.1&nbsp;</td> <td class="tcr rb">1830</td> <td class="tcc">6.5&nbsp;</td> <td class="tcr rb">2000</td></tr>
+<tr><td class="tcr lb rb">14,000</td> <td class="tcc">11.0</td> <td class="tcr rb">1270</td> <td class="tcc">15.0</td> <td class="tcr rb">930</td> <td class="tcc">10.0</td> <td class="tcr rb">1400</td> <td class="tcc">8.4&nbsp;</td> <td class="tcr rb">1670</td></tr>
+<tr><td class="tcr lb rb">15,000</td> <td class="tcc">15.1</td> <td class="tcr rb">990</td> <td class="tcc">19.5</td> <td class="tcr rb">770</td> <td class="tcc">· ·</td> <td class="tcc rb">· ·</td> <td class="tcc">11.9</td> <td class="tcr rb">1260</td></tr>
+<tr><td class="tcr lb rb bb">16,000</td> <td class="tcc bb">21.4</td> <td class="tcr rb bb">750</td> <td class="tcc bb">27.5</td> <td class="tcr rb bb">580</td> <td class="tcc bb">· ·</td> <td class="tcc rb bb">· ·</td> <td class="tcc bb">21.0</td> <td class="tcr rb bb">760</td></tr>
+</table></div>
+
+<p>Some typical flux-density curves of iron and steel as used in
+dynamo and transformer building are given in fig. 4.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:650px; height:413px" src="images/img229b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 4.</span></td></tr></table>
+
+<p>The numbers in Table III. well illustrate the fact that the
+permeability, &mu; = B/H has a maximum value corresponding to a
+certain flux density. The tables are also explanatory of the fact
+that mild steel has gradually replaced iron in the manufacture
+of dynamo electromagnets and transformer-cores.</p>
+
+<p>Broadly speaking, the materials which are now employed
+in the manufacture of the cores of electromagnets for technical
+purposes of various kinds may be said to fall into three classes,
+namely, forgings, castings and stampings. In some cases the
+iron or steel core which is to be magnetized is simply a mass of
+iron hammered or pressed into shape by hydraulic pressure;
+in other cases it has to be fused and cast; and for certain other
+purposes it must be rolled first into thin sheets, which are subsequently
+stamped out into the required forms.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:356px; height:434px" src="images/img229c.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 5.</span></td></tr></table>
+
+<p>For particular purposes it is necessary to obtain the highest
+possible magnetic permeability corresponding to a high, or the
+highest attainable flux density. This is generally the case in
+the electromagnets which are employed as the field magnets in
+dynamo machines. It may generally be said that whilst the best
+wrought iron, such as annealed Low Moor or Swedish iron, is
+more permeable for low flux densities than steel castings, the
+cast steel may surpass the wrought metal for high flux density.
+For most electro-technical purposes the best magnetic results
+are given by the employment of forged ingot-iron. This material
+is probably the most permeable throughout the whole scale of
+attainable flux densities. It is slightly superior to wrought iron,
+and it only becomes inferior to the highest class of cast steel
+when the flux density is pressed above 18,000 C.G.S. units (see
+fig. 5). For flux densities above 13,000 the forged ingot-iron
+has now practically replaced for electric engineering purposes
+the Low Moor or Swedish iron. Owing to the method of its
+production, it might in truth be called a soft steel with a very
+small percentage of combined carbon. The best description of
+this material is conveyed by the German term &ldquo;Flusseisen,&rdquo;
+but its nearest British equivalent is &ldquo;ingot-iron.&rdquo; Chemically
+speaking, the material is for all practical purposes very nearly
+pure iron. The same may be said of the cast steels now much
+employed for the production of dynamo magnet cores. The
+cast steel which is in demand for this purpose has a slightly
+lower permeability than the ingot-iron for low flux densities,
+but for flux densities above 16,000 the required result may be
+more cheaply obtained with a steel casting than with a forging.
+When high tensile strength is required in addition to considerable
+magnetic permeability, it has been found advantageous to employ
+a steel containing 5% of nickel. The rolled sheet iron and sheet
+steel which is in request for the construction of magnet cores,
+especially those in which the exciting current is an alternating
+current, are, generally speaking, produced from Swedish iron.
+Owing to the mechanical treatment necessary to reduce the
+material to a thin sheet, the permeability at low flux densities
+is rather higher than, although at high flux densities it is inferior
+<span class="pagenum"><a name="page230" id="page230"></a>230</span>
+to, the same iron and steel when tested in bulk. For most
+purposes, however, where a laminated iron magnet core is
+required, the flux density is not pressed up above 6000 units,
+and it is then more important to secure small hysteresis loss than
+high permeability. The magnetic permeability of cast iron is
+much inferior to that of wrought or ingot-iron, or the mild steels
+taken at the same flux densities.</p>
+
+<p>The following Table IV. gives the flux density and permeability
+of a typical cast iron taken by J.A. Fleming by the
+ballistic method:&mdash;</p>
+
+<p class="pt1 center"><span class="sc">Table IV.</span>&mdash;<i>Magnetic Permeability and Magnetization Curve of
+Cast Iron.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tcc lb rb tb">H</td> <td class="tcc rb tb">B</td> <td class="tcc rb2 tb">&mu;</td> <td class="tcc rb tb">H</td> <td class="tcc rb tb">B</td> <td class="tcc rb2 tb">&mu;</td> <td class="tcc rb tb">H</td> <td class="tcc rb tb">B</td> <td class="tcc rb tb">&mu;</td></tr>
+<tr><td class="tcr lb rb">.19</td> <td class="tcr rb">27</td> <td class="tcr rb2">139</td> <td class="tcr rb">8.84</td> <td class="tcr rb">4030</td> <td class="tcr rb2">456</td> <td class="tcr rb">44.65</td> <td class="tcr rb">8,071</td> <td class="tcr rb">181</td></tr>
+<tr><td class="tcr lb rb">.41</td> <td class="tcr rb">62</td> <td class="tcr rb2">150</td> <td class="tcr rb">10.60</td> <td class="tcr rb">4491</td> <td class="tcr rb2">424</td> <td class="tcr rb">56.57</td> <td class="tcr rb">8,548</td> <td class="tcr rb">151</td></tr>
+<tr><td class="tcr lb rb">1.11</td> <td class="tcr rb">206</td> <td class="tcr rb2">176</td> <td class="tcr rb">12.33</td> <td class="tcr rb">4884</td> <td class="tcr rb2">396</td> <td class="tcr rb">71.98</td> <td class="tcr rb">9,097</td> <td class="tcr rb">126</td></tr>
+<tr><td class="tcr lb rb">2.53</td> <td class="tcr rb">768</td> <td class="tcr rb2">303</td> <td class="tcr rb">13.95</td> <td class="tcr rb">5276</td> <td class="tcr rb2">378</td> <td class="tcr rb">88.99</td> <td class="tcr rb">9,600</td> <td class="tcr rb">108</td></tr>
+<tr><td class="tcr lb rb">3.41</td> <td class="tcr rb">1251</td> <td class="tcr rb2">367</td> <td class="tcr rb">15.61</td> <td class="tcr rb">5504</td> <td class="tcr rb2">353</td> <td class="tcr rb">106.35</td> <td class="tcr rb">10,066</td> <td class="tcr rb">95</td></tr>
+<tr><td class="tcr lb rb">4.45</td> <td class="tcr rb">1898</td> <td class="tcr rb2">427</td> <td class="tcr rb">18.21</td> <td class="tcr rb">5829</td> <td class="tcr rb2">320</td> <td class="tcr rb">120.60</td> <td class="tcr rb">10,375</td> <td class="tcr rb">86</td></tr>
+<tr><td class="tcr lb rb">5.67</td> <td class="tcr rb">2589</td> <td class="tcr rb2">456</td> <td class="tcr rb">26.37</td> <td class="tcr rb">6814</td> <td class="tcr rb2">258</td> <td class="tcr rb">140.37</td> <td class="tcr rb">10,725</td> <td class="tcr rb">76</td></tr>
+<tr><td class="tcr lb rb bb">7.16</td> <td class="tcr rb bb">3350</td> <td class="tcr rb2 bb">468</td> <td class="tcr rb bb">36.54</td> <td class="tcr rb bb">7580</td> <td class="tcr rb2 bb">207</td> <td class="tcr rb bb">152.73</td> <td class="tcr rb bb">10,985</td> <td class="tcr rb bb">72</td></tr>
+</table>
+
+<p>The metal of which the tests are given in Table IV. contained
+2% of silicon, 2.85% of total carbon, and 0.5% of manganese.
+It will be seen that a magnetizing force of about 5 C.G.S. units is
+sufficient to impart to a wrought-iron ring a flux density of
+18,000 C.G.S. units, but the same force hardly produces more
+than one-tenth of this flux density in cast iron.</p>
+
+<p>The testing of sheet iron and steel for magnetic hysteresis
+loss has developed into an important factory process, giving
+as it does a means of ascertaining the suitability of the metal
+for use in the manufacture of transformers and cores of alternating-current
+electromagnets.</p>
+
+<p>In Table V. are given the results of hysteresis tests by Ewing on
+samples of commercial sheet iron and steel. The numbers VII.,
+VIII., IX. and X. refer to the same samples as those for which
+permeability results are given in Table III.</p>
+
+<p class="pt1 center"><span class="sc">Table V.</span>&mdash;<i>Hysteresis Loss in Transformer-iron.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb" rowspan="2">Maximum<br />Flux<br />Density<br />B.</td> <td class="tccm allb" colspan="4">Ergs per Cubic Centimetre<br />per Cycle.</td> <td class="tccm allb" colspan="4">Watts per &#8468; at a Frequency<br />of 100.</td></tr>
+
+<tr><td class="tccm allb">VII.<br /><br />Swedish<br />Iron.</td> <td class="tccm allb">VIII.<br />Forged<br />Scrap-<br />iron.</td>
+ <td class="tccm allb">IX.<br /><br />Ingot-<br />steel.</td> <td class="tccm allb">X.<br />Soft<br />Iron<br />Wire.</td>
+ <td class="tccm allb">VII.</td> <td class="tccm allb">VIII.</td> <td class="tccm allb">IX.</td> <td class="tccm allb">X.</td></tr>
+
+<tr><td class="tcc lb rb">2000</td> <td class="tcr rb">240</td> <td class="tcr rb">400</td> <td class="tcr rb">215</td> <td class="tcr rb">600</td> <td class="tcc rb">0.141</td> <td class="tcc rb">0.236</td> <td class="tcc rb">0.127</td> <td class="tcc rb">0.356</td></tr>
+<tr><td class="tcc lb rb">3000</td> <td class="tcr rb">520</td> <td class="tcr rb">790</td> <td class="tcr rb">430</td> <td class="tcr rb">1150</td> <td class="tcc rb">0.306</td> <td class="tcc rb">0.465</td> <td class="tcc rb">0.253</td> <td class="tcc rb">0.630</td></tr>
+<tr><td class="tcc lb rb">4000</td> <td class="tcr rb">830</td> <td class="tcr rb">1220</td> <td class="tcr rb">700</td> <td class="tcr rb">1780</td> <td class="tcc rb">0.490</td> <td class="tcc rb">0.720</td> <td class="tcc rb">0.410</td> <td class="tcc rb">1.050</td></tr>
+<tr><td class="tcc lb rb">5000</td> <td class="tcr rb">1190</td> <td class="tcr rb">1710</td> <td class="tcr rb">1000</td> <td class="tcr rb">2640</td> <td class="tcc rb">0.700</td> <td class="tcc rb">1.010</td> <td class="tcc rb">0.590</td> <td class="tcc rb">1.550</td></tr>
+<tr><td class="tcc lb rb">6000</td> <td class="tcr rb">1600</td> <td class="tcr rb">2260</td> <td class="tcr rb">1350</td> <td class="tcr rb">3360</td> <td class="tcc rb">0.940</td> <td class="tcc rb">1.330</td> <td class="tcc rb">0.790</td> <td class="tcc rb">1.980</td></tr>
+<tr><td class="tcc lb rb">7000</td> <td class="tcr rb">2020</td> <td class="tcr rb">2940</td> <td class="tcr rb">1730</td> <td class="tcr rb">4300</td> <td class="tcc rb">1.200</td> <td class="tcc rb">1.730</td> <td class="tcc rb">1.020</td> <td class="tcc rb">2.530</td></tr>
+<tr><td class="tcc lb rb">8000</td> <td class="tcr rb">2510</td> <td class="tcr rb">3710</td> <td class="tcr rb">2150</td> <td class="tcr rb">5300</td> <td class="tcc rb">1.480</td> <td class="tcc rb">2.180</td> <td class="tcc rb">1.270</td> <td class="tcc rb">3.120</td></tr>
+<tr><td class="tcc lb rb bb">9000</td> <td class="tcr rb bb">3050</td> <td class="tcr rb bb">4560</td> <td class="tcr rb bb">2620</td> <td class="tcr rb bb">6380</td> <td class="tcc rb bb">1.800</td> <td class="tcc rb bb">2.680</td> <td class="tcc rb bb">1.540</td> <td class="tcc rb bb">3.750</td></tr>
+</table>
+
+<p>In Table VI. are given the results of a magnetic test of
+some exceedingly good transformer-sheet rolled from Swedish
+iron.</p>
+
+<p class="pt1 center"><span class="sc">Table VI.</span>&mdash;<i>Hysteresis Loss in Strip of Transformer-plate rolled
+Swedish Iron.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb">Maximum Flux<br />Density B.</td> <td class="tccm allb">Ergs per Cubic Centimetre<br />per Cycle.</td> <td class="tccm allb">Watts per &#8468; at a<br />Frequency of 100.</td></tr>
+
+<tr><td class="tcc lb rb">2000</td> <td class="tcc rb">&ensp;220</td> <td class="tcc rb">0.129</td></tr>
+<tr><td class="tcc lb rb">3000</td> <td class="tcc rb">&ensp;410</td> <td class="tcc rb">0.242</td></tr>
+<tr><td class="tcc lb rb">4000</td> <td class="tcc rb">&ensp;640</td> <td class="tcc rb">0.376</td></tr>
+<tr><td class="tcc lb rb">5000</td> <td class="tcc rb">&ensp;910</td> <td class="tcc rb">0.535</td></tr>
+<tr><td class="tcc lb rb">6000</td> <td class="tcc rb">1200</td> <td class="tcc rb">0.710</td></tr>
+<tr><td class="tcc lb rb">7000</td> <td class="tcc rb">1520</td> <td class="tcc rb">0.890</td></tr>
+<tr><td class="tcc lb rb">8000</td> <td class="tcc rb">1900</td> <td class="tcc rb">1.120</td></tr>
+<tr><td class="tcc lb rb bb">9000</td> <td class="tcc rb bb">2310</td> <td class="tcc rb bb">1.360</td></tr>
+</table>
+
+<p>In Table VII. are given some values obtained by Fleming for
+the hysteresis loss in the sample of cast iron, the permeability test
+of which is recorded in Table IV.</p>
+
+<p><span class="sc">Table VII.</span>&mdash;<i>Observations on the Magnetic Hysteresis of Cast Iron.</i></p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb" rowspan="2">Loop.</td> <td class="tccm allb" rowspan="2">B (max.)</td> <td class="tccm allb" colspan="2">Hysteresis Loss.</td></tr>
+<tr><td class="tccm allb">Ergs per cc.<br />per Cycle.</td> <td class="tccm allb">Watts per &#8468; per.<br />100 Cycles per sec.</td></tr>
+
+<tr><td class="tcr lb rb">I.</td> <td class="tcc rb">1475</td> <td class="tcc rb">&emsp;466</td> <td class="tcc rb">&ensp;.300</td></tr>
+<tr><td class="tcr lb rb">II.</td> <td class="tcc rb">2545</td> <td class="tcc rb">&ensp;1,288</td> <td class="tcc rb">&ensp;.829</td></tr>
+<tr><td class="tcr lb rb">III.</td> <td class="tcc rb">3865</td> <td class="tcc rb">&ensp;2,997</td> <td class="tcc rb">1.934</td></tr>
+<tr><td class="tcr lb rb">IV.</td> <td class="tcc rb">5972</td> <td class="tcc rb">&ensp;7,397</td> <td class="tcc rb">4.765</td></tr>
+<tr><td class="tcr lb rb bb">V.</td> <td class="tcc rb bb">8930</td> <td class="tcc rb bb">13,423</td> <td class="tcc rb bb">8.658</td></tr>
+</table>
+
+<p>For most practical purposes the constructor of electromagnetic
+machinery requires his iron or steel to have some one of the following
+characteristics. If for dynamo or magnet making, it should
+have the highest possible permeability at a flux density corresponding
+to practically maximum magnetization. If for transformer
+or alternating-current magnet building, it should have
+the smallest possible hysteresis loss at a maximum flux density
+of 2500 C.G.S. units during the cycle. If required for permanent
+magnet making, it should have the highest possible coercivity
+combined with a high retentivity. Manufacturers of iron and
+steel are now able to meet these demands in a very remarkable
+manner by the commercial production of material of a quality
+which at one time would have been considered a scientific
+curiosity.</p>
+
+<p>It is usual to specify iron and steel for the first purpose by
+naming the minimum permeability it should possess corresponding
+to a flux density of 18,000 C.G.S. units; for the second,
+by stating the hysteresis loss in watts per &#8468; per 100 cycles
+per second, corresponding to a maximum flux density of 2500
+C.G.S. units during the cycle; and for the third, by mentioning
+the coercive force required to reduce to zero magnetization a
+sample of the metal in the form of a long bar magnetized to a
+stated magnetization. In the cyclical reversal of magnetization
+of iron we have two modes to consider. In the first case, which is
+that of the core of the alternating transformer, the magnetic
+force passes through a cycle of values, the iron remaining
+stationary, and the direction of the
+magnetic force being always the same.
+In the other case, that of the dynamo
+armature core, the direction of the
+magnetic force in the iron is constantly
+changing, and at the same time
+undergoing a change in magnitude.</p>
+
+<p>It has been shown by F.G. Baily
+(<i>Proc. Roy. Soc.</i>, 1896) that if a mass
+of laminated iron is rotating in a
+magnetic field which remains constant
+in direction and magnitude in any
+one experiment, the hysteresis loss
+rises to a maximum as the magnitude
+of the flux density in the iron is
+increased and then falls away again to
+nearly zero value. These observations have been confirmed
+by other observers. The question has been much debated
+whether the values of the hysteresis loss obtained by these
+two different methods are identical for magnetic cycles in which
+the flux density reaches the same maximum value. This question
+is also connected with another one, namely, whether the hysteresis
+loss per cycle is or is not a function of the speed with which the
+cycle is traversed. Early experiments by C.P. Steinmetz and
+others seemed to show that there was a difference between slow-speed
+and high-speed hysteresis cycles, but later experiments
+by J. Hopkinson and by A. Tanakadaté, though not absolutely
+exhaustive, tend to prove that up to 400 cycles per second the
+hysteresis loss per cycle is practically unchanged.</p>
+
+<p>Experiments made in 1896 by R. Beattie and R.C. Clinker on
+magnetic hysteresis in rotating fields were partly directed to
+determine whether the hysteresis loss at moderate flux densities,
+such as are employed in transformer work, was the same as that
+found by measurements made with alternating-current fields
+on the same iron and steel specimens (see <i>The Electrician</i>, 1896,
+<span class="pagenum"><a name="page231" id="page231"></a>231</span>
+37, p. 723). These experiments showed that over moderate ranges
+of induction, such as may be expected in electro-technical work,
+the hysteresis loss per cycle per cubic centimetre was practically
+the same when the iron was tested in an alternating field with a
+periodicity of 100, the field remaining constant in direction,
+and when the iron was tested in a rotating field giving the same
+maximum flux density.</p>
+
+<p>With respect to the variation of hysteresis loss in magnetic
+cycles having different maximum values for the flux density,
+Steinmetz found that the hysteresis loss (W), as measured by
+the area of the complete (B, H) cycle and expressed in ergs per
+centimetre-cube per cycle, varies proportionately to a constant
+called the <i>hysteretic constant</i>, and to the 1.6th power of the
+maximum flux density (B), or W = &eta;B<span class="sp">1.6</span>.</p>
+
+<p>The hysteretic constants (&eta;) for various kinds of iron and steel
+are given in the table below:&mdash;</p>
+
+<table class="ws f90" summary="Contents">
+<tr><td class="tcc cl">Metal.</td> <td class="tcc cl">Hysteretic Constant.</td></tr>
+
+<tr><td class="tcl">Swedish wrought iron, well annealed</td> <td class="tcc">.0010 to .0017</td></tr>
+<tr><td class="tcl">Annealed cast steel of good quality; small</td> <td class="tcc">&nbsp;</td></tr>
+<tr><td class="tcl">&emsp; percentage of carbon</td> <td class="tcc">.0017 to .0029</td></tr>
+<tr><td class="tcl">Cast Siemens-Martin steel</td> <td class="tcc">.0019 to .0028</td></tr>
+<tr><td class="tcl">Cast ingot-iron</td> <td class="tcc">.0021 to .0026</td></tr>
+<tr><td class="tcl">Cast steel, with higher percentages of carbon,</td> <td class="tcc">&nbsp;</td></tr>
+<tr><td class="tcl">&emsp; or inferior qualities of wrought iron</td> <td class="tcc">.0031 to .0054</td></tr>
+</table>
+
+<p>Steinmetz&rsquo;s law, though not strictly true for very low or very
+high maximum flux densities, is yet a convenient empirical rule
+for obtaining approximately the hysteresis loss at any one
+maximum flux density and knowing it at another, provided
+these values fall within a range varying say from 1 to 9000
+C.G.S. units. (See <span class="sc"><a href="#artlinks">Magnetism</a></span>.)</p>
+
+<p>The standard maximum flux density which is adopted in
+electro-technical work is 2500, hence in the construction of the
+cores of alternating-current electromagnets and transformers
+iron has to be employed having a known hysteretic constant
+at the standard flux density. It is generally expressed by stating
+the number of watts per &#8468; of metal which would be dissipated
+for a frequency of 100 cycles, and a maximum flux density
+(B max.) during the cycle of 2500. In the case of good iron or
+steel for transformer-core making, it should not exceed 1.25 watt
+per &#8468; per 100 cycles per 2500 B (maximum value).</p>
+
+<p>It has been found that if the sheet iron employed for cores
+of alternating electromagnets or transformers is heated to a
+temperature somewhere in the neighbourhood of 200° C. the
+hysteresis loss is very greatly increased. It was noticed in 1894
+by G.W. Partridge that alternating-current transformers which
+had been in use some time had a very considerably augmented
+core loss when compared with their initial condition. O.T.
+Bláthy and W.M. Mordey in 1895 showed that this augmentation
+in hysteresis loss in iron was due to heating. H.F. Parshall
+investigated the effect up to moderate temperatures, such as
+140° C., and an extensive series of experiments was made in
+1898 by S.R. Roget (<i>Proc. Roy. Soc.</i>, 1898, 63, p. 258, and 64,
+p. 150). Roget found that below 40° C. a rise in temperature
+did not produce any augmentation in the hysteresis loss in iron,
+but if it is heated to between 40° C. and 135° C. the hysteresis
+loss increases continuously with time, and this increase is now
+called &ldquo;ageing&rdquo; of the iron. It proceeds more slowly as the
+temperature is higher. If heated to above 135° C., the hysteresis
+loss soon attains a maximum, but then begins to decrease.
+Certain specimens heated to 160° C. were found to have their
+hysteresis loss doubled in a few days. The effect seems to come
+to a maximum at about 180° C. or 200° C. Mere lapse of time
+does not remove the increase, but if the iron is reannealed the
+augmentation in hysteresis disappears. If the iron is heated
+to a higher temperature, say between 300° C. and 700° C.,
+Roget found the initial rise of hysteresis happens more quickly,
+but that the metal soon settles down into a state in which the
+hysteresis loss has a small but still augmented constant value.
+The augmentation in value, however, becomes more nearly zero
+as the temperature approaches 700° C. Brands of steel are now
+obtainable which do not age in this manner, but these <i>non-ageing</i>
+varieties of steel have not generally such low initial hysteresis
+values as the &ldquo;Swedish Iron,&rdquo; commonly considered best for
+the cores of transformers and alternating-current magnets.</p>
+
+<p>The following conclusions have been reached in the matter:&mdash;(1)
+Iron and mild steel in the annealed state are more liable to
+change their hysteresis value by heating than when in the
+harder condition; (2) all changes are removed by re-annealing;
+(3) the changes thus produced by heating affect not only the
+amount of the hysteresis loss, but also the form of the lower part
+of the (B, H) curve.</p>
+
+<p><i>Forms of Electromagnet.</i>&mdash;The form which an electromagnet
+must take will greatly depend upon the purposes for which it is
+to be used. A design or form of electromagnet which will be
+very suitable for some purposes will be useless for others.
+Supposing it is desired to make an electromagnet which shall
+be capable of undergoing very rapid changes of strength, it
+must have such a form that the coercivity of the material is
+overcome by a self-demagnetizing force. This can be achieved
+by making the magnet in the form of a short and stout bar rather
+than a long thin one. It has already been explained that the
+ends or poles of a polar magnet exert a demagnetizing power
+upon the mass of the metal in the interior of the bar. If then
+the electromagnet has the form of a long thin bar, the length of
+which is several hundred times its diameter, the poles are very
+far removed from the centre of the bar, and the demagnetizing
+action will be very feeble; such a long thin electromagnet,
+although made of very soft iron, retains a considerable amount
+of magnetism after the magnetizing force is withdrawn. On the
+other hand, a very thick bar very quickly demagnetizes itself,
+because no part of the metal is far removed from the action of the
+free poles. Hence when, as in many telegraphic instruments, a
+piece of soft iron, called an armature, has to be attracted to the
+poles of a horseshoe-shaped electromagnet, this armature should
+be prevented from quite touching the polar surfaces of the magnet.
+If a soft iron mass does quite touch the poles, then it completes
+the magnetic circuit and abolishes the free poles, and the magnet
+is to a very large extent deprived of its self-demagnetizing power.
+This is the explanation of the well-known fact that after exciting
+the electromagnet and then stopping the current, it still requires
+a good pull to detach the &ldquo;keeper&rdquo;; but when once the keeper
+has been detached, the magnetism is found to have nearly
+disappeared. An excellent form of electromagnet for the production
+of very powerful fields has been designed by H. du
+Bois (fig. 6).</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:500px; height:525px" src="images/img231.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span>&mdash;Du Bois&rsquo;s Electromagnet.</td></tr></table>
+
+<p>Various forms of electromagnets used in connexion with
+<span class="pagenum"><a name="page232" id="page232"></a>232</span>
+dynamo machines are considered in the article <span class="sc"><a href="#artlinks">Dynamo</a></span>, and there
+is, therefore, no necessity to refer particularly to the numerous
+different shapes and types employed in electrotechnics.</p>
+
+<div class="condensed">
+<p><span class="sc">Bibliography.</span>&mdash;For additional information on the above subject
+the reader may be referred to the following works and original
+papers:&mdash;</p>
+
+<p>H. du Bois, <i>The Magnetic Circuit in Theory and Practice</i>; S.P.
+Thompson, <i>The Electromagnet</i>; J.A. Fleming, <i>Magnets and Electric
+Currents</i>; J.A. Ewing, <i>Magnetic Induction in Iron and other Metals</i>;
+J.A. Fleming, &ldquo;The Ferromagnetic Properties of Iron and Steel,&rdquo;
+<i>Proceedings of Sheffield Society of Engineers and Metallurgists</i> (Oct.
+1897); J.A. Ewing, &ldquo;The Magnetic Testing of Iron and Steel,&rdquo;
+<i>Proc. Inst. Civ. Eng.</i>, 1896, 126, p. 185; H.F. Parshall, &ldquo;The
+Magnetic Data of Iron and Steel,&rdquo; <i>Proc. Inst. Civ. Eng.</i>, 1896,
+126, p. 220; J.A. Ewing, &ldquo;The Molecular Theory of Induced
+Magnetism,&rdquo; <i>Phil. Mag.</i>, Sept. 1890; W.M. Mordey, &ldquo;Slow Changes
+in the Permeability of Iron,&rdquo; <i>Proc. Roy. Soc.</i> 57, p. 224; J.A.
+Ewing, &ldquo;Magnetism,&rdquo; James Forrest Lecture, <i>Proc. Inst. Civ. Eng.</i>
+138; S.P. Thompson, &ldquo;Electromagnetic Mechanism,&rdquo; <i>Electrician</i>,
+26, pp. 238, 269, 293; J.A. Ewing, &ldquo;Experimental Researches in
+Magnetism,&rdquo; <i>Phil. Trans.</i>, 1885, part ii.; Ewing and Klassen,
+&ldquo;Magnetic Qualities of Iron,&rdquo; <i>Proc. Roy. Soc.</i>, 1893.</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1l" id="ft1l" href="#fa1l"><span class="fn">1</span></a> In the <i>Annals of Philosophy</i> for November 1821 is a long article
+entitled &ldquo;Electromagnetism&rdquo; by Oersted, in which he gives a
+detailed account of his discovery. He had his thoughts turned to
+it as far back as 1813, but not until the 20th of July 1820 had he
+actually made his discovery. He seems to have been arranging a
+compass needle to observe any deflections during a storm, and placed
+near it a platinum wire through which a galvanic current was passed.</p>
+
+<p><a name="ft2l" id="ft2l" href="#fa2l"><span class="fn">2</span></a> See <i>Trans. Soc. Arts</i>, 1825, 43, p. 38, in which a figure of Sturgeon&rsquo;s
+electromagnet is given as well as of other pieces of apparatus for
+which the Society granted him a premium and a silver medal.</p>
+
+<p><a name="ft3l" id="ft3l" href="#fa3l"><span class="fn">3</span></a> See S.P. Thompson, <i>The Electromagnet</i> (London, 1891); J.A.
+Fleming, <i>A Handbook for the Electrical Laboratory and Testing Room</i>,
+vol. 2 (London, 1903); J.A. Ewing, <i>Magnetic Induction in Iron and
+other Metals</i> (London, 1903, 3rd ed.).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROMETALLURGY.<a name="ar72" id="ar72"></a></span> The present article, as explained
+under <span class="sc"><a href="#ar66">Electrochemistry</a></span>, treats only of those processes in
+which electricity is applied to the production of chemical reactions
+or molecular changes at furnace temperatures. In
+many of these the application of heat is necessary to bring
+the substances used into the liquid state for the purpose of
+electrolysis, aqueous solutions being unsuitable. Among the
+earliest experiments in this branch of the subject were
+those of Sir H. Davy, who in 1807 (<i>Phil. Trans.</i>, 1808,
+p. 1), produced the alkali metals by passing an intense current
+of electricity from a platinum wire to a platinum dish,
+through a mass of fused caustic alkali. The action was started
+in the cold, the alkali being slightly moistened to render it a
+conductor; then, as the current passed, heat was produced
+and the alkali fused, the metal being deposited in the liquid
+condition. Later, A. Matthiessen (<i>Quarterly Journ. Chem. Soc.</i>
+viii. 30) obtained potassium by the electrolysis of a mixture
+of potassium and calcium chlorides fused over a lamp. There
+are here foreshadowed two types of electrolytic furnace-operations:
+(<i>a</i>) those in which external heating maintains the
+electrolyte in the fused condition, and (<i>b</i>) those in which a current-density
+is applied sufficiently high to develop the heat necessary
+to effect this object unaided. Much of the earlier electro-metallurgical
+work was done with furnaces of the (<i>a</i>) type, while
+nearly all the later developments have been with those of class
+(<i>b</i>). There is a third class of operations, exemplified by the
+manufacture of calcium carbide, in which electricity is employed
+solely as a heating agent; these are termed <i>electrothermal</i>, as
+distinguished from <i>electrolytic</i>. In certain electrothermal
+processes (<i>e.g.</i> calcium carbide production) the heat from the
+current is employed in raising mixtures of substances to the
+temperature at which a desired chemical reaction will take
+place between them, while in others (<i>e.g.</i> the production of
+graphite from coke or gas-carbon) the heat is applied solely to
+the production of molecular or physical changes. In ordinary
+electrolytic work only the continuous current may of course
+be used, but in electrothermal work an alternating current is
+equally available.</p>
+
+<p><i>Electric Furnaces.</i>&mdash;Independently of the question of the
+application of external heating, the furnaces used in electrometallurgy
+may be broadly classified into (i.) arc furnaces, in
+which the intense heat of the electric arc is utilized, and (ii.)
+resistance and incandescence furnaces, in which the heat is
+generated by an electric current overcoming the resistance
+of an inferior conductor.</p>
+
+<p>Excepting such experimental arrangements as that of C.M.
+Despretz (<i>C.R.</i>, 1849, 29) for use on a small scale in the laboratory,
+Pichou in France and J.H. Johnson in England
+appear, in 1853, to have introduced the earliest
+<span class="sidenote">Arc furnaces.</span>
+practical form of furnace. In these arrangements,
+which were similar if not identical, the furnace charge was
+crushed to a fine powder and passed through two or more electric
+arcs in succession. When used for ore smelting, the reduced
+metal and the accompanying slag were to be caught, after leaving
+the arc and while still liquid, in a hearth fired with ordinary
+fuel. Although this primitive furnace could be made to act, its
+efficiency was low, and the use of a separate fire was disadvantageous.
+In 1878 Sir William Siemens patented a form of furnace<a name="fa1m" id="fa1m" href="#ft1m"><span class="sp">1</span></a>
+which is the type of a very large number of those designed by
+later inventors.</p>
+
+<div class="condensed">
+<p>In the best-known form a plumbago crucible was used with a
+hole cut in the bottom to receive a carbon rod, which was ground
+in so as to make a tight joint. This rod was connected with the
+positive pole of the dynamo or electric generator. The crucible
+was fitted with a cover in which were two holes; one at the side to
+serve at once as sight-hole and charging door, the other in the
+centre to allow a second carbon rod to pass freely (without touching)
+into the interior. This rod was connected with the negative pole of
+the generator, and was suspended from one arm of a balance-beam,
+while from the other end of the beam was suspended a vertical hollow
+iron cylinder, which could be moved into or out of a wire coil or
+solenoid joined as a shunt across the two carbon rods of the furnace.
+The solenoid was above the iron cylinder, the supporting rod of which
+passed through it as a core. When the furnace with this well-known
+regulating device was to be used, say, for the melting of metals or
+other conductors of electricity, the fragments of metal were placed
+in the crucible and the positive electrode was brought near them.
+Immediately the current passed through the solenoid it caused the
+iron cylinder to rise, and, by means of its supporting rod, forced the
+end of the balance beam upwards, so depressing the other end that
+the negative carbon rod was forced downwards into contact with the
+metal in the crucible. This action completed the furnace-circuit,
+and current passed freely from the positive carbon through the
+fragments of metal to the negative carbon, thereby reducing the
+current through the shunt. At once the attractive force of the
+solenoid on the iron cylinder was automatically reduced, and the
+falling of the latter caused the negative carbon to rise, starting an
+arc between it and the metal in the crucible. A counterpoise was
+placed on the solenoid end of the balance beam to act against the
+attraction of the solenoid, the position of the counterpoise determining
+the length of the arc in the crucible. Any change in the resistance
+of the arc, either by lengthening, due to the sinking of the charge
+in the crucible, or by the burning of the carbon, affected the proportion
+of current flowing in the two shunt circuits, and so altered
+the position of the iron cylinder in the solenoid that the length of
+arc was, within limits, automatically regulated. Were it not for the
+use of some such device the arc would be liable to constant fluctuation
+and to frequent extinction. The crucible was surrounded with a
+bad conductor of heat to minimize loss by radiation. The positive
+carbon was in some cases replaced by a water-cooled metal tube, or
+ferrule, closed, of course, at the end inserted in the crucible. Several
+modifications were proposed, in one of which, intended for the heating
+of non-conducting substances, the electrodes were passed horizontally
+through perforations in the upper part of the crucible walls, and the
+charge in the lower part of the crucible was heated by radiation.</p>
+</div>
+
+<p>The furnace used by Henri Moissan in his experiments on
+reactions at high temperatures, on the fusion and volatilization
+of refractory materials, and on the formation of carbides, silicides
+and borides of various metals, consisted, in its simplest form,
+of two superposed blocks of lime or of limestone with a central
+cavity cut in the lower block, and with a corresponding but much
+shallower inverted cavity in the upper block, which thus formed
+the lid of the furnace. Horizontal channels were cut on opposite
+walls, through which the carbon poles or electrodes were passed
+into the upper part of the cavity. Such a furnace, to take a
+current of 4 H.P. (say, of 60 amperes and 50 volts), measured
+externally about 6 by 6 by 7 in., and the electrodes were about
+0.4 in. in diameter, while for a current of 100 H.P. (say, of 746
+amperes and 100 volts) it measured about 14 by 12 by 14 in.,
+and the electrodes were about 1.5 in. in diameter. In the latter
+case the crucible, which was placed in the cavity immediately
+beneath the arc, was about 3 in. in diameter (internally), and
+about 3½ in. in height. The fact that energy is being used at
+so high a rate as 100 H.P. on so small a charge of material
+sufficiently indicates that the furnace is only used for experimental
+work, or for the fusion of metals which, like tungsten
+or chromium, can only be melted at temperatures attainable
+by electrical means. Moissan succeeded in fusing about ¾ &#8468; of
+either of these metals in 5 or 6 minutes in a furnace similar to
+that last described. He also arranged an experimental tube-furnace
+by passing a carbon tube horizontally beneath the arc
+<span class="pagenum"><a name="page233" id="page233"></a>233</span>
+in the cavity of the lime blocks. When prolonged heating is
+required at very high temperatures it is found necessary to line
+the furnace-cavity with alternate layers of magnesia and carbon,
+taking care that the lamina next to the lime is of magnesia;
+if this were not done the lime in contact with the carbon crucible
+would form calcium carbide and would slag down, but magnesia
+does not yield a carbide in this way. Chaplet has patented
+a muffle or tube furnace, similar in principle, for use on a larger
+scale, with a number of electrodes placed above and below the
+muffle-tube. The arc furnaces now widely used in the manufacture
+of calcium carbide on a large scale are chiefly developments
+of the Siemens furnace. But whereas, from its construction,
+the Siemens furnace was intermittent in operation,
+necessitating stoppage of the current while the contents of the
+crucible were poured out, many of the newer forms are specially
+designed either to minimize the time required in effecting the
+withdrawal of one charge and the introduction of the next, or
+to ensure absolute continuity of action, raw material being
+constantly charged in at the top and the finished substance
+and by-products (slag, &amp;c.) withdrawn either continuously or
+at intervals, as sufficient quantity shall have accumulated. In
+the King furnace, for example, the crucible, or lowest part of the
+furnace, is made detachable, so that when full it may be removed
+and an empty crucible substituted. In the United States a
+revolving furnace is used which is quite continuous in action.</p>
+
+<p>The class of furnaces heated by electrically incandescent
+materials has been divided by Borchers into two groups: (1)
+those in which the substance is heated by contact
+with a substance offering a high resistance to the
+<span class="sidenote">Incandescence furnaces.</span>
+current passing through it, and (2) those in which the
+substance to be heated itself affords the resistance to
+the passage of the current whereby electric energy is converted
+into heat. Practically the first of these furnaces was that of
+Despretz, in which the mixture to be heated was placed in a
+carbon tube rendered incandescent by the passage of a current
+through its substance from end to end. In 1880 W. Borchers
+introduced his resistance-furnace, which, in one sense, is the
+converse of the Despretz apparatus. A thin carbon pencil,
+forming a bridge between two stout carbon rods, is set in the
+midst of the mixture to be heated. On passing a current through
+the carbon the small rod is heated to incandescence, and imparts
+heat to the surrounding mass. On a larger scale several pencils
+are used to make the connexions between carbon blocks which
+form the end walls of the furnace, while the side walls are of
+fire-brick laid upon one another without mortar. Many of the
+furnaces now in constant use depend mainly on this principle,
+a core of granular carbon fragments stamped together in the
+direct line between the electrodes, as in Acheson&rsquo;s carborundum
+furnace, being substituted for the carbon pencils. In other
+cases carbon fragments are mixed throughout the charge, as
+in E.H. and A.H. Cowles&rsquo;s zinc-smelting retort. In practice, in
+these furnaces, it is possible for small local arcs to be temporarily
+set up by the shifting of the charge, and these would contribute
+to the heating of the mass. In the remaining class of furnace,
+in which the electrical resistance of the charge itself is utilized,
+are the continuous-current furnaces, such as are used for the
+smelting of aluminium, and those alternating-current furnaces,
+(<i>e.g.</i> for the production of calcium carbide) in which a portion
+of the charge is first actually fused, and then maintained in the
+molten condition by the current passing through it, while the
+reaction between further portions of the charge is proceeding.</p>
+
+<p>For ordinary metallurgical work the electric furnace, requiring
+as it does (excepting where waterfalls or other cheap sources
+of power are available) the intervention of the boiler
+and steam-engine, or of the gas or oil engine, with a
+<span class="sidenote">Uses and advantages.</span>
+consequent loss of energy, has not usually proved so
+economical as an ordinary direct fired furnace. But in
+some cases in which the current is used for electrolysis and for
+the production of extremely high temperatures, for which the
+calorific intensity of ordinary fuel is insufficient, the electric
+furnace is employed with advantage. The temperature of the
+electric furnace, whether of the arc or incandescence type, is
+practically limited to that at which the least easily vaporized
+material available for electrodes is converted into vapour. This
+material is carbon, and as its vaporizing point is (estimated at)
+over 3500° C., and less than 4000° C., the temperature of the
+electric furnace cannot rise much above 3500° C. (6330° F.);
+but H. Moissan showed that at this temperature the most stable
+of mineral combinations are dissociated, and the most refractory
+elements are converted into vapour, only certain borides, silicides
+and metallic carbides having been found to resist the action of
+the heat. It is not necessary that all electric furnaces shall be
+run at these high temperatures; obviously, those of the incandescence
+or resistance type may be worked at any convenient
+temperature below the maximum. The electric furnace has
+several advantages as compared with some of the ordinary types
+of furnace, arising from the fact that the heat is generated from
+within the mass of material operated upon, and (unlike the blast-furnace,
+which presents the same advantage) without a large
+volume of gaseous products of combustion and atmospheric
+nitrogen being passed through it. In ordinary reverberatory
+and other heating furnaces the burning fuel is without the mass,
+so that the vessel containing the charge, and other parts of the
+plant, are raised to a higher temperature than would otherwise
+be necessary, in order to compensate for losses by radiation,
+convection and conduction. This advantage is especially
+observed in some cases in which the charge of the furnace is
+liable to attack the containing vessel at high temperatures,
+as it is often possible to maintain the outer walls of the electric
+furnace relatively cool, and even to keep them lined with a
+protecting crust of unfused charge. Again, the construction
+of electric furnaces may often be exceedingly crude and simple;
+in the carborundum furnace, for example, the outer walls are
+of loosely piled bricks, and in one type of furnace the charge is
+simply heaped on the ground around the carbon resistance used
+for heating, without containing-walls of any kind. There is,
+however, one (not insuperable) drawback in the use of the electric
+furnace for the smelting of pure metals. Ordinarily carbon is
+used as the electrode material, but when carbon comes in contact
+at high temperatures with any metal that is capable of forming
+a carbide a certain amount of combination between them is inevitable,
+and the carbon thus introduced impairs the mechanical
+properties of the ultimate metallic product. Aluminium, iron,
+platinum and many other metals may thus take up so much
+carbon as to become brittle and unforgeable. It is for this reason
+that Siemens, Borchers and others substituted a hollow water-cooled
+metal block for the carbon cathode upon which the melted
+metal rests while in the furnace. Liquid metal coming in contact
+with such a surface forms a crust of solidified metal over it, and
+this crust thickens up to a certain point, namely, until the heat
+from within the furnace just overbalances that lost by conduction
+through the solidified crust and the cathode material to the flowing
+water. In such an arrangement, after the first instant, the
+melted metal in the furnace does not come in contact with the
+cathode material.</p>
+
+<p><i>Electrothermal Processes.</i>&mdash;In these processes the electric
+current is used solely to generate heat, either to induce chemical
+reactions between admixed substances, or to produce a physical
+(allotropic) modification of a given substance. Borchers predicted
+that, at the high temperatures available with the electric
+furnace, every oxide would prove to be reducible by the action
+of carbon, and this prediction has in most instances been justified.
+Alumina and lime, for example, which cannot be reduced at
+ordinary furnace temperatures, readily give up their oxygen
+to carbon in the electric furnace, and then combine with an
+excess of carbon to form metallic carbides. In 1885 the brothers
+Cowles patented a process for the electrothermal reduction of
+oxidized ores by exposure to an intense current of electricity
+when admixed with carbon in a retort. Later in that year they
+patented a process for the reduction of aluminium by carbon,
+and in 1886 an electric furnace with sliding carbon rods passed
+through the end walls to the centre of a rectangular furnace.
+The impossibility of working with just sufficient carbon to reduce
+the alumina, without using any excess which would be free to
+<span class="pagenum"><a name="page234" id="page234"></a>234</span>
+form at least so much carbide as would suffice, when diffused
+through the metal, to render it brittle, practically restricts the
+<span class="sidenote">Aluminium alloys.</span>
+use of such processes to the production of aluminium
+alloys. Aluminium bronze (aluminium and copper)
+and ferro-aluminium (aluminium and iron) have
+been made in this way; the latter is the more satisfactory
+product, because a certain proportion of carbon is
+expected in an alloy of this character, as in ferromanganese and
+cast iron, and its presence is not objectionable. The furnace is
+built of fire-brick, and may measure (internally) 5 ft. in length
+by 1 ft. 8 in. in width, and 3 ft. in height. Into each end wall
+is built a short iron tube sloping downwards towards the centre,
+and through this is passed a bundle of five 3-in. carbon rods,
+bound together at the outer end by being cast into a head of
+cast iron for use with iron alloys, or of cast copper for aluminium
+bronze. This head slides freely in the cast iron tubes, and is
+connected by a copper rod with one of the terminals of the
+dynamo supplying the current. The carbons can thus, by the
+application of suitable mechanism, be withdrawn from or plunged
+into the furnace at will. In starting the furnace, the bottom
+is prepared by ramming it with charcoal-powder that has been
+soaked in milk of lime and dried, so that each particle is coated
+with a film of lime, which serves to reduce the loss of current
+by conduction through the lining when the furnace becomes
+hot. A sheet iron case is then placed within the furnace, and
+the space between it and the walls rammed with limed charcoal;
+the interior is filled with fragments of the iron or copper to be
+alloyed, mixed with alumina and coarse charcoal, broken pieces
+of carbon being placed in position to connect the electrodes.
+The iron case is then removed, the whole is covered with charcoal,
+and a cast iron cover with a central flue is placed above all.
+The current, either continuous or alternating, is then started,
+and continued for about 1 to 1½ hours, until the operation is
+complete, the carbon rods being gradually withdrawn as the
+action proceeds. In such a furnace a continuous current, for
+example, of 3000 amperes, at 50 to 60 volts, may be used at first,
+increasing to 5000 amperes in about half an hour. The reduction
+is not due to electrolysis, but to the action of carbon on alumina,
+a part of the carbon in the charge being consumed and evolved
+as carbon monoxide gas, which burns at the orifice in the cover
+so long as reduction is taking place. The reduced aluminium
+alloys itself immediately with the fused globules of metal in
+its midst, and as the charge becomes reduced the globules of
+alloy unite until, in the end, they are run out of the tap-hole
+after the current has been diverted to another furnace. It was
+found in practice (in 1889) that the expenditure of energy per
+pound of reduced aluminium was about 23 H.P.-hours, a
+number considerably in excess of that required at the present
+time for the production of pure aluminium by the electrolytic
+process described in the article <span class="sc"><a href="#artlinks">Aluminium</a></span>. Calcium carbide,
+graphite (<i>q.v.</i>), phosphorus (<i>q.v.</i>) and carborundum (<i>q.v.</i>) are now
+extensively manufactured by the operations outlined above.</p>
+
+<p><i>Electrolytic Processes.</i>&mdash;The isolation of the metals sodium
+and potassium by Sir Humphry Davy in 1807 by the electrolysis
+of the fused hydroxides was one of the earliest applications of
+the electric current to the extraction of metals. This pioneering
+work showed little development until about the middle of the
+19th century. In 1852 magnesium was isolated electrolytically
+by R. Bunsen, and this process subsequently received much
+attention at the hands of Moissan and Borchers. Two years
+later Bunsen and H.E. Sainte Claire Deville working independently
+obtained aluminium (<i>q.v.</i>) by the electrolysis of the fused
+double sodium aluminium chloride. Since that date other
+processes have been devised and the electrolytic processes have
+entirely replaced the older methods of reduction with sodium.
+Methods have also been discovered for the electrolytic manufacture
+of calcium (<i>q.v.</i>), which have had the effect of converting
+a laboratory curiosity into a product of commercial importance.
+Barium and strontium have also been produced by electro-metallurgical
+methods, but the processes have only a laboratory
+interest at present. Lead, zinc and other metals have also been
+reduced in this manner.</p>
+
+<div class="condensed">
+<p>For further information the following books, in addition to those
+mentioned at the end of the article <span class="sc"><a href="#ar66">Electrochemistry</a></span>, may be
+consulted: Borchers, <i>Handbuch der Elektrochemie</i>; <i>Electric Furnaces</i>
+(Eng. trans. by H.G. Solomon, 1908); Moissan, <i>The Electric Furnace</i>
+(1904); J. Escard, <i>Fours électriques</i> (1905); <i>Les Industries électrochimiques</i>
+(1907).</p>
+</div>
+<div class="author">(W. G. M.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1m" id="ft1m" href="#fa1m"><span class="fn">1</span></a> Cf. Siemens&rsquo;s account of the use of this furnace for experimental
+purposes in <i>British Association Report</i> for 1882.</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROMETER<a name="ar73" id="ar73"></a></span>, an instrument for measuring difference
+of potential, which operates by means of electrostatic force
+and gives the measurement either in arbitrary or in absolute
+units (see <span class="sc"><a href="#artlinks">Units, Physical</a></span>). In the last case the instrument
+is called an absolute electrometer. Lord Kelvin has classified
+electrometers into (1) Repulsion, (2) Attracted disk, and (3)
+Symmetrical electrometers (see W. Thomson, <i>Brit. Assoc. Report</i>,
+1867, or <i>Reprinted Papers on Electrostatics and Magnetization</i>,
+p. 261).</p>
+
+<p><i>Repulsion Electrometers.</i>&mdash;The simplest form of repulsion
+electrometer is W. Henley&rsquo;s pith ball electrometer (<i>Phil. Trans.</i>,
+1772, 63, p. 359) in which the repulsion of a straw ending in a
+pith ball from a fixed stem is indicated on a graduated arc (see
+<span class="sc"><a href="#ar77">Electroscope</a></span>). A double pith ball repulsion electrometer
+was employed by T. Cavallo in 1777.</p>
+
+<div class="condensed">
+<p>It may be pointed out that such an arrangement is not merely an
+arbitrary electrometer, but may become an absolute electrometer
+within certain rough limits. Let two spherical pith balls of radius r
+and weight W, covered with gold-leaf so as to be conducting, be
+suspended by parallel silk threads of length l so as just to touch each
+other. If then the balls are both charged to a potential V they will
+repel each other, and the threads will stand out at an angle 2&theta;,
+which can be observed on a protractor. Since the electrical repulsion
+of the balls is equal to C²V²4l² sin² &theta; dynes, where C = r is the capacity
+of either ball, and this force is balanced by the restoring force due
+to their weight, Wg dynes, where g is the acceleration of gravity, it
+is easy to show that we have</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">V =</td> <td>2l sin &theta; &radic;<span class="ov">Wg tan &theta;</span></td>
+<td rowspan="2"></td></tr>
+<tr><td class="denom">r</td></tr></table>
+
+<p class="noind">as an expression for their common potential V, provided that the
+balls are small and their distance sufficiently great not sensibly to
+disturb the uniformity of electric charge upon them. Observation of
+&theta; with measurement of the value of l and r reckoned in centimetres
+and W in grammes gives us the potential difference of the balls in
+absolute C.G.S. or electrostatic units. The gold-leaf electroscope
+invented by Abraham Bennet (see <span class="sc"><a href="#ar77">Electroscope</a></span>) can in like
+manner, by the addition of a scale to observe the divergence of the
+gold-leaves, be made a repulsion electrometer.</p>
+</div>
+
+<table class="flt" style="float: right; width: 390px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:353px; height:373px" src="images/img234.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 1.</span>&mdash;Snow-Harris&rsquo;s Disk Electrometer.</td></tr></table>
+
+<p><i>Attracted Disk Electrometers.</i>&mdash;A form of attracted disk
+absolute electrometer was devised by A. Volta. It consisted
+of a plane conducting plate forming one pan of a balance which
+was suspended over another insulated plate which could be
+electrified. The attraction between the two plates was balanced
+by a weight put in
+the opposite pan.
+A similar electric
+balance was subsequently
+devised by
+Sir W. Snow-Harris,<a name="fa1n" id="fa1n" href="#ft1n"><span class="sp">1</span></a>
+one of whose instruments
+is shown in
+fig. 1. C is an insulated
+disk over
+which is suspended
+another disk attached
+to the arm
+of a balance. A
+weight is put in the
+opposite scale pan
+and a measured
+charge of electricity
+is given to the disk
+C just sufficient to
+tip over the balance.
+Snow-Harris found that this charge varied as the square root
+of the weight in the opposite pan, thus showing that the
+<span class="pagenum"><a name="page235" id="page235"></a>235</span>
+attraction between the disks at given distance apart varies as
+the square of their difference of potential.</p>
+
+<p>The most important improvements in connexion with electrometers
+are due, however, to Lord Kelvin, who introduced the
+guard plate and used gravity or the torsion of a wire as a means
+for evaluating the electrical forces.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:499px; height:265px" src="images/img235a.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span>&mdash;Kelvin&rsquo;s Portable<br />Electrometer.</td>
+<td class="caption"><span class="sc">&emsp; Fig. 3. &emsp;&emsp;&emsp;</span></td></tr></table>
+
+<div class="condensed">
+<p>His portable electrometer is shown in fig. 2. H H (see fig. 3) is a
+plane disk of metal called the guard plate, fixed to the inner coating
+of a small Leyden jar (see fig. 2). At F a square hole is cut out of
+H H, and into this fits loosely without touching, like a trap door,
+a square piece of aluminium foil having a projecting tail, which carries
+at its end a stirrup L, crossed by a fine hair (see fig. 3). The square
+piece of aluminium is pivoted round a horizontal stretched wire.
+If then another horizontal disk G is placed over the disk H H and a
+difference of potential made between G and H H, the movable
+aluminium trap door F will be attracted by the fixed plate G.
+Matters are so arranged by giving a torsion to the wire carrying the
+aluminium disk F that for a certain potential difference between the
+plates H and G, the movable part F comes into a definite sighted
+position, which is observed by means of a small lens. The plate G
+(see fig. 2) is moved up and down, parallel to itself, by means of a
+screw. In using the instrument the conductor, whose potential is
+to be tested, is connected to the plate G. Let this potential be
+denoted by V, and let v be the potential of the guard plate and the
+aluminium flap. This last potential is maintained constant by
+guard plate and flap being part of the interior coating of a charged
+Leyden jar. Since the distribution of electricity may be considered
+to be constant over the surface S of the attracted disk, the mechanical
+force f on it is given by the expression,<a name="fa2n" id="fa2n" href="#ft2n"><span class="sp">2</span></a></p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">f =</td> <td>S (V &minus; v)²</td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">8&pi;d²</td></tr></table>
+
+<table class="flt" style="float: right; width: 250px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:209px; height:347px" src="images/img235b.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 4.</span>&mdash;Kelvin&rsquo;s Absolute
+Electrometer.</td></tr></table>
+
+<p class="noind">where d is the distance between the two plates. If this distance is
+varied until the attracted disk comes into a definite sighted position
+as seen by observing the end of the
+index through the lens, then since the
+force f is constant, being due to the
+torque applied by the wire for a definite
+angle of twist, it follows that the difference
+of potential of the two plates
+varies as their distance. If then two
+experiments are made, first with the
+upper plate connected to earth, and
+secondly, connected to the object being
+tested, we get an expression for the
+potential V of this conductor in the
+form</p>
+
+<p class="center">V = A (d&prime; &minus; d),</p>
+
+<p class="noind">where d and d&prime; are the distances of the
+fixed and movable plates from one
+another in the two cases, and A is some
+constant. We thus find V in terms of
+the constant and the difference of the
+two screw readings.</p>
+
+<p>Lord Kelvin&rsquo;s absolute electrometer
+(fig. 4) involves the same principle.
+There is a certain fixed guard disk B
+having a hole in it which is loosely occupied
+by an aluminium trap door plate,
+shielded by D and suspended on springs, so that its surface is parallel
+with that of the guard plate. Parallel to this is a second movable plate
+A, the distances between the two being measurable by means of a
+screw. The movable plate can be drawn down into a definite sighted
+position when a difference of potential is made between the two
+plates. This sighted position is such that the surface of the trap
+door plate is level with that of the guard plate, and is determined
+by observations made with the lenses H and L. The movable plate
+can be thus depressed by placing on it a certain standard weight W
+grammes.</p>
+
+<p>Suppose it is required to measure the difference of potentials V
+and V&prime; of two conductors. First one and then the other conductor
+is connected with the electrode of the lower or movable plate, which
+is moved by the screw until the index attached to the attracted disk
+shows it to be in the sighted position. Let the screw readings in
+the two cases be d and d&prime;. If W is the weight required to depress the
+attracted disk into the same sighted position when the plates are
+unelectrified and g is the acceleration of gravity, then the difference
+of potentials of the conductors tested is expressed by the formula</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">V &minus; V&prime; = (d &minus; d&prime;) <span class="f200">&radic;</span></td> <td><span class="ov">8&pi;gW</span></td>
+<td rowspan="2">,</td></tr>
+<tr><td class="denom">S</td></tr></table>
+
+<p class="noind">where S denotes the area of the attracted disk.</p>
+
+<p>The difference of potentials is thus determined in terms of a
+weight, an area and a distance, in absolute C.G.S. measure or electrostatic
+units.</p>
+</div>
+
+<table class="flt" style="float: right; width: 200px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:164px; height:154px" src="images/img235c.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 5.</span></td></tr></table>
+
+<p><i>Symmetrical Electrometers</i> include the dry pile electrometer
+and Kelvin&rsquo;s quadrant electrometer. The principle underlying
+these instruments is that we can
+measure differences of potential by means
+of the motion of an electrified body in a
+symmetrical field of electric force. In the
+dry pile electrometer a single gold-leaf is
+hung up between two plates which are
+connected to the opposite terminals of a
+dry pile so that a certain constant difference
+of potential exists between these
+plates. The original inventor of this
+instrument was T.G.B. Behrens (<i>Gilb.
+Ann.</i>, 1806, 23), but it generally bears the name of J.G.F.
+von Bohnenberger, who slightly modified its form. G.T. Fechner
+introduced the important improvement of using only one pile,
+which he removed from the immediate neighbourhood of the
+suspended leaf. W.G. Hankel still further improved the dry
+pile electrometer by giving a slow motion movement to the two
+plates, and substituted a galvanic battery with a large number of
+cells for the dry pile, and also employed a divided scale to measure
+the movements of the gold-leaf (<i>Pogg. Ann.</i>, 1858, 103). If the
+gold-leaf is unelectrified, it is not acted upon by the two plates
+placed at equal distances on either side of it, but if its potential
+is raised or lowered it is attracted by one disk and repelled by
+the other, and the displacement becomes a measure of its
+potential.</p>
+
+<table class="flt" style="float: left; width: 340px;" summary="Illustration">
+<tr><td class="figleft1"><img style="width:302px; height:365px" src="images/img235d.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 6.</span>&mdash;Kelvin&rsquo;s Quadrant Electrometer.</td></tr></table>
+
+<p>A vast improvement in this instrument was made by the
+invention of the quadrant electrometer by Lord Kelvin, which is
+the most sensitive form
+of electrometer yet devised.
+In this instrument
+(see fig. 5) a flat paddle-shaped
+needle of aluminium
+foil U is supported
+by a bifilar suspension
+consisting of two cocoon
+fibres. This needle is suspended
+in the interior
+of a glass vessel partly
+coated with tin-foil on
+the outside and inside,
+forming therefore a Leyden
+jar (see fig. 6). In
+the bottom of the vessel
+is placed some sulphuric
+acid, and a platinum wire
+attached to the suspended
+needle dips into this acid.
+By giving a charge to
+this Leyden jar the needle can thus be maintained at a certain
+constant high potential. The needle is enclosed by a sort of
+flat box divided into four insulated quadrants A, B, C, D (fig. 5),
+whence the name. The opposite quadrants are connected together
+by thin platinum wires. These quadrants are insulated
+<span class="pagenum"><a name="page236" id="page236"></a>236</span>
+from the needle and from the case, and the two pairs are connected
+to two electrodes. When the instrument is to be used to determine
+the potential difference between two conductors, they are
+connected to the two opposite pairs of quadrants. The needle
+in its normal position is symmetrically placed with regard to
+the quadrants, and carries a mirror by means of which its displacement
+can be observed in the usual manner by reflecting
+the ray of light from it. If the two quadrants are at different
+potentials, the needle moves from one quadrant towards the
+other, and the image of a spot of light on the scale is therefore
+displaced. Lord Kelvin provided the instrument with two
+necessary adjuncts, viz. a replenisher or rotating electrophorus
+(<i>q.v.</i>), by means of which the charge of the Leyden jar which forms
+the enclosing vessel can be increased or diminished, and also a
+small aluminium balance plate or gauge, which is in principle the
+same as the attracted disk portable electrometer by means of
+which the potential of the inner coating of the Leyden jar is
+preserved at a known value.</p>
+
+<div class="condensed">
+<p>According to the mathematical theory of the instrument,<a name="fa3n" id="fa3n" href="#ft3n"><span class="sp">3</span></a> if V
+and V&prime; are the potentials of the quadrants and v is the potential of
+the needle, then the torque acting upon the needle to cause rotation
+is given by the expression,</p>
+
+<p class="center">C (V &minus; V&prime;) {v &minus; ½ (V + V&prime;)},</p>
+
+<p class="noind">where C is some constant. If v is very large compared with the
+mean value of the potentials of the two quadrants, as it usually is,
+then the above expression indicates that the couple varies as the
+difference of the potentials between the quadrants.</p>
+
+<p>Dr J. Hopkinson found, however, before 1885, that the above
+formula does not agree with observed facts (<i>Proc. Phys. Soc. Lond.</i>,
+1885, 7, p. 7). The formula indicates that the sensibility of the instrument
+should increase with the charge of the Leyden jar or needle,
+whereas Hopkinson found that as the potential of the needle was
+increased by working the replenisher of the jar, the deflection due
+to three volts difference between the quadrants first increased and
+then diminished. He found that when the potential of the needle
+exceeded a certain value, of about 200 volts, for the particular
+instrument he was using (made by White of Glasgow), the above
+formula did not hold good. W.E. Ayrton, J. Perry and W.E.
+Sumpner, who in 1886 had noticed the same fact as Hopkinson,
+investigated the matter in 1891 (<i>Proc. Roy. Soc.</i>, 1891, 50, p. 52;
+<i>Phil. Trans.</i>, 1891, 182, p. 519). Hopkinson had been inclined to
+attribute the anomaly to an increase in the tension of the bifilar
+threads, owing to a downward pull on the needle, but they showed
+that this theory would not account for the discrepancy. They
+found from observations that the particular quadrant electrometer
+they used might be made to follow one or other of three distinct laws.
+If the quadrants were near together there were certain limits between
+which the potential of the needle might vary without producing more
+than a small change in the deflection corresponding with the fixed
+potential difference of the quadrants. For example, when the
+quadrants were about 2.5 mm. apart and the suspended fibres near
+together at the top, the deflection produced by a P.D. of 1.45 volts
+between the quadrants only varied about 11% when the potential
+of the needle varied from 896 to 3586 volts. When the fibres were
+far apart at the top a similar flatness was obtained in the curve
+with the quadrants about 1 mm. apart. In this case the deflection
+of the needle was practically quite constant when its potential varied
+from 2152 to 3227 volts. When the quadrants were about 3.9 mm.
+apart, the deflection for a given P.D. between the quadrants was
+almost directly proportional to the potential of the needle. In other
+words, the electrometer nearly obeyed the theoretical law. Lastly,
+when the quadrants were 4 mm. or more apart, the deflection increased
+much more rapidly than the potential, so that a maximum
+sensibility bordering on instability was obtained. Finally, these observers
+traced the variation to the fact that the wire supporting the
+aluminium needle as well as the wire which connects the needle with
+the sulphuric acid in the Leyden jar in the White pattern of Leyden
+jar is enclosed in a metallic guard tube to screen the wire from
+external action. In order that the needle may project outside
+the guard tube, openings are made in its two sides; hence the moment
+the needle is deflected each half of it becomes unsymmetrically
+placed relatively to the two metallic pieces which join the upper and
+lower half of the guard tube. Guided by these experiments, Ayrton,
+Perry and Sumpner constructed an improved unifilar quadrant
+electrometer which was not only more sensitive than the White
+pattern, but fulfilled the theoretical law of working. The bifilar
+suspension was abandoned, and instead a new form of adjustable
+magnetic control was adopted. All the working parts of the instrument
+were supported on the base, so that on removing a glass shade
+which serves as a Leyden jar they can be got at and adjusted in
+position. The conclusion to which the above observers came was
+that any quadrant electrometer made in any manner does not
+necessarily obey a law of deflection making the deflections proportional
+to the potential difference of the quadrants, but that an
+electrometer can be constructed which does fulfil the above law.</p>
+
+<p>The importance of this investigation resides in the fact that an
+electrometer of the above pattern can be used as a wattmeter (<i>q.v.</i>),
+provided that the deflection of the needle is proportional to the
+potential difference of the quadrants. This use of the instrument
+was proposed simultaneously in 1881 by Professors Ayrton and G.F.
+Fitzgerald and M.A. Potier. Suppose we have an inductive and a
+non-inductive circuit in series, which is traversed by a periodic
+current, and that we desire to know the power being absorbed to the
+inductive circuit. Let v<span class="su">1</span>, v<span class="su">2</span>, v<span class="su">3</span> be the instantaneous potentials of
+the two ends and middle of the circuit; let a quadrant electrometer
+be connected first with the quadrants to the two ends of the inductive
+circuit and the needle to the far end of the non-inductive circuit,
+and then secondly with the needle connected to one of the quadrants
+(see fig. 5). Assuming the electrometer to obey the above-mentioned
+theoretical law, the first reading is proportional to</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">v<span class="su">1</span> &minus; v<span class="su">2</span>
+ <span class="f150">{</span> v<span class="su">3</span> &minus;</td> <td>v<span class="su">1</span> + v<span class="su">2</span></td>
+<td rowspan="2"><span class="f150">}</span></td></tr>
+<tr><td class="denom">2</td></tr></table>
+
+<p class="noind">and the second to</p>
+
+<table class="math0" summary="math">
+<tr><td rowspan="2">v<span class="su">1</span> &minus; v<span class="su">2</span>
+ <span class="f150">{</span> v<span class="su">2</span> &minus;</td> <td>v<span class="su">1</span> + v<span class="su">2</span></td>
+<td rowspan="2"><span class="f150">}</span>.</td></tr>
+<tr><td class="denom">2</td></tr></table>
+
+<p class="noind">The difference of the readings is then proportional to</p>
+
+<p class="center">(v<span class="su">1</span> &minus; v<span class="su">2</span>) (v<span class="su">2</span> &minus; v<span class="su">3</span>).</p>
+
+<p class="noind">But this last expression is proportional to the instantaneous power
+taken up in the inductive circuit, and hence the difference of the
+two readings of the electrometer is proportional to the mean power
+taken up in the circuit (<i>Phil. Mag.</i>, 1891, 32, p. 206). Ayrton and
+Perry and also P.R. Blondlot and P. Curie afterwards suggested
+that a single electrometer could be constructed with two pairs of
+quadrants and a duplicate needle on one stem, so as to make two
+readings simultaneously and produce a deflection proportional at
+once to the power being taken up in the inductive circuit.</p>
+</div>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter"><img style="width:476px; height:532px" src="images/img236.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 7.</span>&mdash;Quadrant Electrometer. Dolezalek Pattern.</td></tr></table>
+
+<p>Quadrant electrometers have also been designed especially
+for measuring extremely small potential differences. An instrument
+of this kind has been constructed by Dr. F. Dolezalek
+(fig. 7). The needle and quadrants are of small size, and the
+electrostatic capacity is correspondingly small. The quadrants
+are mounted on pillars of amber which afford a very high
+insulation. The needle, a piece of paddle-shaped paper thinly
+coated with silver foil, is suspended by a quartz fibre, its extreme
+lightness making it possible to use a very feeble controlling force
+without rendering the period of oscillation unduly great. The
+resistance offered by the air to a needle of such light construction
+suffices to render the motion nearly dead-beat. Throughout a
+wide range the deflections are proportional to the potential
+difference producing them. The needle is charged to a potential
+<span class="pagenum"><a name="page237" id="page237"></a>237</span>
+of 50 to 200 volts by means of a dry pile or voltaic battery, or
+from a lighting circuit. To facilitate the communication of
+the charge to the needle, the quartz fibre and its attachments
+are rendered conductive by a thin film of solution of hygroscopic
+salt such as calcium chloride. The lightness of the needle enables
+the instrument to be moved without fear of damaging the suspension.
+The upper end of the quartz fibre is rotated by a torsion
+head, and a metal cover serves to screen the instrument from stray
+electrostatic fields. With a quartz fibre 0.009 mm. thick and
+60 mm. long, the needle being charged to 110 volts, the period
+and swing of the needle was 18 seconds. With the scale at a
+distance of two metres, a deflection of 130 mm. was produced by
+an electromotive force of 0.1 volt. By using a quartz fibre of
+about half the above diameter the sensitiveness was much
+increased. An instrument of this form is valuable in measuring
+small alternating currents by the fall of potential produced
+down a known resistance. In the same way it may be employed
+to measure high potentials by measuring the fall of potential
+down a fraction of a known non-inductive resistance. In this
+last case, however, the capacity of the electrometer used must be
+small, otherwise an error is introduced.<a name="fa4n" id="fa4n" href="#ft4n"><span class="sp">4</span></a></p>
+
+<div class="condensed">
+<p>See, in addition to references already given, A. Gray, <i>Absolute
+Measurements in Electricity and Magnetism</i> (London, 1888), vol. i.
+p. 254; A. Winkelmann, <i>Handbuch der Physik</i> (Breslau, 1905),
+pp. 58-70, which contains a large number of references to original
+papers on electrometers.</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1n" id="ft1n" href="#fa1n"><span class="fn">1</span></a> It is probable that an experiment of this kind had been made as
+far back as 1746 by Daniel Gralath, of Danzig, who has some claims
+to have suggested the word &ldquo;electrometer&rdquo; in connexion with it.
+See Park Benjamin, <i>The Intellectual Rise in Electricity</i> (London, 1895),
+p. 542.</p>
+
+<p><a name="ft2n" id="ft2n" href="#fa2n"><span class="fn">2</span></a> See Maxwell, <i>Treatise on Electricity and Magnetism</i> (2nd ed.),
+i. 308.</p>
+
+<p><a name="ft3n" id="ft3n" href="#fa3n"><span class="fn">3</span></a> See Maxwell, <i>Electricity and Magnetism</i> (2nd ed., Oxford, 1881),
+vol. i. p. 311.</p>
+
+<p><a name="ft4n" id="ft4n" href="#fa4n"><span class="fn">4</span></a> See J.A. Fleming, <i>Handbook for the Electrical Laboratory and
+Testing Room</i>, vol. i. p. 448 (London, 1901).</p>
+</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTRON<a name="ar74" id="ar74"></a></span>, the name suggested by Dr G. Johnstone Stoney
+in 1891 for the natural unit of electricity to which he had drawn
+attention in 1874, and subsequently applied to the ultra-atomic
+particles carrying negative charges of electricity, of which
+Professor Sir J.J. Thomson proved in 1897 that the cathode
+rays consisted. The electrons, which Thomson at first called
+corpuscles, are point charges of negative electricity, their inertia
+showing them to have a mass equal to about <span class="spp">1</span>&frasl;<span class="suu">2000</span> that of
+the hydrogen atom. They are apparently derivable from all
+kinds of matter, and are believed to be components at any rate
+of the chemical atom. The electronic theory of the chemical
+atom supposes, in fact, that atoms are congeries of electrons
+in rapid orbital motion. The size of the electron is to that of an
+atom roughly in the ratio of a pin&rsquo;s head to the dome of St
+Paul&rsquo;s cathedral. The electron is always associated with the unit
+charge of negative electricity, and it has been suggested that
+its inertia is wholly electrical. For further details see the
+articles on <span class="sc"><a href="#ar63">Electricity</a></span>; <span class="sc"><a href="#artlinks">Magnetism</a></span>; <span class="sc"><a href="#artlinks">Matter</a></span>; <span class="sc"><a href="#artlinks">Radioactivity</a></span>;
+<span class="sc"><a href="#artlinks">Conduction, Electric</a></span>; <i>The Electron Theory</i>, E.
+Fournier d&rsquo;Albe (London, 1907); and the original papers of
+Dr G. Johnstone Stoney, <i>Proc. Brit. Ass.</i> (Belfast, August 1874),
+&ldquo;On the Physical Units of Nature,&rdquo; and <i>Trans. Royal Dublin
+Society</i> (1891), 4, p. 583.</p>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROPHORUS<a name="ar75" id="ar75"></a></span>, an instrument invented by Alessandro
+Volta in 1775, by which mechanical work is transformed into
+electrostatic charge by the aid of a small initial charge of electricity.
+The operation depends on the facts of electrostatic induction
+discovered by John Canton in 1753, and, independently,
+by J.K. Wilcke in 1762 (see <span class="sc"><a href="#ar63">Electricity</a></span>). Volta, in a letter
+to J. Priestley on the 10th of June 1775 (see <i>Collezione dell&rsquo; opere</i>,
+ed. 1816, vol. i. p. 118), described the invention of a device
+he called an <i>elettroforo perpetuo</i>, based on the fact that a conductor
+held near an electrified body and touched by the finger
+was found, when withdrawn, to possess an electric charge of
+opposite sign to that of the electrified body. His electrophorus
+in one form consisted of a disk of non-conducting material, such
+as pitch or resin, placed between two metal sheets, one being
+provided with an insulating handle. For the pitch or resin
+may be substituted a sheet of glass, ebonite, india-rubber or
+any other good dielectric placed upon a metallic sheet, called
+the sole-plate. To use the apparatus the surface of the dielectric
+is rubbed with a piece of warm flannel, silk or catskin, so as to
+electrify it, and the upper metal plate is then placed upon it.
+Owing to the irregularities in the surfaces of the dielectric and
+upper plate the two are only in contact at a few points, and owing
+to the insulating quality of the dielectric its surface electrical
+charge cannot move over it. It therefore acts inductively upon
+the upper plate and induces on the adjacent surface an electric
+charge of opposite sign. Suppose, for instance, that the dielectric
+is a plate of resin rubbed with catskin, it will then be negatively
+electrified and will act by induction on the upper plate across
+the film of air separating the upper resin surface and lower
+surface of the upper metal plate. If the upper plate is touched
+with the finger or connected to earth for a moment, a negative
+charge will escape from the metal plate to earth at that moment.
+The arrangement thus constitutes a condenser; the upper plate
+on its under surface carries a charge of positive electricity and
+the resin plate a charge of negative electricity on its upper
+surface, the air film between them being the dielectric of the
+condenser. If, therefore, the upper plate is elevated, mechanical
+work has to be done to separate the two electric charges. Accordingly
+on raising the upper plate, the charge on it, in old-fashioned
+nomenclature, becomes <i>free</i> and can be communicated
+to any other insulated conductor at a lower potential, the upper
+plate thereby becoming more or less discharged. On placing
+the upper plate again on the resin and touching it for a moment,
+the process can be repeated, and so at the expense of mechanical
+work done in lifting the upper plate against the mutual attraction
+of two electric charges of opposite sign, an indefinitely large
+electric charge can be accumulated and given to any other
+suitable conductor. In course of time, however, the surface charge
+of the resin becomes dissipated and it then has to be again excited.
+To avoid the necessity for touching the upper plate every time
+it is put down on the resin, a metal pin may be brought through
+the insulator from the sole-plate so that each time that the
+upper plate is put down on the resin it is automatically connected
+to earth. We are thus able by a process of merely lifting the
+upper plate repeatedly to convey a large electrical charge to
+some conductor starting from the small charge produced by
+friction on the resin. The above explanation does not take into
+account the function of the sole-plate, which is important. The
+sole-plate serves to increase the electrical capacity of the upper
+plate when placed down upon the resin or excited insulator.
+Hence when so placed it takes a larger charge. When touched
+by the finger the upper plate is brought to zero potential. If
+then the upper plate is lifted by its insulating handle its capacity
+becomes diminished. Since, however, it carries with it the charge
+it had when resting on the resin, its potential becomes increased
+as its capacity becomes less, and it therefore rises to a high
+potential, and will give a spark if the knuckle is approached to
+it when it is lifted after having been touched and raised.</p>
+
+<p>The study of Volta&rsquo;s electrophorus at once suggested the
+performance of these cyclical operations by some form of rotation
+instead of elevation, and led to the invention of various
+forms of doubler or multiplier. The instrument was thus the
+first of a long series of machines for converting mechanical work
+into electrostatic energy, and the predecessor of the modern
+type of influence machine (see <span class="sc"><a href="#ar61">Electrical Machine</a></span>). Volta
+himself devised a double and reciprocal electrophorus and also
+made mention of the subject of multiplying condensers in a paper
+published in the <i>Phil. Trans.</i> for 1782 (p. 237, and appendix,
+p. vii.). He states, however, that the use of a condenser in
+connexion with an electrophorus to make evident and multiply
+weak charges was due to T. Cavallo (<i>Phil. Trans.</i>, 1788).</p>
+
+<div class="condensed">
+<p>For further information see S.P. Thompson, &ldquo;The Influence
+Machine from 1788 to 1888,&rdquo; <i>Journ. Inst. Tel. Eng.</i>, 1888, 17, p. 569.
+Many references to original papers connected with the electrophorus
+will be found in A. Winkelmann&rsquo;s <i>Handbuch der Physik</i> (Breslau,
+1905), vol. iv. p. 48.</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+
+<hr class="art" />
+<p><span class="bold">ELECTROPLATING<a name="ar76" id="ar76"></a></span>, the art of depositing metals by the
+electric current. In the article <span class="sc"><a href="#ar70">Electrolysis</a></span> it is shown how
+the passage of an electric current through a solution containing
+metallic ions involves the deposition of the metal on the cathode.
+Sometimes the metal is deposited in a pulverulent form, at others
+as a firm tenacious film, the nature of the deposit being dependent
+upon the particular metal, the concentration of the solution, the
+difference of potential between the electrodes, and other experimental
+conditions. As the durability of the electro-deposited
+<span class="pagenum"><a name="page238" id="page238"></a>238</span>
+coat on plated wares of all kinds is of the utmost importance,
+the greatest care must be taken to ensure its complete adhesion.
+This can only be effected if the surface of the metal on which
+the deposit is to be made is chemically clean. Grease must
+be removed by potash, whiting or other means, and tarnish
+by an acid or potassium cyanide, washing in plenty of water
+being resorted to after each operation. The vats for depositing
+may be of enamelled iron, slate, glazed earthenware, glass,
+lead-lined wood, &amp;c. The current densities and potential
+differences frequently used for some of the commoner metals
+are given in the following table, taken from M&rsquo;Millan&rsquo;s <i>Treatise
+on Electrometallurgy</i>. It must be remembered, however, that
+variations in conditions modify the electromotive force required
+for any given process. For example, a rise in temperature of
+the bath causes an increase in its conductivity, so that a lower
+E.M.F. will suffice to give the required current density; on the
+other hand, an abnormally great distance between the electrodes,
+or a diminution in acidity of an acid bath, or in the strength of
+the solution used, will increase the resistance, and so require
+the application of a higher E.M.F.</p>
+
+<table class="ws" summary="Contents">
+<tr><td class="tccm allb" rowspan="2">Metal.</td> <td class="tccm allb" colspan="2">Amperes.</td> <td class="tccm allb" rowspan="2">Volts between<br />Anode and<br />Cathode.</td></tr>
+<tr><td class="tccm allb">Per sq. decimetre<br />of Cathode<br />Surface.</td> <td class="tccm allb">Per sq. in. of<br />Cathode<br />Surface.</td></tr>
+
+<tr><td class="tcl lb rb">Antimony</td> <td class="tcc rb">0.4-0.5</td> <td class="tcc rb">0.02-0.03</td> <td class="tcc rb">1.0-1.2</td></tr>
+<tr><td class="tcl lb rb">Brass</td> <td class="tcc rb">0.5-0.8</td> <td class="tcc rb">0.03-0.05</td> <td class="tcc rb">3.0-4.0</td></tr>
+<tr><td class="tcl lb rb">Copper, acid bath</td> <td class="tcc rb">1.0-1.5</td> <td class="tcc rb">0.065-0.10</td> <td class="tcc rb">0.5-1.5</td></tr>
+<tr><td class="tcl lb rb">Copper, alkaline bath</td> <td class="tcc rb">0.3-0.5</td> <td class="tcc rb">0.02-0.03</td> <td class="tcc rb">3.0-5.0</td></tr>
+<tr><td class="tcl lb rb">Gold</td> <td class="tcc rb">0.1</td> <td class="tcc rb">0.006</td> <td class="tcc rb">0.5-4.0</td></tr>
+<tr><td class="tcl lb rb">Iron</td> <td class="tcc rb">0.5</td> <td class="tcc rb">0.03</td> <td class="tcc rb">1.0</td></tr>
+<tr><td class="tcl lb rb">Nickel, at first</td> <td class="tcc rb">1.4-1.5</td> <td class="tcc rb">0.09-0.10</td> <td class="tcc rb">5.0</td></tr>
+<tr><td class="tcl lb rb">Nickel, after</td> <td class="tcc rb">0.2-0.3</td> <td class="tcc rb">0.015-0.02</td> <td class="tcc rb">1.5-2.0</td></tr>
+<tr><td class="tcl lb rb">Nickel, on zinc</td> <td class="tcc rb">0.4</td> <td class="tcc rb">0.025</td> <td class="tcc rb">4.0-5.0</td></tr>
+<tr><td class="tcl lb rb">Silver</td> <td class="tcc rb">0.2-0.5</td> <td class="tcc rb">0.015-0.03</td> <td class="tcc rb">0.75-1.0</td></tr>
+<tr><td class="tcl lb rb bb">Zinc</td> <td class="tcc rb bb">0.3-0.6</td> <td class="tcc rb bb">0.02-0.04</td> <td class="tcc rb bb">2.5-3.0</td></tr>
+</table>
+
+<p>Large objects are suspended in the tanks by hooks or wires,
+care being taken to shift their position and so avoid wire-marks.
+Small objects are often heaped together in perforated trays or
+ladles, the cathode connecting-rod being buried in the midst of
+them. These require constant shifting because the objects are
+in contact at many points, and because the top ones shield those
+below from the depositing action of the current. Hence processes
+have been patented in which the objects to be plated are suspended
+in revolving drums between the anodes, the rotation of the drum
+causing the constant renewal of surfaces and affording a burnishing
+action at the same time. Care must be taken not to expose goods
+in the plating-bath to too high a current density, else they may
+be &ldquo;burnt&rdquo;; they must never be exposed one at a time to the
+full anode surface, with the current flowing in an empty bath,
+but either one piece at a time should be replaced, or some of the
+anodes should be transferred temporarily to the place of the
+cathodes, in order to distribute the current over a sufficient
+cathode-area. Burnt deposits are dark-coloured, or even pulverulent
+and useless. The strength of the current may also
+be regulated by introducing lengths of German silver or iron
+wire, carbon rod, or other inferior conductors in the path of the
+current, and a series of such resistances should always be provided
+close to the tanks. Ammeters to measure the volume, and voltmeters
+to determine the pressure of current supplied to the baths,
+should also be provided. Very irregular surfaces may require
+the use of specially shaped anodes in order that the distance
+between the electrodes may be fairly uniform, otherwise the
+portion of the cathode lying nearest to the anode may receive
+an undue share of the current, and therefore a greater thickness
+of coat. Supplementary anodes are sometimes used in difficult
+cases of this kind. Large metallic surfaces (especially external
+surfaces) are sometimes plated by means of a &ldquo;doctor,&rdquo; which,
+in its simplest form, is a brush constantly wetted with the
+electrolyte, with a wire anode buried amid the hairs or bristles;
+this brush is painted slowly over the surface of the metal to be
+coated, which must be connected to the negative terminal of the
+electrical generator. Under these conditions electrolysis of the
+solution in the brush takes place. Iron ships&rsquo; plates have recently
+been coated with copper in sections (to prevent the adhesion of
+barnacles), by building up a temporary trough against the side
+of the ship, making the thoroughly cleansed plate act both as
+cathode and as one side of the trough. Decorative plating-work
+in several colours (<i>e.g.</i> &ldquo;parcel-gilding&rdquo;) is effected by painting
+a portion of an object with a stopping-out (<i>i.e.</i> a non-conducting)
+varnish, such as copal varnish, so that this portion is not coated.
+The varnish is then removed, a different design stopped out, and
+another metal deposited. By varying this process, designs in
+metals of different colours may readily be obtained.</p>
+
+<p>Reference must be made to the textbooks (see <span class="sc"><a href="#ar66">Electrochemistry</a></span>)
+for a fuller account of the very varied solutions and
+methods employed for electroplating with silver, gold, copper,
+iron and nickel. It should be mentioned here, however, that
+solutions which would deposit their metal on any object by simple
+immersion should not be generally used for electroplating that
+object, as the resulting deposit is usually non-adhesive. For
+this reason the acid copper-bath is not used for iron or zinc
+objects, a bath containing copper cyanide or
+oxide dissolved in potassium cyanide being
+substituted. This solution, being an inferior
+conductor of electricity, requires a much higher
+electromotive force to drive the current through
+it, and is therefore more costly in use. It is,
+however, commonly employed hot, whereby its
+resistance is reduced. <i>Zinc</i> is commonly deposited
+by electrolysis on iron or steel goods
+which would ordinarily be &ldquo;galvanized,&rdquo; but
+which for any reason may not conveniently be
+treated by the method of immersion in fused
+zinc. The zinc cyanide bath may be used
+for small objects, but for heavy goods the
+sulphate bath is employed. Sherard Cowper-Coles
+patented a process in which, working
+with a high current density, a lead anode is used, and
+powdered zinc is kept suspended in the solution to maintain
+the proportion of zinc in the electrolyte, and so to
+guard against the gradual acidification of the bath. <i>Cobalt</i>
+is deposited by a method analogous to that used for its sister-metal
+nickel. <i>Platinum</i>, <i>palladium</i> and <i>tin</i> are occasionally
+deposited for special purposes. In the deposition of <i>gold</i> the
+colour of the deposit is influenced by the presence of impurities
+in the solution; when copper is present, some is deposited with
+the gold, imparting to it a reddish colour, whilst a little silver
+gives it a greenish shade. Thus so-called coloured-gold deposits
+may be produced by the judicious introduction of suitable
+impurities. Even pure gold, it may be noted, is darker or lighter
+in colour according as a stronger or a weaker current is used.
+The electro-deposition of <i>brass</i>&mdash;mainly on iron ware, such as
+bedstead tubes&mdash;is now very widely practised, the bath employed
+being a mixture of copper, zinc and potassium cyanides, the
+proportions of which vary according to the character of the brass
+required, and to the mode of treatment. The colour depends
+in part upon the proportion of copper and zinc, and in part upon
+the current density, weaker currents tending to produce a redder
+or yellower metal. Other alloys may be produced, such as bronze,
+or German silver, by selecting solutions (usually cyanides) from
+which the current is able to deposit the constituent metals
+simultaneously.</p>
+
+<p>Electrolysis has in a few instances been applied to processes
+of manufacture. For example, Wilde produced copper printing
+surfaces for calico printing-rollers and the like by immersing
+rotating iron cylinders as cathodes in a copper bath. Elmore,
+Dumoulin, Cowper-Coles and others have prepared copper
+cylinders and plates by depositing copper on rotating mandrels
+with special arrangements. Others have arranged a means of
+obtaining high conductivity wire from cathode-copper without
+fusion, by depositing the metal in the form of a spiral strip on
+a cylinder, the strip being subsequently drawn down in the
+usual way; at present, however, the ordinary methods of wire
+<span class="pagenum"><a name="page239" id="page239"></a>239</span>
+production are found to be cheaper. J.W. Swan (<i>Journ. Inst.
+Elec. Eng.</i>, 1898, vol. xxvii. p. 16) also worked out, but did not
+proceed with, a process in which a copper wire whilst receiving
+a deposit of copper was continuously passed through the draw-plate,
+and thus indefinitely extended in length. Cowper-Coles
+(<i>Journ. Inst. Elec. Eng.</i>, 1898, 27, p. 99) very successfully
+produced true parabolic reflectors for projectors, by depositing
+copper upon carefully ground and polished glass surfaces rendered
+conductive by a film of deposited silver.</p>
+
+
+<hr class="art" />
+
+<table class="flt" style="float: right; width: 160px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:119px; height:433px" src="images/img239a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 1.</span>&mdash;Henley&rsquo;s
+Electroscope.</td></tr></table>
+
+<p><span class="bold">ELECTROSCOPE,<a name="ar77" id="ar77"></a></span> an instrument for detecting differences of
+electric potential and hence electrification. The earliest form
+of scientific electroscope was the <i>versorium</i>
+or electrical needle of William Gilbert (1544-1603),
+the celebrated author of the treatise
+<i>De magnete</i> (see <span class="sc"><a href="#ar63">Electricity</a></span>). It consisted
+simply of a light metallic needle balanced on
+a pivot like a compass needle. Gilbert employed
+it to prove that numerous other
+bodies besides amber are susceptible of being
+electrified by friction.<a name="fa1o" id="fa1o" href="#ft1o"><span class="sp">1</span></a> In this case the
+visible indication consisted in the attraction
+exerted between the electrified body and the
+light pivoted needle which was acted upon
+and electrified by induction. The next improvement
+was the invention of simple forms
+of repulsion electroscope. Two similarly
+electrified bodies repel each other. Benjamin
+Franklin employed the repulsion of two linen
+threads, C.F. de C. du Fay, J. Canton, W.
+Henley and others devised the pith ball, or
+double straw electroscope (fig. 1). T. Cavallo
+about 1770 employed two fine silver wires
+terminating in pith balls suspended in a glass
+vessel having strips of tin-foil pasted down
+the sides (fig. 2). The object of the thimble-shaped
+dome was to keep moisture from the
+stem from which the pith balls were supported, so that the
+apparatus could be used in the open air even in the rainy
+weather. Abraham Bennet (<i>Phil. Trans.</i>, 1787, 77, p. 26)
+invented the modern form of gold-leaf electroscope. Inside
+a glass shade he fixed to an insulated wire a pair of strips
+of gold-leaf (fig. 3). The wire terminated in a plate or
+knob outside the vessel. When an electrified body was held
+near or in contact with the knob, repulsion of the gold leaves
+ensued. Volta added the condenser (<i>Phil. Trans.</i>, 1782),
+which greatly increased the power of the instrument. M.
+Faraday, however, showed long subsequently that to bestow
+upon the indications of such an electroscope definite meaning
+it was necessary to place a cylinder of metallic gauze connected
+to the earth inside the vessel, or better still, to line the glass
+shade with tin-foil connected to the earth and observe through
+a hole the indications of the gold leaves (fig. 4). Leaves of
+aluminium foil may with advantage be substituted for gold-leaf,
+and a scale is sometimes added to indicate the angular divergence
+of the leaves.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:504px; height:373px" src="images/img239b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 2.</span>&mdash;Cavallo&rsquo;s Electroscope.</td>
+<td class="caption"><span class="sc">Fig. 3.</span>&mdash;Bennet&rsquo;s<br />Electroscope.</td></tr></table>
+
+<p>The uses of an electroscope are, first, to ascertain if any body
+is in a state of electrification, and secondly, to indicate the sign
+of that charge. In connexion with the modern study of radioactivity,
+the electroscope has become an instrument of great
+usefulness, far outrivalling the spectroscope in sensibility.
+Radio-active bodies are chiefly recognized by the power they
+possess of rendering the air in their neighbourhood conductive;
+hence the electroscope detects the presence of a radioactive body
+by losing an electric charge given to it more quickly than it
+would otherwise do. A third great use of the electroscope is
+therefore to detect electric conductivity either in the air or in
+any other body.</p>
+
+<table class="flt" style="float: right; width: 220px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:179px; height:278px" src="images/img239c.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 4.</span>&mdash;Gold-Leaf
+Electroscope.</td></tr></table>
+
+<p>To detect electrification it is best to charge the electroscope
+by induction. If an electrified body is held near the gold-leaf
+electroscope the leaves diverge with electricity of the same sign
+as that of the body being tested. If, without removing the
+electrified body, the plate or knob of the electroscope is touched,
+the leaves collapse. If the electroscope is insulated once more and
+the electrified body removed, the leaves
+again diverge with electricity of the
+opposite sign to that of the body being
+tested. The sign of charge is then determined
+by holding near the electroscope a
+glass rod rubbed with silk or a sealing-wax
+rod rubbed with flannel. If the
+approach of the glass rod causes the
+leaves in their final state to collapse,
+then the charge in the rod was positive,
+but if it causes them to expand still
+more the charge was negative, and vice
+versa for the sealing-wax rod. When
+employing a Volta condensing electroscope,
+the following is the method of
+procedure:&mdash;The top of the electroscope
+consists of a flat, smooth plate
+of lacquered brass on which another plate of brass rests,
+separated from it by three minute fragments of glass or
+shellac, or a film of shellac varnish. If the electrified body
+is touched against the upper plate whilst at the same time the
+lower plate is put to earth, the condenser formed of the two plates
+and the film of air or varnish becomes charged with positive
+electricity on the one plate and negative on the other. On insulating
+the lower plate and raising the upper plate by the glass
+handle, the capacity of the condenser formed by the plates is
+vastly decreased, but since the charge on the lower plate including
+the gold leaves attached to it remains the same, as the capacity
+of the system is reduced the potential is raised and therefore the
+gold leaves diverge widely. Volta made use of such an electroscope
+in his celebrated experiments (1790-1800) to prove that
+metals placed in contact with one another are brought to different
+potentials, in other words to prove the existence of so-called
+contact electricity. He was assisted to detect the small potential
+differences then in question by the use of a multiplying condenser
+or revolving doubler (see <span class="sc"><a href="#ar61">Electrical Machine</a></span>). To employ the
+electroscope as a means of detecting radioactivity, we have first
+to test the leakage quality of the electroscope itself. Formerly
+it was usual to insulate the rod of the electroscope by passing it
+through a hole in a cork or mass of sulphur fixed in the top of
+the glass vessel within which the gold leaves were suspended.
+A further improvement consisted in passing the metal wire to
+which the gold leaves were attached through a glass tube much
+wider than the rod, the latter being fixed concentrically in the
+glass tube by means of solid shellac melted and run in. This
+insulation, however, is not sufficiently good for an electroscope
+intended for the detection of radioactivity; for this purpose
+<span class="pagenum"><a name="page240" id="page240"></a>240</span>
+it must be such that the leaves will remain for hours or days in
+a state of steady divergence when an electrical charge has been
+given to them.</p>
+
+<table class="flt" style="float: right; width: 240px;" summary="Illustration">
+<tr><td class="figright1"><img style="width:190px; height:118px" src="images/img240a.jpg" alt="" /></td></tr>
+<tr><td class="caption1"><span class="sc">Fig. 5.</span>&mdash;Curie&rsquo;s Electroscope.</td></tr></table>
+
+<p>In their researches on radioactivity M. and Mme P. Curie
+employed an electroscope made as follows:&mdash;A metal case
+(fig. 5), having two holes in its sides, has a vertical brass strip B
+attached to the inside of the lid by a block of sulphur SS or any
+other good insulator. Joined to the strip is a transverse wire
+terminating at one end in a knob C,
+and at the other end in a condenser
+plate P&prime;. The strip B carries also a
+strip of gold-leaf L, and the metal case
+is connected to earth. If a charge is
+given to the electroscope, and if any
+radioactive material is placed on a
+condenser plate P attached to the
+outer case, then this substance bestows
+conductivity on the air between the plates P and P&prime;,
+and the charge of the electroscope begins to leak away. The
+collapse of the gold-leaf is observed through an aperture in
+the case by a <span class="correction" title="amended from miscroscope">microscope</span>, and the time taken by the gold-leaf
+to fall over a certain distance is proportional to the
+ionizing current, that is, to the intensity of the radioactivity
+of the substance.</p>
+
+
+<p>A very similar form of electroscope was employed by J.P.L.J.
+Elster and H.F.K. Geitel (fig. 6), and also by C.T.R. Wilson
+(see <i>Proc. Roy. Soc.</i>, 1901, 68, p. 152). A metal box has a metal
+strip B suspended from a block or insulator by means of a bit of
+sulphur or amber S, and to it is fastened a strip of gold-leaf L.
+The electroscope is provided with a charging rod C. In a dry
+atmosphere sulphur or amber is an early perfect insulator,
+and hence if the air in the interior of the box is kept dry by
+calcium chloride, the electroscope will hold its charge for a
+long time. Any divergence or collapse of the gold-leaf can be
+viewed by a microscope through an aperture in the side of the
+case.</p>
+
+<table class="nobctr" style="clear: both;" summary="Illustration">
+<tr><td class="figcenter" colspan="2"><img style="width:447px; height:178px" src="images/img240b.jpg" alt="" /></td></tr>
+<tr><td class="caption"><span class="sc">Fig. 6.</span>&mdash;Elster and<br />
+Geitel Electroscope.</td>
+<td class="caption"><span class="sc">Fig. 7.</span>&mdash;Wilson&rsquo;s Electroscope.</td></tr></table>
+
+<p>Another type of sensitive electroscope is one devised by
+C.T.R. Wilson (<i>Proc. Cam. Phil. Soc.</i>, 1903, 12, part 2). It consists
+of a metal box placed on a tilting stand (fig. 7). At one end
+is an insulated plate P kept at a potential of 200 volts or so above
+the earth by a battery. At the other end is an insulated metal
+wire having attached to it a thin strip of gold-leaf L. If the plate
+P is electrified it attracts the strip which stretches out towards it.
+Before use the strip is for one moment connected to the case, and
+the arrangement is then tilted until the strip extends at a certain
+angle. If then the strip of gold-leaf is raised or lowered in potential
+it moves to or from the plate P, and its movement can be observed
+by a microscope through a hole in the side of the box. There is
+a particular angle of tilt of the case which gives a maximum
+sensitiveness. Wilson found that with the plate electrified to
+207 volts and with a tilt of the case of 30°, if the gold-leaf was
+raised one volt in potential above the case, it moved over 200
+divisions of the micrometer scale in the eye-piece of the microscope,
+54 divisions being equal to one millimetre. In using the
+instrument the insulated rod to which the gold-leaf is attached
+is connected to the conductor, the potential of which is being
+examined. In the use of all these electroscopic instruments it
+is essential to bear in mind (as first pointed out by Lord Kelvin)
+that what a gold-leaf electroscope really indicates is the difference
+of potential between the gold-leaf and the solid walls enclosing
+the air space in which they move.<a name="fa2o" id="fa2o" href="#ft2o"><span class="sp">1</span></a> If these enclosing walls are
+made of anything else than perfectly conducting material, then
+the indications of the instrument may be uncertain and meaningless.
+As already mentioned, Faraday remedied this defect by
+coating the inside of the glass vessel in which the gold-leaves were
+suspended to form an electroscope with tinfoil (see fig. 4).
+In spite of these admonitions all but a few instrument makers
+have continued to make the vicious type of instrument consisting
+of a pair of gold-leaves suspended within a glass shade or bottle,
+no means being provided for keeping the walls of the vessel
+continually at zero potential.</p>
+
+<div class="condensed">
+<p>See J. Clerk Maxwell, <i>Treatise on Electricity and Magnetism</i>, vol. i.
+p. 300 (2nd ed., Oxford, 1881); H.M. Noad, <i>A Manual of Electricity</i>,
+vol. i. p. 25 (London, 1855); E. Rutherford, <i>Radioactivity</i>.</p>
+</div>
+<div class="author">(J. A. F.)</div>
+
+<hr class="foot" /> <div class="note">
+
+<p><a name="ft1o" id="ft1o" href="#fa1o"><span class="fn">1</span></a> See the English translation by the Gilbert Club of Gilbert&rsquo;s <i>De
+magnete</i>, p. 49 (London, 1900).</p>
+
+<p><a name="ft2o" id="ft2o" href="#fa2o"><span class="fn">1</span></a> See Lord Kelvin, "Report on Electrometers and Electrostatic
+Measurements," <i>Brit. Assoc. Report</i> for 1867, or Lord Kelvin's
+<i>Reprint of Papers on Electrostatics and Magnetism</i>, p. 260.</p>
+</div>
+
+<hr class="art" />
+
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 9, Slice 2, by Various
+
+*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 9 SL 2 ***
+
+***** This file should be named 35092-h.htm or 35092-h.zip *****
+This and all associated files of various formats will be found in:
+        https://www.gutenberg.org/3/5/0/9/35092/
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+Updated editions will replace the previous one--the old editions
+will be renamed.
+
+Creating the works from public domain print editions means that no
+one owns a United States copyright in these works, so the Foundation
+(and you!) can copy and distribute it in the United States without
+permission and without paying copyright royalties.  Special rules,
+set forth in the General Terms of Use part of this license, apply to
+copying and distributing Project Gutenberg-tm electronic works to
+protect the PROJECT GUTENBERG-tm concept and trademark.  Project
+Gutenberg is a registered trademark, and may not be used if you
+charge for the eBooks, unless you receive specific permission.  If you
+do not charge anything for copies of this eBook, complying with the
+rules is very easy.  You may use this eBook for nearly any purpose
+such as creation of derivative works, reports, performances and
+research.  They may be modified and printed and given away--you may do
+practically ANYTHING with public domain eBooks.  Redistribution is
+subject to the trademark license, especially commercial
+redistribution.
+
+
+
+*** START: FULL LICENSE ***
+
+THE FULL PROJECT GUTENBERG LICENSE
+PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK
+
+To protect the Project Gutenberg-tm mission of promoting the free
+distribution of electronic works, by using or distributing this work
+(or any other work associated in any way with the phrase "Project
+Gutenberg"), you agree to comply with all the terms of the Full Project
+Gutenberg-tm License (available with this file or online at
+https://gutenberg.org/license).
+
+
+Section 1.  General Terms of Use and Redistributing Project Gutenberg-tm
+electronic works
+
+1.A.  By reading or using any part of this Project Gutenberg-tm
+electronic work, you indicate that you have read, understand, agree to
+and accept all the terms of this license and intellectual property
+(trademark/copyright) agreement.  If you do not agree to abide by all
+the terms of this agreement, you must cease using and return or destroy
+all copies of Project Gutenberg-tm electronic works in your possession.
+If you paid a fee for obtaining a copy of or access to a Project
+Gutenberg-tm electronic work and you do not agree to be bound by the
+terms of this agreement, you may obtain a refund from the person or
+entity to whom you paid the fee as set forth in paragraph 1.E.8.
+
+1.B.  "Project Gutenberg" is a registered trademark.  It may only be
+used on or associated in any way with an electronic work by people who
+agree to be bound by the terms of this agreement.  There are a few
+things that you can do with most Project Gutenberg-tm electronic works
+even without complying with the full terms of this agreement.  See
+paragraph 1.C below.  There are a lot of things you can do with Project
+Gutenberg-tm electronic works if you follow the terms of this agreement
+and help preserve free future access to Project Gutenberg-tm electronic
+works.  See paragraph 1.E below.
+
+1.C.  The Project Gutenberg Literary Archive Foundation ("the Foundation"
+or PGLAF), owns a compilation copyright in the collection of Project
+Gutenberg-tm electronic works.  Nearly all the individual works in the
+collection are in the public domain in the United States.  If an
+individual work is in the public domain in the United States and you are
+located in the United States, we do not claim a right to prevent you from
+copying, distributing, performing, displaying or creating derivative
+works based on the work as long as all references to Project Gutenberg
+are removed.  Of course, we hope that you will support the Project
+Gutenberg-tm mission of promoting free access to electronic works by
+freely sharing Project Gutenberg-tm works in compliance with the terms of
+this agreement for keeping the Project Gutenberg-tm name associated with
+the work.  You can easily comply with the terms of this agreement by
+keeping this work in the same format with its attached full Project
+Gutenberg-tm License when you share it without charge with others.
+
+1.D.  The copyright laws of the place where you are located also govern
+what you can do with this work.  Copyright laws in most countries are in
+a constant state of change.  If you are outside the United States, check
+the laws of your country in addition to the terms of this agreement
+before downloading, copying, displaying, performing, distributing or
+creating derivative works based on this work or any other Project
+Gutenberg-tm work.  The Foundation makes no representations concerning
+the copyright status of any work in any country outside the United
+States.
+
+1.E.  Unless you have removed all references to Project Gutenberg:
+
+1.E.1.  The following sentence, with active links to, or other immediate
+access to, the full Project Gutenberg-tm License must appear prominently
+whenever any copy of a Project Gutenberg-tm work (any work on which the
+phrase "Project Gutenberg" appears, or with which the phrase "Project
+Gutenberg" is associated) is accessed, displayed, performed, viewed,
+copied or distributed:
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+1.E.2.  If an individual Project Gutenberg-tm electronic work is derived
+from the public domain (does not contain a notice indicating that it is
+posted with permission of the copyright holder), the work can be copied
+and distributed to anyone in the United States without paying any fees
+or charges.  If you are redistributing or providing access to a work
+with the phrase "Project Gutenberg" associated with or appearing on the
+work, you must comply either with the requirements of paragraphs 1.E.1
+through 1.E.7 or obtain permission for the use of the work and the
+Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or
+1.E.9.
+
+1.E.3.  If an individual Project Gutenberg-tm electronic work is posted
+with the permission of the copyright holder, your use and distribution
+must comply with both paragraphs 1.E.1 through 1.E.7 and any additional
+terms imposed by the copyright holder.  Additional terms will be linked
+to the Project Gutenberg-tm License for all works posted with the
+permission of the copyright holder found at the beginning of this work.
+
+1.E.4.  Do not unlink or detach or remove the full Project Gutenberg-tm
+License terms from this work, or any files containing a part of this
+work or any other work associated with Project Gutenberg-tm.
+
+1.E.5.  Do not copy, display, perform, distribute or redistribute this
+electronic work, or any part of this electronic work, without
+prominently displaying the sentence set forth in paragraph 1.E.1 with
+active links or immediate access to the full terms of the Project
+Gutenberg-tm License.
+
+1.E.6.  You may convert to and distribute this work in any binary,
+compressed, marked up, nonproprietary or proprietary form, including any
+word processing or hypertext form.  However, if you provide access to or
+distribute copies of a Project Gutenberg-tm work in a format other than
+"Plain Vanilla ASCII" or other format used in the official version
+posted on the official Project Gutenberg-tm web site (www.gutenberg.org),
+you must, at no additional cost, fee or expense to the user, provide a
+copy, a means of exporting a copy, or a means of obtaining a copy upon
+request, of the work in its original "Plain Vanilla ASCII" or other
+form.  Any alternate format must include the full Project Gutenberg-tm
+License as specified in paragraph 1.E.1.
+
+1.E.7.  Do not charge a fee for access to, viewing, displaying,
+performing, copying or distributing any Project Gutenberg-tm works
+unless you comply with paragraph 1.E.8 or 1.E.9.
+
+1.E.8.  You may charge a reasonable fee for copies of or providing
+access to or distributing Project Gutenberg-tm electronic works provided
+that
+
+- You pay a royalty fee of 20% of the gross profits you derive from
+     the use of Project Gutenberg-tm works calculated using the method
+     you already use to calculate your applicable taxes.  The fee is
+     owed to the owner of the Project Gutenberg-tm trademark, but he
+     has agreed to donate royalties under this paragraph to the
+     Project Gutenberg Literary Archive Foundation.  Royalty payments
+     must be paid within 60 days following each date on which you
+     prepare (or are legally required to prepare) your periodic tax
+     returns.  Royalty payments should be clearly marked as such and
+     sent to the Project Gutenberg Literary Archive Foundation at the
+     address specified in Section 4, "Information about donations to
+     the Project Gutenberg Literary Archive Foundation."
+
+- You provide a full refund of any money paid by a user who notifies
+     you in writing (or by e-mail) within 30 days of receipt that s/he
+     does not agree to the terms of the full Project Gutenberg-tm
+     License.  You must require such a user to return or
+     destroy all copies of the works possessed in a physical medium
+     and discontinue all use of and all access to other copies of
+     Project Gutenberg-tm works.
+
+- You provide, in accordance with paragraph 1.F.3, a full refund of any
+     money paid for a work or a replacement copy, if a defect in the
+     electronic work is discovered and reported to you within 90 days
+     of receipt of the work.
+
+- You comply with all other terms of this agreement for free
+     distribution of Project Gutenberg-tm works.
+
+1.E.9.  If you wish to charge a fee or distribute a Project Gutenberg-tm
+electronic work or group of works on different terms than are set
+forth in this agreement, you must obtain permission in writing from
+both the Project Gutenberg Literary Archive Foundation and Michael
+Hart, the owner of the Project Gutenberg-tm trademark.  Contact the
+Foundation as set forth in Section 3 below.
+
+1.F.
+
+1.F.1.  Project Gutenberg volunteers and employees expend considerable
+effort to identify, do copyright research on, transcribe and proofread
+public domain works in creating the Project Gutenberg-tm
+collection.  Despite these efforts, Project Gutenberg-tm electronic
+works, and the medium on which they may be stored, may contain
+"Defects," such as, but not limited to, incomplete, inaccurate or
+corrupt data, transcription errors, a copyright or other intellectual
+property infringement, a defective or damaged disk or other medium, a
+computer virus, or computer codes that damage or cannot be read by
+your equipment.
+
+1.F.2.  LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right
+of Replacement or Refund" described in paragraph 1.F.3, the Project
+Gutenberg Literary Archive Foundation, the owner of the Project
+Gutenberg-tm trademark, and any other party distributing a Project
+Gutenberg-tm electronic work under this agreement, disclaim all
+liability to you for damages, costs and expenses, including legal
+fees.  YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
+LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
+PROVIDED IN PARAGRAPH 1.F.3.  YOU AGREE THAT THE FOUNDATION, THE
+TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
+LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
+INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
+DAMAGE.
+
+1.F.3.  LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
+defect in this electronic work within 90 days of receiving it, you can
+receive a refund of the money (if any) you paid for it by sending a
+written explanation to the person you received the work from.  If you
+received the work on a physical medium, you must return the medium with
+your written explanation.  The person or entity that provided you with
+the defective work may elect to provide a replacement copy in lieu of a
+refund.  If you received the work electronically, the person or entity
+providing it to you may choose to give you a second opportunity to
+receive the work electronically in lieu of a refund.  If the second copy
+is also defective, you may demand a refund in writing without further
+opportunities to fix the problem.
+
+1.F.4.  Except for the limited right of replacement or refund set forth
+in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER
+WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
+WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE.
+
+1.F.5.  Some states do not allow disclaimers of certain implied
+warranties or the exclusion or limitation of certain types of damages.
+If any disclaimer or limitation set forth in this agreement violates the
+law of the state applicable to this agreement, the agreement shall be
+interpreted to make the maximum disclaimer or limitation permitted by
+the applicable state law.  The invalidity or unenforceability of any
+provision of this agreement shall not void the remaining provisions.
+
+1.F.6.  INDEMNITY - You agree to indemnify and hold the Foundation, the
+trademark owner, any agent or employee of the Foundation, anyone
+providing copies of Project Gutenberg-tm electronic works in accordance
+with this agreement, and any volunteers associated with the production,
+promotion and distribution of Project Gutenberg-tm electronic works,
+harmless from all liability, costs and expenses, including legal fees,
+that arise directly or indirectly from any of the following which you do
+or cause to occur: (a) distribution of this or any Project Gutenberg-tm
+work, (b) alteration, modification, or additions or deletions to any
+Project Gutenberg-tm work, and (c) any Defect you cause.
+
+
+Section  2.  Information about the Mission of Project Gutenberg-tm
+
+Project Gutenberg-tm is synonymous with the free distribution of
+electronic works in formats readable by the widest variety of computers
+including obsolete, old, middle-aged and new computers.  It exists
+because of the efforts of hundreds of volunteers and donations from
+people in all walks of life.
+
+Volunteers and financial support to provide volunteers with the
+assistance they need are critical to reaching Project Gutenberg-tm's
+goals and ensuring that the Project Gutenberg-tm collection will
+remain freely available for generations to come.  In 2001, the Project
+Gutenberg Literary Archive Foundation was created to provide a secure
+and permanent future for Project Gutenberg-tm and future generations.
+To learn more about the Project Gutenberg Literary Archive Foundation
+and how your efforts and donations can help, see Sections 3 and 4
+and the Foundation web page at https://www.pglaf.org.
+
+
+Section 3.  Information about the Project Gutenberg Literary Archive
+Foundation
+
+The Project Gutenberg Literary Archive Foundation is a non profit
+501(c)(3) educational corporation organized under the laws of the
+state of Mississippi and granted tax exempt status by the Internal
+Revenue Service.  The Foundation's EIN or federal tax identification
+number is 64-6221541.  Its 501(c)(3) letter is posted at
+https://pglaf.org/fundraising.  Contributions to the Project Gutenberg
+Literary Archive Foundation are tax deductible to the full extent
+permitted by U.S. federal laws and your state's laws.
+
+The Foundation's principal office is located at 4557 Melan Dr. S.
+Fairbanks, AK, 99712., but its volunteers and employees are scattered
+throughout numerous locations.  Its business office is located at
+809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email
+business@pglaf.org.  Email contact links and up to date contact
+information can be found at the Foundation's web site and official
+page at https://pglaf.org
+
+For additional contact information:
+     Dr. Gregory B. Newby
+     Chief Executive and Director
+     gbnewby@pglaf.org
+
+
+Section 4.  Information about Donations to the Project Gutenberg
+Literary Archive Foundation
+
+Project Gutenberg-tm depends upon and cannot survive without wide
+spread public support and donations to carry out its mission of
+increasing the number of public domain and licensed works that can be
+freely distributed in machine readable form accessible by the widest
+array of equipment including outdated equipment.  Many small donations
+($1 to $5,000) are particularly important to maintaining tax exempt
+status with the IRS.
+
+The Foundation is committed to complying with the laws regulating
+charities and charitable donations in all 50 states of the United
+States.  Compliance requirements are not uniform and it takes a
+considerable effort, much paperwork and many fees to meet and keep up
+with these requirements.  We do not solicit donations in locations
+where we have not received written confirmation of compliance.  To
+SEND DONATIONS or determine the status of compliance for any
+particular state visit https://pglaf.org
+
+While we cannot and do not solicit contributions from states where we
+have not met the solicitation requirements, we know of no prohibition
+against accepting unsolicited donations from donors in such states who
+approach us with offers to donate.
+
+International donations are gratefully accepted, but we cannot make
+any statements concerning tax treatment of donations received from
+outside the United States.  U.S. laws alone swamp our small staff.
+
+Please check the Project Gutenberg Web pages for current donation
+methods and addresses.  Donations are accepted in a number of other
+ways including including checks, online payments and credit card
+donations.  To donate, please visit: https://pglaf.org/donate
+
+
+Section 5.  General Information About Project Gutenberg-tm electronic
+works.
+
+Professor Michael S. Hart was the originator of the Project Gutenberg-tm
+concept of a library of electronic works that could be freely shared
+with anyone.  For thirty years, he produced and distributed Project
+Gutenberg-tm eBooks with only a loose network of volunteer support.
+
+
+Project Gutenberg-tm eBooks are often created from several printed
+editions, all of which are confirmed as Public Domain in the U.S.
+unless a copyright notice is included.  Thus, we do not necessarily
+keep eBooks in compliance with any particular paper edition.
+
+
+Most people start at our Web site which has the main PG search facility:
+
+     https://www.gutenberg.org
+
+This Web site includes information about Project Gutenberg-tm,
+including how to make donations to the Project Gutenberg Literary
+Archive Foundation, how to help produce our new eBooks, and how to
+subscribe to our email newsletter to hear about new eBooks.
+
+
+</pre>
+
+</body>
+</html>
+
+
+
+
diff --git a/35092-h/images/img140.jpg b/35092-h/images/img140.jpg
new file mode 100644
index 0000000..275340d
--- /dev/null
+++ b/35092-h/images/img140.jpg
diff --git a/35092-h/images/img143a.jpg b/35092-h/images/img143a.jpg
new file mode 100644
index 0000000..cce5f27
--- /dev/null
+++ b/35092-h/images/img143a.jpg
diff --git a/35092-h/images/img143b.jpg b/35092-h/images/img143b.jpg
new file mode 100644
index 0000000..1265c6a
--- /dev/null
+++ b/35092-h/images/img143b.jpg
diff --git a/35092-h/images/img144.jpg b/35092-h/images/img144.jpg
new file mode 100644
index 0000000..b729789
--- /dev/null
+++ b/35092-h/images/img144.jpg
diff --git a/35092-h/images/img148a.jpg b/35092-h/images/img148a.jpg
new file mode 100644
index 0000000..b8b627f
--- /dev/null
+++ b/35092-h/images/img148a.jpg
diff --git a/35092-h/images/img148b.jpg b/35092-h/images/img148b.jpg
new file mode 100644
index 0000000..70e1a16
--- /dev/null
+++ b/35092-h/images/img148b.jpg
diff --git a/35092-h/images/img148c.jpg b/35092-h/images/img148c.jpg
new file mode 100644
index 0000000..627fe09
--- /dev/null
+++ b/35092-h/images/img148c.jpg
diff --git a/35092-h/images/img148d.jpg b/35092-h/images/img148d.jpg
new file mode 100644
index 0000000..910cd0e
--- /dev/null
+++ b/35092-h/images/img148d.jpg
diff --git a/35092-h/images/img149a.jpg b/35092-h/images/img149a.jpg
new file mode 100644
index 0000000..8c27ba0
--- /dev/null
+++ b/35092-h/images/img149a.jpg
diff --git a/35092-h/images/img149b.jpg b/35092-h/images/img149b.jpg
new file mode 100644
index 0000000..c59a96b
--- /dev/null
+++ b/35092-h/images/img149b.jpg
diff --git a/35092-h/images/img149c.jpg b/35092-h/images/img149c.jpg
new file mode 100644
index 0000000..0eeda60
--- /dev/null
+++ b/35092-h/images/img149c.jpg
diff --git a/35092-h/images/img149d.jpg b/35092-h/images/img149d.jpg
new file mode 100644
index 0000000..dd9f410
--- /dev/null
+++ b/35092-h/images/img149d.jpg
diff --git a/35092-h/images/img149e.jpg b/35092-h/images/img149e.jpg
new file mode 100644
index 0000000..60df477
--- /dev/null
+++ b/35092-h/images/img149e.jpg
diff --git a/35092-h/images/img150a.jpg b/35092-h/images/img150a.jpg
new file mode 100644
index 0000000..8c08d94
--- /dev/null
+++ b/35092-h/images/img150a.jpg
diff --git a/35092-h/images/img150b.jpg b/35092-h/images/img150b.jpg
new file mode 100644
index 0000000..80785cb
--- /dev/null
+++ b/35092-h/images/img150b.jpg
diff --git a/35092-h/images/img150c.jpg b/35092-h/images/img150c.jpg
new file mode 100644
index 0000000..d79a2c2
--- /dev/null
+++ b/35092-h/images/img150c.jpg
diff --git a/35092-h/images/img151a.jpg b/35092-h/images/img151a.jpg
new file mode 100644
index 0000000..eef6748
--- /dev/null
+++ b/35092-h/images/img151a.jpg
diff --git a/35092-h/images/img151b.jpg b/35092-h/images/img151b.jpg
new file mode 100644
index 0000000..ac8803f
--- /dev/null
+++ b/35092-h/images/img151b.jpg
diff --git a/35092-h/images/img151c.jpg b/35092-h/images/img151c.jpg
new file mode 100644
index 0000000..5d00ec5
--- /dev/null
+++ b/35092-h/images/img151c.jpg
diff --git a/35092-h/images/img152a.jpg b/35092-h/images/img152a.jpg
new file mode 100644
index 0000000..4bb7739
--- /dev/null
+++ b/35092-h/images/img152a.jpg
diff --git a/35092-h/images/img152b.jpg b/35092-h/images/img152b.jpg
new file mode 100644
index 0000000..2240527
--- /dev/null
+++ b/35092-h/images/img152b.jpg
diff --git a/35092-h/images/img152c.jpg b/35092-h/images/img152c.jpg
new file mode 100644
index 0000000..4b0ce8b
--- /dev/null
+++ b/35092-h/images/img152c.jpg
diff --git a/35092-h/images/img152d.jpg b/35092-h/images/img152d.jpg
new file mode 100644
index 0000000..397d206
--- /dev/null
+++ b/35092-h/images/img152d.jpg
diff --git a/35092-h/images/img152e.jpg b/35092-h/images/img152e.jpg
new file mode 100644
index 0000000..9c4e04b
--- /dev/null
+++ b/35092-h/images/img152e.jpg
diff --git a/35092-h/images/img152f.jpg b/35092-h/images/img152f.jpg
new file mode 100644
index 0000000..f2343f1
--- /dev/null
+++ b/35092-h/images/img152f.jpg
diff --git a/35092-h/images/img153a.jpg b/35092-h/images/img153a.jpg
new file mode 100644
index 0000000..7b3479a
--- /dev/null
+++ b/35092-h/images/img153a.jpg
diff --git a/35092-h/images/img153b.jpg b/35092-h/images/img153b.jpg
new file mode 100644
index 0000000..1faab09
--- /dev/null
+++ b/35092-h/images/img153b.jpg
diff --git a/35092-h/images/img153c.jpg b/35092-h/images/img153c.jpg
new file mode 100644
index 0000000..e2cc089
--- /dev/null
+++ b/35092-h/images/img153c.jpg
diff --git a/35092-h/images/img154.jpg b/35092-h/images/img154.jpg
new file mode 100644
index 0000000..91c554f
--- /dev/null
+++ b/35092-h/images/img154.jpg
diff --git a/35092-h/images/img155a.jpg b/35092-h/images/img155a.jpg
new file mode 100644
index 0000000..3e0457e
--- /dev/null
+++ b/35092-h/images/img155a.jpg
diff --git a/35092-h/images/img155b.jpg b/35092-h/images/img155b.jpg
new file mode 100644
index 0000000..324db63
--- /dev/null
+++ b/35092-h/images/img155b.jpg
diff --git a/35092-h/images/img155c.jpg b/35092-h/images/img155c.jpg
new file mode 100644
index 0000000..86479d7
--- /dev/null
+++ b/35092-h/images/img155c.jpg
diff --git a/35092-h/images/img157.jpg b/35092-h/images/img157.jpg
new file mode 100644
index 0000000..618cf0c
--- /dev/null
+++ b/35092-h/images/img157.jpg
diff --git a/35092-h/images/img176a.jpg b/35092-h/images/img176a.jpg
new file mode 100644
index 0000000..37e3d01
--- /dev/null
+++ b/35092-h/images/img176a.jpg
diff --git a/35092-h/images/img176b.jpg b/35092-h/images/img176b.jpg
new file mode 100644
index 0000000..e3d34c0
--- /dev/null
+++ b/35092-h/images/img176b.jpg
diff --git a/35092-h/images/img177a.jpg b/35092-h/images/img177a.jpg
new file mode 100644
index 0000000..bba58d4
--- /dev/null
+++ b/35092-h/images/img177a.jpg
diff --git a/35092-h/images/img177b.jpg b/35092-h/images/img177b.jpg
new file mode 100644
index 0000000..684efd5
--- /dev/null
+++ b/35092-h/images/img177b.jpg
diff --git a/35092-h/images/img177c.jpg b/35092-h/images/img177c.jpg
new file mode 100644
index 0000000..27c3b58
--- /dev/null
+++ b/35092-h/images/img177c.jpg
diff --git a/35092-h/images/img178a.jpg b/35092-h/images/img178a.jpg
new file mode 100644
index 0000000..86b5e67
--- /dev/null
+++ b/35092-h/images/img178a.jpg
diff --git a/35092-h/images/img178b.jpg b/35092-h/images/img178b.jpg
new file mode 100644
index 0000000..cc3c5a9
--- /dev/null
+++ b/35092-h/images/img178b.jpg
diff --git a/35092-h/images/img179a.jpg b/35092-h/images/img179a.jpg
new file mode 100644
index 0000000..d130798
--- /dev/null
+++ b/35092-h/images/img179a.jpg
diff --git a/35092-h/images/img179b.jpg b/35092-h/images/img179b.jpg
new file mode 100644
index 0000000..685723e
--- /dev/null
+++ b/35092-h/images/img179b.jpg
diff --git a/35092-h/images/img194a.jpg b/35092-h/images/img194a.jpg
new file mode 100644
index 0000000..3d3890a
--- /dev/null
+++ b/35092-h/images/img194a.jpg
diff --git a/35092-h/images/img194b.jpg b/35092-h/images/img194b.jpg
new file mode 100644
index 0000000..8dfeae4
--- /dev/null
+++ b/35092-h/images/img194b.jpg
diff --git a/35092-h/images/img195.jpg b/35092-h/images/img195.jpg
new file mode 100644
index 0000000..9ed5013
--- /dev/null
+++ b/35092-h/images/img195.jpg
diff --git a/35092-h/images/img196.jpg b/35092-h/images/img196.jpg
new file mode 100644
index 0000000..1fa0cc5
--- /dev/null
+++ b/35092-h/images/img196.jpg
diff --git a/35092-h/images/img198.jpg b/35092-h/images/img198.jpg
new file mode 100644
index 0000000..4224f57
--- /dev/null
+++ b/35092-h/images/img198.jpg
diff --git a/35092-h/images/img203a.jpg b/35092-h/images/img203a.jpg
new file mode 100644
index 0000000..c2cafb9
--- /dev/null
+++ b/35092-h/images/img203a.jpg
diff --git a/35092-h/images/img203b.jpg b/35092-h/images/img203b.jpg
new file mode 100644
index 0000000..100f001
--- /dev/null
+++ b/35092-h/images/img203b.jpg
diff --git a/35092-h/images/img204a.jpg b/35092-h/images/img204a.jpg
new file mode 100644
index 0000000..c5bbc8b
--- /dev/null
+++ b/35092-h/images/img204a.jpg
diff --git a/35092-h/images/img204b.jpg b/35092-h/images/img204b.jpg
new file mode 100644
index 0000000..ffce455
--- /dev/null
+++ b/35092-h/images/img204b.jpg
diff --git a/35092-h/images/img206a.jpg b/35092-h/images/img206a.jpg
new file mode 100644
index 0000000..7d4b40b
--- /dev/null
+++ b/35092-h/images/img206a.jpg
diff --git a/35092-h/images/img206b.jpg b/35092-h/images/img206b.jpg
new file mode 100644
index 0000000..74125ac
--- /dev/null
+++ b/35092-h/images/img206b.jpg
diff --git a/35092-h/images/img207a.jpg b/35092-h/images/img207a.jpg
new file mode 100644
index 0000000..7effad8
--- /dev/null
+++ b/35092-h/images/img207a.jpg
diff --git a/35092-h/images/img207b.jpg b/35092-h/images/img207b.jpg
new file mode 100644
index 0000000..0139ce6
--- /dev/null
+++ b/35092-h/images/img207b.jpg
diff --git a/35092-h/images/img207c.jpg b/35092-h/images/img207c.jpg
new file mode 100644
index 0000000..043e458
--- /dev/null
+++ b/35092-h/images/img207c.jpg
diff --git a/35092-h/images/img208.jpg b/35092-h/images/img208.jpg
new file mode 100644
index 0000000..7db118a
--- /dev/null
+++ b/35092-h/images/img208.jpg
diff --git a/35092-h/images/img211.jpg b/35092-h/images/img211.jpg
new file mode 100644
index 0000000..e903fe5
--- /dev/null
+++ b/35092-h/images/img211.jpg
diff --git a/35092-h/images/img212.jpg b/35092-h/images/img212.jpg
new file mode 100644
index 0000000..0b293d9
--- /dev/null
+++ b/35092-h/images/img212.jpg
diff --git a/35092-h/images/img213.jpg b/35092-h/images/img213.jpg
new file mode 100644
index 0000000..b5a5320
--- /dev/null
+++ b/35092-h/images/img213.jpg
diff --git a/35092-h/images/img214.jpg b/35092-h/images/img214.jpg
new file mode 100644
index 0000000..52c6032
--- /dev/null
+++ b/35092-h/images/img214.jpg
diff --git a/35092-h/images/img216.jpg b/35092-h/images/img216.jpg
new file mode 100644
index 0000000..93953cc
--- /dev/null
+++ b/35092-h/images/img216.jpg
diff --git a/35092-h/images/img217.jpg b/35092-h/images/img217.jpg
new file mode 100644
index 0000000..f75b438
--- /dev/null
+++ b/35092-h/images/img217.jpg
diff --git a/35092-h/images/img219.jpg b/35092-h/images/img219.jpg
new file mode 100644
index 0000000..f3495fd
--- /dev/null
+++ b/35092-h/images/img219.jpg
diff --git a/35092-h/images/img227a.jpg b/35092-h/images/img227a.jpg
new file mode 100644
index 0000000..48cbadb
--- /dev/null
+++ b/35092-h/images/img227a.jpg
diff --git a/35092-h/images/img227b.jpg b/35092-h/images/img227b.jpg
new file mode 100644
index 0000000..060a9e5
--- /dev/null
+++ b/35092-h/images/img227b.jpg
diff --git a/35092-h/images/img229a.jpg b/35092-h/images/img229a.jpg
new file mode 100644
index 0000000..8d66972
--- /dev/null
+++ b/35092-h/images/img229a.jpg
diff --git a/35092-h/images/img229b.jpg b/35092-h/images/img229b.jpg
new file mode 100644
index 0000000..f82ad2d
--- /dev/null
+++ b/35092-h/images/img229b.jpg
diff --git a/35092-h/images/img229c.jpg b/35092-h/images/img229c.jpg
new file mode 100644
index 0000000..2925493
--- /dev/null
+++ b/35092-h/images/img229c.jpg
diff --git a/35092-h/images/img231.jpg b/35092-h/images/img231.jpg
new file mode 100644
index 0000000..c1f8098
--- /dev/null
+++ b/35092-h/images/img231.jpg
diff --git a/35092-h/images/img234.jpg b/35092-h/images/img234.jpg
new file mode 100644
index 0000000..95c1247
--- /dev/null
+++ b/35092-h/images/img234.jpg
diff --git a/35092-h/images/img235a.jpg b/35092-h/images/img235a.jpg
new file mode 100644
index 0000000..ce3e56f
--- /dev/null
+++ b/35092-h/images/img235a.jpg
diff --git a/35092-h/images/img235b.jpg b/35092-h/images/img235b.jpg
new file mode 100644
index 0000000..d580639
--- /dev/null
+++ b/35092-h/images/img235b.jpg
diff --git a/35092-h/images/img235c.jpg b/35092-h/images/img235c.jpg
new file mode 100644
index 0000000..cc58e7a
--- /dev/null
+++ b/35092-h/images/img235c.jpg
diff --git a/35092-h/images/img235d.jpg b/35092-h/images/img235d.jpg
new file mode 100644
index 0000000..39693f9
--- /dev/null
+++ b/35092-h/images/img235d.jpg
diff --git a/35092-h/images/img236.jpg b/35092-h/images/img236.jpg
new file mode 100644
index 0000000..069a89e
--- /dev/null
+++ b/35092-h/images/img236.jpg
diff --git a/35092-h/images/img239a.jpg b/35092-h/images/img239a.jpg
new file mode 100644
index 0000000..cb595f3
--- /dev/null
+++ b/35092-h/images/img239a.jpg
diff --git a/35092-h/images/img239b.jpg b/35092-h/images/img239b.jpg
new file mode 100644
index 0000000..03bc1dd
--- /dev/null
+++ b/35092-h/images/img239b.jpg
diff --git a/35092-h/images/img239c.jpg b/35092-h/images/img239c.jpg
new file mode 100644
index 0000000..1f7601a
--- /dev/null
+++ b/35092-h/images/img239c.jpg
diff --git a/35092-h/images/img240a.jpg b/35092-h/images/img240a.jpg
new file mode 100644
index 0000000..b596e59
--- /dev/null
+++ b/35092-h/images/img240a.jpg
diff --git a/35092-h/images/img240b.jpg b/35092-h/images/img240b.jpg
new file mode 100644
index 0000000..771afbc
--- /dev/null
+++ b/35092-h/images/img240b.jpg
diff --git a/35092.txt b/35092.txt
new file mode 100644
index 0000000..8517033
--- /dev/null
+++ b/35092.txt
@@ -0,0 +1,16337 @@
+The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition,
+Volume 9, Slice 2, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2
+       "Ehud" to "Electroscope"
+
+Author: Various
+
+Release Date: January 27, 2011 [EBook #35092]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 9 SL 2 ***
+
+
+
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+
+
+
+
+
+
+
+Transcriber's notes:
+
+(1) Numbers following letters (without space) like C2 were originally
+      printed in subscript. Letter subscripts are preceded by an
+      underscore, like C_n.
+
+(2) Characters following a carat (^) were printed in superscript.
+
+(3) Side-notes were relocated to function as titles of their respective
+      paragraphs.
+
+(4) Macrons and breves above letters and dots below letters were not
+      inserted.
+
+(5) dP stands for the partial-derivative symbol, or curled 'd'.
+
+(6) [oo] stands for the infinity symbol, and [int] for the integral
+      symbol.
+
+(7) The following typographical errors have been corrected:
+
+    ARTICLE EKATERINOSLAV: "Nearly 40,000 persons find occupation in
+      factories, the most important being iron-works and agricultural
+      machinery works, though there are also tobacco ... " 'important'
+      amended from 'imporant'.
+
+    ARTICLE ELASTICITY: "The limits of perfect elasticity as regards
+      change of shape, on the other hand, are very low, if they exist at
+      all, for glasses and other hard, brittle solids; but a class of
+      metals including copper, brass, steel, and platinum are very
+      perfectly elastic as regards distortion, provided that the
+      distortion is not too great." Missing 'and' after 'steel'.
+
+    ARTICLE ELASTICITY: "The parts of the radii vectors within the
+     sphere ..." 'vectors' amended from 'vectores'.
+
+    ARTICLE ELBE: "Its total length is 725 m., of which 190 are in
+      Bohemia, 77 in the kingdom of Saxony, and 350 in Prussia, the
+      remaining 108 being in Hamburg and other states of Germany." 'Its'
+      amended from 'it'.
+
+    ARTICLE ELBE: "Finally, in 1870, 1,000,000 thalers were paid to
+      Mecklenburg and 85,000 thalers to Anhalt, which thereupon abandoned
+      all claims to levy tolls upon the Elbe shipping, and thus
+      navigation on the river became at last entirely free. 'Anhalt'
+      amended from 'Anhal'.
+
+    ARTICLE ELBE: "... after driving back at Lobositz the Austrian
+      forces which were hastening to their assistance; but only nine
+      months later he lost his reputation for "invincibility" by his
+      crushing defeat at Kolin ..." 'assistance' amended from
+      'asistance'.
+
+    ARTICLE ELECTRICITY: "De la Rive reviews the subject in his large
+      Treatise on Electricity and Magnetism, vol. ii. ch. iii. The writer
+      made a contribution to the discussion in 1874 ..." 'Magnetism'
+      amended from 'Magnestism'.
+
+    ARTICLE ELECTRICITY SUPPLY: "... or by means of overhead wires
+      within restricted areas, but the limitations proved uneconomical
+      and the installations were for the most part merged into larger
+      undertakings sanctioned by parliamentary powers." 'limitations'
+      amended from 'limitatons'.
+
+    ARTICLE ELECTROKINETICS: "A vector can most conveniently be
+      represented by a symbol such as a + ib, where a stands for any
+      length of a units measured horizontally and b for a length b units
+      measured vertically, and the symbol i is a sign of perpendicularity
+      ..." 'symbol' amended from 'smybol'.
+
+    ARTICLE ELECTROSCOPE: "The collapse of the gold-leaf is observed
+      through an aperture in the case by a microscope, and the time taken
+      by the gold-leaf to fall over a certain distance is proportional to
+      the ionizing current, that is, to the intensity of the
+      radioactivity of the substance. 'microscope' amended from
+      'miscroscope'.
+
+
+
+
+          ENCYCLOPAEDIA BRITANNICA
+
+  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
+           AND GENERAL INFORMATION
+
+              ELEVENTH EDITION
+
+
+            VOLUME IX, SLICE II
+
+           Ehud to Electroscope
+
+
+
+
+ARTICLES IN THIS SLICE:
+
+
+  EHUD                                ELBERFELD
+  EIBENSTOCK                          ELBEUF
+  EICHBERG, JULIUS                    ELBING
+  EICHENDORFF, JOSEPH, FREIHERR VON   ELBOW
+  EICHHORN, JOHANN GOTTFRIED          ELBURZ
+  EICHHORN, KARL FRIEDRICH            ELCHE
+  EICHSTATT                           ELCHINGEN
+  EICHWALD, KARL EDUARD VON           ELDAD BEN MAHLI
+  EIDER (river of Prussia)            ELDER (ruler or officer)
+  EIDER (duck)                        ELDER (shrubs and trees)
+  EIFEL                               ELDON, JOHN SCOTT
+  EIFFEL TOWER                        EL DORADO
+  EILDON HILLS                        ELDUAYEN, JOSE DE
+  EILENBURG                           ELEANOR OF AQUITAINE
+  EINBECK                             ELEATIC SCHOOL
+  EINDHOVEN                           ELECAMPANE
+  EINHARD                             ELECTION (politics)
+  EINHORN, DAVID                      ELECTION (English law choice)
+  EINSIEDELN                          ELECTORAL COMMISSION
+  EISENACH                            ELECTORS
+  EISENBERG                           ELECTRA
+  EISENERZ                            ELECTRICAL MACHINE
+  EISLEBEN                            ELECTRIC EEL
+  EISTEDDFOD                          ELECTRICITY
+  EJECTMENT                           ELECTRICITY SUPPLY
+  EKATERINBURG                        ELECTRIC WAVES
+  EKATERINODAR                        ELECTROCHEMISTRY
+  EKATERINOSLAV (Russian government)  ELECTROCUTION
+  EKATERINOSLAV (Russian town)        ELECTROKINETICS
+  EKHOF, KONRAD                       ELECTROLIER
+  EKRON                               ELECTROLYSIS
+  ELABUGA                             ELECTROMAGNETISM
+  ELAM                                ELECTROMETALLURGY
+  ELAND                               ELECTROMETER
+  ELASTICITY                          ELECTRON
+  ELATERITE                           ELECTROPHORUS
+  ELATERIUM                           ELECTROPLATING
+  ELBA                                ELECTROSCOPE
+  ELBE
+
+
+
+
+EHUD, in the Bible, a "judge" who delivered Israel from the Moabites
+(Judg. iii. 12-30). He was sent from Ephraim to bear tribute to Eglon
+king of Moab, who had crossed over the Jordan and seized the district
+around Jericho. Being, like the Benjamites, left-handed (cf. xx. 16), he
+was able to conceal a dagger and strike down the king before his
+intentions were suspected. He locked Eglon in his chamber and escaped.
+The men from Mt Ephraim collected under his leadership and by seizing
+the fords of the Jordan were able to cut off the Moabites. He is called
+the son of Gera a Benjamite, but since both Ehud and Gera are tribal
+names (2 Sam. xvi. 5, 1 Chron. viii. 3, 5 sq.) it has been thought that
+this notice is not genuine. The tribe of Benjamin rarely appears in the
+old history of the Hebrews before the time of Saul. See further
+BENJAMIN; JUDGES.
+
+
+
+
+EIBENSTOCK, a town of Germany, in the kingdom of Saxony, near the Mulde,
+on the borders of Bohemia, 17 m. by rail S.S.E. of Zwickau. Pop. (1905)
+7460. It is a principal seat of the tambour embroidery which was
+introduced in 1775 by Clara Angermann. It possesses chemical and tobacco
+manufactories, and tin and iron works. It has also a large cattle
+market. Eibenstock, together with Schwarzenberg, was acquired by
+purchase in 1533 by Saxony and was granted municipal rights in the
+following year.
+
+
+
+
+EICHBERG, JULIUS (1824-1893), German musical composer, was born at
+Dusseldorf on the 13th of June 1824. When he was nineteen he entered the
+Brussels Conservatoire, where he took first prizes for violin-playing
+and composition. For eleven years he occupied the post of professor in
+the Conservatoire of Geneva. In 1857 he went to the United States,
+staying two years in New York and then proceeding to Boston, where he
+became director of the orchestra at the Boston Museum. In 1867 he
+founded the Boston Conservatory of Music. Eichberg published several
+educational works on music; and his four operettas, _The Doctor of
+Alcantara_, _The Rose of Tyrol_, _The Two Cadis_ and _A Night in Rome_,
+were highly popular. He died in Boston on the 18th of January 1893.
+
+
+
+
+EICHENDORFF, JOSEPH, FREIHERR VON (1788-1857), German poet and
+romance-writer, was born at Lubowitz, near Ratibor, in Silesia, on the
+10th of March 1788. He studied law at Halle and Heidelberg from 1805 to
+1808. After a visit to Paris he went to Vienna, where he resided until
+1813, when he joined the Prussian army as a volunteer in the famous
+Lutzow corps. When peace was concluded in 1815, he left the army, and in
+the following year he was appointed to a judicial office at Breslau. He
+subsequently held similar offices at Danzig, Konigsberg and Berlin.
+Retiring from public service in 1844, he lived successively in Danzig,
+Vienna, Dresden and Berlin. He died at Neisse on the 26th of November
+1857. Eichendorff was one of the most distinguished of the later members
+of the German romantic school. His genius was essentially lyrical. Thus
+he is most successful in his shorter romances and dramas, where
+constructive power is least called for. His first work, written in 1811,
+was a romance, _Ahnung und Gegenwart_ (1815). This was followed at short
+intervals by several others, among which the foremost place is by
+general consent assigned to _Aus dem Leben eines Taugenichts_ (1826),
+which has often been reprinted. Of his dramas may be mentioned _Ezzelin
+von Romano_ (1828); and _Der letzte Held von Marienburg_ (1830), both
+tragedies; and a comedy, _Die Freier_ (1833). He also translated several
+of Calderon's religious dramas (_Geistliche Schauspiele_, 1846). It is,
+however, through his lyrics (_Gedichte_, first collected 1837) that
+Eichendorff is best known; he is the greatest lyric poet of the romantic
+movement. No one has given more beautiful expression than he to the
+poetry of a wandering life; often, again, his lyrics are exquisite word
+pictures interpreting the mystic meaning of the moods of nature, as in
+_Nachts_, or the old-time mystery which yet haunts the twilight forests
+and feudal castles of Germany, as in the dramatic lyric _Waldesgesprach_
+or _Auf einer Burg_. Their language is simple and musical, which makes
+them very suitable for singing, and they have been often set, notably by
+Schubert and Schumann.
+
+In the later years of his life Eichendorff published several works on
+subjects in literary history and criticism such as _Uber die ethische
+und religiose Bedeutung der neuen romantischen Poesie in Deutschland_
+(1847), _Der deutsche Roman des 18. Jahrhunderts in seinem Verhaltniss
+zum Christenthum_ (1851), and _Geschichte der poetischen Litteratur
+Deutschlands_ (1856), but the value of these works is impaired by the
+author's reactionary standpoint. An edition of his collected works in
+six volumes, appeared at Leipzig in 1870.
+
+  Eichendorff's _Samtliche Werke_ appeared in 6 vols., 1864 (reprinted
+  1869-1870); his _Samtliche poetische Werke_ in 4 vols. (1883). The
+  latest edition is that edited by R. von Gottschall in 4 vols. (1901).
+  A good selection edited by M. Kaoch will be found in vol. 145 of
+  Kurschner's _Deutsche Nationalliteratur_ (1893). Eichendorff's
+  critical writings were collected in 1866 under the title _Vermischte
+  Schriften_ (5 vols.). Cp. H. von Eichendorff's biographical
+  introduction to the _Samtliche Werke_; also H. Keiter, _Joseph von
+  Eichendorff_ (Cologne, 1887); H.A. Kruger, _Der junge Eichendorff_
+  (Oppeln, 1898).
+
+
+
+
+EICHHORN, JOHANN GOTTFRIED (1752-1827), German theologian, was born at
+Dorrenzimmern, in the principality of Hohenlohe-Oehringen, on the 16th
+of October 1752. He was educated at the state school in Weikersheim,
+where his father was superintendent, at the gymnasium at Heilbronn and
+at the university of Gottingen (1770-1774), studying under J.D.
+Michaelis. In 1774 he received the rectorship of the gymnasium at
+Ohrdruf, in the duchy of Gotha, and in the following year was made
+professor of Oriental languages at Jena. On the death of Michaelis in
+1788 he was elected professor _ordinarius_ at Gottingen, where he
+lectured not only on Oriental languages and on the exegesis of the Old
+and New Testaments, but also on political history. His health was
+shattered in 1825, but he continued his lectures until attacked by fever
+on the 14th of June 1827. He died on the 27th of that month. Eichhorn
+has been called "the founder of modern Old Testament criticism." He
+first properly recognized its scope and problems, and began many of its
+most important discussions. "My greatest trouble," he says in the
+preface to the second edition of his _Einleitung_, "I had to bestow on a
+hitherto unworked field--on the investigation of the inner nature of the
+Old Testament with the help of the Higher Criticism (not a new name to
+any humanist)." His investigations led him to the conclusion that "most
+of the writings of the Hebrews have passed through several hands." He
+took for granted that all the so-called supernatural facts relating to
+the Old and New Testaments were explicable on natural principles. He
+sought to judge them from the standpoint of the ancient world, and to
+account for them by the superstitious beliefs which were then generally
+in vogue. He did not perceive in the biblical books any religious ideas
+of much importance for modern times; they interested him merely
+historically and for the light they cast upon antiquity. He regarded
+many books of the Old Testament as spurious, questioned the genuineness
+of _2 Peter_ and _Jude_, denied the Pauline authorship of _Timothy_ and
+_Titus_, and suggested that the canonical gospels were based upon
+various translations and editions of a primary Aramaic gospel. He did
+not appreciate as sufficiently as David Strauss and the Tubingen critics
+the difficulties which a natural theory has to surmount, nor did he
+support his conclusions by such elaborate discussions as they deemed
+necessary.
+
+  His principal works were--_Geschichte des Ostindischen Handels vor
+  Mohammed_ (Gotha, 1775); _Allgemeine Bibliothek der biblischen
+  Literatur_ (10 vols., Leipzig, 1787-1801); _Einleitung in das Alte
+  Testament_ (3 vols., Leipzig, 1780-1783); _Einleitung in das Neue
+  Testament_ (1804-1812); _Einleitung in die apokryphischen Bucher des
+  Alten Testaments_ (Gott., 1795); _Commentarius in apocalypsin Joannis_
+  (2 vols., Gott., 1791); _Die Hebr. Propheten_ (3 vols., Gott.,
+  1816-1819); _Allgemeine Geschichte der Cultur und Literatur des neuern
+  Europa_ (2 vols., Gott., 1796-1799); _Literargeschichte_ (1st vol.,
+  Gott., 1799, 2nd ed. 1813, 2nd vol. 1814); _Geschichte der Literatur
+  von ihrem Anfange bis auf die neuesten Zeiten_ (5 vols., Gott.,
+  1805-1812); _Ubersicht der Franzosischen Revolution_ (2 vols., Gott.,
+  1797); _Weltgeschichte_ (3rd ed., 5 vols., Gott., 1819-1820);
+  _Geschichte der drei letzten Jahrhunderte_ (3rd ed., 6 vols., Hanover,
+  1817-1818); _Urgeschichte des erlauchten Hauses der Welfen_ (Hanover,
+  1817).
+
+  See R.W. Mackay, _The Tubingen School and its Antecedents_ (1863), pp.
+  103 ff.; Otto Pfleiderer, _Development of Theology_ (1890), p. 209;
+  T.K. Cheyne, _Founders of Old Testament Criticism_ (1893), pp. 13 ff.
+
+
+
+
+EICHHORN, KARL FRIEDRICH (1781-1854), German jurist, son of the
+preceding, was born at Jena on the 20th of November 1781. He entered the
+university of Gottingen in 1797. In 1805 he obtained the professorship
+of law at Frankfort-on-Oder, holding it till 1811, when he accepted the
+same chair at Berlin. On the call to arms in 1813 he became a captain of
+horse, and received at the end of the war the decoration of the Iron
+Cross. In 1817 he was offered the chair of law at Gottingen, and,
+preferring it to the Berlin professorship, taught there with great
+success till ill-health compelled him to resign in 1828. His successor
+in the Berlin chair having died in 1832, he again entered on its duties,
+but resigned two years afterwards. In 1832 he also received an
+appointment in the ministry of foreign affairs, which, with his labours
+on many state committees and his legal researches and writings, occupied
+him till his death at Cologne on the 4th of July 1854. Eichhorn is
+regarded as one of the principal authorities on German constitutional
+law. His chief work is _Deutsche Staats- und Rechtsgeschichte_
+(Gottingen, 1808-1823, 5th ed. 1843-1844). In company with Savigny and
+J.F.L. Goschen he founded the _Zeitschrift fur geschichtliche
+Rechtswissenschaft_. He was the author besides of _Einleitung in das
+deutsche Privatrecht mit Einschluss des Lehnrechts_ (Gott., 1823) and
+the _Grundsatze des Kirchenrechts der Katholischen und der Evangelischen
+Religionspartei in Deutschland_, 2 Bde. (ib., 1831-1833).
+
+  See Schulte, _Karl Friedrich Eichhorn, sein Leben und Wirken_ (1884).
+
+
+
+
+EICHSTATT, a town and episcopal see of Germany, in the kingdom of
+Bavaria, in the deep and romantic valley of the Altmuhl, 35 m. S. of
+Nuremberg, on the railway to Ingolstadt and Munich. Pop. (1905) 7701.
+The town, with its numerous spires and remains of medieval
+fortifications, is very picturesque. It has an Evangelical and seven
+Roman Catholic churches, among the latter the cathedral of St Wilibald
+(first bishop of Eichstatt),--with the tomb of the saint and numerous
+pictures and relics,--the church of St Walpurgis, sister of Wilibald,
+whose remains rest in the choir, and the Capuchin church, a copy of the
+Holy Sepulchre. Of its secular buildings the most noticeable are the
+town hall and the Leuchtenberg palace, once the residence of the prince
+bishops and later of the dukes of Leuchtenberg (now occupied by the
+court of justice of the district), with beautiful grounds. The
+Wilibaldsburg, built on a neighbouring hill in the 14th century by
+Bishop Bertold of Hohenzollern, was long the residence of the prince
+bishops of Eichstatt, and now contains an historical museum. There are
+an episcopal lyceum, a clerical seminary, a classical and a modern
+school, and numerous religious houses. The industries of the town
+include bootmaking, brewing and the production of lithographic stones.
+
+Eichstatt (Lat. _Aureatum_ or _Rubilocus_) was originally a Roman
+station which, after the foundation of the bishopric by Boniface in 745,
+developed into a considerable town, which was surrounded with walls in
+908. The bishops of Eichstatt were princes of the Empire, subject to the
+spiritual jurisdiction of the archbishops of Mainz, and ruled over
+considerable territories in the Circle of Franconia. In 1802 the see was
+secularized and incorporated in Bavaria. In 1817 it was given, with the
+duchy of Leuchtenberg, as a mediatized domain under the Bavarian crown,
+by the king of Bavaria to his son-in-law Eugene de Beauharnais,
+ex-viceroy of Italy, henceforth styled duke of Leuchtenberg. In 1855 it
+reverted to the Bavarian crown.
+
+
+
+
+EICHWALD, KARL EDUARD VON (1795-1876), Russian geologist and physician,
+was born at Mitau in Courland on the 4th of July 1795. He became doctor
+of medicine and professor of zoology in Kazan in 1823; four years later
+professor of zoology and comparative anatomy at Vilna; in 1838 professor
+of zoology, mineralogy and medicine at St Petersburg; and finally
+professor of palaeontology in the institute of mines in that city. He
+travelled much in the Russian empire, and was a keen observer of its
+natural history and geology. He died at St Petersburg on the 10th of
+November 1876. His published works include _Reise auf dem Caspischen
+Meere und in den Caucasus_, 2 vols. (Stuttgart and Tubingen, 1834-1838);
+_Die Urwelt Russlands_ (St Petersburg, 1840-1845); _Lethaea Rossica, ou
+paleontologie de la Russie_, 3 vols. (Stuttgart, 1852-1868), with
+Atlases.
+
+
+
+
+EIDER, a river of Prussia, in the province of Schleswig-Holstein. It
+rises to the south of Kiel, in Lake Redder, flows first north, then west
+(with wide-sweeping curves), and after a course of 117 m. enters the
+North Sea at Tonning. It is navigable up to Rendsburg, and is embanked
+through the marshes across which it runs in its lower course. Since the
+reign of Charlemagne, the Eider (originally _Agyr Dor_--Neptune's gate)
+was known as _Romani terminus imperii_ and was recognized as the
+boundary of the Empire in 1027 by the emperor Conrad II., the founder of
+the Salian dynasty. In the controversy arising out of the
+Schleswig-Holstein Question, which culminated in the war of Austria and
+Prussia against Denmark in 1864, the Eider gave its name to the "Eider
+Danes," the _intransigeant_ Danish party which maintained that Schleswig
+(Sonderjylland, South Jutland) was by nature and historical tradition an
+integral part of Denmark. The Eider Canal (_Eider-Kanal_), which was
+constructed between 1777 and 1784, leaves the Eider at the point where
+the river turns to the west and enters the Bay of Kiel at Holtenau. It
+was hampered by six sluices, but was used annually by some 4000 vessels,
+and until its conversion in 1887-1895 into the Kaiser Wilhelm Canal
+afforded the only direct connexion between the North Sea and the Baltic.
+
+
+
+
+EIDER (Icelandic, _Aedur_), a large marine duck, the _Somateria
+mollissima_ of ornithologists, famous for its down, which, from its
+extreme lightness and elasticity, is in great request for filling
+bed-coverlets. This bird generally frequents low rocky islets near the
+coast, and in Iceland and Norway has long been afforded every
+encouragement and protection, a fine being inflicted for killing it
+during the breeding-season, or even for firing a gun near its haunts,
+while artificial nesting-places are in many localities contrived for its
+further accommodation. From the care thus taken of it in those countries
+it has become exceedingly tame at its chief resorts, which are strictly
+regarded as property, and the taking of eggs or down from them, except
+by authorized persons, is severely punished by law. In appearance the
+eider is somewhat clumsy, though it flies fast and dives admirably. The
+female is of a dark reddish-brown colour barred with brownish-black. The
+adult male in spring is conspicuous by his pied plumage of velvet-black
+beneath, and white above: a patch of shining sea-green on his head is
+only seen on close inspection. This plumage he is considered not to
+acquire until his third year, being when young almost exactly like the
+female, and it is certain that the birds which have not attained their
+full dress remain in flocks by themselves without going to the
+breeding-stations. The nest is generally in some convenient corner among
+large stones, hollowed in the soil, and furnished with a few bits of dry
+grass, seaweed or heather. By the time that the full number of eggs
+(which rarely if ever exceeds five) is laid the down is added. Generally
+the eggs and down are taken at intervals of a few days by the owners of
+the "eider-fold," and the birds are thus kept depositing both during the
+whole season; but some experience is needed to ensure the greatest
+profit from each commodity. Every duck is ultimately allowed to hatch an
+egg or two to keep up the stock, and the down of the last nest is
+gathered after the birds have left the spot. The story of the drake's
+furnishing down, after the duck's supply is exhausted is a fiction. He
+never goes near the nest. The eggs have a strong flavour, but are much
+relished by both Icelanders and Norwegians. In the Old World the eider
+breeds in suitable localities from Spitsbergen to the Farne Islands off
+the coast of Northumberland--where it is known as St Cuthbert's duck.
+Its food consists of marine animals (molluscs and crustaceans), and
+hence the young are not easily reared in captivity. The eider of the New
+World differs somewhat, and has been described as a distinct species
+(_S. dresseri_). Though much diminished in numbers by persecution, it is
+still abundant on the coast of Newfoundland and thence northward. In
+Greenland also eiders are very plentiful, and it is supposed that
+three-fourths of the supply of down sent to Copenhagen comes from that
+country. The limits of the eider's northern range are not known, but the
+Arctic expedition of 1875 did not meet with it after leaving the Danish
+settlements, and its place was taken by an allied species, the king-duck
+(_S. spectabilis_), a very beautiful bird which sometimes appears on the
+British coast. The female greatly resembles that of the eider, but the
+male has a black chevron on his chin and a bright orange prominence on
+his forehead, which last seems to have given the species its English
+name. On the west coast of North America the eider is represented by a
+species (_S. v-nigrum_) with a like chevron, but otherwise resembling
+the Atlantic bird. In the same waters two other fine species are also
+found (_S. fischeri_ and _S. stelleri_), one of which (the latter) also
+inhabits the Arctic coast of Russia and East Finmark and has twice
+reached England. The Labrador duck (_S. labradoria_), now extinct, also
+belongs to this group.     (A. N.)
+
+
+
+
+EIFEL, a district of Germany, in the Prussian Rhine Province, between
+the Rhine, the Moselle and the frontier of the grand duchy of Luxemburg.
+It is a hilly region, most elevated in the eastern part (Hohe Eifel),
+where there are several points from 2000 up to 2410 ft. above sea-level.
+In the west is the Schneifels or Schnee-Eifel; and the southern part,
+where the most picturesque scenery and chief geological interest is
+found, is called the Vorder Eifel.
+
+The Eifel is an ancient massif of folded Devonian rocks upon the margins
+of which, near Hillesheim and towards Bitburg and Trier, rest
+unconformably the nearly undisturbed sandstones, marls and limestones of
+the Trias. On the southern border, at Wittlich, the terrestrial deposits
+of the Permian Rothliegende are also met with. The slates and sandstones
+of the Lower Devonian form by far the greater part of the region; but
+folded amongst these, in a series of troughs running from south-west to
+north-east lie the fossiliferous limestones of the Middle Devonian, and
+occasionally, as for example near Budesheim, a few small patches of the
+Upper Devonian. Upon the ancient floor of folded Devonian strata stand
+numerous small volcanic cones, many of which, though long extinct, are
+still very perfect in form. The precise age of the eruptions is
+uncertain. The only sign of any remaining volcanic activity is the
+emission in many places of carbon dioxide and of heated waters. There is
+no historic or legendary record of any eruption, but nevertheless the
+eruptions must have continued to a very recent geological period. The
+lavas of Papenkaule are clearly posterior to the excavation of the
+valley of the Kyll, and an outflow of basalt has forced the Uess to seek
+a new course. The volcanic rocks occur both as tuffs and as lava-flows.
+They are chiefly leucite and nepheline rocks, such as leucitite,
+leucitophyre and nephelinite, but basalt and trachyte also occur. The
+leucite lavas of Niedermendig contain hauyne in abundance. The most
+extensive and continuous area of volcanic rocks is that surrounding the
+Laacher See and extending eastwards to Neuwied and Coblenz and even
+beyond the Rhine.
+
+The numerous so-called crater-lakes or _maare_ of the Eifel present
+several features of interest. They do not, as a rule, lie in true
+craters at the summit of volcanic cones, but rather in hollows which
+have been formed by explosions. The most remarkable group is that of
+Daun, where the three depressions of Gemund, Weinfeld and Schalkenmehren
+have been hollowed out in the Lower Devonian strata. The first of these
+shows no sign of either lavas or scoriae, but volcanic rocks occur on
+the margins of the other two. The two largest lakes in the Eifel region,
+however, are the Laacher See in the hills west of Andernach on the
+Rhine, and the Pulvermaar S.E. of the Daun group, with its shores of
+peculiar volcanic sand, which also appears in its waters as a black
+powder (_pulver_).
+
+
+
+
+EIFFEL TOWER. Erected for the exposition of 1889, the Eiffel Tower, in
+the Champ de Mars, Paris, is by far the highest artificial structure in
+the world, and its height of 300 metres (984 ft.) surpasses that of the
+obelisk at Washington by 429 ft., and that of St Paul's cathedral by 580
+ft. Its framework is composed essentially of four uprights, which rise
+from the corners of a square measuring 100 metres on the side; thus the
+area it covers at its base is nearly 2-1/2 acres. These uprights are
+supported on huge piers of masonry and concrete, the foundations for
+which were carried down, by the aid of iron caissons and compressed air,
+to a depth of about 15 metres on the side next the Seine, and about 9
+metres on the other side. At first they curve upwards at an angle of 54
+deg.; then they gradually become straighter, until they unite in a
+single shaft rather more than half-way up. The first platform, at a
+height of 57 metres, has an area of 5860 sq. yds., and is reached either
+by staircases or lifts. The next, accessible by lifts only, is 115
+metres up, and has an area of 32 sq. yds; while the third, at 276,
+supports a pavilion capable of holding 800 persons. Nearly 25 metres
+higher up still is the lantern, with a gallery 5 metres in diameter. The
+work of building this structure, which is mainly composed of iron
+lattice-work, was begun on the 28th of January 1887, and the full height
+was reached on the 13th of March 1889. Besides being one of the sights
+of Paris, to which visitors resort in order to enjoy the extensive view
+that can be had from its higher galleries on a clear day, the tower is
+used to some extent for scientific and semi-scientific purposes; thus
+meteorological observations are carried on. The engineer under whose
+direction the tower was constructed was Alexandre Gustave Eiffel (born
+at Dijon on the 15th of December 1832), who had already had a wide
+experience in the construction of large metal bridges, and who designed
+the huge sluices for the Panama Canal, when it was under the French
+company.
+
+
+
+
+EILDON HILLS, a group of three conical hills, of volcanic origin, in
+Roxburghshire, Scotland, 1 m. S. by E. of Melrose, about equidistant
+from Melrose and St Boswells stations on the North British railway. They
+were once known as Eldune--the _Eldunum_ of Simeon of Durham (fl.
+1130)--probably derived from the Gaelic _aill_, "rock," and _dun_,
+"hill"; but the name is also said to be a corruption of the Cymric
+_moeldun_, "bald hill." The northern peak is 1327 ft. high, the central
+1385 ft. and the southern 1216 ft. Whether or not the Roman station of
+_Trimontium_ was situated here is matter of controversy. According to
+General William Roy (1726-1790) Trimontium--so called, according to this
+theory, from the triple Eildon heights--was Old Melrose; other
+authorities incline to place the station on the northern shore of the
+Solway Firth. The Eildons have been the subject of much legendary lore.
+Michael Scot (1175-1234), acting as a confederate of the Evil One (so
+the fable runs) cleft Eildon Hill, then a single cone, into the three
+existing peaks. Another legend states that Arthur and his knights sleep
+in a vault beneath the Eildons. A third legend centres in Thomas of
+Erceldoune. The Eildon Tree Stone, a large moss-covered boulder, lying
+on the high road as it bends towards the west within 2 m. of Melrose,
+marks the spot where the Fairy Queen led him into her realms in the
+heart of the hills. Other places associated with this legend may still
+be identified. Huntly Banks, where "true Thomas" lay and watched the
+queen's approach, is half a mile west of the Eildon Tree Stone, and on
+the west side of the hills is Bogle Burn, a streamlet that feeds the
+Tweed and probably derives its name from his ghostly visitor. Here, too,
+is Rhymer's glen, although the name was invented by Sir Walter Scott,
+who added the dell to his Abbotsford estate. Bowden, to the south of the
+hills, was the birthplace of the poets Thomas Aird (1802-1876) and James
+Thomson, and its parish church contains the burial-place of the dukes of
+Roxburghe. Eildon Hall is a seat of the duke of Buccleuch.
+
+
+
+
+EILENBURG, a town of Germany, in the Prussian province of Saxony, on an
+island formed by the Mulde, 31 m. E. from Halle, at the junction of the
+railways Halle-Cottbus and Leipzig-Eilenburg. Pop. (1905) 15,145. There
+are three churches, two Evangelical and one Roman Catholic. The
+industries of the town include the manufacture of chemicals, cloth,
+quilting, calico, cigars and agricultural implements, bleaching, dyeing,
+basket-making, carriage-building and trade in cattle. In the
+neighbourhood is the iron foundry of Erwinhof. Opposite the town, on the
+steep left bank of the Mulde, is the castle from which it derives its
+name, the original seat of the noble family of Eulenburg. This castle
+(Ilburg) is mentioned in records of the reigns of Henry the Fowler as an
+important outpost against the Sorbs and Wends. The town itself,
+originally called Mildenau, is of great antiquity. It is first mentioned
+as a town in 981, when it belonged to the house of Wettin and was the
+chief town of the East Mark. In 1386 it was incorporated in the
+margraviate of Meissen. In 1815 it passed to Prussia.
+
+  See Gundermann, _Chronik der Stadt Eilenburg_ (Eilenburg, 1879).
+
+
+
+
+EINBECK, or EIMBECK, a town of Germany, in the Prussian province of
+Hanover, on the Ilm, 50 m. by rail S. of Hanover. Pop. (1905) 8709. It
+is an old-fashioned town with many quaint wooden houses, notable among
+them the "Northeimhaus," a beautiful specimen of medieval architecture.
+There are several churches, among them the Alexanderkirche, containing
+the tombs of the princes of Grubenhagen, and a synagogue. The schools
+include a _Realgymnasium_ (i.e. predominantly for "modern" subjects),
+technical schools for the advanced study of machine-making, for weaving
+and for the textile industries, a preparatory training-college and a
+police school. The industries include brewing, weaving and the
+manufacture of cloth, carpets, tobacco, sugar, leather-grease, toys and
+roofing-felt.
+
+Einbeck grew up originally round the monastery of St Alexander (founded
+1080), famous for its relic of the True Blood. It is first recorded as a
+town in 1274, and in the 14th century was the seat of the princes of
+Grubenhagen, a branch of the ducal house of Brunswick. The town
+subsequently joined the Hanseatic League. In the 15th century it became
+famous for its beer ("Eimbecker," whence the familiar "Bock"). In 1540
+the Reformation was introduced by Duke Philip of Brunswick-Saltzderhelden
+(d. 1551), with the death of whose son Philip II. (1596) the Grubenhagen
+line became extinct. In 1626, during the Thirty Years' War, Einbeck was
+taken by Pappenheim and in October 1641 by Piccolomini. In 1643 it was
+evacuated by the Imperialists. In 1761 its walls were razed by the
+French.
+
+  See H.L. Harland, _Gesch. der Stadt Einbeck_, 2 Bde. (Einbeck,
+  1854-1859; abridgment, ib. 1881).
+
+
+
+
+EINDHOVEN, a town in the province of North Brabant, Holland, and a
+railway junction 8 m. by rail W. by S. of Helmond. Pop. (1900) 4730.
+Like Tilburg and Helmond it has developed in modern times into a
+flourishing industrial centre, having linen, woollen, cotton, tobacco
+and cigar, matches, &c., factories and several breweries.
+
+
+
+
+EINHARD (c. 770-840), the friend and biographer of Charlemagne; he is
+also called Einhartus, Ainhardus or Heinhardus, in some of the early
+manuscripts. About the 10th century the name was altered into Agenardus,
+and then to Eginhardus, or Eginhartus, but, although these variations
+were largely used in the English and French languages, the form
+Einhardus, or Einhartus, is unquestionably the right one.
+
+According to the statement of Walafrid Strabo, Einhard was born in the
+district which is watered by the river Main, and his birth has been
+fixed at about 770. His parents were of noble birth, and were probably
+named Einhart and Engilfrit; and their son was educated in the monastery
+of Fulda, where he was certainly residing in 788 and in 791. Owing to
+his intelligence and ability he was transferred, not later than 796,
+from Fulda to the palace of Charlemagne by abbot Baugulf; and he soon
+became very intimate with the king and his family, and undertook various
+important duties, one writer calling him _domesticus palatii regalis_.
+He was a member of the group of scholars who gathered around Charlemagne
+and was entrusted with the charge of the public buildings, receiving,
+according to a fashion then prevalent, the scriptural name of Bezaleel
+(Exodus xxxi. 2 and xxxv. 30-35) owing to his artistic skill. It has
+been supposed that he was responsible for the erection of the basilica
+at Aix-la-Chapelle, where he resided with the emperor, and the other
+buildings mentioned in chapter xvii. of his _Vita Karoli Magni_, but
+there is no express statement to this effect. In 806 Charlemagne sent
+him to Rome to obtain the signature of Pope Leo III. to a will which he
+had made concerning the division of his empire; and it was possibly
+owing to Einhard's influence that in 813, after the death of his two
+elder sons, the emperor made his remaining son, Louis, a partner with
+himself in the imperial dignity. When Louis became sole emperor in 814
+he retained his father's minister in his former position; then in 817
+made him tutor to his son, Lothair, afterwards the emperor Lothair I.;
+and showed him many other marks of favour. Einhard married Emma, or
+Imma, a sister of Bernharius, bishop of Worms, and a tradition of the
+12th century represented this lady as a daughter of Charlemagne, and
+invented a romantic story with regard to the courtship which deserves to
+be noticed as it frequently appears in literature. Einhard is said to
+have visited the emperor's daughter regularly and secretly, and on one
+occasion a fall of snow made it impossible for him to walk away without
+leaving footprints, which would lead to his detection. This risk,
+however, was obviated by the foresight of Emma, who carried her lover
+across the courtyard of the palace; a scene which was witnessed by
+Charlemagne, who next morning narrated the occurrence to his
+counsellors, and asked for their advice. Very severe punishments were
+suggested for the clandestine lover, but the emperor rewarded the
+devotion of the pair by consenting to their marriage. This story is, of
+course, improbable, and is further discredited by the fact that Einhard
+does not mention Emma among the number of Charlemagne's children.
+Moreover, a similar story has been told of a daughter of the emperor
+Henry III. It is uncertain whether Einhard had any children. He
+addressed a letter to a person named Vussin, whom he calls _fili_ and
+_mi nate_, but, as Vussin is not mentioned in documents in which his
+interests as Einhard's son would have been concerned, it is possible
+that he was only a young man in whom he took a special interest. In
+January 815 the emperor Louis I. bestowed on Einhard and his wife the
+domains of Michelstadt and Mulinheim in the Odenwald, and in the charter
+conveying these lands he is called simply Einhardus, but, in a document
+dated the 2nd of June of the same year, he is referred to as abbot.
+After this time he is mentioned as head of several monasteries: St
+Peter, Mount Blandin and St Bavon at Ghent, St Servais at Maastricht, St
+Cloud near Paris, and Fontenelle near Rouen, and he also had charge of
+the church of St John the Baptist at Pavia.
+
+During the quarrels which took place between Louis I. and his sons, in
+consequence of the emperor's second marriage, Einhard's efforts were
+directed to making peace, but after a time he grew tired of the troubles
+and intrigues of court life. In 818 he had given his estate at
+Michelstadt to the abbey of Lorsch, but he retained Mulinheim, where
+about 827 he founded an abbey and erected a church, to which he
+transported some relics of St Peter and St Marcellinus, which he had
+procured from Rome. To Mulinheim, which was afterwards called
+Seligenstadt, he finally retired in 830. His wife, who had been his
+constant helper, and whom he had not put away on becoming an abbot, died
+in 836, and after receiving a visit from the emperor, Einhard died on
+the 14th of March 840. He was buried at Seligenstadt, and his epitaph
+was written by Hrabanus Maurus. Einhard was a man of very short
+stature, a feature on which Alcuin wrote an epigram. Consequently he was
+called _Nardulus_, a diminutive form of Einhardus, and his great
+industry and activity caused him to be likened to an ant. He was also a
+man of learning and culture. Reaping the benefits of the revival of
+learning brought about by Charlemagne, he was on intimate terms with
+Alcuin, was well versed in Latin literature, and knew some Greek. His
+most famous work is his _Vita Karoli Magni_, to which a prologue was
+added by Walafrid Strabo. Written in imitation of the _De vitis
+Caesarum_ of Suetonius, this is the best contemporary account of the
+life of Charlemagne, and could only have been written by one who was
+very intimate with the emperor and his court. It is, moreover, a work of
+some artistic merit, although not free from inaccuracies. It was written
+before 821, and having been very popular during the middle ages, was
+first printed at Cologne in 1521. G.H. Pertz collated more than sixty
+manuscripts for his edition of 1829, and others have since come to
+light. Other works by Einhard are: _Epistolae_, which are of
+considerable importance for the history of the times; _Historia
+translationis beatorum Christi martyrum Marcellini et Petri_, which
+gives a curious account of how the bones of these martyrs were stolen
+and conveyed to Seligenstadt, and what miracles they wrought; and _De
+adoranda cruce_, a treatise which has only recently come to light, and
+which has been published by E. Dummler in the _Neues Archiv der
+Gesellschaft fur altere deutsche Geschichtskunde_, Band xi. (Hanover,
+1886). It has been asserted that Einhard was the author of some of the
+Frankish annals, and especially of part of the annals of Lorsch
+(_Annales Laurissenses majores_), and part of the annals of Fulda
+(_Annales Fuldenses_). Much discussion has taken place on this question,
+and several of the most eminent of German historians, Ranke among them,
+have taken part therein, but no certain decision has been reached.
+
+  The literature on Einhard is very extensive, as nearly all those who
+  deal with Charlemagne, early German and early French literature, treat
+  of him. Editions of his works are by A. Teulet, _Einhardi omnia quae
+  extant opera_ (Paris, 1840-1843), with a French translation; P. Jaffe,
+  in the _Bibliotheca rerum Germanicarum_, Band iv. (Berlin, 1867); G.H.
+  Pertz in the _Monumenta Germaniae historica_, Bande i. and ii.
+  (Hanover, 1826-1829), and J.P. Migne in the _Patrologia Latina_, tomes
+  97 and 104 (Paris, 1866). The _Vita Karoli Magni_, edited by G.H.
+  Pertz and G. Waitz, has been published separately (Hanover, 1880).
+  Among the various translations of the _Vita_ may be mentioned an
+  English one by W. Glaister (London, 1877) and a German one by O. Abel
+  (Leipzig, 1893). For a complete bibliography of Einhard, see A.
+  Potthast, _Bibliotheca historica_, pp. 394-397 (Berlin, 1896), and W.
+  Wattenbach, _Deutschlands Geschichtsquellen_, Band i. (Berlin, 1904).
+       (A. W. H.*)
+
+
+
+
+EINHORN, DAVID (1809-1879), leader of the Jewish reform movement in the
+United States of America, was born in Bavaria. He was a supporter of the
+principles of Abraham Geiger (q.v.), and while still in Germany
+advocated the introduction of prayers in the vernacular, the exclusion
+of nationalistic hopes from the synagogue service, and other ritual
+modifications. In 1855 he migrated to America, where he became the
+acknowledged leader of reform, and laid the foundation of the regime
+under which the mass of American Jews (excepting the newly arrived
+Russians) now worship. In 1858 he published his revised prayer book,
+which has formed the model for all subsequent revisions. In 1861 he
+strongly supported the anti-slavery party, and was forced to leave
+Baltimore where he then ministered. He continued his work first in
+Philadelphia and later in New York.     (I. A.)
+
+
+
+
+EINSIEDELN, the most populous town in the Swiss canton of Schwyz. It is
+built on the right bank of the Alpbach (an affluent of the Sihl), at a
+height of 2908 ft. above the sea-level on a rather bare moorland, and by
+rail is 25 m. S.E. of Zurich, or by a round-about railway route about 38
+m. north of Schwyz, with which it communicates directly over the Hacken
+Pass (4649 ft.) or the Holzegg Pass (4616 ft.). In 1900 the population
+was 8496, all (save 75) Romanists and all (save 111) German-speaking.
+The town is entirely dependent on the great Benedictine abbey that rises
+slightly above it to the east. Close to its present site Meinrad, a
+hermit, was murdered in 861 by two robbers, whose crime was made known
+by Meinrad's two pet ravens. Early in the 10th century Benno, a hermit,
+rebuilt the holy man's cell, but the abbey proper was not founded till
+about 934, the church having been consecrated (it is said by Christ
+Himself) in 948. In 1274 the dignity of a prince of the Holy Roman
+Empire was confirmed by the emperor to the reigning abbot. Originally
+under the protection of the counts of Rapperswil (to which town on the
+lake of Zurich the old pilgrims' way still leads over the Etzel Pass,
+3146 ft., with its chapel and inn), this position passed by marriage
+with their heiress in 1295 to the Laufenburg or cadet line of the
+Habsburgs, but from 1386 was permanently occupied by Schwyz. A black
+wooden image of the Virgin and the fame of St Meinrad caused the throngs
+of pilgrims to resort to Einsiedeln in the middle ages, and even now it
+is much frequented, particularly about the 14th of September. The
+existing buildings date from the 18th century only, while the treasury
+and the library still contain many precious objects, despite the sack by
+the French in 1798. There are now about 100 fully professed monks, who
+direct several educational institutions. The Black Virgin has a special
+chapel in the stately church. Zwingli was the parish priest of
+Einsiedeln 1516-1518 (before he became a Protestant), while near the
+town Paracelsus (1493-1541), the celebrated philosopher, was born.
+
+  See Father O. Ringholz, _Geschichte d. furstl. Benediktinerstiftes
+  Einsiedeln_, vol. i. (to 1526), (Einsiedeln, 1904).     (W. A. B. C.)
+
+
+
+
+EISENACH, a town of Germany, second capital of the grand-duchy of
+Saxe-Weimar-Eisenach, lies at the north-west foot of the Thuringian
+forest, at the confluence of the Nesse and Horsel, 32 m. by rail W. from
+Erfurt. Pop. (1905) 35,123. The town mainly consists of a long street,
+running from east to west. Off this are the market square, containing
+the grand-ducal palace, built in 1742, where the duchess Helene of
+Orleans long resided, the town-hall, and the late Gothic St
+Georgenkirche; and the square on which stands the Nikolaikirche, a fine
+Romanesque building, built about 1150 and restored in 1887. Noteworthy
+are also the Klemda, a small castle dating from 1260; the Lutherhaus, in
+which the reformer stayed with the Cotta family in 1498; the house in
+which Sebastian Bach was born, and that (now a museum) in which Fritz
+Reuter lived (1863-1874). There are monuments to the two former in the
+town, while the resting-place of the latter in the cemetery is marked by
+a less pretentious memorial. Eisenach has a school of forestry, a school
+of design, a classical school (_Gymnasium_) and modern school
+(_Realgymnasium_), a deaf and dumb school, a teachers' seminary, a
+theatre and a Wagner museum. The most important industries of the town
+are worsted-spinning, carriage and wagon building, and the making of
+colours and pottery. Among others are the manufacture of cigars, cement
+pipes, iron-ware and machines, alabaster ware, shoes, leather, &c.,
+cabinet-making, brewing, granite quarrying and working, tile-making, and
+saw- and corn-milling.
+
+The natural beauty of its surroundings and the extensive forests of the
+district have of late years attracted many summer residents.
+Magnificently situated on a precipitous hill, 600 ft. above the town to
+the south, is the historic Wartburg (q.v.), the ancient castle of the
+landgraves of Thuringia, famous as the scene of the contest of
+Minnesingers immortalized in Wagner's Tannhauser, and as the place where
+Luther, on his return from the diet of Worms in 1521, was kept in hiding
+and made his translation of the Bible. On a high rock adjacent to the
+Wartburg are the ruins of the castle of Madelstein.
+
+Eisenach (_Isenacum_) was founded in 1070 by Louis II. the Springer,
+landgrave of Thuringia, and its history during the middle ages was
+closely bound up with that of the Wartburg, the seat of the landgraves.
+The Klemda, mentioned above, was built by Sophia (d. 1284), daughter of
+the landgrave Louis IV., and wife of Duke Henry II. of Brabant, to
+defend the town against Henry III., margrave of Meissen, during the
+succession contest that followed the extinction of the male line of the
+Thuringian landgraves in 1247. The principality of Eisenach fell to the
+Saxon house of Wettin in 1440, and in the partition of 1485 formed part
+of the territories given to the Ernestine line. It was a separate Saxon
+duchy from 1596 to 1638, from 1640 to 1644, and again from 1662 to
+1741, when it finally fell to Saxe-Weimar. The town of Eisenach, by
+reason of its associations, has been a favourite centre for the
+religious propaganda of Evangelical Germany, and since 1852 it has been
+the scene of the annual conference of the German Evangelical Church,
+known as the Eisenach conference.
+
+  See Trinius, _Eisenach und Umgebung_ (Minden, 1900); and H.A. Daniel,
+  _Deutschland_ (Leipzig, 1895), and further references in U. Chevalier,
+  "Repertoire des sources," &c., _Topo-bibliogr._ (Montbeliard,
+  1894-1899), s.v.
+
+
+
+
+EISENBERG (_Isenberg_), a town of Germany, in the duchy of
+Saxe-Altenburg, on a plateau between the rivers Saale and Elster, 20 m.
+S.W. from Zeitz, and connected with the railway Leipzig-Gera by a branch
+to Crossen. Pop. (1905) 8824. It possesses an old castle, several
+churches and monuments to Duke Christian of Saxe-Eisenberg (d. 1707),
+Bismarck, and the philosopher Karl Christian Friedrich Krause (q.v.).
+Its principal industries are weaving, and the manufacture of machines,
+ovens, furniture, pianos, porcelain and sausages.
+
+  See Back, _Chronik der Sladt und des Amtes Eisenberg_ (Eisenb., 1843).
+
+
+
+
+EISENERZ ("Iron ore"), a market-place and old mining town in Styria,
+Austria, 68 m. N.W. of Graz by rail. Pop. (1900) 6494. It is situated in
+a deep valley, dominated on the east by the Pfaffenstein (6140 ft.), on
+the west by the Kaiserschild (6830 ft.), and on the south by the Erzberg
+(5030 ft.). It has an interesting example of a medieval fortified
+church, a Gothic edifice founded by Rudolph of Habsburg in the 13th
+century and rebuilt in the 16th. The Erzberg or Ore Mountain furnishes
+such rich ore that it is quarried in the open air like stone, in the
+summer months. There is documentary evidence of the mines having been
+worked as far back as the 12th century. They afford employment to two or
+three thousand hands in summer and about half as many in winter, and
+yield some 800,000 tons of iron per annum. Eisenerz is connected with
+the mines by the Erzberg railway, a bold piece of engineering work, 14
+m. long, constructed on the Abt's rack-and-pinion system. It passes
+through some beautiful scenery, and descends to Vordernberg (pop. 3111),
+an important centre of the iron trade situated on the south side of the
+Erzberg. Eisenerz possesses, in addition, twenty-five furnaces, which
+produce iron, and particularly steel, of exceptional excellence. A few
+miles to the N.W. of Eisenerz lies the castle of Leopoldstein, and near
+it the beautiful Leopoldsteiner Lake. This lake, with its dark-green
+water, situated at an altitude of 2028 ft., and surrounded on all sides
+by high peaks, is not big, but is very deep, having a depth of 520 ft.
+
+
+
+
+EISLEBEN (Lat. _Islebia_), a town of Germany, in the Prussian province of
+Saxony, 24 m. W. by N. from Halle, on the railway to Nordhausen and
+Cassel. Pop. (1905) 23,898. It is divided into an old and a new town
+(Altstadt and Neustadt). Among its principal buildings are the church of
+St Andrew (Andreaskirche), which contains numerous monuments of the counts
+of Mansfeld; the church of St Peter and St Paul (Peter-Paulkirche),
+containing the font in which Luther was baptized; the royal gymnasium
+(classical school), founded by Luther shortly before his death in 1546;
+and the hospital. Eisleben is celebrated as the place where Luther was
+born and died. The house in which he was born was burned in 1689, but was
+rebuilt in 1693 as a free school for orphans. This school fell into decay
+under the regime of the kingdom of Westphalia, but was restored in 1817 by
+King Frederick William III. of Prussia, who, in 1819, transferred it to a
+new building behind the old house. The house in which Luther died was
+restored towards the end of the 19th century, and his death chamber is
+still preserved. A bronze statue of Luther by Rudolf Siemering (1835-1905)
+was unveiled in 1883. Eisleben has long been the centre of an important
+mining district (Luther was a miner's son), the principal products being
+silver and copper. It possesses smelting works and a school of mining.
+
+The earliest record of Eisleben is dated 974. In 1045, at which time it
+belonged to the counts of Mansfeld, it received the right to hold
+markets, coin money, and levy tolls. From 1531 to 1710 it was the seat
+of the cadet line of the counts of Mansfeld-Eisleben. After the
+extinction of the main line of the counts of Mansfeld, Eisleben fell to
+Saxony, and, in the partition of Saxony by the congress of Vienna in
+1815, was assigned to Prussia.
+
+  See G. Grossler, _Urkundliche Gesch. Eislebens bis zum Ende des 12.
+  Jahrhunderts_ (Halle, 1875); _Chronicon Islebiense; Eisleben
+  Stadtchronik aus den Jahren_ 1520-1738, edited from the original, with
+  notes by Grossler and Sommer (Eisleben, 1882).
+
+
+
+
+EISTEDDFOD (plural Eisteddfodau), the national bardic congress of Wales,
+the objects of which are to encourage bardism and music and the general
+literature of the Welsh, to maintain the Welsh language and customs of
+the country, and to foster and cultivate a patriotic spirit amongst the
+people. This institution, so peculiar to Wales, is of very ancient
+origin.[1] The term _Eisteddfod_, however, which means "a session" or
+"sitting," was probably not applied to bardic congresses before the 12th
+century.
+
+The Eisteddfod in its present character appears to have originated in
+the time of Owain ap Maxen Wledig, who at the close of the 4th century
+was elected to the chief sovereignty of the Britons on the departure of
+the Romans. It was at this time, or soon afterwards, that the laws and
+usages of the Gorsedd were codified and remodelled, and its motto of "Y
+gwir yn erbyn y byd" (The truth against the world) given to it. "Chairs"
+(with which the Eisteddfod as a national institution is now inseparably
+connected) were also established, or rather perhaps resuscitated, about
+the same time. The chair was a kind of convention where disciples were
+trained, and bardic matters discussed preparatory to the great Gorsedd,
+each chair having a distinctive motto. There are now existing four
+chairs in Wales,--namely, the "royal" chair of Powys, whose motto is "A
+laddo a leddir" (He that slayeth shall be slain); that of Gwent and
+Glamorgan, whose motto is "Duw a phob daioni" (God and all goodness);
+that of Dyfed, whose motto is "Calon wrth galon" (Heart with heart); and
+that of Gwynedd, or North Wales, whose motto is "Iesu," or "O Iesu! na'd
+gamwaith" (Jesus, or Oh Jesus! suffer not iniquity).
+
+The first Eisteddfod of which any account seems to have descended to us
+was one held on the banks of the Conway in the 6th century, under the
+auspices of Maelgwn Gwynedd, prince of North Wales. Maelgwn on this
+occasion, in order to prove the superiority of vocal song over
+instrumental music, is recorded to have offered a reward to such bards
+and minstrels as should swim over the Conway. There were several
+competitors, but on their arrival on the opposite shore the harpers
+found themselves unable to play owing to the injury their harps had
+sustained from the water, while the bards were in as good tune as ever.
+King Cadwaladr also presided at an Eisteddfod about the middle of the
+7th century.
+
+Griffith ap Cynan, prince of North Wales, who had been born in Ireland,
+brought with him from that country many Irish musicians, who greatly
+improved the music of Wales. During his long reign of 56 years he
+offered great encouragement to bards, harpers and minstrels, and framed
+a code of laws for their better regulation. He held an Eisteddfod about
+the beginning of the 12th century at Caerwys in Flintshire, "to which
+there repaired all the musicians of Wales, and some also from England
+and Scotland." For many years afterwards the Eisteddfod appears to have
+been held triennially, and to have enforced the rigid observance of the
+enactments of Griffith ap Cynan. The places at which it was generally
+held were Aberffraw, formerly the royal seat of the princes of North
+Wales; Dynevor, the royal castle of the princes of South Wales; and
+Mathrafal, the royal palace of the princes of Powys: and in later times
+Caerwys in Flintshire received that honourable distinction, it having
+been the princely residence of Llewelyn the Last. Some of these
+Eisteddfodau were conducted in a style of great magnificence, under the
+patronage of the native princes. At Christmas 1107 Cadwgan, the son of
+Bleddyn ap Cynfyn, prince of Powys, held an Eisteddfod in Cardigan
+Castle, to which he invited the bards, harpers and minstrels, "the best
+to be found in all Wales"; and "he gave them chairs and subjects of
+emulation according to the custom of the feasts of King Arthur." In 1176
+Rhys ab Gruffydd, prince of South Wales, held an Eisteddfod in the same
+castle on a scale of still greater magnificence, it having been
+proclaimed, we are told, a year before it took place, "over Wales,
+England, Scotland, Ireland and many other countries."
+
+On the annexation of Wales to England, Edward I. deemed it politic to
+sanction the bardic Eisteddfod by his famous statute of Rhuddlan. In the
+reign of Edward III. Ifor Hael, a South Wales chieftain, held one at his
+mansion. Another was held in 1451, with the permission of the king, by
+Griffith ab Nicholas at Carmarthen, in princely style, where Dafydd ab
+Edmund, an eminent poet, signalized himself by his wonderful powers of
+versification in the Welsh metres, and whence "he carried home on his
+shoulders the silver chair" which he had fairly won. Several
+Eisteddfodau, were held, one at least by royal mandate, in the reign of
+Henry VII. In 1523 one was held at Caerwys before the chamberlain of
+North Wales and others, by virtue of a commission issued by Henry VIII.
+In the course of time, through relaxation of bardic discipline, the
+profession was assumed by unqualified persons, to the great detriment of
+the regular bards. Accordingly in 1567 Queen Elizabeth issued a
+commission for holding an Eisteddfod at Caerwys in the following year,
+which was duly held, when degrees were conferred on 55 candidates,
+including 20 harpers. From the terms of the royal proclamation we find
+that it was then customary to bestow "a silver harp" on the chief of the
+faculty of musicians, as it had been usual to reward the chief bard with
+"a silver chair." This was the last Eisteddfod appointed by royal
+commission, but several others of some importance were held during the
+16th and 17th centuries, under the patronage of the earl of Pembroke,
+Sir Richard Neville, and other influential persons. Amongst these the
+last of any particular note was one held in Bewper Castle, Glamorgan, by
+Sir Richard Basset in 1681.
+
+During the succeeding 130 years Welsh nationality was at its lowest ebb,
+and no general Eisteddfod on a large scale appears to have been held
+until 1819, though several small ones were held under the auspices of
+the Gwyneddigion Society, established in 1771,--the most important being
+those at Corwen (1789), St Asaph (1790) and Caerwys (1798).
+
+At the close of the Napoleonic wars, however, there was a general
+revival of Welsh nationality, and numerous Welsh literary societies were
+established throughout Wales, and in the principal English towns. A
+large Eisteddfod was held under distinguished patronage at Carmarthen in
+1819, and from that time to the present they have been held (together
+with numerous local Eisteddfodau), almost without intermission,
+annually. The Eisteddfod at Llangollen in 1858 is memorable for its
+archaic character, and the attempts then made to revive the ancient
+ceremonies, and restore the ancient vestments of druids, bards and
+ovates.
+
+To constitute a provincial Eisteddfod it is necessary that it should be
+proclaimed by a graduated bard of a Gorsedd a year and a day before it
+takes place. A local one may be held without such a proclamation. A
+provincial Eisteddfod generally lasts three, sometimes four days. A
+president and a conductor are appointed for each day. The proceedings
+commence with a Gorsedd meeting, opened with sound of trumpet and other
+ceremonies, at which candidates come forward and receive bardic degrees
+after satisfying the presiding bard as to their fitness. At the
+subsequent meetings the president gives a brief address; the bards
+follow with poetical addresses; adjudications are made, and prizes and
+medals with suitable devices are given to the successful competitors for
+poetical, musical and prose compositions, for the best choral and solo
+singing, and singing with the harp or "Pennillion singing"[2] as it is
+called, for the best playing on the harp or stringed or wind
+instruments, as well as occasionally for the best specimens of
+handicraft and art. In the evening of each day a concert is given,
+generally attended by very large numbers. The great day of the
+Eisteddfod is the "chair" day--usually the third or last day--the grand
+event of the Eisteddfod being the adjudication on the chair subject, and
+the chairing and investiture of the fortunate winner. This is the
+highest object of a Welsh bard's ambition. The ceremony is an imposing
+one, and is performed with sound of trumpet. (See also the articles
+BARD, CELT: _Celtic Literature_, and WALES.)     (R. W.*)
+
+
+FOOTNOTE:
+
+  [1] According to the Welsh Triads and other historical records, the
+    _Gorsedd_ or assembly (an essential part of the modern Eisteddfod,
+    from which indeed the latter sprung) is as old at least as the time
+    of Prydain the son of Aedd the Great, who lived many centuries before
+    the Christian era. Upon the destruction of the political ascendancy
+    of the Druids, the Gorsedd lost its political importance, though it
+    seems to have long afterwards retained its institutional character as
+    the medium for preserving the laws, doctrines and traditions of
+    bardism.
+
+  [2] According to Jones's _Bardic Remains_, "To sing 'Pennillion' with
+    a Welsh harp is not so easily accomplished as may be imagined. The
+    singer is obliged to follow the harper, who may change the tune, or
+    perform variations _ad libitum_, whilst the vocalist must keep time,
+    and end precisely with the strain. The singer does not commence with
+    the harper, but takes the strain up at the second, third or fourth
+    bar, as best suits the 'pennill' he intends to sing.... Those are
+    considered the best singers who can adapt stanzas of various metres
+    to one melody, and who are acquainted with the twenty-four measures
+    according to the bardic laws and rules of composition."
+
+
+
+
+EJECTMENT (Lat. e, out, and _jacere_, to throw), in English law, an
+action for the recovery of the possession of land, together with damages
+for the wrongful withholding thereof. In the old classifications of
+actions, as real or personal, this was known as a mixed action, because
+its object was twofold, viz. to recover both the realty and personal
+damages. It should be noted that the term "ejectment" applies in law to
+distinct classes of proceedings--ejectments as between rival claimants
+to land, and ejectments as between those who hold, or have held, the
+relation of landlord and tenant. Under the Rules of the Supreme Court,
+actions in England for the recovery of land are commenced and proceed in
+the same manner as ordinary actions. But the historical interest
+attaching to the action of ejectment is so great as to render some
+account of it necessary.
+
+The form of the action as it prevailed in the English courts down to the
+Common Law Procedure Act 1852 was a series of fictions, among the most
+remarkable to be found in the entire body of English law. A, the person
+claiming title to land, delivered to B, the person in possession, a
+declaration in ejectment in which C and D, fictitious persons, were
+plaintiff and defendant. C stated that A had devised the land to him for
+a term of years, and that he had been ousted by D. A notice signed by D
+informed B of the proceedings, and advised him to apply to be made
+defendant in D's place, as he, D, having no title, did not intend to
+defend the suit. If B did not so apply, judgment was given against D,
+and possession of the lands was given to A. But if B did apply, the
+Court allowed him to defend the action only on condition that he
+admitted the three fictitious averments--the lease, the entry and the
+ouster--which, together with title, were the four things necessary to
+maintain an action of ejectment. This having been arranged the action
+proceeded, B being made defendant instead of D. The names used for the
+fictitious parties were John Doe, plaintiff, and Richard Roe, defendant,
+who was called "the casual ejector." The explanation of these mysterious
+fictions is this. The writ _de ejectione firmae_ was invented about the
+beginning of the reign of Edward III. as a remedy to a lessee for years
+who had been ousted of his term. It was a writ of trespass, and carried
+damages, but in the time of Henry VII., if not before that date, the
+courts of common law added thereto a species of remedy neither warranted
+by the original writ nor demanded by the declaration, viz. a judgment to
+recover so much of the term as was still to run, and a writ of
+possession thereupon. The next step was to extend the remedy--limited
+originally to leaseholds--to cases of disputed title to freeholds. This
+was done indirectly by the claimant entering on the land and there
+making a lease for a term of years to another person; for it was only a
+term that could be recovered by the action, and to create a term
+required actual possession in the granter. The lessee remained on the
+land, and the next person who entered even by chance was accounted an
+ejector of the lessee, who then served upon him a writ of trespass and
+ejectment. The case then went to trial as on a common action of
+trespass; and the claimant's title, being the real foundation of the
+lessee's right, was thus indirectly determined. These proceedings might
+take place without the knowledge of the person really in possession; and
+to prevent the abuse of the action a rule was laid down that the
+plaintiff in ejectment must give notice to the party in possession, who
+might then come in and defend the action. When the action came into
+general use as a mode of trying the title to freeholds, the actual
+entry, lease and ouster which were necessary to found the action were
+attended with much inconvenience, and accordingly Lord Chief Justice
+Rolle during the Protectorate (c. 1657) substituted for them the
+fictitious averments already described. The action of ejectment is now
+only a curiosity of legal history. Its fictitious suitors were swept
+away by the Common Law Procedure Act of 1852. A form of writ was
+prescribed, in which the person in possession of the disputed premises
+by name and all persons entitled to defend the possession were informed
+that the plaintiff claimed to be entitled to possession, and required to
+appear in court to defend the possession of the property or such part of
+it as they should think fit. In the form of the writ and in some other
+respects ejectment still differed from other actions. But, as already
+mentioned, it has now been assimilated (under the name of action for the
+recovery of lands) to ordinary actions by the Rules of the Supreme
+Court. It is commenced by writ of summons, and--subject to the rules as
+to summary judgments (_v. inf._)--proceeds along the usual course of
+pleadings and trial to judgment; but is subject to one special rule,
+viz: that except by leave of the Court or a judge the only claims which
+may be joined with one for recovery of land are claims in respect of
+arrears of rent or double value for holding over, or mesne profits (i.e.
+the value of the land during the period of illegal possession), or
+damages for breach of a contract under which the premises are held or
+for any wrong or injury to the premises claimed (R.S.C., O. xviii. r.
+2). These claims were formerly recoverable by an independent action.
+
+With regard to actions for the recovery of land--apart from the
+relationship of landlord and tenant--the only point that need be noted
+is the presumption of law in favour of the actual possessor of the land
+in dispute. Where the action is brought by a landlord against his
+tenant, there is of course no presumption against the landlord's title
+arising from the tenant's possession. By the Common Law Procedure Act
+1852 (ss. 210-212) special provision was made for the prompt recovery of
+demised premises where half a year's rent was in arrear and the landlord
+was entitled to re-enter for non-payment. These provisions are still in
+force, but advantage is now more generally taken of the summary judgment
+procedure introduced by the Rules of the Supreme Court (Order 3, r. 6.).
+This procedure may be adopted when (a) the tenant's term has expired,
+(b) or has been duly determined by notice to quit, or (c) has become
+liable to forfeiture for non-payment of rent, and applies not only to
+the tenant but to persons claiming under him. The writ is specially
+endorsed with the plaintiff's claim to recover the land with or without
+rent or mesne profits, and summary judgment obtained if no substantial
+defence is disclosed. Where an action to recover land is brought against
+the tenant by a person claiming adversely to the landlord, the tenant is
+bound, under penalty of forfeiting the value of three years' improved or
+rack rent of the premises, to give notice to the landlord in order that
+he may appear and defend his title. Actions for the recovery of land,
+other than land belonging to spiritual corporations and to the crown,
+are barred in 12 years (Real Property Limitation Acts 1833 (s. 29) and
+1874 (s. 1). A landlord can recover possession in the county court (i.)
+by an action for the recovery of possession, where neither the value of
+the premises nor the rent exceeds L100 a year, and the tenant is holding
+over (County Courts Acts of 1888, s. 138, and 1903, s. 3); (ii.) by "an
+action of ejectment," where (a) the value or rent of the premises does
+not exceed L100, (b) half a year's rent is in arrear, and (c) no
+sufficient distress (see RENT) is to be found on the premises (Act of
+1888, s. 139; Act of 1903, s. 3; County Court Rules 1903, Ord. v. rule
+3). Where a tenant at a rent not exceeding L20 a year of premises at
+will, or for a term not exceeding 7 years, refuses nor neglects, on the
+determination or expiration of his interest, to deliver up possession,
+such possession may be recovered by proceedings before justices under
+the Small Tenements Recovery Act 1838, an enactment which has been
+extended to the recovery of allotments. Under the Distress for Rent Act
+1737, and the Deserted Tenements Act 1817, a landlord can have himself
+put by the order of two justices into premises deserted by the tenant
+where half a year's rent is owing and no sufficient distress can be
+found.
+
+In _Ireland_, the practice with regard to the recovery of land is
+regulated by the Rules of the Supreme Court 1891, made under the
+Judicature (Ireland) Act 1877; and resembles that of England. Possession
+may be recovered summarily by a special indorsement of the writ, as in
+England; and there are analogous provisions with regard to the recovery
+of small tenements (see Land Act, 1860 ss. 84 and 89). The law with
+regard to the ejectment or eviction of tenants is consolidated by the
+Land Act 1860. (See ss. 52-66, 68-71, and further under LANDLORD AND
+TENANT.)
+
+In _Scotland_, the recovery of land is effected by an action of
+"removing" or summary ejection. In the case of a tenant "warning" is
+necessary unless he is bound by his lease to remove without warning. In
+the case of possessors without title, or a title merely precarious, no
+warning is needed. A summary process of removing from small holdings is
+provided for by Sheriff Courts (Scotland) Acts of 1838 and 1851.
+
+In the United States, the old English action of ejectment was adopted to
+a very limited extent, and where it was so adopted has often been
+superseded, as in Connecticut, by a single action for all cases of
+ouster, disseisin or ejectment. In this action, known as an action of
+disseisin or ejectment, both possession of the land and damages may be
+recovered. In some of the states a tenant against whom an action of
+ejectment is brought by a stranger is bound under a penalty, as in
+England, to give notice of the claim to the landlord in order that he
+may appear and defend his title.
+
+In _French law_ the landlord's claim for rent is fairly secured by the
+hypothec, and by summary powers which exist for the seizure of the
+effects of defaulting tenants. Eviction or annulment of a lease can only
+be obtained through the judicial tribunals. The Civil Code deals with
+the position of a tenant in case of the sale of the property leased. If
+the lease is by authentic act (_acte authentique_) or has an ascertained
+date, the purchaser cannot evict the tenant unless a right to do so was
+reserved on the lease (art. 1743), and then only on payment of an
+indemnity (arts. 1744-1747). If the lease is not by authentic act, or
+has not an ascertained date, the purchaser is not liable for indemnity
+(art. 1750). The tenant of rural lands is bound to give the landlord
+notice of acts of usurpation (art. 1768). There are analogous provisions
+in the Civil Codes of Belgium (arts. 1743 et seq.), Holland (arts. 1613,
+1614), Portugal (art. 1572); and see the German Civil Code (arts. 535 et
+seq.). In many of the colonies there are statutory provisions for the
+recovery of land or premises on the lines of English law (cf. Ontario,
+Rev. Stats. 1897, c. 170. ss. 19 et seq.; Manitoba, Rev. Stats. 1902, c.
+1903). In others (e.g. New Zealand, Act. No. 55 of 1893, ss. 175-187;
+British Columbia, Revised Statutes, 1897, c. 182: Cyprus, Ord. 15 of
+1895) there has been legislation similar to the Small Tenements Recovery
+Act 1838.
+
+  AUTHORITIES.--_English Law_: Cole on _Ejectment_; Digby, _History of
+  Real Property_ (3rd ed., London, 1884); Pollock and Maitland, _History
+  of English Law_ (Cambridge, 1895); Foa, _Landlord and Tenant_ (4th
+  ed., London, 1907); Fawcett, _Landlord and Tenant_ (London, 1905).
+  _Irish Law_: Nolan and Kane's _Statutes relating to the Law of
+  Landlord and Tenant_ (5th ed., Dublin, 1898); Wylie's _Judicature
+  Acts_ (Dublin, 1900). _Scots Law_: Hunter on _Landlord and Tenant_
+  (4th ed., Edin., 1878); Erskine's _Principles_ (20th ed., Edin.,
+  1903). _American Law: Two Centuries' Growth of American Law_ (New York
+  and London, 1901); Bouvier's _Law Dictionary_ (Boston and London,
+  1897); Stimson, _American Statute Law_ (Boston, 1886).     (A. W. R.)
+
+
+
+
+EKATERINBURG, a town of Russia, in the government of Perm, 311 m. by
+rail S.E. of the town of Perm, on the Iset river, near the E. foot of
+the Ural Mountains, in 56 deg. 49' N. and 60 deg. 35' E., at an
+altitude of 870 ft. above sea-level. It is the most important town of
+the Urals. Pop. (1860) 19,830; (1897) 55,488. The streets are broad and
+regular, and several of the houses of palatial proportions. In 1834
+Ekaterinburg was made the see of a suffragan bishop of the Orthodox
+Greek Church. There are two cathedrals--St Catherine's, founded in 1758,
+and that of the Epiphany, in 1774--and a museum of natural history,
+opened in 1853. Ekaterinburg is the seat of the central mining
+administration of the Ural region, and has a chemical laboratory for the
+assay of gold, a mining school, the Ural Society of Naturalists, and a
+magnetic and meteorological observatory. Besides the government mint for
+copper coinage, which dates from 1735, the government engineering works,
+and the imperial factory for the cutting and polishing of malachite,
+jasper, marble, porphyry and other ornamental stones, the industrial
+establishments comprise candle, paper, soap and machinery works, flour
+and woollen mills, and tanneries. There is a lively trade in cattle,
+cereals, iron, woollen and silk goods, and colonial products; and two
+important fairs are held annually. Nearly forty gold and platinum mines,
+over thirty iron-works, and numerous other factories are scattered over
+the district, while wheels, travelling boxes, hardware, boots and so
+forth are extensively made in the villages. Ekaterinburg took its origin
+from the mining establishments founded by Peter the Great in 1721, and
+received its name in honour of his wife, Catherine I. Its development
+was greatly promoted in 1763 by the diversion of the Siberian highway
+from Verkhoturye to this place.
+
+
+
+
+EKATERINODAR, a town of South Russia, chief town of the province of
+Kuban, on the right bank of the river Kuban, 85 m. E.N.E. of
+Novo-rossiysk on the railway to Rostov-on-Don, and in 45 deg. 3' N. and
+38 deg. 50' E. It is badly built, on a swampy site exposed to the
+inundations of the river; and its houses, with few exceptions, are
+slight structures of wood and plaster. Founded by Catherine II. in 1794
+on the site of an old town called Tmutarakan, as a small fort and
+Cossack settlement, its population grew from 9620 in 1860 to 65,697 in
+1897. It has various technical schools, an experimental fruit-farm, a
+military hospital, and a natural history museum. A considerable trade is
+carried on, especially in cereals.
+
+
+
+
+EKATERINOSLAV, a government of south Russia, having the governments of
+Poltava and Kharkov on the N., the territory of the Don Cossacks on the
+E., the Sea of Azov and Taurida on the S., and Kherson on the W. Area,
+24,478 sq. m. Its surface is undulating steppe, sloping gently south and
+north, with a few hills reaching 1200 ft. in the N.E., where a slight
+swelling (the Don Hills) compels the Don to make a great curve
+eastwards. Another chain of hills, to which the eastward bend of the
+Dnieper is due, rises in the west. These hills have a crystalline core
+(granites, syenites and diorites), while the surface strata belong to
+the Carboniferous, Permian, Cretaceous and Tertiary formations. The
+government is rich in minerals, especially in coal--the mines lie in the
+middle of the Donets coalfield--iron ores, fireclay and rock-salt, and
+every year the mining output increases in quantity, especially of coal
+and iron. Granite, limestone, grindstone, slate, with graphite,
+manganese and mercury are found. The government is drained by the
+Dnieper, the Don and their tributaries (e.g. the Donets and Volchya) and
+by several affluents (e.g. the Kalmius) of the Sea of Azov. The soil is
+the fertile black earth, but the crops occasionally suffer from drought,
+the average annual rainfall being only 15 in. Forests are scarce. Pop.
+(1860) 1,138,750; (1897) 2,118,946, chiefly Little Russians, with Great
+Russians, Greeks (48,740), Germans (80,979), Rumanians and a few
+gypsies. Jews constitute 4.7% of the population. The estimated
+population in 1906 was 2,708,700.
+
+Wheat and other cereals are extensively grown; other noteworthy crops
+are potatoes, tobacco and grapes. Nearly 40,000 persons find occupation
+in factories, the most important being iron-works and agricultural
+machinery works, though there are also tobacco, glass, soap and candle
+factories, potteries, tanneries and breweries. In the districts of
+Mariupol the making of agricultural implements and machinery is carried
+on extensively as a domestic industry in the villages. Bees are kept in
+very considerable numbers. Fishing employs many persons in the Don and
+the Dnieper. Cereals are exported in large quantities via the Dnieper,
+the Sevastopol railway, and the port of Mariupol. The chief towns of the
+eight districts, with their populations in 1897, are Ekaterinoslav
+(135,552 inhabitants in 1900), Alexandrovsk (28,434), Bakhmut (30,585),
+Mariupol (31,772), Novomoskovsk (12,862), Pavlograd (17,188),
+Slavyanoserbsk (3120), and Verkhne-dnyeprovsk (11,607).
+
+
+
+
+EKATERINOSLAV, a town of Russia, capital of the government of the same
+name, on the right bank of the Dnieper above the rapids, 673 m. by rail
+S.S.W. of Moscow, in 48 deg. 21' N. and 35 deg. 4' E., at an altitude of
+210 ft. Pop. (1861) 18,881, without suburbs; (1900) 135,552. If the
+suburb of Novyikoindak be included, the town extends for upwards of 4 m.
+along the river. The oldest part lies very low and is much exposed to
+floods. Contiguous to the towns on the N.W. is the royal village of
+Novyimaidani or the New Factories. The bishop's palace, mining academy,
+archaeological museum and library are the principal public buildings.
+The house now occupied by the Nobles Club was formerly inhabited by the
+author and statesman Potemkin. Ekaterinoslav is a rapidly growing city,
+with a number of technical schools, and is an important depot for timber
+floated down the Dnieper, and also for cereals. Its iron-works,
+flour-mills and agricultural machinery works give occupation to over
+5000 persons. In fact since 1895 the city has become the centre of
+numerous Franco-Belgian industrial undertakings. In addition to the
+branches just mentioned, there are tobacco factories and breweries.
+Considerable trade is carried on in cattle, cereals, horses and wool,
+there being three annual fairs. On the site of the city there formerly
+stood the Polish castle of Koindak, built in 1635, and destroyed by the
+Cossacks. The existing city was founded by Potemkin in 1786, and in the
+following year Catherine II. laid the foundation-stone of the cathedral,
+though it was not actually built until 1830-1835. On the south side of
+it is a bronze statue of the empress, put up in 1846. Paul I. changed
+the name of the city to Novo-rossiysk, but the original name was
+restored in 1802.
+
+
+
+
+EKHOF, KONRAD (1720-1778), German actor, was born in Hamburg on the 12th
+of August 1720. In 1739 he became a member of Johann Friedrich
+Schonemann's (1704-1782) company in Luneburg, and made his first
+appearance there on the 15th of January 1740 as Xiphares in Racine's
+_Mithridate_. From 1751 the Schonemann company performed mainly in
+Hamburg and at Schwerin, where Duke Christian Louis II. of
+Mecklenburg-Schwerin made them comedians to the court. During this
+period Ekhof founded a theatrical academy, which, though short-lived,
+was of great importance in helping to raise the standard of German
+acting and the status of German actors. In 1757 Ekhof left Schonemann to
+join Franz Schuch's company at Danzig; but he soon returned to Hamburg,
+where, in conjunction with two other actors, he succeeded Schonemann in
+the direction of the company. He resigned this position, however, in
+favour of H.G. Koch, with whom he acted until 1764, when he joined K.E.
+Ackermann's company. In 1767 was founded the National Theatre at
+Hamburg, made famous by Lessing's _Hamburgische Dramaturgie_, and Ekhof
+was the leading member of the company. After the failure of the
+enterprise Ekhof was for a time in Weimar, and ultimately became
+co-director of the new court theatre at Gotha. This, the first
+permanently established theatre in Germany, was opened on the 2nd of
+October 1775. Ekhof's reputation was now at its height; Goethe called
+him the only German tragic actor; and in 1777 he acted with Goethe and
+Duke Charles Augustus at a private performance at Weimar, dining
+afterwards with the poet at the ducal table. He died on the 16th of June
+1778. His versatility may be judged from the fact that in the comedies
+of Goldoni and Moliere he was no less successful than in the tragedies
+of Lessing and Shakespeare. He was regarded by his contemporaries as an
+unsurpassed exponent of naturalness on the stage; and in this respect he
+has been not unfairly compared with Garrick. His fame, however, was
+rapidly eclipsed by that of Friedrich U.L. Schroder. His literary
+efforts were chiefly confined to translations from French authors.
+
+  See H. Uhde, biography of Ekhof in vol. iv. of _Der neue Plutarch_
+  (1876), and J. Ruschner, _K. Ekhofs Leben und Wirken_ (1872). Also H.
+  Devrient, _J.F. Schonemann und seine Schauspielergesellschaft_ (1895).
+
+
+
+
+EKRON (better, as in the Septuagint and Josephus, ACCARON, [Greek:
+Akkaron]), a royal city of the Philistines commonly identified with the
+modern Syrian village of `Akir, 5 m. from Ramleh, on the southern slope
+of a low ridge separating the plain of Philistia from Sharon. It lay
+inland and off the main line of traffic. Though included by the
+Israelites within the limits of the tribe of Judah, and mentioned in
+Judges xix. as one of the cities of Dan, it was in Philistine possession
+in the days of Samuel, and apparently maintained its independence.
+According to the narrative of the Hebrew text, here differing from the
+Greek text and Josephus (which read Askelon), it was the last town to
+which the ark was transferred before its restoration to the Israelites.
+Its maintenance of a sanctuary of Baal Zebub is mentioned in 2 Kings i.
+From Assyrian inscriptions it has been gathered that Padi, king of
+Ekron, was for a time the vassal of Hezekiah of Judah, but regained his
+independence when the latter was hard pressed by Sennacherib. A notice
+of its history in 147 B.C. is found in 1 Macc. x. 89; after the fall of
+Jerusalem A.D. 70 it was settled by Jews. At the time of the crusades it
+was still a large village. Recently a Jewish agricultural colony has
+been settled there. The houses are built of mud, and in the absence of
+visible remains of antiquity, the identification of the site is
+questionable. The neighbourhood is fertile.     (R. A. S. M.)
+
+
+
+
+ELABUGA, a town of Russia, in the government of Vyatka, on the Kama
+river, 201 m. by steamboat down the Volga from Kazan and then up the
+Kama. It has flour-mills, and carries on a brisk trade in exporting
+corn. Pop. (1897) 9776.
+
+The famous _Ananiynskiy Mogilnik_ (burial-place) is on the right bank of
+the Kama, 3 m. above the town. It was discovered in 1858, was excavated
+by Alabin, Lerch and Nevostruyev, and has since supplied extremely
+valuable collections belonging to the Stone, Bronze and Iron Ages. It
+consisted of a mound, about 500 ft. in circumference, adorned with
+decorated stones (which have disappeared), and contained an inner wall,
+65 ft. in circumference, made of uncemented stone flags. Nearly fifty
+skeletons were discovered, mostly lying upon charred logs, surrounded
+with cinerary urns filled with partially burned bones. A great variety
+of bronze decorations and glazed clay pearls were strewn round the
+skeletons. The knives, daggers and arrowpoints are of slate, bronze and
+iron, the last two being very rough imitations of stone implements. One
+of the flags bore the image of a man, without moustaches or beard,
+dressed in a costume and helmet recalling those of the Circassians.
+
+
+
+
+ELAM, the name given in the Bible to the province of Persia called
+Susiana by the classical geographers, from Susa or Shushan its capital.
+In one passage, however (Ezra iv. 9), it is confined to Elymais, the
+north-western part of the province, and its inhabitants distinguished
+from those of Shushan, which elsewhere (Dan. viii. 2) is placed in Elam.
+Strabo (xv. 3. 12, &c.) makes Susiana a part of Persia proper, but a
+comparison of his account with those of Ptolemy (vi. 3. 1, &c.) and
+other writers would limit it to the mountainous district to the east of
+Babylonia, lying between the Oroatis and the Tigris, and stretching from
+India to the Persian Gulf. Along with this mountainous district went a
+fertile low tract of country on the western side, which also included
+the marshes at the mouths of the Euphrates and Tigris and the
+north-eastern coast land of the Gulf. This low tract, though producing
+large quantities of grain, was intensely hot in summer; the high
+regions, however, were cool and well watered.
+
+The whole country was occupied by a variety of tribes, speaking
+agglutinative dialects for the most part, though the western districts
+were occupied by Semites. Strabo (xi. 13. 3, 6), quoting from Nearchus,
+seems to include the Susians under the Elymaeans, whom he associates
+with the Uxii, and places on the frontiers of Persia and Susa; but
+Pliny more correctly makes the Eulaeus the boundary between Susiana and
+Elymais (_N.H._ vi. 29-31). The Uxii are described as a robber tribe in
+the mountains adjacent to Media, and their name is apparently to be
+identified with the title given to the whole of Susiana in the Persian
+cuneiform inscriptions, _Uwaja_, i.e. "Aborigines." Uwaja is probably
+the origin of the modern Khuzistan, though Mordtmann would derive the
+latter from [Arab script] "a sugar-reed." Immediately bordering on the
+Persians were the Amardians or Mardians, as well as the people of
+Khapirti (Khatamti, according to Scheil), the name given to Susiana in
+the Neo-Susian texts. Khapirti appears as Apir in the inscriptions of
+Mal-Amir, which fix the locality of the district. Passing over the
+Messabatae, who inhabited a valley which may perhaps be the modern
+Mah-Sabadan, as well as the level district of Yamutbal or Yatbur which
+separated Elam from Babylonia, and the smaller districts of Characene,
+Cabandene, Corbiana and Gabiene mentioned by classical authors, we come
+to the fourth principal tribe of Susiana, the Cissii (Aesch. _Pers._ 16;
+Strabo xv. 3. 2) or Cossaei (Strabo xi. 5. 6, xvi. 11. 17; Arr. _Ind._
+40; Polyb. v. 54, &c.), the Kassi of the cuneiform inscriptions. So
+important were they, that the whole of Susiana was sometimes called
+Cissia after them, as by Herodotus (iii. 91, v. 49, &c.). In fact
+Susiana was only a late name for the country, dating from the time when
+Susa had been made a capital of the Persian empire. In the Sumerian
+texts of Babylonia it was called Numma, "the Highlands," of which Elamtu
+or Elamu, "Elam," was the Semitic translation. Apart from Susa, the most
+important part of the country was Anzan (Anshan, contracted Assan),
+where the native population maintained itself unaffected by Semitic
+intrusion. The exact position of Anzan is still disputed, but it
+probably included originally the site of Susa and was distinguished from
+it only when Susa became the seat of a Semitic government. In the
+lexical tablets Anzan is given as the equivalent of Elamtu, and the
+native kings entitle themselves kings of "Anzan and Susa," as well as
+"princes of the Khapirti."
+
+The principal mountains of Elam were on the north, called Charbanus and
+Cambalidus by Pliny (vi. 27, 31), and belonging to the Parachoathras
+chain. There were numerous rivers flowing into either the Tigris or the
+Persian Gulf. The most important were the Ulai or Eulaeus (_Kuran_) with
+its tributary the Pasitigris, the Choaspes (_Kerkhah_), the Coprates
+(river of _Diz_ called Itite in the inscriptions), the Hedyphon or
+Hedypnus (_Jerrahi_), and the Croatis (_Hindyan_), besides the
+monumental Surappi and Ukni, perhaps to be identified with the Hedyphon
+and Oroatis, which fell into the sea in the marshy region at the mouth
+of the Tigris. Shushan or Susa, the capital now marked by the mounds of
+_Shush_, stood near the junction of the Choaspes and Eulaeus (see SUSA);
+and Badaca, Madaktu in the inscriptions, lay between the _Shapur_ and
+the river of _Diz_. Among the other chief cities mentioned in the
+inscriptions may be named Naditu, Khaltemas, Din-sar, Bubilu, Bit-imbi,
+Khidalu and Nagitu on the sea-coast. Here, in fact, lay some of the
+oldest and wealthiest towns, the sites of which have, however, been
+removed inland by the silting up of the shore. J. de Morgan's
+excavations at Susa have thrown a flood of light on the early history of
+Elam and its relations to Babylon. The earliest settlement there goes
+back to neolithic times, but it was already a fortified city when Elam
+was conquered by Sargon of Akkad (3800 B.C.) and Susa became the seat of
+a Babylonian viceroy. From this time onward for many centuries it
+continued under Semitic suzerainty, its high-priests, also called "Chief
+Envoys of Elam, Sippara and Susa," bearing sometimes Semitic, sometimes
+native "Anzanite" names. One of the kings of the dynasty of Ur built at
+Susa. Before the rise of the First Dynasty of Babylon, however, Elam had
+recovered its independence, and in 2280 B.C. the Elamite king
+Kutur-Nakhkhunte made a raid in Babylonia and carried away from Erech
+the image of the goddess Nana. The monuments of many of his successors
+have been discovered by de Morgan and their inscriptions deciphered by
+v. Scheil. One of them was defeated by Ammi-zadoq of Babylonia (c. 2100
+B.C.); another would have been the Chedor-laomer (Kutur-Lagamar) of
+Genesis xiv. One of the greatest builders among them was Untas-GAL (the
+pronunciation of the second element in the name is uncertain). About
+1330 B.C. Khurba-tila was captured by Kuri-galzu III., the Kassite king
+of Babylonia, but a later prince Kidin-Khutrutas avenged his defeat, and
+Sutruk-Nakhkhunte (1220 B.C.) carried fire and sword through Babylonia,
+slew its king Zamama-sum-iddin and carried away a stela of Naram-Sin and
+the famous code of laws of Khammurabi from Sippara, as well as a stela
+of Manistusu from Akkuttum or Akkad. He also conquered the land of
+Asnunnak and carried off from Padan a stela belonging to a refugee from
+Malatia. He was succeeded by his son who was followed on the throne by
+his brother, one of the great builders of Elam. In 750 B.C. Umbadara was
+king of Elam; Khumban-igas was his successor in 742 B.C. In 720 B.C. the
+latter prince met the Assyrians under Sargon at Dur-ili in Yamutbal, and
+though Sargon claims a victory the result was that Babylonia recovered
+its independence under Merodach-baladan and the Assyrian forces were
+driven north. From this time forward it was against Assyria instead of
+Babylonia that Elam found itself compelled to exert its strength, and
+Elamite policy was directed towards fomenting revolt in Babylonia and
+assisting the Babylonians in their struggle with Assyria. In 716 B.C.
+Khumban-igas died and was followed by his nephew, Sutruk-Nakhkhunte. He
+failed to make head against the Assyrians; the frontier cities were
+taken by Sargon and Merodach-baladan was left to his fate. A few years
+later (704 B.C.) the combined forces of Elam and Babylonia were
+overthrown at Kis, and in the following year the Kassites were reduced
+to subjection. The Elamite king was dethroned and imprisoned in 700 B.C.
+by his brother Khallusu, who six years later marched into Babylonia,
+captured the son of Sennacherib, whom his father had placed there as
+king, and raised a nominee of his own, Nergal-yusezib, to the throne.
+Khallusu was murdered in 694 B.C., after seeing the maritime part of his
+dominions invaded by the Assyrians. His successor Kudur-Nakhkhunte
+invaded Babylonia; he was repulsed, however, by Sennacherib, 34 of his
+cities were destroyed, and he himself fled from Madaktu to Khidalu. The
+result was a revolt in which he was killed after a reign of ten months.
+His brother Umman-menan at once collected allies and prepared for
+resistance to the Assyrians. But the terrible defeat at Khalule broke
+his power; he was attacked by paralysis shortly afterwards, and
+Khumba-Khaldas II. followed him on the throne (689 B.C.). The new king
+endeavoured to gain Assyrian favour by putting to death the son of
+Merodach-baladan, but was himself murdered by his brothers Urtaki and
+Teumman (681 B.C.), the first of whom seized the crown. On his death
+Teumman succeeded and almost immediately provoked a quarrel with
+Assur-bani-pal by demanding the surrender of his nephews who had taken
+refuge at the Assyrian court. The Assyrians pursued the Elamite army to
+Susa, where a battle was fought on the banks of the Eulaeus, in which
+the Elamites were defeated, Teumman captured and slain, and Umman-igas,
+the son of Urtaki, made king, his younger brother Tammaritu being given
+the district of Khidalu. Umman-igas afterwards assisted in the revolt of
+Babylonia under Samas-sum-yukin, but his nephew, a second Tammaritu,
+raised a rebellion against him, defeated him in battle, cut off his head
+and seized the crown. Tammaritu marched to Babylonia; while there, his
+officer Inda-bigas made himself master of Susa and drove Tammaritu to
+the coast whence he fled to Assur-bani-pal. Inda-bigas was himself
+overthrown and slain by a new pretender, Khumba-Khaldas III., who was
+opposed, however, by three other rivals, two of whom maintained
+themselves in the mountains until the Assyrian conquest of the country,
+when Tammaritu was first restored and then imprisoned, Elam being
+utterly devastated. The return of Khumba-Khaldas led to a fresh Assyrian
+invasion; the Elamite king fled from Madaktu to Dur-undasi; Susa and
+other cities were taken, and the Elamite army almost exterminated on the
+banks of the Itite. The whole country was reduced to a desert, Susa was
+plundered and razed to the ground, the royal sepulchres were desecrated,
+and the images of the gods and of 32 kings "in silver, gold, bronze and
+alabaster," were carried away. All this must have happened about 640
+B.C. After the fall of the Assyrian empire Elam was occupied by the
+Persian Teispes, the forefather of Cyrus, who, accordingly, like his
+immediate successors, is called in the inscriptions "king of Anzan."
+Susa once more became a capital, and on the establishment of the Persian
+empire remained one of the three seats of government, its language, the
+Neo-Susian, ranking with the Persian of Persepolis and the Semitic of
+Babylon as an official tongue. In the reign of Darius, however, the
+Susianians attempted to revolt, first under Assina or Atrina, the son of
+Umbadara, and later under Martiya, the son of Issainsakria, who called
+himself Immanes; but they gradually became completely Aryanized, and
+their agglutinative dialects were supplanted by the Aryan Persian from
+the south-east.
+
+Elam, "the land of the cedar-forest," with its enchanted trees, figured
+largely in Babylonian mythology, and one of the adventures of the hero
+Gilgamesh was the destruction of the tyrant Khumbaba who dwelt in the
+midst of it. A list of the Elamite deities is given by Assur-bani-pal;
+at the head of them was In-Susinak, "the lord of the Susians,"--a title
+which went back to the age of Babylonian suzerainty,--whose image and
+oracle were hidden from the eyes of the profane. Nakhkhunte, according
+to Scheil, was the Sun-goddess, and Lagamar, whose name enters into that
+of Chedor-laomer, was borrowed from Semitic Babylonia.
+
+  See W.K. Loftus, _Chaldaea and Susiana_ (1857); A. Billerbeck, _Susa_
+  (1893); J. de Morgan, _Memoires de la Delegation en Perse_ (9 vols.,
+  1899-1906).     (A. H. S.)
+
+
+
+
+ELAND (= elk), the Dutch name for the largest of the South African
+antelopes (_Taurotragus oryx_), a species near akin to the kudu, but
+with horns present in both sexes, and their spiral much closer, being in
+fact screw-like instead of corkscrew-like. There is also a large dewlap,
+while old bulls have a thick forelock. In the typical southern form the
+body-colour is wholly pale fawn, but north of the Orange river the body
+is marked by narrow vertical white lines, this race being known as _T.
+oryx livingstonei_. In Senegambia the genus is represented by _T.
+derbianus_, a much larger animal, with a dark neck; while in the
+Bahr-el-Ghazal district there is a gigantic local race of this species
+(_T. derbianus giganteus_).     (R. L.*)
+
+
+
+
+ELASTICITY. 1. Elasticity is the property of recovery of an original
+size or shape. A body of which the size, or shape, or both size and
+shape, have been altered by the application of forces may, and generally
+does, tend to return to its previous size and shape when the forces
+cease to act. Bodies which exhibit this tendency are said to be
+_elastic_ (from Greek, [Greek: elaunein], to drive). All bodies are more
+or less elastic as regards size; and all solid bodies are more or less
+elastic as regards shape. For example: gas contained in a vessel, which
+is closed by a piston, can be compressed by additional pressure applied
+to the piston; but, when the additional pressure is removed, the gas
+expands and drives the piston outwards. For a second example: a steel
+bar hanging vertically, and loaded with one ton for each square inch of
+its sectional area, will have its length increased by about seven
+one-hundred-thousandths of itself, and its sectional area diminished by
+about half as much; and it will spring back to its original length and
+sectional area when the load is gradually removed. Such changes of size
+and shape in bodies subjected to forces, and the recovery of the
+original size and shape when the forces cease to act, become conspicuous
+when the bodies have the forms of thin wires or planks; and these
+properties of bodies in such forms are utilized in the construction of
+spring balances, carriage springs, buffers and so on.
+
+It is a familiar fact that the hair-spring of a watch can be coiled and
+uncoiled millions of times a year for several years without losing its
+elasticity; yet the same spring can have its shape permanently altered
+by forces which are much greater than those to which it is subjected in
+the motion of the watch. The incompleteness of the recovery from the
+effects of great forces is as important a fact as the practical
+completeness of the recovery from the effects of comparatively small
+forces. The fact is referred to in the distinction between "perfect"
+and "imperfect" elasticity; and the limitation which must be imposed
+upon the forces in order that the elasticity may be perfect leads to the
+investigation of "limits of elasticity" (see SS 31, 32 below). Steel
+pianoforte wire is perfectly elastic within rather wide limits, glass
+within rather narrow limits; building stone, cement and cast iron appear
+not to be perfectly elastic within any limits, however narrow. When the
+limits of elasticity are not exceeded no injury is done to a material or
+structure by the action of the forces. The strength or weakness of a
+material, and the safety or insecurity of a structure, are thus closely
+related to the elasticity of the material and to the change of size or
+shape of the structure when subjected to forces. The "science of
+elasticity" is occupied with the more abstract side of this relation,
+viz. with the effects that are produced in a body of definite size,
+shape and constitution by definite forces; the "science of the strength
+of materials" is occupied with the more concrete side, viz. with the
+application of the results obtained in the science of elasticity to
+practical questions of strength and safety (see STRENGTH OF MATERIALS).
+
+2. _Stress._--Every body that we know anything about is always under the
+action of forces. Every body upon which we can experiment is subject to
+the force of gravity, and must, for the purpose of experiment, be
+supported by other forces. Such forces are usually applied by way of
+pressure upon a portion of the surface of the body; and such pressure is
+exerted by another body in contact with the first. The supported body
+exerts an equal and opposite pressure upon the supporting body across
+the portion of surface which is common to the two. The same thing is
+true of two portions of the same body. If, for example, we consider the
+two portions into which a body is divided by a (geometrical) horizontal
+plane, we conclude that the lower portion supports the upper portion by
+pressure across the plane, and the upper portion presses downwards upon
+the lower portion with an equal pressure. The pressure is still exerted
+when the plane is not horizontal, and its direction may be obliquely
+inclined to, or tangential to, the plane. A more precise meaning is
+given to "pressure" below. It is important to distinguish between the
+two classes of forces: forces such as the force of gravity, which act
+all through a body, and forces such as pressure applied over a surface.
+The former are named "body forces" or "volume forces," and the latter
+"surface tractions." The action between two portions of a body separated
+by a geometrical surface is of the nature of surface traction. Body
+forces are ultimately, when the volumes upon which they act are small
+enough, proportional to the volumes; surface tractions, on the other
+hand, are ultimately, when the surfaces across which they act are small
+enough, proportional to these surfaces. Surface tractions are always
+exerted by one body upon another, or by one part of a body upon another
+part, across a surface of contact; and a surface traction is always to
+be regarded as one aspect of a "stress," that is to say of a pair of
+equal and opposite forces; for an equal traction is always exerted by
+the second body, or part, upon the first across the surface.
+
+3. The proper method of estimating and specifying stress is a matter of
+importance, and its character is necessarily mathematical. The
+magnitudes of the surface tractions which compose a stress are estimated
+as so much force (in dynes or tons) per unit of area (per sq. cm. or per
+sq. in.). The traction across an assigned plane at an assigned point is
+measured by the mathematical limit of the fraction F/S, where F denotes
+the numerical measure of the force exerted across a small portion of the
+plane containing the point, and S denotes the numerical measure of the
+area of this portion, and the limit is taken by diminishing S
+indefinitely. The traction may act as "tension," as it does in the case
+of a horizontal section of a bar supported at its upper end and hanging
+vertically, or as "pressure," as it does in the case of a horizontal
+section of a block resting on a horizontal plane, or again it may act
+obliquely or even tangentially to the separating plane. Normal tractions
+are reckoned as positive when they are tensions, negative when they are
+pressures. Tangential tractions are often called "shears" (see S 7
+below). Oblique tractions can always be resolved, by the vector law,
+into normal and tangential tractions. In a fluid at rest the traction
+across any plane at any point is normal to the plane, and acts as
+pressure. For the complete specification of the "state of stress" at any
+point of a body, we should require to know the normal and tangential
+components of the traction across every plane drawn through the point.
+Fortunately this requirement can be very much simplified (see SS 6, 7
+below).
+
+  4. In general let [nu] denote the direction of the normal drawn in a
+  specified sense to a plane drawn through a point O of a body; and let
+  T_[nu] denote the traction exerted across the plane, at the point O,
+  by the portion of the body towards which [nu] is drawn upon the
+  remaining portion. Then T{[nu]} is a vector quantity, which has a
+  definite magnitude (estimated as above by the limit of a fraction of
+  the form F/S) and a definite direction. It can be specified completely
+  by its components X_[nu], Y_[nu], Z_[nu], referred to fixed
+  rectangular axes of x, y, z. When the direction of [nu] is that of the
+  axis of x, in the positive sense, the components are denoted by X_x,
+  Y_x, Z_x; and a similar notation is used when the direction of [nu] is
+  that of y or z, the suffix x being replaced by y or z.
+
+5. Every body about which we know anything is always in a state of
+stress, that is to say there are always internal forces acting between
+the parts of the body, and these forces are exerted as surface tractions
+across geometrical surfaces drawn in the body. The body, and each part
+of the body, moves under the action of all the forces (body forces and
+surface tractions) which are exerted upon it; or remains at rest if
+these forces are in equilibrium. This result is expressed analytically
+by means of certain equations--the "equations of motion" or "equations
+of equilibrium" of the body.
+
+  Let [rho] denote the density of the body at any point, X, Y, Z, the
+  components parallel to the axes of x, y, z of the body forces,
+  estimated as so much force per unit of mass; further let f_x, f_y, f_z
+  denote the components, parallel to the same axes, of the acceleration
+  of the particle which is momentarily at the point (x, y, z). The
+  equations of motion express the result that the rates of change of the
+  momentum, and of the moment of momentum, of any portion of the body
+  are those due to the action of all the forces exerted upon the portion
+  by other bodies, or by other portions of the same body. For the
+  changes of momentum, we have three equations of the type
+      _ _ _                 _ _            _ _ _
+     / / /                 / /            / / /
+     | | |[rho]Xdx dy dz + | |X_[nu] dS = | | |[rho]f_x dx dy dz,  (1)
+    _/_/_/                _/_/           _/_/_/
+
+  in which the volume integrations are taken through the volume of the
+  portion of the body, the surface integration is taken over its
+  surface, and the notation X_[nu] is that of S 4, the direction of [nu]
+  being that of the normal to this surface drawn outwards. For the
+  changes of moment of momentum, we have three equations of the type
+      _ _ _                         _ _
+     / / /                         / /
+     | | |[rho](yZ - zY)dx dy dz + | |(yZ_[nu] - zY_[nu])dS =
+    _/_/_/                        _/_/
+         _ _ _
+        / / /
+        | | |[rho](yf_z - zf_y)dx dy dz. (2)
+       _/_/_/
+
+  The equations (1) and (2) are the equations of motion of any kind of
+  body. The equations of equilibrium are obtained by replacing the
+  right-hand members of these equations by zero.
+
+  6. These equations can be used to obtain relations between the values
+  of X_[nu], Y_[nu], ... for different directions [nu]. When the
+  equations are applied to a very small volume, it appears that the
+  terms expressed by surface integrals would, unless they tend to zero
+  limits in a higher order than the areas of the surfaces, be very great
+  compared with the terms expressed by volume integrals. We conclude
+  that the surface tractions on the portion of the body which is bounded
+  by any very small closed surface, are ultimately in equilibrium. When
+  this result is interpreted for a small portion in the shape of a
+  tetrahedron, having three of its faces at right angles to the
+  co-ordinate axes, it leads to three equations of the type
+
+    X_[nu] = X_x cos(x, [nu]) + X_y cos(y, [nu]) + X_z cos(z, [nu]), (1)
+
+  where [nu] is the direction of the normal (drawn outwards) to the
+  remaining face of the tetrahedron, and (x, [nu]) ... denote the angles
+  which this normal makes with the axes. Hence X_[nu], ... for any
+  direction [nu] are expressed in terms of X_x,.... When the above
+  result is interpreted for a very small portion in the shape of a cube,
+  having its edges parallel to the co-ordinate axes, it leads to the
+  equations
+
+    Y_z = Z_y,   Z_x = X_z,   X_y = Y_x.  (2)
+
+  When we substitute in the general equations the particular results
+  which are thus obtained, we find that the equations of motion take
+  such forms as
+
+             dPX_x   dPX_y   dPZ_x
+    [rho]X + ----- + ----- + ----- = [rho] f_x,  (3)
+              dPx     dPy     dPz
+
+  and the equations of moments are satisfied identically. The equations
+  of equilibrium are obtained by replacing the right-hand members by
+  zero.
+
+7. A state of stress in which the traction across any plane of a set of
+parallel planes is normal to the plane, and that across any
+perpendicular plane vanishes, is described as a state of "simple
+tension" ("simple pressure" if the traction is negative). A state of
+stress in which the traction across any plane is normal to the plane,
+and the traction is the same for all planes passing through any point,
+is described as a state of "uniform tension" ("uniform pressure" if the
+traction is negative). Sometimes the phrases "isotropic tension" and
+"hydrostatic pressure" are used instead of "uniform" tension or
+pressure. The distinction between the two states, simple tension and
+uniform tension, is illustrated in fig. 1.
+
+[Illustration: FIG. 1.]
+
+A state of stress in which there is purely tangential traction on a
+plane, and no normal traction on any perpendicular plane, is described
+as a state of "shearing stress." The result (2) of S 6 shows that
+tangential tractions occur in pairs. If, at any point, there is
+tangential traction, in any direction, on a plane parallel to this
+direction, and if we draw through the point a plane at right angles to
+the direction of this traction, and therefore containing the normal to
+the first plane, then there is equal tangential traction on this second
+plane in the direction of the normal to the first plane. The result is
+illustrated in fig. 2, where a rectangular block is subjected on two
+opposite faces to opposing tangential tractions, and is held in
+equilibrium by equal tangential tractions applied to two other faces.
+
+[Illustration: FIG. 2.]
+
+Through any point there always pass three planes, at right angles to
+each other, across which there is no tangential traction. These planes
+are called the "principal planes of stress," and the (normal) tractions
+across them the "principal stresses." Lines, usually curved, which have
+at every point the direction of a principal stress at the point, are
+called "lines of stress."
+
+8. It appears that the stress at any point of a body is completely
+specified by six quantities, which can be taken to be the X_x, Y_y, Z_z
+and Y_z, Z_x, X_y of S 6. The first three are tensions (pressures if
+they are negative) across three planes parallel to fixed rectangular
+directions, and the remaining three are tangential tractions across the
+same three planes. These six quantities are called the "components of
+stress." It appears also that the components of stress are connected
+with each other, and with the body forces and accelerations, by the
+three partial differential equations of the type (3) of S 6. These
+equations are available for the purpose of determining the state of
+stress which exists in a body of definite form subjected to definite
+forces, but they are not sufficient for the purpose (see S 38 below). In
+order to effect the determination it is necessary to have information
+concerning the constitution of the body, and to introduce subsidiary
+relations founded upon this information.
+
+9. The definite mathematical relations which have been found to connect
+the components of stress with each other, and with other quantities,
+result necessarily from the formation of a clear conception of the
+nature of stress. They do not admit of experimental verification,
+because the stress within a body does not admit of direct measurement.
+Results which are deduced by the aid of these relations can be compared
+with experimental results. If any discrepancy were observed it would not
+be interpreted as requiring a modification of the concept of stress, but
+as affecting some one or other of the subsidiary relations which must
+be introduced for the purpose of obtaining the theoretical result.
+
+10. _Strain._--For the specification of the changes of size and shape
+which are produced in a body by any forces, we begin by defining the
+"average extension" of any linear element or "filament" of the body. Let
+l0 be the length of the filament before the forces are applied, l its
+length when the body is subjected to the forces. The average extension
+of the filament is measured by the fraction (l - l0)/l0. If this
+fraction is negative there is "contraction." The "extension at a point"
+of a body in any assigned direction is the mathematical limit of this
+fraction when one end of the filament is at the point, the filament has
+the assigned direction, and its length is diminished indefinitely. It is
+clear that all the changes of size and shape of the body are known when
+the extension at every point in every direction is known.
+
+  The relations between the extensions in different directions around
+  the same point are most simply expressed by introducing the extensions
+  in the directions of the co-ordinate axes and the angles between
+  filaments of the body which are initially parallel to these axes. Let
+  e_(xx), e_(yy), e_(zz) denote the extensions parallel to the axes of
+  x, y, z, and let e_(yz), e_(zx), e_(xy) denote the cosines of the
+  angles between the pairs of filaments which are initially parallel to
+  the axes of y and z, z and x, x and y. Also let e denote the extension
+  in the direction of a line the direction cosines of which are l, m, n.
+  Then, if the changes of size and shape are slight, we have the
+  relation
+
+    e = e_(xx)l^2 + e_(yy)m^2 + e_(zz)n^2 + e_(yz)mn + e_(zx)nl + e_(xy)lm.
+
+The body which undergoes the change of size or shape is said to be
+"strained," and the "strain" is determined when the quantities e_(xx),
+e_(yy), e_(zz) and e_(yz), e_(zx), e_(xy) defined above are known at
+every point of it. These quantities are called "components of strain."
+The three of the type e_(xx) are extensions, and the three of the type
+e_(yz) are called "shearing strains" (see S 12 below).
+
+11. All the changes of relative position of particles of the body are
+known when the strain is known, and conversely the strain can be
+determined when the changes of relative position are given. These
+changes can be expressed most simply by the introduction of a vector
+quantity to represent the displacement of any particle.
+
+  When the body is deformed by the action of any forces its particles
+  pass from the positions which they occupied before the action of the
+  forces into new positions. If x, y, z are the co-ordinates of the
+  position of a particle in the first state, its co-ordinates in the
+  second state may be denoted by x + u, y + v, z + w. The quantities, u,
+  v, w are the "components of displacement." When these quantities are
+  small, the strain is connected with them by the equations
+
+    e_(xx) = dPu/dPx,  e_(yy) = dPv/dPy,  e_(zz) = dPw/dPz,        \
+                                                                   |
+             dPw   dPv            dPu   dPw            dPv   dPu    >(1)
+    e_(yz) = --- + ---,  e_(zx) = --- + ---,  e_(xy) = --- + --- . |
+             dPy   dPz            dPz   dPx            dPx   dPy   /
+
+12. These equations enable us to determine more exactly the nature of
+the "shearing strains" such as e_(xy). Let u, for example, be of the
+form sy, where s is constant, and let v and w vanish. Then e_(xy) = s,
+and the remaining components of strain vanish. The nature of the strain
+(called "simple shear") is simply appreciated by imagining the body to
+consist of a series of thin sheets, like the leaves of a book, which lie
+one over another and are all parallel to a plane (that of x, z); and the
+displacement is seen to consist in the shifting of each sheet relative
+to the sheet below in a direction (that of x) which is the same for all
+the sheets. The displacement of any sheet is proportional to its
+distance y from a particular sheet, which remains undisplaced. The
+shearing strain has the effect of distorting the shape of any portion of
+the body without altering its volume. This is shown in fig. 3, where a
+square ABCD is distorted by simple shear (each point moving parallel to
+the line marked xx) into a rhombus A'B'C'D', as if by an extension of
+the diagonal BD and a contraction of the diagonal AC, which extension
+and contraction are adjusted so as to leave the area unaltered. In the
+general case, where u is not of the form sy and v and w do not vanish,
+the shearing strains such as e_(xy) result from the composition of pairs
+of simple shears of the type which has just been explained.
+
+  13. Besides enabling us to express the extension in any direction and
+  the changes of relative direction of any filaments of the body, the
+  components of strain also express the changes of size of volumes and
+  areas. In particular, the "cubical dilatation," that is to say, the
+  increase of volume per unit of volume, is expressed by the quantity
+
+                                dPu   dPv   dPw
+    e_(xx) + e_(yy) + e_(zz) or --- + --- + ---.
+                                dPx   dPy   dPz
+
+  When this quantity is negative there is "compression."
+
+[Illustration: FIG. 3.]
+
+14. It is important to distinguish between two types of strain: the
+"rotational" type and the "irrotational" type. The distinction is
+illustrated in fig. 3, where the figure A"B"C"D" is obtained from the
+figure ABCD by contraction parallel to AC and extension parallel to BD,
+and the figure A'B'C'D' can be obtained from ABCD by the same
+contraction and extension followed by a rotation through the angle
+A"OA'. In strains of the irrotational type there are at any point three
+filaments at right angles to each other, which are such that the
+particles which lie in them before strain continue to lie in them after
+strain. A small spherical element of the body with its centre at the
+point becomes a small ellipsoid with its axes in the directions of these
+three filaments. In the case illustrated in the figure, the lines of the
+filaments in question, when the figure ABCD is strained into the figure
+A"B"C"D", are OA, OB and a line through O at right angles to their
+plane. In strains of the rotational type, on the other hand, the single
+existing set of three filaments (issuing from a point) which cut each
+other at right angles both before and after strain do not retain their
+directions after strain, though one of them may do so in certain cases.
+In the figure, the lines of the filaments in question, when the figure
+ABCD is strained into A'B'C'D', are OA, OB and a line at right angles to
+their plane before strain, and after strain they are OA', OB', and the
+same third line. A rotational strain can always be analysed into an
+irrotational strain (or "pure" strain) followed by a rotation.
+
+  Analytically, a strain is irrotational if the three quantities
+
+    dPw   dPv    dPu   dPw    dPv   dPu
+    --- - ---,   --- - ---,   --- - ---.
+    dPy   dPz    dPz   dPx    dPx   dPy
+
+  vanish, rotational if any one of them is different from zero. The
+  halves of these three quantities are the components of a vector
+  quantity called the "rotation."
+
+  15. Whether the strain is rotational or not, there is always one set
+  of three linear elements issuing from any point which cut each other
+  at right angles both before and after strain. If these directions are
+  chosen as axes of x, y, z, the shearing strains e_(yz), e_(zx), e_(xy)
+  vanish at this point. These directions are called the "principal axes
+  of strain," and the extensions in the directions of these axes the
+  "principal extensions."
+
+16. It is very important to observe that the relations between
+components of strain and components of displacement imply relations
+between the components of strain themselves. If by any process of
+reasoning we arrive at the conclusion that the state of strain in a body
+is such and such a state, we have a test of the possibility or
+impossibility of our conclusion. The test is that, if the state of
+strain is a possible one, then there must be a displacement which can
+be associated with it in accordance with the equations (1) of S 11.
+
+  We may eliminate u, v, w from these equations. When this is done we
+  find that the quantities e_(xx), ... e_(yz) are connected by the two
+  sets of equations
+
+    dP^2e_(yy)   dP^2e_(zz)   dP^2e_(yz)   \
+    ---------- + ---------- = ----------   |
+       dPz^2       dPy^2        dPydPz     |
+                                           |
+    dP^2e_(zz)   dP^2e_(xx)   dP^2e_(zx)   |
+    ---------- + ---------- = ----------    > (1)
+       dPx^2       dPz^2        dPzdPx     |
+                                           |
+    dP^2e_(xx)   dP^2e_(yy)   dP^2e_(xy)   |
+    ---------- + ---------- = ----------   |
+       dPy^2       dPx^2        dPxdPy     /
+
+  and
+
+      dP^2e_(xx)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   \
+    2 ---------- = --- ( - -------- + -------- + -------- )  |
+        dPydPz     dPx  \    dPx        dPy        dPz   /   |
+                                                             |
+      dP^2e_(yy)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   |
+    2 ---------- = --- (   -------- - -------- + -------- )   > (2)
+        dPzdPx     dPy  \    dPx        dPy        dPz   /   |
+                                                             |
+      dP^2e_(zz)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   |
+    2 ---------- = --- (   -------- + -------- - -------- )  |
+        dPxdPy     dPz  \    dPx        dPy        dPz   /   /
+
+These equations are known as the _conditions of compatibility of
+strain-components_. The components of strain which specify any possible
+strain satisfy them. Quantities arrived at in any way, and intended to
+be components of strain, if they fail to satisfy these equations, are
+not the components of any possible strain; and the theory or speculation
+by which they are reached must be modified or abandoned.
+
+  When the components of strain have been found in accordance with these
+  and other necessary equations, the displacement is to be found by
+  solving the equations (1) of S 11, considered as differential
+  equations to determine u, v, w. The most general possible solution
+  will differ from any other solution by terms which contain arbitrary
+  constants, and these terms represent a possible displacement. This
+  "complementary displacement" involves no strain, and would be a
+  possible displacement of an ideal perfectly rigid body.
+
+17. The relations which connect the strains with each other and with the
+displacement are geometrical relations resulting from the definitions of
+the quantities and not requiring any experimental verification. They do
+not admit of such verification, because the strain within a body cannot
+be measured. The quantities (belonging to the same category) which can
+be measured are displacements of points on the surface of a body. For
+example, on the surface of a bar subjected to tension we may make two
+fine transverse scratches, and measure the distance between them before
+and after the bar is stretched. For such measurements very refined
+instruments are required. Instruments for this purpose are called
+barbarously "extensometers," and many different kinds have been devised.
+From measurements of displacement by an extensometer we may deduce the
+average extension of a filament of the bar terminated by the two
+scratches. In general, when we attempt to measure a strain, we really
+measure some displacements, and deduce the values, not of the strain at
+a point, but of the average extensions of some particular linear
+filaments of a body containing the point; and these filaments are, from
+the nature of the case, nearly always superficial filaments.
+
+18. In the case of transparent materials such as glass there is
+available a method of studying experimentally the state of strain within
+a body. This method is founded upon the result that a piece of glass
+when strained becomes doubly refracting, with its optical principal axes
+at any point in the directions of the principal axes of strain (S 15) at
+the point. When the piece has two parallel plane faces, and two of the
+principal axes of strain at any point are parallel to these faces,
+polarized light transmitted through the piece in a direction normal to
+the faces can be used to determine the directions of the principal axes
+of the strain at any point. If the directions of these axes are known
+theoretically the comparison of the experimental and theoretical results
+yields a test of the theory.
+
+19. _Relations between Stresses and Strains._--The problem of the
+extension of a bar subjected to tension is the one which has been most
+studied experimentally, and as a result of this study it is found that
+for most materials, including all metals except cast metals, the
+measurable extension is proportional to the applied tension, provided
+that this tension is not too great. In interpreting this result it is
+assumed that the tension is uniform over the cross-section of the bar,
+and that the extension of longitudinal filaments is uniform throughout
+the bar; and then the result takes the form of a law of proportionality
+connecting stress and strain: The tension is proportional to the
+extension. Similar results are found for the same materials when other
+methods of experimenting are adopted, for example, when a bar is
+supported at the ends and bent by an attached load and the deflexion is
+measured, or when a bar is twisted by an axial couple and the relative
+angular displacement of two sections is measured. We have thus very
+numerous experimental verifications of the famous law first enunciated
+by Robert Hooke in 1678 in the words "_Ut Tensio sic vis_"; that is,
+"the Power of any spring is in the same proportion as the Tension
+(--stretching) thereof." The most general statement of Hooke's Law in
+modern language would be:--_Each of the six components of stress at any
+point of a body is a linear function of the six components of strain at
+the point._ It is evident from what has been said above as to the nature
+of the measurement of stresses and strains that this law in all its
+generality does not admit of complete experimental verification, and
+that the evidence for it consists largely in the agreement of the
+results which are deduced from it in a theoretical fashion with the
+results of experiments. Of such results one of a general character may
+be noted here. If the law is assumed to be true, and the equations of
+motion of the body (S 5) are transformed by means of it into
+differential equations for determining the components of displacement,
+these differential equations admit of solutions which represent periodic
+vibratory displacements (see S 85 below). The fact that solid bodies can
+be thrown into states of isochronous vibration has been emphasized by
+G.G. Stokes as a peremptory proof of the truth of Hooke's Law.
+
+20. According to the statement of the generalized Hooke's Law the
+stress-components vanish when the strain-components vanish. The
+strain-components contemplated in experiments upon which the law is
+founded are measured from a zero of reckoning which corresponds to the
+state of the body subjected to experiment before the experiment is made,
+and the stress-components referred to in the statement of the law are
+those which are called into action by the forces applied to the body in
+the course of the experiment. No account is taken of the stress which
+must already exist in the body owing to the force of gravity and the
+forces by which the body is supported. When it is desired to take
+account of this stress it is usual to suppose that the strains which
+would be produced in the body if it could be freed from the action of
+gravity and from the pressures of supports are so small that the strains
+produced by the forces which are applied in the course of the experiment
+can be compounded with them by simple superposition. This supposition
+comes to the same thing as measuring the strain in the body, not from
+the state in which it was before the experiment, but from an ideal state
+(the "unstressed" state) in which it would be entirely free from
+internal stress, and allowing for the strain which would be produced by
+gravity and the supporting forces if these forces were applied to the
+body when free from stress. In most practical cases the initial strain
+to be allowed for is unimportant (see SS 91-93 below).
+
+21. Hooke's law of proportionality of stress and strain leads to the
+introduction of important physical constants: the _moduluses of
+elasticity_ of a body. Let a bar of uniform section (of area [omega]) be
+stretched with tension T, which is distributed uniformly over the
+section, so that the stretching force is Tw[omega], and let the bar be
+unsupported at the sides. The bar will undergo a longitudinal extension
+of magnitude T/E, where E is a constant quantity depending upon the
+material. This constant is called _Young's modulus_ after Thomas Young,
+who introduced it into the science in 1807. The quantity E is of the
+same nature as a traction, that is to say, it is measured as a force
+estimated per unit of area. For steel it is about 2.04 X 10^12 dynes per
+square centimetre, or about 13,000 tons per sq. in.
+
+22. The longitudinal extension of the bar under tension is not the only
+strain in the bar. It is accompanied by a lateral contraction by which
+all the transverse filaments of the bar are shortened. The amount of
+this contraction is [sigma]T/E, where [sigma] is a certain number called
+_Poisson's ratio_, because its importance was at first noted by S.D.
+Poisson in 1828. Poisson arrived at the existence of this contraction,
+and the corresponding number [sigma], from theoretical considerations,
+and his theory led him to assign to [sigma] the value 1/4. Many
+experiments have been made with the view of determining [sigma], with
+the result that it has been found to be different for different
+materials, although for very many it does not differ much from 1/4. For
+steel the best value (Amagat's) is 0.268. Poisson's theory admits of
+being modified so as to agree with the results of experiment.
+
+23. The behaviour of an elastic solid body, strained within the limits
+of its elasticity, is entirely determined by the constants E and [sigma]
+if the body is _isotropic_, that is to say, if it has the same quality
+in all directions around any point. Nevertheless it is convenient to
+introduce other constants which are related to the action of particular
+sorts of forces. The most important of these are the "modulus of
+compression" (or "bulk modulus") and the "rigidity" (or "modulus of
+shear"). To define the _modulus of compression_, we suppose that a solid
+body of any form is subjected to uniform hydrostatic pressure of amount
+p. The state of stress within it will be one of uniform pressure, the
+same at all points, and the same in all directions round any point.
+There will be compression, the same at all points, and proportional to
+the pressure; and the amount of the compression can be expressed as p/k.
+The quantity k is the modulus of compression. In this case the linear
+contraction in any direction is p/3k; but in general the linear
+extension (or contraction) is not one-third of the cubical dilatation
+(or compression).
+
+24. To define the _rigidity_, we suppose that a solid body is subjected
+to forces in such a way that there is shearing stress within it. For
+example, a cubical block may be subjected to opposing tractions on
+opposite faces acting in directions which are parallel to an edge of the
+cube and to both the faces. Let S be the amount of the traction, and let
+it be uniformly distributed over the faces. As we have seen (S 7), equal
+tractions must act upon two other faces in suitable directions in order
+to maintain equilibrium (see fig. 2 of S 7). The two directions involved
+may be chosen as axes of x, y as in that figure. Then the state of
+stress will be one in which the stress-component denoted by X_y is equal
+to S, and the remaining stress-components vanish; and the strain
+produced in the body is shearing strain of the type denoted by e _(xy).
+The amount of the shearing strain is S/[mu], and the quantity [mu] is the
+"rigidity."
+
+25. The modulus of compression and the rigidity are quantities of the
+same kind as Young's modulus. The modulus of compression of steel is
+about 1.43 X 10^12 dynes per square centimetre, the rigidity is about
+8.19 X 10^11 dynes per square centimetre. It must be understood that the
+values for different specimens of nominally the same material may differ
+considerably.
+
+  The modulus of compression k and the rigidity [mu] of an isotropic
+  material are connected with the Young's modulus E and Poisson's ratio
+  [sigma] of the material by the equations
+
+    k = E/3(1 - 2[sigma]),   [mu] = E/2(1 + [sigma]).
+
+  26. Whatever the forces acting upon an isotropic solid body may be,
+  provided that the body is strained within its limits of elasticity,
+  the strain-components are expressed in terms of the stress-components
+  by the equations
+
+    e_(xx) = (X_x - [sigma]Y_y - [sigma]Z_z)/E,  e_(yz) = Y_z/[mu], \
+    e_(yy) = (Y_y - [sigma]Z_z - [sigma]X_x)/E,  e_(zx) = Z_x/[mu],  > (1)
+    e_(zz) = (Z_z - [sigma]X_x - [sigma]Y_y)/E,  e_(xy) = X_y/[mu]. /
+
+  If we introduce a quantity [lambda], of the same nature as E or [mu], by
+  the equation
+
+    [lambda] = E[sigma]/(1 + [sigma])(1 - 2[sigma]),  (2)
+
+  we may express the stress-components in terms of the strain-components
+  by the equations
+
+    X_x = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2[mu]e_(xx), Y_z = [mu]e_(yz), \
+    Y_y = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2[mu]e_(yy), Z_x = [mu]e_(zx),  > (3)
+    Z_z = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2[mu]e_(zz), X_y = [mu]e_(xy); /
+
+  and then the behaviour of the body under the action of any forces
+  depends upon the two constants [lambda] and [mu]. These two constants
+  were introduced by G. Lame in his treatise of 1852. The importance of
+  the quantity [mu] had been previously emphasized by L.J. Vicat and G.G.
+  Stokes.
+
+  27. The potential energy per unit of volume (often called the
+  "resilience") stored up in the body by the strain is equal to
+
+    1/2([lambda] + 2[mu])(e_(xx) + e_(yy) + e_(zz))^2 + 1/2[mu][e^2_(yz) + e^2_(zx) +
+      e^2_(xy) - 4e_(yy)e_(zz) - 4e_(zz)e_(xx) - 4e_(xx)e_(yy)],
+
+  or the equivalent expression
+
+    1/2[(X^2_x + Y^2_y + Z^2_z) - 2[sigma](Y_yZ_z + Z_zX_x + X_xY_y) +
+      2(1 + [sigma])(Y^2_z + Z^2_x + X^2_y)]/E.
+
+  The former of these expressions is called the
+  "strain-energy-function."
+
+28. The Young's modulus E of a material is often determined
+experimentally by the direct method of the extensometer (S 17), but more
+frequently it is determined indirectly by means of a result obtained in
+the theory of the flexure of a bar (see SS 47, 53 below). The rigidity
+[mu] is usually determined indirectly by means of results obtained in
+the theory of the torsion of a bar (see SS 41, 42 below). The modulus of
+compression k may be determined directly by means of the piezometer, as
+was done by E.H. Amagat, or it may be determined indirectly by means of
+a result obtained in the theory of a tube under pressure, as was done by
+A. Mallock (see S 78 below). The value of Poisson's ratio [sigma] is
+generally inferred from the relation connecting it with E and [mu] or
+with E and k, but it may also be determined indirectly by means of a
+result obtained in the theory of the flexure of a bar (S 47 below), as
+was done by M.A. Cornu and A. Mallock, or directly by a modification of
+the extensometer method, as has been done recently by J. Morrow.
+
+29. The _elasticity of a fluid_ is always expressed by means of a single
+quantity of the same kind as the _modulus of compression_ of a solid
+body. To any increment of pressure, which is not too great, there
+corresponds a proportional cubical compression, and the amount of this
+compression for an increment [delta]p of pressure can be expressed as
+[delta]p/k. The quantity that is usually tabulated is the reciprocal of
+k, and it is called the _coefficient of compressibility_. It is the
+amount of compression per unit increase of pressure. As a physical
+quantity it is of the same dimensions as the reciprocal of a pressure
+(or of a force per unit of area). The pressures concerned are usually
+measured in atmospheres (1 atmosphere = 1.014 X 10^6 dynes per sq. cm.).
+For water the coefficient of compressibility, or the compression per
+atmosphere, is about 4.5 X 10^-5. This gives for k the value 2.22 X
+10^10 dynes per sq. cm. The Young's modulus and the rigidity of a fluid
+are always zero.
+
+30. The relations between stress and strain in a material which is not
+isotropic are much more complicated. In such a material the Young's
+modulus depends upon the direction of the tension, and its variations
+about a point are expressed by means of a surface of the fourth degree.
+The Poisson's ratio depends upon the direction of the contracted lateral
+filaments as well as upon that of the longitudinal extended ones. The
+rigidity depends upon both the directions involved in the specification
+of the shearing stress. In general there is no simple relation between
+the Young's moduluses and Poisson's ratios and rigidities for assigned
+directions and the modulus of compression. Many materials in common use,
+all fibrous woods for example, are actually _aeolotropic_ (that is to
+say, are not isotropic), but the materials which are aeolotropic in the
+most regular fashion are natural crystals. The elastic behaviour of
+crystals has been studied exhaustively by many physicists, and in
+particular by W. Voigt. The strain-energy-function is a homogeneous
+quadratic function of the six strain-components, and this function may
+have as many as 21 independent coefficients, taking the place in the
+general case of the 2 coefficients [lambda], [mu] which occur when the
+material is isotropic--a result first obtained by George Green in 1837.
+The best experimental determinations of the coefficients have been made
+indirectly by Voigt by means of results obtained in the theories of the
+torsion and flexure of aeolotropic bars.
+
+31. _Limits of Elasticity._--A solid body which has been strained by
+considerable forces does not in general recover its original size and
+shape completely after the forces cease to act. The strain that is left
+is called _set_. If set occurs the elasticity is said to be
+"imperfect," and the greatest strain (or the greatest load) of any
+specified type, for which no set occurs, defines the "limit of perfect
+elasticity" corresponding to the specified type of strain, or of stress.
+All fluids and many solid bodies, such as glasses and crystals, as well
+as some metals (copper, lead, silver) appear to be perfectly elastic as
+regards change of volume within wide limits; but malleable metals and
+alloys can have their densities permanently increased by considerable
+pressures. The limits of perfect elasticity as regards change of shape,
+on the other hand, are very low, if they exist at all, for glasses and
+other hard, brittle solids; but a class of metals including copper,
+brass, steel, and platinum are very perfectly elastic as regards
+distortion, provided that the distortion is not too great. The question
+can be tested by observation of the torsional elasticity of thin fibres
+or wires. The limits of perfect elasticity are somewhat ill-defined,
+because an experiment cannot warrant us in asserting that there is no
+set, but only that, if there is any set, it is too small to be observed.
+
+32. A different meaning may be, and often is, attached to the phrase
+"limits of elasticity" in consequence of the following experimental
+result:--Let a bar be held stretched under a moderate tension, and let
+the extension be measured; let the tension be slightly increased and the
+extension again measured; let this process be continued, the tension
+being increased by equal increments. It is found that when the tension
+is not too great the extension increases by equal increments (as nearly
+as experiment can decide), but that, as the tension increases, a stage
+is reached in which the extension increases faster than it would do if
+it continued to be proportional to the tension. The beginning of this
+stage is tolerably well marked. Some time before this stage is reached
+the limit of perfect elasticity is passed; that is to say, if the load
+is removed it is found that there is some permanent set. The limiting
+tension beyond which the above law of proportionality fails is often
+called the "limit of _linear_ elasticity." It is higher than the limit
+of perfect elasticity. For steel bars of various qualities J.
+Bauschinger found for this limit values varying from 10 to 17 tons per
+square inch. The result indicates that, when forces which produce any
+kind of strain are applied to a solid body and are gradually increased,
+the strain at any instant increases proportionally to the forces up to a
+stage beyond that at which, if the forces were removed, the body would
+completely recover its original size and shape, but that the increase of
+strain ceases to be proportional to the increase of load when the load
+surpasses a certain limit. There would thus be, for any type of strain,
+a _limit of linear elasticity_, which exceeds the limit of perfect
+elasticity.
+
+33. A body which has been strained beyond the limit of linear elasticity
+is often said to have suffered an "over-strain." When the load is
+removed, the _set_ which can be observed is not entirely permanent; but
+it gradually diminishes with lapse of time. This phenomenon is named
+"elastic after-working." If, on the other hand, the load is maintained
+constant, the strain is gradually increased. This effect indicates a
+gradual flowing of solid bodies under great stress; and a similar effect
+was observed in the experiments of H. Tresca on the punching and
+crushing of metals. It appears that all solid bodies under sufficiently
+great loads become "plastic," that is to say, they take a set which
+gradually increases with the lapse of time. No plasticity is observed
+when the limit of linear elasticity is not exceeded.
+
+34. The values of the elastic limits are affected by overstrain. If the
+load is maintained for some time, and then removed, the limit of linear
+elasticity is found to be higher than before. If the load is not
+maintained, but is removed and then reapplied, the limit is found to be
+lower than before. During a period of rest a test piece recovers its
+elasticity after overstrain.
+
+35. The effects of repeated loading have been studied by A. Wohler, J.
+Bauschinger, O. Reynolds and others. It has been found that, after many
+repetitions of rather rapidly alternating stress, pieces are fractured
+by loads which they have many times withstood. It is not certain whether
+the fracture is in every case caused by the gradual growth of minute
+flaws from the beginning of the series of tests, or whether the elastic
+quality of the material suffers deterioration apart from such flaws. It
+appears, however, to be an ascertained result that, so long as the limit
+of linear elasticity is not exceeded, repeated loads and rapidly
+alternating loads do not produce failure of the material.
+
+36. The question of the conditions of safety, or of the conditions in
+which rupture is produced, is one upon which there has been much
+speculation, but no completely satisfactory result has been obtained. It
+has been variously held that rupture occurs when the numerically
+greatest principal stress exceeds a certain limit, or when this stress
+is tension and exceeds a certain limit, or when the greatest difference
+of two principal stresses (called the "stress-difference") exceeds a
+certain limit, or when the greatest extension or the greatest shearing
+strain or the greatest strain of any type exceeds a certain limit. Some
+of these hypotheses appear to have been disproved. It was held by G.F.
+Fitzgerald (_Nature_, Nov. 5, 1896) that rupture is not produced by
+pressure symmetrically applied all round a body, and this opinion has
+been confirmed by the recent experiments of A. Foppl. This result
+disposes of the greatest stress hypothesis and also of the greatest
+strain hypothesis. The fact that short pillars can be crushed by
+longitudinal pressure disposes of the greatest tension hypothesis, for
+there is no tension in the pillar. The greatest extension hypothesis
+failed to satisfy some tests imposed by H. Wehage, who experimented with
+blocks of wrought iron subjected to equal pressures in two directions at
+right angles to each other. The greatest stress-difference hypothesis
+and the greatest shearing strain hypothesis would lead to practically
+identical results, and these results have been held by J.J. Guest to
+accord well with his experiments on metal tubes subjected to various
+systems of combined stress; but these experiments and Guest's conclusion
+have been criticized adversely by O. Mohr, and the question cannot be
+regarded as settled. The fact seems to be that the conditions of rupture
+depend largely upon the nature of the test (tensional, torsional,
+flexural, or whatever it may be) that is applied to a specimen, and that
+no general formula holds for all kinds of tests. The best modern
+technical writings emphasize the importance of the limits of linear
+elasticity and of tests of dynamical resistance (S 87 below) as well as
+of statical resistance.
+
+37. The question of the conditions of rupture belongs rather to the
+science of the strength of materials than to the science of elasticity
+(S 1); but it has been necessary to refer to it briefly here, because
+there is no method except the methods of the theory of elasticity for
+determining the state of stress or strain in a body subjected to forces.
+Whatever view may ultimately be adopted as to the relation between the
+conditions of safety of a structure and the state of stress or strain in
+it, the calculation of this state by means of the theory or by
+experimental means (as in S 18) cannot be dispensed with.
+
+  38. _Methods of determining the Stress in a Body subjected to given
+  Forces._--To determine the state of stress, or the state of strain, in
+  an isotropic solid body strained within its limits of elasticity by
+  given forces, we have to use (i.) the equations of equilibrium, (ii.)
+  the conditions which hold at the bounding surface, (iii.) the
+  relations between stress-components and strain-components, (iv.) the
+  relations between strain-components and displacement. The equations of
+  equilibrium are (with notation already used) three partial
+  differential equations of the type
+
+    dPX_x   dPX_y   dPZ_z
+    ----- + ----- + ----- + [rho]X = 0.  (1)
+     dPx     dPy     dPz
+
+  The conditions which hold at the bounding surface are three equations
+  of the type
+
+    X_x cos(x, [nu]) + X_y cos(y, [nu]) + Z_x cos(z, [nu]) = X`_[nu], (2)
+
+  where [nu] denotes the direction of the outward-drawn normal to the
+  bounding surface, and X`_[nu] denotes the x-component of the applied
+  surface traction. The relations between stress-components and
+  strain-components are expressed by either of the sets of equations (1)
+  or (3) of S 26. The relations between strain-components and
+  displacement are the equations (1) of S 11, or the equivalent
+  conditions of compatibility expressed in equations (1) and (2) of S
+  16.
+
+  39. We may proceed by either of two methods. In one method we
+  eliminate the stress-components and the strain-components and retain
+  only the components of displacement. This method leads (with notation
+  already used) to three partial differential equations of the type
+
+                      dP   /dPu   dPv   dPw\         /dP^2u   dP^2u   dP^2u\
+    ([lambda] + [mu]) --- ( --- + --- + --- ) + [mu]( ----- + ----- + ----- ) + [rho]X = 0, (3)
+                      dPx  \dPx   dPy   dPz/         \dPx^2   dPy^2   dPz^2/
+
+  and three boundary conditions of the type
+                                                     _
+                          /dPu   dPv   dPw\         |               dPu
+    [lambda] cos(x, [nu])( --- + --- + --- ) + [mu] | 2 cos(x, [nu])---
+                          \dPx   dPy   dPz/         |_              dPx
+                                                             _
+                     /dPv   dPu\                 /dPu   dPw\  |
+      + cos(y, [nu])( -- + --   ) + cos(z, [nu])( -- + --   ) | = X`_[nu], (4)
+                     \dPx   dPy/                 \dPz   dPx/ _|
+
+  In the alternative method we eliminate the strain-components and the
+  displacements. This method leads to a system of partial differential
+  equations to be satisfied by the stress-components. In this system
+  there are three equations of the type
+
+    dPX_x   dPX_y   dPX_z
+    ----- + ----- + ----- + [rho]X = 0,  (1 _bis_)
+     dPx     dPy     dPz
+
+  three of the type
+
+    dP^2X_x   dP^2X_x   dP^2X_x        1      dP^2
+    ------- + ------- + ------- + ----------- ----- (X_x + Y_y + Z_z) =
+     dPx^2     dPy^2     dPz^2    1 + [sigma] dPx^2
+
+          [sigma]       /dPX   dPY   dPZ\           dPX
+      -  ---------[rho]( --- + --- + --- ) - 2[rho] ---,  (5)
+         1-[sigma]      \dPx   dPy   dPz/           dPx
+
+  and three of the type
+
+    dP^2Y_z   dP^2Y_z   dP^2Y_z        1       dP^2
+    ------- + ------- + ------- + ----------- ------ (X_x + Y_y + Z_z) =
+     dPx^2     dPy^2     dPz^2    1 + [sigma] dPydPz
+
+              /dPZ   dPY\
+      - [rho]( --- + --- ), (6)
+              \dPy   dPz/
+
+  the equations of the two latter types being necessitated by the
+  conditions of compatibility of strain-components. The solutions of
+  these equations have to be adjusted so that the boundary conditions of
+  the type (2) may be satisfied.
+
+  40. It is evident that whichever method is adopted the mathematical
+  problem is in general very complicated. It is also evident that, if we
+  attempt to proceed by help of some intuition as to the nature of the
+  stress or strain, our intuition ought to satisfy the tests provided by
+  the above systems of equations. Neglect of this precaution has led to
+  many errors. Another source of frequent error lies in the neglect of
+  the conditions in which the above systems of equations are correct.
+  They are obtained by help of the supposition that the relative
+  displacements of the parts of the strained body are small. The
+  solutions of them must therefore satisfy the test of smallness of the
+  relative displacements.
+
+41. Torsion.--As a first example of the application of the theory we
+take the problem of the torsion of prisms. This problem, considered
+first by C.A. Coulomb in 1784, was finally solved by B. de Saint-Venant
+in 1855. The problem is this:--A cylindrical or prismatic bar is held
+twisted by terminal couples; it is required to determine the state of
+stress and strain in the interior. When the bar is a circular cylinder
+the problem is easy. Any section is displaced by rotation about the
+central-line through a small angle, which is proportional to the
+distance z of the section from a fixed plane at right angles to this
+line. This plane is a terminal section if one of the two terminal
+sections is not displaced. The angle through which the section z rotates
+is [tau]z, where [tau] is a constant, called the amount of the twist;
+and this constant [tau] is equal to G/[mu]I, where G is the twisting
+couple, and I is the moment of inertia of the cross-section about the
+central-line. This result is often called "Coulomb's law." The stress
+within the bar is shearing stress, consisting, as it must, of two sets
+of equal tangential tractions on two sets of planes which are at right
+angles to each other. These planes are the cross-sections and the axial
+planes of the bar. The tangential traction at any point of the
+cross-section is directed at right angles to the axial plane through the
+point, and the tangential traction on the axial plane is directed
+parallel to the length of the bar. The amount of either at a distance r
+from the axis is [mu][tau]r or Gr/I. The result that G = [mu][tau]I can
+be used to determine [mu] experimentally, for [tau] may be measured and
+G and I are known.
+
+42. When the cross-section of the bar is not circular it is clear that
+this solution fails; for the existence of tangential traction, near the
+prismatic bounding surface, on any plane which does not cut this surface
+at right angles, implies the existence of traction applied to this
+surface. We may attempt to modify the theory by retaining the
+supposition that the stress consists of shearing stress, involving
+tangential traction distributed in some way over the cross-sections.
+Such traction is obviously a necessary constituent of any stress-system
+which could be produced by terminal couples around the axis. We should
+then know that there must be equal tangential traction directed along
+the length of the bar, and exerted across some planes or other which are
+parallel to this direction. We should also know that, at the bounding
+surface, these planes must cut this surface at right angles. The
+corresponding strain would be shearing strain which could involve (i.) a
+sliding of elements of one cross-section relative to another, (ii.) a
+relative sliding of elements of the above mentioned planes in the
+direction of the length of the bar. We could conclude that there may be
+a longitudinal displacement of the elements of the cross-sections. We
+should then attempt to satisfy the conditions of the problem by
+supposing that this is the character of the strain, and that the
+corresponding displacement consists of (i.) a rotation of the
+cross-sections in their planes such as we found in the case of the
+circle, (ii.) a distortion of the cross-sections into curved surfaces by
+a displacement (w) which is directed normally to their planes and varies
+in some manner from point to point of these planes. We could show that
+all the conditions of the problem are satisfied by this assumption,
+provided that the longitudinal displacement (w), considered as a
+function of the position of a point (x, y) in the cross-section,
+satisfies the equation
+
+  dP^2w   dP^2w
+  ----- + ----- = 0,  (1)
+  dPx^2   dPy^2
+
+and the boundary condition
+
+   / dPw         \                  / dPw         \
+  (  --- - [tau]y ) cos(x, [nu]) + (  --- + [tau]x ) cos(y, [nu]) = 0, (2)
+   \ dPx         /                  \ dPy         /
+
+where [tau] denotes the amount of the twist, and [nu] the direction of
+the normal to the boundary. The solution is known for a great many forms
+of section. (In the particular case of a circular section w vanishes.)
+The tangential traction at any point of the cross-section is directed
+along the tangent to that curve of the family [psi] = const. which
+passes through the point, [psi] being the function determined by the
+equations
+
+  dPw         /dP[psi]    \    dPw           /dP[psi]    \
+  --- = [tau]( ------- + y ),  --- = - [tau]( ------- + x ).
+  dPx         \  dPy      /    dPy           \  dPx      /
+
+The amount of the twist [tau] produced by terminal couples of magnitude
+G is G/C, where C is a constant, called the "torsional rigidity" of the
+prism, and expressed by the formula
+            _  _  _                          _
+           /  /  |  /dP[psi]\^2   /dP[psi]\^2 |
+  C = [mu] |  |  | ( ------- ) + ( ------- )  | dxdy,
+          _/ _/  |_ \  dPx  /     \  dPy  /  _|
+
+the integration being taken over the cross-section. When the coefficient
+of [mu] in the expression for C is known for any section, [mu] can be
+determined by experiment with a bar of that form of section.
+
+43. The distortion of the cross-sections into curved surfaces is shown
+graphically by drawing the contour lines (w = const.). In general the
+section is divided into a number of compartments, and the portions that
+lie within two adjacent compartments are respectively concave and
+convex. This result is illustrated in the accompanying figures (fig. 4
+for the ellipse, given by x^2/b^2 + y^2/c^2 = 1; fig. 5 for the
+equilateral triangle, given by (x + (1/3)a) [x^2 - 3y^2 - (4/3)ax +
+(4/9)a^2] = 0; fig. 6 for the square).
+
+[Illustration: FIG. 4.]
+
+44. The distribution of the shearing stress over the cross-section is
+determined by the function [psi], already introduced. If we draw the
+curves [psi] = const., corresponding to any form of section, for
+equidifferent values of the constant, the tangential traction at any
+point on the cross-section is directed along the tangent to that curve
+of the family which passes through the point, and the magnitude of it is
+inversely proportional to the distance between consecutive curves of the
+family. Fig. 7 illustrates the result in the case of the _equilateral_
+triangle. The boundary is, of course, one of the lines. The "lines of
+shearing stress" which can thus be drawn are in every case identical
+with the lines of flow of frictionless liquid filling a cylindrical
+vessel of the same cross-section as the bar, when the liquid circulates
+in the plane of the section with uniform spin. They are also the same as
+the contour lines of a flexible and slightly extensible membrane, of
+which the edge has the same form as the bounding curve of the
+cross-section of the bar, when the membrane is fixed at the edge and
+slightly deformed by uniform pressure.
+
+[Illustration: FIG. 5.]
+
+[Illustration: FIG. 6.]
+
+[Illustration: FIG. 7.]
+
+45. Saint-Venant's theory shows that the true torsional rigidity is in
+general less than that which would be obtained by extending Coulomb's
+law (G = [mu][tau]I) to sections which are not circular. For an elliptic
+cylinder of sectional area [omega] and moment of inertia I about its
+central-line the torsional rigidity is [mu][omega]^4/4[pi]^2I, and this
+formula is not far from being correct for a very large number of
+sections. For a bar of square section of side a centimetres, the
+torsional rigidity in C.G.S. units is (0.1406)[mu]a^4 approximately,
+[mu] being expressed in dynes per square centimetre. How great the
+defect of the true value from that given by extending Coulomb's law may
+be in the case of sections with projecting corners is shown by the
+diagrams (fig. 8 especially no. 4). In these diagrams the upper of the
+two numbers under each figure indicates the fraction which the true
+torsional rigidity corresponding to the section is of that value which
+would be obtained by extending Coulomb's law; and the lower of the two
+numbers indicates the ratio which the torsional rigidity for a bar of
+the corresponding section bears to that of a bar of circular section of
+the same material and of equal sectional area. These results have an
+important practical application, inasmuch as they show that
+strengthening ribs and projections, such as are introduced in
+engineering to give stiffness to beams, have the reverse of a good
+effect when torsional stiffness is an object, although they are of great
+value in increasing the resistance to bending. The theory shows further
+that the resistance to torsion is very seriously diminished when there
+is in the surface any dent approaching to a re-entrant angle. At such a
+place the shearing strain tends to become infinite, and some permanent
+set is produced by torsion. In the case of a section of any form, the
+strain and stress are greatest at points on the contour, and these
+points are in many cases the points of the contour which are nearest to
+the centroid of the section. The theory has also been applied to show
+that a longitudinal flaw near the axis of a shaft transmitting a
+torsional couple has little influence on the strength of the shaft, but
+that in the neighbourhood of a similar flaw which is much nearer to the
+surface than to the axis the shearing strain may be nearly doubled, and
+thus the possibility of such flaws is a source of weakness against which
+special provision ought to be made.
+
+[Illustration: FIG. 8.--Diagrams showing Torsional Rigidities.
+
+  (1) Rectilineal square. .84346. .88326.
+  (2) Square with curved corners and hollow sides. .8186. .8666.
+  (3) Square with acute angles and hollow sides. .7783. .8276.
+  (4) Star with four rounded points, being a curve of the eighth degree.
+        .5374. .6745.
+  (5) Equilateral triangle. .60000. .72552.]
+
+[Illustration: FIG. 9.]
+
+46. _Bending of Beams._--As a second example of the application of the
+general theory we take the problem of the flexure of a beam. In this
+case also we begin by forming a simple intuition as to the nature of the
+strain and the stress. On the side of the beam towards the centre of
+curvature the longitudinal filaments must be contracted, and on the
+other side they must be extended. If we assume that the cross-sections
+remain plane, and that the central-line is unaltered in length, we see
+(at once from fig. 9) that the extensions (or contractions) are given by
+the formula y/R, where y denotes the distance of a longitudinal filament
+from the plane drawn through the unstrained central-line at right-angles
+to the plane of bending, and R is the radius of curvature of the curve
+into which this line is bent (shown by the dotted line in the figure).
+Corresponding to this strain there must be traction acting across the
+cross-sections. If we assume that there is no other stress, then the
+magnitude of the traction in question is Ey/R, where E is Young's
+modulus, and it is tension on the side where the filaments are extended
+and pressure on the side where they are contracted. If the plane of
+bending contains a set of principal axes of the cross-sections at their
+centroids, these tractions for the whole cross-section are equivalent to
+a couple of moment EI/R, where I now denotes the moment of inertia of
+the cross-section about an axis through its centroid at right angles to
+the plane of bending, and the plane of the couple is the plane of
+bending. Thus a beam of any form of section can be held bent in a
+"principal plane" by terminal couples of moment M, that is to say by a
+"bending moment" M; the central-line will take a curvature M/EI, so that
+it becomes an arc of a circle of radius EI/M; and the stress at any
+point will be tension of amount My/I, where y denotes distance (reckoned
+positive towards the side remote from the centre of curvature) from that
+plane which initially contains the central-line and is at right angles
+to the plane of the couple. This plane is called the "neutral plane."
+The restriction that the beam is bent in a principal plane means that
+the plane of bending contains one set of principal axes of the
+cross-sections at their centroids; in the case of a beam of rectangular
+section the plane would bisect two opposite edges at right angles. In
+order that the theory may hold good the radius of curvature must be very
+large.
+
+47. In this problem of the bending of a beam by terminal couples the
+stress is tension, determined as above, and the corresponding strain
+consists therefore of longitudinal extension of amount My/EI or y/R
+(contraction if y is negative), accompanied by lateral contraction of
+amount [sigma]My/EI or [sigma]y/R (extension if y is negative), [sigma]
+being Poisson's ratio for the material. Our intuition of the nature of
+the strain was imperfect, inasmuch as it took no account of these
+lateral strains. The necessity for introducing them was pointed out by
+Saint-Venant. The effect of them is a change of shape of the
+cross-sections in their own planes. This is shown in an exaggerated way
+in fig. 10, where the rectangle ABCD represents the cross-section of the
+unstrained beam, or a rectangular portion of this cross-section, and the
+curvilinear figure A'B'C'D' represents in an exaggerated fashion the
+cross-section (or the corresponding portion of the cross-section) of the
+same beam, when bent so that the centre of curvature of the central-line
+(which is at right angles to the plane of the figure) is on the line EF
+produced beyond F. The lines A'B' and C'D' are approximately circles of
+radii R/[sigma], when the central-line is a circle of radius R, and
+their centres are on the line FE produced beyond E. Thus the neutral
+plane, and each of the faces that is parallel to it, becomes strained
+into an _anticlastic surface_, whose principal curvatures are in the
+ratio [sigma] : 1. The general appearance of the bent beam is shown in
+an exaggerated fashion in fig. 11, where the traces of the surface into
+which the neutral plane is bent are dotted. The result that the ratio of
+the principal curvatures of the anticlastic surfaces, into which the top
+and bottom planes of the beam (of rectangular section) are bent, is
+Poisson's ratio [sigma], has been used for the experimental
+determination of [sigma]. The result that the radius of curvature of the
+bent central-line is EI/M is used in the experimental determination of
+E. The quantity EI is often called the "flexural rigidity" of the beam.
+There are two principal flexural rigidities corresponding to bending in
+the two principal planes (cf. S 62 below).
+
+[Illustration: FIG. 10.]
+
+[Illustration: FIG. 11.]
+
+[Illustration: FIG. 12.]
+
+48. That this theory requires modification, when the load does not
+consist simply of terminal couples, can be seen most easily by
+considering the problem of a beam loaded at one end with a weight W, and
+supported in a horizontal position at its other end. The forces that are
+exerted at any section p, to balance the weight W, must reduce
+statically to a vertical force W and a couple, and these forces arise
+from the action of the part Ap on the part Bp (see fig. 12), i.e. from
+the stresses across the section at p. The couple is equal to the moment
+of the applied load W about an axis drawn through the centroid of the
+section p at right angles to the plane of bending. This moment is called
+the "bending moment" at the section, it is the product of the load W and
+the distance of the section from the loaded end, so that it varies
+uniformly along the length of the beam. The stress that suffices in the
+simpler problem gives rise to no vertical force, and it is clear that in
+addition to longitudinal tensions and pressures there must be tangential
+tractions on the cross-sections. The resultant of these tangential
+tractions must be a force equal to W, and directed vertically; but the
+direction of the traction at a point of the cross-section need not in
+general be vertical. The existence of tangential traction on the
+cross-sections implies the existence of equal tangential traction,
+directed parallel to the central-line, on some planes or other which are
+parallel to this line, the two sets of tractions forming a shearing
+stress. We conclude that such shearing stress is a necessary constituent
+of the stress-system in the beam bent by terminal transverse load. We
+can develop a theory of this stress-system from the assumptions (i.)
+that the tension at any point of the cross-section is related to the
+bending moment at the section by the same law as in the case of uniform
+bending by terminal couples; (ii.) that, in addition to this tension,
+there is at any point shearing stress, involving tangential tractions
+acting in appropriate directions upon the elements of the
+cross-sections. When these assumptions are made it appears that there is
+one and only one distribution of shearing stress by which the conditions
+of the problem can be satisfied. The determination of the amount and
+direction of this shearing stress, and of the corresponding strains and
+displacements, was effected by Saint-Venant and R.F.A. Clebsch for a
+number of forms of section by means of an analysis of the same kind as
+that employed in the solution of the torsion problem.
+
+[Illustration: FIG. 13.]
+
+  49. Let l be the length of the beam, x the distance of the section p
+  from the fixed end A, y the distance of any point below the horizontal
+  plane through the centroid of the section at A, then the bending
+  moment at p is W(l - x), and the longitudinal tension P or X_x at any
+  point on the cross-section is - W(l - x)y/I, and this is related to
+  the bending moment exactly as in the simpler problem.
+
+  50. The expressions for the shearing stresses depend on the shape of
+  the cross-section. Taking the beam to be of isotropic material and the
+  cross-section to be an ellipse of semiaxes a and b (fig. 13), the a
+  axis being vertical in the unstrained state, and drawing the axis z at
+  right angles to the plane of flexure, we find that the vertical
+  shearing stress U or X_y at any point (y, z) on any cross-section is
+
+    2W[(a^2 - y^2){2a^2(1 + [sigma]) + b^2} - z^2a^2(1 - 2[sigma])]
+    ---------------------------------------------------------------.
+                 [pi]a^3b(1 + [sigma])(3a^2 + b^2)
+
+  The resultant of these stresses is W, but the amount at the centroid,
+  which is the maximum amount, exceeds the average amount, W/[pi]ab, in
+  the ratio
+
+    {4a^2(1 + [sigma]) + 2b^2}/(3a^2 + b^2)(1 + [sigma]).
+
+  If [sigma] = 1/4, this ratio is 7/5 for a circle, nearly 4/3 for a flat
+  elliptic bar with the longest diameter vertical, nearly 8/5 for a flat
+  elliptic bar with the longest diameter horizontal.
+
+  In the same problem the horizontal shearing stress T or Z_x at any
+  point on any cross-section is of amount
+
+      4Wyz{a^2(1 + [sigma]) + b^2[sigma]}
+    - -----------------------------------.
+       [pi]a^3b(1 + [sigma])(3a^2 + b^2)
+
+  The resultant of these stresses vanishes; but, taking as before
+  [sigma] = 1/4, and putting for the three cases above a = b, a = 10b,
+  b = 10a, we find that the ratio of the maximum of this stress to the
+  average vertical shearing stress has the values 3/5, nearly 1/15, and
+  nearly 4. Thus the stress T is of considerable importance when the
+  beam is a plank.
+
+  As another example we may consider a circular tube of external radius
+  r0 and internal radius r1. Writing P, U, T for X_x, X_y, Z_x, we find
+
+                  4W
+    P = - -----------------(l - x)y,
+          [pi](r0^4 - r1^4)
+                                         _
+                      W                 |                /
+    U = ------------------------------- |(3 + 2[sigma]) (r0^2 + r1^2 - y^2
+        2(1 + [sigma])[pi](r0^4 - r1^4) |_               \
+                                                       _
+            r0^2r1^2              \                     |
+       - ------------- (y^2 - z^2) ) - (1 - 2[sigma])z^2|
+         (y^2 + z^2)^2            /                    _|
+
+                      W
+  T = - ------------------------------
+        (1 + [sigma])[pi](r0^4 - r1^4)
+     _                                            _
+    |                                 r0^2r1^2     |
+    | 1 + 2[sigma] + (3 + 2[sigma]) -------------  | yz;
+    |_                              (y^2 + z^2)^2 _|
+
+  and for a tube of radius r and small thickness t the value of P and
+  the maximum values of U and T reduce approximately to
+
+    P = - W(l - x)y/[pi]r^3t
+
+    U_max. = W/[pi]rt,  T_max. = W/2[pi]rt.
+
+  The greatest value of U is in this case approximately twice its
+  average value, but it is possible that these results for the bending
+  of very thin tubes may be seriously at fault if the tube is not
+  plugged, and if the load is not applied in the manner contemplated in
+  the theory (cf. S 55). In such cases the extensions and contractions
+  of the longitudinal filaments may be practically confined to a small
+  part of the material near the ends of the tube, while the rest of the
+  tube is deformed without stretching.
+
+51. The tangential tractions U, T on the cross-sections are necessarily
+accompanied by tangential tractions on the longitudinal sections, and on
+each such section the tangential traction is parallel to the central
+line; on a vertical section z = const. its amount at any point is T, and
+on a horizontal section y = const. its amount at any point is U.
+
+The internal stress at any point is completely determined by the
+components P, U, T, but these are not principal stresses (S 7). Clebsch
+has given an elegant geometrical construction for determining the
+principal stresses at any point when the values of P, U, T are known.
+
+[Illustration: FIG. 14.]
+
+  From the point O (fig. 14) draw lines OP, OU, OT, to represent the
+  stresses P, U, T at O, on the cross-section through O, in magnitude,
+  direction and sense, and compound U and T into a resultant represented
+  by OE; the plane EOP is a principal plane of stress at O, and the
+  principal stress at right angles to this plane vanishes. Take M the
+  middle point of OP, and with centre M and radius ME describe a circle
+  cutting the line OP in A and B; then OA and OB represent the
+  magnitudes of the two remaining principal stresses. On AB describe a
+  rectangle ABDC so that DC passes through E; then OC is the direction
+  of the principal stress represented in magnitude by OA, and OD is the
+  direction of the principal stress represented in magnitude by OB.
+
+[Illustration: FIG. 15.]
+
+52. As regards the strain in the beam, the longitudinal and lateral
+extensions and contractions depend on the bending moment in the same way
+as in the simpler problem; but, the bending moment being variable, the
+anticlastic curvature produced is also variable. In addition to these
+extensions and contractions there are shearing strains corresponding to
+the shearing stresses T, U. The shearing strain corresponding to T
+consists of a relative sliding parallel to the central-line of different
+longitudinal linear elements combined with a relative sliding in a
+transverse horizontal direction of elements of different cross-sections;
+the latter of these is concerned in the production of those
+displacements by which the variable anticlastic curvature is brought
+about; to see the effect of the former we may most suitably consider,
+for the case of an elliptic cross-section, the distortion of the shape
+of a rectangular portion of a plane of the material which in the natural
+state was horizontal; all the boundaries of such a portion become
+parabolas of small curvature, which is variable along the length of the
+beam, and the particular effect under consideration is the change of the
+transverse horizontal linear elements from straight lines such as HK to
+parabolas such as H'K' (fig. 15); the lines HL and KM are parallel to
+the central-line, and the figure is drawn for a plane above the neutral
+plane. When the cross-section is not an ellipse the character of the
+strain is the same, but the curves are only approximately parabolic.
+
+The shearing strain corresponding to U is a distortion which has the
+effect that the straight vertical filaments become curved lines which
+cut the longitudinal filaments obliquely, and thus the cross-sections do
+not remain plane, but become curved surfaces, and the tangent plane to
+any one of these surfaces at the centroid cuts the central line
+obliquely (fig. 16). The angle between these tangent planes and the
+central-line is the same at all points of the line; and, if it is
+denoted by 1/2[pi] + s0, the value of s0 is expressible as
+
+  shearing stress at centroid
+  ---------------------------,
+    rigidity of material
+
+and it thus depends on the shape of the cross-section; for the elliptic
+section of S 50 its value is
+
+    4W    2a^2(1 + [sigma]) + b^2
+  ------- -----------------------;
+  E[pi]ab       3a^2 + b^2
+
+for a circle (with [sigma] = 1/4) this becomes 7W/2E[pi]a^2. The
+vertical filament through the centroid of any cross-section becomes a
+cubical parabola, as shown in fig. 16, and the contour lines of the
+curved surface into which any cross-section is distorted are shown in
+fig. 17 for a circular section.
+
+[Illustration: FIG. 16.]
+
+53. The deflection of the beam is determined from the equation
+
+  curvature of central line = bending moment :- flexural rigidity,
+
+and the special conditions at the supported end; there is no alteration
+of this statement on account of the shears. As regards the special
+condition at an end which is _encastree_, or built in, Saint-Venant
+proposed to assume that the central tangent plane of the cross-section
+at the end is vertical; with this assumption the tangent to the central
+line at the end is inclined downwards and makes an angle s0 with the
+horizontal (see fig. 18); it is, however, improbable that this condition
+is exactly realized in practice. In the application of the theory to the
+experimental determination of Young's modulus, the small angle which the
+central-line at the support makes with the horizontal is an unknown
+quantity, to be eliminated by observation of the deflection at two or
+more points.
+
+54. We may suppose the displacement in a bent beam to be produced by the
+following operations: (1) the central-line is deflected into its curved
+form, (2) the cross-sections are rotated about axes through their
+centroids at right angles to the plane of flexure so as to make angles
+equal to 1/2[pi] + s0 with the central-line, (3) each cross-section is
+distorted in its own plane in such a way that the appropriate variable
+anticlastic curvature is produced, (4) the cross-sections are further
+distorted into curved surfaces. The contour lines of fig. 17 show the
+disturbance from the central tangent plane, not from the original
+vertical plane.
+
+[Illustration: FIG. 17.]
+
+55. _Practical Application of Saint-Venant's Theory._--The theory above
+described is exact provided the forces applied to the loaded end, which
+have W for resultant, are distributed over the terminal section in a
+particular way, not likely to be realized in practice; and the
+application to practical problems depends on a principle due to
+Saint-Venant, to the effect that, except for comparatively small
+portions of the beam near to the loaded and fixed ends, the resultant
+only is effective, and its mode of distribution does not seriously
+affect the internal strain and stress. In fact, the actual stress is
+that due to forces with the required resultant distributed in the manner
+contemplated in the theory, superposed upon that due to a certain
+distribution of forces on each terminal section which, if applied to a
+rigid body, would keep it in equilibrium; according to Saint-Venant's
+principle, the stresses and strains due to such distributions of force
+are unimportant except near the ends. For this principle to be exactly
+applicable it is necessary that the length of the beam should be very
+great compared with any linear dimension of its cross-section; for the
+practical application it is sufficient that the length should be about
+ten times the greatest diameter.
+
+56. In recent years the problem of the bending of a beam by loads
+distributed along its length has been much advanced. It is now
+practically solved for the case of a load distributed uniformly, or
+according to any rational algebraic law, and it is also solved for the
+case where the thickness is small compared with the length and depth, as
+in a plate girder, and the load is distributed in any way. These
+solutions are rather complicated and difficult to interpret. The case
+which has been worked out most fully is that of a transverse load
+distributed uniformly along the length of the beam. In this case two
+noteworthy results have been obtained. The first of these is that the
+central-line in general suffers extension. This result had been found
+experimentally many years before. In the case of the plate girder loaded
+uniformly along the top, this extension is just half as great as the
+extension of the central-line of the same girder when free at the ends,
+supported along the base, and carrying the same load along the top. The
+second noteworthy result is that the curvature of the strained
+central-line is not proportional to the bending moment. Over and above
+the curvature which would be found from the ordinary relation--
+
+  curvature of central-line = bending moment :- flexural rigidity,
+
+there is an additional curvature which is the same at all the
+cross-sections. In ordinary cases, provided the length is large compared
+with any linear dimension of the cross-section, this additional
+curvature is small compared with that calculated from the ordinary
+formula, but it may become important in cases like that of suspension
+bridges, where a load carried along the middle of the roadway is
+supported by tensions in rods attached at the sides.
+
+[Illustration: FIG. 18.]
+
+57. When the ordinary relation between the curvature and the bending
+moment is applied to the calculation of the deflection of _continuous
+beams_ it must not be forgotten that a correction of the kind just
+mentioned may possibly be requisite. In the usual method of treating the
+problem such corrections are not considered, and the ordinary relation
+is made the basis of the theory. In order to apply this relation to the
+calculation of the deflection, it is necessary to know the bending
+moment at every point; and, since the pressures of the supports are not
+among the data of the problem, we require a method of determining the
+bending moments at the supports either by calculation or in some other
+way. The calculation of the bending moment can be replaced by a method
+of graphical construction, due to Mohr, and depending on the two
+following theorems:--
+
+(i.) The curve of the central-line of each span of a beam, when the
+bending moment M is given,[1] is identical with the catenary or
+funicular curve passing through the ends of the span under a
+(fictitious) load per unit length of the span equal to M/EI, the
+horizontal tension in the funicular being unity.
+
+(ii.) The directions of the tangents to this funicular curve at the ends
+of the span are the same for all statically equivalent systems of
+(fictitious) load.
+
+When M is known, the magnitude of the resultant shearing stress at any
+section is dM/dx, where x is measured along the beam.
+
+[Illustration: FIG. 19.]
+
+[Illustration: FIG. 20.]
+
+  58. Let l be the length of a span of a loaded beam (fig. 19), M1 and
+  M2 the bending moments at the ends, M the bending moment at a section
+  distant x from the end (M1), M' the bending moment at the same section
+  when the same span with the same load is simply supported; then M is
+  given by the formula
+
+                l - x      x
+    M = M' + M1 ----- + M2 --,
+                  l        l
+
+  and thus a fictitious load statically equivalent to M/EI can be easily
+  found when M' has been found. If we draw a curve (fig. 20) to pass
+  through the ends of the span, so that its ordinate represents the
+  value of M'/EI, the corresponding fictitious loads are statically
+  equivalent to a single load, of amount represented by the area of the
+  curve, placed at the point of the span vertically above the centre of
+  gravity of this area. If PN is the ordinate of this curve, and if at
+  the ends of the span we erect ordinates in the proper sense to
+  represent M1/EI and M2/EI, the bending moment at any point is
+  represented by the length PQ.[2] For a uniformly distributed load the
+  curve of M' is a parabola M' = 1/2wx(l - x), where w is the load per
+  unit of length; and the statically equivalent fictitious load is
+  (1/12)wl^3/EI placed at the middle point G of the span; also the loads
+  statically equivalent to the fictitious loads M1(l - x)/lEI and
+  M2x/lEI are 1/2M1l/EI and 1/2M2l/EI placed at the points g, g' of
+  trisection of the span. The funicular polygon for the fictitious loads
+  can thus be drawn, and the direction of the central-line at the
+  supports is determined when the bending moments at the supports are
+  known.
+
+  [Illustration: FIG. 21.]
+
+  59. When there is more than one span the funiculars in question may be
+  drawn for each of the spans, and, if the bending moments at the ends
+  of the extreme spans are known, the intermediate ones can be
+  determined. This determination depends on two considerations: (1) the
+  fictitious loads corresponding to the bending moment at any support
+  are proportional to the lengths of the spans which abut on that
+  support; (2) the sides of two funiculars that end at any support
+  coincide in direction. Fig. 21 illustrates the method for the case of
+  a uniform beam on three supports A, B, C, the ends A and C being
+  freely supported. There will be an unknown bending moment M0 at B, and
+  the system[3] of fictitious loads is (1/12)wAB^3/EI at G the middle
+  point of AB, (1/12)wBC^3/EI at G' the middle point of BC, -1/2M0AB/EI
+  at g and -1/2M0BC/EI at g', where g and g' are the points of
+  trisection nearer to B of the spans AB, BC. The centre of gravity of
+  the two latter is a fixed point independent of M0, and the line VK of
+  the figure is the vertical through this point. We draw AD and CE to
+  represent the loads at G and G' in magnitude; then D and E are fixed
+  points. We construct any triangle UVW whose sides UV, UW pass through
+  D, B, and whose vertices lie on the verticals gU, VK, g'W; the point F
+  where VW meets DB is a fixed point, and the lines EF, DK are the two
+  sides (2, 4) of the required funiculars which do not pass through A, B
+  or C. The remaining sides (1, 3, 5) can then be drawn, and the side 3
+  necessarily passes through B; for the triangle UVW and the triangle
+  whose sides are 2, 3, 4 are in perspective.
+
+  [Illustration: FIG. 22.]
+
+  The bending moment M0 is represented in the figure by the vertical
+  line BH where H is on the continuation of the side 4, the scale being
+  given by
+
+    BH     1/2M0BC
+    -- = ----------- ;
+    CE   (1/12)wBC^3
+
+  this appears from the diagrams of forces, fig. 22, in which the
+  oblique lines are marked to correspond to the sides of the funiculars
+  to which they are parallel.
+
+  In the application of the method to more complicated cases there are
+  two systems of fixed points corresponding to F, by means of which the
+  sides of the funiculars are drawn.
+
+60. _Finite Bending of Thin Rod._--The equation
+
+  curvature = bending moment :- flexural rigidity
+
+may also be applied to the problem of the flexure in a principal plane
+of a very thin rod or wire, for which the curvature need not be small.
+When the forces that produce the flexure are applied at the ends only,
+the curve into which the central-line is bent is one of a definite
+family of curves, to which the name _elastica_ has been given, and there
+is a division of the family into two species according as the external
+forces are applied directly to the ends or are applied to rigid arms
+attached to the ends; the curves of the former species are characterized
+by the presence of inflections at all the points at which they cut the
+line of action of the applied forces.
+
+[Illustration: FIG. 23.]
+
+  We select this case for consideration. The problem of determining the
+  form of the curve (cf. fig. 23) is mathematically identical with the
+  problem of determining the motion of a simple circular pendulum
+  oscillating through a finite angle, as is seen by comparing the
+  differential equation of the curve
+
+       d^2[phi]
+    EI -------- + W sin [phi] = 0
+         ds^2
+
+  with the equation of motion of the pendulum
+
+      d^2[phi]
+    l -------- + g sin [phi] = 0.
+        dt^2
+
+  The length L of the curve between two inflections corresponds to the
+  time of oscillation of the pendulum from rest to rest, and we thus
+  have
+
+    L [root](W/EI) = 2K,
+
+  where K is the real quarter period of elliptic functions of modulus
+  sin 1/2[alpha], and [alpha] is the angle at which the curve cuts the
+  line of action of the applied forces. Unless the length of the rod
+  exceeds [pi][root](EI/W) it will not bend under the force, but when
+  the length is great enough there may be more than two points of
+  inflection and more than one bay of the curve; for n bays (n + 1
+  inflections) the length must exceed n[pi][root](EI/W). Some of the
+  forms of the curve are shown in fig. 24.
+
+  [Illustration: FIG. 24.]
+
+  For the form d, in which two bays make a figure of eight, we have
+
+    L[root](W/EI) = 4.6, [alpha] = 130 deg.
+
+  approximately. It is noteworthy that whenever the length and force
+  admit of a sinuous form, such as [alpha] or b, with more than two
+  inflections, there is also possible a crossed form, like e, with two
+  inflections only; the latter form is stable and the former unstable.
+
+61. The particular case of the above for which [alpha] is very small is
+a curve of sines of small amplitude, and the result in this case has
+been applied to the problem of the buckling of struts under thrust. When
+the strut, of length L', is maintained upright at its lower end, and
+loaded at its upper end, it is simply contracted, unless L'^2W >
+1/4[pi]^2EI, for the lower end corresponds to a point at which the
+tangent is vertical on an elastica for which the line of inflections is
+also vertical, and thus the length must be half of one bay (fig. 25, a).
+For greater lengths or loads the strut tends to bend or buckle under the
+load. For a very slight excess of L'^2W above 1/4[pi]^2EI, the theory on
+which the above discussion is founded, is not quite adequate, as it
+assumes the central-line of the strut to be free from extension or
+contraction, and it is probable that bending without extension does not
+take place when the length or the force exceeds the critical value but
+slightly. It should be noted also that the formula has no application to
+short struts, as the theory from which it is derived is founded on the
+assumption that the length is great compared with the diameter (cf. S
+56).
+
+[Illustration: FIG. 25.]
+
+The condition of buckling, corresponding to the above, for a long strut,
+of length L', when both ends are free to turn is L'^2W > [pi]^2EI; for
+the central-line forms a complete bay (fig. 25, b); if both ends are
+maintained in the same vertical line, the condition is L'^2W >
+4[pi]^2EI, the central-line forming a complete bay and two half bays
+(fig. 25, c).
+
+[Illustration: FIG. 26.]
+
+62. In our consideration of flexure it has so far been supposed that the
+bending takes place in a principal plane. We may remove this restriction
+by resolving the forces that tend to produce bending into systems of
+forces acting in the two principal planes. To each plane there
+corresponds a particular flexural rigidity, and the systems of forces in
+the two planes give rise to independent systems of stress, strain and
+displacement, which must be superposed in order to obtain the actual
+state. Applying this process to the problem of SS 48-54, and supposing
+that one principal axis of a cross-section at its centroid makes an
+angle [theta] with the vertical, then for any shape of section the
+neutral surface or locus of unextended fibres cuts the section in a line
+DD', which is conjugate to the vertical diameter CP with respect to any
+ellipse of inertia of the section. The central-line is bent into a plane
+curve which is not in a vertical plane, but is in a plane through the
+line CY which is perpendicular to DD' (fig. 26).
+
+63. _Bending and Twisting of Thin Rods._--When a very thin rod or wire
+is bent and twisted by applied forces, the forces on any part of it
+limited by a normal section are balanced by the tractions across the
+section, and these tractions are statically equivalent to certain forces
+and couples at the centroid of the section; we shall call them the
+_stress-resultants_ and the _stress-couples_. The stress-couples consist
+of two flexural couples in the two principal planes, and the torsional
+couple about the tangent to the central-line. The torsional couple is
+the product of the torsional rigidity and the twist produced; the
+torsional rigidity is exactly the same as for a straight rod of the same
+material and section twisted without bending, as in Saint-Venant's
+torsion problem (S 42). The twist [tau] is connected with the
+deformation of the wire in this way: if we suppose a very small ring
+which fits the cross-section of the wire to be provided with a pointer
+in the direction of one principal axis of the section at its centroid,
+and to move along the wire with velocity v, the pointer will rotate
+about the central-line with angular velocity [tau]v. The amount of the
+flexural couple for either principal plane at any section is the product
+of the flexural rigidity for that plane, and the resolved part in that
+plane of the curvature of the central line at the centroid of the
+section; the resolved part of the curvature along the normal to any
+plane is obtained by treating the curvature as a vector directed along
+the normal to the osculating plane and projecting this vector. The
+flexural couples reduce to a single couple in the osculating plane
+proportional to the curvature when the two flexural rigidities are
+equal, and in this case only.
+
+The stress-resultants across any section are tangential forces in the
+two principal planes, and a tension or thrust along the central-line;
+when the stress-couples and the applied forces are known these
+stress-resultants are determinate. The existence, in particular, of the
+resultant tension or thrust parallel to the central-line does not imply
+sensible extension or contraction of the central filament, and the
+tension per unit area of the cross-section to which it would be
+equivalent is small compared with the tensions and pressures in
+longitudinal filaments not passing through the centroid of the section;
+the moments of the latter tensions and pressures constitute the flexural
+couples.
+
+64. We consider, in particular, the case of a naturally straight spring
+or rod of circular section, radius c, and of homogeneous isotropic
+material. The torsional rigidity is 1/4E[pi]c^4/(1 + [sigma]); and the
+flexural rigidity, which is the same for all planes through the
+central-line, is 1/4E[pi]c^4; we shall denote these by C and A
+respectively. The rod may be held bent by suitable forces into a curve
+of double curvature with an amount of twist [tau], and then the
+torsional couple is C[tau], and the flexural couple in the osculating
+plane is A/[rho], where [rho] is the radius of circular curvature. Among
+the curves in which the rod can be held by forces and couples applied at
+its ends only, one is a circular helix; and then the applied forces and
+couples are equivalent to a wrench about the axis of the helix.
+
+  Let [alpha] be the angle and r the radius of the helix, so that [rho]
+  is r sec^2[alpha]; and let R and K be the force and couple of the
+  wrench (fig. 27).
+
+  Then the couple formed by R and an equal and opposite force at any
+  section and the couple K are equivalent to the torsional and flexural
+  couples at the section, and this gives the equations for R and K
+
+          sin [alpha] cos^3 [alpha]           cos [alpha]
+    R = A ------------------------- - C[tau] ------------,
+                    r^2                            r
+
+          cos^3 [alpha]
+    K = A ------------- + C[tau] sin [alpha].
+                r
+
+  The thrust across any section is R sin [alpha] parallel to the tangent
+  to the helix, and the shearing stress-resultant is R cos [alpha] at
+  right angles to the osculating plane.
+
+  [Illustration: FIG. 27.]
+
+  When the twist is such that, if the rod were simply unbent, it would
+  also be untwisted, [tau] is (sin [alpha] cos [alpha])/r, and then,
+  restoring the values of A and C, we have
+
+         E[pi]c^4    [sigma]
+    R =  -------- ------------ sin [alpha] cos^2 [alpha],
+           4r^2    1 + [sigma]
+
+        E[pi]c^4  1 + [sigma] cos^2 [alpha]
+    K = --------  ------------------------- cos [alpha].
+            4r           1 + [sigma]
+
+  65. The theory of spiral springs affords an application of these
+  results. The stress-couples called into play when a naturally helical
+  spring ([alpha], r) is held in the form of a helix ([alpha]', r'), are
+  equal to the differences between those called into play when a
+  straight rod of the same material and section is held in the first
+  form, and those called into play when it is held in the second form.
+
+  Thus the torsional couple is
+
+       /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha] \
+    C ( ------------------------- - ------------------------ ),
+       \           r'                          r            /
+
+  and the flexural couple is
+
+       /cos^2 [alpha]'   cos^2 [alpha]\
+    A ( -------------- - ------------  ).
+       \     r'                r      /
+
+  The wrench (R, K) along the axis by which the spring can be held in
+  the form ([alpha]', r') is given by the equations
+
+          sin [alpha]'  /cos^2 [alpha]'   cos^2 [alpha]\
+    R = A ------------ ( -------------- - ------------- ) -
+              r'        \       r'            r        /
+
+         cos [alpha]'  /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha]\
+      C ------------- ( ------------------------- - ----------------------- ),
+              r'       \           r'                          r           /
+
+                        /cos^2 [alpha]'   cos^2 [alpha]\
+    K = A cos [alpha]' ( -------------- - ------------- ) +
+                        \      r'               r      /
+
+                      /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha]\
+      C sin [alpha]' ( ------------------------- - ----------------------- ).
+                      \           r'                           r          /
+
+  When the spring is slightly extended by an axial force F, = -R, and
+  there is no couple, so that K vanishes, and [alpha]', r' differ very
+  little from [alpha], r, it follows from these equations that the axial
+  elongation, [delta]x, is connected with the axial length x and the
+  force F by the equation
+
+        E[pi]c^4        sin [alpha]        [delta]x
+    F = -------- ------------------------- --------,
+          4r^2   1 + [sigma] cos^2 [alpha]     x
+
+  and that the loaded end is rotated about the axis of the helix through
+  a small angle
+
+    4[sigma]Fxr cos [alpha]
+    -----------------------
+           E[pi]c^4
+
+  the sense of the rotation being such that the spring becomes more
+  tightly coiled.
+
+66. A horizontal pointer attached to a vertical spiral spring would be
+made to rotate by loading the spring, and the angle through which it
+turns might be used to measure the load, at any rate, when the load is
+not too great; but a much more sensitive contrivance is the twisted
+strip devised by W.E. Ayrton and J. Perry. A very thin, narrow
+rectangular strip of metal is given a permanent twist about its
+longitudinal middle line, and a pointer is attached to it at right
+angles to this line. When the strip is subjected to longitudinal tension
+the pointer rotates through a considerable angle. G.H. Bryan (_Phil.
+Mag._, December 1890) has succeeded in constructing a theory of the
+action of the strip, according to which it is regarded as a strip of
+_plating_ in the form of a right helicoid, which, after extension of the
+middle line, becomes a portion of a slightly different helicoid; on
+account of the thinness of the strip, the change of curvature of the
+surface is considerable, even when the extension is small, and the
+pointer turns with the generators of the helicoid.
+
+  If b stands for the breadth and t for the thickness of the strip, and
+  [tau] for the permanent twist, the approximate formula for the angle
+  [theta] through which the strip is untwisted on the application of a
+  load W was found to be
+
+                        Wb[tau](1 + [sigma])
+    [theta] = ---------------------------------------.
+                     /    (1 + [sigma])   b^4[tau]^2\
+              2Et^3 ( 1 + ------------- - ---------- )
+                     \         30             t^2   /
+
+  The quantity b[tau] which occurs in the formula is the total twist in
+  a length of the strip equal to its breadth, and this will generally be
+  very small; if it is small of the same order as t/b, or a higher
+  order, the formula becomes 1/2Wb[tau](1+[sigma])/Et^3, with sufficient
+  approximation, and this result appears to be in agreement with
+  observations of the behaviour of such strips.
+
+67. _Thin Plate under Pressure._--The theory of the deformation of
+plates, whether plane or curved, is very intricate, partly because of
+the complexity of the kinematical relations involved. We shall here
+indicate the nature of the effects produced in a thin plane plate, of
+isotropic material, which is slightly bent by pressure. This theory
+should have an application to the stress produced in a ship's plates. In
+the problem of the cylinder under internal pressure (S 77 below) the
+most important stress is the circumferential tension, counteracting the
+tendency of the circular filaments to expand under the pressure; but in
+the problem of a plane plate some of the filaments parallel to the plane
+of the plate are extended and others are contracted, so that the
+tensions and pressures along them give rise to resultant couples but not
+always to resultant forces. Whatever forces are applied to bend the
+plate, these couples are always expressible, at least approximately in
+terms of the principal curvatures produced in the surface which, before
+strain, was the middle plane of the plate. The simplest case is that of
+a rectangular plate, bent by a distribution of couples applied to its
+edges, so that the middle surface becomes a cylinder of large radius R;
+the requisite couple per unit of length of the straight edges is of
+amount C/R, where C is a certain constant; and the requisite couple per
+unit of length of the circular edges is of amount C[sigma]/R, the latter
+being required to resist the tendency to anticlastic curvature (cf. S
+47). If normal sections of the plate are supposed drawn through the
+generators and circular sections of the cylinder, the action of the
+neighbouring portions on any portion so bounded involves flexural
+couples of the above amounts. When the plate is bent in any manner, the
+curvature produced at each section of the middle surface may be regarded
+as arising from the superposition of two cylindrical curvatures; and the
+flexural couples across normal sections through the lines of curvature,
+estimated per unit of length of those lines, are C(1/R1 + [sigma]/R2)
+and C(1/R2 + [sigma]/R1), where R1 and R2 are the principal radii of
+curvature. The value of C for a plate of small thickness 2h is
+(2/3)Eh^3/(1 - [sigma]^2). Exactly as in the problem of the beam (SS 48,
+56), the action between neighbouring portions of the plate generally
+involves shearing stresses across normal sections as well as flexural
+couples; and the resultants of these stresses are determined by the
+conditions that, with the flexural couples, they balance the forces
+applied to bend the plate.
+
+[Illustration: FIG. 28.]
+
+  68. To express this theory analytically, let the middle plane of the
+  plate in the unstrained position be taken as the plane of (x, y), and
+  let normal sections at right angles to the axes of x and y be drawn
+  through any point. After strain let w be the displacement of this
+  point in the direction perpendicular to the plane, marked p in fig.
+  28. If the axes of x and y were parallel to the lines of curvature at
+  the point, the flexural couple acting across the section normal to x
+  (or y) would have the axis of y (or x) for its axis; but when the
+  lines of curvature are inclined to the axes of co-ordinates, the
+  flexural couple across a section normal to either axis has a component
+  about that axis as well as a component about the perpendicular axis.
+  Consider an element ABCD of the section at right angles to the axis of
+  x, contained between two lines near together and perpendicular to the
+  middle plane. The action of the portion of the plate to the right upon
+  the portion to the left, across the element, gives rise to a couple
+  about the middle line (y) of amount, estimated per unit of length of
+  that line, equal to
+
+       /dP^2w          dP^2w \
+    C ( ----- + [sigma]-----  ), = G1,
+       \dPx^2          dPy^2 /
+
+  say, and to a couple, similarly estimated, about the normal (x) of
+  amount
+
+                   dP^2w
+    -C(1-[sigma]) ------, = H,
+                  dPxdPy
+
+  say. The corresponding couples on an element of a section at right
+  angles to the axis of y, estimated per unit of length of the axis of
+  x, are of amounts
+
+        /dP^2w          dP^2w\
+     -C( ----- + [sigma]----- ), = G2
+        \dPy^2          dPx^2/
+
+  say, and -H. The resultant S1 of the shearing stresses on the element
+  ABCD, estimated as before, is given by the equation
+
+         dPG1   dPH
+    S1 = ---- - ---
+         dPx    dPy
+
+  (cf. S 57), and the corresponding resultant S2 for an element
+  perpendicular to the axis of y is given by the equation
+
+          dPH   dPG2
+    S2= - --- - ----.
+          dPx   dPy
+
+  If the plate is bent by a pressure p per unit of area, the equation of
+  equilibrium is
+
+    dPS1   dPS2
+    ---- + ---- = p, or, in terms of w,
+    dPx    dPy
+
+    dP^4w   dP^4w      dP^4w      p
+    ----- + ----- + 2---------- = --.
+    dPx^4   dPy^4    dPx^2dPy^2   C
+
+  This equation, together with the special conditions at the rim,
+  suffices for the determination of w, and then all the quantities here
+  introduced are determined. Further, the most important of the
+  stress-components are those which act across elements of normal
+  sections: the tension in direction x, at a distance z from the middle
+  plane measured in the direction of p, is of amount
+
+      3Cz   /dP^2w          dP^2w\
+    - ---- ( ----- + [sigma]----- ),
+      2h^3  \dPx^2          dPy^2/
+
+  and there is a corresponding tension in direction y; the shearing
+  stress consisting of traction parallel to y on planes x = const., and
+  traction parallel to x on planes y = const., is of amount
+
+    3C(1 - [sigma])z  dP^2w
+    ---------------- ------;
+          2h^3       dPxdPy
+
+  these tensions and shearing stresses are equivalent to two principal
+  tensions, in the directions of the lines of curvature of the surface
+  into which the middle plane is bent, and they give rise to the
+  flexural couples.
+
+  69. In the special example of a circular plate, of radius a, supported
+  at the rim, and held bent by a uniform pressure p, the value of w at a
+  point distant r from the axis is
+
+    1  p               /5 + [sigma]         \
+    -- -- (a^2 - r^2) ( ----------- a^2 - r^2),
+    64 C               \1 + [sigma]         /
+
+  and the most important of the stress components is the radial tension,
+  of which the amount at any point is (3/32)(3 + [sigma])pz(a^2 - r)/h^3;
+  the maximum radial tension is about (1/3)(a/h)^2p, and, when the
+  thickness is small compared with the diameter, this is a large
+  multiple of p.
+
+70. _General Theorems._--Passing now from these questions of flexure and
+torsion, we consider some results that can be deduced from the general
+equations of equilibrium of an elastic solid body.
+
+The form of the general expression for the potential energy (S 27)
+stored up in the strained body leads, by a general property of quadratic
+functions, to a reciprocal theorem relating to the effects produced in
+the body by two different systems of forces, viz.: The whole work done
+by the forces of the first system, acting over the displacements
+produced by the forces of the second system, is equal to the whole work
+done by the forces of the second system, acting over the displacements
+produced by the forces of the first system. By a suitable choice of the
+second system of forces, the average values of the component stresses
+and strains produced by given forces, considered as constituting the
+first system, can be obtained, even when the distribution of the stress
+and strain cannot be determined.
+
+[Illustration: FIG. 29.]
+
+  Taking for example the problem presented by an isotropic body of any
+  form[4] pressed between two parallel planes distant l apart (fig. 29),
+  and denoting the resultant pressure by p, we find that the diminution
+  of volume -[delta]v is given by the equation
+
+    -[delta]v = lp/3k,
+
+  where k is the modulus of compression, equal to (1/3)E/(1 - 2[sigma]).
+  Again, take the problem of the changes produced in a heavy body by
+  different ways of supporting it; when the body is suspended from one
+  or more points in a horizontal plane its volume is increased by
+
+    [delta]v = Wh/3k,
+
+  where W is the weight of the body, and h the depth of its centre of
+  gravity below the plane; when the body is supported by upward
+  vertical pressures at one or more points in a horizontal plane the
+  volume is diminished by
+
+    -[delta]v = Wh'/3k,
+
+  where h' is the height of the centre of gravity above the plane; if
+  the body is a cylinder, of length l and section A, standing with its
+  base on a smooth horizontal plane, its length is shortened by an
+  amount
+
+    -[delta]l = Wl/2EA;
+
+  if the same cylinder lies on the plane with its generators horizontal,
+  its length is increased by an amount
+
+    [delta]l = [sigma]Wh'/EA.
+
+
+
+71. In recent years important results have been found by considering the
+effects produced in an elastic solid by forces applied at isolated
+points.
+
+  Taking the case of a single force F applied at a point in the
+  interior, we may show that the stress at a distance r from the point
+  consists of
+
+  (1) a radial pressure of amount
+
+    2 - [sigma]   F   cos [theta]
+    ----------- ----- -----------,
+    1 - [sigma] 4[pi]     r^2
+
+  (2) tension in all directions at right angles to the radius of amount
+
+     1 - 2[sigma]  F cos [theta]
+    -------------- -------------,
+    2(1 - [sigma])   4[pi]r^2
+
+  (3) shearing stress consisting of traction acting along the radius
+  dr on the surface of the cone [theta] = const. and traction acting
+  along the meridian d[theta] on the surface of the sphere r = const. of
+  amount
+
+     1 - 2[sigma]    F   sin [theta]
+    -------------- ----- -----------,
+    2(1 - [sigma]) 4[pi]     r^2
+
+  where [theta] is the angle between the radius vector r and the line of
+  action of F. The line marked T in fig. 30 shows the direction of the
+  tangential traction on the spherical surface.
+
+  [Illustration: FIG. 30.]
+
+  Thus the lines of stress are in and perpendicular to the meridian
+  plane, and the direction of one of those in the meridian plane is
+  inclined to the radius vector r at an angle
+
+                 /2 - 4[sigma]            \
+    1/2tan^(-1) ( ------------ tan [theta] ).
+                 \5 - 4[sigma]            /
+
+  The corresponding displacement at any point is compounded of a radial
+  displacement of amount
+
+     1 + [sigma]     F    cos [theta]
+    -------------- ------ -----------
+    2(1 - [sigma]) 4[pi]E      r
+
+  and a displacement parallel to the line of action of F of amount
+
+    (3 - 4[sigma])(1 + [sigma])   F    1
+    --------------------------- ------ --.
+          2(1 - [sigma])        4[pi]E r
+
+  The effects of forces applied at different points and in different
+  directions can be obtained by summation, and the effect of
+  continuously distributed forces can be obtained by integration.
+
+72. The stress system considered in S 71 is equivalent, on the plane
+through the origin at right angles to the line of action of F, to a
+resultant pressure of magnitude 1/2F at the origin and a radial traction
+of amount
+
+   1 - 2[sigma]      F
+  -------------- --------,
+  2(1 - [sigma]) 4[pi]r^2
+
+and, by the application of this system of tractions to a solid bounded
+by a plane, the displacement just described would be produced. There is
+also another stress system for a solid so bounded which is equivalent,
+on the same plane, to a resultant pressure at the origin, and a radial
+traction proportional to 1/r^2, but these are in the ratio 2[pi]:r^(-2),
+instead of being in the ratio 4[pi](1 - [sigma]) : (1 - 2[sigma])r^(-2).
+
+[Illustration: FIG. 31.]
+
+  The second stress system (see fig. 31) consists of:
+
+  (1) radial pressure F'r^(-2),
+
+  (2) tension in the meridian plane across the radius vector of amount
+
+    F'r^(-2) cos [theta] /(1 + cos [theta]),
+
+  (3) tension across the meridian plane of amount
+
+    F'r^(-2)/(l + cos [theta]),
+
+  (4) shearing stress as in S 71 of amount
+
+    F'r^(-2) sin [theta]/(1 + cos [theta]),
+
+  and the stress across the plane boundary consists of a resultant
+  pressure of magnitude 2[pi]F' and a radial traction of amount
+  F'r^(-2). If then we superpose the component stresses of the last
+  section multiplied by 4(1 - [sigma])W/F, and the component stresses
+  here written down multiplied by -(1 - 2[sigma])W/2[pi]F', the stress
+  on the plane boundary will reduce to a single pressure W at the
+  origin. We shall thus obtain the stress system at any point due to
+  such a force applied at one point of the boundary.
+
+  In the stress system thus arrived at the traction across any plane
+  parallel to the boundary is directed away from the place where W is
+  supported, and its amount is 3W cos^2[theta]/2[pi]r^2. The
+  corresponding displacement consists of
+
+  (1) a horizontal displacement radially outwards from the vertical
+  through the origin of amount
+
+    W(1 + [sigma]) sin [theta]  /               1 - 2[sigma]  \
+    -------------------------- ( cos [theta] - --------------- ),
+             2[pi]Er            \              1 + cos [theta]/
+
+  (2) a vertical displacement downwards of amount
+
+    W(1 + [sigma])
+    -------------- {2(1 - [sigma]) + cos^2[theta]}.
+       2[pi]Er
+
+  The effects produced by a system of loads on a solid bounded by a
+  plane can be deduced.
+
+The results for a solid body bounded by an infinite plane may be
+interpreted as giving the local effects of forces applied to a small
+part of the surface of a body. The results show that pressure is
+transmitted into a body from the boundary in such a way that the
+traction at a point on a section parallel to the boundary is the same at
+all points of any sphere which touches the boundary at the point of
+pressure, and that its amount at any point is inversely proportional to
+the square of the radius of this sphere, while its direction is that of
+a line drawn from the point of pressure to the point at which the
+traction is estimated. The transmission of force through a solid body
+indicated by this result was strikingly demonstrated in an attempt that
+was made to measure the lunar deflexion of gravity; it was found that
+the weight of the observer on the floor of the laboratory produced a
+disturbance of the instrument sufficient to disguise completely the
+effect which the instrument had been designed to measure (see G.H.
+Darwin, _The Tides and Kindred Phenomena in the Solar System_, London,
+1898).
+
+73. There is a corresponding theory of two-dimensional systems, that is
+to say, systems in which either the displacement is parallel to a fixed
+plane, or there is no traction across any plane of a system of parallel
+planes. This theory shows that, when pressure is applied at a point of
+the edge of a plate in any direction in the plane of the plate, the
+stress developed in the plate consists exclusively of radial pressure
+across any circle having the point of pressure as centre, and the
+magnitude of this pressure is the same at all points of any circle which
+touches the edge at the point of pressure, and its amount at any point
+is inversely proportional to the radius of this circle. This result
+leads to a number of interesting solutions of problems relating to plane
+systems; among these may be mentioned the problem of a circular plate
+strained by any forces applied at its edge.
+
+74. The results stated in S 72 have been applied to give an account of
+the nature of the actions concerned in the impact of two solid bodies.
+The dissipation of energy involved in the impact is neglected, and the
+resultant pressure between the bodies at any instant during the impact
+is equal to the rate of destruction of momentum of either along the
+normal to the plane of contact drawn towards the interior of the other.
+It has been shown that in general the bodies come into contact over a
+small area bounded by an ellipse, and remain in contact for a time which
+varies inversely as the fifth root of the initial relative velocity.
+
+  For equal spheres of the same material, with [sigma] = 1/4, impinging
+  directly with relative velocity v, the patches that come into contact
+  are circles of radius
+
+     /45[pi]\ ^(1/5)  /v \ ^(2/5)
+    ( ------ )       ( -- )      r,
+     \ 256  /         \V /
+
+  where r is the radius of either, and V the velocity of longitudinal
+  waves in a thin bar of the material. The duration of the impact is
+  approximately
+
+              /2025[pi]^2\ ^(1/5)       r
+    (2.9432) ( ---------- )      --------------- .
+              \   512    /       v^(1/5) V^(4/5)
+
+  For two steel spheres of the size of the earth impinging with a
+  velocity of 1 cm. per second the duration of the impact would be about
+  twenty-seven hours. The fact that the duration of impact is, for
+  moderate velocities, a considerable multiple of the time taken by a
+  wave of compression to travel through either of two impinging bodies
+  has been ascertained experimentally, and constitutes the reason for
+  the adequacy of the statical theory here described.
+
+75. _Spheres and Cylinders._--Simple results can be found for spherical
+and cylindrical bodies strained by radial forces.
+
+  For a sphere of radius a, and of homogeneous isotropic material of
+  density [rho], strained by the mutual gravitation of its parts, the
+  stress at a distance r from the centre consists of
+
+  (1) uniform hydrostatic pressure of amount (1/10)g[rho]a(3 -
+  [sigma])/(1 - [sigma]),
+
+  (2) radial tension of amount (1/10)g[rho](r^2/a)(3 - [sigma])/(1
+  -[sigma]),
+
+  (3) uniform tension at right angles to the radius vector of amount
+
+    (1/10)g[rho](r^2/a) (1 + 3[sigma])/(1 - [sigma]),
+
+  where g is the value of gravity at the surface. The corresponding
+  strains consist of
+
+  (1) uniform contraction of all lines of the body of amount
+
+    (1/30)k^(-1)g[rho]a(3 - [sigma])/(1 - [sigma]),
+
+  (2) radial extension of amount (1/10)k^(-1)g[rho](r^2/a)(1 +
+  [sigma])/(1 - [sigma]),
+
+  (3) extension in any direction at right angles to the radius vector of
+  amount
+
+    (1/30)k^(-1)g[rho](r^2/a) (1 + [sigma])/(1 - [sigma]),
+
+  where k is the modulus of compression. The volume is diminished by the
+  fraction g[rho]a/5k of itself. The parts of the radii vectors within
+  the sphere r = a{(3 - [sigma])/(3 + 3[sigma])}^(1/2) are contracted,
+  and the parts without this sphere are extended. The application of the
+  above results to the state of the interior of the earth involves a
+  neglect of the caution emphasized in S 40, viz. that the strain
+  determined by the solution must be small if the solution is to be
+  accepted. In a body of the size and mass of the earth, and having a
+  resistance to compression and a rigidity equal to those of steel, the
+  radial contraction at the centre, as given by the above solution,
+  would be nearly 1/3, and the radial extension at the surface nearly
+  1/6, and these fractions can by no means be regarded as "small."
+
+  76. In a spherical shell of homogeneous isotropic material, of
+  internal radius r1 and external radius r0, subjected to pressure p0 on
+  the outer surface, and p1 on the inner surface, the stress at any
+  point distant r from the centre consists of
+
+                                                  p1r1^3 - p0r0^3
+  (1) uniform tension in all directions of amount ---------------,
+                                                    r0^3 - r1^3
+
+                                  p1 - p0    r0^3 r1^3
+  (2) radial pressure of amount -----------  ---------,
+                                r0^3 - r1^3     r^3
+
+  (3) tension in all directions at right angles to the radius vector of
+  amount
+
+          p1 - p0   r0^3 r1^3
+    1/2 ----------- ---------.
+        r0^3 - r1^3    r^3
+
+  The corresponding strains consist of
+
+  (1) uniform extension of all lines of the body of amount
+
+    1  p1r1^3 - p0r0^3
+    -- ---------------,
+    3k   r0^3 - r1^3
+
+                                     1     p1 - p0   r0^3 r1^3
+  (2) radial contraction of amount ----- ----------- ---------,
+                                   2[mu] r0^3 - r1^3    r^3
+
+  (3) extension in all directions at right angles to the radius vector
+  of amount
+
+      1     p1 - p0   r0^3 r1^3
+    ----- ----------- ---------,
+    4[mu] r0^3 - r1^3    r^3
+
+  where [mu] is the modulus of rigidity of the material, = 1/2E/(1 +
+  [sigma]). The volume included between the two surfaces of the body is
+  increased
+
+                  p1r1^3 - p0r0^3
+  by the fraction --------------- of itself, and the volume within the
+                  k(r0^3 - r1^3)
+
+  inner surface is increased by the fraction
+
+    3(p1 - p0)     r0^3      p1r1^3 - p0r0^3
+    ---------- ----------- + ---------------
+      4[mu]    r0^3 - r1^3   k(r0^3 - r1^3)
+
+  of itself. For a shell subject only to internal pressure p the
+  greatest extension is the extension at right angles to the radius at
+  the inner surface, and its amount is
+
+        pr1^3    / 1     1   r0^3 \
+    ----------- ( -- + ----- ----  );
+    r0^3 - r1^3  \3k   4[mu] r1^3 /
+
+  the greatest tension is the transverse tension at the inner surface,
+  and its amount is p(1/2 r0^3 + r1^3)/(r0^3 - r1^3).
+
+  77. In the problem of a cylindrical shell under pressure a
+  complication may arise from the effects of the ends; but when the ends
+  are free from stress the solution is very simple. With notation
+  similar to that in S 76 it can be shown that the stress at a distance
+  r from the axis consists of
+
+  (1) uniform tension in all directions at right angles to the axis of
+  amount
+
+    p1r1^2 - p0r0^2
+    ---------------,
+      r0^2 - r1^2
+
+                                  p1 - p0   r0^2 r1^2
+  (2) radial pressure of amount ----------- ---------,
+                                r0^2 - r1^2    r^2
+
+  (3) hoop tension numerically equal to this radial pressure.
+
+  The corresponding strains consist of
+
+  (1) uniform extension of all lines of the material at right angles to
+  the axis of amount
+
+    1 - [sigma] p1r1^2 - p0r0^2
+    ----------- ---------------,
+         E        r0^2 - r1^2
+
+  (2) radial contraction of amount
+
+    1 + [sigma]   p1 - p0   r0^2 r1^2
+    ----------- ----------- ---------,
+         E      r0^2 - r1^2    r^2
+
+  (3) extension along the circular filaments numerically equal to this
+  radial contraction,
+
+  (4) uniform contraction of the longitudinal filaments of amount
+
+    2[sigma] p1r1^2 - p0r0^2
+    -------- ---------------.
+       E       r0^2 - r1^2
+
+  For a shell subject only to internal pressure p the greatest extension
+  is the circumferential extension at the inner surface, and its amount
+  is
+
+    p   /r0^2 + r1^2          \
+    -- ( ----------- + [sigma] );
+    E   \r0^2 - r1^2          /
+
+  the greatest tension is the hoop tension at the inner surface, and its
+  amount is p(r0^2 + r1^2)/(r0^2 - r1^2).
+
+  78. When the ends of the tube, instead of being free, are closed by
+  disks, so that the tube becomes a closed cylindrical vessel, the
+  longitudinal extension is determined by the condition that the
+  resultant longitudinal tension in the walls balances the resultant
+  normal pressure on either end. This condition gives the value of the
+  extension of the longitudinal filaments as
+
+    (p1r1^2 - p0r0^2)/3k(r0^2 - r1^2),
+
+  where k is the modulus of compression of the material. The result may
+  be applied to the experimental determination of k, by measuring the
+  increase of length of a tube subjected to internal pressure (A.
+  Mallock, _Proc. R. Soc. London_, lxxiv., 1904, and C. Chree, _ibid._).
+
+79. The results obtained in S 77 have been applied to gun construction;
+we may consider that one cylinder is heated so as to slip over another
+upon which it shrinks by cooling, so that the two form a single body in
+a condition of initial stress.
+
+  We take P as the measure of the pressure between the two, and p for
+  the pressure within the inner cylinder by which the system is
+  afterwards strained, and denote by r' the radius of the common
+  surface. To obtain the stress at any point we superpose the
+
+                                         r1^2 r0^2 - r^2
+  system consisting of radial pressure p ---- ----------- and hoop tension
+                                         r^2  r0^2 - r1^2
+
+     r1^2  r0^2 + r^2
+   p ---- -----------  upon a system which, for the outer cylinder,
+     r^2  r0^2 - r1^2
+
+                                r'^2  r0^2 - r^2
+  consists of radial pressure P ---- -----------
+                                r^2  r0^2 - r'^2
+
+                     r'^2  r0^2 + r^2
+  and hoop tension P ---- -----------, and for the inner cylinder consists
+                     r^2  r0^2 - r'^2
+
+                        r'^2  r^2 - r1^2                    r'^2  r^2 + r1^2
+  of radial pressure  P ---- ----------- and hoop tension P ---- -----------.
+                        r^2  r'^2 - r1^2                    r^2  r'^2 - r1^2
+
+  The hoop tension at the inner surface is less than it would be for a
+  tube of equal thickness without initial stress in the ratio
+
+        P     2r'^2     r0^2 + r1^2
+    1 - -- -----------  ----------- : 1.
+        p  r0^2 + r1^2  r'^2 - r1^2
+
+  This shows how the strength of the tube is increased by the initial
+  stress. When the initial stress is produced by tightly wound wire, a
+  similar gain of strength accrues.
+
+80. In the problem of determining the distribution of stress and strain
+in a circular cylinder, rotating about its axis, simple solutions have
+been obtained which are sufficiently exact for the two special cases of
+a thin disk and a long shaft.
+
+  Suppose that a circular disk of radius a and thickness 2l, and of
+  density [rho], rotates about its axis with angular velocity [omega],
+  and consider the following systems of superposed stresses at any point
+  distant r from the axis and z from the middle plane:
+
+  (1) uniform tension in all directions at right angles to the axis of
+  amount (1/8)[omega]^2[rho]a^2(3 + [sigma]),
+
+  (2) radial pressure of amount (1/8)[omega]^2[rho]r^2(3 + [sigma]),
+
+  (3) pressure along the circular filaments of amount
+  (1/8)[omega]^2[rho]r^2(1 + 3[sigma]),
+
+  (4) uniform tension in all directions at right angles to the axis of
+  amount (1/6)[omega]^2[rho](l^2 - 3z^2)[sigma](1 + [sigma])/(1 -
+  [sigma]).
+
+  The corresponding strains may be expressed as
+
+  (1) uniform extension of all filaments at right angles to the axis of
+  amount
+
+    1 - [sigma]
+    ----------- (1/8)[omega]^2[rho]a^2(3 + [sigma]),
+         E
+
+  (2) radial contraction of amount
+
+    1 - [sigma]^2
+    ------------- (3/8)[omega]^2[rho]r^2,
+          E
+
+  (3) contraction along the circular filaments of amount
+
+    1 - [sigma]^2
+    ------------- (1/8)[omega]^2[rho]r^2,
+          E
+
+  (4) extension of all filaments at right angles to the axis of amount
+
+    (1/E)(1/6)[omega]^2[rho][l^2 - (3_x)^2][sigma](1+[sigma]),
+
+  (5) contraction of the filaments normal to the plane of the disk of
+  amount
+
+    2[sigma]
+    -------- (1/8)[omega]^2[rho]a^2(3 + [sigma])
+       E
+
+       [sigma]
+     - ------- 1/2 [omega]^2[rho]r^2(1 + [sigma])
+          E
+
+       2[sigma]                                        (1 + [sigma])
+     + -------- (1/6)[omega]^2[rho](l^2 - 3z^2)[sigma] -------------.
+          E                                            (1 - [sigma])
+
+  The greatest extension is the circumferential extension near the
+  centre, and its amount is
+
+    (3 + [sigma])(1 - [sigma])                     [sigma](1 + [sigma])
+    -------------------------- [omega]^2[rho]a^2 + -------------------- [omega]^2[rho]l^2.
+                8E                                          6E
+
+  [Illustration: FIG. 32.]
+
+  The longitudinal contraction is required to make the plane faces of
+  the disk free from pressure, and the terms in l and z enable us to
+  avoid tangential traction on any cylindrical surface. The system of
+  stresses and strains thus expressed satisfies all the conditions,
+  except that there is a small radial tension on the bounding surface of
+  amount per unit area (1/6)[omega]^2[rho](l^2 - 3z^2)[sigma](1 +
+  [sigma])/(1 - [sigma]). The resultant of these tensions on any part of
+  the edge of the disk vanishes, and the stress in question is very
+  small in comparison with the other stresses involved when the disk is
+  thin; we may conclude that, for a thin disk, the expressions given
+  represent the actual condition at all points which are not very close
+  to the edge (cf. S 55). The effect to the longitudinal contraction is
+  that the plane faces become slightly concave (fig. 32).
+
+  81. The corresponding solution for a disk with a circular axle-hole
+  (radius b) will be obtained from that given in the last section by
+  superposing the following system of additional stresses:
+
+  (1) radial tension of amount (1/8)[omega]^2[rho]b^2(1 - a^2/r^2)(3 +
+  [sigma]),
+
+  (2) tension along the circular filaments of amount
+
+    (1/8)[omega]^2[rho]b^2(1 + a^2/r^2)(3 + [sigma]).
+
+  The corresponding additional strains are
+
+  (1) radial contraction of amount
+                 _                                _
+    3 + [sigma] |              a^2                 |
+    ----------- | (1 + [sigma])--- - (1 - [sigma]) | [omega]^2[rho]b^2,
+        8E      |_             r^2                _|
+
+  (2) extension along the circular filaments of amount
+                 _                               _
+    3 + [sigma] |             a^2                 |
+    ----------- |(1 + [sigma])--- + (1 - [sigma]) | [omega]^2[rho]b^2.
+        8E      |_            r^2                _|
+
+  (3) contraction of the filaments parallel to the axis of amount
+
+    [sigma](3 + [sigma])
+    -------------------- [omega]^2[rho]b^2.
+             4E
+
+  Again, the greatest extension is the circumferential extension at the
+  inner surface, and, when the hole is very small, its amount is nearly
+  double what it would be for a complete disk.
+
+  82. In the problem of the rotating shaft we have the following
+  stress-system:
+
+  (1) radial tension of amount
+
+    (1/8)[omega]^2[rho](a^2 - r^2)(3 - 2[sigma])/(1-[sigma]),
+
+  (2) circumferential tension of amount
+
+    (1/8)[omega]^2[rho]{(a^2(3 - 2[sigma])/(1-[sigma])
+      - r^2(1 + 2[sigma])/(1 - [sigma])},
+
+  (3) longitudinal tension of amount
+
+    1/4[omega]^2[rho](a^2 - 2r^2)[sigma]/(1 - [sigma]).
+
+  The resultant longitudinal tension at any normal section vanishes, and
+  the radial tension vanishes at the bounding surface; and thus the
+  expressions here given may be taken to represent the actual condition
+  at all points which are not very close to the ends of the shaft. The
+  contraction of the longitudinal filaments is uniform and equal to
+  1/2[omega]^2[rho]a^2[sigma]/E. The greatest extension in the rotating
+  shaft is the circumferential extension close to the axis, and its
+  amount is (1/8)[omega]^2[rho]a^2(3 - 5[sigma])/E(1 - [sigma]).
+
+  The value of any theory of the strength of long rotating shafts
+  founded on these formulae is diminished by the circumstance that at
+  sufficiently high speeds the shaft may tend to take up a curved form,
+  the straight form being unstable. The shaft is then said to _whirl_.
+  This occurs when the period of rotation of the shaft is very nearly
+  coincident with one of its periods of lateral vibration. The lowest
+  speed at which whirling can take place in a shaft of length l, freely
+  supported at its ends, is given by the formula
+
+    [omega]^2[rho] = 1/4Ea^2([pi]/l)^4.
+
+  As in S 61, this formula should not be applied unless the length of
+  the shaft is a considerable multiple of its diameter. It implies that
+  whirling is to be expected whenever [omega] approaches this critical
+  value.
+
+83. When the forces acting upon a spherical or cylindrical body are not
+radial, the problem becomes more complicated. In the case of the sphere
+deformed by any forces it has been completely solved, and the solution
+has been applied by Lord Kelvin and Sir G.H. Darwin to many interesting
+questions of cosmical physics. The nature of the stress produced in the
+interior of the earth by the weight of continents and mountains, the
+spheroidal figure of a rotating solid planet, the rigidity of the earth,
+are among the questions which have in this way been attacked. Darwin
+concluded from his investigation that, to support the weight of the
+existing continents and mountain ranges, the materials of which the
+earth is composed must, at great depths (1600 kilometres), have at least
+the strength of granite. Kelvin concluded from his investigation that
+the actual heights of the tides in the existing oceans can be accounted
+for only on the supposition that the interior of the earth is solid, and
+of rigidity nearly as great as, if not greater than, that of steel.
+
+  84. Some interesting problems relating to the strains produced in a
+  cylinder of finite length by forces distributed symmetrically round
+  the axis have been solved. The most important is that of a cylinder
+  crushed between parallel planes in contact with its plane ends. The
+  solution was applied to explain the discrepancies that have been
+  observed in different tests of crushing strength according as the ends
+  of the test specimen are or are not prevented from spreading. It was
+  applied also to explain the fact that in such tests small conical
+  pieces are sometimes cut out at the ends subjected to pressure.
+
+85. _Vibrations and Waves._--When a solid body is struck, or otherwise
+suddenly disturbed, it is thrown into a state of vibration. There always
+exist dissipative forces which tend to destroy the vibratory motion, one
+cause of the subsidence of the motion being the communication of energy
+to surrounding bodies. When these dissipative forces are disregarded, it
+is found that an elastic solid body is capable of vibrating in such a
+way that the motion of any particle is simple harmonic motion, all the
+particles completing their oscillations in the same period and being at
+any instant in the same phase, and the displacement of any selected one
+in any particular direction bearing a definite ratio to the displacement
+of an assigned one in an assigned direction. When a body is moving in
+this way it is said to be _vibrating in a normal mode_. For example,
+when a tightly stretched string of negligible flexural rigidity, such as
+a violin string may be taken to be, is fixed at the ends, and vibrates
+transversely in a normal mode, the displacements of all the particles
+have the same direction, and their magnitudes are proportional at any
+instant to the ordinates of a curve of sines. Every body possesses an
+infinite number of normal modes of vibration, and the _frequencies_ (or
+numbers of vibrations per second) that belong to the different modes
+form a sequence of increasing numbers. For the string, above referred
+to, the fundamental tone and the various overtones form an harmonic
+scale, that is to say, the frequencies of the normal modes of vibration
+are proportional to the integers 1, 2, 3, .... In all these modes except
+the first the string vibrates as if it were divided into a number of
+equal pieces, each having fixed ends; this number is in each case the
+integer defining the frequency. In general the normal modes of vibration
+of a body are distinguished one from another by the number and situation
+of the surfaces (or other _loci_) at which some characteristic
+displacement or traction vanishes. The problem of determining the normal
+modes and frequencies of free vibration of a body of definite size,
+shape and constitution, is a mathematical problem of a similar character
+to the problem of determining the state of stress in the body when
+subjected to given forces. The bodies which have been most studied are
+strings and thin bars, membranes, thin plates and shells, including
+bells, spheres and cylinders. Most of the results are of special
+importance in their bearing upon the theory of sound.
+
+  86. The most complete success has attended the efforts of
+  mathematicians to solve the problem of free vibrations for an
+  isotropic sphere. It appears that the modes of vibration fall into two
+  classes: one characterized by the absence of a radial component of
+  displacement, and the other by the absence of a radial component of
+  rotation (S 14). In each class there is a doubly infinite number of
+  modes. The displacement in any mode is determined in terms of a single
+  spherical harmonic function, so that there are modes of each class
+  corresponding to spherical harmonics of every integral degree; and for
+  each degree there is an infinite number of modes, differing from one
+  another in the number and position of the concentric spherical
+  surfaces at which some characteristic displacement vanishes. The most
+  interesting modes are those in which the sphere becomes slightly
+  spheroidal, being alternately prolate and oblate during the course of
+  a vibration; for these vibrations tend to be set up in a spherical
+  planet by tide-generating forces. In a sphere of the size of the
+  earth, supposed to be incompressible and as rigid as steel, the period
+  of these vibrations is 66 minutes.
+
+87. The theory of free vibrations has an important bearing upon the
+question of the strength of structures subjected to sudden blows or
+shocks. The stress and strain developed in a body by sudden applications
+of force may exceed considerably those which would be produced by a
+gradual application of the same forces. Hence there arises the general
+question of _dynamical resistance_, or of the resistance of a body to
+forces applied so quickly that the inertia of the body comes sensibly
+into play. In regard to this question we have two chief theoretical
+results. The first is that the strain produced by a force suddenly
+applied may be as much as twice the statical strain, that is to say, as
+the strain which would be produced by the same force when the body is
+held in equilibrium under its action; the second is that the sudden
+reversal of the force may produce a strain three times as great as the
+statical strain. These results point to the importance of specially
+strengthening the parts of any machine (e.g. screw propeller shafts)
+which are subject to sudden applications or reversals of load. The
+theoretical limits of twice, or three times, the statical strain are not
+in general attained. For example, if a thin bar hanging vertically from
+its upper end is suddenly loaded at its lower end with a weight equal to
+its own weight, the greatest dynamical strain bears to the greatest
+statical strain the ratio 1.63 : 1; when the attached weight is four
+times the weight of the bar the ratio becomes 1.84 : 1. The method by
+which the result just mentioned is reached has recently been applied to
+the question of the breaking of winding ropes used in mines. It appeared
+that, in order to bring the results into harmony with the observed
+facts, the strain in the supports must be taken into account as well as
+the strain in the rope (J. Perry, _Phil. Mag._, 1906 (vi.), vol. ii.).
+
+88. The immediate effect of a blow or shock, locally applied to a body,
+is the generation of a wave which travels through the body from the
+locality first affected. The question of the propagation of waves
+through an elastic solid body is historically of very great importance;
+for the first really successful efforts to construct a theory of
+elasticity (those of S.D. Poisson, A.L. Cauchy and G. Green) were
+prompted, at least in part, by Fresnel's theory of the propagation of
+light by transverse vibrations. For many years the luminiferous medium
+was identified with the isotropic solid of the theory of elasticity.
+Poisson showed that a disturbance communicated to the body gives rise to
+two waves which are propagated through it with different velocities; and
+Sir G.G. Stokes afterwards showed that the quicker wave is a wave of
+irrotational dilatation, and the slower wave is a wave of rotational
+distortion accompanied by no change of volume. The velocities of the two
+waves in a solid of density [rho] are [root]{([lambda] + 2[mu])/[rho]}
+and [root]([mu]/[rho]), [lambda] and [mu] being the constants so denoted
+in S 26. When the surface of the body is free from traction, the waves
+on reaching the surface are reflected; and thus after a little time the
+body would, if there were no dissipative forces, be in a very complex
+state of motion due to multitudes of waves passing to and fro through
+it. This state can be expressed as a state of vibration, in which the
+motions belonging to the various normal modes (S 85) are superposed,
+each with an appropriate amplitude and phase. The waves of dilatation
+and distortion do not, however, give rise to different modes of
+vibration, as was at one time supposed, but any mode of vibration in
+general involves both dilatation and rotation. There are exceptional
+results for solids of revolution; such solids possess normal modes of
+vibration which involve no dilatation. The existence of a boundary to
+the solid body has another effect, besides reflexion, upon the
+propagation of waves. Lord Rayleigh has shown that any disturbance
+originating at the surface gives rise to waves which travel away over
+the surface as well as to waves which travel through the interior; and
+any internal disturbance, on reaching the surface, also gives rise to
+such superficial waves. The velocity of the superficial waves is a
+little less than that of the waves of distortion: 0.9554
+[root]([mu]/[rho]) when the material is incompressible
+0.9194[root]([mu]/[rho]) when the Poisson's ratio belonging to the
+material is 1/4.
+
+89. These results have an application to the propagation of earthquake
+shocks (see also EARTHQUAKE). An internal disturbance should, if the
+earth can be regarded as solid, give rise to three wave-motions: two
+propagated through the interior of the earth with different velocities,
+and a third propagated over the surface. The results of seismographic
+observations have independently led to the recognition of three phases
+of the recorded vibrations: a set of "preliminary tremors" which are
+received at different stations at such times as to show that they are
+transmitted directly through the interior of the earth with a velocity
+of about 10 km. per second, a second set of preliminary tremors which
+are received at different stations at such times as to show that they
+are transmitted directly through the earth with a velocity of about 5
+km. per second, and a "main shock," or set of large vibrations, which
+becomes sensible at different stations at such times as to show that a
+wave is transmitted over the surface of the earth with a velocity of
+about 3 km. per second. These results can be interpreted if we assume
+that the earth is a solid body the greater part of which is practically
+homogeneous, with high values for the rigidity and the resistance to
+compression, while the superficial portions have lower values for these
+quantities. The rigidity of the central portion would be about
+(1.4)10^12 dynes per square cm., which is considerably greater than that
+of steel, and the resistance to compression would be about (3.8)10^12
+dynes per square cm. which is much greater than that of any known
+material. The high value of the resistance to compression is not
+surprising when account is taken of the great pressures, due to
+gravitation, which must exist in the interior of the earth. The high
+value of the rigidity can be regarded as a confirmation of Lord Kelvin's
+estimate founded on tidal observations (S 83).
+
+90. _Strain produced by Heat._--The mathematical theory of elasticity as
+at present developed takes no account of the strain which is produced in
+a body by unequal heating. It appears to be impossible in the present
+state of knowledge to form as in S 39 a system of differential equations
+to determine both the stress and the temperature at any point of a solid
+body the temperature of which is liable to variation. In the cases of
+isothermal and adiabatic changes, that is to say, when the body is
+slowly strained without variation of temperature, and also when the
+changes are effected so rapidly that there is no gain or loss of heat by
+any element, the internal energy of the body is sufficiently expressed
+by the strain-energy-function (SS 27, 30). Thus states of equilibrium
+and of rapid vibration can be determined by the theory that has been
+explained above. In regard to thermal effects we can obtain some
+indications from general thermodynamic theory. The following passages
+extracted from the article "Elasticity" contributed to the 9th edition
+of the _Encyclopaedia Britannica_ by Sir W. Thomson (Lord Kelvin)
+illustrate the nature of these indications:--"From thermodynamic theory
+it is concluded that cold is produced whenever a solid is strained by
+opposing, and heat when it is strained by yielding to, any elastic force
+of its own, the strength of which would diminish if the temperature were
+raised; but that, on the contrary, heat is produced when a solid is
+strained against, and cold when it is strained by yielding to, any
+elastic force of its own, the strength of which would increase if the
+temperature were raised. When the strain is a condensation or
+dilatation, uniform in all directions, a fluid may be included in the
+statement. Hence the following propositions:--
+
+"(1) A cubical compression of any elastic fluid or solid in an ordinary
+condition causes an evolution of heat; but, on the contrary, a cubical
+compression produces cold in any substance, solid or fluid, in such an
+abnormal state that it would contract if heated while kept under
+constant pressure. Water below its temperature (3.9 deg. Cent.) of
+maximum density is a familiar instance.
+
+"(2) If a wire already twisted be suddenly twisted further, always,
+however, within its limits of elasticity, cold will be produced; and if
+it be allowed suddenly to untwist, heat will be evolved from itself
+(besides heat generated externally by any work allowed to be wasted,
+which it does in untwisting). It is assumed that the torsional rigidity
+of the wire is diminished by an elevation of temperature, as the writer
+of this article had found it to be for copper, iron, platinum and other
+metals.
+
+"(3) A spiral spring suddenly drawn out will become lower in
+temperature, and will rise in temperature when suddenly allowed to draw
+in. [This result has been experimentally verified by Joule
+('Thermodynamic Properties of Solids,' _Phil. Trans._, 1858) and the
+amount of the effect found to agree with that calculated, according to
+the preceding thermodynamic theory, from the amount of the weakening of
+the spring which he found by experiment.]
+
+"(4) A bar or rod or wire of any substance with or without a weight hung
+on it, or experiencing any degree of end thrust, to begin with, becomes
+cooled if suddenly elongated by end pull or by diminution of end thrust,
+and warmed if suddenly shortened by end thrust or by diminution of end
+pull; except abnormal cases in which with constant end pull or end
+thrust elevation of temperature produces shortening; in every such case
+pull or diminished thrust produces elevation of temperature, thrust or
+diminished pull lowering of temperature.
+
+"(5) An india-rubber band suddenly drawn out (within its limits of
+elasticity) becomes warmer; and when allowed to contract, it becomes
+colder. Any one may easily verify this curious property by placing an
+india-rubber band in slight contact with the edges of the lips, then
+suddenly extending it--it becomes very perceptibly warmer: hold it for
+some time stretched nearly to breaking, and then suddenly allow it to
+shrink--it becomes quite startlingly colder, the cooling effect being
+sensible not merely to the lips but to the fingers holding the band. The
+first published statement of this curious observation is due to J. Gough
+(_Mem. Lit. Phil. Soc. Manchester_, 2nd series, vol. i. p. 288), quoted
+by Joule in his paper on 'Thermodynamic Properties of Solids' (cited
+above). The thermodynamic conclusion from it is that an india-rubber
+band, stretched by a constant weight of sufficient amount hung on it,
+must, when heated, pull up the weight, and, when cooled, allow the
+weight to descend: this Gough, independently of thermodynamic theory,
+had found to be actually the case. The experiment any one can make with
+the greatest ease by hanging a few pounds weight on a common
+india-rubber band, and taking a red-hot coal in a pair of tongs, or a
+red-hot poker, and moving it up and down close to the band. The way in
+which the weight rises when the red-hot body is near, and falls when it
+is removed, is quite startling. Joule experimented on the amount of
+shrinking per degree of elevation of temperature, with different weights
+hung on a band of vulcanized india-rubber, and found that they closely
+agreed with the amounts calculated by Thomson's theory from the heating
+effects of pull, and cooling effects of ceasing to pull, which he had
+observed in the same piece of india-rubber."
+
+91. _Initial Stress._--It has been pointed out above (S 20) that the
+"unstressed" state, which serves as a zero of reckoning for strains and
+stresses is never actually attained, although the strain (measured from
+this state), which exists in a body to be subjected to experiment, may
+be very slight. This is the case when the "initial stress," or the
+stress existing before the experiment, is small in comparison with the
+stress developed during the experiment, and the limit of linear
+elasticity (S 32) is not exceeded. The existence of initial stress has
+been correlated above with the existence of body forces such as the
+force of gravity, but it is not necessarily dependent upon such forces.
+A sheet of metal rolled into a cylinder, and soldered to maintain the
+tubular shape, must be in a state of considerable initial stress quite
+apart from the action of gravity. Initial stress is utilized in many
+manufacturing processes, as, for example, in the construction of
+ordnance, referred to in S 79, in the winding of golf balls by means of
+india-rubber in a state of high tension (see the report of the case _The
+Haskell Golf Ball Company_ v. _Hutchinson & Main_ in _The Times_ of
+March 1, 1906). In the case of a body of ordinary dimensions it is such
+internal stress as this which is especially meant by the phrase
+"initial stress." Such a body, when in such a state of internal stress,
+is sometimes described as "self-strained." It would be better described
+as "self-stressed." The somewhat anomalous behaviour of cast iron has
+been supposed to be due to the existence within the metal of initial
+stress. As the metal cools, the outer layers cool more rapidly than the
+inner, and thus the state of initial stress is produced. When cast iron
+is tested for tensile strength, it shows at first no sensible range
+either of perfect elasticity or of linear elasticity; but after it has
+been loaded and unloaded several times its behaviour begins to be more
+nearly like that of wrought iron or steel. The first tests probably
+diminish the initial stress.
+
+  92. From a mathematical point of view the existence of initial stress
+  in a body which is "self-stressed" arises from the fact that the
+  equations of equilibrium of a body free from body forces or surface
+  tractions, viz. the equations of the type
+
+    dPX_x   dPX_y   dPZ_x
+    ----- + ----- + ----- = 0,
+     dPx     dPy     dPz
+
+  possess solutions which differ from zero. If, in fact, [phi]1, [phi]2,
+  [phi]3 denote any arbitrary functions of x, y, z, the equations are
+  satisfied by putting
+
+          dP^2[phi]3   dP^2[phi]2               dP^2[phi]1
+    X_x = ---------- + ----------, ..., Y_z = - ----------, ...;
+             dPy^2        dPz                     dPydPz
+
+  and it is clear that the functions [phi]1, [phi]2, [phi]3 can be
+  adjusted in an infinite number of ways so that the bounding surface of
+  the body may be free from traction.
+
+93. Initial stress due to body forces becomes most important in the case
+of a gravitating planet. Within the earth the stress that arises from
+the mutual gravitation of the parts is very great. If we assumed the
+earth to be an elastic solid body with moduluses of elasticity no
+greater than those of steel, the strain (measured from the unstressed
+state) which would correspond to the stress would be much too great to
+be calculated by the ordinary methods of the theory of elasticity (S
+75). We require therefore some other method of taking account of the
+initial stress. In many investigations, for example those of Lord Kelvin
+and Sir G.H. Darwin referred to in S 83, the difficulty is turned by
+assuming that the material may be treated as practically incompressible;
+but such investigations are to some extent incomplete, so long as the
+corrections due to a finite, even though high, resistance to compression
+remain unknown. In other investigations, such as those relating to the
+propagation of earthquake shocks and to gravitational instability, the
+possibility of compression is an essential element of the problem. By
+gravitational instability is meant the tendency of gravitating matter to
+condense into nuclei when slightly disturbed from a state of uniform
+diffusion; this tendency has been shown by J.H. Jeans (_Phil. Trans_. A.
+201, 1903) to have exerted an important influence upon the course of
+evolution of the solar system. For the treatment of such questions Lord
+Rayleigh (_Proc. R. Soc. London_, A. 77, 1906) has advocated a method
+which amounts to assuming that the initial stress is hydrostatic
+pressure, and that the actual state of stress is to be obtained by
+superposing upon this initial stress a stress related to the state of
+strain (measured from the initial state) by the same formulae as hold
+for an elastic solid body free from initial stress. The development of
+this method is likely to lead to results of great interest.
+
+  AUTHORITIES.--In regard to the analysis requisite to prove the results
+  set forth above, reference may be made to A.E.H. Love, _Treatise on
+  the Mathematical Theory of Elasticity_ (2nd ed., Cambridge, 1906),
+  where citations of the original authorities will also be found. The
+  following treatises may be mentioned: Navier, _Resume des lecons sur
+  l'application de la mecanique_ (3rd ed., with notes by Saint-Venant,
+  Paris, 1864); G. Lame, _Lecons sur la theorie mathematique de
+  l'elasticite des corps solides_ (Paris, 1852); A. Clebsch, _Theorie
+  der Elasticitat fester Korper_ (Leipzig, 1862; French translation with
+  notes by Saint-Venant, Paris, 1883); F. Neumann, _Vorlesungen uber die
+  Theorie der Elasticitat_ (Leipzig, 1885); Thomson and Tait, _Natural
+  Philosophy_ (Cambridge, 1879, 1883); Todhunter and Pearson, _History
+  of the Elasticity and Strength of Materials_ (Cambridge, 1886-1893).
+  The article "Elasticity" by Sir W. Thomson (Lord Kelvin) in 9th ed. of
+  _Encyc. Brit_. (reprinted in his _Mathematical and Physical Papers_,
+  iii., Cambridge, 1890) is especially valuable, not only for the
+  exposition of the theory and its practical applications, but also for
+  the tables of physical constants which are there given.
+       (A. E. H. L.)
+
+
+FOOTNOTES:
+
+  [1] The sign of M is shown by the arrow-heads in fig. 19, for which,
+    with y downwards,
+
+         d^2y
+      EI ---- + M = 0.
+         dx^2
+
+  [2] The figure is drawn for a case where the bending moment has the
+    same sign throughout.
+
+  [3] M0 is taken to have, as it obviously has, the opposite sense to
+    that shown in fig. 19.
+
+  [4] The line joining the points of contact must be normal to the
+    planes.
+
+
+
+
+ELATERITE, also termed ELASTIC BITUMEN and MINERAL CAOUTCHOUC, a mineral
+hydrocarbon, which occurs at Castleton in Derbyshire, in the lead mines
+of Odin and elsewhere. It varies somewhat in consistency, being
+sometimes soft, elastic and sticky; often closely resembling
+india-rubber; and occasionally hard and brittle. It is usually dark
+brown in colour and slightly translucent. A substance of similar
+physical character is found in the Coorong district of South Australia,
+and is hence termed coorongite, but Prof. Ralph Tate considers this to
+be a vegetable product.
+
+
+
+
+ELATERIUM, a drug consisting of a sediment deposited by the juice of the
+fruit of _Ecballium Elaterium_, the squirting cucumber, a native of the
+Mediterranean region. The plant, which is a member of the natural order
+Cucurbitaceae, resembles the vegetable marrow in its growth. The fruit
+resembles a small cucumber, and when ripe is highly turgid, and
+separates almost at a touch from the fruit stalk. The end of the stalk
+forms a stopper, on the removal of which the fluid contents of the
+fruit, together with the seeds, are squirted through the aperture by the
+sudden contraction of the wall of the fruit. To prepare the drug the
+fruit is sliced lengthwise and slightly pressed; the greenish and
+slightly turbid juice thus obtained is strained and set aside; and the
+deposit of elaterium formed after a few hours is collected on a linen
+filter, rapidly drained, and dried on porous tiles at a gentle heat.
+Elaterium is met with in commerce in light, thin, friable, flat or
+slightly incurved opaque cakes, of a greyish-green colour, bitter taste
+and tea-like smell.
+
+The drug is soluble in alcohol, but insoluble in water and ether. The
+official dose is 1/10-1/2 grain, and the British pharmacopeia directs
+that the drug is to contain from 20 to 25% of the active principle
+elaterinum or elaterin. A resin in the natural product aids its action.
+Elaterin is extracted from elaterium by chloroform and then precipitated
+by ether. It has the formula C_20H_28O5. It forms colourless scales
+which have a bitter taste, but it is highly inadvisable to taste either
+this substance or elaterium. Its dose is 1/40-1/10 grain, and the
+British pharmacopeia contains a useful preparation, the Pulvis Elaterini
+Compositus, which contains one part of the active principle in forty.
+
+The action of this drug resembles that of the saline aperients, but is
+much more powerful. It is the most active hydragogue purgative known,
+causing also much depression and violent griping. When injected
+subcutaneously it is inert, as its action is entirely dependent upon its
+admixture with the bile. The drug is undoubtedly valuable in cases of
+dropsy and Bright's disease, and also in cases of cerebral haemorrhage,
+threatened or present. It must not be used except in urgent cases, and
+must invariably be employed with the utmost care, especially if the
+state of the heart be unsatisfactory.
+
+
+
+
+ELBA (Gr. [Greek: Aithalia]; Lat. _Ilva_), an island off the W. coast of
+Italy, belonging to the province of Leghorn, from which it is 45 m. S.,
+and 7 m. S.W. of Piombino, the nearest point of the mainland. Pop.
+(1901) 25,043 (including Pianosa). It is about 19 m. long, 6-1/2 m.
+broad, and 140 sq. m. in area; and its highest point is 3340 ft. (Monte
+Capanne). It forms, like Giglio and Monte Cristo, part of a sunken
+mountain range extending towards Corsica and Sardinia.
+
+The oldest rocks of Elba consist of schist and serpentine which in the
+eastern part of the island are overlaid by beds containing Silurian and
+Devonian fossils. The Permian may be represented, but the Trias is
+absent, and in general the older Palaeozoic rocks are overlaid directly
+by the Rhaetic and Lias. The Liassic beds are often metamorphosed and
+the limestones contain garnet and wollastonite. The next geological
+formation which is represented is the Eocene, consisting of nummulitic
+limestone, sandstone and schist. The Miocene and Pliocene are absent.
+The most remarkable feature in the geology of Elba is the extent of the
+granitic and ophiolitic eruptions of the Tertiary period. Serpentines,
+peridotites and diabases are interstratified with the Eocene deposits.
+The granite, which is intruded through the Eocene beds, is associated
+with a pegmatite containing tourmaline and cassiterite. The celebrated
+iron ore of Elba is of Tertiary age and occurs indifferently in all the
+older rocks. The deposits are superficial, resulting from the opening
+out of veins at the surface, and consist chiefly of haematite. These
+ores were worked by the ancients, but so inefficiently that their
+spoil-heaps can be smelted again with profit. This process is now gone
+through on the island itself. The granite was also quarried by the
+Romans, but is not now much worked.
+
+Parts of the island are fertile, and the cultivation of vines, and the
+tunny and sardine fishery, also give employment to a part of the
+population. The capital of the island is Portoferraio--pop. (1901)
+5987--in the centre of the N. coast, enclosed by an amphitheatre of
+lofty mountains, the slopes of which are covered with villas and
+gardens. This is the best harbour, the ancient _Portus Argous_. The town
+was built and fortified by Cosimo I. in 1548, who called it Cosmopolis.
+Above the harbour, between the forts Stella and Falcone, is the palace
+of Napoleon I., and 4 m. to the S.W. is his villa; while on the N. slope
+of Monte Capanne is another of his country houses. The other villages in
+the island are Campo nell' Elba, on the S. near the W. end, Marciana and
+Marciana Marina on the N. of the island near the W. extremity, Porto
+Longone, on the E. coast, with picturesque Spanish fortifications,
+constructed in 1602 by Philip III.; Rio dell' Elba and Rio Marina, both
+on the E. side of the island, in the mining district. At Le Grotte,
+between Portoferraio and Rio dell' Elba, and at Capo Castello, on the
+N.E. of the island, are ruins of Roman date.
+
+Elba was famous for its mines in early times, and the smelting furnaces
+gave it its Greek name of [Greek: A'thalia] ("soot island"). In Roman
+times, and until 1900, however, owing to lack of fuel, the smelting was
+done on the mainland. In 453 B.C. Elba was devastated by a Syracusan
+squadron. From the 11th to the 14th century it belonged to Pisa, and in
+1399 came under the dukes of Piombino. In 1548 it was ceded by them to
+Cosimo I. of Florence. In 1596 Porto Longone was taken by Philip III. of
+Spain, and retained until 1709, when it was ceded to Naples. In 1802 the
+island was given to France by the peace of Amiens. On Napoleon's
+deposition, the island was ceded to him with full sovereign rights, and
+he resided there from the 5th of May 1814 to the 26th of February 1815.
+After his fall it was restored to Tuscany, and passed with it to Italy
+in 1860.
+
+  See Sir R. Colt Hoare, _A Tour through the Island of Elba_ (London,
+  1814).
+
+
+
+
+ELBE (the _Albis_ of the Romans and the _Labe_ of the Czechs), a river
+of Germany, which rises in Bohemia not far from the frontiers of
+Silesia, on the southern side of the Riesengebirge, at an altitude of
+about 4600 ft. Of the numerous small streams (Seifen or Flessen as they
+are named in the district) whose confluent waters compose the infant
+river, the most important are the Weisswasser, or White Water, and the
+Elbseifen, which is formed in the same neighbourhood, but at a little
+lower elevation. After plunging down the 140 ft. of the Elbfall, the
+latter stream unites with the steep torrential Weisswasser at
+Madelstegbaude, at an altitude of 2230 ft., and thereafter the united
+stream of the Elbe pursues a southerly course, emerging from the
+mountain glens at Hohenelbe (1495 ft.), and continuing on at a soberer
+pace to Pardubitz, where it turns sharply to the west, and at Kolin (730
+ft.), some 27 m. farther on, bends gradually towards the north-west. A
+little above Brandeis it picks up the Iser, which, like itself, comes
+down from the Riesengebirge, and at Melnik it has its stream more than
+doubled in volume by the Moldau, a river which winds northwards through
+the heart of Bohemia in a sinuous, trough-like channel carved through
+the plateaux. Some miles lower down, at Leitmeritz (433 ft.), the waters
+of the Elbe are tinted by the reddish Eger, a stream which drains the
+southern slopes of the Erzgebirge. Thus augmented, and swollen into a
+stream 140 yds. wide, the Elbe carves a path through the basaltic mass
+of the Mittelgebirge, churning its way through a deep, narrow rocky
+gorge. Then the river winds through the fantastically sculptured
+sandstone mountains of the "Saxon Switzerland," washing successively the
+feet of the lofty Lilienstein (932 ft. above the Elbe), the scene of one
+of Frederick the Great's military exploits in the Seven Years' War,
+Konigstein (797 ft. above the Elbe), where in times of war Saxony has
+more than once stored her national purse for security, and the pinnacled
+rocky wall of the Bastei, towering 650 ft. above the surface of the
+stream. Shortly after crossing the Bohemian-Saxon frontier, and whilst
+still struggling through the sandstone defiles, the stream assumes a
+north-westerly direction, which on the whole it preserves right away to
+the North Sea. At Pirna the Elbe leaves behind it the stress and turmoil
+of the Saxon Switzerland, rolls through Dresden, with its noble river
+terraces, and finally, beyond Meissen, enters on its long journey across
+the North German plain, touching Torgau, Wittenberg, Magdeburg,
+Wittenberge, Hamburg, Harburg and Altona on the way, and gathering into
+itself the waters of the Mulde and Saale from the left, and those of the
+Schwarze Elster, Havel and Elde from the right. Eight miles above
+Hamburg the stream divides into the Norder (or Hamburg) Elbe and the
+Suder (or Harburg) Elbe, which are linked together by several
+cross-channels, and embrace in their arms the large island of
+Wilhelmsburg and some smaller ones. But by the time the river reaches
+Blankenese, 7 m. below Hamburg, all these anastomosing branches have
+been reunited, and the Elbe, with a width of 4 to 9 m. between bank and
+bank, travels on between the green marshes of Holstein and Hanover until
+it becomes merged in the North Sea off Cuxhaven. At Kolin the width is
+about 100 ft., at the mouth of the Moldau about 300, at Dresden 960, and
+at Magdeburg over 1000. From Dresden to the sea the river has a total
+fall of only 280 ft., although the distance is about 430 m. For the 75
+m. between Hamburg and the sea the fall is only 3-1/4 ft. One consequence
+of this is that the bed of the river just below Hamburg is obstructed by
+a bar, and still lower down is choked with sandbanks, so that navigation
+is confined to a relatively narrow channel down the middle of the
+stream. But unremitting efforts have been made to maintain a sufficient
+fairway up to Hamburg (q.v.). The tide advances as far as Geesthacht, a
+little more than 100 m. from the sea. The river is navigable as far as
+Melnik, that is, the confluence of the Moldau, a distance of 525 m., of
+which 67 are in Bohemia. Its total length is 725 m., of which 190 are in
+Bohemia, 77 in the kingdom of Saxony, and 350 in Prussia, the remaining
+108 being in Hamburg and other states of Germany. The area of the
+drainage basin is estimated at 56,000 sq. m.
+
+_Navigation._--Since 1842, but more especially since 1871, improvements
+have been made in the navigability of the Elbe by all the states which
+border upon its banks. As a result of these labours there is now in the
+Bohemian portion of the river a minimum depth of 2 ft. 8 in., whilst
+from the Bohemian frontier down to Magdeburg the minimum depth is 3 ft.,
+and from Magdeburg to Hamburg, 3 ft. 10 in. In 1896 and 1897 Prussia and
+Hamburg signed covenants whereby two channels are to be kept open to a
+depth of 9-3/4 ft., a width of 656 ft., and a length of 550 yds. between
+Bunthaus and Ortkathen, just above the bifurcation of the Norder Elbe
+and the Suder Elbe. In 1869 the maximum burden of the vessels which were
+able to ply on the upper Elbe was 250 tons; but in 1899 it was increased
+to 800 tons. The large towns through which the river flows have vied
+with one another in building harbours, providing shipping accommodation,
+and furnishing other facilities for the efficient navigation of the
+Elbe. In this respect the greatest efforts have naturally been made by
+Hamburg; but Magdeburg, Dresden, Meissen, Riesa, Tetschen, Aussig and
+other places have all done their relative shares, Magdeburg, for
+instance, providing a commercial harbour and a winter harbour. In spite,
+however, of all that has been done, the Elbe remains subject to serious
+inundations at periodic intervals. Among the worst floods were those of
+the years 1774, 1799, 1815, 1830, 1845, 1862, 1890 and 1909. The growth
+of traffic up and down the Elbe has of late years become very
+considerable. A towing chain, laid in the bed of the river, extends from
+Hamburg to Aussig, and by this means, as by paddle-tug haulage, large
+barges are brought from the port of Hamburg into the heart of Bohemia.
+The fleet of steamers and barges navigating the Elbe is in point of fact
+greater than on any other German river. In addition to goods thus
+conveyed, enormous quantities of timber are floated down the Elbe; the
+weight of the rafts passing the station of Schandau on the Saxon
+Bohemian frontier amounting in 1901 to 333,000 tons.
+
+A vast amount of traffic is directed to Berlin, by means of the
+Havel-Spree system of canals, to the Thuringian states and the Prussian
+province of Saxony, to the kingdom of Saxony and Bohemia, and to the
+various riverine states and provinces of the lower and middle Elbe. The
+passenger traffic, which is in the hands of the Sachsisch-Bohmische
+Dampfschifffahrtsgesellschaft is limited to Bohemia and Saxony, steamers
+plying up and down the stream from Dresden to Melnik, occasionally
+continuing the journey up the Moldau to Prague, and down the river as
+far as Riesa, near the northern frontier of Saxony, and on the average
+1-1/2 million passengers are conveyed.
+
+In 1877-1879, and again in 1888-1895, some 100 m. of canal were dug, 5
+to 6-1/2 ft. deep and of various widths, for the purpose of connecting
+the Elbe, through the Havel and the Spree, with the system of the Oder.
+The most noteworthy of these connexions are the Elbe Canal (14-1/4 m.
+long), the Reek Canal (9-1/2 m.), the Rudersdorfer Gewasser (11-1/2 m.),
+the Rheinsberger Canal (11-1/4 m.), and the Sacrow-Paretzer Canal (10
+m.), besides which the Spree has been canalized for a distance of 28 m.,
+and the Elbe for a distance of 70 m. Since 1896 great improvements have
+been made in the Moldau and the Bohemian Elbe, with the view of
+facilitating communication between Prague and the middle of Bohemia
+generally on the one hand, and the middle and lower reaches of the Elbe
+on the other. In the year named a special commission was appointed for
+the regulation of the Moldau and Elbe between Prague and Aussig, at a
+cost estimated at about L1,000,000, of which sum two-thirds were to be
+borne by the Austrian empire and one-third by the kingdom of Bohemia.
+The regulation is effected by locks and movable dams, the latter so
+designed that in times of flood or frost they can be dropped flat on the
+bottom of the river. In 1901 the Austrian government laid before the
+Reichsrat a canal bill, with proposals for works estimated to take
+twenty years to complete, and including the construction of a canal
+between the Oder, starting at Prerau, and the upper Elbe at Pardubitz,
+and for the canalization of the Elbe from Pardubitz to Melnik (see
+AUSTRIA: _Waterways_). In 1900 Lubeck was put into direct communication
+with the Elbe at Lauenburg by the opening of the Elbe-Trave Canal, 42 m.
+in length, and constructed at a cost of L1,177,700, of which the state
+of Lubeck contributed L802,700, and the kingdom of Prussia L375,000. The
+canal has been made 72 ft. wide at the bottom, 105 to 126 ft. wide at
+the top, has a minimum depth of 8-1/6 ft., and is equipped with seven
+locks, each 262-1/2 ft. long and 39-1/4 ft. wide. It is thus able to
+accommodate vessels up to 800 tons burden; and the passage from Lubeck
+to Lauenburg occupies 18 to 21 hours. In the first year of its being
+open (June 1900 to June 1901) a total of 115,000 tons passed through the
+canal.[1] A gigantic project has also been put forward for providing
+water communication between the Rhine and the Elbe, and so with the
+Oder, through the heart of Germany. This scheme is known as the Midland
+Canal. Another canal has been projected for connecting Kiel with the
+Elbe by means of a canal trained through the Plon Lakes.
+
+_Bridges._--The Elbe is crossed by numerous bridges, as at Koniggratz,
+Pardubitz, Kolin, Leitmeritz, Tetschen, Schandau, Pirna, Dresden,
+Meissen, Torgau, Wittenberg, Rosslau, Barby, Magdeburg, Rathenow,
+Wittenberge, Domitz, Lauenburg, and Hamburg and Harburg. At all these
+places there are railway bridges, and nearly all, but more especially
+those in Bohemia, Saxony and the middle course of the river--these last
+on the main lines between Berlin and the west and south-west of the
+empire--possess a greater or less strategic value. At Leitmeritz there
+is an iron trellis bridge, 600 yds long. Dresden has four bridges, and
+there is a fifth bridge at Loschwitz, about 3 m. above the city. Meissen
+has a railway bridge, in addition to an old road bridge. Magdeburg is
+one of the most important railway centres in northern Germany; and the
+Elbe, besides being bridged--it divides there into three arms--several
+times for vehicular traffic, is also spanned by two fine railway
+bridges. At both Hamburg and Harburg, again, there are handsome railway
+bridges, the one (1868-1873 and 1894) crossing the northern Elbe, and
+the other (1900) the southern Elbe; and the former arm is also crossed
+by a fine triple-arched bridge (1888) for vehicular traffic.
+
+_Fish._--The river is well stocked with fish, both salt-water and
+fresh-water species being found in its waters, and several varieties of
+fresh-water fish in its tributaries. The kinds of greatest economic
+value are sturgeon, shad, salmon, lampreys, eels, pike and whiting.
+
+_Tolls._--In the days of the old German empire no fewer than thirty-five
+different tolls were levied between Melnik and Hamburg, to say nothing
+of the special dues and privileged exactions of various riparian owners
+and political authorities. After these had been _de facto_, though not
+_de jure_, in abeyance during the period of the Napoleonic wars, a
+commission of the various Elbe states met and drew up a scheme for their
+regulation, and the scheme, embodied in the Elbe Navigation Acts, came
+into force in 1822. By this a definite number of tolls, at fixed rates,
+was substituted for the often arbitrary tolls which had been exacted
+previously. Still further relief was afforded in 1844 and in 1850, on
+the latter occasion by the abolition of all tolls between Melnik and the
+Saxon frontier. But the number of tolls was only reduced to one, levied
+at Wittenberge, in 1863, about one year after Hanover was induced to
+give up the Stade or Brunsbuttel toll in return for a compensation of
+2,857,340 thalers. Finally, in 1870, 1,000,000 thalers were paid to
+Mecklenburg and 85,000 thalers to Anhalt, which thereupon abandoned all
+claims to levy tolls upon the Elbe shipping, and thus navigation on the
+river became at last entirely free.
+
+_History._--The Elbe cannot rival the Rhine in the picturesqueness of
+the scenery it travels through, nor in the glamour which its romantic
+and legendary associations exercise over the imagination. But it
+possesses much to charm the eye in the deep glens of the Riesengebirge,
+amid which its sources spring, and in the bizarre rock-carving of the
+Saxon Switzerland. It has been indirectly or directly associated with
+many stirring events in the history of the German peoples. In its lower
+course, whatever is worthy of record clusters round the historical
+vicissitudes of Hamburg--its early prominence as a missionary centre
+(Ansgar) and as a bulwark against Slav and marauding Northman, its
+commercial prosperity as a leading member of the Hanseatic League, and
+its sufferings during the Napoleonic wars, especially at the hands of
+the ruthless Davout. The bridge over the river at Dessau recalls the hot
+assaults of the _condottiere_ Ernst von Mansfeld in April 1626, and his
+repulse by the crafty generalship of Wallenstein. But three years later
+this imperious leader was checked by the heroic resistance of the
+"Maiden" fortress of Magdeburg; though two years later still she lost
+her reputation, and suffered unspeakable horrors at the hands of Tilly's
+lawless and unlicensed soldiery. Muhlberg, just outside the Saxon
+frontier, is the place where Charles V. asserted his imperial authority
+over the Protestant elector of Saxony, John Frederick, the Magnanimous
+or Unfortunate, in 1547. Dresden, Aussig and Leitmeritz are all
+reminiscent of the fierce battles of the Hussite wars, and the last
+named of the Thirty Years' War. But the chief historical associations of
+the upper (i.e. the Saxon and Bohemian) Elbe are those which belong to
+the Seven Years' War, and the struggle of the great Frederick of Prussia
+against the power of Austria and her allies. At Pirna (and Lilienstein)
+in 1756 he caught the entire Saxon army in his fowler's net, after
+driving back at Lobositz the Austrian forces which were hastening to
+their assistance; but only nine months later he lost his reputation for
+"invincibility" by his crushing defeat at Kolin, where the great highway
+from Vienna to Dresden crosses the Elbe. Not many miles distant, higher
+up the stream, another decisive battle was fought between the same
+national antagonists, but with a contrary result, on the memorable 3rd
+of July 1866.
+
+  See M. Buchheister, "Die Elbe u. der Hafen von Hamburg," in _Mitteil.
+  d. Geog. Gesellsch. in Hamburg_ (1899), vol. xv. pp. 131-188; V. Kurs,
+  "Die kunstlichen Wasserstrassen des deutschen Reichs," in _Geog.
+  Zeitschrift_ (1898), pp. 601-617; and (the official) _Der Elbstrom_
+  (1900); B. Weissenborn, _Die Elbzolle und Elbstapelplatze im
+  Mittelalter_ (Halle, 1900); Daniel, _Deutschland_; and A. Supan,
+  _Wasserstrassen und Binnenschifffahrt_ (Berlin, 1902).
+
+
+FOOTNOTE:
+
+  [1] See _Der Bau des Elbe-Trave Canals und seine Vorgeschichte_
+    (Lubeck, 1900).
+
+
+
+
+ELBERFELD, a manufacturing town of Germany, in the Prussian Rhine
+province, on the Wupper, and immediately west of and contiguous to
+Barmen (q.v.). Pop. (1816) 21,710; (1840) 31,514; (1885) 109,218; (1905)
+167,382. Elberfeld-Barmen, although administratively separate,
+practically form a single whole. It winds, a continuous strip of houses
+and factories, for 9 m. along the deep valley, on both banks of the
+Wupper, which is crossed by numerous bridges, the engirdling hills
+crowned with woods. Local intercommunication is provided by an electric
+tramway line and a novel hanging railway--on the Langen mono-rail
+system--suspended over the bed of the river, with frequent stations. In
+the centre of the town are a number of irregular and narrow streets, and
+the river, polluted by the refuse of dye-works and factories,
+constitutes a constant eyesore. Yet within recent years great
+alterations have been effected; in the newer quarters are several
+handsome streets and public buildings; in the centre many insanitary
+dwellings have been swept away, and their place occupied by imposing
+blocks of shops and business premises, and a magnificent new town-hall,
+erected in a dominant position. Among the most recent improvements must
+be mentioned the Brausenwerther Platz, flanked by the theatre, the
+public baths, and the railway station and administrative offices. There
+are eleven Evangelical and five Roman Catholic churches (noticeable
+among the latter the Suitbertuskirche), a synagogue, and chapels of
+various other sects. Among other public buildings may be enumerated the
+civic hall, the law courts and the old town-hall.
+
+The town is particularly rich in educational, industrial, philanthropic
+and religious institutions. The schools include the Gymnasium (founded
+in 1592 by the Protestant community as a Latin school), the
+Realgymnasium (founded in 1830, for "modern" subjects and Latin), the
+Oberrealschule and Realschule (founded 1893, the latter wholly
+"modern"), two girls' high schools, a girls' middle-class school, a
+large number of popular schools, a mechanics' and polytechnic school, a
+school of mechanics, an industrial drawing school, a commercial school,
+and a school for the deaf and dumb. There are also a theatre, an
+institute of music, a library, a museum, a zoological garden, and
+numerous scientific societies. The town is the seat of the Berg Bible
+Society. The majority of the inhabitants are Protestant, with a strong
+tendency towards Pietism; but the Roman Catholics number upwards of
+40,000, forming about one-fourth of the total population. The industries
+of Elberfeld are on a scale of great magnitude. It is the chief centre
+in Germany of the cotton, wool, silk and velvet manufactures, and of
+upholstery, drapery and haberdashery of all descriptions, of printed
+calicoes, of Turkey-red and other dyes, and of fine chemicals. Leather
+and rubber goods, gold, silver and aluminium wares, machinery,
+wall-paper, and stained glass are also among other of its staple
+products. Commerce is lively and the exports to foreign countries are
+very considerable. The railway system is well devised to meet the
+requirements of its rapidly increasing trade. Two main lines of railway
+traverse the valley; that on the south is the main line from
+Aix-la-Chapelle, Cologne and Dusseldorf to central Germany and Berlin,
+that on the north feeds the important towns of the Ruhr valley.
+
+The surroundings of Elberfeld are attractive, and public grounds and
+walks have been recently opened on the hills around with results
+eminently beneficial to the health of the population.
+
+In the 12th century the site of Elberfeld was occupied by the castle of
+the lords of Elverfeld, feudatories of the archbishops of Cologne. The
+fief passed later into the possession of the counts of Berg. The
+industrial development of the place started with a colony of bleachers,
+attracted by the clear waters of the Wupper, who in 1532 were granted
+the exclusive privilege of bleaching yarn. It was not, however, until
+1610 that Elberfeld was raised to the status of a town, and in 1640 was
+surrounded with walls. In 1760 the manufacture of silk was introduced,
+and dyeing with Turkey-red in 1780; but it was not till the end of the
+century that its industries developed into importance under the
+influence of Napoleon's continental system, which barred out British
+competition. In 1815 Elberfeld was assigned by the congress of Vienna,
+with the grand-duchy of Berg, to Prussia, and its prosperity rapidly
+developed under the Prussian Zollverein.
+
+  See Coutelle, _Elberfeld, topographisch-statistische Darstellung_
+  (Elberfeld, 1853); Schell, _Geschichte der Stadt Elberfeld_ (1900); A.
+  Shadwell, _Industrial Efficiency_ (London, 1906); and Jorde, _Fuhrer
+  durch Elberfeld und seine Umgebung_ (1902).
+
+
+
+
+ELBEUF, a town of northern France in the department of Seine-Inferieure,
+14 m. S.S.W. of Rouen by the western railway. Pop. (1906) 17,800.
+Elbeuf, a town of wide, clean streets, with handsome houses and
+factories, stands on the left bank of the Seine at the foot of hills
+over which extends the forest of Elbeuf. A tribunal and chamber of
+commerce, a board of trade-arbitrators, a lycee, a branch of the Bank of
+France, a school of industry, a school of cloth manufacture and a museum
+of natural history are among its institutions. The churches of St
+Etienne and St Jean, both of the Renaissance period with later
+additions, preserve stained glass of the 16th century. The
+hotel-de-ville and the Cercle du Commerce are the chief modern
+buildings. The town with its suburbs, Orival, Caudebec-les-Elbeuf, St
+Aubin and St Pierre, is one of the principal and most ancient seats of
+the woollen manufacture in France; more than half the inhabitants are
+directly maintained by the staple industry and numbers more by the
+auxiliary crafts. As a river-port it has a brisk trade in the produce of
+the surrounding district as well as in the raw materials of its
+manufactures, especially in wool from La Plata, Australia and Germany.
+Two bridges, one of them a suspension-bridge, communicate with St Aubin
+on the opposite bank of the Seine, and steamboats ply regularly to
+Rouen.
+
+Elbeuf was, in the 13th century, the centre of an important fief held by
+the house of Harcourt, but its previous history goes back at least to
+the early years of the Norman occupation, when it appears under the name
+of Hollebof. It passed into the hands of the houses of Rieux and
+Lorraine, and was raised to the rank of a duchy in the peerage of France
+by Henry III. in favour of Charles of Lorraine (d. 1605), grandson of
+Claude, duke of Guise, master of the hounds and master of the horse of
+France. The last duke of Elbeuf was Charles Eugene of Lorraine, prince
+de Lambesc, who distinguished himself in 1789 by his energy in
+repressing risings of the people at Paris. He fought in the army of the
+Bourbons, and later in the service of Austria, and died in 1825.
+
+
+
+
+ELBING, a seaport town of Germany, in the kingdom of Prussia, 49 m. by
+rail E.S.E. of Danzig, on the Elbing, a small river which flows into the
+Frische Haff about 5 m. from the town, and is united with the Nogat or
+eastern arm of the Vistula by means of the Kraffohl canal. Pop. (1905)
+55,627. By the Elbing-Oberlandischer canal, 110 m. long, constructed in
+1845-1860, Lakes Geserich and Drewenz are connected with Lake Drausen,
+and consequently with the port of Elbing. The old town was formerly
+surrounded by fortifications, but of these only a few fragments remain.
+There are several churches, among them the Marienkirche (dating from the
+15th century and restored in 1887), a classical school (Gymnasium)
+founded in 1536, a modern school (Realschule), a public library of over
+28,000 volumes, and several charitable institutions. The town-hall
+(1894) contains a historical museum.
+
+Elbing is a place of rapidly growing industries. At the great Schichau
+iron-works, which employ thousands of workmen, are built most of the
+torpedo-boats and destroyers for the German navy, as well as larger
+craft, locomotives and machinery. In addition to this there are at
+Elbing important iron foundries, and manufactories of machinery, cigars,
+lacquer and metal ware, flax and hemp yarn, cotton, linen, organs, &c.
+There is a considerable trade also in agricultural produce.
+
+The origin of Elbing was a colony of traders from Lubeck and Bremen,
+which established itself under the protection of a castle of the
+Teutonic Knights, built in 1237. In 1246 the town acquired "Lubeck
+rights," i.e. the full autonomy conceded by the charter of the emperor
+Frederick II. in 1226 (see LUBECK), and it was early admitted to the
+Hanseatic League. In 1454 the town repudiated the overlordship of the
+Teutonic Order, and placed itself under the protection of the king of
+Poland, becoming the seat of a Polish voivode. From this event dates a
+decline in its prosperity, a decline hastened by the wars of the early
+18th century. In 1698, and again in 1703, it was seized by the elector
+of Brandenburg as security for a debt due to him by the Polish king. It
+was taken and held to ransom by Charles XII. of Sweden, and in 1710 was
+captured by the Russians. In 1772, when it fell to Prussia through the
+first partition of Poland, it was utterly decayed.
+
+  See Fuchs, _Gesch. der Stadt Elbing_ (Elbing, 1818-1852); Rhode, _Der
+  Elbinger Kreis in topographischer, historischer, und statistischer
+  Hinsicht_ (Danzig, 1871); Wernick, _Elbing_ (Elbing, 1888).
+
+
+
+
+ELBOW, in anatomy, the articulation of the _humerus_, the bone of the
+upper arm, and the _ulna_ and _radius_, the bones of the forearm (see
+JOINTS). The word is thus applied to things which are like this joint in
+shape, such as a sharp bend of a stream or river, an angle in a tube,
+&c. The word is derived from the O. Eng. _elnboga_, a combination of
+_eln_, the forearm, and _boga_, a bow or bend. This combination is
+common to many Teutonic languages, cf. Ger. _Ellbogen_. _Eln_ still
+survives in the name of a linear measure, the "ell," and is derived from
+the O. Teut. _alina_, cognate with Lat. _ulna_ and Gr. [Greek: olene],
+the forearm. The use of the arm as a measure of length is illustrated by
+the uses of _ulna_, in Latin, cubit, and fathom.
+
+
+
+
+ELBURZ, or ALBURZ (from O. Pers. _Hara-bere-zaiti_, the "High
+Mountain"), a great chain of mountains in northern Persia, separating
+the Caspian depression from the Persian highlands, and extending without
+any break for 650 m. from the western shore of the Caspian Sea to
+north-eastern Khorasan. According to the direction, or strike, of its
+principal ranges the Elburz may be divided into three sections: the
+first 120 m. in length with a direction nearly N. to S., the second 240
+m. in length with a direction N.W. to S.E., and the third 290 m. in
+length striking S.W. to N.E. The first section, which is connected with
+the system of the Caucasus, and begins west of Lenkoran in 39 deg. N.
+and 45 deg. E., is known as the Talish range and has several peaks 9000
+to 10,000 ft. in height. It runs almost parallel to the western shore of
+the Caspian, and west of Astara is only 10 or 12 m. distant from the
+sea. At the point west of Resht, where the direction of the principal
+range changes to one of N.W. to S.E., the second section of the Elburz
+begins, and extends from there to beyond Mount Demavend, east of
+Teheran. South of Resht this section is broken through at almost a right
+angle by the Safid Rud (White river), and along it runs the principal
+commercial road between the Caspian and inner Persia,
+Resht-Kazvin-Teheran. The Elburz then splits into three principal ranges
+running parallel to one another and connected at many places by
+secondary ranges and spurs. Many peaks of the ranges in this section
+have an altitude of 11,000 to 13,000 ft., and the elevation of the
+passes leading over the ranges varies between 7000 and 10,000 ft. The
+highest peaks are situated in the still unexplored district of Talikan,
+N.W. of Teheran, and thence eastwards to beyond Mount Demavend. The part
+of the Elburz immediately north of Teheran is known as the Kuh i Shimran
+(mountain of Shimran, from the name of the Shimran district on its
+southern slopes) and culminates in the Sar i Tochal (12,600 ft.). Beyond
+it, and between the border of Talikan in the N.W. and Mount Demavend in
+the N.E., are the ranges Azadbur, Kasil, Kachang, Kendevan, Shahzad,
+Varzeh, Derbend i Sar and others, with elevations of 12,000 to 13,500
+ft., while Demavend towers above them all with its altitude of 19,400
+ft. The eastern foot of Demavend is washed by the river Herhaz (called
+Lar river in its upper course), which there breaks through the Elburz in
+a S.-N. direction in its course to the Caspian, past the city of Amol.
+The third section of the Elburz, with its principal ranges striking S.W.
+to N.E., has a length of about 290 m., and ends some distance beyond
+Bujnurd in northern Khorasan, where it joins the Ala Dagh range, which
+has a direction to the S.E., and, continuing with various appellations
+to northern Afghanistan, unites with the Paropamisus. For about
+two-thirds of its length--from its beginning to Khush Yailak--the third
+section consists of three principal ranges connected by lateral ranges
+and spurs. It also has many peaks over 10,000 ft. in height, and the
+Nizva mountain on the southern border of the unexplored district of
+Hazarjirib, north of Semnan, and the Shahkuh, between Shahrud and
+Astarabad, have an elevation exceeding 13,000 ft. Beyond Khush Yailak
+(meaning "pleasant summer quarters"), with an elevation of 10,000 ft.,
+are the Kuh i Buhar (8000) and Kuh i Suluk (8000), which latter joins
+the Ala Dagh (11,000).
+
+The northern slopes of the Elburz and the lowlands which lie between
+them and the Caspian, and together form the provinces of Gilan,
+Mazandaran and Astarabad, are covered with dense forest and traversed by
+hundreds (Persian writers say 1362) of perennial rivers and streams. The
+breadth of the lowlands between the foot of the hills and the sea is
+from 2 to 25 m., the greatest breadth being in the meridian of Resht in
+Gilan, and in the districts of Amol, Sari and Barfurush in Mazandaran.
+The inner slopes and ranges of the Elburz south of the principal
+watershed, generally the central one of the three principal ranges which
+are outside of the fertilizing influence of the moisture brought from
+the sea, have little or no natural vegetation, and those farthest south
+are, excepting a few stunted cypresses, completely arid and bare.
+
+"North of the principal watershed forest trees and general verdure
+refresh the eye. Gurgling water, strips of sward and tall forest trees,
+backed by green hills, make a scene completely unlike the usual monotony
+of Persian landscape. The forest scenery much resembles that of England,
+with fine oaks and greensward. South of the watershed the whole aspect
+of the landscape is as hideous and disappointing as scenery in
+Afghanistan. Ridge after ridge of bare hill and curtain behind curtain
+of serrated mountain, certainly sometimes of charming greys and blues,
+but still all bare and naked, rugged and arid" ("Beresford Lovett,
+_Proc. R.G.S._, Feb. 1883).
+
+The higher ranges of the Elburz are snow-capped for the greater part of
+the year, and some, which are not exposed to the refracted heat from the
+arid districts of inner Persia, are rarely without snow. Water is
+plentiful in the Elburz, and situated in well-watered valleys and gorges
+are innumerable flourishing villages, embosomed in gardens and orchards,
+with extensive cultivated fields and meadows, and at higher altitudes
+small plateaus, under snow until March or April, afford cool camping
+grounds to the nomads of the plains, and luxuriant grazing to their
+sheep and cattle during the summer.     (A. H.-S.)
+
+
+
+
+ELCHE, a town of eastern Spain, in the province of Alicante, on the
+river Vinalapo. Pop. (1900) 27,308. Elche is the meeting-place of three
+railways, from Novelda, Alicante and Murcia. It contains no building of
+high architectural merit, except, perhaps, the collegiate church of
+Santa Maria, with its lofty blue-tiled dome and fine west doorway. But
+the costume and physiognomy of the inhabitants, the narrow streets and
+flat-roofed, whitewashed houses, and more than all, the thousands of
+palm-trees in its gardens and fields, give the place a strikingly
+Oriental aspect, and render it unique among the cities of Spain. The
+cultivation of the palm is indeed the principal occupation; and though
+the dates are inferior to those of the Barbary States, upwards of 22,500
+tons are annually exported. The blanched fronds are also sold in large
+quantities for the processions of Palm Sunday, and after they have
+received the blessing of the priest they are regarded throughout Spain
+as certain defences against lightning. Other thriving local industries
+include the manufacture of oil, soap, flour, leather, alcohol and
+esparto grass rugs. The harbour of Elche is Santa Pola (pop. 4100),
+situated 6 m. E.S.E., where the Vinalapo enters the Mediterranean, after
+forming the wide lagoon known as the Albufera de Elche.
+
+Elche is usually identified with the Iberian _Helike_, afterwards the
+Roman colony of _Ilici_ or _Illici_. From the 8th century to the 13th it
+was held by the Moors, who finally failed to recapture it from the
+Spaniards in 1332.
+
+
+
+
+ELCHINGEN, a village of Germany, in the kingdom of Bavaria, not far from
+the Danube, 5 m. N.E. from Ulm. Here, on the 14th of October 1805, the
+Austrians under Laudon were defeated by the French under Ney, who by
+taking the bridge decided the day and gained for himself the title of
+duke of Elchingen.
+
+
+
+
+ELDAD BEN MAHLI, also surnamed had-Dani, Abu-Dani, David-had-Dani, or
+the Danite, Jewish traveller, was the supposed author of a Jewish
+travel-narrative of the 9th century A.D., which enjoyed great authority
+in the middle ages, especially on the question of the Lost Ten Tribes.
+Eldad first set out to visit his Hebrew brethren in Africa and Asia. His
+vessel was wrecked, and he fell into the hands of cannibals; but he was
+saved by his leanness, and by the opportune invasion of a neighbouring
+tribe. After spending four years with his new captors, he was ransomed
+by a fellow-countryman, a merchant of the tribe of Issachar. He then
+(according to his highly fabulous narrative) visited the territory of
+Issachar, in the mountains of Media and Persia; he also describes the
+abodes of Zabulon, on the "other side" of the Paran Mountains, extending
+to Armenia and the Euphrates; of Reuben, on another side of the same
+mountains; of Ephraim and Half Manasseh, in Arabia, not far from Mecca;
+and of Simeon and the other Half of Manasseh, in Chorazin, six months'
+journey from Jerusalem. Dan, he declares, sooner than join in Jeroboam's
+scheme of an Israelite war against Judah, had migrated to Cush, and
+finally, with the help of Naphthali, Asher and Gad, had founded an
+independent Jewish kingdom in the Gold Land of Havila, beyond Abyssinia.
+The tribe of Levi had also been miraculously guided, from near Babylon,
+to Havila, where they were enclosed and protected by the mystic river
+Sambation or Sabbation, which on the Sabbath, though calm, was veiled in
+impenetrable mist, while on other days it ran with a fierce
+untraversable current of stones and sand.
+
+Apart from these tales, we have the genuine Eldad, a celebrated Jewish
+traveller and philologist; who flourished c. A.D. 830-890; to whom the
+work above noticed is ascribed; who was a native either of S. Arabia,
+Palestine or Media; who journeyed in Egypt, Mesopotamia, North Africa,
+and Spain; who spent several years at Kairawan in Tunis; who died on a
+visit to Cordova, and whose authority, as to the lost tribes, is
+supported by a great Hebrew doctor of his own time, Zemah Gaon, the
+rector of the Academy at Sura (A.D. 889-898). It is possible that a
+certain relationship exists (as suggested by Epstein and supported by
+D.H. Muller) between the famous apocryphal _Letter of Prester John_ (of
+c. A.D. 1165) and the narrative of Eldad; but the affinity is not close.
+Eldad is quoted as an authority on linguistic difficulties by the
+leading medieval Jewish grammarians and lexicographers.
+
+  The work ascribed to Eldad is in Hebrew, divided into six chapters,
+  probably abbreviated from the original text. The first edition
+  appeared at Mantua about 1480; the second at Constantinople in 1516;
+  this was reprinted at Venice in 1544 and 1605, and at Jessnitz in
+  1722. A Latin version by Gilb. Genebrard was published at Paris in
+  1563, under the title of _Eldad Danius ... de Judaeis clausis eorumque
+  in Aethiopia ... imperio_, and was afterwards incorporated in the
+  translator's _Chronologia Hebraeorum_ of 1584; a German version
+  appeared at Prague in 1695, and another at Jessnitz in 1723. In 1838
+  E. Carmoly edited and translated a fuller recension which he had found
+  in a MS. from the library of Eliezer Ben Hasan, forwarded to him by
+  David Zabach of Morocco (see _Relation d'Eldad le Danite_, Paris,
+  1838). Both forms are printed by Dr Jellinek in his _Bet-ha-Midrasch_,
+  vols. ii. p. 102, &c., and iii. p. 6, &c. (Leipzig, 1853-1855). See
+  also Bartolocci, _Bibliotheca magna Rabbinica_, i. 101-130; Furst,
+  _Bibliotheca Judaica_, i. 30, &c.; Hirsch Graetz, _Geschichte der
+  Juden_ (3rd ed., Leipzig, 1895), v. 239-244; Rossi, _Dizionario degli
+  Ebrei_; Steinschneider, _Cat. librorum Hebraeorum in bibliotheca
+  Bodleiana_, cols. 923-925; Kitto's _Biblical Cyclopaedia_ (3rd
+  edition, _sub nomine_); Abr. Epstein, _Eldad ha-Dani_ (Pressburg,
+  1891); D.H. Muller, "Die Recensionen und Versionen des Eldad
+  had-Dani," in _Denkschriften d. Wiener Akad._ (Phil.-Hist. Cl.), vol.
+  xli. (1892), pp. 1-80.
+
+
+
+
+ELDER (Gr. [Greek: presbuteros]), the name given at different times to a
+ruler or officer in certain political and ecclesiastical systems of
+government.
+
+1. The office of elder is in its origin political and is a relic of the
+old patriarchal system. The unit of primitive society is always the
+family; the only tie that binds men together is that of kinship. "The
+eldest male parent," to quote Sir Henry Maine,[1] "is absolutely
+supreme in his household. His dominion extends to life and death and is
+as unqualified over his children and their houses as over his slaves."
+The tribe, which is a later development, is always an aggregate of
+families or clans, not a collection of individuals. "The union of
+several clans for common political action," as Robertson Smith says,
+"was produced by the pressure of practical necessity, and always tended
+towards dissolution when this practical pressure was withdrawn. The only
+organization for common action was that the leading men of the clans
+consulted together in time of need, and their influence led the masses
+with them. Out of these conferences arose the senates of elders found in
+the ancient states of Semitic and Aryan antiquity alike."[2] With the
+development of civilization there came a time when age ceased to be an
+indispensable condition of leadership. The old title was, however,
+generally retained, e.g. the [Greek: gerontes] so often mentioned in
+Homer, the [Greek: gerousia] of the Dorian states, the _senatus_ and the
+_patres conscripti_ of Rome, the sheikh or elder of Arabia, the alderman
+of an English borough, the seigneur (Lat. _senior_) of feudal France.
+
+2. It was through the influence of Judaism that the originally political
+office of elder passed over into the Christian Church and became
+ecclesiastical. The Israelites inherited the office from their Semitic
+ancestors (just as did the Moabites and the Midianites, of whose elders
+we read in Numbers xxii. 7), and traces of it are found throughout their
+history. Mention is made in Judges viii. 14 of the elders of Succoth
+whom "Gideon taught with thorns of the wilderness and with briers." It
+was to the elders of Israel in Egypt that Moses communicated the plan of
+Yahweh for the redemption of the people (Exodus iii. 16). During the
+sojourn in the wilderness the elders were the intermediaries between
+Moses and the people, and it was out of the ranks of these elders that
+Moses chose a council of seventy "to bear with him the burden of the
+people" (Numbers xi. 16). The elders were the governors of the people
+and the administrators of justice. There are frequent references to
+their work in the latter capacity in the book of Deuteronomy, especially
+in relation to the following crimes--the disobedience of sons; slander
+against a wife; the refusal of levirate marriage; manslaughter; and
+blood-revenge. Their powers were gradually curtailed by (a) the
+development of the monarchy, to which of course they were in subjection,
+and which became the court of appeal in questions of law;[3] (b) the
+appointment of special judges, probably chosen from amongst the elders
+themselves, though their appointment meant the loss of privilege to the
+general body; (c) the rise of the priestly orders, which usurped many of
+the prerogatives that originally belonged to the elders. But in spite of
+the rise of new authorities, the elders still retained a large amount of
+influence. We hear of them frequently in the Persian, Greek and Roman
+periods. In the New Testament the members of the Sanhedrin in Jerusalem
+are very frequently termed "elders" or [Greek: presbyteroi], and from
+them the name was taken over by the Church.
+
+3. The name "elder" was probably the first title bestowed upon the
+officers of the Christian Church--since the word deacon does not occur
+in connexion with the appointment of the Seven in Acts vi. Its universal
+adoption is due not only to its currency amongst the Jews, but also to
+the fact that it was frequently used as the title of magistrates in the
+cities and villages of Asia Minor. For the history of the office of
+elder in the early Church and the relation between elders and bishops
+see PRESBYTER.
+
+4. In modern times the use of the term is almost entirely confined to
+the Presbyterian church, the officers of which are always called elders.
+According to the Presbyterian theory of church government there are two
+classes of elders--"teaching elders," or those specially set apart to
+the pastoral office, and "ruling elders," who are laymen, chosen
+generally by the congregation and set apart by ordination to be
+associated with the pastor in the oversight and government of the
+church. When the word is used without any qualification it is
+understood to apply to the latter class alone. For an account of the
+duties, qualifications and powers of elders in the Presbyterian Church
+see PRESBYTERIANISM.
+
+  See W.R. Smith, _History of the Semites_; H. Maine, _Ancient Law_; E.
+  Schurer, _The Jewish People in the Time of Christ_; J. Wellhausen,
+  _History of Israel and Judah_; G.A. Deissmann, _Bible Studies_, p.
+  154.
+
+
+FOOTNOTES:
+
+  [1] _Ancient Law_, p. 126.
+
+  [2] _Religion of the Semites_, p. 34.
+
+  [3] There is a hint at this even in the Pentateuch, "every great
+    matter they shall bring unto thee, but every small matter they shall
+    judge themselves."
+
+
+
+
+ELDER (O. Eng. _ellarn_; Ger. _Holunder_; Fr. _sureau_), the popular
+designation of the deciduous shrubs and trees constituting the genus
+_Sambucus_ of the natural order Caprifoliaceae. The Common Elder, _S.
+nigra_, the bourtree of Scotland, is found in Europe, the north of
+Africa, Western Asia, the Caucasus, and Southern Siberia; in sheltered
+spots it attains a height of over 20 ft. The bark is smooth; the shoots
+are stout and angular, and the leaves glabrous, pinnate, with oval or
+elliptical leaflets. The flowers, which form dense flat-topped clusters
+(corymbose cymes), with five main branches, have a cream-coloured,
+gamopetalous, five-lobed corolla, five stamens, and three sessile
+stigmas; the berries are purplish-black, globular and three- or
+four-seeded, and ripen about September. The elder thrives best in moist,
+well-drained situations, but can be grown in a great diversity of soils.
+It grows readily from young shoots, which after a year are fit for
+transplantation. It is found useful for making screen-fences in bleak,
+exposed situations, and also as a shelter for other shrubs in the
+outskirts of plantations. By clipping two or three times a year, it may
+be made close and compact in growth. The young trees furnish a brittle
+wood, containing much pith; the wood of old trees is white, hard and
+close-grained, polishes well, and is employed for shoemakers' pegs,
+combs, skewers, mathematical instruments and turned articles. Young
+elder twigs deprived of pith have from very early times been in request
+for making whistles, popguns and other toys.
+
+The elder was known to the ancients for its medicinal properties, and in
+England the inner bark was formerly administered as a cathartic. The
+flowers (_sambuci flores_) contain a volatile oil, and serve for the
+distillation of elder-flower water (_aqua sambuci_), used in
+confectionery, perfumes and lotions. The leaves of the elder are
+employed to impart a green colour to fat and oil (_unguentum sambuci
+foliorum_ and _oleum viride_), and the berries for making wine, a common
+adulterant of port. The leaves and bark emit a sickly odour, believed to
+be repugnant to insects. Christopher Gullet (_Phil. Trans._, 1772, lxii.
+p. 348) recommends that cabbages, turnips, wheat and fruit trees, to
+preserve them from caterpillars, flies and blight, should be whipped
+with twigs of young elder. According to German folklore, the hat must be
+doffed in the presence of the elder-tree; and in certain of the English
+midland counties a belief was once prevalent that the cross of Christ
+was made from its wood, which should therefore never be used as fuel, or
+treated with disrespect (see _Quart. Rev._ cxiv. 233). It was, however,
+a common medieval tradition, alluded to by Ben Jonson, Shakespeare and
+other writers, that the elder was the tree on which Judas hanged
+himself; and on this account, probably, to be crowned with elder was in
+olden times accounted a disgrace. In Cymbeline (act iv. s. 2) "the
+stinking elder" is mentioned as a symbol of grief. In Denmark the tree
+is supposed by the superstitious to be under the protection of the
+"Elder-mother": its flowers may not be gathered without her leave; its
+wood must not be employed for any household furniture; and a child
+sleeping in an elder-wood cradle would certainly be strangled by the
+Elder-mother.
+
+Several varieties are known in cultivation: _aurea_, golden elder, has
+golden-yellow leaves; _laciniata_, parsley-leaved elder, has the
+leaflets cut into fine segments; _rotundifolia_ has rounded leaflets;
+forms also occur with variegated white and yellow leaves, and
+_virescens_ is a variety having white bark and green-coloured berries.
+The scarlet-berried elder, _S. racemosa_, is the handsomest species of
+the genus. It is a native of various parts of Europe, growing in Britain
+to a height of over 15 ft., but often producing no fruit. The dwarf
+elder or Danewort (supposed to have been introduced into Britain by the
+Danes), _S. Ebulus_, a common European species, reaches a height of
+about 6 ft. Its cyme is hairy, has three principal branches, and is
+smaller than that of _S. nigra_; the flowers are white tipped with
+pink. All parts of the plant are cathartic and emetic.
+
+
+
+
+ELDON, JOHN SCOTT, 1st EARL OF (1751-1838), lord high chancellor of
+England, was born at Newcastle on the 4th of June 1751. His grandfather,
+William Scott of Sandgate, a suburb of Newcastle, was clerk to a
+"fitter"--a sort of water-carrier and broker of coals. His father, whose
+name also was William, began life as an apprentice to a fitter, in which
+service he obtained the freedom of Newcastle, becoming a member of the
+gild of Hoastmen (coal-fitters); later in life he became a principal in
+the business, and attained a respectable position as a merchant in
+Newcastle, accumulating property worth nearly L20,000.
+
+John Scott was educated at the grammar school of his native town. He was
+not remarkable at school for application to his studies, though his
+wonderful memory enabled him to make good progress in them; he
+frequently played truant and was whipped for it, robbed orchards, and
+indulged in other questionable schoolboy freaks; nor did he always come
+out of his scrapes with honour and a character for truthfulness. When he
+had finished his education at the grammar school, his father thought of
+apprenticing him to his own business, to which an elder brother Henry
+had already devoted himself; and it was only through the interference of
+his elder brother William (afterwards Lord Stowell, q.v.), who had
+already obtained a fellowship at University College, Oxford, that it was
+ultimately resolved that he should continue the prosecution of his
+studies. Accordingly, in 1766, John Scott entered University College
+with the view of taking holy orders and obtaining a college living. In
+the year following he obtained a fellowship, graduated B.A. in 1770, and
+in 1771 won the prize for the English essay, the only university prize
+open in his time for general competition.
+
+His wife was the eldest daughter of Aubone Surtees, a Newcastle banker.
+The Surtees family objected to the match, and attempted to prevent it;
+but a strong attachment had sprung up between them. On the 18th November
+1772 Scott, with the aid of a ladder and an old friend, carried off the
+lady from her father's house in the Sandhill, across the border to
+Blackshiels, in Scotland, where they were married. The father of the
+bridegroom objected not to his son's choice, but to the time he chose to
+marry; for it was a blight on his son's prospects, depriving him of his
+fellowship and his chance of church preferment. But while the bride's
+family refused to hold intercourse with the pair, Mr Scott, like a
+prudent man and an affectionate father, set himself to make the best of
+a bad matter, and received them kindly, settling on his son L2000. John
+returned with his wife to Oxford, and continued to hold his fellowship
+for what is called the year of grace given after marriage, and added to
+his income by acting as a private tutor. After a time Mr Surtees was
+reconciled with his daughter, and made a liberal settlement on her.
+
+John Scott's year of grace closed without any college living falling
+vacant; and with his fellowship he gave up the church and turned to the
+study of law. He became a student at the Middle Temple in January 1773.
+In 1776 he was called to the bar, intending at first to establish
+himself as an advocate in his native town, a scheme which his early
+success led him to abandon, and he soon settled to the practice of his
+profession in London, and on the northern circuit. In the autumn of the
+year in which he was called to the bar his father died, leaving him a
+legacy of L1000 over and above the L2000 previously settled on him.
+
+In his second year at the bar his prospects began to brighten. His
+brother William, who by this time held the Camden professorship of
+ancient history, and enjoyed an extensive acquaintance with men of
+eminence in London, was in a position materially to advance his
+interests. Among his friends was the notorious Andrew Bowes of Gibside,
+to the patronage of whose house the rise of the Scott family was largely
+owing. Bowes having contested Newcastle and lost it, presented an
+election petition against the return of his opponent. Young Scott was
+retained as junior counsel in the case, and though he lost the petition
+he did not fail to improve the opportunity which it afforded for
+displaying his talents. This engagement, in the commencement of his
+second year at the bar, and the dropping in of occasional fees, must
+have raised his hopes; and he now abandoned the scheme of becoming a
+provincial barrister. A year or two of dull drudgery and few fees
+followed, and he began to be much depressed. But in 1780 we find his
+prospects suddenly improved, by his appearance in the case of _Ackroyd_
+v. _Smithson_, which became a leading case settling a rule of law; and
+young Scott, having lost his point in the inferior court, insisted on
+arguing it, on appeal, against the opinion of his clients, and carried
+it before Lord Thurlow, whose favourable consideration he won by his
+able argument. The same year Bowes again retained him in an election
+petition; and in the year following Scott greatly increased his
+reputation by his appearance as leading counsel in the Clitheroe
+election petition. From this time his success was certain. In 1782 he
+obtained a silk gown, and was so far cured of his early modesty that he
+declined accepting the king's counselship if precedence over him were
+given to his junior, Thomas (afterwards Lord) Erskine, though the latter
+was the son of a peer and a most accomplished orator. He was now on the
+high way to fortune. His health, which had hitherto been but
+indifferent, strengthened with the demands made upon it; his talents,
+his power of endurance, and his ambition all expanded together. He
+enjoyed a considerable practice in the northern part of his circuit,
+before parliamentary committees and at the chancery bar. By 1787 his
+practice at the equity bar had so far increased that he was obliged to
+give up the eastern half of his circuit (which embraced six counties)
+and attend it only at Lancaster.
+
+In 1782 he entered parliament for Lord Weymouth's close borough of
+Weobley, which Lord Thurlow obtained for him without solicitation. In
+parliament he gave a general and independent support to Pitt. His first
+parliamentary speeches were directed against Fox's India Bill. They were
+unsuccessful. In one he aimed at being brilliant; and becoming merely
+laboured and pedantic, he was covered with ridicule by Sheridan, from
+whom he received a lesson which he did not fail to turn to account. In
+1788 he was appointed solicitor-general, and was knighted, and at the
+close of this year he attracted attention by his speeches in support of
+Pitt's resolutions on the state of the king (George III., who then
+laboured under a mental malady) and the delegation of his authority. It
+is said that he drew the Regency Bill, which was introduced in 1789. In
+1793 Sir John Scott was promoted to the office of attorney-general, in
+which it fell to him to conduct the memorable prosecutions for high
+treason against British sympathizers with French republicanism,--amongst
+others, against the celebrated Horne Tooke. These prosecutions, in most
+cases, were no doubt instigated by Sir John Scott, and were the most
+important proceedings in which he was ever professionally engaged. He
+has left on record, in his _Anecdote Book_, a defence of his conduct in
+regard to them. A full account of the principal trials, and of the
+various legislative measures for repressing the expressions of popular
+opinion for which he was more or less responsible, will be found in
+Twiss's _Public and Private Life of the Lord Chancellor Eldon_, and in
+the _Lives of the Lord Chancellors_, by Lord Campbell.
+
+In 1799 the office of chief justice of the Court of Common Pleas falling
+vacant, Sir John Scott's claim to it was not overlooked; and after
+seventeen years' service in the Lower House, he entered the House of
+Peers as Baron Eldon. In February 1801 the ministry of Pitt was
+succeeded by that of Addington, and the chief justice now ascended the
+woolsack. The chancellorship was given to him professedly on account of
+his notorious anti-Catholic zeal. From the peace of Amiens (1802) till
+1804 Lord Eldon appears to have interfered little in politics. In the
+latter year we find him conducting the negotiations which resulted in
+the dismissal of Addington and the recall of Pitt to office as prime
+minister. Lord Eldon was continued in office as chancellor under Pitt;
+but the new administration was of short duration, for on the 23rd of
+January 1806 Pitt died, worn out with the anxieties of office, and his
+ministry was succeeded by a coalition, under Lord Grenville. The death
+of Fox, who became foreign secretary and leader of the House of Commons,
+soon, however, broke up the Grenville administration; and in the spring
+of 1807 Lord Eldon once more, under Lord Liverpool's administration,
+returned to the woolsack, which, from that time, he continued to occupy
+for about twenty years, swaying the cabinet, and being in all but name
+prime minister of England. It was not till April 1827, when the
+premiership, vacant through the paralysis of Lord Liverpool, fell to
+Canning, the chief advocate of Roman Catholic emancipation, that Lord
+Eldon, in the seventy-sixth year of his age, finally resigned the
+chancellorship. When, after the two short administrations of Canning and
+Goderich, it fell to the duke of Wellington to construct a cabinet, Lord
+Eldon expected to be included, if not as chancellor, at least in some
+important office, but he was overlooked, at which he was much chagrined.
+Notwithstanding his frequent protests that he did not covet power, but
+longed for retirement, we find him again, so late as 1835, within three
+years of his death, in hopes of office under Peel. He spoke in
+parliament for the last time in July 1834.
+
+In 1821 Lord Eldon had been created Viscount Encombe and earl of Eldon
+by George IV., whom he managed to conciliate, partly, no doubt, by
+espousing his cause against his wife, whose advocate he had formerly
+been, and partly through his reputation for zeal against the Roman
+Catholics. In the same year his brother William, who from 1798 had
+filled the office of judge of the High Court of Admiralty, was raised to
+the peerage under the title of Lord Stowell.
+
+Lord Eldon's wife, his dear "Bessy," his love for whom is a beautiful
+feature in his life, died before him, on the 28th of June 1831. By
+nature she was of simple character, and by habits acquired during the
+early portion of her husband's career almost a recluse. Two of their
+sons reached maturity--John, who died in 1805, and William Henry John,
+who died unmarried in 1832. Lord Eldon himself survived almost all his
+immediate relations. His brother William died in 1836. He himself died
+in London on the 13th of January 1838, leaving behind him two daughters,
+Lady Frances Bankes and Lady Elizabeth Repton, and a grandson John
+(1805-1854), who succeeded him as second earl, the title subsequently
+passing to the latter's son John (b. 1846).
+
+Lord Eldon was no legislator--his one aim in politics was to keep in
+office, and maintain things as he found them; and almost the only laws he
+helped to pass were laws for popular coercion. For nearly forty years he
+fought against every improvement in law, or in the constitution--calling
+God to witness, on the smallest proposal of reform, that he foresaw from
+it the downfall of his country. Without any political principles,
+properly so called, and without interest in or knowledge of foreign
+affairs, he maintained himself and his party in power for an
+unprecedented period by his great tact, and in virtue of his two great
+political properties--of zeal against every species of reform, and zeal
+against the Roman Catholics. To pass from his political to his judicial
+character is to shift to ground on which his greatness is universally
+acknowledged. His judgments, which have received as much praise for their
+accuracy as abuse for their clumsiness and uncouthness, fill a small
+library. But though intimately acquainted with every nook and cranny of
+the English law, he never carried his studies into foreign fields, from
+which to enrich our legal literature; and it must be added that against
+the excellence of his judgments, in too many cases, must be set off the
+hardships, worse than injustice, that arose from his protracted delays in
+pronouncing them. A consummate judge and the narrowest of politicians, he
+was doubt on the bench, and promptness itself in the political arena. For
+literature, as for art, he had no feeling. What intervals of leisure he
+enjoyed from the cares of office he filled up with newspapers and the
+gossip of old cronies. Nor were his intimate associates men of refinement
+and taste; they were rather good fellows who quietly enjoyed a good
+bottle and a joke; he uniformly avoided encounters of wit with his
+equals. He is said to have been parsimonious, and certainly he was
+quicker to receive than to reciprocate hospitalities; but his mean
+establishment and mode of life are explained by the retired habits of his
+wife, and her dislike of company. His manners were very winning and
+courtly, and in the circle of his immediate relatives he is said to have
+always been lovable and beloved.
+
+"In his person," says Lord Campbell, "Lord Eldon was about the middle
+size, his figure light and athletic, his features regular and handsome,
+his eye bright and full, his smile remarkably benevolent, and his whole
+appearance prepossessing. The advance of years rather increased than
+detracted from these personal advantages. As he sat on the
+judgment-seat, 'the deep thought betrayed in his furrowed brow--the
+large eyebrows, overhanging eyes that seemed to regard more what was
+taking place within than around him--his calmness, that would have
+assumed a character of sternness but for its perfect placidity--his
+dignity, repose and venerable age, tended at once to win confidence and
+to inspire respect' (Townsend). He had a voice both sweet and
+deep-toned, and its effect was not injured by his Northumbrian burr,
+which, though strong, was entirely free from harshness and vulgarity."
+
+  AUTHORITIES.--Horace Twiss, _Life of Lord Chancellor Eldon_ (1844);
+  W.E. Surtees, _Sketch of the Lives of Lords Stowell and Eldon_ (1846);
+  Lord Campbell, _Lives of the Chancellors_; W.C. Townsend, _Lives of
+  Twelve Eminent Judges_ (1846); _Greville Memoirs_.
+
+
+
+
+EL DORADO (Span. "the gilded one"), a name applied, first, to the king
+or chief priest of a South American tribe who was said to cover himself
+with gold dust at a yearly religious festival held near Santa Fe de
+Bogota; next, to a legendary city called Manoa or Omoa; and lastly, to a
+mythical country in which gold and precious stones were found in
+fabulous abundance. The legend, which has never been traced to its
+ultimate source, had many variants, especially as regards the situation
+attributed to Manoa. It induced many Spanish explorers to lead
+expeditions in search of treasure, but all failed. Among the most famous
+were the expedition undertaken by Diego de Ordaz, whose lieutenant
+Martinez claimed to have been rescued from shipwreck, conveyed inland,
+and entertained at Omoa by "El Dorado" himself (1531); and the journeys
+of Orellana (1540-1541), who passed down the Rio Napo to the valley of
+the Amazon; that of Philip von Hutten (1541-1545), who led an exploring
+party from Coro on the coast of Caracas; and of Gonzalo Ximenes de
+Quesada (1569), who started from Santa Fe de Bogota. Sir Walter Raleigh,
+who resumed the search in 1595, described Manoa as a city on Lake Parima
+in Guiana. This lake was marked on English and other maps until its
+existence was disproved by A. von Humboldt (1769-1859). Meanwhile the
+name of El Dorado came to be used metaphorically of any place where
+wealth could be rapidly acquired. It was given to a county in
+California, and to towns and cities in various states. In literature
+frequent allusion is made to the legend, perhaps the best-known
+references being those in Milton's _Paradise Lost_ (vi. 411) and
+Voltaire's _Candide_ (chs. 18, 19).
+
+  See A.F.A. Bandelier, _The Gilded Man, El Dorado_ (New York, 1893).
+
+
+
+
+ELDUAYEN, JOSE DE, 1st Marquis del Pazo de la Merced (1823-1898),
+Spanish politician, was born in Madrid on the 22nd of June 1823. He was
+educated in the capital, took the degree of civil engineer, and as such
+directed important works in Asturias and Galicia, entered the Cortes in
+1856 as deputy for Vigo, and sat in all the parliaments until 1867 as
+member of the Union Liberal with Marshal O'Donnell. He attacked the
+Miraflores cabinet in 1864, and became under-secretary of the home
+office when Canovas was minister in 1865. He was made a councillor of
+state in 1866, and in 1868 assisted the other members of the Union
+Liberal in preparing the revolution. In the Cortes of 1872 he took much
+part in financial debates. He accepted office as member of the last
+Sagasta cabinet under King Amadeus. On the proclamation of the republic
+Elduayen very earnestly co-operated in the Alphonsist conspiracy, and
+endeavoured to induce the military and politicians to work together. He
+went abroad to meet and accompany the prince after the _pronunciamiento_
+of Marshal Campos, landed with him at Valencia, was made governor of
+Madrid, a marquis, grand cross of Charles III., and minister for the
+colonies in 1878. He accepted the portfolio of foreign affairs in the
+Canovas cabinet from 1883 to 1885, and was made a life senator. He
+always prided himself on having been one of the five members of the
+Cortes of 1870 who voted for Alphonso XII. when that parliament elected
+Amadeus of Savoy. He died at Madrid on the 24th of June 1898.
+
+
+
+
+ELEANOR OF AQUITAINE (c. 1122-1204), wife of the English king Henry II.,
+was the daughter and heiress of Duke William X. of Aquitaine, whom she
+succeeded in April 1137. In accordance with arrangements made by her
+father, she at once married Prince Louis, the heir to the French crown,
+and a month later her husband became king of France under the title of
+Louis VII. Eleanor bore Louis two daughters but no sons. This was
+probably the reason why their marriage was annulled by mutual consent in
+1151, but contemporary scandal-mongers attributed the separation to the
+king's jealousy. It was alleged that, while accompanying her husband on
+the Second Crusade (1146-1149), Eleanor had been unduly familiar with
+her uncle, Raymond of Antioch. Chronology is against this hypothesis,
+since Louis and she lived on good terms together for two years after the
+Crusade. There is still less ground for the supposition that Henry of
+Anjou, whom she married immediately after the divorce, had been her
+lover before it. This second marriage, with a youth some years her
+junior, was purely political. The duchy of Aquitaine required a strong
+ruler, and the union with Anjou was eminently desirable. Louis, who had
+hoped that Aquitaine would descend to his daughters, was mortified and
+alarmed by the Angevin marriage; all the more so when Henry of Anjou
+succeeded to the English crown in 1154. From this event dates the
+beginning of the secular strife between England and France which runs
+like a red thread through medieval history.
+
+Eleanor bore to her second husband five sons and three daughters; John,
+the youngest of their children, was born in 1167. But her relations with
+Henry passed gradually through indifference to hatred. Henry was an
+unfaithful husband, and Eleanor supported her sons in their great
+rebellion of 1173. Throughout the latter years of the reign she was kept
+in a sort of honourable confinement. It was during her captivity that
+Henry formed his connexion with Rosamond Clifford, the Fair Rosamond of
+romance. Eleanor, therefore, can hardly have been responsible for the
+death of this rival, and the romance of the poisoned bowl appears to be
+an invention of the next century.
+
+Under the rule of Richard and John the queen became a political
+personage of the highest importance. To both her sons the popularity
+which she enjoyed in Aquitaine was most valuable. But in other
+directions also she did good service. She helped to frustrate the
+conspiracy with France which John concocted during Richard's captivity.
+She afterwards reconciled the king and the prince, thus saving for John
+the succession which he had forfeited by his misconduct. In 1199 she
+crushed an Angevin rising in favour of John's nephew, Arthur of
+Brittany. In 1201 she negotiated a marriage between her grand-daughter,
+Blanche of Castile, and Louis of France, the grandson of her first
+husband. It was through her staunch defence of Mirabeau in Poitou that
+John got possession of his nephew's person. She died on the 1st of April
+1204, and was buried at Fontevrault. Although a woman of strong passions
+and great abilities she is, historically, less important as an
+individual than as the heiress of Aquitaine, a part of which was,
+through her second marriage, united to England for some four hundred
+years.
+
+  See the chronicles cited for the reigns of Henry II., Richard I. and
+  John. Also Sir J.H. Ramsay, _Angevin Empire_ (London, 1903); K.
+  Norgate, _England under the Angevin Kings_ (London, 1887); and A.
+  Strickland, _Lives of the Queens of England_, vol. i. (1841).
+       (H. W. C. D.)
+
+
+
+
+ELEATIC SCHOOL, a Greek school of philosophy which came into existence
+towards the end of the 6th century B.C., and ended with Melissus of
+Samos (fl. c. 450 B.C.). It took its name from Elea, a Greek city of
+lower Italy, the home of its chief exponents, Parmenides and Zeno. Its
+foundation is often attributed to Xenophanes of Colophon, but, although
+there is much in his speculations which formed part of the later Eleatic
+doctrine, it is probably more correct to regard Parmenides as the
+founder of the school. At all events, it was Parmenides who gave it its
+fullest development. The main doctrines of the Eleatics were evolved in
+opposition, on the one hand, to the physical theories of the early
+physical philosophers who explained all existence in terms of primary
+matter (see IONIAN SCHOOL), and, on the other hand, to the theory of
+Heraclitus that all existence may be summed up as perpetual change. As
+against these theories the Eleatics maintained that the true explanation
+of things lies in the conception of a universal unity of being. The
+senses with their changing and inconsistent reports cannot cognize this
+unity; it is by thought alone that we can pass beyond the false
+appearances of sense and arrive at the knowledge of being, at the
+fundamental truth that "the All is One." There can be no creation, for
+being cannot come from not-being; a thing cannot arise from that which
+is different from it. The errors of common opinion arise to a great
+extent from the ambiguous use of the verb "to be," which may imply
+existence or be merely the copula which connects subject and predicate.
+
+In these main contentions the Eleatic school achieved a real advance,
+and paved the way to the modern conception of metaphysics. Xenophanes in
+the middle of the 6th century had made the first great attack on the
+crude mythology of early Greece, including in his onslaught the whole
+anthropomorphic system enshrined in the poems of Homer and Hesiod. In
+the hands of Parmenides this spirit of free thought developed on
+metaphysical lines. Subsequently, whether from the fact that such bold
+speculations were obnoxious to the general sense of propriety in Elea,
+or from the inferiority of its leaders, the school degenerated into
+verbal disputes as to the possibility of motion, and similar academic
+trifling. The best work of the school was absorbed in the Platonic
+metaphysic (see E. Caird, _Evolution of Theology in the Greek
+Philosophers_, 1904).
+
+  See further the articles on XENOPHANES; PARMENIDES; ZENO (of Elea);
+  MELISSUS, with the works there quoted; also the histories of
+  philosophy by Zeller, Gomperz, Windelband, &c.
+
+
+
+
+ELECAMPANE (Med. Lat. _Enula Campana_), a perennial composite plant, the
+_Inula Helenium_ of botanists, which is common in many parts of Britain,
+and ranges throughout central and southern Europe, and in Asia as far
+eastwards as the Himalayas. It is a rather rigid herb, the stem of which
+attains a height of from 3 to 5 ft.; the leaves are large and toothed,
+the lower ones stalked, the rest embracing the stem; the flowers are
+yellow, 2 in. broad, and have many rays, each three-notched at the
+extremity. The root is thick, branching and mucilaginous, and has a
+warm, bitter taste and a camphoraceous odour. For medicinal purposes it
+should be procured from plants not more than two or three years old.
+Besides _inulin_, C_12H_20O_10, a body isomeric with starch, the root
+contains _helenin_, C6H8O, a stearoptene, which may be prepared in white
+acicular crystals, insoluble in water, but freely soluble in alcohol.
+When freed from the accompanying inula-camphor by repeated
+crystallization from alcohol, helenin melts at 110 deg. C. By the
+ancients the root was employed both as a medicine and as a condiment,
+and in England it was formerly in great repute as an aromatic tonic and
+stimulant of the secretory organs. "The fresh roots of elecampane
+preserved with sugar, or made into a syrup or conserve," are recommended
+by John Parkinson in his _Theatrum Botanicum_ as "very effectual to warm
+a cold and windy stomack, and the pricking and stitches therein or in
+the sides caused by the Spleene, and to helpe the cough, shortnesse of
+breath, and wheesing in the Lungs." As a drug, however, the root is now
+seldom resorted to except in veterinary practice, though it is
+undoubtedly possessed of antiseptic properties. In France and
+Switzerland it is used in the manufacture of absinthe.
+
+
+
+
+ELECTION (from Lat. _eligere_, to pick out), the method by which a
+choice or selection is made by a constituent body (the electors or
+electorate) of some person to fill a certain office or dignity. The
+procedure itself is called an election. Election, as a special form of
+selection, is naturally a loose term covering many subjects; but except
+in the theological sense (the doctrine of election), as employed by
+Calvin and others, for the choice by God of His "elect," the legal sense
+(see ELECTION, _in law_, below), and occasionally as a synonym for
+personal choice (one's own "election"), it is confined to the selection
+by the preponderating vote of some properly constituted body of electors
+of one of two or more candidates, sometimes for admission only to some
+private social position (as in a club), but more particularly in
+connexion with public representative positions in political government.
+It is thus distinguished from arbitrary methods of appointment, either
+where the right of nominating rests in an individual, or where pure
+chance (such as selection by lot) dictates the result. The part played
+by different forms of election in history is alluded to in numerous
+articles in this work, dealing with various countries and various
+subjects. It is only necessary here to consider certain important
+features in the elections, as ordinarily understood, namely, the
+exercise of the right of voting for political and municipal offices in
+the United Kingdom and America. See also the articles PARLIAMENT;
+REPRESENTATION; VOTING; BALLOT, &c., and UNITED STATES: _Political
+Institutions_. For practical details as to the conduct of political
+elections in England reference must be made to the various text-books on
+the subject; the candidate and his election agent require to be on their
+guard against any false step which might invalidate his return.
+
+_Law in the United Kingdom._--Considerable alterations have been made in
+recent years in the law of Great Britain and Ireland relating to the
+procedure at parliamentary and municipal elections, and to election
+petitions.
+
+As regards parliamentary elections (which may be either the "general
+election," after a dissolution of parliament, or "by-elections," when
+casual vacancies occur during its continuance), the most important of
+the amending statutes is the Corrupt and Illegal Practices Act 1883.
+This act, and the Parliamentary Elections Act 1868, as amended by it,
+and other enactments dealing with corrupt practices, are temporary acts
+requiring annual renewal. As regards municipal elections, the Corrupt
+Practices (Municipal Elections) Act 1872 has been repealed by the
+Municipal Corporations Act 1882 for England, and by the Local Government
+(Ireland) Act 1898 for Ireland. The governing enactments for England are
+now the Municipal Corporations Act 1882, part iv., and the Municipal
+Elections (Corrupt and Illegal Practices) Act 1884, the latter annually
+renewable. The provisions of these enactments have been applied with
+necessary modifications to municipal and other local government
+elections in Ireland by orders of the Irish Local Government Board made
+under powers conferred by the Local Government (Ireland) Act 1898. In
+Scotland the law regulating municipal and other local government
+elections is now to be found in the Elections (Scotland) (Corrupt and
+Illegal Practices) Act 1890.
+
+The alterations in the law have been in the direction of greater
+strictness in regard to the conduct of elections, and increased control
+in the public interest over the proceedings on election petitions.
+Various acts and payments which were previously lawful in the absence of
+any corrupt bargain or motive are now altogether forbidden under the
+name of "illegal practices" as distinguished from "corrupt practices."
+Failure on the part of a parliamentary candidate or his election agent
+to comply with the requirements of the law in any particular is
+sufficient to invalidate the return (see the articles BRIBERY and
+CORRUPT PRACTICES). Certain relaxations are, however, allowed in
+consideration of the difficulty of absolutely avoiding all deviation
+from the strict rules laid down. Thus, where the judges who try an
+election petition report that there has been treating, undue influence,
+or any illegal practice by the candidate or his election agent, but that
+it was trivial, unimportant and of a limited character, and contrary to
+the orders and without the sanction or connivance of the candidate or
+his election agent, and that the candidate and his election agent took
+all reasonable means for preventing corrupt and illegal practices, and
+that the election was otherwise free from such practices on their part,
+the election will not be avoided. The court has also the power to
+relieve from the consequences of certain innocent contraventions of the
+law caused by inadvertence or miscalculation.
+
+
+  Election petitions.
+
+The inquiry into a disputed parliamentary election was formerly
+conducted before a committee of the House of Commons, chosen as nearly
+as possible from both sides of the House for that particular business.
+The decisions of these tribunals laboured under the suspicion of being
+prompted by party feeling, and by an act of 1868 the jurisdiction was
+finally transferred to judges of the High Court, notwithstanding the
+general unwillingness of the bench to accept a class of business which
+they feared might bring their integrity into dispute. Section 11 of the
+act ordered, _inter alia_, that the trial of every election petition
+shall be conducted before a _puisne judge_ of one of the common law
+courts at Westminster and Dublin; that the said courts shall each select
+a judge to be placed on the rota for the trial of election petitions;
+that the said judges shall try petitions standing for trial according to
+seniority or otherwise, as they may agree; that the trial shall take
+place in the county or borough to which the petition refers, unless the
+court should think it desirable to hold it elsewhere. The judge shall
+determine "whether the member whose return is complained of, or any and
+what other person, was duly returned and elected, or whether the
+election was void," and shall certify his determination to the speaker.
+When corrupt practices have been charged the judge shall also report (1)
+whether any such practice has been committed by or with the knowledge or
+consent of any candidate, and the nature thereof; (2) the names of
+persons proved to have been guilty of any corrupt practice; and (3)
+whether corrupt practices have extensively prevailed at the election.
+Questions of law were to be referred to the decision of the court of
+common pleas. On the abolition of that court by the Judicature Act 1873,
+the jurisdiction was transferred to the common pleas division, and again
+on the abolition of that division was transferred to the king's bench
+division, in whom it is now vested. The rota of judges for the trial of
+election petitions is also supplied by the king's bench division. The
+trial now takes place before two judges instead of one; and, when
+necessary, the number of judges on the rota may be increased. Both the
+judges who try a petition are to sign the certificates to be made to the
+speaker. If they differ as to the validity of a return, they are to
+state such difference in their certificate, and the return is to be held
+good; if they differ as to a report on any other matter, they are to
+certify their difference and make no report on such matter. The director
+of public prosecutions attends the trial personally or by
+representative. It is his duty to watch the proceedings in the public
+interest, to issue summonses to witnesses whose evidence is desired by
+the court, and to prosecute before the election court or elsewhere those
+persons whom he thinks to have been guilty of corrupt or illegal
+practices at the election in question. If an application is made for
+leave to withdraw a petition, copies of the affidavits in support are to
+be delivered to him; and he is entitled to be heard and to call evidence
+in opposition to such application. Witnesses are not excused from
+answering criminating questions; but their evidence cannot be used
+against them in any proceedings except criminal proceedings for perjury
+in respect of that evidence. If a witness answers truly all questions
+which he is required by the court to answer, he is entitled to receive a
+certificate of indemnity, which will save him from all proceedings for
+any offence under the Corrupt Practices Acts committed by him before the
+date of the certificate at or in relation to the election, except
+proceedings to enforce any incapacity incurred by such offence. An
+application for leave to withdraw a petition must be supported by
+affidavits from all the parties to the petition and their solicitors,
+and by the election agents of all of the parties who were candidates at
+the election. Each of these affidavits is to state that to the best of
+the deponent's knowledge and belief there has been no agreement and no
+terms or undertaking made or entered into as to the withdrawal, or, if
+any agreement has been made, shall state its terms. The applicant and
+his solicitor are also to state in their affidavits the grounds on which
+the petition is sought to be withdrawn. If any person makes an agreement
+for the withdrawal of a petition in consideration of a money payment, or
+of the promise that the seat shall be vacated or another petition
+withdrawn, or omits to state in his affidavit that he has made an
+agreement, lawful or unlawful, for the withdrawal, he is guilty of an
+indictable misdemeanour. The report of the judges to the speaker is to
+contain particulars as to illegal practices similar to those previously
+required as to corrupt practices; and they are to report further whether
+any candidate has been guilty by his agents of an illegal practice, and
+whether certificates of indemnity have been given to persons reported
+guilty of corrupt or illegal practices.
+
+The Corrupt Practices Acts apply, with necessary variations in details,
+to parliamentary elections in Scotland and Ireland.
+
+The amendments in the law as to municipal elections are generally
+similar to those which have been made in parliamentary election law. The
+procedure on trial of petitions is substantially the same, and wherever
+no other provision is made by the acts or rules the procedure on the
+trial of parliamentary election petitions is to be followed. Petitions
+against municipal elections were dealt with in 35 & 36 Vict. c. 60. The
+election judges appoint a number of barristers, not exceeding five, as
+commissioners to try such petitions. No barrister can be appointed who
+is of less than fifteen years' standing, or a member of parliament, or
+holder of any office of profit (other than that of recorder) under the
+crown; nor can any barrister try a petition in any borough in which he
+is recorder or in which he resides, or which is included in his circuit.
+The barrister sits without a jury. The provisions are generally similar
+to those relating to parliamentary elections. The petition may allege
+that the election was avoided as to the borough or ward on the ground of
+general bribery, &c., or that the election of the person petitioned
+against was avoided by corrupt practices, or by personal
+disqualification, or that he had not the majority of lawful votes. The
+commissioner who tries a petition sends to the High Court a certificate
+of the result, together with reports as to corrupt and illegal
+practices, &c., similar to those made to the speaker by the judges who
+try a parliamentary election petition. The Municipal Elections (Corrupt
+and Illegal Practices) Act 1884 applied to school board elections
+subject to certain variations, and has been extended by the Local
+Government Act 1888 to county council elections, and by the Local
+Government Act 1894 to elections by parochial electors. The law in
+Scotland is on the same lines, and extends to all non-parliamentary
+elections, and, as has been stated, the English statutes have been
+applied with adaptations to all municipal and local government elections
+in Ireland.
+
+_United States._--Elections are much more frequent in the United States
+than they are in Great Britain, and they are also more complicated. The
+terms of elective officers are shorter; and as there are also more
+offices to be filled, the number of persons to be voted for is
+necessarily much greater. In the year of a presidential election the
+citizen may be called upon to vote at one time for all of the following:
+(1) National candidates--president and vice-president (indirectly
+through the electoral college) and members of the House of
+Representatives; (2) state candidates--governor, members of the state
+legislature, attorney-general, treasurer, &c.; (3) county
+candidates--sheriff, county judges, district attorney, &c.; (4)
+municipal or town candidates--mayor, aldermen, selectmen, &c. The number
+of persons actually voted for may therefore be ten or a dozen, or it may
+be many more. In addition, the citizen is often called upon to vote yea
+or nay on questions such as amendments to the state constitutions,
+granting of licences, and approval or disapproval of new municipal
+undertakings. As there may be, and generally is, more than one candidate
+for each office, and as all elections are now, and have been for many
+years, conducted by ballot, the total number of names to appear on the
+ballot may be one hundred or may be several hundred. These names are
+arranged in different ways, according to the laws of the different
+states. Under the Massachusetts law, which is considered the best by
+reformers, the names of candidates for each office are arranged
+alphabetically on a "blanket" ballot, as it is called from its size, and
+the elector places a mark opposite the names of such candidates as he
+may wish to vote for. Other states, New York for example, have the
+blanket system, but the names of the candidates are arranged in party
+columns. Still other states allow the grouping on one ballot of all the
+candidates of a single party, and there would be therefore as many
+separate ballots in such states as there were parties in the field.
+
+The qualifications for voting, while varying in the different states in
+details, are in their main features the same throughout the Union. A
+residence in the state is required of from three months to two years.
+Residence is also necessary, but for a shorter period, in the county,
+city or town, or voting precinct. A few states require the payment of a
+poll tax. Some require that the voter shall be able to read and
+understand the Constitution. This latter qualification has been
+introduced into several of the Southern states, partly at least to
+disqualify the ignorant coloured voters. In all, or practically all, the
+states idiots, convicts and the insane are disqualified; in some states
+paupers; in some of the Western states the Chinese. In some states women
+are allowed to vote on certain questions, or for the candidates for
+certain offices, especially school officials; and in four of the Western
+states women have the same rights of suffrage as men. The number of
+those who are qualified to vote, but do not avail themselves of the
+right, varies greatly in the different states and according to the
+interest taken in the election. As a general rule, but subject to
+exceptions, the national elections call out the largest number, the
+state elections next, and the local elections the smallest number of
+voters. In an exciting national election between 80 and 90% of the
+qualified voters actually vote, a proportion considerably greater than
+in Great Britain or Germany.
+
+The tendency of recent years has been towards a decrease both in the
+number and in the frequency of elections. A president and vice-president
+are voted for every fourth year, in the years divisible by four, on the
+first Tuesday following the first Monday of November. Members of the
+national House of Representatives are chosen for two years on the
+even-numbered years. State and local elections take place in accordance
+with state laws, and may or may not be on the same day as the national
+elections. Originally the rule was for the states to hold annual
+elections; in fact, so strongly did the feeling prevail of the need in a
+democratic country for frequent elections, that the maxim "where annual
+elections end, tyranny begins," became a political proverb. But opinion
+gradually changed even in the older or Eastern states, and in 1909
+Massachusetts and Rhode Island were the only states in the Union holding
+annual elections for governor and both houses of the state legislature.
+In the Western states especially state officers are chosen for longer
+terms--in the case of the governor often for four years--and the number
+of elections has correspondingly decreased. Another cause of the
+decrease in the number of elections is the growing practice of holding
+all the elections of any year on one and the same day. Before the Civil
+War Pennsylvania held its state elections several months before the
+national elections. Ohio and Indiana, until 1885 and 1881 respectively,
+held their state elections early in October. Maine, Vermont and Arkansas
+keep to September. The selection of one day in the year for all
+elections held in that year has resulted in a considerable decrease in
+the total number.
+
+Another tendency of recent years, but not so pronounced, is to hold
+local elections in what is known as the "off" year; that is, on the
+odd-numbered year, when no national election is held. The object of this
+reform is to encourage independent voting. The average American citizen
+is only too prone to carry his national political predilections into
+local elections, and to vote for the local nominees of his party,
+without regard to the question of fitness of candidates and the
+fundamental difference of issues involved. This tendency to vote the
+entire party ticket is the more pronounced because under the system of
+voting in use in many of the states all the candidates of the party are
+arranged on one ticket, and it is much easier to vote a straight or
+unaltered ticket than to change or "scratch" it. Again, the voter,
+especially the ignorant one, refrains from scratching his ticket, lest
+in some way he should fail to comply with the technicalities of the law
+and his vote be lost. On the other hand, if local elections are held on
+the "off" or odd year, and there be no national or state candidates, the
+voter feels much more free to select only those candidates whom he
+considers best qualified for the various offices.
+
+On the important question of the purity of elections it is difficult to
+speak with precision. In many of the states, especially those with an
+enlightened public spirit, such as most of the New England states and
+many of the North-Western, the elections are fairly conducted, there
+being no intimidation at all, little or no bribery, and an honest count.
+It can safely be said that through the Union as a whole the tendency of
+recent years has been decidedly towards greater honesty of elections.
+This is owing to a number of causes: (1) The selection of a single day
+for all elections, and the consequent immense number voting on that day.
+Some years ago, when for instance the Ohio and Indiana elections were
+held a few weeks before the general election, each party strained every
+nerve to carry them, for the sake of prestige and the influence on other
+states. In fact, presidential elections were often felt to turn on the
+result in these early voting states, and the party managers were none
+too scrupulous in the means employed to carry them. Bribery has
+decreased in such states since the change of election day to that of the
+rest of the country. (2) The enactment in most of the states of the
+Australian or secret ballot (q.v.) laws. These have led to the secrecy
+of the ballot, and hence to a greater or less extent have prevented
+intimidation and bribery. (3) Educational or other such test, more
+particularly in the Southern states, the object of which is to exclude
+the coloured, and especially the ignorant coloured, voters from the
+polls. In those southern states in which the coloured vote was large,
+and still more in those in which it was the majority, it was felt among
+the whites that intimidation or ballot-box stuffing was justified by the
+necessity of white supremacy. With the elimination of the coloured vote
+by educational or other tests the honesty of elections has increased.
+(4) The enactment of new and more stringent registration laws. Under
+these laws only those persons are allowed to vote whose names have been
+placed on the rolls a certain number of days or months before election.
+These rolls are open to public inspection, and the names may be
+challenged at the polls, and "colonization" or repeating is therefore
+almost impossible. (5) The reform of the civil service and the gradual
+elimination of the vicious principle of "to the victors belong the
+spoils." With the reform of the civil service elections become less a
+scramble for office and more a contest of political or economic
+principle. They bring into the field, therefore, a better class of
+candidates. (6) The enactment in a number of states of various other
+laws for the prevention of corrupt practices, for the publication of
+campaign expenses, and for the prohibition of party workers from coming
+within a certain specified distance of the polls. In the state of
+Massachusetts, for instance, an act passed in 1892, and subsequently
+amended, provides that political committees shall file a full statement,
+duly sworn to, of all campaign expenditures made by them. The act
+applies to all public elections except that of town officers, and also
+covers nominations by caucuses and conventions as well. Apart from his
+personal expenses such as postage, travelling expenses, &c., a candidate
+is prohibited from spending anything himself to promote either his
+nomination or his election, but he is allowed to contribute to the
+treasury of the political committee. The law places no limit on the
+amount that these committees may spend. The reform sought by the law is
+thorough publicity, and not only are details of receipts and
+expenditures to be published, but the names of contributors and the
+amount of their contributions. In the state of New York the act which
+seeks to prevent corrupt practices relies in like manner on the efficacy
+of publicity, but it is less effective than the Massachusetts law in
+that it provides simply for the filing by the candidates themselves of
+sworn statements of their own expenses. There is nothing to prevent
+their contributing to political committees, and the financial methods
+and the amounts expended by such committees are not made public. But
+behind all these causes that have led to more honest elections lies the
+still greater one of a healthier public spirit. In the reaction
+following the Civil War all reforms halted. In recent years, however, a
+new and healthier interest has sprung up in things political; and one
+result of this improved civic spirit is seen in the various laws for
+purification of elections. It may now be safely affirmed that in the
+majority of states the elections are honestly conducted; that
+intimidation, bribery, stuffing of the ballot boxes or other forms of
+corruption, when they exist, are owing in large measure to temporary or
+local causes; and that the tendency of recent years has been towards a
+decrease in all forms of corruption.
+
+The expenses connected with elections, such as the renting and preparing
+of the polling-places, the payment of the clerks and other officers who
+conduct the elections and count the vote, are borne by the community. A
+candidate therefore is not, as far as the law is concerned, liable to
+any expense whatever. As a matter of fact he does commonly contribute to
+the party treasury, though in the case of certain candidates,
+particularly those for the presidency and for judicial offices,
+financial contributions are not general. The amount of a candidate's
+contribution varies greatly, according to the office sought, the state
+in which he lives, and his private wealth. On one occasion, in a
+district in New York, a candidate for Congress is credibly believed to
+have spent at one election $50,000. On the other hand, in a
+Congressional election in a certain district in Massachusetts, the only
+expenditure of one of the candidates was for the two-cent stamp placed
+on his letter of acceptance. No estimate of the average amount expended
+can be made. It is, however, the conclusion of Mr Bryce, in his
+_American Commonwealth_, that as a rule a seat in Congress costs the
+candidate less than a seat for a county division in the House of
+Commons. (See also BALLOT.)
+
+
+
+
+ELECTION, in English law, the obligation imposed upon a party by courts
+of equity to choose between two inconsistent or alternative rights or
+claims in cases where there is a clear intention of the person from whom
+he derives one that he should not enjoy both. Thus a testator died
+seized of property in fee simple and in fee tail--he had two daughters,
+and devised the fee simple property to one and the entailed property to
+the other; the first one claimed to have her share of the entailed
+property as coparcener and also to retain the benefit she took under the
+will. It was held that she was put to her election whether she would
+take under the will and renounce her claim to the entailed property or
+take against the will, in which case she must renounce the benefits she
+took under the will in so far as was necessary to compensate her sister.
+As the essence of the doctrine is compensation, a person electing
+against a document does not lose all his rights under it, but the court
+will sequester so much only of the benefit intended for him as will
+compensate the persons disappointed by his election. For the same reason
+it is necessary that there should be a free and disposable fund passing
+by the instrument from which compensation can be made in the event of
+election against the will. If, therefore, a man having a special power
+of appointment appoint the fund equally between two persons, one being
+an object of the power and the other not an object, no question of
+election arises, but the appointment to the person not an object is bad.
+
+Election, though generally arising in cases of wills, may also arise in
+the case of a deed. There is, however, a distinction to be observed. In
+the case of a will a clear intention on the part of the testator that he
+meant to dispose of property not his own must be shown, and parol
+evidence is not admissible as to this. In the case of a deed, however,
+no such intention need be shown, for if a deed confers a benefit and
+imposes a liability on the same person he cannot be allowed to accept
+the one and reject the other, but this must be distinguished from cases
+where two separate gifts are given to a person, one beneficial and the
+other onerous. In such a case no question of election arises and he may
+take the one and reject the other, unless, indeed, there are words used
+which make the one conditional on the acceptance of the other.
+
+Election is either express, e.g. by deed, or implied; in the latter case
+it is often a question of considerable difficulty whether there has in
+fact been an election or not; each case must depend upon the particular
+circumstances, but quite generally it may be said that the person who
+has elected must have been capable of electing, aware of the existence
+of the doctrine of election, and have had the opportunity of satisfying
+himself of the relative value of the properties between which he has
+elected. In the case of infants the court will sometimes elect after an
+inquiry as to which course is the most advantageous, or if there is no
+immediate urgency, will allow the matter to stand over till the infant
+attains his majority. In the cases of married women and lunatics the
+courts will exercise the right for them. It sometimes happens that the
+parties have so dealt with the property that it would be inequitable to
+disturb it; in such cases the court will not interfere in order to allow
+of election.
+
+
+
+
+ELECTORAL COMMISSION, in United States history, a commission created to
+settle the disputed presidential election of 1876. In this election
+Samuel J. Tilden, the Democratic candidate, received 184 uncontested
+electoral votes, and Rutherford B. Hayes, the Republican candidate,
+163.[1] The states of Florida, Louisiana, Oregon and South Carolina,
+with a total of 22 votes, each sent in two sets of electoral ballots,[2]
+and from each of these states except Oregon one set gave the whole vote
+to Tilden and the other gave the whole vote to Hayes. From Oregon one
+set of ballots gave the three electoral votes of the state to Hayes; the
+other gave two votes to Hayes and one to Tilden.
+
+The election of a president is a complex proceeding, the method being
+indicated partly in the Constitution, and being partly left to Congress
+and partly to the states. The manner of selecting the electors is left
+to state law; the electoral ballots are sent to the president of the
+Senate, who "shall, in the presence of the Senate and House of
+Representatives, open all certificates, and the votes shall then be
+counted." Concerning this provision many questions of vital importance
+arose in 1876: Did the president of the Senate count the votes, the
+houses being mere witnesses; or did the houses count them, the
+president's duties being merely ministerial? Did counting imply the
+determination of what should be counted, or was it a mere arithmetical
+process; that is, did the Constitution itself afford a method of
+settling disputed returns, or was this left to legislation by Congress?
+Might Congress or an officer of the Senate go behind a state's
+certificate and review the acts of its certifying officials? Might it go
+further and examine into the choice of electors? And if it had such
+powers, might it delegate them to a commission? As regards the procedure
+of Congress, it seems that, although in early years the president of the
+Senate not only performed or overlooked the electoral count but also
+exercised discretion in some matters very important in 1876, Congress
+early began to assert power, and, at least from 1821 onward, controlled
+the count, claiming complete power. The fact, however, that the Senate
+in 1876 was controlled by the Republicans and the House by the
+Democrats, lessened the chances of any harmonious settlement of these
+questions by Congress. The country seemed on the verge of civil war.
+Hence it was that by an act of the 29th of January 1877, Congress
+created the Electoral Commission to pass upon the contested returns,
+giving it "the same powers, if any" possessed by itself in the premises,
+the decisions to stand unless rejected by the two houses separately. The
+commission was composed of five Democratic and five Republican
+Congressmen, two justices of the Supreme Court of either party, and a
+fifth justice chosen by these four. As its members of the commission the
+Senate chose G.F. Edmunds of Vermont, O.P. Morton of Indiana, and F.T.
+Frelinghuysen of New Jersey (Republicans); and A.G. Thurman of Ohio and
+T.F. Bayard of Delaware (Democrats). The House chose Henry B. Payne of
+Ohio, Eppa Hunton of Virginia, and Josiah G. Abbott of Massachusetts
+(Democrats); and George F. Hoar of Massachusetts and James A. Garfield
+of Ohio (Republicans). The Republican judges were William Strong and
+Samuel F. Miller; the Democratic, Nathan Clifford and Stephen J. Field.
+These four chose as the fifteenth member Justice Joseph P. Bradley, a
+Republican but the only member not selected avowedly as a partisan. As
+counsel for the Democratic candidate there appeared before the
+commission at different times Charles O'Conor of New York, Jeremiah S.
+Black of Pennsylvania, Lyman Trumbull of Illinois, R.T. Merrick of the
+District of Columbia, Ashbel Green of New Jersey, Matthew H. Carpenter
+of Wisconsin, George Hoadley of Ohio, and W.C. Whitney of New York. W.M.
+Evarts and E.W. Stoughton of New York and Samuel Shellabarger and
+Stanley Matthews of Ohio appeared regularly in behalf of Mr Hayes.
+
+The popular vote seemed to indicate that Hayes had carried South
+Carolina and Oregon, and Tilden Florida and Louisiana. It was evident,
+however, that Hayes could secure the 185 votes necessary to elect only
+by gaining every disputed ballot. As the choice of Republican electors
+in Louisiana had been accomplished by the rejection of several thousand
+Democratic votes by a Republican returning board, the Democrats insisted
+that the commission should go behind the returns and correct injustice;
+the Republicans declared that the state's action was final, and that to
+go behind the returns would be invading its sovereignty. When this
+matter came before the commission it virtually accepted the Republican
+contention, ruling that it could not go behind the returns except on the
+superficial issues of manifest fraud therein or the eligibility of
+electors to their office under the Constitution; that is, it could not
+investigate antecedents of fraud or misconduct of state officials in the
+results certified. All vital questions were settled by the votes of
+eight Republicans and seven Democrats; and as the Republican Senate
+would never concur with the Democratic House in overriding the
+decisions, all the disputed votes were awarded to Mr Hayes, who
+therefore was declared elected.
+
+The strictly partisan votes of the commission and the adoption by
+prominent Democrats and Republicans, both within and without the
+commission, of an attitude toward states-rights principles quite
+inconsistent with party tenets and tendencies, have given rise to much
+severe criticism. The Democrats and the country, however, quietly
+accepted the decision. The judgments underlying it were two: (1) That
+Congress rightly claimed the power to settle such contests within the
+limits set; (2) that, as Justice Miller said regarding these limits, the
+people had never at any time intended to give to Congress the power, by
+naming the electors, to "decide who are to be the president and
+vice-president of the United States."
+
+There is no doubt that Mr Tilden was morally entitled to the presidency,
+and the correction of the Louisiana frauds would certainly have given
+satisfaction then and increasing satisfaction later, in the retrospect,
+to the country. The commission might probably have corrected the frauds
+without exceeding its Congressional precedents. Nevertheless, the
+principles of its decisions must be recognized by all save
+ultra-nationalists as truer to the spirit of the Constitution and
+promising more for the good of the country than would have been the
+principles necessary to a contrary decision.
+
+By an act of the 3rd of February 1887 the electoral procedure is
+regulated in great detail. Under this act determination by a state of
+electoral disputes is conclusive, subject to certain formalities that
+guarantee definite action and accurate certification. These formalities
+constitute "regularity," and are in all cases judgable by Congress. When
+Congress is forced by the lack or evident inconclusiveness of state
+action, or by conflicting state action, to decide disputes, votes are
+lost unless both houses concur.
+
+  AUTHORITIES.--J.F. Rhodes, _History of the United States_, vol. 7,
+  covering 1872-1877 (New York, 1906); P.L. Haworth, _The Hayes-Tilden
+  disputed Presidential Election of 1876_ (Cleveland, 1906); J.W.
+  Burgess, _Political Science Quarterly_, vol. 3 (1888), pp. 633-653,
+  "The Law of the Electoral Count"; and for the sources. Senate
+  Miscellaneous Document No. 5 (vol. 1), and House Miscel. Doc. No. 13
+  (vol. 2), 44 Congress, 2 Session,--_Count of the Electoral Vote.
+  Proceedings of Congress and Electoral Commission_,--the latter
+  identical with _Congressional Record_, vol. 5, pt. 4, 44 Cong., 2
+  Session; also about twenty volumes of evidence on the state elections
+  involved. The volume called _The Presidential Counts_ (New York, 1877)
+  was compiled by Mr. Tilden and his secretary.
+
+
+FOOTNOTES:
+
+  [1] The election of a vice-president was, of course, involved also.
+    William A. Wheeler was the Republican candidate, and Thomas A.
+    Hendricks the Democratic.
+
+  [2] A second set of electoral ballots had also been sent in from
+    Vermont, where Hayes had received a popular majority vote of 24,000.
+    As these ballots had been transmitted in an irregular manner, the
+    president of the Senate refused to receive them, and was sustained in
+    this action by the upper House.
+
+
+
+
+ELECTORS (Ger. _Kurfursten_, from _Kuren_, O.H.G. _kiosan_, choose,
+elect, and _Furst_, prince), a body of German princes, originally seven
+in number, with whom rested the election of the German king, from the
+13th until the beginning of the 19th century. The German kings, from the
+time of Henry the Fowler (919-936) till the middle of the 13th century,
+succeeded to their position partly by heredity, and partly by election.
+Primitive Germanic practice had emphasized the element of heredity.
+_Reges ex nobilitate sumunt_: the man whom a German tribe recognized as
+its king must be in the line of hereditary descent from Woden; and
+therefore the genealogical trees of early Teutonic kings (as, for
+instance, in England those of the Kentish and West Saxon sovereigns) are
+carefully constructed to prove that descent from the god which alone
+will constitute a proper title for his descendants. Even from the first,
+however, there had been some opening for election; for the principle of
+primogeniture was not observed, and there might be several competing
+candidates, all of the true Woden stock. One of these competing
+candidates would have to be recognized (as the Anglo-Saxons said,
+_geceosan_); and to this limited extent Teutonic kings may be termed
+elective from the very first. In the other nations of western Europe
+this element of election dwindled, and the principle of heredity alone
+received legal recognition; in medieval Germany, on the contrary, the
+principle of heredity, while still exercising an inevitable natural
+force, sank formally into the background, and legal recognition was
+finally given to the elective principle. _De facto_, therefore, the
+principle of heredity exercises in Germany a great influence, an
+influence never more striking than in the period which follows on the
+formal recognition of the elective principle, when the Habsburgs (like
+the Metelli at Rome) _fato imperatores fiunt: de jure_, each monarch
+owes his accession simply and solely to the vote of an electoral
+college.
+
+This difference between the German monarchy and the other monarchies of
+western Europe may be explained by various considerations. Not the least
+important of these is what seems a pure accident. Whereas the Capetian
+monarchs, during the three hundred years that followed on the election
+of Hugh Capet in 987, always left an heir male, and an heir male of full
+age, the German kings again and again, during the same period, either
+left a minor to succeed to their throne, or left no issue at all. The
+principle of heredity began to fail because there were no heirs. Again
+the strength of tribal feeling in Germany made the monarchy into a
+prize, which must not be the apanage of any single tribe, but must
+circulate, as it were, from Franconian to Saxon, from Saxon to Bavarian,
+from Bavarian to Franconian, from Franconian to Swabian; while the
+growing power of the baronage, and its habit of erecting anti-kings to
+emphasize its opposition to the crown (as, for instance, in the reign of
+Henry IV.), coalesced with and gave new force to the action of tribal
+feeling. Lastly, the fact that the German kings were also Roman emperors
+finally and irretrievably consolidated the growing tendency towards the
+elective principle. The principle of heredity had never held any great
+sway under the ancient Roman Empire (see under EMPEROR); and the
+medieval Empire, instituted as it was by the papacy, came definitely
+under the influence of ecclesiastical prepossessions in favour of
+election. The church had substituted for that descent from Woden, which
+had elevated the old pagan kings to their thrones, the conception that
+the monarch derived his crown from the choice of God, after the manner
+of Saul; and the theoretical choice of God was readily turned into the
+actual choice of the church, or, at any rate, of the general body of
+churchmen. If an ordinary king is thus regarded by the church as
+essentially elected, much more will the emperor, connected as he is with
+the church as one of its officers, be held to be also elected; and as a
+bishop is chosen by the chapter of his diocese, so, it will be thought,
+must the emperor be chosen by some corresponding body in his empire.
+Heredity might be tolerated in a mere matter of kingship: the precious
+trust of imperial power could not be allowed to descend according to the
+accidents of family succession. To Otto of Freising (_Gesta Frid._ ii.
+1) it is already a point of right vindicated for itself by the
+excellency of the Roman Empire, as a matter of singular prerogative,
+that it should not descend _per sanguinis propaginem, sed per principum
+electionem_.
+
+The accessions of Conrad II. (see Wipo, _Vita Cuonradi_, c. 1-2), of
+Lothair II. (see _Narratio de electione Lotharii_, M.G.H. _Scriptt._
+xii. p. 510), of Conrad III. (see Otto of Freising, _Chronicon_, vii.
+22) and of Frederick I. (see Otto of Freising, _Gesta Frid._ ii. 1) had
+all been marked by an element, more or less pronounced, of election.
+That element is perhaps most considerable in the case of Lothair, who
+had no rights of heredity to urge. Here we read of ten princes being
+selected from the princes of the various duchies, to whose choice the
+rest promise to assent, and of these ten selecting three candidates, one
+of whom, Lothair, is finally chosen (apparently by the whole assembly)
+in a somewhat tumultuary fashion. In this case the electoral assembly
+would seem to be, in the last resort, the whole diet of all the princes.
+But a _de facto_ pre-eminence in the act of election is already, during
+the 12th century, enjoyed by the three Rhenish archbishops, probably
+because of the part they afterwards played at the coronation, and also
+by the dukes of the great duchies--possibly because of the part they too
+played, as vested for the time with the great offices of the household,
+at the coronation feast.[1] Thus at the election of Lothair it is the
+archbishop of Mainz who conducts the proceedings; and the election is
+not held to be final until the duke of Bavaria has given his assent. The
+fact is that, votes being weighed by quality as well as by quantity (see
+DIET), the votes of the archbishops and dukes, which would first be
+taken, would of themselves, if unanimous, decide the election. To
+prevent tumultuary elections, it was well that the election should be
+left exclusively with these great dignitaries; and this is what, by the
+middle of the 13th century, had eventually been done.
+
+The chaos of the interregnum from 1198 to 1212 showed the way for the
+new departure; the chaos of the great interregnum (1250-1273) led to its
+being finally taken. The decay of the great duchies, and the narrowing
+of the class of princes into a close corporation, some of whose members
+were the equals of the old dukes in power, introduced difficulties and
+doubts into the practice of election which had been used in the 12th
+century. The contested election of the interregnum of 1198-1212 brought
+these difficulties and doubts into strong relief. The famous bull of
+Innocent III. (_Venerabilem_), in which he decided for Otto IV. against
+Philip of Swabia, on the ground that, though he had fewer votes than
+Philip, he had a majority of the votes of those _ad quos principaliter
+spectat electio_, made it almost imperative that there should be some
+definition of these principal electors. The most famous attempt at such
+a definition is that of the _Sachsenspiegel_, which was followed, or
+combated, by many other writers in the first half of the 13th century.
+Eventually the contested election of 1257 brought light and definition.
+Here we find seven potentates acting--the same seven whom the Golden
+Bull recognizes in 1356; and we find these seven described in an
+official letter to the pope, as _principes vocem in hujusmodi electione
+habentes, qui sunt septem numero_. The doctrine thus enunciated was at
+once received. The pope acknowledged it in two bulls (1263); a cardinal,
+in a commentary on the bull _Venerabilem_ of Innocent III., recognized
+it about the same time; and the erection of statues of the seven
+electors at Aix-la-Chapelle gave the doctrine a visible and outward
+expression.
+
+By the date of the election of Rudolph of Habsburg (1273) the seven
+electors may be regarded as a definite body, with an acknowledged right.
+But the definition and the acknowledgment were still imperfect. (1) The
+composition of the electoral body was uncertain in two respects. The
+duke of Bavaria claimed as his right the electoral vote of the king of
+Bohemia; and the practice of _partitio_ in electoral families tended to
+raise further difficulties about the exercise of the vote. The Golden
+Bull of 1356 settled both these questions. Bohemia (of which Charles
+IV., the author of the Golden Bull, was himself the king) was assigned
+the electoral vote in preference to Bavaria; and a provision annexing
+the electoral vote to a definite territory, declaring that territory
+indivisible, and regulating its descent by the rule of primogeniture
+instead of partition, swept away the old difficulties which the custom
+of partition had raised. After 1356 the seven electors are regularly the
+three Rhenish archbishops, Mainz, Cologne and Trier, and four lay
+magnates, the palatine of the Rhine, the duke of Saxony, the margrave of
+Brandenburg, and the king of Bohemia; the three former being vested with
+the three archchancellorships, and the four latter with the four offices
+of the royal household (see HOUSEHOLD). (2) The rights of the seven
+electors, in their collective capacity as an electoral college, were a
+matter of dispute with the papacy. The result of the election, whether
+made, as at first, by the princes generally or, as after 1257, by the
+seven electors exclusively, was in itself simply the creation of a
+German king--an _electio in regem_. But since 962 the German king was
+also, after coronation by the pope, Roman emperor. Therefore the
+election had a double result: the man elected was not only _electus in
+regem_, but also _promovendus ad imperium_. The difficulty was to define
+the meaning of the term _promovendus_. Was the king elect _inevitably_
+to become emperor? or did the _promotio_ only follow at the discretion
+of the pope, if he thought the king elect fit for promotion? and if so,
+to what extent, and according to what standard, did the pope judge of
+such fitness? Innocent III. had already claimed, in the bull
+_Venerabilem_, (1) that the electors derived their power of election, so
+far as it made an emperor, from the Holy See (which had originally
+"translated" the Empire from the East to the West), and (2) that the
+papacy had a _jus et auctoritas examinandi personam electam in regem et
+promovendam ad imperium_. The latter claim he had based on the fact that
+he anointed, consecrated and crowned the emperor--in other words, that
+he gave a spiritual office according to spiritual methods, which
+entitled him to inquire into the fitness of the recipient of that
+office, as a bishop inquires into the fitness of a candidate for
+ordination. Innocent had put forward this claim as a ground for deciding
+between competing candidates: Boniface VIII. pressed the claim against
+Albert I. in 1298, even though his election was unanimous; while John
+XXII. exercised it in its harshest form, when in 1324 he ex-communicated
+Louis IV. for using the title and exerting the rights even of king
+without previous papal confirmation. This action ultimately led to a
+protest from the electors themselves, whose right of election would have
+become practically meaningless, if such assumptions had been tolerated.
+A meeting of the electors (_Kurverein_) at Rense in 1338 declared (and
+the declaration was reaffirmed by a diet at Frankfort in the same year)
+that _postquam aliquis eligitur in Imperatorem sive Regem ab Electoribus
+Imperii concorditer, vel majori parte eorundem, statim ex sola electione
+est Rex verus et Imperator Romanus censendus ... nec Papae sive Sedis
+Apostolicae ... approbatione ... indiget_. The doctrine thus positively
+affirmed at Rense is negatively reaffirmed in the Golden Bull, in which
+a significant silence is maintained in regard to papal rights. But the
+doctrine was not in practice followed: Sigismund himself did not venture
+to dispense with papal approbation.
+
+By the end of the 14th century the position of the electors, both
+individually and as a corporate body, had become definite and precise.
+Individually, they were distinguished from all other princes, as we have
+seen, by the indivisibility of their territories and by the custom of
+primogeniture which secured that indivisibility; and they were still
+further distinguished by the fact that their person, like that of the
+emperor himself, was protected by the law of treason, while their
+territories were only subject to the jurisdiction of their own courts.
+They were independent territorial sovereigns; and their position was at
+once the envy and the ideal of the other princes of Germany. Such had been
+the policy of Charles IV.; and thus had he, in the Golden Bull, sought to
+magnify the seven electors, and himself as one of the seven, in his
+capacity of king of Bohemia, even at the expense of the Empire, and of
+himself in his capacity of emperor. Powerful as they were, however, in
+their individual capacity, the electors showed themselves no less powerful
+as a corporate body. As such a corporate body, they may be considered from
+three different points of view, and as acting in three different
+capacities. They are an electoral body, choosing each successive emperor;
+they are one of the three colleges of the imperial diet (see DIET); and
+they are also an electoral union (_Kurfurstenverein_), acting as a
+separate and independent political organ even after the election, and
+during the reign, of the monarch. It was in this last capacity that they
+had met at Rense in 1338; and in the same capacity they acted repeatedly
+during the 15th century. According to the Golden Bull, such meetings were
+to be annual, and their deliberations were to concern "the safety of the
+Empire and the world." Annual they never were; but occasionally they
+became of great importance. In 1424, during the attempt at reform
+occasioned by the failure of German arms against the Hussites, the
+_Kurfurstenverein_ acted, or at least it claimed to act, as the
+predominant partner in a duumvirate, in which the unsuccessful Sigismund
+was relegated to a secondary position. During the long reign of Frederick
+III.--a reign in which the interests of Austria were cherished, and the
+welfare of the Empire neglected, by that apathetic yet tenacious
+emperor--the electors once more attempted, in the year 1453, to erect a
+new central government in place of the emperor, a government which, if not
+conducted by themselves directly in their capacity of a
+_Kurfurstenverein_, should at any rate be under their influence and
+control. So, they hoped, Germany might be able to make head against that
+papal aggression, to which Frederick had yielded, and to take a leading
+part in that crusade against the Turks, which he had neglected. Like the
+previous attempt at reform during the Hussite wars, the scheme came to
+nothing; the forces of disunion in Germany were too strong for any central
+government, whether monarchical and controlled by the emperor, or
+oligarchical and controlled by the electors. But a final attempt, the most
+strenuous of all, was made in the reign of Maximilian I., and under the
+influence of Bertold, elector and archbishop of Mainz. The council of
+1500, in which the electors (with the exception of the king of Bohemia)
+were to have sat, and which would have been under their control,
+represents the last effective attempt at a real _Reichsregiment_.
+Inevitably, however, it shipwrecked on the opposition of Maximilian; and
+though the attempt was again made between 1521 and 1530, the idea of a
+real central government under the control of the electors perished, and
+the development of local administration by the circle took its place.
+
+In the course of the 16th century a new right came to be exercised by
+the electors. As an electoral body (that is to say, in the first of the
+three capacities distinguished above), they claimed, at the election of
+Charles V. in 1519 and at subsequent elections, to impose conditions on
+the elected monarch, and to determine the terms on which he should
+exercise his office in the course of his reign. This _Wahlcapitulation_,
+similar to the _Pacta Conventa_ which limited the elected kings of
+Poland, was left by the diet to the discretion of the electors, though
+after the treaty of Westphalia an attempt was made, with some little
+success,[2] to turn the capitulation into a matter of legislative
+enactment by the diet. From this time onwards the only fact of
+importance in the history of the electors is the change which took place
+in the composition of their body during the 17th and 18th centuries.
+From the Golden Bull to the treaty of Westphalia (1356-1648) the
+composition of the electoral body had remained unchanged. In 1623,
+however, in the course of the Thirty Years' War, the vote of the count
+palatine of the Rhine had been transferred to the duke of Bavaria; and
+at the treaty of Westphalia the vote, with the office of imperial butler
+which it carried, was left to Bavaria, while an eighth vote, along with
+the new office of imperial treasurer, was created for the count
+palatine. In 1708 a ninth vote, along with the office of imperial
+standard-bearer, was created for Hanover; while finally, in 1778, the
+vote of Bavaria and the office of imperial butler returned to the counts
+palatine, as heirs of the duchy, on the extinction of the ducal line,
+while the new vote created for the Palatinate in 1648, with the office
+of imperial treasurer, was transferred to Brunswick-Luneburg (Hanover)
+in lieu of the one which this house already held. In 1806, on the
+dissolution of the Holy Roman Empire, the electors ceased to exist.
+
+  LITERATURE.--T. Lindner, _Die deutschen Konigswahlen und die
+  Entstehung des Kurfurstentums_ (1893), and _Der Hergang bei den
+  deutschen Konigswahlen_ (1899); R. Kirchhofer, _Zur Entstehung des
+  Kurkollegiums_ (1893); W. Maurenbrecher, _Geschichte der deutschen
+  Konigswahlen_ (1889); and G. Blondel, _Etude sur Frederic II_, p. 27
+  sqq. See also J. Bryce, _Holy Roman Empire_ (edition of 1904), c. ix.;
+  and R. Schroder, _Lehrbuch der deutschen Rechtsgeschichte_, pp.
+  471-481 and 819-820.     (E. Br.)
+
+
+FOOTNOTES:
+
+  [1] This is the view of the _Sachsenspiegel_, and also of Albert of
+    Stade (quoted in Schroder, p. 476, n. 27): "Palatinus eligit, quia
+    dapifer est; dux Saxoniae, quia marescalcus," &c. Schroder points out
+    (p. 479, n. 45) that "participation in the coronation feast is an
+    express recognition of the king"; and those who are to discharge
+    their office in the one must have had a prominent voice in the other.
+
+  [2] See Schroder's _Lehrbuch der deutschen Rechtsgeschichte_, p. 820.
+
+
+
+
+ELECTRA ([Greek: Elektra]), "the bright one," in Greek mythology. (1)
+One of the seven Pleiades, daughter of Atlas and Pleione. She is closely
+connected with the old constellation worship and the religion of
+Samothrace, the chief seat of the Cabeiri (q.v.), where she was
+generally supposed to dwell. By Zeus she was the mother of Dardanus,
+Iasion (or Eetion), and Harmonia; but in the Italian tradition, which
+represented Italy as the original home of the Trojans, Dardanus was her
+son by a king of Italy named Corythus. After her amour with Zeus,
+Electra fled to the Palladium as a suppliant, but Athena, enraged that
+it had been touched by one who was no longer a maiden, flung Electra and
+the image from heaven to earth, where it was found by Ilus, and taken by
+him to Ilium; according to another tradition, Electra herself took it to
+Ilium, and gave it to her son Dardanus (Schol. Eurip. _Phoen._ 1136). In
+her grief at the destruction of the city she plucked out her hair and
+was changed into a comet; in another version Electra and her six sisters
+had been placed among the stars as the Pleiades, and the star which she
+represented lost its brilliancy after the fall of Troy. Electra's
+connexion with Samothrace (where she was also called Electryone and
+Strategis) is shown by the localization of the carrying off of her
+reputed daughter Harmonia by Cadmus, and by the fact that, according to
+Athenicon (the author of a work on Samothrace quoted by the scholiast on
+Apollonius Rhodius i. 917), the Cabeiri were Dardanus and Iasion. The
+gate Electra at Thebes and the fabulous island Electris were said to
+have been called after her (Apollodorus iii. 10. 12; Servius on _Aen._
+iii. 167, vii. 207, x. 272, _Georg._ i. 138).
+
+(2) Daughter of Agamemnon and Clytaemnestra, sister of Orestes and
+Iphigeneia. She does not appear in Homer, although according to Xanthus
+(regarded by some as a fictitious personage), to whom Stesichorus was
+indebted for much in his _Oresteia_, she was identical with the Homeric
+Laodice, and was called Electra because she remained so long unmarried
+([Greek: 'A-lektra]). She was said to have played an important part in
+the poem of Stesichorus, and subsequently became a favourite figure in
+tragedy. After the murder of her father on his return from Troy by her
+mother and Aegisthus, she saved the life of her brother Orestes by
+sending him out of the country to Strophius, king of Phanote in Phocis,
+who had him brought up with his own son Pylades. Electra, cruelly
+ill-treated by Clytaemnestra and her paramour, never loses hope that her
+brother will return to avenge his father. When grown up, Orestes, in
+response to frequent messages from his sister, secretly repairs with
+Pylades to Argos, where he pretends to be a messenger from Strophius
+bringing the news of the death of Orestes. Being admitted to the palace,
+he slays both Aegisthus and Clytaemnestra. According to another story
+(Hyginus, _Fab._ 122), Electra, having received a false report that
+Orestes and Pylades had been sacrificed to Artemis in Tauris, went to
+consult the oracle at Delphi. In the meantime Aletes, the son of
+Aegisthus, seized the throne of Mycenae. Her arrival at Delphi coincided
+with that of Orestes and Iphigeneia. The same messenger, who had already
+communicated the false report of the death of Orestes, informed her that
+he had been slain by Iphigeneia. Electra in her rage seized a burning
+brand from the altar, intending to blind her sister; but at the critical
+moment Orestes appeared, recognition took place, and the brother and
+sister returned to Mycenae. Aletes was slain by Orestes, and Electra
+became the wife of Pylades. The story of Electra is the subject of the
+_Choephori_ of Aeschylus, the _Electra_ of Sophocles and the _Electra_
+of Euripides. It is in the Sophoclean play that Electra is most
+prominent.
+
+  There are many variations in the treatment of the legend, for which,
+  as also for a discussion of the modern plays on the subject by
+  Voltaire and Alfieri, see Jebb's Introduction to his edition of the
+  _Electra_ of Sophocles.
+
+
+
+
+ELECTRICAL (or ELECTROSTATIC) MACHINE, a machine operating by manual or
+other power for transforming mechanical work into electric energy in the
+form of electrostatic charges of opposite sign delivered to separate
+conductors. Electrostatic machines are of two kinds: (1) Frictional, and
+(2) Influence machines.
+
+[Illustration: FIG. 1.--Ramsden's electrical machine.]
+
+_Frictional Machines._--A primitive form of frictional electrical
+machine was constructed about 1663 by Otto von Guericke (1602-1686). It
+consisted of a globe of sulphur fixed on an axis and rotated by a winch,
+and it was electrically excited by the friction of warm hands held
+against it. Sir Isaac Newton appears to have been the first to use a
+glass globe instead of sulphur (_Optics_, 8th Query). F. Hawksbee in
+1709 also used a revolving glass globe. A metal chain resting on the
+globe served to collect the charge. Later G.M. Bose (1710-1761), of
+Wittenberg, added the prime conductor, an insulated tube or cylinder
+supported on silk strings, and J.H. Winkler (1703-1770), professor of
+physics at Leipzig, substituted a leather cushion for the hand. Andreas
+Gordon (1712-1751) of Erfurt, a Scotch Benedictine monk, first used a
+glass cylinder in place of a sphere. Jesse Ramsden (1735-1800) in 1768
+constructed his well-known form of plate electrical machine (fig. 1). A
+glass plate fixed to a wooden or metal shaft is rotated by a winch. It
+passes between two rubbers made of leather, and is partly covered with
+two silk aprons which extend over quadrants of its surface. Just below
+the places where the aprons terminate, the glass is embraced by two
+insulated metal forks having the sharp points projecting towards the
+glass, but not quite touching it. The glass is excited positively by
+friction with the rubbers, and the charge is drawn off by the action of
+the points which, when acted upon inductively, discharge negative
+electricity against it. The insulated conductor to which the points are
+connected therefore becomes positively electrified. The cushions must be
+connected to earth to remove the negative electricity which accumulates
+on them. It was found that the machine acted better if the rubbers were
+covered with bisulphide of tin or with F. von Kienmayer's amalgam,
+consisting of one part of zinc, one of tin and two of mercury. The
+cushions were greased and the amalgam in a state of powder spread over
+them. Edward Nairne's electrical machine (1787) consisted of a glass
+cylinder with two insulated conductors, called prime conductors, on
+glass legs placed near it. One of these carried the leather exacting
+cushions and the other the collecting metal points, a silk apron
+extending over the cylinder from the cushion almost to the points. The
+rubber was smeared with amalgam. The function of the apron is to prevent
+the escape of electrification from the glass during its passage from the
+rubber to the collecting points. Nairne's machine could give either
+positive or negative electricity, the first named being collected from
+the prime conductor carrying the collecting points and the second from
+the prime conductor carrying the cushion.
+
+[Illustration: FIG. 2.]
+
+_Influence Machines._--Frictional machines are, however, now quite
+superseded by the second class of instrument mentioned above, namely,
+influence machines. These operate by electrostatic induction and convert
+mechanical work into electrostatic energy by the aid of a small initial
+charge which is continually being replenished or reinforced. The general
+principle of all the machines described below will be best understood by
+considering a simple ideal case. Imagine two Leyden jars with large
+brass knobs, A and B, to stand on the ground (fig. 2). Let one jar be
+initially charged with positive electricity on its inner coating and the
+other with negative, and let both have their outsides connected to
+earth. Imagine two insulated balls A' and B' so held that A' is near A
+and B' is near B. Then the positive charge on A induces two charges on
+A', viz.: a negative on the side nearest and a positive on the side most
+removed. Likewise the negative charge on B induces a positive charge on
+the side of B' nearest to it and repels negative electricity to the far
+side. Next let the balls A' and B' be connected together for a moment by
+a wire N called a neutralizing conductor which is subsequently removed.
+Then A' will be left negatively electrified and B' will be left
+positively electrified. Suppose that A' and B' are then made to change
+places. To do this we shall have to exert energy to remove A' against
+the attraction of A and B' against the attraction of B. Finally let A'
+be brought in contact with B and B' with A. The ball A' will give up its
+charge of negative electricity to the Leyden jar B, and the ball B' will
+give up its positive charge to the Leyden jar A. This transfer will take
+place because the inner coatings of the Leyden jars have greater
+capacity with respect to the earth than the balls. Hence the charges of
+the jars will be increased. The balls A' and B' are then practically
+discharged, and the above cycle of operations may be repeated. Hence,
+however small may be the initial charges of the Leyden jars, by a
+principle of accumulation resembling that of compound interest, they can
+be increased as above shown to any degree. If this series of operations
+be made to depend upon the continuous rotation of a winch or handle, the
+arrangement constitutes an electrostatic influence machine. The
+principle therefore somewhat resembles that of the self-exciting dynamo.
+
+
+  Bennet's Doubler.
+
+The first suggestion for a machine of the above kind seems to have grown
+out of the invention of Volta's electrophorus. Abraham Bennet, the
+inventor of the gold leaf electroscope, described a doubler or machine
+for multiplying electric charges (_Phil. Trans._, 1787).
+
+  The principle of this apparatus may be explained thus. Let A and C be
+  two fixed disks, and B a disk which can be brought at will within a
+  very short distance of either A or C. Let us suppose all the plates to
+  be equal, and let the capacities of A and C in presence of B be each
+  equal to p, and the coefficient of induction between A and B, or C and
+  B, be q. Let us also suppose that the plates A and C are so distant
+  from each other that there is no mutual influence, and that p' is the
+  capacity of one of the disks when it stands alone. A small charge Q is
+  communicated to A, and A is insulated, and B, uninsulated, is brought
+  up to it; the charge on B will be--(q/p)Q. B is now uninsulated and
+  brought to face C, which is uninsulated; the charge on C will be
+  (q/p)^2Q. C is now insulated and connected with A, which is always
+  insulated. B is then brought to face A and uninsulated, so that the
+  charge on A becomes rQ, where
+
+           p      /    q^2\
+    r = -------- ( 1 + --- ).
+        (p + p')  \    p^2/
+
+  A is now disconnected from C, and here the first operation ends. It is
+  obvious that at the end of n such operations the charge on A will be
+  r^_(n)Q, so that the charge goes on increasing in geometrical
+  progression. If the distance between the disks could be made
+  infinitely small each time, then the multiplier r would be 2, and the
+  charge would be doubled each time. Hence the name of the apparatus.
+
+[Illustration: FIG. 3.--Nicholson's Revolving Doubler.]
+
+
+  Nicholson's doubler.
+
+Erasmus Darwin, B. Wilson, G.C. Bohnenberger and J.C.E. Peclet devised
+various modifications of Bennet's instrument (see S.P. Thompson, "The
+Influence Machine from 1788 to 1888," _Journ. Soc. Tel. Eng._, 1888, 17,
+p. 569). Bennet's doubler appears to have given a suggestion to William
+Nicholson (_Phil. Trans._, 1788, p. 403) of "an instrument which by
+turning a winch produced the two states of electricity without friction
+or communication with the earth." This "revolving doubler," according to
+the description of Professor S.P. Thompson (_loc. cit._), consists of
+two fixed plates of brass A and C (fig. 3), each two inches in diameter
+and separately supported on insulating arms in the same plane, so that a
+third revolving plate B may pass very near them without touching. A
+brass ball D two inches in diameter is fixed on the end of the axis that
+carries the plate B, and is loaded within at one side, so as to act as a
+counterpoise to the revolving plate B. The axis P N is made of varnished
+glass, and so are the axes that join the three plates with the brass
+axis N O. The axis N O passes through the brass piece M, which stands on
+an insulating pillar of glass, and supports the plates A and C. At one
+extremity of this axis is the ball D, and the other is connected with a
+rod of glass, N P, upon which is fixed the handle L, and also the piece
+G H, which is separately insulated. The pins E, F rise out of the back
+of the fixed plates A and C, at unequal distances from the axis. The
+piece K is parallel to G H, and both of them are furnished at their ends
+with small pieces of flexible wire that they may touch the pins E, F in
+certain points of their revolution. From the brass piece M there stands
+out a pin I, to touch against a small flexible wire or spring which
+projects sideways from the rotating plate B when it comes opposite A.
+The wires are so adjusted by bending that B, at the moment when it is
+opposite A, communicates with the ball D, and A communicates with C
+through GH; and half a revolution later C, when B comes opposite to it,
+communicates with the ball D through the contact of K with F. In all
+other positions A, B, C and D are completely disconnected from each
+other. Nicholson thus described the operation of his machine:--
+
+  "When the plates A and B are opposite each other, the two fixed plates
+  A and C may be considered as one mass, and the revolving plate B,
+  together with the ball D, will constitute another mass. All the
+  experiments yet made concur to prove that these two masses will not
+  possess the same electric state.... The redundant electricities in the
+  masses under consideration will be unequally distributed; the plate A
+  will have about ninety-nine parts, and the plate C one; and, for the
+  same reason, the revolving plate B will have ninety-nine parts of the
+  opposite electricity, and the ball D one. The rotation, by destroying
+  the contacts, preserves this unequal distribution, and carries B from
+  A to C at the same time that the tail K connects the ball with the
+  plate C. In this situation, the electricity in B acts upon that in C,
+  and produces the contrary state, by virtue of the communication
+  between C and the ball; which last must therefore acquire an
+  electricity of the same kind with that of the revolving plate. But the
+  rotation again destroys the contact and restores B to its first
+  situation opposite A. Here, if we attend to the effect of the whole
+  revolution, we shall find that the electric states of the respective
+  masses have been greatly increased; for the ninety-nine parts in A and
+  B remain, and the one part of electricity in C has been increased so
+  as nearly to compensate ninety-nine parts of the opposite electricity
+  in the revolving plate B, while the communication produced an opposite
+  mutation in the electricity of the ball. A second rotation will, of
+  course, produce a proportional augmentation of these increased
+  quantities; and a continuance of turning will soon bring the
+  intensities to their maximum, which is limited by an explosion between
+  the plates" (_Phil. Trans._, 1788, p. 405).
+
+[Illustration: FIG. 4.--Belli's Doubler.]
+
+
+  Belli's doubler.
+
+Nicholson described also another apparatus, the "spinning condenser,"
+which worked on the same principle. Bennet and Nicholson were followed
+by T. Cavallo, John Read, Bohnenberger, C.B. Desormes and J.N.P.
+Hachette and others in the invention of various forms of rotating
+doubler. A simple and typical form of doubler, devised in 1831 by G.
+Belli (fig. 4), consisted of two curved metal plates between which
+revolved a pair of balls carried on an insulating stem. Following the
+nomenclature usual in connexion with dynamos we may speak of the
+conductors which carry the initial charges as the field plates, and of
+the moving conductors on which are induced the charges which are
+subsequently added to those on the field plates, as the carriers. The
+wire which connects two armature plates for a moment is the neutralizing
+conductor. The two curved metal plates constitute the field plates and
+must have original charges imparted to them of opposite sign. The
+rotating balls are the carriers, and are connected together for a moment
+by a wire when in a position to be acted upon inductively by the field
+plates, thus acquiring charges of opposite sign. The moment after they
+are separated again. The rotation continuing the ball thus negatively
+charged is made to give up this charge to that negatively electrified
+field plate, and the ball positively charged its charge to the
+positively electrified field plate, by touching little contact springs.
+In this manner the field plates accumulate charges of opposite sign.
+
+[Illustration: FIG. 5.--Varley's Machine.]
+
+
+  Varley's machine.
+
+Modern types of influence machine may be said to date from 1860 when
+C.F. Varley patented a type of influence machine which has been the
+parent of numerous subsequent forms (_Brit. Pat. Spec._ No. 206 of
+1860). In it the field plates were sheets of tin-foil attached to a
+glass plate (fig. 5). In front of them a disk of ebonite or glass,
+having carriers of metal fixed to its edge, was rotated by a winch. In
+the course of their rotation two diametrically opposite carriers touched
+against the ends of a neutralizing conductor so as to form for a moment
+one conductor, and the moment afterwards these two carriers were
+insulated, one carrying away a positive charge and the other a negative.
+Continuing their rotation, the positively charged carrier gave up its
+positive charge by touching a little knob attached to the positive field
+plate, and similarly for the negative charge carrier. In this way the
+charges on the field plates were continually replenished and reinforced.
+Varley also constructed a multiple form of influence machine having six
+rotating disks, each having a number of carriers and rotating between
+field plates. With this apparatus he obtained sparks 6 in. long, the
+initial source of electrification being a single Daniell cell.
+
+
+  Toepler machine.
+
+Varley was followed by A.J.I. Toepler, who in 1865 constructed an
+influence machine consisting of two disks fixed on the same shaft and
+rotating in the same direction. Each disk carried two strips of tin-foil
+extending nearly over a semi-circle, and there were two field plates,
+one behind each disk; one of the plates was positively and the other
+negatively electrified. The carriers which were touched under the
+influence of the positive field plate passed on and gave up a portion of
+their negative charge to increase that of the negative field plate; in
+the same way the carriers which were touched under the influence of the
+negative field plate sent a part of their charge to augment that of the
+positive field plate. In this apparatus one of the charging rods
+communicated with one of the field plates, but the other with the
+neutralizing brush opposite to the other field plate. Hence one of the
+field plates would always remain charged when a spark was taken at the
+transmitting terminals.
+
+[Illustration: FIG. 6.--Holtz's Machine.]
+
+
+  Holtz machine.
+
+Between 1864 and 1880, W.T.B. Holtz constructed and described a large
+number of influence machines which were for a long time considered the
+most advanced development of this type of electrostatic machine. In one
+form the Holtz machine consisted of a glass disk mounted on a horizontal
+axis F (fig. 6) which could be made to rotate at a considerable speed by
+a multiplying gear, part of which is seen at X. Close behind this disk
+was fixed another vertical disk of glass in which were cut two windows
+B, B. On the side of the fixed disk next the rotating disk were pasted
+two sectors of paper A, A, with short blunt points attached to them
+which projected out into the windows on the side away from the rotating
+disk. On the other side of the rotating disk were placed two metal combs
+C, C, which consisted of sharp points set in metal rods and were each
+connected to one of a pair of discharge balls E, D, the distance between
+which could be varied. To start the machine the balls were brought in
+contact, one of the paper armatures electrified, say, with positive
+electricity, and the disk set in motion. Thereupon very shortly a
+hissing sound was heard and the machine became harder to turn as if the
+disk were moving through a resisting medium. After that the discharge
+balls might be separated a little and a continuous series of sparks or
+brush discharges would take place between them. If two Leyden jars L, L
+were hung upon the conductors which supported the combs, with their
+outer coatings put in connexion with one another by M, a series of
+strong spark discharges passed between the discharge balls. The action
+of the machine is as follows: Suppose one paper armature to be charged
+positively, it acts by induction on the right hand comb, causing
+negative electricity to issue from the comb points upon the glass
+revolving disk; at the same time the positive electricity passes through
+the closed discharge circuit to the left comb and issues from its teeth
+upon the part of the glass disk at the opposite end of the diameter.
+This positive electricity electrifies the left paper armature by
+induction, positive electricity issuing from the blunt point upon the
+side farthest from the rotating disk. The charges thus deposited on the
+glass disk are carried round so that the upper half is electrified
+negatively on both sides and the lower half positively on both sides,
+the sign of the electrification being reversed as the disk passes
+between the combs and the armature by discharges issuing from them
+respectively. If it were not for leakage in various ways, the
+electrification would go on everywhere increasing, but in practice a
+stationary state is soon attained. Holtz's machine is very uncertain in
+its action in a moist climate, and has generally to be enclosed in a
+chamber in which the air is kept artificially dry.
+
+
+  Voss's machine.
+
+Robert Voss, a Berlin instrument maker, in 1880 devised a form of
+machine in which he claimed that the principles of Toepler and Holtz
+were combined. On a rotating glass or ebonite disk were placed carriers
+of tin-foil or metal buttons against which neutralizing brushes touched.
+This armature plate revolved in front of a field plate carrying two
+pieces of tin-foil backed up by larger pieces of varnished paper. The
+studs on the armature plate were charged inductively by being connected
+for a moment by a neutralizing wire as they passed in front of the field
+plates, and then gave up their charges partly to renew the field charges
+and partly to collecting combs connected to discharge balls. In general
+design and construction, the manner of moving the rotating plate and in
+the use of the two Leyden jars in connexion with the discharge balls,
+Voss borrowed his ideas from Holtz.
+
+
+  Wimshurst machine.
+
+All the above described machines, however, have been thrown into the
+shade by the invention of a greatly improved type of influence machine
+first constructed by James Wimshurst about 1878. Two glass disks are
+mounted on two shafts in such a manner that, by means of two belts and
+pulleys worked from a winch shaft, the disks can be rotated rapidly in
+opposite directions close to each other (fig. 7). These glass disks
+carry on them a certain number (not less than 16 or 20) tin-foil
+carriers which may or may not have brass buttons upon them. The glass
+plates are well varnished, and the carriers are placed on the outer
+sides of the two glass plates. As therefore the disks revolve, these
+carriers travel in opposite directions, coming at intervals in
+opposition to each other. Each upright bearing carrying the shafts of
+the revolving disks also carries a neutralizing conductor or wire ending
+in a little brush of gilt thread. The neutralizing conductors for each
+disk are placed at right angles to each other. In addition there are
+collecting combs which occupy an intermediate position and have sharp
+points projecting inwards, and coming near to but not touching the
+carriers. These combs on opposite sides are connected respectively to
+the inner coatings of two Leyden jars whose outer coatings are in
+connexion with one another.
+
+[Illustration: FIG. 7.--Wimshurst's Machine.]
+
+The operation of the machine is as follows: Let us suppose that one of
+the studs on the back plate is positively electrified and one at the
+opposite end of a diameter is negatively electrified, and that at that
+moment two corresponding studs on the front plate passing opposite to
+these back studs are momentarily connected together by the neutralizing
+wire belonging to the front plate. The positive stud on the back plate
+will act inductively on the front stud and charge it negatively, and
+similarly for the other stud, and as the rotation continues these
+charged studs will pass round and give up most of their charge through
+the combs to the Leyden jars. The moment, however, a pair of studs on
+the front plate are charged, they act as field plates to studs on the
+back plate which are passing at the moment, provided these last are
+connected by the back neutralizing wire. After a few revolutions of the
+disks half the studs on the front plate at any moment are charged
+negatively and half positively and the same on the back plate, the
+neutralizing wires forming the boundary between the positively and
+negatively charged studs. The diagram in fig. 8, taken by permission
+from S.P. Thompson's paper (_loc. cit._), represents a view of the
+distribution of these charges on the front and back plates respectively.
+It will be seen that each stud is in turn both a field plate and a
+carrier having a charge induced on it, and then passing on in turn
+induces further charges on other studs. Wimshurst constructed numerous
+very powerful machines of this type, some of them with multiple plates,
+which operate in almost any climate, and rarely fail to charge
+themselves and deliver a torrent of sparks between the discharge balls
+whenever the winch is turned. He also devised an alternating current
+electrical machine in which the discharge balls were alternately
+positive and negative. Large Wimshurst multiple plate influence machines
+are often used instead of induction coils for exciting Rontgen ray tubes
+in medical work. They give very steady illumination on fluorescent
+screens.
+
+[Illustration: FIG. 8.--Action of the Wimshurst Machine.]
+
+In 1900 it was found by F. Tudsbury that if an influence machine is
+enclosed in a metallic chamber containing compressed air, or better,
+carbon dioxide, the insulating properties of compressed gases enable a
+greatly improved effect to be obtained owing to the diminution of the
+leakage across the plates and from the supports. Hence sparks can be
+obtained of more than double the length at ordinary atmospheric
+pressure. In one case a machine with plates 8 in. in diameter which
+could give sparks 2.5 in. at ordinary pressure gave sparks of 5, 7, and
+8 in. as the pressure was raised to 15, 30 and 45 lb. above the normal
+atmosphere.
+
+[Illustration: FIG. 9.--Lord Kelvin's Replenisher.
+
+  C, C, Metal carriers fixed to ebonite cross-arm.
+  F, F, Brass field-plates or conductors.
+  a, a, Receiving springs.
+  n, n, Connecting springs or neutralizing brushes.]
+
+The action of Lord Kelvin's replenisher (fig. 9) used by him in
+connexion with his electrometers for maintaining their charge, closely
+resembles that of Belli's doubler and will be understood from fig. 9.
+Lord Kelvin also devised an influence machine, commonly called a "mouse
+mill," for electrifying the ink in connexion with his siphon recorder.
+It was an electrostatic and electromagnetic machine combined, driven by
+an electric current and producing in turn electrostatic charges of
+electricity. In connexion with this subject mention must also be made of
+the water dropping influence machine of the same inventor.[1]
+
+The action and efficiency of influence machines have been investigated
+by F. Rossetti, A. Righi and F.W.G. Kohlrausch. The electromotive force
+is practically constant no matter what the velocity of the disks, but
+according to some observers the internal resistance decreases as the
+velocity increases. Kohlrausch, using a Holtz machine with a plate 16
+in. in diameter, found that the current given by it could only
+electrolyse acidulated water in 40 hours sufficient to liberate one
+cubic centimetre of mixed gases. E.E.N. Mascart, A. Roiti, and E.
+Bouchotte have also examined the efficiency and current producing power
+of influence machines.
+
+  BIBLIOGRAPHY.--In addition to S.P. Thompson's valuable paper on
+  influence machines (to which this article is much indebted) and other
+  references given, see J. Clerk Maxwell, _Treatise on Electricity and
+  Magnetism_ (2nd ed., Oxford, 1881), vol. i. p. 294; J.D. Everett,
+  _Electricity_ (expansion of part iii. of Deschanel's _Natural
+  Philosophy_) (London, 1901), ch. iv. p. 20; A. Winkelmann, _Handbuch
+  der Physik_ (Breslau, 1905), vol. iv. pp. 50-58 (contains a large
+  number of references to original papers); J. Gray, _Electrical
+  Influence Machines, their Development and Modern Forms_ (London,
+  1903).     (J. A. F.)
+
+
+FOOTNOTE:
+
+  [1] See Lord Kelvin, _Reprint of Papers on Electrostatics and
+    Magnetism_ (1872); "Electrophoric Apparatus and Illustrations of
+    Voltaic Theory," p. 319; "On Electric Machines Founded on Induction
+    and Convection," p. 330; "The Reciprocal Electrophorus," p. 337.
+
+
+
+
+ELECTRIC EEL (_Gymnotus electricus_), a member of the family of fishes
+known as _Gymnotidae_. In spite of their external similarity the
+_Gymnotidae_ have nothing to do with the eels (_Anguilla_). They
+resemble the latter in the elongation of the body, the large number of
+vertebrae (240 in _Gymnotus_), and the absence of pelvic fins; but they
+differ in all the more important characters of internal structure. They
+are in fact allied to the carps or _Cyprinidae_ and the cat-fishes or
+_Siluridae_. In common with these two families and the _Characinidae_ of
+Africa and South America, the _Gymnotidae_ possess the peculiar
+structures called _ossicula auditus_ or Weberian ossicles. These are a
+chain of small bones belonging to the first four vertebrae, which are
+much modified, and connecting the air-bladder with the auditory organs.
+Such an agreement in the structure of so complicated and specialized an
+apparatus can only be the result of a community of descent of the
+families possessing it. Accordingly these families are now placed
+together in a distinct sub-order, the Ostariophysi. The _Gymnotidae_ are
+strongly modified and degraded _Characinidae_. In them the dorsal and
+caudal fins are very rudimentary or absent, and the anal is very long,
+extending from the anus, which is under the head or throat, to the end
+of the body.
+
+_Gymnotus_ is the only genus of the family which possesses electric
+organs. These extend the whole length of the tail, which is four-fifths
+of the body. They are modifications of the lateral muscles and are
+supplied with numerous branches of the spinal nerves. They consist of
+longitudinal columns, each composed of an immense number of "electric
+plates." The posterior end of the organ is positive, the anterior
+negative, and the current passes from the tail to the head. The maximum
+shock is given when the head and tail of the _Gymnotus_ are in contact
+with different points in the surface of some other animal. _Gymnotus
+electricus_ attains a length of 3 ft. and the thickness of a man's
+thigh, and frequents the marshes of Brazil and the Guianas, where it is
+regarded with terror, owing to the formidable electrical apparatus with
+which it is provided. When this natural battery is discharged in a
+favourable position, it is sufficiently powerful to stun the largest
+animal; and according to A. von Humboldt, it has been found necessary to
+change the line of certain roads passing through the pools frequented by
+the electric eels. These fish are eaten by the Indians, who, before
+attempting to capture them, seek to exhaust their electrical power by
+driving horses into the ponds. By repeated discharges upon these they
+gradually expend this marvellous force; after which, being defenceless,
+they become timid, and approach the edge for shelter, when they fall an
+easy prey to the harpoon. It is only after long rest and abundance of
+food that the fish is able to resume the use of its subtle weapon.
+Humboldt's description of this method of capturing the fish has not,
+however, been verified by recent travellers.
+
+
+
+
+ELECTRICITY. This article is devoted to a general sketch of the history
+of the development of electrical knowledge on both the theoretical and
+the practical sides. The two great branches of electrical theory which
+concern the phenomena of electricity at rest, or "frictional" or
+"static" electricity, and of electricity in motion, or electric
+currents, are treated in two separate articles, ELECTROSTATICS and
+ELECTROKINETICS. The phenomena attendant on the passage of electricity
+through solids, through liquids and through gases, are described in the
+article CONDUCTION, ELECTRIC, and also ELECTROLYSIS, and the propagation
+of electrical vibrations in ELECTRIC WAVES. The interconnexion of
+magnetism (which has an article to itself) and electricity is discussed
+in ELECTROMAGNETISM, and these manifestations in nature in ATMOSPHERIC
+ELECTRICITY; AURORA POLARIS and MAGNETISM, TERRESTRIAL. The general
+principles of electrical engineering will be found in ELECTRICITY
+SUPPLY, and further details respecting the generation and use of
+electrical power are given in such articles as DYNAMO; MOTORS, ELECTRIC;
+TRANSFORMERS; ACCUMULATOR; POWER TRANSMISSION: _Electric_; TRACTION;
+LIGHTING: _Electric_; ELECTROCHEMISTRY and ELECTROMETALLURGY. The
+principles of telegraphy (land, submarine and wireless) and of telephony
+are discussed in the articles TELEGRAPH and TELEPHONE, and various
+electrical instruments are treated in separate articles such as
+AMPEREMETER; ELECTROMETER; GALVANOMETER; VOLTMETER; WHEATSTONE'S BRIDGE;
+POTENTIOMETER; METER, ELECTRIC; ELECTROPHORUS; LEYDEN JAR; &c.
+
+The term "electricity" is applied to denote the physical agency which
+exhibits itself by effects of attraction and repulsion when particular
+substances are rubbed or heated, also in certain chemical and
+physiological actions and in connexion with moving magnets and metallic
+circuits. The name is derived from the word _electrica_, first used by
+William Gilbert (1544-1603) in his epoch-making treatise _De magnete,
+magneticisque corporibus, et de magno magnete tellure_, published in
+1600,[1] to denote substances which possess a similar property to amber
+(= _electrum_, from [Greek: elektron]) of attracting light objects when
+rubbed. Hence the phenomena came to be collectively called electrical, a
+term first used by William Barlowe, archdeacon of Salisbury, in 1618,
+and the study of them, electrical science.
+
+
+_Historical Sketch._
+
+Gilbert was the first to conduct systematic scientific experiments on
+electrical phenomena. Prior to his date the scanty knowledge possessed
+by the ancients and enjoyed in the middle ages began and ended with
+facts said to have been familiar to Thales of Miletus (600 B.C.) and
+mentioned by Theophrastus (321 B.C.) and Pliny (A.D. 70), namely, that
+amber, jet and one or two other substances possessed the power, when
+rubbed, of attracting fragments of straw, leaves or feathers. Starting
+with careful and accurate observations on facts concerning the
+mysterious properties of amber and the lodestone, Gilbert laid the
+foundations of modern electric and magnetic science on the true
+experimental and inductive basis. The subsequent history of electricity
+may be divided into four well-marked periods. The first extends from the
+date of publication of Gilbert's great treatise in 1600 to the invention
+by Volta of the voltaic pile and the first production of the electric
+current in 1799. The second dates from Volta's discovery to the
+discovery by Faraday in 1831 of the induction of electric currents and
+the creation of currents by the motion of conductors in magnetic fields,
+which initiated the era of modern electrotechnics. The third covers the
+period between 1831 and Clerk Maxwell's enunciation of the
+electromagnetic theory of light in 1865 and the invention of the
+self-exciting dynamo, which marks another great epoch in the development
+of the subject; and the fourth comprises the modern development of
+electric theory and of absolute quantitative measurements, and above
+all, of the applications of this knowledge in electrical engineering. We
+shall sketch briefly the historical progress during these various
+stages, and also the growth of electrical theories of electricity during
+that time.
+
+FIRST PERIOD.--Gilbert was probably led to study the phenomena of the
+attraction of iron by the lodestone in consequence of his conversion to
+the Copernican theory of the earth's motion, and thence proceeded to
+study the attractions produced by amber. An account of his electrical
+discoveries is given in the _De magnete_, lib. ii. cap. 2.[2] He
+invented the _versorium_ or electrical needle and proved that
+innumerable bodies he called _electrica_, when rubbed, can attract the
+needle of the versorium (see ELECTROSCOPE). Robert Boyle added many new
+facts and gave an account of them in his book, _The Origin of
+Electricity_. He showed that the attraction between the rubbed body and
+the test object is mutual. Otto von Guericke (1602-1686) constructed the
+first electrical machine with a revolving ball of sulphur (see
+ELECTRICAL MACHINE), and noticed that light objects were repelled after
+being attracted by excited electrics. Sir Isaac Newton substituted a
+ball of glass for sulphur in the electrical machine and made other not
+unimportant additions to electrical knowledge. Francis Hawksbee (d.
+1713) published in his book _Physico-Mechanical Experiments_ (1709), and
+in several Memoirs in the _Phil. Trans._ about 1707, the results of his
+electrical inquiries. He showed that light was produced when mercury was
+shaken up in a glass tube exhausted of its air. Dr Wall observed the
+spark and crackling sound when warm amber was rubbed, and compared them
+with thunder and lightning (_Phil. Trans._, 1708, 26, p. 69). Stephen
+Gray (1696-1736) noticed in 1720 that electricity could be excited by
+the friction of hair, silk, wool, paper and other bodies. In 1729 Gray
+made the important discovery that some bodies were conductors and others
+non-conductors of electricity. In conjunction with his friend Granville
+Wheeler (d. 1770), he conveyed the electricity from rubbed glass, a
+distance of 886 ft., along a string supported on silk threads (_Phil.
+Trans._, 1735-1736, 39, pp. 16, 166 and 400). Jean Theophile Desaguliers
+(1683-1744) announced soon after that electrics were non-conductors, and
+conductors were non-electrics. C.F. de C. du Fay (1699-1739) made the
+great discovery that electricity is of two kinds, vitreous and resinous
+(_Phil. Trans._, 1733, 38, p. 263), the first being produced when glass,
+crystal, &c. are rubbed with silk, and the second when resin, amber,
+silk or paper, &c. are excited by friction with flannel. He also
+discovered that a body charged with positive or negative electricity
+repels a body free to move when the latter is charged with electricity
+of like sign, but attracts it if it is charged with electricity of
+opposite sign, i.e. positive repels positive and negative repels
+negative, but positive attracts negative. It is to du Fay also that we
+owe the abolition of the distinction between electrics and
+non-electrics. He showed that all substances could be electrified by
+friction, but that to electrify conductors they must be insulated or
+supported on non-conductors. Various improvements were made in the
+electrical machine, and thereby experimentalists were provided with the
+means of generating strong electrification; C.F. Ludolff (1707-1763) of
+Berlin in 1744 succeeded in igniting ether with the electric spark
+(_Phil. Trans._, 1744, 43, p. 167).
+
+  For a very full list of the papers and works of these early electrical
+  philosophers, the reader is referred to the bibliography on
+  Electricity in Dr Thomas Young's _Natural Philosophy_, vol. ii. p.
+  415.
+
+In 1745 the important invention of the Leyden jar or condenser was made
+by E.G. von Kleist of Kammin, and almost simultaneously by Cunaeus and
+Pieter van Musschenbroek (1692-1761) of Leiden (see LEYDEN JAR). Sir
+William Watson (1715-1787) in England first observed the flash of light
+when a Leyden jar is discharged, and he and Dr John Bevis (1695-1771)
+suggested coating the jar inside and outside with tinfoil. Watson
+carried out elaborate experiments to discover how far the electric
+discharge of the jar could be conveyed along metallic wires and was able
+to accomplish it for a distance of 2 m., making the important
+observation that the electricity appeared to be transmitted
+instantaneously.
+
+_Franklin's Researches._--Benjamin Franklin (1706-1790) was one of the
+great pioneers of electrical science, and made the ever-memorable
+experimental identification of lightning and electric spark. He argued
+that electricity is not created by friction, but merely collected from
+its state of diffusion through other matter by which it is attracted. He
+asserted that the glass globe, when rubbed, attracted the electrical
+fire, and took it from the rubber, the same globe being disposed, when
+the friction ceases, to give out its electricity to any body which has
+less. In the case of the charged Leyden jar, he asserted that the inner
+coating of tinfoil had received more than its ordinary quantity of
+electricity, and was therefore electrified positively, or plus, while
+the outer coating of tinfoil having had its ordinary quantity of
+electricity diminished, was electrified negatively, or minus. Hence the
+cause of the shock and spark when the jar is discharged, or when the
+superabundant or plus electricity of the inside is transferred by a
+conducting body to the defective or minus electricity of the outside.
+This theory of the Leyden phial Franklin supported very ingeniously by
+showing that the outside and the inside coating possessed electricities
+of opposite sign, and that, in charging it, exactly as much electricity
+is added on one side as is subtracted from the other. The abundant
+discharge of electricity by points was observed by Franklin is his
+earliest experiments, and also the power of points to conduct it
+copiously from an electrified body. Hence he was furnished with a simple
+method of collecting electricity from other bodies, and he was enabled
+to perform those remarkable experiments which are chiefly connected with
+his name. Hawksbee, Wall and J.A. Nollet (1700-1770) had successively
+suggested the identity of lightning and the electric spark, and of
+thunder and the snap of the spark. Previously to the year 1750, Franklin
+drew up a statement, in which he showed that all the general phenomena
+and effects which were produced by electricity had their counterparts in
+lightning. After waiting some time for the erection of a spire at
+Philadelphia, by means of which he hoped to bring down the electricity
+of a thunderstorm, he conceived the idea of sending up a kite among
+thunder-clouds. With this view he made a small cross of two small light
+strips of cedar, the arms being sufficiently long to reach to the four
+corners of a large thin silk handkerchief when extended. The corners of
+the handkerchief were tied to the extremities of the cross, and when the
+body of the kite was thus formed, a tail, loop and string were added to
+it. The body was made of silk to enable it to bear the violence and wet
+of a thunderstorm. A very sharp pointed wire was fixed at the top of the
+upright stick of the cross, so as to rise a foot or more above the wood.
+A silk ribbon was tied to the end of the twine next the hand, and a key
+suspended at the junction of the twine and silk. In company with his
+son, Franklin raised the kite like a common one, in the first
+thunderstorm, which happened in the month of June 1752. To keep the silk
+ribbon dry, he stood within a door, taking care that the twine did not
+touch the frame of the door; and when the thunder-clouds came over the
+kite he watched the state of the string. A cloud passed without any
+electrical indications, and he began to despair of success. At last,
+however, he saw the loose filaments of the twine standing out every way,
+and he found them to be attracted by the approach of his finger. The
+suspended key gave a spark on the application of his knuckle, and when
+the string had become wet with the rain the electricity became abundant.
+A Leyden jar was charged at the key, and by the electric fire thus
+obtained spirits were inflamed, and many other experiments performed
+which had been formerly made by excited electrics. In subsequent trials
+with another apparatus, he found that the clouds were sometimes
+positively and sometimes negatively electrified, and so demonstrated the
+perfect identity of lightning and electricity. Having thus succeeded in
+drawing the electric fire from the clouds, Franklin conceived the idea
+of protecting buildings from lightning by erecting on their highest
+parts pointed iron wires or conductors communicating with the ground.
+The electricity of a hovering or a passing cloud would thus be carried
+off slowly and silently; and if the cloud was highly charged, the
+lightning would strike in preference the elevated conductors.[3] The
+most important of Franklin's electrical writings are his _Experiments
+and Observations on Electricity made at Philadelphia_, 1751-1754; his
+_Letters on Electricity_; and various memoirs and letters in the _Phil.
+Trans._ from 1756 to 1760.
+
+About the same time that Franklin was making his kite experiment in
+America, T.F. Dalibard (1703-1779) and others in France had erected a
+long iron rod at Marli, and obtained results agreeing with those of
+Franklin. Similar investigations were pursued by many others, among whom
+Father G.B. Beccaria (1716-1781) deserves especial mention. John Canton
+(1718-1772) made the important contribution to knowledge that
+electricity of either sign could be produced on nearly any body by
+friction with appropriate substances, and that a rod of glass roughened
+on one half was excited negatively in the rough part and positively in
+the smooth part by friction with the same rubber. Canton first suggested
+the use of an amalgam of mercury and tin for use with glass cylinder
+electrical machines to improve their action. His most important
+discovery, however, was that of electrostatic induction, the fact that
+one electrified body can produce charges of electricity upon another
+insulated body, and that when this last is touched it is left
+electrified with a charge of opposite sign to that of the inducing
+charge (_Phil. Trans._, 1753-1754). We shall make mention lower down of
+Canton's contributions to electrical theory. Robert Symmer (d. 1763)
+showed that quite small differences determined the sign of the
+electrification that was generated by the friction of two bodies one
+against the other. Thus wearing a black and a white silk stocking one
+over the other, he found they were electrified oppositely when rubbed
+and drawn off, and that such a rubbed silk stocking when deposited in a
+Leyden jar gave up its electrification to the jar (_Phil. Trans._,
+1759). Ebenezer Kinnersley (1711-1778) of Philadelphia made useful
+observations on the elongation and fusion of iron wires by electrical
+discharges (_Phil. Trans._, 1763). A contemporary of Canton and
+co-discoverer with him of the facts of electrostatic induction was the
+Swede, Johann Karl Wilcke (1732-1796), then resident in Germany, who in
+1762 published an account of experiments in which a metal plate held
+above the upper surface of a glass table was subjected to the action of
+a charge on an electrified metal plate held below the glass (_Kon.
+Schwedische Akad. Abhandl._, 1762, 24, p. 213).
+
+_Pyro-electricity._--The subject of pyro-electricity, or the power
+possessed by some minerals of becoming electrified when merely heated,
+and of exhibiting positive and negative electricity, now began to
+attract notice. It is possible that the _lyncurium_ of the ancients,
+which according to Theophrastus attracted light bodies, was tourmaline,
+a mineral found in Ceylon, which had been christened by the Dutch with
+the name of _aschentrikker_, or the attractor of ashes. In 1717 Louis
+Lemery exhibited to the Paris Academy of Sciences a stone from Ceylon
+which attracted light bodies; and Linnaeus in mentioning his experiments
+gives the stone the name of _lapis electricus_. Giovanni Caraffa, duca
+di Noja (1715-1768), was led in 1758 to purchase some of the stones
+called tourmaline in Holland, and, assisted by L.J.M. Daubenton and
+Michel Adanson, he made a series of experiments with them, a description
+of which he gave in a letter to G.L.L. Buffon in 1759. The subject,
+however, had already engaged the attention of the German philosopher,
+F.U.T. Aepinus, who published an account of them in 1756. Hitherto
+nothing had been said respecting the necessity of heat to excite the
+tourmaline; but it was shown by Aepinus that a temperature between
+99-1/2 deg. and 212 deg. Fahr. was requisite for the development of its
+attractive powers. Benjamin Wilson (_Phil. Trans._, 1763, &c.), J.
+Priestley, and Canton continued the investigation, but it was reserved
+for the Abbe Hauy to throw a clear light on this curious branch of the
+science (_Traite de mineralogie_, 1801). He found that the electricity
+of the tourmaline decreased rapidly from the summits or poles towards
+the middle of the crystal, where it was imperceptible; and he discovered
+that if a tourmaline is broken into any number of fragments, each
+fragment, when excited, has two opposite poles. Hauy discovered the same
+property in the Siberian and Brazilian topaz, borate of magnesia,
+mesotype, prehnite, sphene and calamine. He also found that the polarity
+which minerals receive from heat has a relation to the secondary forms
+of their crystals--the tourmaline, for example, having its resinous pole
+at the summit of the crystal which has three faces. In the other
+pyro-electric crystals above mentioned, Hauy detected the same deviation
+from the rules of symmetry in their secondary crystals which occurs in
+tourmaline. C.P. Brard (1788-1838) discovered that pyro-electricity was
+a property of axinite; and it was afterwards detected in other minerals.
+In repeating and extending the experiments of Hauy much later, Sir David
+Brewster discovered that various artificial salts were pyro-electric,
+and he mentions the tartrates of potash and soda and tartaric acid as
+exhibiting this property in a very strong degree. He also made many
+experiments with the tourmaline when cut into thin slices, and reduced
+to the finest powder, in which state each particle preserved its
+pyro-electricity; and he showed that scolezite and mesolite, even when
+deprived of their water of crystallization and reduced to powder, retain
+their property of becoming electrical by heat. When this white powder is
+heated and stirred about by any substance whatever, it collects in
+masses like new-fallen snow, and adheres to the body with which it is
+stirred.
+
+  For Sir David Brewster's work on pyro-electricity, see _Trans. Roy.
+  Soc. Edin._, 1845, also _Phil. Mag._, Dec. 1847. The reader will also
+  find a full discussion on the subject in the _Treatise on
+  Electricity_, by A. de la Rive, translated by C.V. Walker (London,
+  1856), vol. ii. part v. ch. i.
+
+_Animal electricity._--The observation that certain animals could give
+shocks resembling the shock of a Leyden jar induced a closer examination
+of these powers. The ancients were acquainted with the benumbing power
+of the torpedo-fish, but it was not till 1676 that modern naturalists
+had their attention again drawn to the fact. E. Bancroft was the first
+person who distinctly suspected that the effects of the torpedo were
+electrical. In 1773 John Walsh (d. 1795) and Jan Ingenhousz (1730-1799)
+proved by many curious experiments that the shock of the torpedo was an
+electrical one (_Phil. Trans._, 1773-1775); and John Hunter (id. 1773,
+1775) examined and described the anatomical structure of its electrical
+organs. A. von Humboldt and Gay-Lussac (_Ann. Chim._, 1805), and Etienne
+Geoffroy Saint-Hilaire (_Gilb. Ann._, 1803) pursued the subject with
+success; and Henry Cavendish (_Phil. Trans._, 1776) constructed an
+artificial torpedo, by which he imitated the actions of the living
+animal. The subject was also investigated (_Phil. Trans._, 1812, 1817)
+by Dr T.J. Todd (1789-1840), Sir Humphry Davy (id. 1829), John Davy (id.
+1832, 1834, 1841) and Faraday (_Exp. Res._, vol. ii.). The power of
+giving electric shocks has been discovered also in the _Gymnotus
+electricus_ (electric eel), the _Malapterurus electricus_, the
+_Trichiurus electricus_, and the _Tetraodon electricus_. The most
+interesting and the best known of these singular fishes is the
+_Gymnotus_ or Surinam eel. Humboldt gives a very graphic account of the
+combats which are carried on in South America between the gymnoti and
+the wild horses in the vicinity of Calabozo.
+
+_Cavendish's Researches._--The work of Henry Cavendish (1731-1810)
+entitles him to a high place in the list of electrical investigators. A
+considerable part of Cavendish's work was rescued from oblivion in 1879
+and placed in an easily accessible form by Professor Clerk Maxwell, who
+edited the original manuscripts in the possession of the duke of
+Devonshire.[4] Amongst Cavendish's important contributions were his
+exact measurements of electrical capacity. The leading idea which
+distinguishes his work from that of his predecessors was his use of the
+phrase "degree of electrification" with a clear scientific definition
+which shows it to be equivalent in meaning to the modern term "electric
+potential." Cavendish compared the capacity of different bodies with
+those of conducting spheres of known diameter and states these
+capacities in "globular inches," a globular inch being the capacity of a
+sphere 1 in. in diameter. Hence his measurements are all directly
+comparable with modern electrostatic measurements in which the unit of
+capacity is that of a sphere 1 centimetre in radius. Cavendish measured
+the capacity of disks and condensers of various forms, and proved that
+the capacity of a Leyden pane is proportional to the surface of the
+tinfoil and inversely as the thickness of the glass. In connexion with
+this subject he anticipated one of Faraday's greatest discoveries,
+namely, the effect of the dielectric or insulator upon the capacity of a
+condenser formed with it, in other words, made the discovery of specific
+inductive capacity (see _Electrical Researches_, p. 183). He made many
+measurements of the electric conductivity of different solids and
+liquids, by comparing the intensity of the electric shock taken through
+his body and various conductors. He seems in this way to have educated
+in himself a very precise "electrical sense," making use of his own
+nervous system as a kind of physiological galvanometer. One of the most
+important investigations he made in this way was to find out, as he
+expressed it, "what power of the velocity the resistance is proportional
+to." Cavendish meant by the term "velocity" what we now call the
+current, and by "resistance" the electromotive force which maintains the
+current. By various experiments with liquids in tubes he found this
+power was nearly unity. This result thus obtained by Cavendish in
+January 1781, that the current varies in direct proportion to the
+electromotive force, was really an anticipation of the fundamental law
+of electric flow, discovered independently by G.S. Ohm in 1827, and
+since known as Ohm's Law. Cavendish also enunciated in 1776 all the laws
+of division of electric current between circuits in parallel, although
+they are generally supposed to have been first given by Sir C.
+Wheatstone. Another of his great investigations was the determination of
+the law according to which electric force varies with the distance.
+Starting from the fact that if an electrified globe, placed within two
+hemispheres which fit over it without touching, is brought in contact
+with these hemispheres, it gives up the whole of its charge to them--in
+other words, that the charge on an electrified body is wholly on the
+surface--he was able to deduce by most ingenious reasoning the law that
+electric force varies inversely as the square of the distance. The
+accuracy of his measurement, by which he established within 2% the above
+law, was only limited by the sensibility, or rather insensibility, of
+the pith ball electrometer, which was his only means of detecting the
+electric charge.[5] In the accuracy of his quantitative measurements and
+the range of his researches and his combination of mathematical and
+physical knowledge, Cavendish may not inaptly be described as the Kelvin
+of the 18th century. Nothing but his curious indifference to the
+publication of his work prevented him from securing earlier recognition
+for it.
+
+_Coulomb's Work._--Contemporary with Cavendish was C.A. Coulomb
+(1736-1806), who in France addressed himself to the same kind of exact
+quantitative work as Cavendish in England. Coulomb has made his name for
+ever famous by his invention and application of his torsion balance to
+the experimental verification of the fundamental law of electric
+attraction, in which, however, he was anticipated by Cavendish, namely,
+that the force of attraction between two small electrified spherical
+bodies varies as the product of their charges and inversely as the
+square of the distance of their centres. Coulomb's work received better
+publication than Cavendish's at the time of its accomplishment, and
+provided a basis on which mathematicians could operate. Accordingly the
+close of the 18th century drew into the arena of electrical
+investigation on its mathematical side P.S. Laplace, J.B. Biot, and
+above all, S.D. Poisson. Adopting the hypothesis of two fluids, Coulomb
+investigated experimentally and theoretically the distribution of
+electricity on the surface of bodies by means of his proof plane. He
+determined the law of distribution between two conducting bodies in
+contact; and measured with his proof plane the density of the
+electricity at different points of two spheres in contact, and
+enunciated an important law. He ascertained the distribution of
+electricity among several spheres (whether equal or unequal) placed in
+contact in a straight line; and he measured the distribution of
+electricity on the surface of a cylinder, and its distribution between
+a sphere and cylinder of different lengths but of the same diameter. His
+experiments on the dissipation of electricity possess also a high value.
+He found that the momentary dissipation was proportional to the degree
+of electrification at the time, and that, when the charge was moderate,
+its dissipation was not altered in bodies of different kinds or shapes.
+The temperature and pressure of the atmosphere did not produce any
+sensible change; but he concluded that the dissipation was nearly
+proportional to the cube of the quantity of moisture in the air.[6] In
+examining the dissipation which takes place along imperfectly insulating
+substances, he found that a thread of gum-lac was the most perfect of
+all insulators; that it insulated ten times as well as a dry silk
+thread; and that a silk thread covered with fine sealing-wax insulated
+as powerfully as gum-lac when it had four times its length. He found
+also that the dissipation of electricity along insulators was chiefly
+owing to adhering moisture, but in some measure also to a slight
+conducting power. For his memoirs see _Mem. de math. et phys. de l'acad.
+de sc._, 1785, &c.
+
+SECOND PERIOD.--We now enter upon the second period of electrical
+research inaugurated by the epoch-making discovery of Alessandro Volta
+(1745-1827). L. Galvani had made in 1790 his historic observations on
+the muscular contraction produced in the bodies of recently killed frogs
+when an electrical machine was being worked in the same room, and
+described them in 1791 (_De viribus electricitatis in motu musculari
+commentarius_, Bologna, 1791). Volta followed up these observations with
+rare philosophic insight and experimental skill. He showed that all
+conductors liquid and solid might be divided into two classes which he
+called respectively conductors of the first and of the second class, the
+first embracing metals and carbon in its conducting form, and the second
+class, water, aqueous solutions of various kinds, and generally those
+now called electrolytes. In the case of conductors of the first class he
+proved by the use of the condensing electroscope, aided probably by some
+form of multiplier or doubler, that a difference of potential (see
+ELECTROSTATICS) was created by the mere contact of two such conductors,
+one of them being positively electrified and the other negatively. Volta
+showed, however, that if a series of bodies of the first class, such as
+disks of various metals, are placed in contact, the potential difference
+between the first and the last is just the same as if they are
+immediately in contact. There is no accumulation of potential. If,
+however, pairs of metallic disks, made, say, of zinc and copper, are
+alternated with disks of cloth wetted with a conductor of the second
+class, such, for instance, as dilute acid or any electrolyte, then the
+effect of the feeble potential difference between one pair of copper and
+zinc disks is added to that of the potential difference between the next
+pair, and thus by a sufficiently long series of pairs any required
+difference of potential can be accumulated.
+
+_The Voltaic Pile._--This led him about 1799 to devise his famous
+voltaic pile consisting of disks of copper and zinc or other metals with
+wet cloth placed between the pairs. Numerous examples of Volta's
+original piles at one time existed in Italy, and were collected together
+for an exhibition held at Como in 1899, but were unfortunately destroyed
+by a disastrous fire on the 8th of July 1899. Volta's description of his
+pile was communicated in a letter to Sir Joseph Banks, president of the
+Royal Society of London, on the 20th of March 1800, and was printed in
+the _Phil. Trans._, vol. 90, pt. 1, p. 405. It was then found that when
+the end plates of Volta's pile were connected to an electroscope the
+leaves diverged either with positive or negative electricity. Volta also
+gave his pile another form, the _couronne des tasses_ (crown of cups),
+in which connected strips of copper and zinc were used to bridge between
+cups of water or dilute acid. Volta then proved that all metals could be
+arranged in an electromotive series such that each became positive when
+placed in contact with the one next below it in the series. The origin
+of the electromotive force in the pile has been much discussed, and
+Volta's discoveries gave rise to one of the historic controversies of
+science. Volta maintained that the mere contact of metals was sufficient
+to produce the electrical difference of the end plates of the pile. The
+discovery that chemical action was involved in the process led to the
+advancement of the chemical theory of the pile and this was strengthened
+by the growing insight into the principle of the conservation of energy.
+In 1851 Lord Kelvin (Sir W. Thomson), by the use of his then
+newly-invented electrometer, was able to confirm Volta's observations on
+contact electricity by irrefutable evidence, but the contact theory of
+the voltaic pile was then placed on a basis consistent with the
+principle of the conservation of energy. A.A. de la Rive and Faraday
+were ardent supporters of the chemical theory of the pile, and even at
+the present time opinions of physicists can hardly be said to be in
+entire accordance as to the source of the electromotive force in a
+voltaic couple or pile.[7]
+
+Improvements in the form of the voltaic pile were almost immediately
+made by W. Cruickshank (1745-1800), Dr W.H. Wollaston and Sir H. Davy,
+and these, together with other eminent continental chemists, such as
+A.F. de Fourcroy, L.J. Thenard and J.W. Ritter (1776-1810), ardently
+prosecuted research with the new instrument. One of the first
+discoveries made with it was its power to electrolyse or chemically
+decompose certain solutions. William Nicholson (1753-1815) and Sir
+Anthony Carlisle (1768-1840) in 1800 constructed a pile of silver and
+zinc plates, and placing the terminal wires in water noticed the
+evolution from these wires of bubbles of gas, which they proved to be
+oxygen and hydrogen. These two gases, as Cavendish and James Watt had
+shown in 1784, were actually the constituents of water. From that date
+it was clearly recognized that a fresh implement of great power had been
+given to the chemist. Large voltaic piles were then constructed by
+Andrew Crosse (1784-1855) and Sir H. Davy, and improvements initiated by
+Wollaston and Robert Hare (1781-1858) of Philadelphia. In 1806 Davy
+communicated to the Royal Society of London a celebrated paper on some
+"Chemical Agencies of Electricity," and after providing himself at the
+Royal Institution of London with a battery of several hundred cells, he
+announced in 1807 his great discovery of the electrolytic decomposition
+of the alkalis, potash and soda, obtaining therefrom the metals
+potassium and sodium. In July 1808 Davy laid a request before the
+managers of the Royal Institution that they would set on foot a
+subscription for the purchase of a specially large voltaic battery; as a
+result he was provided with one of 2000 pairs of plates, and the first
+experiment performed with it was the production of the electric arc
+light between carbon poles. Davy followed up his initial work with a
+long and brilliant series of electrochemical investigations described
+for the most part in the _Phil. Trans._ of the Royal Society.
+
+_Magnetic Action of Electric Current._--Noticing an analogy between the
+polarity of the voltaic pile and that of the magnet, philosophers had
+long been anxious to discover a relation between the two, but twenty
+years elapsed after the invention of the pile before Hans Christian
+Oersted (1777-1851), professor of natural philosophy in the university
+of Copenhagen, made in 1819 the discovery which has immortalized his
+name. In the _Annals of Philosophy_ (1820, 16, p. 273) is to be found an
+English translation of Oersted's original Latin essay (entitled
+"Experiments on the Effect of a Current of Electricity on the Magnetic
+Needle"), dated the 21st of July 1820, describing his discovery. In it
+Oersted describes the action he considers is taking place around the
+conductor joining the extremities of the pile; he speaks of it as the
+electric conflict, and says: "It is sufficiently evident that the
+electric conflict is not confined to the conductor, but is dispersed
+pretty widely in the circumjacent space. We may likewise conclude that
+this conflict performs circles round the wire, for without this
+condition it seems impossible that one part of the wire when placed
+below the magnetic needle should drive its pole to the east, and when
+placed above it, to the west." Oersted's important discovery was the
+fact that when a wire joining the end plates of a voltaic pile is held
+near a pivoted magnet or compass needle, the latter is deflected and
+places itself more or less transversely to the wire, the direction
+depending upon whether the wire is above or below the needle, and on the
+manner in which the copper or zinc ends of the pile are connected to it.
+It is clear, moreover, that Oersted clearly recognized the existence of
+what is now called the magnetic field round the conductor. This
+discovery of Oersted, like that of Volta, stimulated philosophical
+investigation in a high degree.
+
+_Electrodynamics._--On the 2nd of October 1820, A.M. Ampere presented to
+the French Academy of Sciences an important memoir,[8] in which he
+summed up the results of his own and D.F.J. Arago's previous
+investigations in the new science of electromagnetism, and crowned that
+labour by the announcement of his great discovery of the dynamical
+action between conductors conveying the electric currents. Ampere in
+this paper gave an account of his discovery that conductors conveying
+electric currents exercise a mutual attraction or repulsion on one
+another, currents flowing in the same direction in parallel conductors
+attracting, and those in opposite directions repelling. Respecting this
+achievement when developed in its experimental and mathematical
+completeness, Clerk Maxwell says that it was "perfect in form and
+unassailable in accuracy." By a series of well-chosen experiments Ampere
+established the laws of this mutual action, and not only explained
+observed facts by a brilliant train of mathematical analysis, but
+predicted others subsequently experimentally realized. These
+investigations led him to the announcement of the fundamental law of
+action between elements of current, or currents in infinitely short
+lengths of linear conductors, upon one another at a distance; summed up
+in compact expression this law states that the action is proportional to
+the product of the current strengths of the two elements, and the
+lengths of the two elements, and inversely proportional to the square of
+the distance between the two elements, and also directly proportional to
+a function of the angles which the line joining the elements makes with
+the directions of the two elements respectively. Nothing is more
+remarkable in the history of discovery than the manner in which Ampere
+seized upon the right clue which enabled him to disentangle the
+complicated phenomena of electrodynamics and to deduce them all as a
+consequence of one simple fundamental law, which occupies in
+electrodynamics the position of the Newtonian law of gravitation in
+physical astronomy.
+
+In 1821 Michael Faraday (1791-1867), who was destined later on to do so
+much for the science of electricity, discovered electromagnetic
+rotation, having succeeded in causing a wire conveying a voltaic current
+to rotate continuously round the pole of a permanent magnet.[9] This
+experiment was repeated in a variety of forms by A.A. De la Rive, Peter
+Barlow (1776-1862), William Ritchie (1790-1837), William Sturgeon
+(1783-1850), and others; and Davy (_Phil. Trans._, 1823) showed that
+when two wires connected with the pole of a battery were dipped into a
+cup of mercury placed on the pole of a powerful magnet, the fluid
+rotated in opposite directions about the two electrodes.
+
+_Electromagnetism._--In 1820 Arago (_Ann. Chim. Phys._, 1820, 15, p. 94)
+and Davy (_Annals of Philosophy_, 1821) discovered independently the
+power of the electric current to magnetize iron and steel. Felix Savary
+(1797-1841) made some very curious observations in 1827 on the
+magnetization of steel needles placed at different distances from a wire
+conveying the discharge of a Leyden jar (_Ann. Chim. Phys._, 1827, 34).
+W. Sturgeon in 1824 wound a copper wire round a bar of iron bent in the
+shape of a horseshoe, and passing a voltaic current through the wire
+showed that the iron became powerfully magnetized as long as the
+connexion with the pile was maintained (_Trans. Soc. Arts_, 1825). These
+researches gave us the electromagnet, almost as potent an instrument of
+research and invention as the pile itself (see ELECTROMAGNETISM).
+
+Ampere had already previously shown that a spiral conductor or solenoid
+when traversed by an electric current possesses magnetic polarity, and
+that two such solenoids act upon one another when traversed by electric
+currents as if they were magnets. Joseph Henry, in the United States,
+first suggested the construction of what were then called intensity
+electromagnets, by winding upon a horseshoe-shaped piece of soft iron
+many superimposed windings of copper wire, insulated by covering it with
+silk or cotton, and then sending through the coils the current from a
+voltaic battery. The dependence of the intensity of magnetization on the
+strength of the current was subsequently investigated (_Pogg. Ann.
+Phys._, 1839, 47) by H.F.E. Lenz (1804-1865) and M.H. von Jacobi
+(1801-1874). J.P. Joule found that magnetization did not increase
+proportionately with the current, but reached a maximum (_Sturgeon's
+Annals of Electricity_, 1839, 4). Further investigations on this subject
+were carried on subsequently by W.E. Weber (1804-1891), J.H.J. Muller
+(1809-1875), C.J. Dub (1817-1873), G.H. Wiedemann (1826-1899), and
+others, and in modern times by H.A. Rowland (1848-1901), Shelford
+Bidwell (b. 1848), John Hopkinson (1849-1898), J.A. Ewing (b. 1855) and
+many others. Electric magnets of great power were soon constructed in
+this manner by Sturgeon, Joule, Henry, Faraday and Brewster. Oersted's
+discovery in 1819 was indeed epoch-making in the degree to which it
+stimulated other research. It led at once to the construction of the
+galvanometer as a means of detecting and measuring the electric current
+in a conductor. In 1820 J.S.C. Schweigger (1779-1857) with his
+"multiplier" made an advance upon Oersted's discovery, by winding the
+wire conveying the electric current many times round the pivoted
+magnetic needle and thus increasing the deflection; and L. Nobili
+(1784-1835) in 1825 conceived the ingenious idea of neutralizing the
+directive effect of the earth's magnetism by employing a pair of
+magnetized steel needles fixed to one axis, but with their magnetic
+poles pointing in opposite directions. Hence followed the astatic
+multiplying galvanometer.
+
+_Electrodynamic Rotation._--The study of the relation between the magnet
+and the circuit conveying an electric current then led Arago to the
+discovery of the "magnetism of rotation." He found that a vibrating
+magnetic compass needle came to rest sooner when placed over a plate of
+copper than otherwise, and also that a plate of copper rotating under a
+suspended magnet tended to drag the magnet in the same direction. The
+matter was investigated by Charles Babbage, Sir J.F.W. Herschel, Peter
+Barlow and others, but did not receive a final explanation until after
+the discovery of electromagnetic induction by Faraday in 1831. Ampere's
+investigations had led electricians to see that the force acting upon a
+magnetic pole due to a current in a neighbouring conductor was such as
+to tend to cause the pole to travel round the conductor. Much ingenuity
+had, however, to be expended before a method was found of exhibiting
+such a rotation. Faraday first succeeded by the simple but ingenious
+device of using a light magnetic needle tethered flexibly to the bottom
+of a cup containing mercury so that one pole of the magnet was just
+above the surface of the mercury. On bringing down on to the mercury
+surface a wire conveying an electric current, and allowing the current
+to pass through the mercury and out at the bottom, the magnetic pole at
+once began to rotate round the wire (_Exper. Res._, 1822, 2, p. 148).
+Faraday and others then discovered, as already mentioned, means to make
+the conductor conveying the current rotate round a magnetic pole, and
+Ampere showed that a magnet could be made to rotate on its own axis when
+a current was passed through it. The difficulty in this case consisted
+in discovering means by which the current could be passed through one
+half of the magnet without passing it through the other half. This,
+however, was overcome by sending the current out at the centre of the
+magnet by means of a short length of wire dipping into an annular groove
+containing mercury. Barlow, Sturgeon and others then showed that a
+copper disk could be made to rotate between the poles of a horseshoe
+magnet when a current was passed through the disk from the centre to the
+circumference, the disk being rendered at the same time freely movable
+by making a contact with the circumference by means of a mercury trough.
+These experiments furnished the first elementary forms of electric
+motor, since it was then seen that rotatory motion could be produced in
+masses of metal by the mutual action of conductors conveying electric
+current and magnetic fields. By his discovery of thermo-electricity in
+1822 (_Pogg. Ann. Phys._, 6), T.J. Seebeck (1770-1831) opened up a new
+region of research (see THERMOELECTRICITY). James Cumming (1777-1861) in
+1823 (_Annals of Philosophy_, 1823) found that the thermo-electric
+series varied with the temperature, and J.C.A. Peltier (1785-1845) in
+1834 discovered that a current passed across the junction of two metals
+either generated or absorbed heat.
+
+_Ohm's Law._--In 1827 Dr G.S. Ohm (1787-1854) rendered a great service
+to electrical science by his mathematical investigation of the voltaic
+circuit, and publication of his paper, _Die galvanische Kette
+mathematisch bearbeitet_. Before his time, ideas on the measurable
+quantities with which we are concerned in an electric circuit were
+extremely vague. Ohm introduced the clear idea of current strength as an
+effect produced by electromotive force acting as a cause in a circuit
+having resistance as its quality, and showed that the current was
+directly proportional to the electromotive force and inversely as the
+resistance. Ohm's law, as it is called, was based upon an analogy with
+the flow of heat in a circuit, discussed by Fourier. Ohm introduced the
+definite conception of the distribution along the circuit of
+"electroscopic force" or tension (_Spannung_), corresponding to the
+modern term potential. Ohm verified his law by the aid of
+thermo-electric piles as sources of electromotive force, and Davy,
+C.S.M. Pouillet (1791-1868), A.C. Becquerel (1788-1878), G.T. Fechner
+(1801-1887), R.H.A. Kohlrausch (1809-1858) and others laboured at its
+confirmation. In more recent times, 1876, it was rigorously tested by G.
+Chrystal (b. 1851) at Clerk Maxwell's instigation (see _Brit. Assoc.
+Report_, 1876, p. 36), and although at its original enunciation its
+meaning was not at first fully apprehended, it soon took its place as
+the expression of the fundamental law of electrokinetics.
+
+_Induction of Electric Currents._--In 1831 Faraday began the
+investigations on electromagnetic induction which proved more fertile in
+far-reaching practical consequences than any of those which even his
+genius gave to the world. These advances all centre round his supreme
+discovery of the induction of electric currents. Fully familiar with the
+fact that an electric charge upon one conductor could produce a charge
+of opposite sign upon a neighbouring conductor, Faraday asked himself
+whether an electric current passing through a conductor could not in any
+like manner induce an electric current in some neighbouring conductor.
+His first experiments on this subject were made in the month of November
+1825, but it was not until the 29th of August 1831 that he attained
+success. On that date he had provided himself with an iron ring, over
+which he had wound two coils of insulated copper wire. One of these
+coils was connected with the voltaic battery and the other with the
+galvanometer. He found that at the moment the current in the battery
+circuit was started or stopped, transitory currents appeared in the
+galvanometer circuit in opposite directions. In ten days of brilliant
+investigation, guided by clear insight from the very first into the
+meaning of the phenomena concerned, he established experimentally the
+fact that a current may be induced in a conducting circuit simply by the
+variation in a magnetic field, the lines of force of which are linked
+with that circuit. The whole of Faraday's investigations on this
+subject can be summed up in the single statement that if a conducting
+circuit is placed in a magnetic field, and if either by variation of the
+field or by movement or variation of the form of the circuit the total
+magnetic flux linked with the circuit is varied, an electromotive force
+is set up in that circuit which at any instant is measured by the rate
+at which the total flux linked with the circuit is changing.
+
+Amongst the memorable achievements of the ten days which Faraday devoted
+to this investigation was the discovery that a current could be induced
+in a conducting wire simply by moving it in the neighbourhood of a
+magnet. One form which this experiment took was that of rotating a
+copper disk between the poles of a powerful electric magnet. He then
+found that a conductor, the ends of which were connected respectively
+with the centre and edge of the disk, was traversed by an electric
+current. This important fact laid the foundation for all subsequent
+inventions which finally led to the production of electromagnetic or
+dynamo-electric machines.
+
+THIRD PERIOD.--With this supremely important discovery of Faraday's we
+enter upon the third period of electrical research, in which that
+philosopher himself was the leading figure. He not only collected the
+facts concerning electromagnetic induction so industriously that nothing
+of importance remained for future discovery, and embraced them all in
+one law of exquisite simplicity, but he introduced his famous conception
+of lines of force which changed entirely the mode of regarding
+electrical phenomena. The French mathematicians, Coulomb, Biot, Poisson
+and Ampere, had been content to accept the fact that electric charges or
+currents in conductors could exert forces on other charges or conductors
+at a distance without inquiring into the means by which this action at a
+distance was produced. Faraday's mind, however, revolted against this
+notion; he felt intuitively that these distance actions must be the
+result of unseen operations in the interposed medium. Accordingly when
+he sprinkled iron filings on a card held over a magnet and revealed the
+curvilinear system of lines of force (see MAGNETISM), he regarded these
+fragments of iron as simple indicators of a physical state in the space
+already in existence round the magnet. To him a magnet was not simply a
+bar of steel; it was the core and origin of a system of lines of
+magnetic force attached to it and moving with it. Similarly he came to
+see an electrified body as a centre of a system of lines of
+electrostatic force. All the space round magnets, currents and electric
+charges was therefore to Faraday the seat of corresponding lines of
+magnetic or electric force. He proved by systematic experiments that the
+electromotive forces set up in conductors by their motions in magnetic
+fields or by the induction of other currents in the field were due to
+the secondary conductor _cutting_ lines of magnetic force. He invented
+the term "electrotonic state" to signify the total magnetic flux due to
+a conductor conveying a current, which was linked with any secondary
+circuit in the field or even with itself.
+
+_Faraday's Researches._--Space compels us to limit our account of the
+scientific work done by Faraday in the succeeding twenty years, in
+elucidating electrical phenomena and adding to the knowledge thereon, to
+the very briefest mention. We must refer the reader for further
+information to his monumental work entitled _Experimental Researches on
+Electricity_, in three volumes, reprinted from the _Phil. Trans._
+between 1831 and 1851. Faraday divided these researches into various
+series. The 1st and 2nd concern the discovery of magneto-electric
+induction already mentioned. The 3rd series (1833) he devoted to
+discussion of the identity of electricity derived from various sources,
+frictional, voltaic, animal and thermal, and he proved by rigorous
+experiments the identity and similarity in properties of the electricity
+generated by these various methods. The 5th series (1833) is occupied
+with his electrochemical researches. In the 7th series (1834) he defines
+a number of new terms, such as electrolyte, electrolysis, anode and
+cathode, &c., in connexion with electrolytic phenomena, which were
+immediately adopted into the vocabulary of science. His most important
+contribution at this date was the invention of the voltameter and his
+enunciation of the laws of electrolysis. The voltameter provided a means
+of measuring quantity of electricity, and in the hands of Faraday and
+his successors became an appliance of fundamental importance. The 8th
+series is occupied with a discussion of the theory of the voltaic pile,
+in which Faraday accumulates evidence to prove that the source of the
+energy of the pile must be chemical. He returns also to this subject in
+the 16th series. In the 9th series (1834) he announced the discovery of
+the important property of electric conductors, since called their
+self-induction or inductance, a discovery in which, however, he was
+anticipated by Joseph Henry in the United States. The 11th series (1837)
+deals with electrostatic induction and the statement of the important
+fact of the specific inductive capacity of insulators or dielectrics.
+This discovery was made in November 1837 when Faraday had no knowledge
+of Cavendish's previous researches into this matter. The 19th series
+(1845) contains an account of his brilliant discovery of the rotation of
+the plane of polarized light by transparent dielectrics placed in a
+magnetic field, a relation which established for the first time a
+practical connexion between the phenomena of electricity and light. The
+20th series (1845) contains an account of his researches on the
+universal action of magnetism and diamagnetic bodies. The 22nd series
+(1848) is occupied with the discussion of magneto-crystallic force and
+the abnormal behaviour of various crystals in a magnetic field. In the
+25th series (1850) he made known his discovery of the magnetic character
+of oxygen gas, and the important principle that the terms paramagnetic
+and diamagnetic are relative. In the 26th series (1850) he returned to a
+discussion of magnetic lines of force, and illuminated the whole subject
+of the magnetic circuit by his transcendent insight into the intricate
+phenomena concerned. In 1855 he brought these researches to a conclusion
+by a general article on magnetic philosophy, having placed the whole
+subject of magnetism and electromagnetism on an entirely novel and solid
+basis. In addition to this he provided the means for studying the
+phenomena not only qualitatively, but also quantitatively, by the
+profoundly ingenious instruments he invented for that purpose.
+
+_Electrical Measurement._--Faraday's ideas thus pressed upon
+electricians the necessity for the quantitative measurement of
+electrical phenomena.[10] It has been already mentioned that Schweigger
+invented in 1820 the "multiplier," and Nobili in 1825 the astatic
+galvanometer. C.S.M. Pouillet in 1837 contributed the sine and tangent
+compass, and W.E. Weber effected great improvements in them and in the
+construction and use of galvanometers. In 1849 H. von Helmholtz devised
+a tangent galvanometer with two coils. The measurement of electric
+resistance then engaged the attention of electricians. By his Memoirs in
+the _Phil. Trans._ in 1843, Sir Charles Wheatstone gave a great impulse
+to this study. He invented the rheostat and improved the resistance
+balance, invented by S.H. Christie (1784-1865) in 1833, and subsequently
+called the Wheatstone Bridge. (See his _Scientific Papers_, published by
+the Physical Society of London, p. 129.) Weber about this date invented
+the electrodynamometer, and applied the mirror and scale method of
+reading deflections, and in co-operation with C.F. Gauss introduced a
+system of absolute measurement of electric and magnetic phenomena. In
+1846 Weber proceeded with improved apparatus to test Ampere's laws of
+electrodynamics. In 1845 H.G. Grassmann (1809-1877) published (_Pogg.
+Ann._ vol. 64) his "Neue Theorie der Electrodynamik," in which he gave
+an elementary law differing from that of Ampere but leading to the same
+results for closed circuits. In the same year F.E. Neumann published
+another law. In 1846 Weber announced his famous hypothesis concerning
+the connexion of electrostatic and electrodynamic phenomena. The work of
+Neumann and Weber had been stimulated by that of H.F.E. Lenz
+(1804-1865), whose researches (_Pogg. Ann._, 1834, 31; 1835, 34) among
+other results led him to the statement of the law by means of which the
+direction of the induced current can be predicted from the theory of
+Ampere, the rule being that the direction of the induced current is
+always such that its electrodynamic action tends to oppose the motion
+which produces it.
+
+Neumann in 1845 did for electromagnetic induction what Ampere did for
+electrodynamics, basing his researches upon the experimental laws of
+Lenz. He discovered a function, which has been called the potential of
+one circuit on another, from which he deduced a theory of induction
+completely in accordance with experiment. Weber at the same time deduced
+the mathematical laws of induction from his elementary law of electrical
+action, and with his improved instruments arrived at accurate
+verifications of the law of induction, which by this time had been
+developed mathematically by Neumann and himself. In 1849 G.R. Kirchhoff
+determined experimentally in a certain case the absolute value of the
+current induced by one circuit in another, and in the same year Erik
+Edland (1819-1888) made a series of careful experiments on the induction
+of electric currents which further established received theories. These
+labours laid the foundation on which was subsequently erected a complete
+system for the absolute measurement of electric and magnetic quantities,
+referring them all to the fundamental units of mass, length and time.
+Helmholtz gave at the same time a mathematical theory of induced
+currents and a valuable series of experiments in support of them (_Pogg.
+Ann._, 1851). This great investigator and luminous expositor just before
+that time had published his celebrated essay, _Die Erhaltung der Kraft_
+("The Conservation of Energy"), which brought to a focus ideas which had
+been accumulating in consequence of the work of J.P. Joule, J.R. von
+Mayer and others, on the transformation of various forms of physical
+energy, and in particular the mechanical equivalent of heat. Helmholtz
+brought to bear upon the subject not only the most profound mathematical
+attainments, but immense experimental skill, and his work in connexion
+with this subject is classical.
+
+_Lord Kelvin's Work._--About 1842 Lord Kelvin (then William Thomson)
+began that long career of theoretical and practical discovery and
+invention in electrical science which revolutionized every department of
+pure and applied electricity. His early contributions to electrostatics
+and electrometry are to be found described in his _Reprint of Papers on
+Electrostatics and Magnetism_ (1872), and his later work in his
+collected _Mathematical and Physical Papers_. By his studies in
+electrostatics, his elegant method of electrical images, his development
+of the theory of potential and application of the principle of
+conservation of energy, as well as by his inventions in connexion with
+electrometry, he laid the foundations of our modern knowledge of
+electrostatics. His work on the electrodynamic qualities of metals,
+thermo-electricity, and his contributions to galvanometry, were not less
+massive and profound. From 1842 onwards to the end of the 19th century,
+he was one of the great master workers in the field of electrical
+discovery and research.[11] In 1853 he published a paper "On Transient
+Electric Currents" (_Phil. Mag._, 1853 [4], 5, p. 393), in which he
+applied the principle of the conservation of energy to the discharge of
+a Leyden jar. He added definiteness to the idea of the self-induction or
+inductance of an electric circuit, and gave a mathematical expression
+for the current flowing out of a Leyden jar during its discharge. He
+confirmed an opinion already previously expressed by Helmholtz and by
+Henry, that in some circumstances this discharge is oscillatory in
+nature, consisting of an alternating electric current of high frequency.
+These theoretical predictions were confirmed and others, subsequently,
+by the work of B.W. Feddersen (b. 1832), C.A. Paalzow (b. 1823), and it
+was then seen that the familiar phenomena of the discharge of a Leyden
+jar provided the means of generating electric oscillations of very high
+frequency.
+
+_Telegraphy._--Turning to practical applications of electricity, we may
+note that electric telegraphy took its rise in 1820, beginning with a
+suggestion of Ampere immediately after Oersted's discovery. It was
+established by the work of Weber and Gauss at Gottingen in 1836, and
+that of C.A. Steinheil (1801-1870) of Munich, Sir W.F. Cooke (1806-1879)
+and Sir C. Wheatstone in England, Joseph Henry and S.F.B. Morse
+(1791-1872) in the United States in 1837. In 1845 submarine telegraphy
+was inaugurated by the laying of an insulated conductor across the
+English Channel by the brothers Brett, and their temporary success was
+followed by the laying in 1851 of a permanent Dover-Calais cable by T.R.
+Crampton. In 1856 the project for an Atlantic submarine cable took shape
+and the Atlantic Telegraph Company was formed with a capital of
+L350,000, with Sir Charles Bright as engineer-in-chief and E.O.W.
+Whitehouse as electrician. The phenomena connected with the propagation
+of electric signals by underground insulated wires had already engaged
+the attention of Faraday in 1854, who pointed out the Leyden-jar-like
+action of an insulated subterranean wire. Scientific and practical
+questions connected with the possibility of laying an Atlantic submarine
+cable then began to be discussed, and Lord Kelvin was foremost in
+developing true scientific knowledge on this subject, and in the
+invention of appliances for utilizing it. One of his earliest and most
+useful contributions (in 1858) was the invention of the mirror
+galvanometer. Abandoning the long and somewhat heavy magnetic needles
+that had been used up to that date in galvanometers, he attached to the
+back of a very small mirror made of microscopic glass a fragment of
+magnetized watch-spring, and suspended the mirror and needle by means of
+a cocoon fibre in the centre of a coil of insulated wire. By this simple
+device he provided a means of measuring small electric currents far in
+advance of anything yet accomplished, and this instrument proved not
+only most useful in pure scientific researches, but at the same time was
+of the utmost value in connexion with submarine telegraphy. The history
+of the initial failures and final success in laying the Atlantic cable
+has been well told by Mr. Charles Bright (see _The Story of the Atlantic
+Cable_, London, 1903).[12] The first cable laid in 1857 broke on the
+11th of August during laying. The second attempt in 1858 was successful,
+but the cable completed on the 5th of August 1858 broke down on the 20th
+of October 1858, after 732 messages had passed through it. The third
+cable laid in 1865 was lost on the 2nd of August 1865, but in 1866 a
+final success was attained and the 1865 cable also recovered and
+completed. Lord Kelvin's mirror galvanometer was first used in receiving
+signals through the short-lived 1858 cable. In 1867 he invented his
+beautiful siphon-recorder for receiving and recording the signals
+through long cables. Later, in conjunction with Prof. Fleeming Jenkin,
+he devised his automatic curb sender, an appliance for sending signals
+by means of punched telegraphic paper tape. Lord Kelvin's contributions
+to the science of exact electric measurement[13] were enormous. His
+ampere-balances, voltmeters and electrometers, and double bridge, are
+elsewhere described in detail (see AMPEREMETER; ELECTROMETER, and
+WHEATSTONE'S BRIDGE).
+
+_Dynamo._--The work of Faraday from 1831 to 1851 stimulated and
+originated an immense mass of scientific research, but at the same time
+practical inventors had not been slow to perceive that it was capable of
+purely technical application. Faraday's copper disk rotated between the
+poles of a magnet, and producing thereby an electric current, became the
+parent of innumerable machines in which mechanical energy was directly
+converted into the energy of electric currents. Of these machines,
+originally called magneto-electric machines, one of the first was
+devised in 1832 by H. Pixii. It consisted of a fixed horseshoe armature
+wound over with insulated copper wire in front of which revolved about a
+vertical axis a horseshoe magnet. Pixii, who invented the split tube
+commutator for converting the alternating current so produced into a
+continuous current in the external circuit, was followed by J. Saxton,
+E.M. Clarke, and many others in the development of the above-described
+magneto-electric machine. In 1857 E.W. Siemens effected a great
+improvement by inventing a shuttle armature and improving the shape of
+the field magnet. Subsequently similar machines with electromagnets were
+introduced by Henry Wilde (b. 1833), Siemens, Wheatstone, W. Ladd and
+others, and the principle of self-excitation was suggested by Wilde,
+C.F. Varley (1828-1883), Siemens and Wheatstone (see DYNAMO). These
+machines about 1866 and 1867 began to be constructed on a commercial
+scale and were employed in the production of the electric light. The
+discovery of electric-current induction also led to the production of
+the induction coil (q.v.), improved and brought to its present
+perfection by W. Sturgeon, E.R. Ritchie, N.J. Callan, H.D. Ruhmkorff
+(1803-1877), A.H.L. Fizeau, and more recently by A. Apps and modern
+inventors. About the same time Fizeau and J.B.L. Foucault devoted
+attention to the invention of automatic apparatus for the production of
+Davy's electric arc (see LIGHTING: _ELECTRIC_), and these appliances in
+conjunction with magneto-electric machines were soon employed in
+lighthouse work. With the advent of large magneto-electric machines the
+era of electrotechnics was fairly entered, and this period, which may be
+said to terminate about 1867 to 1869, was consummated by the theoretical
+work of Clerk Maxwell.
+
+_Maxwell's Researches._--James Clerk Maxwell (1831-1879) entered on his
+electrical studies with a desire to ascertain if the ideas of Faraday,
+so different from those of Poisson and the French mathematicians, could
+be made the foundation of a mathematical method and brought under the
+power of analysis.[14] Maxwell started with the conception that all
+electric and magnetic phenomena are due to effects taking place in the
+dielectric or in the ether if the space be vacuous. The phenomena of
+light had compelled physicists to postulate a space-filling medium, to
+which the name ether had been given, and Henry and Faraday had long
+previously suggested the idea of an electromagnetic medium. The
+vibrations of this medium constitute the agency called light. Maxwell
+saw that it was unphilosophical to assume a multiplicity of ethers or
+media until it had been proved that one would not fulfil all the
+requirements. He formulated the conception, therefore, of electric
+charge as consisting in a displacement taking place in the dielectric or
+electromagnetic medium (see ELECTROSTATICS). Maxwell never committed
+himself to a precise definition of the physical nature of electric
+displacement, but considered it as defining that which Faraday had
+called the polarization in the insulator, or, what is equivalent, the
+number of lines of electrostatic force passing normally through a unit
+of area in the dielectric. A second fundamental conception of Maxwell
+was that the electric displacement whilst it is changing is in effect an
+electric current, and creates, therefore, magnetic force. The total
+current at any point in a dielectric must be considered as made up of
+two parts: first, the true conduction current, if it exists; and second,
+the rate of change of dielectric displacement. The fundamental fact
+connecting electric currents and magnetic fields is that the line
+integral of magnetic force taken once round a conductor conveying an
+electric current is equal to 4 [pi]-times the surface integral of the
+current density, or to 4 [pi]-times the total current flowing through
+the closed line round which the integral is taken (see ELECTROKINETICS).
+A second relation connecting magnetic and electric force is based upon
+Faraday's fundamental law of induction, that the rate of change of the
+total magnetic flux linked with a conductor is a measure of the
+electromotive force created in it (see ELECTROKINETICS). Maxwell also
+introduced in this connexion the notion of the vector potential.
+Coupling together these ideas he was finally enabled to prove that the
+propagation of electric and magnetic force takes place through space
+with a certain velocity determined by the dielectric constant and the
+magnetic permeability of the medium. To take a simple instance, if we
+consider an electric current as flowing in a conductor it is, as Oersted
+discovered, surrounded by closed lines of magnetic force. If we imagine
+the current in the conductor to be instantaneously reversed in
+direction, the magnetic force surrounding it would not be instantly
+reversed everywhere in direction, but the reversal would be propagated
+outwards through space with a certain velocity which Maxwell showed was
+inversely as the square root of the product of the magnetic permeability
+and the dielectric constant or specific inductive capacity of the
+medium.
+
+These great results were announced by him for the first time in a paper
+presented in 1864 to the Royal Society of London and printed in the
+_Phil. Trans._ for 1865, entitled "A Dynamical Theory of the
+Electromagnetic Field." Maxwell showed in this paper that the velocity
+of propagation of an electromagnetic impulse through space could also be
+determined by certain experimental methods which consisted in measuring
+the same electric quantity, capacity, resistance or potential in two
+ways. W.E. Weber had already laid the foundations of the absolute system
+of electric and magnetic measurement, and proved that a quantity of
+electricity could be measured either by the force it exercises upon
+another static or stationary quantity of electricity, or magnetically by
+the force this quantity of electricity exercises upon a magnetic pole
+when flowing through a neighbouring conductor. The two systems of
+measurement were called respectively the electrostatic and the
+electromagnetic systems (see UNITS, PHYSICAL). Maxwell suggested new
+methods for the determination of this ratio of the electrostatic to the
+electromagnetic units, and by experiments of great ingenuity was able to
+show that this ratio, which is also that of the velocity of the
+propagation of an electromagnetic impulse through space, is identical
+with that of light. This great fact once ascertained, it became clear
+that the notion that electric phenomena are affections of the
+luminiferous ether was no longer a mere speculation but a scientific
+theory capable of verification. An immediate deduction from Maxwell's
+theory was that in transparent dielectrics, the dielectric constant or
+specific inductive capacity should be numerically equal to the square of
+the refractive index for very long electric waves. At the time when
+Maxwell developed his theory the dielectric constants of only a few
+transparent insulators were known and these were for the most part
+measured with steady or unidirectional electromotive force. The only
+refractive indices which had been measured were the optical refractive
+indices of a number of transparent substances. Maxwell made a comparison
+between the optical refractive index and the dielectric constant of
+paraffin wax, and the approximation between the numerical values of the
+square of the first and that of the last was sufficient to show that
+there was a basis for further work. Maxwell's electric and magnetic
+ideas were gathered together in a great mathematical treatise on
+electricity and magnetism which was published in 1873.[15] This book
+stimulated in a most remarkable degree theoretical and practical
+research into the phenomena of electricity and magnetism. Experimental
+methods were devised for the further exact measurements of the
+electromagnetic velocity and numerous determinations of the dielectric
+constants of various solids, liquids and gases, and comparisons of these
+with the corresponding optical refractive indices were conducted. This
+early work indicated that whilst there were a number of cases in which
+the square of optical refractive index for long waves and the
+dielectric constant of the same substance were sufficiently close to
+afford an apparent confirmation of Maxwell's theory, yet in other cases
+there were considerable divergencies. L. Boltzmann (1844-1907) made a
+large number of determinations for solids and for gases, and the
+dielectric constants of many solid and liquid substances were determined
+by N.N. Schiller (b. 1848), P.A. Silow (b. 1850), J. Hopkinson and
+others. The accumulating determinations of the numerical value of the
+electromagnetic velocity (v) from the earliest made by Lord Kelvin (Sir
+W. Thomson) with the aid of King and M^cKichan, or those of Clerk
+Maxwell, W.E. Ayrton and J. Perry, to more recent ones by J.J. Thomson,
+F. Himstedt, H.A. Rowland, E.B. Rosa, J.S.H. Pellat and H.A. Abraham,
+showed it to be very close to the best determinations of the velocity of
+light (see UNITS, PHYSICAL). On the other hand, the divergence in some
+cases between the square of the optical refractive index and the
+dielectric constant was very marked. Hence although Maxwell's theory of
+electrical action when first propounded found many adherents in Great
+Britain, it did not so much dominate opinion on the continent of Europe.
+
+FOURTH PERIOD.--With the publication of Clerk Maxwell's treatise in
+1873, we enter fully upon the fourth and modern period of electrical
+research. On the technical side the invention of a new form of armature
+for dynamo electric machines by Z.T. Gramme (1826-1901) inaugurated a
+departure from which we may date modern electrical engineering. It will
+be convenient to deal with technical development first.
+
+_Technical Development._--As far back as 1841 large magneto-electric
+machines driven by steam power had been constructed, and in 1856 F.H.
+Holmes had made a magneto machine with multiple permanent magnets which
+was installed in 1862 in Dungeness lighthouse. Further progress was made
+in 1867 when H. Wilde introduced the use of electromagnets for the field
+magnets. In 1860 Dr Antonio Pacinotti invented what is now called the
+toothed ring winding for armatures and described it in an Italian
+journal, but it attracted little notice until reinvented in 1870 by
+Gramme. In this new form of bobbin, the armature consisted of a ring of
+iron wire wound over with an endless coil of wire and connected to a
+commutator consisting of copper bars insulated from one another. Gramme
+dynamos were then soon made on the self-exciting principle. In 1873 at
+Vienna the fact was discovered that a dynamo machine of the Gramme type
+could also act as an electric motor and was set in rotation when a
+current was passed into it from another similar machine. Henceforth the
+electric transmission of power came within the possibilities of
+engineering.
+
+_Electric Lighting._--In 1876, Paul Jablochkov (1847-1894), a Russian
+officer, passing through Paris, invented his famous electric candle,
+consisting of two rods of carbon placed side by side and separated from
+one another by an insulating material. This invention in conjunction
+with an alternating current dynamo provided a new and simple form of
+electric arc lighting. Two years afterwards C.F. Brush, in the United
+States, produced another efficient form of dynamo and electric arc lamp
+suitable for working in series (see LIGHTING: _Electric_), and these
+inventions of Brush and Jablochkov inaugurated commercial arc lighting.
+The so-called subdivision of electric light by incandescent lighting
+lamps then engaged attention. E.A. King in 1845 and W.E. Staite in 1848
+had made incandescent electric lamps of an elementary form, and T.A.
+Edison in 1878 again attacked the problem of producing light by the
+incandescence of platinum. It had by that time become clear that the
+most suitable material for an incandescent lamp was carbon contained in
+a good vacuum, and St G. Lane Fox and Sir J.W. Swan in England, and T.A.
+Edison in the United States, were engaged in struggling with the
+difficulties of producing a suitable carbon incandescence electric lamp.
+Edison constructed in 1879 a successful lamp of this type consisting of
+a vessel wholly of glass containing a carbon filament made by
+carbonizing paper or some other carbonizable material, the vessel being
+exhausted and the current led into the filament through platinum wires.
+In 1879 and 1880, Edison in the United States, and Swan in conjunction
+with C.H. Stearn in England, succeeded in completely solving the
+practical problems. From and after that date incandescent electric
+lighting became commercially possible, and was brought to public notice
+chiefly by an electrical exhibition held at the Crystal Palace, near
+London, in 1882. Edison, moreover, as well as Lane-Fox, had realized the
+idea of a public electric supply station, and the former proceeded to
+establish in Pearl Street, New York, in 1881, the first public electric
+supply station. A similar station in England was opened in the basement
+of a house in Holborn Viaduct, London, in March 1882. Edison, with
+copious ingenuity, devised electric meters, electric mains, lamp
+fittings and generators complete for the purpose. In 1881 C.A. Faure
+made an important improvement in the lead secondary battery which G.
+Plante (1834-1889) had invented in 1859, and storage batteries then
+began to be developed as commercial appliances by Faure, Swan, J.S.
+Sellon and many others (see ACCUMULATOR). In 1882, numerous electric
+lighting companies were formed for the conduct of public and private
+lighting, but an electric lighting act passed in that year greatly
+hindered commercial progress in Great Britain. Nevertheless the delay
+was utilized in the completion of inventions necessary for the safe and
+economical distribution of electric current for the purpose of electric
+lighting.
+
+_Telephone._--Going back a few years we find the technical applications
+of electrical invention had developed themselves in other directions.
+Alexander Graham Bell in 1876 invented the speaking telephone (q.v.),
+and Edison and Elisha Gray in the United States followed almost
+immediately with other telephonic inventions for electrically
+transmitting speech. About the same time D.E. Hughes in England invented
+the microphone. In 1879 telephone exchanges began to be developed in the
+United States, Great Britain and other countries.
+
+_Electric Power._--Following on the discovery in 1873 of the reversible
+action of the dynamo and its use as a motor, efforts began to be made to
+apply this knowledge to transmission of power, and S.D. Field, T.A.
+Edison, Leo Daft, E.M. Bentley and W.H. Knight, F.J. Sprague, C.J. Van
+Depoele and others between 1880 and 1884 were the pioneers of electric
+traction. One of the earliest electric tram cars was exhibited by E.W.
+and W. Siemens in Paris in 1881. In 1883 Lucien Gaulard, following a
+line of thought opened by Jablochkov, proposed to employ high pressure
+alternating currents for electric distributions over wide areas by means
+of transformers. His ideas were improved by Carl Zipernowsky and O.T.
+Blathy in Hungary and by S.Z. de Ferranti in England, and the
+alternating current transformer (see TRANSFORMERS) came into existence.
+Polyphase alternators were first exhibited at the Frankfort electrical
+exhibition in 1891, developed as a consequence of scientific researches
+by Galileo Ferraris (1847-1897), Nikola Tesla, M.O. von
+Dolivo-Dobrowolsky and C.E.L. Brown, and long distance transmission of
+electrical power by polyphase electrical currents (see POWER
+TRANSMISSION: _Electric_) was exhibited in operation at Frankfort in
+1891. Meanwhile the early continuous current dynamos devised by Gramme,
+Siemens and others had been vastly improved in scientific principle and
+practical construction by the labours of Siemens, J. Hopkinson, R.E.B.
+Crompton, Elihu Thomson, Rudolf Eickemeyer, Thomas Parker and others,
+and the theory of the action of the dynamo had been closely studied by
+J. and E. Hopkinson, G. Kapp, S.P. Thompson, C.P. Steinmetz and J.
+Swinburne, and great improvements made in the alternating current dynamo
+by W.M. Mordey, S.Z. de Ferranti and Messrs Ganz of Budapest. Thus in
+twenty years from the invention of the Gramme dynamo, electrical
+engineering had developed from small beginnings into a vast industry.
+The amendment, in 1888, of the Electric Lighting Act of 1882, before
+long caused a huge development of public electric lighting in Great
+Britain. By the end of the 19th century every large city in Europe and
+in North and South America was provided with a public electric supply
+for the purposes of electric lighting. The various improvements in
+electric illuminants, such as the Nernst oxide lamp, the tantalum and
+osmium incandescent lamps, and improved forms of arc lamp, enclosed,
+inverted and flame arcs, are described under LIGHTING: _Electric_.
+
+Between 1890 and 1900, electric traction advanced rapidly in the United
+States of America but more slowly in England. In 1902 the success of
+deep tube electric railways in Great Britain was assured, and in 1904
+main line railways began to abandon, at least experimentally, the steam
+locomotive and substitute for it the electric transmission of power.
+Long distance electrical transmission had been before that time
+exemplified in the great scheme of utilizing the falls of Niagara. The
+first projects were discussed in 1891 and 1892 and completed practically
+some ten years later. In this scheme large turbines were placed at the
+bottom of hydraulic fall tubes 150 ft. deep, the turbines being coupled
+by long shafts with 5000 H.P. alternating current dynamos on the
+surface. By these electric current was generated and transmitted to
+towns and factories around, being sent overhead as far as Buffalo, a
+distance of 18 m. At the end of the 19th century electrochemical
+industries began to be developed which depended on the possession of
+cheap electric energy. The production of aluminium in Switzerland and
+Scotland, carborundum and calcium carbide in the United States, and soda
+by the Castner-Kellner process, began to be conducted on an immense
+scale. The early work of Sir W. Siemens on the electric furnace was
+continued and greatly extended by Henri Moissan and others on its
+scientific side, and electrochemistry took its place as one of the most
+promising departments of technical research and invention. It was
+stimulated and assisted by improvements in the construction of large
+dynamos and increased knowledge concerning the control of powerful
+electric currents.
+
+In the early part of the 20th century the distribution in bulk of
+electric energy for power purposes in Great Britain began to assume
+important proportions. It was seen to be uneconomical for each city and
+town to manufacture its own supply since, owing to the intermittent
+nature of the demand for current for lighting, the price had to be kept
+up to 4d. and 6d. per unit. It was found that by the manufacture in
+bulk, even by steam engines, at primary centres the cost could be
+considerably reduced, and in numerous districts in England large power
+stations began to be erected between 1903 and 1905 for the supply of
+current for power purposes. This involved almost a revolution in the
+nature of the tools used, and in the methods of working, and may
+ultimately even greatly affect the factory system and the concentration
+of population in large towns which was brought about in the early part
+of the 19th century by the invention of the steam engine.
+
+
+_Development of Electric Theory._
+
+Turning now to the theory of electricity, we may note the equally
+remarkable progress made in 300 years in scientific insight into the
+nature of the agency which has so recast the face of human society.
+There is no need to dwell upon the early crude theories of the action of
+amber and lodestone. In a true scientific sense no hypothesis was
+possible, because few facts had been accumulated. The discoveries of
+Stephen Gray and C.F. de C. du Fay on the conductivity of some bodies
+for the electric agency and the dual character of electrification gave
+rise to the first notions of electricity as an imponderable fluid, or
+non-gravitative subtile matter, of a more refined and penetrating kind
+than ordinary liquids and gases. Its duplex character, and the fact that
+the electricity produced by rubbing glass and vitreous substances was
+different from that produced by rubbing sealing-wax and resinous
+substances, seemed to necessitate the assumption of two kinds of
+electric fluid; hence there arose the conception of _positive_ and
+_negative_ electricity, and the two-fluid theory came into existence.
+
+_Single-fluid Theory._--The study of the phenomena of the Leyden jar and
+of the fact that the inside and outside coatings possessed opposite
+electricities, so that in charging the jar as much positive electricity
+is added to one side as negative to the other, led Franklin about 1750
+to suggest a modification called the single fluid theory, in which the
+two states of electrification were regarded as not the results of two
+entirely different fluids but of the addition or subtraction of one
+electric fluid from matter, so that positive electrification was to be
+looked upon as the result of increase or addition of something to
+ordinary matter and negative as a subtraction. The positive and negative
+electrifications of the two coatings of the Leyden jar were therefore to
+be regarded as the result of a transformation of something called
+electricity from one coating to the other, by which process a certain
+measurable quantity became so much less on one side by the same amount
+by which it became more on the other. A modification of this single
+fluid theory was put forward by F.U.T. Aepinus which was explained and
+illustrated in his _Tentamen theoriae electricitatis et magnetismi_,
+published in St Petersburg in 1759. This theory was founded on the
+following principles:--(1) the particles of the electric fluid repel
+each other with a force decreasing as the distance increases; (2) the
+particles of the electric fluid attract the atoms of all bodies and are
+attracted by them with a force obeying the same law; (3) the electric
+fluid exists in the pores of all bodies, and while it moves without any
+obstruction in conductors such as metals, water, &c., it moves with
+extreme difficulty in so-called non-conductors such as glass, resin,
+&c.; (4) electrical phenomena are produced either by the transference of
+the electric fluid of a body containing more to one containing less, or
+from its attraction and repulsion when no transference takes place.
+Electric attractions and repulsions were, however, regarded as
+differential actions in which the mutual repulsion of the particles of
+electricity operated, so to speak, in antagonism to the mutual
+attraction of particles of matter for one another and of particles of
+electricity for matter. Independently of Aepinus, Henry Cavendish put
+forward a single-fluid theory of electricity (_Phil. Trans._, 1771, 61,
+p. 584), in which he considered it in more precise detail.
+
+_Two-fluid Theory._--In the elucidation of electrical phenomena,
+however, towards the end of the 18th century, a modification of the
+two-fluid theory seems to have been generally preferred. The notion then
+formed of the nature of electrification was something as follows:--All
+bodies were assumed to contain a certain quantity of a so-called neutral
+fluid made up of equal quantities of positive and negative electricity,
+which when in this state of combination neutralized one another's
+properties. The neutral fluid could, however, be divided up or separated
+into its two constituents, and these could be accumulated on separate
+conductors or non-conductors. This view followed from the discovery of
+the facts of electric induction of J. Canton (1753, 1754). When, for
+instance, a positively electrified body was found to induce upon another
+insulated conductor a charge of negative electricity on the side nearest
+to it, and a charge of positive electricity on the side farthest from
+it, this was explained by saying that the particles of each of the two
+electric fluids repelled one another but attracted those of the positive
+fluid. Hence the operation of the positive charge upon the neutral fluid
+was to draw towards the positive the negative constituent of the neutral
+charge and repel to the distant parts of the conductor the positive
+constituent.
+
+C.A. Coulomb experimentally proved that the law of attraction and
+repulsion of simple electrified bodies was that the force between them
+varied inversely as the square of the distance and thus gave
+mathematical definiteness to the two-fluid hypothesis. It was then
+assumed that each of the two constituents of the neutral fluid had an
+atomic structure and that the so-called particles of one of the electric
+fluids, say positive, repelled similar particles with a force varying
+inversely as a square of the distance and attracted those of the
+opposite fluid according to the same law. This fact and hypothesis
+brought electrical phenomena within the domain of mathematical analysis
+and, as already mentioned, Laplace, Biot, Poisson, G.A.A. Plana
+(1781-1846), and later Robert Murphy (1806-1843), made them the subject
+of their investigations on the mode in which electricity distributes
+itself on conductors when in equilibrium.
+
+_Faraday's Views._--The two-fluid theory may be said to have held the
+field until the time when Faraday began his researches on electricity.
+After he had educated himself by the study of the phenomena of lines of
+magnetic force in his discoveries on electromagnetic induction, he
+applied the same conception to electrostatic phenomena, and thus created
+the notion of lines of electrostatic force and of the important function
+of the dielectric or non-conductor in sustaining them. Faraday's notion
+as to the nature of electrification, therefore, about the middle of the
+19th century came to be something as follows:--He considered that the
+so-called charge of electricity on a conductor was in reality nothing on
+the conductor or in the conductor itself, but consisted in a state of
+strain or polarization, or a physical change of some kind in the
+particles of the dielectric surrounding the conductor, and that it was
+this physical state in the dielectric which constituted electrification.
+Since Faraday was well aware that even a good vacuum can act as a
+dielectric, he recognized that the state he called dielectric
+polarization could not be wholly dependent upon the presence of
+gravitative matter, but that there must be an electromagnetic medium of
+a supermaterial nature. In the 13th series of his _Experimental
+Researches on Electricity_ he discussed the relation of a vacuum to
+electricity. Furthermore his electrochemical investigations, and
+particularly his discovery of the important law of electrolysis, that
+the movement of a certain quantity of electricity through an electrolyte
+is always accompanied by the transfer of a certain definite quantity of
+matter from one electrode to another and the liberation at these
+electrodes of an equivalent weight of the ions, gave foundation for the
+idea of a definite atomic charge of electricity. In fact, long
+previously to Faraday's electrochemical researches, Sir H. Davy and J.J.
+Berzelius early in the 19th century had advanced the hypothesis that
+chemical combination was due to electric attractions between the
+electric charges carried by chemical atoms. The notion, however, that
+electricity is atomic in structure was definitely put forward by Hermann
+von Helmholtz in a well-known Faraday lecture. Helmholtz says: "If we
+accept the hypothesis that elementary substances are composed of atoms,
+we cannot well avoid concluding that electricity also is divided into
+elementary portions which behave like atoms of electricity."[16] Clerk
+Maxwell had already used in 1873 the phrase, "a molecule of
+electricity."[17] Towards the end of the third quarter of the 19th
+century it therefore became clear that electricity, whatever be its
+nature, was associated with atoms of matter in the form of exact
+multiples of an indivisible minimum electric charge which may be
+considered to be "Nature's unit of electricity." This ultimate unit of
+electric quantity Professor Johnstone Stoney called an _electron_.[18]
+The formulation of electrical theory as far as regards operations in
+space free from matter was immensely assisted by Maxwell's mathematical
+theory. Oliver Heaviside after 1880 rendered much assistance by reducing
+Maxwell's mathematical analysis to more compact form and by introducing
+greater precision into terminology (see his _Electrical Papers_, 1892).
+This is perhaps the place to refer also to the great services of Lord
+Rayleigh to electrical science. Succeeding Maxwell as Cavendish
+professor of physics at Cambridge in 1880, he soon devoted himself
+especially to the exact redetermination of the practical electrical
+units in absolute measure. He followed up the early work of the British
+Association Committee on electrical units by a fresh determination of
+the ohm in absolute measure, and in conjunction with other work on the
+electrochemical equivalent of silver and the absolute electromotive
+force of the Clark cell may be said to have placed exact electrical
+measurement on a new basis. He also made great additions to the theory
+of alternating electric currents, and provided fresh appliances for
+other electrical measurements (see his _Collected Scientific Papers_,
+Cambridge, 1900).
+
+_Electro-optics._--For a long time Faraday's observation on the rotation
+of the plane of polarized light by heavy glass in a magnetic field
+remained an isolated fact in electro-optics. Then M.E. Verdet
+(1824-1860) made a study of the subject and discovered that a solution
+of ferric perchloride in methyl alcohol rotated the plane of
+polarization in an opposite direction to heavy glass (_Ann. Chim.
+Phys._, 1854, 41, p. 370; 1855, 43, p. 37; _Com. Rend._, 1854, 39, p.
+548). Later A.A.E.E. Kundt prepared metallic films of iron, nickel and
+cobalt, and obtained powerful negative optical rotation with them
+(_Wied. Ann._, 1884, 23, p. 228; 1886, 27, p. 191). John Kerr
+(1824-1907) discovered that a similar effect was produced when plane
+polarized light was reflected from the pole of a powerful magnet (_Phil.
+Mag._, 1877, [5], 3, p. 321, and 1878, 5, p. 161). Lord Kelvin showed
+that Faraday's discovery demonstrated that some form of rotation was
+taking place along lines of magnetic force when passing through a
+medium.[19] Many observers have given attention to the exact
+determination of Verdet's constant of rotation for standard substances,
+e.g. Lord Rayleigh for carbon bisulphide,[20] and Sir W.H. Perkin for an
+immense range of inorganic and organic bodies.[21] Kerr also discovered
+that when certain homogeneous dielectrics were submitted to electric
+strain, they became birefringent (_Phil. Mag._, 1875, 50, pp. 337 and
+446). The theory of electro-optics received great attention from Kelvin,
+Maxwell, Rayleigh, G.F. Fitzgerald, A. Righi and P.K.L. Drude, and
+experimental contributions from innumerable workers, such as F.T.
+Trouton, O.J. Lodge and J.L. Howard, and many others.
+
+_Electric Waves._--In the decade 1880-1890, the most important advance
+in electrical physics was, however, that which originated with the
+astonishing researches of Heinrich Rudolf Hertz (1857-1894). This
+illustrious investigator was stimulated, by a certain problem brought to
+his notice by H. von Helmholtz, to undertake investigations which had
+for their object a demonstration of the truth of Maxwell's principle
+that a variation in electric displacement was in fact an electric
+current and had magnetic effects. It is impossible to describe here the
+details of these elaborate experiments; the reader must be referred to
+Hertz's own papers, or the English translation of them by Prof. D.E.
+Jones. Hertz's great discovery was an experimental realization of a
+suggestion made by G.F. Fitzgerald (1851-1901) in 1883 as to a method of
+producing electric waves in space. He invented for this purpose a
+radiator consisting of two metal rods placed in one line, their inner
+ends being provided with poles nearly touching and their outer ends with
+metal plates. Such an arrangement constitutes in effect a condenser, and
+when the two plates respectively are connected to the secondary
+terminals of an induction coil in operation, the plates are rapidly and
+alternately charged, and discharged across the spark gap with electrical
+oscillations (see ELECTROKINETICS). Hertz then devised a wave detecting
+apparatus called a resonator. This in its simplest form consisted of a
+ring of wire nearly closed terminating in spark balls very close
+together, adjustable as to distance by a micrometer screw. He found that
+when the resonator was placed in certain positions with regard to the
+oscillator, small sparks were seen between the micrometer balls, and
+when the oscillator was placed at one end of a room having a sheet of
+zinc fixed against the wall at the other end, symmetrical positions
+could be found in the room at which, when the resonator was there
+placed, either no sparks or else very bright sparks occurred at the
+poles. These effects, as Hertz showed, indicated the establishment of
+stationary electric waves in space and the propagation of electric and
+magnetic force through space with a finite velocity. The other
+additional phenomena he observed finally contributed an all but
+conclusive proof of the truth of Maxwell's views. By profoundly
+ingenious methods Hertz showed that these invisible electric waves could
+be reflected and refracted like waves of light by mirrors and prisms,
+and that familiar experiments in optics could be repeated with electric
+waves which could not affect the eye. Hence there arose a new science of
+electro-optics, and in all parts of Europe and the United States
+innumerable investigators took possession of the novel field of research
+with the greatest delight. O.J. Lodge,[22] A. Righi,[23] J.H.
+Poincare,[24] V.F.K. Bjerknes, P.K.L. Drude, J.J. Thomson,[25] John
+Trowbridge, Max Abraham, and many others, contributed to its
+elucidation.
+
+In 1892, E. Branly of Paris devised an appliance for detecting these
+waves which subsequently proved to be of immense importance. He
+discovered that they had the power of affecting the electric
+conductivity of materials when in a state of powder, the majority of
+metallic filings increasing in conductivity. Lodge devised a similar
+arrangement called a coherer, and E. Rutherford invented a magnetic
+detector depending on the power of electric oscillations to demagnetize
+iron or steel. The sum total of all these contributions to electrical
+knowledge had the effect of establishing Maxwell's principles on a firm
+basis, but they also led to technical inventions of the very greatest
+utility. In 1896 G. Marconi applied a modified and improved form of
+Branly's wave detector in conjunction with a novel form of radiator for
+the telegraphic transmission of intelligence through space without
+wires, and he and others developed this new form of telegraphy with the
+greatest rapidity and success into a startling and most useful means of
+communicating through space electrically without connecting wires.
+
+_Electrolysis._--The study of the transfer of electricity through
+liquids had meanwhile received much attention. The general facts and
+laws of electrolysis (q.v.) were determined experimentally by Davy and
+Faraday and confirmed by the researches of J.F. Daniell, R.W. Bunsen and
+Helmholtz. The modern theory of electrolysis grew up under the hands of
+R.J.E. Clausius, A.W. Williamson and F.W.G. Kohlrausch, and received a
+great impetus from the work of Svante Arrhenius, J.H. Van't Hoff, W.
+Ostwald, H.W. Nernst and many others. The theory of the ionization of
+salts in solution has raised much discussion amongst chemists, but the
+general fact is certain that electricity only moves through liquids in
+association with matter, and simultaneously involves chemical
+dissociation of molecular groups.
+
+_Discharge through Gases._--Many eminent physicists had an instinctive
+feeling that the study of the passage of electricity through gases would
+shed much light on the intrinsic nature of electricity. Faraday devoted
+to a careful examination of the phenomena the XIII^th series of his
+_Experimental Researches_, and among the older workers in this field
+must be particularly mentioned J. Plucker, J.W. Hittorf, A.A. de la
+Rive, J.P. Gassiot, C.F. Varley, and W. Spottiswoode and J. Fletcher
+Moulton. It has long been known that air and other gases at the pressure
+of the atmosphere were very perfect insulators, but that when they were
+rarefied and contained in glass tubes with platinum electrodes sealed
+through the glass, electricity could be passed through them under
+sufficient electromotive force and produced a luminous appearance known
+as the electric glow discharge. The so-called vacuum tubes constructed
+by H. Geissler (1815-1879) containing air, carbonic acid, hydrogen, &c.,
+under a pressure of one or two millimetres, exhibit beautiful
+appearances when traversed by the high tension current produced by the
+secondary circuit of an induction coil. Faraday discovered the existence
+of a dark space round the negative electrode which is usually known as
+the "Faraday dark space." De la Rive added much to our knowledge of the
+subject, and J. Plucker and his disciple J.W. Hittorf examined the
+phenomena exhibited in so-called high vacua, that is, in exceedingly
+rarefied gases. C.F. Varley discovered the interesting fact that no
+current could be sent through the rarefied gas unless a certain minimum
+potential difference of the electrodes was excited. Sir William Crookes
+took up in 1872 the study of electric discharge through high vacua,
+having been led to it by his researches on the radiometer. The
+particular details of the phenomena observed will be found described in
+the article CONDUCTION, ELECTRIC (S III.). The main fact discovered by
+researches of Plucker, Hittorf and Crookes was that in a vacuum tube
+containing extremely rarefied air or other gas, a luminous discharge
+takes place from the negative electrode which proceeds in lines normal
+to the surface of the negative electrode and renders phosphorescent both
+the glass envelope and other objects placed in the vacuum tube when it
+falls upon them. Hittorf made in 1869 the discovery that solid objects
+could cast shadows or intercept this cathode discharge. The cathode
+discharge henceforth engaged the attention of many physicists. Varley
+had advanced tentatively the hypothesis that it consisted in an actual
+projection of electrified matter from the cathode, and Crookes was led
+by his researches in 1870, 1871 and 1872 to embrace and confirm this
+hypothesis in a modified form and announce the existence of a fourth
+state of matter, which he called radiant matter, demonstrating by many
+beautiful and convincing experiments that there was an actual projection
+of material substance of some kind possessing inertia from the surface
+of the cathode. German physicists such as E. Goldstein were inclined to
+take another view. Sir J.J. Thomson, the successor of Maxwell and Lord
+Rayleigh in the Cavendish chair of physics in the university of
+Cambridge, began about the year 1899 a remarkable series of
+investigations on the cathode discharge, which finally enabled him to
+make a measurement of the ratio of the electric charge to the mass of
+the particles of matter projected from the cathode, and to show that
+this electric charge was identical with the atomic electric charge
+carried by a hydrogen ion in the act of electrolysis, but that the mass
+of the cathode particles, or "corpuscles" as he called them, was far
+less, viz. about 1/2000th part of the mass of a hydrogen atom.[26] The
+subject was pursued by Thomson and the Cambridge physicists with great
+mathematical and experimental ability, and finally the conclusion was
+reached that in a high vacuum tube the electric charge is carried by
+particles which have a mass only a fraction, as above mentioned, of that
+of the hydrogen atom, but which carry a charge equal to the unit
+electric charge of the hydrogen ion as found by electrochemical
+researches.[27] P.E.A. Lenard made in 1894 (_Wied. Ann. Phys._, 51, p.
+225) the discovery that these cathode particles or corpuscles could pass
+through a window of thin sheet aluminium placed in the wall of the
+vacuum tube and give rise to a class of radiation called the Lenard
+rays. W.C. Rontgen of Munich made in 1896 his remarkable discovery of
+the so-called X or Rontgen rays, a class of radiation produced by the
+impact of the cathode particles against an impervious metallic screen or
+anticathode placed in the vacuum tube. The study of Rontgen rays was
+ardently pursued by the principal physicists in Europe during the years
+1897 and 1898 and subsequently. The principal property of these Rontgen
+rays which attracted public attention was their power of passing through
+many solid bodies and affecting a photographic plate. Hence some
+substances were opaque to them and others transparent. The astonishing
+feat of photographing the bones of the living animal within the tissues
+soon rendered the Rontgen rays indispensable in surgery and directed an
+army of investigators to their study.
+
+_Radioactivity._--One outcome of all this was the discovery by H.
+Becquerel in 1896 that minerals containing uranium, and particularly the
+mineral known as pitchblende, had the power of affecting sensitive
+photographic plates enclosed in a black paper envelope when the mineral
+was placed on the outside, as well as of discharging a charged
+electroscope (_Com. Rend._, 1896, 122, p. 420). This research opened a
+way of approach to the phenomena of radioactivity, and the history of
+the steps by which P. Curie and Madame Curie were finally led to the
+discovery of radium is one of the most fascinating chapters in the
+history of science. The study of radium and radioactivity (see
+RADIOACTIVITY) led before long to the further remarkable knowledge that
+these so-called radioactive materials project into surrounding space
+particles or corpuscles, some of which are identical with those
+projected from the cathode in a high vacuum tube, together with others
+of a different nature. The study of radioactivity was pursued with great
+ability not only by the Curies and A. Debierne, who associated himself
+with them, in France, but by E. Rutherford and F. Soddy in Canada, and
+by J.J. Thomson, Sir William Crookes, Sir William Ramsay and others in
+England.
+
+_Electronic Theory._--The final outcome of these investigations was the
+hypothesis that Thomson's corpuscles or particles composing the cathode
+discharge in a high vacuum tube must be looked upon as the ultimate
+constituent of what we call negative electricity; in other words, they
+are atoms of negative electricity, possessing, however, inertia, and
+these negative electrons are components at any rate of the chemical
+atom. Each electron is a point-charge of negative electricity equal to
+3.9 X 10^(-10) of an electrostatic unit or to 1.3 X 10^(-20) of an
+electromagnetic unit, and the ratio of its charge to its mass is nearly
+2 X 10^7 using E.M. units. For the hydrogen atom the ratio of charge to
+mass as deduced from electrolysis is about 10^4. Hence the mass of an
+electron is 1/2000th of that of a hydrogen atom. No one has yet been
+able to isolate positive electrons, or to give a complete demonstration
+that the whole inertia of matter is only electric inertia due to what
+may be called the inductance of the electrons. Prof. Sir J. Larmor
+developed in a series of very able papers (_Phil. Trans._, 1894, 185;
+1895, 186; 1897, 190), and subsequently in his book _Aether and Matter_
+(1900), a remarkable hypothesis of the structure of the electron or
+corpuscle, which he regards as simply a strain centre in the aether or
+electromagnetic medium, a chemical atom being a collection of positive
+and negative electrons or strain centres in stable orbital motion round
+their common centre of mass (see AETHER). J.J. Thomson also developed
+this hypothesis in a profoundly interesting manner, and we may therefore
+summarize very briefly the views held on the nature of electricity and
+matter at the beginning of the 20th century by saying that the term
+electricity had come to be regarded, in part at least, as a collective
+name for electrons, which in turn must be considered as constituents of
+the chemical atom, furthermore as centres of certain lines of
+self-locked and permanent strain existing in the universal aether or
+electromagnetic medium. Atoms of matter are composed of congeries of
+electrons and the inertia of matter is probably therefore only the
+inertia of the electromagnetic medium.[28] Electric waves are produced
+wherever electrons are accelerated or retarded, that is, whenever the
+velocity of an electron is changed or accelerated positively or
+negatively. In every solid body there is a continual atomic
+dissociation, the result of which is that mixed up with the atoms of
+chemical matter composing them we have a greater or less percentage of
+free electrons. The operation called an electric current consists in a
+diffusion or movement of these electrons through matter, and this is
+controlled by laws of diffusion which are similar to those of the
+diffusion of liquids or gases. Electromotive force is due to a
+difference in the density of the electronic population in different or
+identical conducting bodies, and whilst the electrons can move freely
+through so-called conductors their motion is much more hindered or
+restricted in non-conductors. Electric charge consists, therefore, in an
+excess or deficit of negative electrons in a body. In the hands of H.A.
+Lorentz, P.K.L. Drude, J. J, Thomson, J. Larmor and many others, the
+electronic hypothesis of matter and of electricity has been developed in
+great detail and may be said to represent the outcome of modern
+researches upon electrical phenomena.
+
+The reader may be referred for an admirable summary of the theories of
+electricity prior to the advent of the electronic hypothesis to J.J.
+Thomson's "Report on Electrical Theories" (_Brit. Assoc. Report_, 1885),
+in which he divides electrical theories enunciated during the 19th
+century into four classes, and summarizes the opinions and theories of
+A.M. Ampere, H.G. Grassman, C.F. Gauss, W.E. Weber, G.F.B. Riemann,
+R.J.E. Clausius, F.E. Neumann and H. von Helmholtz.
+
+  BIBLIOGRAPHY.--M. Faraday, _Experimental Researches in Electricity_ (3
+  vols., London, 1839, 1844, 1855); A.A. De la Rive, _Treatise on
+  Electricity_ (3 vols., London, 1853, 1858); J. Clerk Maxwell, _A
+  Treatise on Electricity and Magnetism_ (2 vols., 3rd ed., 1892); id.,
+  _Scientific Papers_ (2 vols., edited by Sir W.J. Niven, Cambridge,
+  1890); H.M. Noad, _A Manual of Electricity_ (2 vols., London, 1855,
+  1857); J.J. Thomson, _Recent Researches in Electricity and Magnetism_
+  (Oxford, 1893); id., _Conduction of Electricity through Gases_
+  (Cambridge, 1903); id., _Electricity and Matter_ (London, 1904); O.
+  Heaviside, _Electromagnetic Theory_ (London, 1893); O.J. Lodge,
+  _Modern Views of Electricity_ (London, 1889); E. Mascart and J.
+  Joubert, _A Treatise on Electricity and Magnetism_, English trans. by
+  E. Atkinson (2 vols., London, 1883); Park Benjamin, _The Intellectual
+  Rise in Electricity_ (London, 1895); G.C. Foster and A.W. Porter,
+  _Electricity and Magnetism_ (London, 1903); A. Gray, _A Treatise on
+  Magnetism and Electricity_ (London, 1898); H.W. Watson and S.H.
+  Burbury, _The Mathematical Theory of Electricity and Magnetism_ (2
+  vols., 1885); Lord Kelvin (Sir William Thomson), _Mathematical and
+  Physical Papers_ (3 vols., Cambridge, 1882); Lord Rayleigh,
+  _Scientific Papers_ (4 vols., Cambridge, 1903); A. Winkelmann,
+  _Handbuch der Physik_, vols. iii. and iv. (Breslau, 1903 and 1905; a
+  mine of wealth for references to original papers on electricity and
+  magnetism from the earliest date up to modern times). For particular
+  information on the modern Electronic theory the reader may consult W.
+  Kaufmann, "The Developments of the Electron Idea." _Physikalische
+  Zeitschrift_ (1st of Oct. 1901), or _The Electrician_ (1901), 48, p.
+  95; H.A. Lorentz, _The Theory of Electrons_ (1909); E.E. Fournier
+  d'Albe, _The Electron Theory_ (London, 1906); H. Abraham and P.
+  Langevin, _Ions, Electrons, Corpuscles_ (Paris, 1905); J.A. Fleming,
+  "The Electronic Theory of Electricity," _Popular Science Monthly_ (May
+  1902); Sir Oliver J. Lodge, _Electrons, or the Nature and Properties
+  of Negative Electricity_ (London, 1907).     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] Gilbert's work, _On the Magnet, Magnetic Bodies and the Great
+    Magnet, the Earth_, has been translated from the rare folio Latin
+    edition of 1600, but otherwise reproduced in its original form by the
+    chief members of the Gilbert Club of England, with a series of
+    valuable notes by Prof. S.P. Thompson (London, 1900). See also _The
+    Electrician_, February 21, 1902.
+
+  [2] See _The Intellectual Rise in Electricity_, ch. x., by Park
+    Benjamin (London, 1895).
+
+  [3] See Sir Oliver Lodge, "Lightning, Lightning Conductors and
+    Lightning Protectors," _Journ. Inst. Elec. Eng._ (1889), 18, p. 386,
+    and the discussion on the subject in the same volume; also the book
+    by the same author on _Lightning Conductors and Lightning Guards_
+    (London, 1892).
+
+  [4] _The Electrical Researches of the Hon. Henry Cavendish
+    1771-1781_, edited from the original manuscripts by J. Clerk Maxwell,
+    F.R.S. (Cambridge, 1879).
+
+  [5] In 1878 Clerk Maxwell repeated Cavendish's experiments with
+    improved apparatus and the employment of a Kelvin quadrant
+    electrometer as a means of detecting the absence of charge on the
+    inner conductor after it had been connected to the outer case, and
+    was thus able to show that if the law of electric attraction varies
+    inversely as the nth power of the distance, then the exponent n must
+    have a value of 2 [+-] 1/21600. See Cavendish's _Electrical
+    Researches_, p. 419.
+
+  [6] Modern researches have shown that the loss of charge is in fact
+    dependent upon the ionization of the air, and that, provided the
+    atmospheric moisture is prevented from condensing on the insulating
+    supports, water vapour in the air does not _per se_ bestow on it
+    conductance for electricity.
+
+  [7] Faraday discussed the chemical theory of the pile and arguments
+    in support of it in the 8th and 16th series of his _Experimental
+    Researches on Electricity_. De la Rive reviews the subject in his
+    large _Treatise on Electricity and Magnetism_, vol. ii. ch. iii. The
+    writer made a contribution to the discussion in 1874 in a paper on
+    "The Contact Theory of the Galvanic Cell," _Phil. Mag._, 1874, 47, p.
+    401. Sir Oliver Lodge reviewed the whole position in a paper in 1885,
+    "On the Seat of the Electromotive Force in a Voltaic Cell," _Journ.
+    Inst. Elec. Eng._, 1885, 14, p. 186.
+
+  [8] "Memoire sur la theorie mathematique des phenomenes
+    electrodynamiques," _Memoires de l'institut_, 1820, 6; see also _Ann.
+    de Chim._, 1820, 15.
+
+  [9] See M. Faraday, "On some new Electro-Magnetical Motions and on
+    the Theory of Magnetism," _Quarterly Journal of Science_, 1822, 12,
+    p. 74; or _Experimental Researches on Electricity_, vol. ii. p. 127.
+
+  [10] Amongst the most important of Faraday's quantitative researches
+    must be included the ingenious and convincing proofs he provided that
+    the production of any quantity of electricity of one sign is always
+    accompanied by the production of an equal quantity of electricity of
+    the opposite sign. See _Experimental Researches on Electricity_, vol.
+    i. S 1177.
+
+  [11] In this connexion the work of George Green (1793-1841) must not
+    be forgotten. Green's _Essay on the Application of Mathematical
+    Analysis to the Theories of Electricity and Magnetism_, published in
+    1828, contains the first exposition of the theory of potential. An
+    important theorem contained in it is known as Green's theorem, and is
+    of great value.
+
+  [12] See also his _Submarine Telegraphs_ (London, 1898).
+
+  [13] The quantitative study of electrical phenomena has been
+    enormously assisted by the establishment of the absolute system of
+    electrical measurement due originally to Gauss and Weber. The British
+    Association for the advancement of science appointed in 1861 a
+    committee on electrical units, which made its first report in 1862
+    and has existed ever since. In this work Lord Kelvin took a leading
+    part. The popularization of the system was greatly assisted by the
+    publication by Prof. J.D. Everett of _The C.G.S. System of Units_
+    (London, 1891).
+
+  [14] The first paper in which Maxwell began to translate Faraday's
+    conceptions into mathematical language was "On Faraday's Lines of
+    Force," read to the Cambridge Philosophical Society on the 10th of
+    December 1855 and the 11th of February 1856. See Maxwell's _Collected
+    Scientific Papers_, i. 155.
+
+  [15] _A Treatise on Electricity and Magnetism_ (2 vols.), by James
+    Clerk Maxwell, sometime professor of experimental physics in the
+    university of Cambridge. A second edition was edited by Sir W.D.
+    Niven in 1881 and a third by Prof. Sir J.J. Thomson in 1891.
+
+  [16] H. von Helmholtz, "On the Modern Development of Faraday's
+    Conception of Electricity," _Journ. Chem. Soc._, 1881, 39, p. 277.
+
+  [17] See Maxwell's _Electricity and Magnetism_, vol. i. p. 350 (2nd
+    ed., 1881).
+
+  [18] "On the Physical Units of Nature," _Phil. Mag._, 1881, [5], 11,
+    p. 381. Also _Trans. Roy. Soc._ (Dublin, 1891), 4, p. 583.
+
+  [19] See Sir W. Thomson, _Proc. Roy. Soc. Lond._, 1856, 8, p. 152; or
+    Maxwell, _Elect. and Mag._, vol. ii. p. 831.
+
+  [20] See Lord Rayleigh, _Proc. Roy. Soc. Lond._, 1884, 37, p. 146;
+    Gordon, _Phil. Trans._, 1877, 167, p. 1; H. Becquerel, _Ann. Chim.
+    Phys._, 1882, [3], 27, p. 312.
+
+  [21] Perkin's Papers are to be found in the _Journ. Chem. Soc.
+    Lond._, 1884, p. 421; 1886, p. 177; 1888, p. 561; 1889, p. 680; 1891,
+    p. 981; 1892, p. 800; 1893, p. 75.
+
+  [22] _The Work of Hertz_ (London, 1894).
+
+  [23] _L'Ottica delle oscillazioni elettriche_ (Bologna, 1897).
+
+  [24] _Les Oscillations electriques_ (Paris, 1894).
+
+  [25] _Recent Researches in Electricity and Magnetism_ (Oxford, 1892).
+
+  [26] See J.J. Thomson, _Proc. Roy. Inst. Lond._, 1897, 15, p. 419;
+   also _Phil. Mag._, 1899, [5], 48, p. 547.
+
+  [27] Later results show that the mass of a hydrogen atom is not far
+    from 1.3 X 10^-24 gramme and that the unit atomic charge or natural
+    unit of electricity is 1.3 X 10^-20 of an electromagnetic C.G.S.
+    unit. The mass of the electron or corpuscle is 7.0 X 10^-28 gramme
+    and its diameter is 3 X 10^-13 centimetre. The diameter of a chemical
+    atom is of the order of 10^-7 centimetre.
+
+    See H.A. Lorentz, "The Electron Theory," _Elektrotechnische
+    Zeitschrift_, 1905, 26, p. 584; or _Science Abstracts_, 1905, 8, A,
+    p. 603.
+
+  [28] See J.J. Thomson, _Electricity and Matter_ (London, 1904).
+
+
+
+
+ELECTRICITY SUPPLY. I. _General Principles._--The improvements made in
+the dynamo and electric motor between 1870 and 1880 and also in the
+details of the arc and incandescent electric lamp towards the close of
+that decade, induced engineers to turn their attention to the question
+of the private and public supply of electric current for the purpose of
+lighting and power. T.A. Edison[1] and St G. Lane Fox[2] were among the
+first to see the possibilities and advantages of public electric supply,
+and to devise plans for its practical establishment. If a supply of
+electric current has to be furnished to a building the option exists in
+many cases of drawing from a public supply or of generating it by a
+private plant.
+
+_Private Plants._--In spite of a great amount of ingenuity devoted to
+the development of the primary battery and the thermopile, no means of
+generation of large currents can compete in economy with the dynamo.
+Hence a private electric generating plant involves the erection of a
+dynamo which may be driven either by a steam, gas or oil engine, or by
+power obtained by means of a turbine from a low or high fall of water.
+It may be either directly coupled to the motor, or driven by a belt; and
+it may be either a continuous-current machine or an alternator, and if
+the latter, either single-phase or polyphase. The convenience of being
+able to employ storage batteries in connexion with a private-supply
+system is so great that unless power has to be transmitted long
+distances, the invariable rule is to employ a continuous-current dynamo.
+Where space is valuable this is always coupled direct to the motor; and
+if a steam-engine is employed, an enclosed engine is most cleanly and
+compact. Where coal or heating gas is available, a gas-engine is
+exceedingly convenient, since it requires little attention. Where coal
+gas is not available, a Dowson gas-producer can be employed. The
+oil-engine has been so improved that it is extensively used in
+combination with a direct-coupled or belt-driven dynamo and thus forms a
+favourite and easily-managed plant for private electric lighting. Lead
+storage cells, however, as at present made, when charged by a
+steam-driven dynamo deteriorate less rapidly than when an oil-engine is
+employed, the reason being that the charging current is more irregular
+in the latter case, since the single cylinder oil-engine only makes an
+impulse every other revolution. In connexion with the generator, it is
+almost the invariable custom to put down a secondary battery of storage
+cells, to enable the supply to be given after the engine has stopped.
+This is necessary, not only as a security for the continuity of supply,
+but because otherwise the costs of labour in running the engine night
+and day become excessive. The storage battery gives its supply
+automatically, but the dynamo and engine require incessant skilled
+attendance. If the building to be lighted is at some distance from the
+engine-house the battery should be placed in the basement of the
+building, and underground or overhead conductors, to convey the charging
+current, brought to it from the dynamo.
+
+It is usual, in the case of electric lighting installations, to reckon
+all lamps in their equivalent number of 8 candle power (c.p.)
+incandescent lamps. In lighting a private house or building, the first
+thing to be done is to settle the total number of incandescent lamps and
+their size, whether 32 c.p., 16 c.p. or 8 c.p. Lamps of 5 c.p. can be
+used with advantage in small bedrooms and passages. Each candle-power in
+the case of a carbon filament lamp can be taken as equivalent to 3.5
+watts, or the 8 c.p. lamp as equal to 30 watts, the 16 c.p. lamp to 60
+watts, and so on. In the case of metallic filament lamps about 1.0 or
+1.25 watts. Hence if the equivalent of 100 carbon filament 8 c.p. lamps
+is required in a building the maximum electric power-supply available
+must be 3000 watts or 3 kilowatts. The next matter to consider is the
+pressure of supply. If the battery can be in a position near the
+building to be lighted, it is best to use 100-volt incandescent lamps
+and enclosed arc lamps, which can be worked singly off the 100-volt
+circuit. If, however, the lamps are scattered over a wide area, or in
+separate buildings somewhat far apart, as in a college or hospital, it
+may be better to select 200 volts as the supply pressure. Arc lamps can
+then be worked three in series with added resistance. The third step is
+to select the size of the dynamo unit and the amount of spare plant. It
+is desirable that there should be at least three dynamos, two of which
+are capable of taking the whole of the full load, the third being
+reserved to replace either of the others when required. The total power
+to be absorbed by the lamps and motors (if any) being given, together
+with an allowance for extensions, the size of the dynamos can be
+settled, and the power of the engines required to drive them determined.
+A good rule to follow is that the indicated horse-power (I.H.P.) of the
+engine should be double the dynamo full-load output in kilowatts; that
+is to say, for a 10-kilowatt dynamo an engine should be capable of
+giving 20 indicated (not nominal) H.P. From the I.H.P. of the engine, if
+a steam engine, the size of the boiler required for steam production
+becomes known. For small plants it is safe to reckon that, including
+water waste, boiler capacity should be provided equal to evaporating 40
+lb. of water per hour for every I.H.P. of the engine. The locomotive
+boiler is a convenient form; but where large amounts of steam are
+required, some modification of the Lancashire boiler or the water-tube
+boiler is generally adopted. In settling the electromotive force of the
+dynamo to be employed, attention must be paid to the question of
+charging secondary cells, if these are used. If a secondary battery is
+employed in connexion with 100-volt lamps, it is usual to put in 53 or
+54 cells. The electromotive force of these cells varies between 2.2 and
+1.8 volts as they discharge; hence the above number of cells is
+sufficient for maintaining the necessary electromotive force. For
+charging, however, it is necessary to provide 2.5 volts per cell, and
+the dynamo must therefore have an electromotive force of 135 volts,
+_plus_ any voltage required to overcome the fall of potential in the
+cable connecting the dynamo with the secondary battery. Supposing this
+to be 10 volts, it is safe to install dynamos having an electromotive
+force of 150 volts, since by means of resistance in the field circuits
+this electromotive force can be lowered to 110 or 115 if it is required
+at any time to dispense with the battery. The size of the secondary cell
+will be determined by the nature of the supply to be given after the
+dynamos have been stopped. It is usual to provide sufficient storage
+capacity to run all the lamps for three or four hours without assistance
+from the dynamo.
+
+  As an example taken from actual practice, the following figures give
+  the capacity of the plant put down to supply 500 8 c.p. lamps in a
+  hospital. The dynamos were 15-unit machines, having a full-load
+  capacity of 100 amperes at 150 volts, each coupled direct to an engine
+  of 25 H.P.; and a double plant of this description was supplied from
+  two steel locomotive boilers, each capable of evaporating 800 lb. of
+  water per hour. One dynamo during the day was used for charging the
+  storage battery of 54 cells; and at night the discharge from the
+  cells, together with the current from one of the dynamos, supplied the
+  lamps until the heaviest part of the load had been taken; after that
+  the current was drawn from the batteries alone. In working such a
+  plant it is necessary to have the means of varying the electromotive
+  force of the dynamo as the charging of the cells proceeds. When they
+  are nearly exhausted, their electromotive force is less than 2 volts;
+  but as the charging proceeds, a counter-electromotive force is
+  gradually built up, and the engineer-in-charge has to raise the
+  voltage of the dynamo in order to maintain a constant charging
+  current. This is effected by having the dynamos designed to give
+  normally the highest E.M.F. required, and then inserting resistance in
+  their field circuits to reduce it as may be necessary. The space and
+  attendance required for an oil-engine plant are much less than for a
+  steam-engine.
+
+_Public Supply._--The methods at present in successful operation for
+public electric supply fall into two broad divisions:--(1)
+continuous-current systems and (2) alternating-current systems.
+Continuous-current systems are either low- or high-pressure. In the
+former the current is generated by dynamos at some pressure less than
+500 volts, generally about 460 volts, and is supplied to users at half
+this pressure by means of a three-wire system (see below) of
+distribution, with or without the addition of storage batteries.
+
+
+  Low-pressure continuous supply.
+
+The general arrangements of a low-pressure continuous-current town
+supply station are as follows:--If steam is the motive power selected,
+it is generated under all the best conditions of economy by a battery of
+boilers, and supplied to engines which are now almost invariably coupled
+direct, each to its own dynamo, on one common bedplate; a multipolar
+dynamo is most usually employed, coupled direct to an enclosed engine.
+Parsons or Curtis steam turbines (see STEAM-ENGINE) are frequently
+selected, since experience has shown that the costs of oil and
+attendance are far less for this type than for the reciprocating engine,
+whilst the floor space and, therefore, the building cost are greatly
+reduced. In choosing the size of unit to be adopted, the engineer has
+need of considerable experience and discretion, and also a full
+knowledge of the nature of the public demand for electric current. The
+rule is to choose as large units as possible, consistent with security,
+because they are proportionately more economical than small ones. The
+over-all efficiency of a steam dynamo--that is, the ratio between the
+electrical power output, reckoned say in kilowatts, and the I.H.P. of
+the engine, reckoned in the same units--is a number which falls rapidly
+as the load decreases, but at full load may reach some such value as 80
+or 85%. It is common to specify the efficiency, as above defined, which
+must be attained by the plant at full-load, and also the efficiencies at
+quarter- and half-load which must be reached or exceeded. Hence in the
+selection of the size of the units the engineer is guided by the
+consideration that whatever units are in use shall be as nearly as
+possible fully loaded. If the demand on the station is chiefly for
+electric lighting, it varies during the hours of the day and night with
+tolerable regularity. If the output of the station, either in amperes or
+watts, is represented by the ordinates of a curve, the abscissae of
+which represent the hours of the day, this load diagram for a supply
+station with lighting load only, is a curve such as is shown in fig. 1,
+having a high peak somewhere between 6 and 8 P.M. The area enclosed by
+this load-diagram compared with the area of the circumscribing rectangle
+is called the _load-factor_ of the station. This varies from day to day
+during the year, but on the average for a simple lighting load is not
+generally above 10 or 12%, and may be lower. Thus the total output from
+the station is only some 10% on an average of that which it would be if
+the supply were at all times equal to the maximum demand. Roughly
+speaking, therefore, the total output of an electric supply station,
+furnishing current chiefly for electric lighting, is at best equal to
+about two hours' supply during the day at full load. Hence during the
+greater part of the twenty-four hours a large part of the plant is lying
+idle. It is usual to provide certain small sets of steam dynamos, called
+the daylight machines, for supplying the demand during the day and later
+part of the evening, the remainder of the machines being called into
+requisition only for a short time. Provision must be made for sufficient
+reserve of plant, so that the breakdown of one or more sets will not
+cripple the output of the station.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+
+  Three-wire system.
+
+Assuming current to be supplied at about 460 volts by different and
+separate steam dynamos, Dy1, Dy2 (fig. 2), the machines are connected
+through proper amperemeters and voltmeters with _omnibus bars_, O1, O2,
+O3, on a main switchboard, so that any dynamo can be put in connexion or
+removed. The switchboard is generally divided into three parts--one
+panel for the connexions of the positive feeders, F1, with the positive
+terminals of the generators; one for the negative feeders, F3, and
+negative generator terminals; while from the third (or middle-wire
+panel) proceed an equal number of middle-wire feeders, F2. These sets of
+conductors are led out into the district to be supplied with current,
+and are there connected into a distributing system, consisting of three
+separate insulated conductors, D1, D2, D3, respectively called the
+positive, middle and negative distributing mains. The lamps in the
+houses, H1, H2, &c., are connected between the middle and negative, and
+the middle and positive, mains by smaller supply and service wires. As
+far as possible the numbers of lamps installed on the two sides of the
+system are kept equal; but since it is not possible to control the
+consumption of current, it becomes necessary to provide at the station
+two small dynamos called the _balancing machines_, B1, B2, connected
+respectively between the middle and positive and the middle and negative
+omnibus bars. These machines may have their shafts connected together,
+or they may be driven by separate steam dynamos; their function is to
+supply the difference in the total current circulating through the whole
+of the lamps respectively on the two opposite sides of the middle wire.
+If storage batteries are employed in the station, it is usual to install
+two complete batteries, S1, S2, which are placed in a separate battery
+room and connected between the middle omnibus bar and the two outer
+omnibus bars. The extra electromotive force required to charge these
+batteries is supplied by two small dynamos b1, b2, called _boosters_. It
+is not unusual to join together the two balancing dynamos and the two
+boosters on one common bedplate, the shafts being coupled and in line,
+and to employ the balancing machines as electromotors to drive the
+boosters as required. By the use of _reversible boosters_, such as those
+made by the Lancashire Dynamo & Motor Company under the patents of
+Turnbull & M^cLeod, having four field windings on the booster magnets
+(see _The Electrician_, 1904, p. 303), it is possible to adjust the
+relative duty of the dynamos and battery so that the load on the supply
+dynamos is always constant. Under these conditions the main engines can
+be worked all the time at their maximum steam economy and a smaller
+engine plant employed. If the load in the station rises above the fixed
+amount, the batteries discharge in parallel with the station dynamos; if
+it falls below, the batteries are charged and the station dynamos take
+the external load.
+
+[Illustration: From _The Electrician_.
+
+FIGS. 3 and 4.--Low-pressure Supply Station.]
+
+
+  Generating stations.
+
+The general arrangements of a low-pressure supply station are shown in
+figs. 3 and 4. It consists of a boiler-house containing a bank of
+boilers, either Lancashire or Babcock & Wilcox being generally used (see
+BOILER), which furnish steam to the engines and dynamos, provision
+being made by duplicate steam-pipes or a ring main so that the failure
+of a single engine or dynamo does not cripple the whole supply. The
+furnace gases are taken through an economizer (generally Green's) so
+that they give up their heat to the cold feed water. If condensing water
+is available the engines are worked condensing, and this is an essential
+condition of economy when steam turbines are employed. Hence, either a
+condensing water pond or a cooling tower has to be provided to cool the
+condensing water and enable it to be used over and over again.
+Preferably the station should be situated near a river or canal and a
+railway siding. The steam dynamos are generally arranged in an
+engine-room so as to be overlooked from a switchboard gallery (fig. 3),
+from which all the control is carried out. The boiler furnaces are
+usually stoked by automatic stokers. Owing to the relatively small load
+factor (say 8 or 10%) of a station giving electric supply for lighting
+only, the object of every station engineer is to cultivate a demand for
+electric current for power during the day-time by encouraging the use of
+electric motors for lifts and other purposes, but above all to create a
+demand for traction purposes. Hence most urban stations now supply
+current not only for electric lighting but for running the town tramway
+system, and this traction load being chiefly a daylight load serves to
+keep the plant employed and remunerative. It is usual to furnish a
+continuous current supply for traction at 500 or 600 volts, although
+some station engineers are advocating the use of higher voltages. In
+those stations which supply current for traction, but which have a
+widely scattered lighting load, _double current_ dynamos are often
+employed, furnishing from one and the same armature a continuous current
+for traction purposes, and an alternating current for lighting purposes.
+
+
+  High-pressure continuous supply.
+
+In some places a high voltage system of electric supply by continuous
+current is adopted. In this case the current is generated at a pressure
+of 1000 or 2000 volts, and transmitted from the generating station by
+conductors, called high-pressure feeders, to certain sub-centres or
+transformer centres, which are either buildings above ground or cellars
+or excavations under the ground. In these transformer centres are placed
+machines, called _continuous-current transformers_, which transform the
+electric energy and create a secondary electric current at a lower
+pressure, perhaps 100 or 150 volts, to be supplied by distributing mains
+to users (see TRANSFORMERS). From these sub-centres insulated conductors
+are run back to the generating station, by which the engineer can start
+or stop the continuous-current rotatory transformers, and at the same
+time inform himself as to their proper action and the electromotive
+force at the secondary terminals. This system was first put in practice
+in Oxford, England, and hence has been sometimes called by British
+engineers "the Oxford system." It is now in operation in a number of
+places in England, such as Wolverhampton, Walsall, and Shoreditch in
+London. It has the advantage that in connexion with the low-pressure
+distributing system secondary batteries can be employed, so that a
+storage of electric energy is effected. Further, continuous-current arc
+lamps can be worked in series off the high-pressure mains, that is to
+say, sets of 20 to 40 arc lamps can be operated for the purpose of
+street lighting by means of the high-pressure continuous current.
+
+
+  Alternating supply.
+
+The alternating current systems in operation at the present time are the
+_single-phase_ system, with distributing transformers or transformer
+sub-centres, and the _polyphase_ systems, in which the alternating
+current is transformed down into an alternating current of low pressure,
+or, by means of rotatory transformers, into a continuous current. The
+general arrangement of a _single-phase_ alternating-current system is as
+follows: The generating station contains a number of alternators, A1 A2
+(fig. 5), producing single-phase alternating current, either at 1000,
+2000, or sometimes, as at Deptford and other places, 10,000 volts. This
+current is distributed from the station either at the pressure at which
+it is generated, or after being transformed up to a higher pressure by
+the transformer T. The alternators are sometimes worked in parallel,
+that is to say, all furnish their current to two common omnibus bars on
+a high-pressure switchboard, and each is switched into circuit at the
+moment when it is brought into step with the other machines, as shown by
+some form of _phase-indicator_. In some cases, instead of the
+high-pressure feeders starting from omnibus bars, each alternator works
+independently and the feeders are grouped together on the various
+alternators as required. A number of high-pressure feeders are carried
+from the main switchboard to various transformer sub-centres or else run
+throughout the district to which current is to be furnished. If the
+system laid down is the transformer sub-centre system, then at each of
+these sub-centres is placed a battery of alternating-current
+transformers, T1 T2 T3, having their primary circuits all joined in
+parallel to the terminals of the high-pressure feeders, and their
+secondary circuits all joined in parallel on a distributing main,
+suitable switches and cut-outs being interposed. The pressure of the
+current is then transformed down by these transformers to the required
+supply pressure. The secondary circuits of these transformers are
+generally provided with three terminals, so as to supply the
+low-pressure side on a three-wire system. It is not advisable to connect
+together directly the secondary circuits of all the different
+sub-centres, because then a fault or short circuit on one secondary
+system affects all the others. In banking together transformers in this
+manner in a sub-station it is necessary to take care that the
+transformation ratio and secondary drop (see TRANSFORMERS) are exactly
+the same, otherwise one transformer will take more than its full share
+of the load and will become overheated. The transformer sub-station
+system can only be adopted where the area of supply is tolerably
+compact. Where the consumers lie scattered over a large area, it is
+necessary to carry the high-pressure mains throughout the area, and to
+place a separate transformer or transformers in each building. From a
+financial point of view, this "house-to-house system" of
+alternating-current supply, generally speaking, is less satisfactory in
+results than the transformer sub-centre system. In the latter some of
+the transformers can be switched off, either by hand or by automatic
+apparatus, during the time when the load is light, and then no power is
+expended in magnetizing their cores. But with the house-to-house system
+the whole of the transformers continually remain connected with the
+high-pressure circuits; hence in the case of supply stations which have
+only an ordinary electric lighting load, and therefore a load-factor not
+above 10%, the efficiency of distribution is considerably diminished.
+
+[Illustration: FIG. 5.]
+
+The single-phase alternating-current system is defective in that it
+cannot be readily combined with secondary batteries for the storage of
+electric energy. Hence in many places preference is now given to the
+_polyphase system_. In such a system a polyphase alternating current,
+either two- or three-phase, is transmitted from the generating station
+at a pressure of 5000 to 10,000 volts, or sometimes higher, and at
+various sub-stations is transformed down, first by static transformers
+into an alternating current of lower pressure, say 500 volts, and then
+by means of rotatory transformers into a continuous current of 500
+volts or lower for use for lighting or traction.
+
+In the case of large cities such as London, New York, Chicago, Berlin
+and Paris the use of small supply stations situated in the interior of
+the city has gradually given way to the establishment of large supply
+stations outside the area; in these alternating current is generated on
+the single or polyphase system at a high voltage and transmitted by
+underground cables to sub-stations in the city, at which it is
+transformed down for distribution for private and public electric
+lighting and for urban electric traction.
+
+Owing to the high relative cost of electric power when generated in
+small amounts and the great advantages of generating it in proximity to
+coal mines and waterfalls, the supply of electric power in bulk to small
+towns and manufacturing districts has become a great feature in modern
+electrical engineering. In Great Britain, where there is little useful
+water power but abundance of coal, electric supply stations for supply
+in bulk have been built in the coal-producing districts of South Wales,
+the Midlands, the Clyde valley and Yorkshire. In these cases the current
+is a polyphase current generated at a high voltage, 5000 to 10,000
+volts, and sometimes raised again in pressure to 20,000 or 40,000 volts
+and transmitted by overhead lines to the districts to be supplied. It is
+there reduced in voltage by transformers and employed as an alternating
+current, or is used to drive polyphase motors coupled to direct current
+generators to reproduce the power in continuous current form. It is then
+distributed for local lighting, street or railway traction, driving
+motors, and metallurgical or electrochemical applications. Experience
+has shown that it is quite feasible to distribute in all directions for
+25 miles round a high-pressure generating station, which thus supplies
+an area of nearly 2000 sq. m. At such stations, employing large turbine
+engines and alternators, electric power may be generated at a works cost
+of 0.375d. per kilowatt (K.W.), the coal cost being less than 0.125d.
+per K.W., and the selling price to large load-factor users not more than
+0.5d. per K.W. The average price of supply from the local generating
+stations in towns and cities is from 3d. to 4d. per unit, electric
+energy for power and heating being charged at a lower rate than that for
+lighting only.
+
+
+  Conductors.
+
+We have next to consider the structure and the arrangement of the
+conductors employed to convey the currents from their place of creation
+to that of utilization. The conductors themselves for the most part
+consist of copper having a conductivity of not less than 98% according
+to Matthiessen's standard. They are distinguished as (1) _External
+conductors_, which are a part of the public supply and belong to the
+corporation or company supplying the electricity; (2) _Internal
+conductors_, or house wiring, forming a part of the structure of the
+house or building supplied and usually the property of its owner.
+
+
+  External conductors.
+
+The external conductors may be overhead or underground. _Overhead_
+conductors may consist of bare stranded copper cables carried on
+porcelain insulators mounted on stout iron or wooden poles. If the
+current is a high-pressure one, these insulators must be carefully
+tested, and are preferably of the pattern known as oil insulators. In
+and near towns it is necessary to employ insulated overhead conductors,
+generally india-rubber-covered stranded copper cables, suspended by
+leather loops from steel bearer wires which take the weight. The British
+Board of Trade have issued elaborate rules for the construction of
+overhead lines to transmit large electric currents. Where telephone and
+telegraph wires pass over such overhead electric lighting wires, they
+have to be protected from falling on the latter by means of guard wires.
+
+By far the largest part, however, of the external electric distribution
+is now carried out by _underground conductors_, which are either bare or
+insulated. Bare copper conductors may be carried underground in culverts
+or chases, air being in this case the insulating material, as in the
+overhead system. A culvert and covered chase is constructed under the
+road or side-walk, and properly shaped oak crossbars are placed in it
+carrying glass or porcelain insulators, on which stranded copper
+cables, or, preferably, copper strips placed edgeways, are stretched and
+supported. The advantages of this method of construction are cheapness
+and the ease with which connexions can be made with service-lines for
+house supply; the disadvantages are the somewhat large space in which
+coal-gas leaking out of gas-pipes can accumulate, and the difficulty of
+keeping the culverts at all times free from rain-water. Moisture has a
+tendency to collect on the negative insulators, and hence to make a dead
+earth on the negative side of the main; while unless the culverts are
+well ventilated, explosions from mixtures of coal-gas and air are liable
+to occur. Insulated cables are insulated either with a material which is
+in itself waterproof, or with one which is only waterproof in so far as
+it is enclosed in a waterproof tube, e.g. of lead. Gutta-percha and
+india-rubber are examples of materials of the former kind. Gutta-percha,
+although practically everlasting when in darkness and laid under water,
+as in the case of submarine cables, has not been found satisfactory for
+use with large systems of electric distribution, although much employed
+for telephone and telegraph work. Insulated underground external
+conductors are of three types:--(a) _Insulated Cables drawn into
+Pipes._--In this system of distribution cast-iron or stoneware pipes, or
+special stoneware conduits, or conduits made of a material called
+bitumen concrete, are first laid underground in the street. These
+contain a number of holes or "ways," and at intervals drawing-in boxes
+are placed which consist of a brick or cast-iron box having a
+water-tight lid, by means of which access is gained to a certain section
+of the conduit. Wires are used to draw in the cables, which are covered
+with either india-rubber or lead, the copper being insulated by means of
+paper, impregnated jute, or other similar material. The advantages of a
+drawing-in system are that spare ways can be left when the conduits are
+put in, so that at a future time fresh cables can be added without
+breaking up the roadway. (b) _Cables in Bitumen._--One of the earliest
+systems of distribution employed by T.A. Edison consisted in fixing two
+segment-shaped copper conductors in a steel tube, the interspace between
+the conductors and the tube being filled in with a bitumen compound. A
+later plan is to lay down an iron trough, in which the cables are
+supported by wooden bearers at proper distances, and fill in the whole
+with natural bitumen. This system has been carried out extensively by
+the Callendar Cable Company. Occasionally concentric lead-covered and
+armoured cables are laid in this way, and then form an expensive but
+highly efficient form of insulated conductor. In selecting a system of
+distribution regard must be paid to the nature of the soil in which the
+cables are laid. Lead is easily attacked by soft water, although under
+some conditions it is apparently exceedingly durable, and an atmosphere
+containing coal-gas is injurious to india-rubber. (c) _Armoured
+Cables._--In a very extensively used system of distribution armoured
+cables are employed. In this case the copper conductors, two, three or
+more in number, may be twisted together or arranged concentrically, and
+insulated by means of specially prepared jute or paper insulation,
+overlaid with a continuous tube of lead. Over the lead, but separated by
+a hemp covering, is put a steel armour consisting of two layers of steel
+strip, wound in opposite directions and kept in place by an external
+covering. Such a cable can be laid directly in the ground without any
+preparation other than the excavation of a simple trench, junction-boxes
+being inserted at intervals to allow of branch cables being taken off.
+The armoured cable used is generally of the concentric pattern (fig. 6).
+It consists of a stranded copper cable composed of a number of wires
+twisted together and overlaid with an insulating material. Outside this
+a tubular arrangement of copper wires and a second layer of insulation,
+and finally a protective covering of lead and steel wires or armour are
+placed. In some cases three concentric cylindrical conductors are formed
+by twisting wires or copper strips with insulating material between. In
+others two or three cables of stranded copper are embedded in insulating
+material and included in a lead sheath. This last type of cable is
+usually called a _two-_ or _three-core_ pattern cable (fig. 7).
+
+[Illustration: FIG. 6.--Armoured Concentric Cable (Section).
+
+  IC, Inner conductor.
+  OC, Outer conductor.
+  I, Insulation.
+  L, Lead sheath.
+  S, Steel armour.
+  H, Hemp covering.]
+
+[Illustration: FIG. 7.--Triple Conductor Armoured Cable (Section).
+
+  C, Copper conductor.
+  I, Insulation.
+  L, Lead sheath.
+  H, Hemp covering.
+  S, Steel armour.]
+
+The arrangement and nature of the external conductors depends on the
+system of electric supply in which they are used. In the case of
+continuous-current supply for incandescent electric lighting and motive
+power in small units, when the external conductors are laid down on the
+three-wire system, each main or branch cable in the street consists of a
+set of three conductors called the positive, middle and negative. Of
+these triple conductors some run from the supply station to various
+points in the area of supply without being tapped, and are called the
+_feeders_; others, called the _distributing mains_, are used for making
+connexions with the service lines of the consumers, one service line, as
+already explained, being connected to the middle conductor, and the
+other to either the positive or the negative one. Since the middle
+conductor serves to convey only the difference between the currents
+being used on the two sides of the system, it is smaller in section than
+the positive and negative ones. In laying out the system great judgment
+has to be exercised as to the selection of the points of attachment of
+the feeders to the distributing mains, the object being to keep a
+constant electric pressure or voltage between the two service-lines in
+all the houses independently of the varying demand for current. Legally
+the suppliers are under regulations to keep the supply voltage constant
+within 4% either way above or below the standard pressure. As a matter
+of fact very few stations do maintain such good regulation. Hence a
+considerable variation in the light given by the incandescent lamps is
+observed, since the candle-power of carbon glow lamps varies as the
+fifth or sixth power of the voltage of supply, i.e. a variation of only
+2% in the supply pressure affects the resulting candle-power of the
+lamps to the extent of 10 or 12%. This variation is, however, less in
+the case of metallic filament lamps (see LIGHTING: _Electric_). In the
+service-lines are inserted the meters for measuring the electric energy
+supplied to the customer (see METER, ELECTRIC).
+
+
+  Interior wiring.
+
+In the interior of houses and buildings the conductors generally consist
+of india-rubber-covered cables laid in wood casing. The copper wire must
+be tinned and then covered, first with a layer of unvulcanized pure
+india-rubber, then with a layer of vulcanized rubber, and lastly with
+one or more layers of protective cotton twist or tape. No conductor of
+this character employed for interior house-wiring should have a smaller
+insulation resistance than 300 megohms per mile when tested with a
+pressure of 600 volts after soaking 24 hours in water. The wood casing
+should, if placed in damp positions or under plaster, be well varnished
+with waterproof varnish. As far as possible all joints in the run of the
+cable should be avoided by the use of the so-called looping-in system,
+and after the wiring is complete, careful tests for insulation should be
+made. The Institution of Electrical Engineers of Great Britain have
+drawn up rules to be followed in interior house-wiring, and the
+principal Fire Insurance offices, following the lead of the Phoenix Fire
+Office, of London, have made regulations which, if followed, are a
+safeguard against bad workmanship and resulting possibility of damage by
+fire. Where fires having an electric origin have taken place, they have
+invariably been traced to some breach of these rules. Opinions differ,
+however, as to the value and security of this method of laying interior
+conductors in buildings, and two or three alternative systems have been
+much employed. In one of these, called the _interior conduit_ system,
+highly insulating waterproof and practically fireproof tubes or conduits
+replace the wooden casing; these, being either of plain insulating
+material, or covered with brass or steel armour, may be placed under
+plaster or against walls. They are connected by bends or joint-boxes.
+The insulated wires being drawn into them, any short circuit or heating
+of the wire cannot give rise to a fire, as it can only take place in the
+interior of a non-inflammable tube. A third system of electric light
+wiring is the safety concentric system, in which concentric conductors
+are used. The inner one, which is well insulated, consists of a
+copper-stranded cable. The outer may be a galvanized iron strand, a
+copper tape or braid, or a brass tube, and is therefore necessarily
+connected with the earth. A fourth system consists in the employment of
+twin insulated wires twisted together and sheathed with a lead tube; the
+conductor thus formed can be fastened by staples against walls, or laid
+under plaster or floors.
+
+The general arrangement for distributing current to the different
+portions of a building for the purpose of electric lighting is to run up
+one or more rising mains, from which branches are taken off to
+distributing boxes on each floor, and from these boxes to carry various
+branch circuits to the lamps. At the distributing boxes are collected
+the cut-outs and switches controlling the various circuits. When
+alternating currents are employed, it is usual to select as a type of
+conductor either twin-twisted conductor or concentric; and the
+employment of these types of cable, rather than two separate cables, is
+essential in any case where there are telephone or telegraph wires in
+proximity, for otherwise the alternating current would create inductive
+disturbances in the telephone circuit. The house-wiring also comprises
+the details of _switches_ for controlling the lamps, _cut-outs_ or fuses
+for preventing an excess of current passing, and fixtures or supports
+for lamps often of an ornamental character. For the details of these,
+special treatises on electric interior wiring must be consulted.
+
+  For further information the reader may be referred to the following
+  books:--C.H. Wordingham, _Central Electrical Stations_ (London, 1901);
+  A. Gay and C.Y. Yeaman, _Central Station Electricity Supply_ (London,
+  1906); S.P. Thompson, _Dynamo Electric Machinery_ (2 vols., London,
+  1905); E. Tremlett Carter and T. Davies, _Motive Power and Gearing_
+  (London, 1906); W.C. Clinton, _Electric Wiring_ (2nd ed., London,
+  1906); W. Perren Maycock, _Electric Wiring, Fitting, Switches and
+  Lamps_ (London, 1899); D. Salomons, _Electric Light Installations_
+  (London, 1894); Stuart A. Russell, _Electric Light Cables_ (London,
+  1901); F.A.C. Perrine, _Conductors for Electrical Distribution_
+  (London, 1903); E. Rosenberg, W.W. Haldane Gee and C. Kinzbrunner,
+  _Electrical Engineering_ (London, 1903); E.C. Metcalfe, _Practical
+  Electric Wiring for Lighting Installations_ (London, 1905); F.C.
+  Raphael, _The Wireman's Pocket Book_ (London, 1903).     (J. A. F.)
+
+
+  History.
+
+II. _Commercial Aspects._--To enable the public supply enterprises
+referred to in the foregoing section to be carried out in England,
+statutory powers became necessary to break up the streets. In the early
+days a few small stations were established for the supply of electricity
+within "block" buildings, or by means of overhead wires within
+restricted areas, but the limitations proved uneconomical and the
+installations were for the most part merged into larger undertakings
+sanctioned by parliamentary powers. In the year 1879 the British
+government had its attention directed for the first time to electric
+lighting as a possible subject for legislation, and the consideration of
+the then existing state of electric lighting was referred to a select
+committee of the House of Commons. No legislative action, however, was
+taken at that time. In fact the invention of the incandescent lamp was
+incomplete--Edison's British master-patent was only filed in Great
+Britain in November 1879. In 1881 and 1882 electrical exhibitions were
+held in Paris and at the Crystal Palace, London, where the improved
+electric incandescent lamp was brought before the general public. In
+1882 parliament passed the first Electric Lighting Act, and considerable
+speculation ensued. The aggregate capital of the companies registered in
+1882-1883 to carry out the public supply of electricity in the United
+Kingdom amounted to L15,000,000, but the onerous conditions of the act
+deterred investors from proceeding with the enterprise. Not one of the
+sixty-two provisional orders granted to companies in 1883 under the act
+was carried out. In 1884 the Board of Trade received only four
+applications for provisional orders, and during the subsequent four
+years only one order was granted. Capitalists declined to go on with a
+business which if successful could be taken away from them by local
+authorities at the end of twenty-one years upon terms of paying only the
+then value of the plant, lands and buildings, without regard to past or
+future profits, goodwill or other considerations. The electrical
+industry in Great Britain ripened at a time when public opinion was
+averse to the creation of further monopolies, the general belief being
+that railway, water and gas companies had in the past received valuable
+concessions on terms which did not sufficiently safeguard the interests
+of the community. The great development of industries by means of
+private enterprise in the early part of the 19th century produced a
+reaction which in the latter part of the century had the effect of
+discouraging the creation by private enterprise of undertakings
+partaking of the nature of monopolies; and at the same time efforts were
+made to strengthen local and municipal institutions by investing them
+with wider functions. There were no fixed principles governing the
+relations between the state or municipal authorities and commercial
+companies rendering monopoly services. The new conditions imposed on
+private enterprise for the purpose of safeguarding the interests of the
+public were very tentative, and a former permanent secretary of the
+Board of Trade has stated that the efforts made by parliament in these
+directions have sometimes proved injurious alike to the public and to
+investors. One of these tentative measures was the Tramways Act 1870,
+and twelve years later it was followed by the first Electric Lighting
+Act.
+
+It was several years before parliament recognized the harm that had been
+done by the passing of the Electric Lighting Act 1882. A select
+committee of the House of Lords sat in 1886 to consider the question of
+reform, and as a result the Electric Lighting Act 1888 was passed. This
+amending act altered the period of purchase from twenty-one to forty-two
+years, but the terms of purchase were not materially altered in favour
+of investors. The act, while stipulating for the consent of local
+authorities to the granting of provisional orders, gives the Board of
+Trade power in exceptional cases to dispense with the consent, but this
+power has been used very sparingly. The right of vetoing an undertaking,
+conferred on local authorities by the Electric Lighting Acts and also by
+the Tramways Act 1870, has frequently been made use of to exact unduly
+onerous conditions from promoters, and has been the subject of complaint
+for years. Although, in the opinion of ministers of the Crown, the
+exercise of the veto by local authorities has on several occasions led
+to considerable scandals, no government has so far been able, owing to
+the very great power possessed by local authorities, to modify the law
+in this respect. After 1888 electric lighting went ahead in Great
+Britain for the first time, although other countries where legislation
+was different had long previously enjoyed its benefits. The developments
+proceeded along three well-defined lines. In London, where none of the
+gas undertakings was in the hands of local authorities, many of the
+districts were allotted to companies, and competition was permitted
+between two and sometimes three companies. In the provinces the cities
+and larger towns were held by the municipalities, while the smaller
+towns, in cases where consents could be obtained, were left to the
+enterprise of companies. Where consents could not be obtained these
+towns were for some time left without supply.
+
+  Some statistics showing the position of the electricity supply
+  business respectively in 1896 and 1906 are interesting as indicating
+  the progress made and as a means of comparison between these two
+  periods of the state of the industry as a whole. In 1896 thirty-eight
+  companies were at work with an aggregate capital of about L6,000,000,
+  and thirty-three municipalities with electric lighting loans of nearly
+  L2,000,000. The figures for 1906, ten years later, show that 187
+  electricity supply companies were in operation with a total investment
+  of close on L32,000,000, and 277 municipalities with loans amounting
+  to close on L36,000,000. The average return on the capital invested in
+  the companies at the later period was 5.1% per annum. In 1896 the
+  average capital expenditure was about L100 per kilowatt of plant
+  installed; and L50 per kilowatt was regarded as a very low record. For
+  1906 the average capital expenditure per kilowatt installed was about
+  L81. The main divisions of the average expenditure are:--
+
+                             1896.   1906.
+    Land and buildings       22.3%   17.8%
+    Plant and machinery      36.7    36.5
+    Mains                    32.2    35.5
+    Meters and instruments    4.6     5.7
+    Provisional orders, &c.   3.2     2.8
+
+  The load connected, expressed in equivalents of eight candle-power
+  lamps, was 2,000,000 in 1896 and 24,000,000 in 1906. About one-third
+  of this load would be for power purposes and about two-thirds for
+  lighting. The Board of Trade units sold were 30,200,000 in 1896 and
+  533,600,000 in 1906, and the average prices per unit obtained were
+  5.7d. and 2.7d. respectively, or a revenue of L717,250 in 1896 and
+  over L6,000,000 in 1906. The working expenses per Board of Trade unit
+  sold, excluding depreciation, sinking fund and interest were as
+  follows:--
+
+                                   1896.    1906.
+    Generation and distribution    2.81d.   .99d.
+    Rent, rates and taxes           .35     .14
+    Management                      .81     .18
+    Sundries                        .10     .02
+                                   ------  ------
+                 Total             4.07d.  1.33d.
+
+  In 1896 the greatest output at one station was about 5-1/2 million
+  units, while in 1906 the station at Manchester had the largest output
+  of over 40 million units.
+
+  The capacity of the plants installed in the United Kingdom in 1906
+  was:--
+
+                               K.W.
+    Continuous current         417,000     / Provinces    333,000
+                                           \ London        84,000
+    Alternating current        132,000     / Provinces     83,000
+                                           \ London        49,000
+    Continuous current and \
+      alternating current   >  480,000     / Provinces    366,000
+      combined             /               \ London       114,000
+                             ---------
+                             1,029,000 k.w.
+
+
+  Economics.
+
+The economics of electric lighting were at first assumed to be similar
+to those of gas lighting. Experience, however, soon proved that there
+were important differences, one being that gas may be stored in
+gasometers without appreciable loss and the work of production carried
+on steadily without reference to fluctuations of demand. Electricity
+cannot be economically stored to the same extent, and for the most part
+it has to be used as it is generated. The demand for electric light is
+practically confined to the hours between sunset and midnight, and it
+rises sharply to a "peak" during this period. Consequently the
+generating station has to be equipped with plant of sufficient capacity
+to cope with the maximum load, although the peak does not persist for
+many minutes--a condition which is very uneconomical both as regards
+capital expenditure and working costs (see LIGHTING: _Electric_). In
+order to obviate the unproductiveness of the generating plant during the
+greater part of the day, electricity supply undertakings sought to
+develop the "daylight" load. This they did by supplying electricity for
+traction purposes, but more particularly for industrial power purposes.
+The difficulties in the way of this line of development, however, were
+that electric power could not be supplied cheaply enough to compete with
+steam, hydraulic, gas and other forms of power, unless it was generated
+on a very large scale, and this large demand could not be developed
+within the restricted areas for which provisional orders were granted
+and under the restrictive conditions of these orders in regard to
+situation of power-house and other matters.
+
+The leading factors which make for economy in electricity supply are the
+magnitude of the output, the load factor, and the diversity factor,
+also the situation of the power house, the means of distribution, and
+the provision of suitable, trustworthy and efficient plant. These
+factors become more favourable the larger the area and the greater and
+more varied the demand to be supplied. Generally speaking, as the output
+increases so the cost per unit diminishes, but the ratio (called the
+load factor) which the output during any given period bears to the
+_maximum_ possible output during the same period has a very important
+influence on costs. The ideal condition would be when a power station is
+working at its normal _maximum_ output continuously night and day. This
+would give a load-factor of 100%, and represents the ultimate ideal
+towards which the electrical engineer strives by increasing the area of
+his operations and consequently also the load and the variety of the
+overlapping demands. It is only by combining a large number of demands
+which fluctuate at different times--that is by achieving a high
+diversity factor--that the supplier of electricity can hope to approach
+the ideal of continuous and steady output. Owing to the dovetailing of
+miscellaneous demands the actual demand on a power station at any moment
+is never anything like the aggregate of all the maximum demands. One
+large station would require a plant of 36,000 k.w. capacity if all the
+demands came upon the station simultaneously, but the maximum demand on
+the generating plant is only 15,000 kilowatts. The difference between
+these two figures may be taken to represent the economy effected by
+combining a large number of demands on one station. In short, the
+keynote of progress in cheap electricity is increased and diversified
+demand combined with concentration of load. The average load-factor of
+all the British electricity stations in 1907 was 14.5%--a figure which
+tends to improve.
+
+
+  Power companies.
+
+Several electric power supply companies have been established in the
+United Kingdom to give practical effect to these principles. The
+Electric Lighting Acts, however, do not provide for the establishment of
+large power companies, and special acts of parliament have had to be
+promoted to authorize these undertakings. In 1898 several bills were
+introduced in parliament for these purposes. They were referred to a
+joint committee of both Houses of Parliament presided over by Lord
+Cross. The committee concluded that, where sufficient public advantages
+are shown, powers should be given for the supply of electricity over
+areas including the districts of several local authorities and involving
+the use of exceptional plant; that the usual conditions of purchase of
+the undertakings by the local authorities did not apply to such
+undertakings; that the period of forty-two years was "none too long" a
+tenure; and that the terms of purchase should be reconsidered. With
+regard to the provision of the Electric Lighting Acts which requires
+that the consent of the local authority should be obtained as a
+condition precedent to the granting of a provisional order, the
+committee was of opinion that the local authority should be entitled to
+be heard by the Board of Trade, but should not have the power of veto.
+No general legislation took place as a result of these recommendations,
+but the undermentioned special acts constituting power supply companies
+were passed.
+
+In 1902 the president of the Board of Trade stated that a bill had been
+drafted which he thought "would go far to meet all the reasonable
+objections that had been urged against the present powers by the local
+authorities." In 1904 the government introduced the Supply of
+Electricity Bill, which provided for the removal of some of the minor
+anomalies in the law relating to electricity. The bill passed through
+all its stages in the House of Lords but was not proceeded with in the
+House of Commons. In 1905 the bill was again presented to parliament but
+allowed to lie on the table. In the words of the president of the Board
+of Trade, there was "difficulty of dealing with this question so long as
+local authorities took so strong a view as to the power which ought to
+be reserved to them in connexion with this enterprise." In the official
+language of the council of the Institution of Electrical Engineers, the
+development of electrical science in the United Kingdom is in a backward
+condition as compared with other countries in respect of the practical
+application to the industrial and social requirements of the nation,
+notwithstanding that Englishmen have been among the first in inventive
+genius. The cause of such backwardness is largely due to the conditions
+under which the electrical industry has been carried on in the country,
+and especially to the restrictive character of the legislation governing
+the initiation and development of electrical power and traction
+undertakings, and to the powers of obstruction granted to local
+authorities. Eventually The Electric Lighting Act 1909 was passed. This
+Act provides:--(1) for the granting of provisional orders authorizing
+any local authority or company to supply electricity in bulk; (2) for
+the exercise of electric lighting powers by local authorities jointly
+under provisional order; (3) for the supply of electricity to railways,
+canals and tramways outside the area of supply with the consent of the
+Board of Trade; (4) for the compulsory acquisition of land for
+generating stations by provisional order; (5) for the exemption of
+agreements for the supply of electricity from stamp duty; and (6) for
+the amendment of regulations relating to July notices, revision of
+maximum price, certification of meters, transfer of powers of
+undertakers, auditors' reports, and other matters.
+
+The first of the Power Bills was promoted in 1898, under which it was
+proposed to erect a large generating station in the Midlands from which
+an area of about two thousand square miles would be supplied. Vigorous
+opposition was organized against the bill by the local authorities and
+it did not pass. The bill was revived in 1899, but was finally crushed.
+In 1900 and following years several power bills were successfully
+promoted, and the following are the areas over which the powers of these
+acts extend:
+
+In Scotland, (1) the Clyde Valley, (2) the county of Fife, (3) the
+districts described as "Scottish Central," comprising Linlithgow,
+Clackmannan, and portions of Dumbarton and Stirling, and (4) the
+Lothians, which include portions of Midlothian, East Lothian, Peebles
+and Lanark.
+
+In England there are companies operating in (1) Northumberland, (2)
+Durham county, (3) Lancashire, (4) South Wales and Carmarthenshire, (5)
+Derbyshire and Nottinghamshire, (6) Leicestershire and Warwickshire, (7)
+Yorkshire, (8) Shropshire, Worcestershire and Staffordshire, (9)
+Somerset, (10) Kent, (11) Cornwall, (12) portions of Gloucestershire,
+(13) North Wales, (14) North Staffordshire, Derbyshire, Denbighshire and
+Flintshire, (15) West Cumberland, (16) the Cleveland district, (17) the
+North Metropolitan district, and (18) the West Metropolitan area. An
+undertaking which may be included in this category, although it is not a
+Power Act company, is the Midland Electric Corporation in South
+Staffordshire. The systems of generation and distribution are generally
+10,000 or 11,000 volts three-phase alternating current.
+
+The powers conferred by these acts were much restricted as a result of
+opposition offered to them. In many cases the larger towns were cut out
+of the areas of supply altogether, but the general rule was that the
+power company was prohibited from supplying direct to a power consumer
+in the area of an authorized distributor without the consent of the
+latter, subject to appeal to the Board of Trade. Even this restricted
+power of direct supply was not embodied in all the acts, the power of
+taking supply in bulk being left only to certain authorized distributors
+and to authorized users such as railways and tramways. Owing chiefly to
+the exclusion of large towns and industrial centres from their areas,
+these power supply companies did not all prove as successful as was
+expected.
+
+In the case of one of the power companies which has been in a favourable
+position for the development of its business, the theoretical
+conclusions in regard to the economy of large production above stated
+have been amply demonstrated in practice. In 1901, when this company was
+emerging from the stage of a simple electric lighting company, the total
+costs per unit were 1.05d. with an output of about 2-1/2 million units per
+annum. In 1905 the output rose to over 30 million units mostly for power
+and traction purposes, and the costs fell to 0.56d. per unit.
+
+An interesting phase of the power supply question has arisen in London.
+Under the general acts it was stipulated that the power-house should be
+erected within the area of supply, and amalgamation of undertakings was
+prohibited. After less than a decade of development several of the
+companies in London found themselves obliged to make considerable
+additions to their generating plants. But their existing buildings were
+full to their utmost capacity, and the difficulties of generating
+cheaply on crowded sites had increased instead of diminished during the
+interval. Several of the companies had to promote special acts of
+parliament to obtain relief, but the idea of a general combination was
+not considered to be within the range of practical politics until 1905,
+when the Administrative County of London Electric Power Bill was
+introduced. Compared with other large cities, the consumption of
+electricity in London is small. The output of electricity in New York
+for all purposes is 971 million units per annum or 282 units per head of
+population. The output of electricity in London is only 42 units per
+head per annum. There are in London twelve local authorities and
+fourteen companies carrying on electricity supply undertakings. The
+capital expenditure is L3,127,000 by the local authorities and
+L12,530,000 by the companies, and their aggregate capacity of plant is
+165,000 k.w. The total output is about 160,000,000 units per annum, the
+total revenue is over L2,000,000, and the gross profit before providing
+for interest and sinking fund charges is L1,158,000. The general average
+cost of production is 1.55d. per unit, and the average price per unit
+sold is 3.16d., but some of the undertakers have already supplied
+electricity to large power consumers at below 1d. per unit. By
+generating on a large scale for a wide variety of demands the promoters
+of the new scheme calculated to be able to offer electrical energy in
+bulk to electricity supply companies and local authorities at prices
+substantially below their costs of production at separate stations, and
+also to provide them and power users with electricity at rates which
+would compete with other forms of power. The authorized capital was
+fixed at L6,666,000, and the initial outlay on the first plant of 90,000
+k.w., mains, &c., was estimated at L2,000,000. The costs of generation
+were estimated at 0.15d. per unit, and the total cost at 0.52d. per unit
+sold. The output by the year 1911 was estimated at 133,500,000 units at
+an average selling price of 0.7d. per unit, to be reduced to 0.55d. by
+1916 when the output was estimated at 600,000,000 units. The bill
+underwent a searching examination before the House of Lords committee
+and was passed in an amended form. At the second reading in the House of
+Commons a strong effort was made to throw it out, but it was allowed to
+go to committee on the condition--contrary to the general
+recommendations of the parliamentary committee of 1898--that a purchase
+clause would be inserted; but amendments were proposed to such an extent
+that the bill was not reported for third reading until the eve of the
+prorogation of parliament. In the following year (1906) the
+Administrative Company's bill was again introduced in parliament, but
+the London County Council, which had previously adopted an attitude both
+hostile and negative, also brought forward a similar bill. Among other
+schemes, one known as the Additional Electric Power Supply Bill was to
+authorize the transmission of current from St Neots in Hunts. This bill
+was rejected by the House of Commons because the promoters declined to
+give precedence to the bill of the London County Council. The latter
+bill was referred to a hybrid committee with instructions to consider
+the whole question of London power supply, but it was ultimately
+rejected. The same result attended a second bill which was promoted by
+the London County Council in 1907. The question was settled by the
+London Electric Supply Act 1908, which constitutes the London County
+Council the purchasing authority (in the place of the local authorities)
+for the electric supply companies in London. This Act also enabled the
+Companies and other authorized undertakers to enter into agreements for
+the exchange of current and the linking-up of stations.
+
+
+  Legislation and regulations.
+
+The general supply of electricity is governed primarily by the two acts
+of parliament passed in 1882 and 1888, which apply to the whole of the
+United Kingdom. Until 1899 the other statutory provisions relating to
+electricity supply were incorporated in provisional orders granted by
+the Board of Trade and confirmed by parliament in respect of each
+undertaking, but in that year an Electric Lighting Clauses Act was
+passed by which the clauses previously inserted in each order were
+standardized. Under these acts the Board of Trade made rules with
+respect to applications for licences and provisional orders, and
+regulations for the protection of the public, and of the electric lines
+and works of the post office, and others, and also drew up a model form
+for provisional orders.
+
+Until the passing of the Electric Lighting Acts, wires could be placed
+wherever permission for doing so could be obtained, but persons breaking
+up streets even with the consent of the local authority were liable to
+indictment for nuisance. With regard to overhead wires crossing the
+streets, the local authorities had no greater power than any member of
+the public, but a road authority having power to make a contract for
+lighting the road could authorize others to erect poles and wires for
+the purpose. A property owner, however, was able to prevent wires from
+being taken over his property. The act of 1888 made all electric lines
+or other works for the supply of electricity, not entirely enclosed
+within buildings or premises in the same occupation, subject to
+regulations of the Board of Trade. The postmaster-general may also
+impose conditions for the protection of the post office. Urban
+authorities, the London County Council, and some other corporations have
+now powers to make by-laws for prevention of obstruction from posts and
+overhead wires for telegraph, telephone, lighting or signalling
+purposes; and electric lighting stations are now subject to the
+provisions of the Factory Acts.
+
+Parliamentary powers to supply electricity can now be obtained by (A)
+Special Act, (B) Licence, or (C) Provisional order.
+
+A. _Special Act._--Prior to the report of Lord Cross's joint committee
+of 1898 (referred to above), only one special act was passed. The
+provisions of the Electric Power Acts passed subsequently are not
+uniform, but the following are some of the usual provisions:--
+
+The company shall not supply electricity for lighting purposes except to
+authorized undertakers, provided that the energy supplied to any person
+for power may be used for lighting any premises on which the power is
+utilized. The company shall not supply energy (except to authorized
+undertakers) in any area which forms part of the area of supply of any
+authorized distributors without their consent, such consent not to be
+unreasonably withheld. The company is bound to supply authorized
+undertakers upon receiving notice and upon the applicants agreeing to
+pay for at least seven years an amount sufficient to yield 20% on the
+outlay (excluding generating plant or wires already installed). Other
+persons to whom the company is authorized to supply may require it upon
+terms to be settled, if not agreed, by the Board of Trade. Dividends are
+usually restricted to 8%, with a provision that the rate may be
+increased upon the average price charged being reduced. The maximum
+charges are usually limited to 3d. per unit for any quantity up to 400
+hours' supply, and 2d. per unit beyond. No preference is to be shown
+between consumers in like circumstances. Many provisions of the general
+Electric Lighting Acts are excluded from these special acts, in
+particular the clause giving the local authority the right to purchase
+the undertaking compulsorily.
+
+B. _Licence._--The only advantages of proceeding by licence are that it
+can be expeditiously obtained and does not require confirmation by
+parliament; but some of the provisions usually inserted in provisional
+orders would be _ultra vires_ in a licence, and the Electric Lighting
+Clauses Act 1899 does not extend to licences. The term of a licence does
+not exceed seven years, but is renewable. The consent of the local
+authority is necessary even to an application for a licence. None of the
+licences that have been granted is now in force.
+
+C. _Provisional Order._--An intending applicant for a provisional order
+must serve notice of his intention on every local authority within the
+proposed area of supply on or before the 1st of July prior to the
+session in which application is to be made to the Board of Trade. This
+provision has given rise to much complaint, as it gives the local
+authorities a long time for bargaining and enables them to supersede
+the company's application by themselves applying for provisional orders.
+The Board of Trade generally give preference to the applications of
+local authorities.
+
+In 1905 the Board of Trade issued a memorandum stating that, in view of
+the revocation of a large number of provisional orders which had been
+obtained by local authorities, or in regard to which local authorities
+had entered into agreements with companies for carrying the orders into
+effect (which agreements were in many cases _ultra vires_ or at least of
+doubtful validity), it appeared undesirable that a local authority
+should apply for a provisional order without having a definite intention
+of exercising the powers, and that in future the Board of Trade would
+not grant an order to a local authority unless the board were satisfied
+that the powers would be exercised within a specified period.
+
+Every undertaking authorized by provisional order is subject to the
+provision of the general act entitling the local authority to purchase
+compulsorily at the end of forty-two years (or shorter period), or after
+the expiration of every subsequent period of ten years (unless varied by
+agreement between the parties with the consent of the Board of Trade),
+so much of the undertaking as is within the jurisdiction of the
+purchasing authority upon the terms of paying the then value of all
+lands, buildings, works, materials and plant, suitable to and used for
+the purposes of the undertaking; provided that the value of such lands,
+&c., shall be deemed to be their fair market value at the time of
+purchase, due regard being had to the nature and then condition and
+state of repair thereof, and to the circumstance that they are in such
+positions as to be ready for immediate working, and to the suitability
+of the same to the purposes of the undertaking, and where a part only of
+the undertaking is purchased, to any loss occasioned by severance, but
+without any addition in respect of compulsory purchase or of goodwill,
+or of any profits which may or might have been or be made from the
+undertaking or any similar consideration. Subject to this right of
+purchase by the local authority, a provisional order (but not a licence)
+may be for such period as the Board of Trade may think proper, but so
+far no limit has been imposed, and unless purchased by a local authority
+the powers are held in perpetuity. No monopoly is granted to
+undertakers, and since 1889 the policy of the Board of Trade has been to
+sanction two undertakings in the same metropolitan area, preferably
+using different systems, but to discourage competing schemes within the
+same area in the provinces. Undertakers must within two years lay mains
+in certain specified streets. After the first eighteen months they may
+be required to lay mains in other streets upon conditions specified in
+the order, and any owner or occupier of premises within 50 yds. of a
+distributing main may require the undertakers to give a supply to his
+premises; but the consumer must pay the cost of the lines laid upon his
+property and of so much outside as exceeds 60 ft. from the main, and he
+must also contract for two and in some cases for three years' supply.
+But undertakers are prohibited in making agreements for supply from
+showing any undue preference. The maximum price in London is 13s. 4d.
+per quarter for any quantity up to 20 units, and beyond that 8d. per
+unit, but 11s. 8d. per quarter up to 20 units and 7d. per unit beyond is
+the more general maximum. The "Bermondsey clause" requires the
+undertakers (local authority) so to fix their charges (not exceeding the
+specified maximum) that the revenue shall not be less than the
+expenditure.
+
+There is no statutory obligation on municipalities to provide for
+depreciation of electricity supply undertakings, but after providing for
+all expenses, interest on loans, and sinking fund instalments, the local
+authority may create a reserve fund until it amounts, with interest, to
+one-tenth of the aggregate capital expenditure. Any deficiency when not
+met out of reserve is payable out of the local rates.
+
+The principle on which the Local Government Board sanctions municipal
+loans for electric lighting undertakings is that the period of the loan
+shall not exceed the life of the works, and that future ratepayers shall
+not be unduly burdened. The periods of the loans vary from ten years for
+accumulators and arc lamps to sixty years for lands. Within the county
+of London the loans raised by the metropolitan borough councils for
+electrical purposes are sanctioned by the London County Council, and
+that body allows a minimum period of twenty years for repayment. Up to
+1904-1905, 245 loans had been granted by the council amounting in the
+aggregate to L4,045,067.
+
+
+  Standardization.
+
+In 1901 the Institution of Civil Engineers appointed a committee to
+consider the advisability of standardizing various kinds of iron and
+steel sections. Subsequently the original reference was enlarged, and in
+1902 the Institution of Electrical Engineers was invited to co-operate.
+The treasury, as well as railway companies, manufacturers and others,
+have made grants to defray the expenses. The committee on electrical
+plant has ten sub-committees. In August 1904 an interim report was
+issued by the sub-committee on generators, motors and transformers,
+dealing with pressures and frequencies, rating of generators and motors,
+direct-current generators, alternating-current generators, and motors.
+
+In 1903 the specification for British standard tramway rails and
+fish-plates was issued, and in 1904 a standard specification for tubular
+tramway poles was issued. A sectional committee was formed in 1904 to
+correspond with foreign countries with regard to the formation of an
+electrical international commission to study the question of an
+international standardization of nomenclature and ratings of electrical
+apparatus and machinery.
+
+
+  The electrical industry.
+
+The electrical manufacturing branch, which is closely related to the
+electricity supply and other operating departments of the electrical
+industry, only dates from about 1880. Since that time it has undergone
+many vicissitudes. It began with the manufacture of small arc lighting
+equipments for railway stations, streets and public buildings. When the
+incandescent lamp became a commercial article, ship-lighting sets and
+installations for theatres and mansions constituted the major portion of
+the electrical work. The next step was the organization of
+house-to-house distribution of electricity from small "central
+stations," ultimately leading to the comprehensive public supply in
+large towns, which involved the manufacture of generating and
+distributing plants of considerable magnitude and complexity. With the
+advent of electric traction about 1896, special machinery had to be
+produced, and at a later stage the manufacturer had to solve problems in
+connexion with bulk supply in large areas and for power purposes. Each
+of these main departments involved changes in ancillary manufactures,
+such as cables, switches, transformers, meters, &c., so that the
+electrical manufacturing industry has been in a constant state of
+transition. At the beginning of the period referred to Germany and
+America were following the lead of England in theoretical developments,
+and for some time Germany obtained electrical machinery from England.
+Now scarcely any electrical apparatus is exported to Germany, and
+considerable imports are received by England from that country and
+America. The explanation is to be found mainly in the fact that the
+adverse legislation of 1882 had the effect of restricting enterprise,
+and while British manufacturers were compulsorily inert during periods
+of impeded growth of the two most important branches of the
+industry--electric lighting and traction--manufacturers in America and
+on the continent of Europe, who were in many ways encouraged by their
+governments, devoted their resources to the establishment of factories
+and electrical undertakings, and to the development of efficient selling
+organizations at home and abroad. When after the amendment of the
+adverse legislation in 1888 a demand for electrical machinery arose in
+England, the foreign manufacturers were fully organized for trade on a
+large scale, and were further aided by fiscal conditions to undersell
+English manufacturers, not only in neutral markets, but even in their
+own country. Successful manufacture on a large scale is possible only by
+standardizing the methods of production. English manufacturers were not
+able to standardize because they had not the necessary output. There had
+been no repetitive demand, and there was no production on a large scale.
+Foreign manufacturers, however, were able to standardize by reason of
+the large uniform demand which existed for their manufactures.
+Statistics are available showing the extent to which the growth of the
+electrical manufacturing industry in Great Britain was delayed. Nearly
+twenty years after the inception of the industry there were only
+twenty-four manufacturing companies registered in the United Kingdom,
+having an aggregate subscribed capital of under L7,000,000. But in 1907
+there were 292 companies with over L42,000,000 subscribed capital. The
+cable and incandescent lamp sections show that when the British
+manufacturers are allowed opportunities they are not slow to take
+advantage of them. The cable-making branch was established under the
+more encouraging conditions of the telegraph industry, and the lamp
+industry was in the early days protected by patents. Other departments
+not susceptible to foreign competition on account of freightage, such as
+the manufacture of storage batteries and rolling stock, are also fairly
+prosperous. In departments where special circumstances offer a prospect
+of success, the technical skill, commercial enterprise and general
+efficiency of British manufacturers manifest themselves by positive
+progress and not merely by the continuance of a struggle against adverse
+conditions. The normal posture of the British manufacturer of electrical
+machinery has been described as one of desperate defence of his home
+trade; that of the foreign manufacturer as one of vigorous attack upon
+British and other open markets. In considering the position of English
+manufacturers as compared with their foreign rivals, some regard should
+be had to the patent laws. One condition of a grant of a patent in most
+foreign countries is that the patent shall be worked in those countries
+within a specified period. But a foreign inventor was until 1907 able to
+secure patent protection in Great Britain without any obligation to
+manufacture there. The effect of this was to encourage the manufacture
+of patented apparatus in foreign countries, and to stimulate their
+exportation to Great Britain in competition with British products. With
+regard to the electrochemical industry the progress which has been
+achieved by other nations, notably Germany, is very marvellous by
+comparison with the advance made by England, but to state the reasons
+why this industry has had such extraordinary development in Germany,
+notwithstanding that many of the fundamental inventions were made in
+England, would require a statement of the marked differences in the
+methods by which industrial progress is promoted in the two countries.
+
+There has been very little solidarity among those interested in the
+commercial development of electricity, and except for the discussion of
+scientific subjects there has been very little organization with the
+object of protecting and promoting common interests. (E. GA.)
+
+
+FOOTNOTES:
+
+  [1] British Patent Specification, No. 5306 of 1878, and No. 602 of
+    1880.
+
+  [2] Ibid. No. 3988 of 1878.
+
+
+
+
+ELECTRIC WAVES. S 1. Clerk Maxwell proved that on his theory
+electromagnetic disturbances are propagated as a wave motion through the
+dielectric, while Lord Kelvin in 1853 (_Phil. Mag._ [4] 5, p. 393)
+proved from electromagnetic theory that the discharge of a condenser is
+oscillatory, a result which Feddersen (_Pogg. Ann._ 103, p. 69, &c.)
+verified by a beautiful series of experiments. The oscillating discharge
+of a condenser had been inferred by Henry as long ago as 1842 from his
+experiments on the magnetization produced in needles by the discharge of
+a condenser. From these two results it follows that electric waves must
+be passing through the dielectric surrounding a condenser in the act of
+discharging, but it was not until 1887 that the existence of such waves
+was demonstrated by direct experiment. This great step was made by Hertz
+(_Wied. Ann._ 34, pp. 155, 551, 609; _Ausbreitung der elektrischen
+Kraft_, Leipzig, 1892), whose experiments on this subject form one of
+the greatest contributions ever made to experimental physics. The
+difficulty which had stood in the way of the observations of these waves
+was the absence of any method of detecting electrical and magnetic
+forces, reversed some millions of times per second, and only lasting for
+an exceedingly short time. This was removed by Hertz, who showed that
+such forces would produce small sparks between pieces of metal very
+nearly in contact, and that these sparks were sufficiently regular to be
+used to detect electric waves and to investigate their properties. Other
+and more delicate methods have subsequently been discovered, but the
+results obtained by Hertz with his detector were of such signal
+importance, that we shall begin our account of experiments on these
+waves by a description of some of Hertz's more fundamental experiments.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+To produce the waves Hertz used two forms of vibrator. The first is
+represented in fig. 1. A and B are two zinc plates about 40 cm. square;
+to these brass rods, C, D, each about 30 cm. long, are soldered,
+terminating in brass balls E and F. To get good results it is necessary
+that these balls should be very brightly polished, and as they get
+roughened by the sparks which pass between them it is necessary to
+repolish them at short intervals; they should be shaded from light and
+from sparks, or other source of ultra-violet light. In order to excite
+the waves, C and D are connected to the two poles of an induction coil;
+sparks cross the air-gap which becomes a conductor, and the charges on
+the plates oscillate backwards and forwards like the charges on the
+coatings of a Leyden jar when it is short-circuited. The object of
+polishing the balls and screening off light is to get a sudden and sharp
+discharge; if the balls are rough there will be sharp points from which
+the charge will gradually leak, and the discharge will not be abrupt
+enough to start electrical vibrations, as these have an exceedingly
+short period. From the open form of this vibrator we should expect the
+radiation to be very large and the rate of decay of the amplitude very
+rapid. Bjerknes (_Wied. Ann._ 44, p. 74) found that the amplitude fell
+to 1/e of the original value, after a time 4T where T was the period of
+the electrical vibrations. Thus after a few vibrations the amplitude
+becomes inappreciable. To detect the waves produced by this vibrator
+Hertz used a piece of copper wire bent into a circle, the ends being
+furnished with two balls, or a ball and a point connected by a screw, so
+that the distance between them admitted of very fine adjustment. The
+radius of the circle for use with the vibrator just described was 35
+cm., and was so chosen that the free period of the detector might be the
+same as that of the vibrator, and the effects in it increased by
+resonance. It is evident, however, that with a primary system as greatly
+damped as the vibrator used by Hertz, we could not expect very marked
+resonance effects, and as a matter of fact the accurate timing of
+vibrator and detector in this case is not very important. With
+electrical vibrators which can maintain a large number of vibrations,
+resonance effects are very striking, as is beautifully shown by the
+following experiment due to Lodge (_Nature_, 41, p. 368), whose
+researches have greatly advanced our knowledge of electric waves. A and
+C (fig. 2) are two Leyden jars, whose inner and outer coatings are
+connected by wires, B and D, bent so as to include a considerable area.
+There is an air-break in the circuit connecting the inside and outside
+of one of the jars, A, and electrical oscillations are started in A by
+joining the inside and outside with the terminals of a coil or
+electrical machine. The circuit in the jar C is provided with a sliding
+piece, F, by means of which the self-induction of the discharging
+circuit, and, therefore, the time of an electrical oscillation of the
+jar, can be adjusted. The inside and outside of this jar are put almost,
+but not quite, into electrical contact by means of a piece of tin-foil,
+E, bent over the lip of the jar. The jars are placed face to face so
+that the circuits B and D are parallel to each other, and approximately
+at right angles to the line joining their centres. When the electrical
+machine is in action sparks pass across the air-break in the circuit in
+A, and by moving the slider F it is possible to find one position for it
+in which sparks pass from the inside to the outside of C across the
+tin-foil, while when the slider is moved a short distance on either side
+of this position the sparks cease.
+
+Hertz found that when he held his detector in the neighbourhood of the
+vibrator minute sparks passed between the balls. These sparks were not
+stopped when a large plate of non-conducting substance, such as the wall
+of a room, was interposed between the vibrator and detector, but a large
+plate of very thin metal stopped them completely.
+
+To illustrate the analogy between electric waves and waves of light
+Hertz found another form of apparatus more convenient. The vibrator
+consisted of two equal brass cylinders, 12 cm. long and 3 cm. in
+diameter, placed with their axes coincident, and in the focal line of a
+large zinc parabolic mirror about 2 m. high, with a focal length of 12.5
+cm. The ends of the cylinders nearest each other, between which the
+sparks passed, were carefully polished. The detector, which was placed
+in the focal line of an equal parabolic mirror, consisted of two lengths
+of wire, each having a straight piece about 50 cm. long and a curved
+piece about 15 cm. long bent round at right angles so as to pass through
+the back of the mirror. The ends which came through the mirror were
+connected with a spark micrometer, the sparks being observed from behind
+the mirror. The mirrors are shown, in fig. 3.
+
+[Illustration: FIG. 3.]
+
+S 2. _Reflection and Refraction._--To show the reflection of the waves
+Hertz placed the mirrors side by side, so that their openings looked in
+the same direction, and their axes converged at a point about 3 m. from
+the mirrors. No sparks were then observed in the detector when the
+vibrator was in action. When, however, a large zinc plate about 2 m.
+square was placed at right angles to the line bisecting the angle
+between the axes of the mirrors sparks became visible, but disappeared
+again when the metal plate was twisted through an angle of about 15 deg.
+to either side. This experiment showed that electric waves are
+reflected, and that, approximately at any rate, the angle of incidence
+is equal to the angle of reflection. To show refraction Hertz used a
+large prism made of hard pitch, about 1.5 m. high, with a slant side of
+1.2 m. and an angle of 30 deg. When the waves from the vibrator passed
+through this the sparks in the detector were not excited when the axes
+of the two mirrors were parallel, but appeared when the axis of the
+mirror containing the detector made a certain angle with the axis of
+that containing the vibrator. When the system was adjusted for minimum
+deviation the sparks were most vigorous when the angle between the axes
+of the mirrors was 22 deg. This corresponds to an index of refraction of
+1.69.
+
+S 3. _Analogy to a Plate of Tourmaline._--If a screen be made by winding
+wire round a large rectangular framework, so that the turns of the wire
+are parallel to one pair of sides of the frame, and if this screen be
+interposed between the parabolic mirrors when placed so as to face each
+other, there will be no sparks in the detector when the turns of the
+wire are parallel to the focal lines of the mirror; but if the frame is
+turned through a right angle so that the wires are perpendicular to the
+focal lines of the mirror the sparks will recommence. If the framework
+is substituted for the metal plate in the experiment on the reflection
+of electric waves, sparks will appear in the detector when the wires are
+parallel to the focal lines of the mirrors, and will disappear when the
+wires are at right angles to these lines. Thus the framework reflects
+but does not transmit the waves when the electric force in them is
+parallel to the wires, while it transmits but does not reflect waves in
+which the electric force is at right angles to the wires. The wire
+framework behaves towards the electric waves exactly as a plate of
+tourmaline does to waves of light. Du Bois and Rubens (_Wied. Ann._ 49,
+p. 593), by using a framework wound with very fine wire placed very
+close together, have succeeded in polarizing waves of radiant heat,
+whose wave length, although longer than that of ordinary light, is very
+small compared with that of electric waves.
+
+S 4. _Angle of Polarization._--When light polarized at right angles to
+the plane of incidence falls on a refracting substance at an angle
+tan^(-1)[mu], where [mu] is the refractive index of the substance, all
+the light is refracted and none reflected; whereas when light is
+polarized in the plane of incidence, some of the light is always
+reflected whatever the angle of incidence. Trouton (_Nature_, 39, p.
+391) showed that similar effects take place with electric waves. From a
+paraffin wall 3 ft. thick, reflection always took place when the
+electric force in the incident wave was at right angles to the plane of
+incidence, whereas at a certain angle of incidence there was no
+reflection when the vibrator was turned, so that the electric force was
+in the plane of incidence. This shows that on the electromagnetic theory
+of light the electric force is at right angles to the plane of
+polarization.
+
+[Illustration: FIG. 4.]
+
+S 5. _Stationary Electrical Vibrations._--Hertz (_Wied. Ann._ 34, p.
+609) made his experiments on these in a large room about 15 m. long. The
+vibrator, which was of the type first described, was placed at one end
+of the room, its plates being parallel to the wall, at the other end a
+piece of sheet zinc about 4 m. by 2 m. was placed vertically against the
+wall. The detector--the circular ring previously described--was held so
+that its plane was parallel to the metal plates of the vibrator, its
+centre on the line at right angles to the metal plate bisecting at right
+angles the spark gap of the vibrator, and with the spark gap of the
+detector parallel to that of the vibrator. The following effects were
+observed when the detector was moved about. When it was close up to the
+zinc plate there were no sparks, but they began to pass feebly as soon
+as it was moved forward a little way from the plate, and increased
+rapidly in brightness until it was about 1.8 m. from the plate, when
+they attained their maximum. When its distance was still further
+increased they diminished in brightness, and vanished again at a
+distance of about 4 m. from the plate. When the distance was still
+further increased they reappeared, attained another maximum, and so on.
+They thus exhibited a remarkable periodicity similar to that which
+occurs when stationary vibrations are produced by the interference of
+direct waves with those reflected from a surface placed at right angles
+to the direction of propagation. Similar periodic alterations in the
+spark were observed by Hertz when the waves, instead of passing freely
+through the air and being reflected by a metal plate at the end of the
+room, were led along wires, as in the arrangement shown in fig. 4. L and
+K are metal plates placed parallel to the plates of the vibrator, long
+parallel wires being attached to act as guides to the waves which were
+reflected from the isolated end. (Hertz used only one plate and one
+wire, but the double set of plates and wires introduced by Sarasin and
+De la Rive make the results more definite.) In this case the detector is
+best placed so that its plane is at right angles to the wires, while the
+air space is parallel to the plane containing the wires. The sparks
+instead of vanishing when the detector is at the far end of the wire are
+a maximum in this position, but wax and wane periodically as the
+detector is moved along the wires. The most obvious interpretation of
+these experiments was the one given by Hertz--that there was
+interference between the direct waves given out by the vibrator and
+those reflected either from the plate or from the ends of the wire, this
+interference giving rise to stationary waves. The places where the
+electric force was a maximum were the places where the sparks were
+brightest, and the places where the electric force was zero were the
+places where the sparks vanished. On this explanation the distance
+between two consecutive places where the sparks vanished would be half
+the wave length of the waves given out by the vibrator.
+
+Some very interesting experiments made by Sarasin and De la Rive
+(_Comptes rendus_, 115, p. 489) showed that this explanation could not
+be the true one, since by using detectors of different sizes they found
+that the distance between two consecutive places where the sparks
+vanished depended mainly upon the size of the detector, and very little
+upon that of the vibrator. With small detectors they found the distance
+small, with large detectors, large; in fact it is directly proportional
+to the diameter of the detector. We can see that this result is a
+consequence of the large damping of the oscillations of the vibrator and
+the very small damping of those of the detector. Bjerknes showed that
+the time taken for the amplitude of the vibrations of the vibrator to
+sink to 1/e of their original value was only 4T, while for the detector
+it was 500T', when T and T' are respectively the times of vibration of
+the vibrator and the detector. The rapid decay of the oscillations of
+the vibrator will stifle the interference between the direct and the
+reflected wave, as the amplitude of the direct wave will, since it is
+emitted later, be much smaller than that of the reflected one, and not
+able to annul its effects completely; while the well-maintained
+vibrations of the detector will interfere and produce the effects
+observed by Sarasin and De la Rive. To see this let us consider the
+extreme case in which the oscillations of the vibrator are absolutely
+dead-beat. Here an impulse, starting from the vibrator on its way to the
+reflector, strikes against the detector and sets it in vibration; it
+then travels up to the plate and is reflected, the electric force in the
+impulse being reversed by reflection. After reflection the impulse again
+strikes the detector, which is still vibrating from the effects of the
+first impact; if the phase of this vibration is such that the reflected
+impulse tends to produce a current round the detector in the same
+direction as that which is circulating from the effects of the first
+impact, the sparks will be increased, but if the reflected impulse tends
+to produce a current in the opposite direction the sparks will be
+diminished. Since the electric force is reversed by reflection, the
+greatest increase in the sparks will take place when the impulse finds,
+on its return, the detector in the opposite phase to that in which it
+left it; that is, if the time which has elapsed between the departure
+and return of the impulse is equal to an odd multiple of half the time
+of vibration of the detector. If d is the distance of the detector from
+the reflector when the sparks are brightest, and V the velocity of
+propagation of electromagnetic disturbance, then 2d/V = (2n + 1)(T'/2);
+where n is an integer and T' the time of vibration of the detector, the
+distance between two spark maxima will be VT'/2, and the places where
+the sparks are a minimum will be midway between the maxima. Sarasin and
+De la Rive found that when the same detector was used the distance
+between two spark maxima was the same with the waves through air
+reflected from a metal plate and with those guided by wires and
+reflected from the free ends of the wire, the inference being that the
+velocity of waves along wires is the same as that through the air. This
+result, which follows from Maxwell's theory, when the wires are not too
+fine, had been questioned by Hertz on account of some of his
+experiments on wires.
+
+S 6. _Detectors._--The use of a detector with a period of vibration of
+its own thus tends to make the experiments more complicated, and many
+other forms of detector have been employed by subsequent experimenters.
+For example, in place of the sparks in air the luminous discharge
+through a rarefied gas has been used by Dragoumis, Lecher (who used
+tubes without electrodes laid across the wires in an arrangement
+resembling that shown in fig. 7) and Arons. A tube containing neon at a
+low pressure is especially suitable for this purpose. Zehnder (_Wied.
+Ann._ 47, p. 777) used an exhausted tube to which an external
+electromotive force almost but not quite sufficient of itself to produce
+a discharge was applied; here the additional electromotive force due to
+the waves was sufficient to start the discharge. Detectors depending on
+the heat produced by the rapidly alternating currents have been used by
+Paalzow and Rubens, Rubens and Ritter, and I. Klemencic. Rubens measured
+the heat produced by a bolometer arrangement, and Klemencic used a
+thermo-electric method for the same purpose; in consequence of the great
+increase in the sensitiveness of galvanometers these methods are now
+very frequently resorted to. Boltzmann used an electroscope as a
+detector. The spark gap consisted of a ball and a point, the ball being
+connected with the electroscope and the point with a battery of 200 dry
+cells. When the spark passed the cells charged up the electroscope.
+Ritter utilized the contraction of a frog's leg as a detector, Lucas and
+Garrett the explosion produced by the sparks in an explosive mixture of
+hydrogen and oxygen; while Bjerknes and Franke used the mechanical
+attraction between oppositely charged conductors. If the two sides of
+the spark gap are connected with the two pairs of quadrants of a very
+delicate electrometer, the needle of which is connected with one pair of
+quadrants, there will be a deflection of the electrometer when the
+detector is struck by electric waves. A very efficient detector is that
+invented by E. Rutherford (_Trans. Roy. Soc._ A. 1897, 189, p. 1); it
+consists of a bundle of fine iron wires magnetized to saturation and
+placed inside a small magnetizing coil, through which the electric waves
+cause rapidly alternating currents to pass which demagnetize the soft
+iron. If the instrument is used to detect waves in air, long straight
+wires are attached to the ends of the demagnetizing coil to collect the
+energy from the field; to investigate waves in wires it is sufficient to
+make a loop or two in the wire and place the magnetized piece of iron
+inside it. The amount of demagnetization which can be observed by the
+change in the deflection of a magnetometer placed near the iron,
+measures the intensity of the electric waves, and very accurate
+determinations can be made with ease with this apparatus. It is also
+very delicate, though in this respect it does not equal the detector to
+be next described, the coherer; Rutherford got indications in 1895 when
+the vibrator was 3/4 of a mile away from the detector, and where the
+waves had to traverse a thickly populated part of Cambridge. It can also
+be used to measure the coefficient of damping of the electric waves, for
+since the wire is initially magnetized to saturation, if the direction
+of the current when it first begins to flow in the magnetizing coil is
+such as to tend to increase the magnetization of the wire, it will
+produce no effect, and it will not be until the current is reversed that
+the wire will lose some of its magnetization. The effect then gives the
+measure of the intensity half a period after the commencement of the
+waves. If the wire is put in the coil the opposite way, i.e. so that the
+magnetic force due to the current begins at once to demagnetize the
+wire, the demagnetization gives a measure of the initial intensity of
+the waves. Comparing this result with that obtained when the wires were
+reversed, we get the coefficient of damping. A very convenient detector
+of electric waves is the one discovered almost simultaneously by
+Fessenden (_Electrotech. Zeits._, 1903, 24, p. 586) and Schlomilch
+(_ibid._ p. 959). This consists of an electrolytic cell in which one of
+the electrodes is an exceedingly fine point. The electromotive force in
+the circuit is small, and there is large polarization in the circuit
+with only a small current. When the circuit is struck by electric waves
+there is an increase in the currents due to the depolarization of the
+circuit. If a galvanometer is in the circuit, the increased deflection
+of the instrument will indicate the presence of the waves.
+
+S 7. _Coherers._--The most sensitive detector of electric waves is the
+"coherer," although for metrical work it is not so suitable as that just
+described. It depends upon the fact discovered by Branly (_Comptes
+rendus_, 111, p. 785; 112, p. 90) that the resistance between loose
+metallic contacts, such as a pile of iron turnings, diminishes when they
+are struck by an electric wave. One of the forms made by Lodge (_The
+Work of Hertz and some of his Successors_, 1894) on this principle
+consists simply of a glass tube containing iron turnings, in contact
+with which are wires led into opposite ends of the tube. The arrangement
+is placed in series with a galvanometer (one of the simplest kind will
+do) and a battery; when the iron turnings are struck by electric waves
+their resistance is diminished and the deflection of the galvanometer is
+increased. Thus the deflection of the galvanometer can be used to
+indicate the arrival of electric waves. The tube must be tapped between
+each experiment, and the deflection of the galvanometer brought back to
+about its original value. This detector is marvellously delicate, but
+not metrical, the change produced in the resistance depending upon so
+many things besides the intensity of the waves that the magnitude of the
+galvanometer deflection is to some extent a matter of chance. Instead of
+the iron turnings we may use two iron wires, one resting on the other;
+the resistance of this contact will be altered by the incidence of the
+waves. To get greater regularity Bose uses, instead of the iron
+turnings, spiral springs, which are pushed against each other by means
+of a screw until the most sensitive state is attained. The sensitiveness
+of the coherer depends on the electromotive force put in the
+galvanometer circuit. Very sensitive ones can be made by using springs
+of very fine silver wire coated electrolytically with nickel. Though the
+impact of electric waves generally produces a diminution of resistance
+with these loose contacts, yet there are exceptions to the rule. Thus
+Branly showed that with lead peroxide, PbO2, there is an increase in
+resistance. Aschkinass proved the same to be true with copper sulphide,
+CuS; and Bose showed that with potassium there is an increase of
+resistance and great power of self-recovery of the original resistance
+after the waves have ceased. Several theories of this action have been
+proposed. Branly (_Lumiere electrique_, 40, p. 511) thought that the
+small sparks which certainly pass between adjacent portions of metal
+clear away layers of oxide or some other kind of non-conducting film,
+and in this way improve the contact. It would seem that if this theory
+is true the films must be of a much more refined kind than layers of
+oxide or dirt, for the coherer effect has been observed with clean
+non-oxidizable metals. Lodge explains the effect by supposing that the
+heat produced by the sparks fuses adjacent portions of metal into
+contact and hence diminishes the resistance; it is from this view of the
+action that the name coherer is applied to the detector. Auerbeck
+thought that the effect was a mechanical one due to the electrostatic
+attractions between the various small pieces of metal. It is probable
+that some or all of these causes are at work in some cases, but the
+effects of potassium make us hesitate to accept any of them as the
+complete explanation. Blanc (_Ann. chim. phys._, 1905, [8] 6, p. 5), as
+the result of a long series of experiments, came to the conclusion that
+coherence is due to pressure. He regarded the outer layers as different
+from the mass of the metal and having a much greater specific
+resistance. He supposed that when two pieces of metal are pressed
+together the molecules diffuse across the surface, modifying the surface
+layers and increasing their conductivity.
+
+  S 8. _Generators of Electric Waves._--Bose (_Phil. Mag._ 43, p. 55)
+  designed an instrument which generates electric waves with a length of
+  not more than a centimetre or so, and therefore allows their
+  properties to be demonstrated with apparatus of moderate dimensions.
+  The waves are excited by sparking between two platinum beads carried
+  by jointed electrodes; a platinum sphere is placed between the beads,
+  and the distance between the beads and the sphere can be adjusted by
+  bending the electrodes. The diameter of the sphere is 8 mm., and the
+  wave length of the shortest electrical waves generated is said to be
+  about 6 mm. The beads are connected with the terminals of a small
+  induction coil, which, with the battery to work it and the sparking
+  arrangement, are enclosed in a metal box, the radiation passing out
+  through a metal tube opposite to the spark gap. The ordinary vibrating
+  break of the coil is not used, a single spark made by making and
+  breaking the circuit by means of a button outside the box being
+  employed instead. The detector is one of the spiral spring coherers
+  previously described; it is shielded from external disturbance by
+  being enclosed in a metal box provided with a funnel-shaped opening to
+  admit the radiation. The wires leading from the coherers to the
+  galvanometer are also surrounded by metal tubes to protect them from
+  stray radiation. The radiating apparatus and the receiver are mounted
+  on stands sliding in an optical bench. If a parallel beam of radiation
+  is required, a cylindrical lens of ebonite or sulphur is mounted in a
+  tube fitting on to the radiator tube and stopped by a guide when the
+  spark is at the principal focal line of the lens. For experiments
+  requiring angular measurements a spectrometer circle is mounted on one
+  of the sliding stands, the receiver being carried on a radial arm and
+  pointing to the centre of the circle. The arrangement is represented
+  in fig. 5.
+
+  [Illustration: FIG. 5.]
+
+  With this apparatus the laws of reflection, refraction and
+  polarization can readily be verified, and also the double refraction
+  of crystals, and of bodies possessing a fibrous or laminated structure
+  such as jute or books. (The double refraction of electric waves seems
+  first to have been observed by Righi, and other researches on this
+  subject have been made by Garbasso and Mack.) Bose showed the rotation
+  of the plane of polarization by means of pieces of twisted jute rope;
+  if the pieces were arranged so that their twists were all in one
+  direction and placed in the path of the radiation, they rotated the
+  plane of polarization in a direction depending upon the direction of
+  twist; if they were mixed so that there were as many twisted in one
+  direction as the other, there was no rotation.
+
+  [Illustration: FIG. 6.]
+
+  A series of experiments showing the complete analogy between electric
+  and light waves is described by Righi in his book _L'Ottica delle
+  oscillazioni elettriche_. Righi's exciter, which is especially
+  convenient when large statical electric machines are used instead of
+  induction coils, is shown in fig. 6. E and F are balls connected with
+  the terminals of the machine, and AB and CD are conductors insulated
+  from each other, the ends B, C, between which the sparks pass, being
+  immersed in vaseline oil. The period of the vibrations given out by
+  the system is adjusted by means of metal plates M and N attached to AB
+  and CD. When the waves are produced by induction coils or by
+  electrical machines the intervals between the emission of different
+  sets of waves occupy by far the largest part of the time. Simon
+  (_Wied. Ann._, 1898, 64, p. 293; _Phys. Zeit._, 1901, 2, p. 253),
+  Duddell (_Electrician_, 1900, 46, p. 269) and Poulsen (_Electrotech.
+  Zeits._, 1906, 27, p. 1070) reduced these intervals very considerably
+  by using the electric arc to excite the waves, and in this way
+  produced electrical waves possessing great energy. In these methods
+  the terminals between which the arc is passing are connected through
+  coils with self-induction L to the plates of a condenser of capacity
+  C. The arc is not steady, but is continually varying. This is
+  especially the case when it passes through hydrogen. These variations
+  excite vibrations with a period 2[pi][root](LC) in the circuit
+  containing the capacity of the self-induction. By this method Duddell
+  produced waves with a frequency of 40,000. Poulsen, who cooled the
+  terminals of the arc, produced waves with a frequency of 1,000,000,
+  while Stechodro (_Ann. der Phys._ 27, p. 225) claims to have produced
+  waves with three hundred times this frequency, i.e. having a wave
+  length of about a metre. When the self-induction and capacity are
+  large so that the frequency comes within the limits of the frequency
+  of audible notes, the system gives out a musical note, and the
+  arrangement is often referred to as the singing arc.
+
+  [Illustration: FIG. 7.]
+
+  [Illustration: FIG. 8.]
+
+  S _9. Waves in Wires._--Many problems on electric waves along wires
+  can readily be investigated by a method due to Lecher (_Wied. Ann._
+  41, p. 850), and known as Lecher's bridge, which furnishes us with a
+  means of dealing with waves of a definite and determinable
+  wave-length. In this arrangement (fig. 7) two large plates A and B
+  are, as in Hertz's exciter, connected with the terminals of an
+  induction coil; opposite these and insulated from them are two smaller
+  plates D, E, to which long parallel wires DFH, EGJ are attached. These
+  wires are bridged across by a wire LM, and their farther ends H, J,
+  may be insulated, or connected together, or with the plates of a
+  condenser. To detect the waves in the circuit beyond the bridge,
+  Lecher used an exhausted tube placed across the wires, and Rubens a
+  bolometer, but Rutherford's detector is the most convenient and
+  accurate. If this detector is placed in a fixed position at the end of
+  the circuit, it is found that the deflections of this detector depend
+  greatly upon the position of the bridge LM, rising rapidly to a
+  maximum for some positions, and falling rapidly away when the bridge
+  is displaced. As the bridge is moved from the coil end towards the
+  detector the deflections show periodic variations, such as are
+  represented in fig. 8 when the ordinates represent the deflections of
+  the detector and the abscissae the distance of the bridge from the
+  ends D, E. The maximum deflections of the detector correspond to the
+  positions in which the two circuits DFLMGE, HLMJ (in which the
+  vibrations are but slightly damped) are in resonance. For since the
+  self-induction and resistance of the bridge LM is very small compared
+  with that of the circuit beyond, it follows from the theory of
+  circuits in parallel that only a small part of the current will in
+  general flow round the longer circuit; it is only when the two
+  circuits DFLMGE, HLMJ are in resonance that a considerable current
+  will flow round the latter. Hence when we get a maximum effect in the
+  detector we know that the waves we are dealing with are those
+  corresponding to the free periods of the system HLMJ, so that if we
+  know the free periods of this circuit we know the wave length of the
+  electric waves under consideration. Thus if the ends of the wires H, J
+  are free and have no capacity, the current along them must vanish at H
+  and J, which must be in opposite electric condition. Hence half the
+  wave length must be an odd submultiple of the length of the circuit
+  HLMJ. If H and J are connected together the wave length must be a
+  submultiple of the length of this circuit. When the capacity at the
+  ends is appreciable the wave length of the circuit is determined by a
+  somewhat complex expression. To facilitate the determination of the
+  wave length in such cases, Lecher introduced a second bridge L'M', and
+  moved this about until the deflection of the detector was a maximum;
+  when this occurs the wave length is one of those corresponding to the
+  closed circuit LMM'L', and must therefore be a submultiple of the
+  length of the circuit. Lecher showed that if instead of using a single
+  wire LM to form the bridge, he used two parallel wires PQ, LM, placed
+  close together, the currents in the further circuit were hardly
+  appreciably diminished when the main wires were cut between PL and QM.
+  Blondlot used a modification of this apparatus better suited for the
+  production of short waves. In his form (fig. 9) the exciter consists
+  of two semicircular arms connected with the terminals of an induction
+  coil, and the long wires, instead of being connected with the small
+  plates, form a circuit round the exciter.
+
+  As an example of the use of Lecher's arrangement, we may quote Drude's
+  application of the method to find the specific induction capacity of
+  dielectrics under electric oscillations of varying frequency. In this
+  application the ends of the wire are connected to the plates of a
+  condenser, the space between whose plates can be filled with the
+  liquid whose specific inductive capacity is required, and the bridge
+  is moved until the detector at the end of the circuit gives the
+  maximum deflection. Then if [lambda] is the wave length of the waves,
+  [lambda] is the wave length of one of the free vibrations of the
+  system HLMJ; hence if C is the capacity of the condenser at the end in
+  electrostatic measure we have
+
+         2[pi]l
+    cot --------
+        [lambda]    C
+    ------------ = ---
+       2[pi]l      C'l
+      --------
+      [lambda]
+
+  where l is the distance of the condenser from the bridge and C' is the
+  capacity of unit length of the wire. In the condenser part of the
+  lines of force will pass through air and part through the dielectric;
+  hence C will be of the form C0+KC1 where K is the specific inductive
+  capacity of the dielectric. Hence if l is the distance of maximum
+  deflection when the dielectric is replaced by air, l' when filled with
+  a dielectric whose specific inductive capacity is known to be K', and
+  l" the distance when filled with the dielectric whose specific
+  inductive capacity is required, we easily see that--
+
+         2[pi]l        2[pi]l'
+    cot -------- - cot --------
+        [lambda]       [lambda]   1 - K'
+    --------------------------- = ------
+         2[pi]l        2[pi]l"    1 - K
+    cot -------- - cot --------
+        [lambda]       [lambda]
+
+  an equation by means of which K can be determined. It was in this way
+  that Drude investigated the specific inductive capacity with varying
+  frequency, and found a falling off in the specific inductive capacity
+  with increase of frequency when the dielectrics contained the radicle
+  OH. In another method used by him the wires were led through long
+  tanks filled with the liquid whose specific inductive capacity was
+  required; the velocity of propagation of the electric waves along the
+  wires in the tank being the same as the velocity of propagation of an
+  electromagnetic disturbance through the liquid filling the tank, if we
+  find the wave length of the waves along the wires in the tank, due to
+  a vibration of a given frequency, and compare this with the wave
+  lengths corresponding to the same frequency when the wires are
+  surrounded by air, we obtain the velocity of propagation of
+  electromagnetic disturbance through the fluid, and hence the specific
+  inductive capacity of the fluid.
+
+  [Illustration: FIG. 9.]
+
+  S 10. _Velocity of Propagation of Electromagnetic Effects through
+  Air._--The experiments of Sarasin and De la Rive already described
+  (see S 5) have shown that, as theory requires, the velocity of
+  propagation of electric effects through air is the same as along
+  wires. The same result had been arrived at by J.J. Thomson, although
+  from the method he used greater differences between the velocities
+  might have escaped detection than was possible by Sarasin and De la
+  Rive's method. The velocity of waves along wires has been directly
+  determined by Blondlot by two different methods. In the first the
+  detector consisted of two parallel plates about 6 cm. in diameter
+  placed a fraction of a millimetre apart, and forming a condenser whose
+  capacity C was determined in electromagnetic measure by Maxwell's
+  method. The plates were connected by a rectangular circuit whose
+  self-induction L was calculated from the dimensions of the rectangle
+  and the size of the wire. The time of vibration T is equal to
+  2[pi][root](LC). (The wave length corresponding to this time is long
+  compared with the length of the circuit, so that the use of this
+  formula is legitimate.) This detector is placed between two parallel
+  wires, and the waves produced by the exciter are reflected from a
+  movable bridge. When this bridge is placed just beyond the detector
+  vigorous sparks are observed, but as the bridge is pushed away a place
+  is reached where the sparks disappear; this place is distance
+  2/[lambda] from the detector, when [lambda] is the wave length of the
+  vibration given out by the detector. The sparks again disappear when
+  the distance of the bridge from the detector is 3[lambda]/4. Thus by
+  measuring the distance between two consecutive positions of the bridge
+  at which the sparks disappear [lambda] can be determined, and v, the
+  velocity of propagation, is equal to [lambda]/T. As the means of a
+  number of experiments Blondlot found v to be 3.02 X 10^10 cm./sec.,
+  which, within the errors of experiment, is equal to 3 X 10^10
+  cm./sec., the velocity of light. A second method used by Blondlot, and
+  one which does not involve the calculation of the period, is as
+  follows:--A and A' (fig. 10) are two equal Leyden jars coated inside
+  and outside with tin-foil. The outer coatings form two separate rings
+  a, a1; a', a'1, and the inner coatings are connected with the poles of
+  the induction coil by means of the metal pieces b, b'. The sharply
+  pointed conductors p and p', the points of which are about 1/2 mm.
+  apart, are connected with the rings of the tin-foil a and a', and two
+  long copper wires pca1, p'c'a'1, 1029 cm. long, connect these points
+  with the other rings a1, a1'. The rings aa', a1a1', are connected by
+  wet strings so as to charge up the jars. When a spark passes between b
+  and b', a spark at once passes between pp', and this is followed by
+  another spark when the waves travelling by the paths a1cp, a'1c'p'
+  reach p and p'. The time between the passage of these sparks, which is
+  the time taken by the waves to travel 1029 cm., was observed by means
+  of a rotating mirror, and the velocity measured in 15 experiments
+  varied between 2.92 X 10^10 and 3.03 X 10^10 cm./sec., thus agreeing
+  well with that deduced by the preceding method. Other determinations
+  of the velocity of electromagnetic propagation have been made by Lodge
+  and Glazebrook, and by Saunders.
+
+  [Illustration: FIG. 10.]
+
+  On Maxwell's electromagnetic theory the velocity of propagation of
+  electromagnetic disturbances should equal the velocity of light, and
+  also the ratio of the electromagnetic unit of electricity to the
+  electrostatic unit. A large number of determinations of this ratio
+  have been made:--
+
+        Observer.            Date.   Ratio 10^10 X.
+    Klemencic                1884    3.019 cm./sec.
+    Himstedt                 1888    3.009 cm./sec.
+    Rowland                  1889    2.9815 cm./sec.
+    Rosa                     1889    2.9993 cm./sec.
+    J.J. Thomson and Searle  1890    2.9955 cm./sec.
+    Webster                  1891    2.987 cm./sec.
+    Pellat                   1891    3.009 cm./sec.
+    Abraham                  1892    2.992 cm./sec.
+    Hurmuzescu               1895    3.002 cm./sec.
+    Rosa                     1908    2.9963 cm./sec.
+
+  The mean of these determinations is 3.001 X 10^10 cm./sec., while the
+  mean of the last five determinations of the velocity of light in air
+  is given by Himstedt as 3.002 X 10^10 cm./sec. From these experiments
+  we conclude that the velocity of propagation of an electromagnetic
+  disturbance is equal to the velocity of light, and to the velocity
+  required by Maxwell's theory.
+
+  In experimenting with electromagnetic waves it is in general more
+  difficult to measure the period of the oscillations than their wave
+  length. Rutherford used a method by which the period of the vibration
+  can easily be determined; it is based upon the theory of the
+  distribution of alternating currents in two circuits ACB, ADB in
+  parallel. If A and B are respectively the maximum currents in the
+  circuits ACB, ADB, then
+
+    A           / S^2 + (N - M)^2p^2 \
+    -- = [root](  ------------------  )
+    B           \ R^2 + (L - M)^2p^2 /
+
+  when R and S are the resistances, L and N the coefficients of
+  self-induction of the circuits ACB, ADB respectively, M the
+  coefficient of mutual induction between the circuits, and p the
+  frequency of the currents. Rutherford detectors were placed in the two
+  circuits, and the circuits adjusted until they showed that A = B; when
+  this is the case
+
+                R^2 - S^2
+    p^2 = ---------------------.
+          N^2 - L^2 - 2M(N - L)
+
+  If we make one of the circuits, ADB, consist of a short length of a
+  high liquid resistance, so that S is large and N small, and the
+  other circuit ACB of a low metallic resistance bent to have
+  considerable self-induction, the preceding equation becomes
+  approximately p = S/L, so that when S and L are known p is readily
+  determined.     (J. J. T.)
+
+
+
+
+ELECTROCHEMISTRY. The present article deals with processes that involve
+the electrolysis of aqueous solutions, whilst those in which electricity
+is used in the manufacture of chemical products at furnace temperatures
+are treated under ELECTROMETALLURGY, although, strictly speaking, in
+some cases (e.g. calcium carbide and phosphorus manufacture) they are
+not truly metallurgical in character. For the theory and elemental laws
+of electro-deposition see ELECTROLYSIS; and for the construction and use
+of electric generators see DYNAMO and BATTERY: _Electric_. The
+importance of the subject may be gauged by the fact that all the
+aluminium, magnesium, sodium, potassium, calcium carbide, carborundum
+and artificial graphite, now placed on the market, is made by electrical
+processes, and that the use of such processes for the refining of copper
+and silver, and in the manufacture of phosphorus, potassium chlorate and
+bleach, already pressing very heavily on the older non-electrical
+systems, is every year extending. The convenience also with which the
+energy of waterfalls can be converted into electric energy has led to
+the introduction of chemical industries into countries and districts
+where, owing to the absence of coal, they were previously unknown.
+Norway and Switzerland have become important producers of chemicals, and
+pastoral districts such as those in which Niagara or Foyers are situated
+manufacturing centres. In this way the development of the
+electrochemical industry is in a marked degree altering the distribution
+of trade throughout the world.
+
+_Electrolytic Refining of Metals._--The principle usually followed in
+the electrolytic refining of metals is to cast the impure metal into
+plates, which are exposed as anodes in a suitable solvent, commonly a
+salt of the metal under treatment. On passing a current of electricity,
+of which the volume and pressure are adjusted to the conditions of the
+electrolyte and electrodes, the anode slowly dissolves, leaving the
+insoluble impurities in the form of a sponge, if the proportion be
+considerable, but otherwise as a mud or slime which becomes detached
+from the anode surface and must be prevented from coming into contact
+with the cathode. The metal to be refined passing into solution is
+concurrently deposited at the cathode. Soluble impurities which are more
+electro-negative than the metal under treatment must, if present, be
+removed by a preliminary process, and the voltage and other conditions
+must be so selected that none of the more electro-positive metals are
+co-deposited with the metal to be refined. From these and other
+considerations it is obvious that (1) the electrolyte must be such as
+will freely dissolve the metal to be refined; (2) the electrolyte must
+be able to dissolve the major portion of the anode, otherwise the mass
+of insoluble matter on the outer layer will prevent access of
+electrolyte to the core, which will thus escape refining; (3) the
+electrolyte should, if possible, be incapable of dissolving metals more
+electro-negative than that to be refined; (4) the proportion of soluble
+electro-positive impurities must not be excessive, or these substances
+will accumulate too rapidly in the solution and necessitate its frequent
+purification; (5) the current density must be so adjusted to the
+strength of the solution and to other conditions that no relatively
+electro-positive metal is deposited, and that the cathode deposit is
+physically suitable for subsequent treatment; (6) the current density
+should be as high as is consistent with the production of a pure and
+sound deposit, without undue expense of voltage, so that the operation
+may be rapid and the "turnover" large; (7) the electrolyte should be as
+good a conductor of electricity as possible, and should not, ordinarily,
+be altered chemically by exposure to air; and (8) the use of porous
+partitions should be avoided, as they increase the resistance and
+usually require frequent renewal. For details of the practical methods
+see GOLD; SILVER; COPPER and headings for other metals.
+
+_Electrolytic Manufacture of Chemical Products._--When an aqueous
+solution of the salt of an alkali metal is electrolysed, the metal
+reacts with the water, as is well known, forming caustic alkali, which
+dissolves in the solution, and hydrogen, which comes off as a gas. So
+early as 1851 a patent was taken out by Cooke for the production of
+caustic alkali without the use of a separate current, by immersing iron
+and copper plates on opposite sides of a porous (biscuit-ware) partition
+in a suitable cell, containing a solution of the salt to be
+electrolysed, at 21 deg.-65 deg. C. (70 deg.-150 deg. F.). The solution
+of the iron anode was intended to afford the necessary energy. In the
+same year another patent was granted to C. Watt for a similar process,
+involving the employment of an externally generated current. When an
+alkaline chloride, say sodium chloride, is electrolysed with one
+electrode immersed in a porous cell, while caustic soda is formed at the
+cathode, chlorine is deposited at the anode. If the latter be insoluble,
+the gas diffuses into the solution and, when this becomes saturated,
+escapes into the air. If, however, no porous division be used to prevent
+the intermingling by diffusion of the anode and cathode solutions, a
+complicated set of subsidiary reactions takes place. The chlorine reacts
+with the caustic soda, forming sodium hypochlorite, and this in turn,
+with an excess of chlorine and at higher temperatures, becomes for the
+most part converted into chlorate, whilst any simultaneous electrolysis
+of a hydroxide or water and a chloride (so that hydroxyl and chlorine
+are simultaneously liberated at the anode) also produces oxygen-chlorine
+compounds direct. At the same time, the diffusion of these compounds
+into contact with the cathode leads to a partial reduction to chloride,
+by the removal of combined oxygen by the instrumentality of the hydrogen
+there evolved. In proportion as the original chloride is thus
+reproduced, the efficiency of the process is of course diminished. It is
+obvious that, with suitable methods and apparatus, the electrolysis of
+alkaline chlorides may be made to yield chlorine, hypochlorites
+(bleaching liquors), chlorates or caustic alkali, but that great care
+must be exercised if any of these products is to be obtained pure and
+with economy. Many patents have been taken out in this branch of
+electrochemistry, but it is to be remarked that that granted to C. Watt
+traversed the whole of the ground. In his process a current was passed
+through a tank divided into two or three cells by porous partitions,
+hoods and tubes were arranged to carry off chlorine and hydrogen
+respectively, and the whole was heated to 120 deg. F. by a steam jacket
+when caustic alkali was being made. Hypochlorites were made, at ordinary
+temperatures, and chlorates at higher temperatures, in a cell without a
+partition in which the cathode was placed horizontally immediately above
+the anode, to favour the mixing of the ascending chlorine with the
+descending caustic solution.
+
+  The relation between the composition of the electrolyte and the
+  various conditions of current-density, temperature and the like has
+  been studied by F. Oettel (_Zeitschrift f. Elektrochem._, 1894, vol.
+  i. pp. 354 and 474) in connexion with the production of hypochlorites
+  and chlorates in tanks without diaphragms, by C. Haussermann and W.
+  Naschold (_Chemiker Zeitung_, 1894, vol. xviii. p. 857) for their
+  production in cells with porous diaphragms, and by F. Haber and S.
+  Grinberg (_Zeitschrift f. anorgan. Chem._, 1898, vol. xvi. pp. 198,
+  329, 438) in connexion with the electrolysis of hydrochloric acid.
+  Oettel, using a 20% solution of potassium chloride, obtained the best
+  yield of hypochlorite with a high current-density, but as soon as
+  1-1/4% of bleaching chlorine (as hypochlorite) was present, the
+  formation of chlorate commenced. The yield was at best very low as
+  compared with that theoretically possible. The best yield of chlorate
+  was obtained when from 1 to 4% of caustic potash was present. With
+  high current-density, heating the solution tended to increase the
+  proportion of chlorate to hypochlorite, but as the proportion of water
+  decomposed is then higher, the amount of chlorine produced must be
+  less and the total chlorine efficiency lower. He also traced a
+  connexion between alkalinity, temperature and current-density, and
+  showed that these conditions should be mutually adjusted. With a
+  current-density of 130 to 140 amperes per sq. ft., at 3 volts, passing
+  between platinum electrodes, he attained to a current-efficiency of
+  52%, and each (British) electrical horse-power hour was equivalent to
+  a production of 1378.5 grains of potassium chlorate. In other words,
+  each pound of chlorate would require an expenditure of nearly 5.1
+  e.h.p. hours. One of the earliest of the more modern processes was
+  that of E. Hermite, which consisted in the production of
+  bleach-liquors by the electrolysis (according to the 1st edition of
+  the 1884 patent) of magnesium or calcium chloride between platinum
+  anodes carried in wooden frames, and zinc cathodes. The solution,
+  containing hypochlorites and chlorates, was then applied to the
+  bleaching of linen, paper-pulp or the like, the solution being used
+  over and over again. Many modifications have been patented by Hermite,
+  that of 1895 specifying the use of platinum gauze anodes, held in
+  ebonite or other frames. Rotating zinc cathodes were used, with
+  scrapers to prevent the accumulation of a layer of insoluble magnesium
+  compounds, which would otherwise increase the electrical resistance
+  beyond reasonable limits. The same inventor has patented the
+  application of electrolysed chlorides to the purification of starch by
+  the oxidation of less stable organic bodies, to the bleaching of oils,
+  and to the purification of coal gas, spirit and other substances. His
+  system for the disinfection of sewage and similar matter by the
+  electrolysis of chlorides, or of sea-water, has been tried, but for
+  the most part abandoned on the score of expense. Reference may be made
+  to papers written in the early days of the process by C.F. Cross and
+  E.J. Bevan (_Journ. Soc. Chem. Industry_, 1887, vol. vi. p. 170, and
+  1888, vol. vii. p. 292), and to later papers by P. Schoop
+  (_Zeitschrift f. Elektrochem._, 1895, vol. ii. pp. 68, 88, 107, 209,
+  289).
+
+  E. Kellner, who in 1886 patented the use of cathode (caustic soda) and
+  anode (chlorine) liquors in the manufacture of cellulose from
+  wood-fibre, and has since evolved many similar processes, has produced
+  an apparatus that has been largely used. It consists of a stoneware
+  tank with a thin sheet of platinum-iridium alloy at either end forming
+  the primary electrodes, and between them a number of glass plates
+  reaching nearly to the bottom, each having a platinum gauze sheet on
+  either side; the two sheets belonging to each plate are in metallic
+  connexion, but insulated from all the others, and form intermediary or
+  bi-polar electrodes. A 10-12% solution of sodium chloride is caused to
+  flow upwards through the apparatus and to overflow into troughs, by
+  which it is conveyed (if necessary through a cooling apparatus) back
+  to the circulating pump. Such a plant has been reported as giving
+  0.229 gallon of a liquor containing 1% of available chlorine per
+  kilowatt hour, or 0.171 gallon per e.h.p. hour. Kellner has also
+  patented a "bleaching-block," as he terms it, consisting of a frame
+  carrying parallel plates similar in principle to those last described.
+  The block is immersed in the solution to be bleached, and may be
+  lifted in or out as required. O. Knofler and Gebauer have also a
+  system of bi-polar electrodes, mounted in a frame in appearance
+  resembling a filter-press.
+
+_Other Electrochemical Processes._--It is obvious that electrolytic
+iodine and bromine, and oxygen compounds of these elements, may be
+produced by methods similar to those applied to chlorides (see ALKALI
+MANUFACTURE and CHLORATES), and Kellner and others have patented
+processes with this end in view. _Hydrogen_ and _oxygen_ may also be
+produced electrolytically as gases, and their respective reducing and
+oxidizing powers at the moment of deposition on the electrode are
+frequently used in the laboratory, and to some extent industrially,
+chiefly in the field of organic chemistry. Similarly, the formation of
+organic halogen products may be effected by electrolytic chlorine, as,
+for example, in the production of _chloral_ by the gradual introduction
+of alcohol into an anode cell in which the electrolyte is a strong
+solution of potassium chloride. Again, anode reactions, such as are
+observed in the electrolysis of the fatty acids, may be utilized, as,
+for example, when the radical CH3CO2--deposited at the anode in the
+electrolysis of acetic acid--is dissociated, two of the groups react to
+give one molecule of _ethane_, C2H6, and two of carbon dioxide. This,
+which has long been recognized as a class-reaction, is obviously capable
+of endless variation. Many electrolytic methods have been proposed for
+the purification of _sugar_; in some of them soluble anodes are used for
+a few minutes in weak alkaline solutions, so that the caustic alkali
+from the cathode reaction may precipitate chemically the hydroxide of
+the anode metal dissolved in the liquid, the precipitate carrying with
+it mechanically some of the impurities present, and thus clarifying the
+solution. In others the current is applied for a longer time to the
+original sugar-solution with insoluble (e.g. carbon) anodes. F. Peters
+has found that with these methods the best results are obtained when
+ozone is employed in addition to electrolytic oxygen. Use has been made
+of electrolysis in _tanning_ operations, the current being passed
+through the tan-liquors containing the hides. The current, by
+endosmosis, favours the passage of the solution into the hide-substance,
+and at the same time appears to assist the chemical combinations there
+occurring; hence a great reduction in the time required for the
+completion of the process. Many patents have been taken out in this
+direction, one of the best known being that of Groth, experimented upon
+by S. Rideal and A.P. Trotter (_Journ. Soc. Chem. Indust._, 1891, vol.
+x. p. 425), who employed copper anodes, 4 sq. ft. in area, with
+current-densities of 0.375 to 1 (ranging in some cases to 7.5) ampere
+per sq. ft., the best results being obtained with the smaller
+current-densities. Electrochemical processes are often indirectly used,
+as for example in the Villon process (_Elec. Rev._, New York, 1899, vol.
+xxxv. p. 375) applied in Russia to the manufacture of alcohol, by a
+series of chemical reactions starting from the production of acetylene
+by the action of water upon calcium carbide. The production of _ozone_
+in small quantities during electrolysis, and by the so-called silent
+discharge, has long been known, and the Siemens induction tube has been
+developed for use industrially. The Siemens and Halske ozonizer, in form
+somewhat resembling the old laboratory instrument, is largely used in
+Germany; working with an alternating current transformed up to 6500
+volts, it has been found to give 280 grains or more of ozone per e.h.p.
+hour. E. Andreoli (whose first British ozone patent was No. 17,426 of
+1891) uses flat aluminium plates and points, and working with an
+alternating current of 3000 volts is said to have obtained 1440 grains
+per e.h.p. hour. Yarnold's process, using corrugated glass plates coated
+on one side with gold or other metal leaf, is stated to have yielded as
+much as 2700 grains per e.h.p. hour. The ozone so prepared has numerous
+uses, as, for example, in bleaching oils, waxes, fabrics, &c.,
+sterilizing drinking-water, maturing wines, cleansing foul beer-casks,
+oxidizing oil, and in the manufacture of vanillin.
+
+  For further information the following books, among others, may be
+  consulted:--Haber, _Grundriss der technischen Elektrochemie_ (Munchen,
+  1898); Borchers and M'Millan, _Electric Smelting and Refining_
+  (London, 1904); E.D. Peters, _Principles of Copper Smelting_ (New
+  York, 1907); F. Peters, _Angewandte Elektrochemie_, vols. ii. and iii.
+  (Leipzig, 1900); Gore, _The Art of Electrolytic Separation of Metals_
+  (London, 1890); Blount, _Practical Electro-Chemistry_ (London, 1906);
+  G. Langbein, _Vollstandiges Handbuch der galvanischen
+  Metall-Niederschlage_ (Leipzig, 1903), Eng. trans. by W.T. Brannt
+  (1909); A. Watt, _Electro-Plating and Electro-Refining of Metals_
+  (London, 1902); W.H. Wahl, _Practical Guide to the Gold and Silver
+  Electroplater, &c._ (Philadelphia, 1883); Wilson, _Stereotyping and
+  Electrotyping_ (London); Lunge, _Sulphuric Acid and Alkali_, vol. iii.
+  (London, 1909). Also papers in various technical periodicals. The
+  industrial aspect is treated in a Gartside Report, _Some
+  Electro-Chemical Centres_ (Manchester, 1908), by J.N. Pring.
+       (W. G. M.)
+
+
+
+
+ELECTROCUTION (an anomalous derivative from "electro-execution"; syn.
+"electrothanasia"), the popular name, invented in America, for the
+infliction of the death penalty on criminals (see CAPITAL PUNISHMENT) by
+passing through the body of the condemned a sufficient current of
+electricity to cause death. The method was first adopted by the state of
+New York, a law making this method obligatory having been passed and
+approved by the governor on the 4th of June 1888. The law provides that
+there shall be present, in addition to the warden, two physicians,
+twelve reputable citizens of full age, seven deputy sheriffs, and such
+ministers, priests or clergymen, not exceeding two, as the criminal may
+request. A post-mortem examination of the body of the convict is
+required, and the body, unless claimed by relatives, is interred in the
+prison cemetery with a sufficient quantity of quicklime to consume it.
+The law became effective in New York on the 1st of January 1889. The
+first criminal to be executed by electricity was William Kemmler, on the
+6th of August 1890, at Auburn prison. The validity of the New York law
+had previously been attacked in regard to this case (_Re Kemmler_, 1889;
+136 U.S. 436), as providing "a cruel and unusual punishment" and
+therefore being contrary to the Constitution; but it was sustained in
+the state courts and finally in the Federal courts. By 1906 about one
+hundred and fifteen murderers had been successfully executed by
+electricity in New York state in Sing Sing, Auburn and Dannemora
+prisons. The method has also been adopted by the states of Ohio (1896),
+Massachusetts (1898), New Jersey (1906), Virginia (1908) and North
+Carolina (1910).
+
+The apparatus consists of a stationary engine, an alternating dynamo
+capable of generating a current at a pressure of 2000 volts, a
+"death-chair" with adjustable head-rest, binding straps and adjustable
+electrodes devised by E.F. Davis, the state electrician of New York. The
+voltmeter, ammeter and switch-board controlling the current are located
+in the execution-room; the dynamo-room is communicated with by electric
+signals. Before each execution the entire apparatus is thoroughly
+tested. When everything is in readiness the criminal is brought in and
+seats himself in the death-chair. His head, chest, arms and legs are
+secured by broad straps; one electrode thoroughly moistened with
+salt-solution is affixed to the head, and another to the calf of one
+leg, both electrodes being moulded so as to secure good contact. The
+application of the current is usually as follows: the contact is made
+with a high voltage (1700-1800 volts) for 5 to 7 seconds, reduced to 200
+volts until a half-minute has elapsed; raised to high voltage for 3 to 5
+seconds, again reduced to low voltage for 3 to 5 seconds, again reduced
+to a low voltage until one minute has elapsed, when it is again raised
+to the high voltage for a few seconds and the contact broken. The
+ammeter usually shows that from 7 to 10 amperes pass through the
+criminal's body. A second or even a third brief contact is sometimes
+made, partly as a precautionary measure, but rather the more completely
+to abolish reflexes in the dead body. Calculations have shown that by
+this method of execution from 7 to 10 h. p. of energy are liberated in
+the criminal's body. The time consumed by the strapping-in process is
+usually about 45 seconds, and the first contact is made about 70 seconds
+after the criminal has entered the death-chamber.
+
+When properly performed the effect is painless and instantaneous death.
+The mechanism of life, circulation and respiration cease with the first
+contact. Consciousness is blotted out instantly, and the prolonged
+application of the current ensures permanent derangement of the vital
+functions beyond recovery. Occasionally the drying of the sponges
+through undue generation of heat causes desquamation or superficial
+blistering of the skin at the site of the electrodes. Post-mortem
+discoloration, or post-mortem lividity, often appears during the first
+contact. The pupils of the eyes dilate instantly and remain dilated
+after death.
+
+The post-mortem examination of "electrocuted" criminals reveals a number
+of interesting phenomena. The temperature of the body rises promptly
+after death to a very high point. At the site of the leg electrode a
+temperature of over 128 deg. F. was registered within fifteen minutes in
+many cases. After the removal of the brain the temperature recorded in
+the spinal canal was often over 120 deg. F. The development of this high
+temperature is to be regarded as resulting from the active metabolism of
+tissues not (somatically) dead within a body where all vital mechanisms
+have been abolished, there being no circulation to carry off the
+generated heat. The heart, at first flaccid when exposed soon after
+death, gradually contracts and assumes a tetanized condition; it empties
+itself of all blood and takes the form of a heart in systole. The lungs
+are usually devoid of blood and weigh only 7 or 8 ounces (avoird.) each.
+The blood is profoundly altered biochemically; it is of a very dark
+colour and it rarely coagulates.     (E. A. S.*)
+
+
+
+
+ELECTROKINETICS, that part of electrical science which is concerned with
+the properties of electric currents.
+
+_Classification of Electric Currents._--Electric currents are classified
+into (a) conduction currents, (b) convection currents, (c) displacement
+or dielectric currents. In the case of conduction currents electricity
+flows or moves through a stationary material body called the conductor.
+In convection currents electricity is carried from place to place with
+and on moving material bodies or particles. In dielectric currents there
+is no continued movement of electricity, but merely a limited
+displacement through or in the mass of an insulator or dielectric. The
+path in which an electric current exists is called an electric circuit,
+and may consist wholly of a conducting body, or partly of a conductor
+and insulator or dielectric, or wholly of a dielectric. In cases in
+which the three classes of currents are present together the true
+current is the sum of each separately. In the case of conduction
+currents the circuit consists of a conductor immersed in a
+non-conductor, and may take the form of a thin wire or cylinder, a
+sheet, surface or solid. Electric conduction currents may take place in
+space of one, two or three dimensions, but for the most part the
+circuits we have to consider consist of thin cylindrical wires or tubes
+of conducting material surrounded with an insulator; hence the case
+which generally presents itself is that of electric flow in space of one
+dimension. Self-closed electric currents taking place in a sheet of
+conductor are called "eddy currents."
+
+Although in ordinary language the current is said to flow in the
+conductor, yet according to modern views the real pathway of the energy
+transmitted is the surrounding dielectric, and the so-called conductor
+or wire merely guides the transmission of energy in a certain direction.
+The presence of an electric current is recognized by three qualities or
+powers: (1) by the production of a magnetic field, (2) in the case of
+conduction currents, by the production of heat in the conductor, and (3)
+if the conductor is an electrolyte and the current unidirectional, by
+the occurrence of chemical decomposition in it. An electric current may
+also be regarded as the result of a movement of electricity across each
+section of the circuit, and is then measured by the quantity conveyed
+per unit of time. Hence if dq is the quantity of electricity which flows
+across any section of the conductor in the element of time dt, the
+current i = dq/dt.
+
+[Illustration: FIG. 1.]
+
+[Illustration: FIG. 2.]
+
+Electric currents may be also classified as constant or variable and as
+unidirectional or "direct," that is flowing always in the same
+direction, or "alternating," that is reversing their direction at
+regular intervals. In the last case the variation of current may follow
+any particular law. It is called a "periodic current" if the cycle of
+current values is repeated during a certain time called the periodic
+time, during which the current reaches a certain maximum value, first in
+one direction and then in the opposite, and in the intervals between has
+a zero value at certain instants. The frequency of the periodic current
+is the number of periods or cycles in one second, and alternating
+currents are described as low frequency or high frequency, in the latter
+case having some thousands of periods per second. A periodic current may
+be represented either by a wave diagram, or by a polar diagram.[1] In
+the first case we take a straight line to represent the uniform flow of
+time, and at small equidistant intervals set up perpendiculars above or
+below the time axis, representing to scale the current at that instant
+in one direction or the other; the extremities of these ordinates then
+define a wavy curve which is called the wave form of the current (fig.
+1). It is obvious that this curve can only be a single valued curve. In
+one particular and important case the form of the current curve is a
+simple harmonic curve or simple sine curve. If T represents the periodic
+time in which the cycle of current values takes place, whilst n is the
+frequency or number of periods per second and p stands for 2[pi]n, and i
+is the value of the current at any instant t, and I its maximum value,
+then in this case we have i = I sin pt. Such a current is called a "sine
+current" or simple periodic current.
+
+In a polar diagram (fig. 2) a number of radial lines are drawn from a
+point at small equiangular intervals, and on these lines are set off
+lengths proportional to the current value of a periodic current at
+corresponding intervals during one complete period represented by four
+right angles. The extremities of these radii delineate a polar curve.
+The polar form of a simple sine current is obviously a circle drawn
+through the origin. As a consequence of Fourier's theorem it follows
+that any periodic curve having any wave form can be imitated by the
+superposition of simple sine currents differing in maximum value and in
+phase.
+
+_Definitions of Unit Electric Current._--In electrokinetic
+investigations we are most commonly limited to the cases of
+unidirectional continuous and constant currents (C.C. or D.C.), or of
+simple periodic currents, or alternating currents of sine form (A.C.). A
+continuous electric current is measured either by the magnetic effect it
+produces at some point outside its circuit, or by the amount of
+electrochemical decomposition it can perform in a given time on a
+selected standard electrolyte. Limiting our consideration to the case of
+linear currents or currents flowing in thin cylindrical wires, a
+definition may be given in the first place of the unit electric current
+in the centimetre, gramme, second (C.G.S.) of electromagnetic
+measurement (see UNITS, PHYSICAL). H.C. Oersted discovered in 1820 that
+a straight wire conveying an electric current is surrounded by a
+magnetic field the lines of which are self-closed lines embracing the
+electric circuit (see ELECTRICITY and ELECTROMAGNETISM). The unit
+current in the electromagnetic system of measurement is defined as the
+current which, flowing in a thin wire bent into the form of a circle of
+one centimetre in radius, creates a magnetic field having a strength of
+2[pi] units at the centre of the circle, and therefore would exert a
+mechanical force of 2[pi] dynes on a unit magnetic pole placed at that
+point (see MAGNETISM). Since the length of the circumference of the
+circle of unit radius is 2[pi] units, this is equivalent to stating that
+the unit current on the electromagnetic C.G.S. system is a current such
+that unit length acts on unit magnetic pole with a unit force at a unit
+of distance. Another definition, called the electrostatic unit of
+current, is as follows: Let any conductor be charged with electricity
+and discharged through a thin wire at such a rate that one electrostatic
+unit of quantity (see ELECTROSTATICS) flows past any section of the wire
+in one unit of time. The electromagnetic unit of current defined as
+above is 3 X 10^10 times larger than the electrostatic unit.
+
+In the selection of a practical unit of current it was considered that
+the electromagnetic unit was too large for most purposes, whilst the
+electrostatic unit was too small; hence a practical unit of current
+called 1 ampere was selected, intended originally to be 1/10 of the
+absolute electromagnetic C.G.S. unit of current as above defined. The
+practical unit of current, called the international ampere, is, however,
+legally defined at the present time as the continuous unidirectional
+current which when flowing through a neutral solution of silver nitrate
+deposits in one second on the cathode or negative pole 0.001118 of a
+gramme of silver. There is reason to believe that the international unit
+is smaller by about one part in a thousand, or perhaps by one part in
+800, than the theoretical ampere defined as 1/10 part of the absolute
+electromagnetic unit. A periodic or alternating current is said to have
+a value of 1 ampere if when passed through a fine wire it produces in
+the same time the same heat as a unidirectional continuous current of 1
+ampere as above electrochemically defined. In the case of a simple
+periodic alternating current having a simple sine wave form, the maximum
+value is equal to that of the equiheating continuous current multiplied
+by [root]2. This equiheating continuous current is called the effective
+or root-mean-square (R.M.S.) value of the alternating one.
+
+_Resistance._--A current flows in a circuit in virtue of an
+electromotive force (E.M.F.), and the numerical relation between the
+current and E.M.F. is determined by three qualities of the circuit
+called respectively, its resistance (R), inductance (L), and capacity
+(C). If we limit our consideration to the case of continuous
+unidirectional conduction currents, then the relation between current
+and E.M.F. is defined by Ohm's law, which states that the numerical
+value of the current is obtained as the quotient of the electromotive
+force by a certain constant of the circuit called its resistance, which
+is a function of the geometrical form of the circuit, of its nature,
+i.e. material, and of its temperature, but is independent of the
+electromotive force or current. The resistance (R) is measured in units
+called ohms and the electromotive force in volts (V); hence for a
+continuous current the value of the current in amperes (A) is obtained
+as the quotient of the electromotive force acting in the circuit
+reckoned in volts by the resistance in ohms, or A = V/R. Ohm established
+his law by a course of reasoning which was similar to that on which
+J.B.J. Fourier based his investigations on the uniform motion of heat in
+a conductor. As a matter of fact, however, Ohm's law merely states the
+direct proportionality of steady current to steady electromotive force
+in a circuit, and asserts that this ratio is governed by the numerical
+value of a quality of the conductor, called its resistance, which is
+independent of the current, provided that a correction is made for the
+change of temperature produced by the current. Our belief, however, in
+its universality and accuracy rests upon the close agreement between
+deductions made from it and observational results, and although it is
+not derivable from any more fundamental principle, it is yet one of the
+most certainly ascertained laws of electrokinetics.
+
+Ohm's law not only applies to the circuit as a whole but to any part of
+it, and provided the part selected does not contain a source of
+electromotive force it may be expressed as follows:--The difference of
+potential (P.D.) between any two points of a circuit including a
+resistance R, but not including any source of electromotive force, is
+proportional to the product of the resistance and the current i in the
+element, provided the conductor remains at the same temperature and the
+current is constant and unidirectional. If the current is varying we
+have, however, to take into account the electromotive force (E.M.F.)
+produced by this variation, and the product Ri is then equal to the
+difference between the observed P.D. and induced E.M.F.
+
+We may otherwise define the resistance of a circuit by saying that it is
+that physical quality of it in virtue of which energy is dissipated as
+heat in the circuit when a current flows through it. The power
+communicated to any electric circuit when a current i is created in it
+by a continuous unidirectional electromotive force E is equal to Ei, and
+the energy dissipated as heat in that circuit by the conductor in a
+small interval of time dt is measured by Ei dt. Since by Ohm's law E =
+Ri, where R is the resistance of the circuit, it follows that the energy
+dissipated as heat per unit of time in any circuit is numerically
+represented by Ri^2, and therefore the resistance is measured by the heat
+produced per unit of current, provided the current is unvarying.
+
+_Inductance._--As soon as we turn our attention, however, to alternating
+or periodic currents we find ourselves compelled to take into account
+another quality of the circuit, called its "inductance." This may be
+defined as that quality in virtue of which energy is stored up in
+connexion with the circuit in a magnetic form. It can be experimentally
+shown that a current cannot be created instantaneously in a circuit by
+any finite electromotive force, and that when once created it cannot be
+annihilated instantaneously. The circuit possesses a quality analogous
+to the inertia of matter. If a current i is flowing in a circuit at any
+moment, the energy stored up in connexion with the circuit is measured
+by 1/2Li^2, where L, the inductance of the circuit, is related to the
+current in the same manner as the quantity called the mass of a body is
+related to its velocity in the expression for the ordinary kinetic
+energy, viz. 1/2Mv^2. The rate at which this conserved energy varies with
+the current is called the "electrokinetic momentum" of this circuit (=
+Li). Physically interpreted this quantity signifies the number of lines
+of magnetic flux due to the current itself which are self-linked with
+its own circuit.
+
+_Magnetic Force and Electric Currents._--In the case of every circuit
+conveying a current there is a certain magnetic force (see MAGNETISM) at
+external points which can in some instances be calculated. Laplace
+proved that the magnetic force due to an element of length dS of a
+circuit conveying a current I at a point P at a distance r from the
+element is expressed by IdS sin [theta]/r^2, where [theta] is the angle
+between the direction of the current element and that drawn between the
+element and the point. This force is in a direction perpendicular to the
+radius vector and to the plane containing it and the element of current.
+Hence the determination of the magnetic force due to any circuit is
+reduced to a summation of the effects due to all the elements of length.
+For instance, the magnetic force at the centre of a circular circuit of
+radius r carrying a steady current I is 2[pi]I/r, since all elements
+are at the same distance from the centre. In the same manner, if we take
+a point in a line at right angles to the plane of the circle through its
+centre and at a distance d, the magnetic force along this line is
+expressed by 2[pi]r^2I/(r^2 + d^2)(3/2). Another important case is that
+of an infinitely long straight current. By summing up the magnetic force
+due to each element at any point P outside the continuous straight
+current I, and at a distance d from it, we can show that it is equal to
+2I/d or is inversely proportional to the distance of the point from the
+wire. In the above formula the current I is measured in absolute
+electromagnetic units. If we reckon the current in amperes A, then I =
+A/10.
+
+It is possible to make use of this last formula, coupled with an
+experimental fact, to prove that the magnetic force due to an element of
+current varies inversely as the square of the distance. If a flat
+circular disk is suspended so as to be free to rotate round a straight
+current which passes through its centre, and two bar magnets are placed
+on it with their axes in line with the current, it is found that the
+disk has no tendency to rotate round the current. This proves that the
+force on each magnetic pole is inversely as its distance from the
+current. But it can be shown that this law of action of the whole
+infinitely long straight current is a mathematical consequence of the
+fact that each element of the current exerts a magnetic force which
+varies inversely as the square of the distance. If the current flows N
+times round the circuit instead of once, we have to insert NA/10 in
+place of I in all the above formulae. The quantity NA is called the
+"ampere-turns" on the circuit, and it is seen that the magnetic field at
+any point outside a circuit is proportional to the ampere-turns on it
+and to a function of its geometrical form and the distance of the point.
+
+[Illustration: FIG. 3.]
+
+[Illustration: FIG. 4.]
+
+There is therefore a distribution of magnetic force in the field of
+every current-carrying conductor which can be delineated by lines of
+magnetic force and rendered visible to the eye by iron filings (see
+Magnetism). If a copper wire is passed vertically through a hole in a
+card on which iron filings are sprinkled, and a strong electric current
+is sent through the circuit, the filings arrange themselves in
+concentric circular lines making visible the paths of the lines of
+magnetic force (fig. 3). In the same manner, by passing a circular wire
+through a card and sending a strong current through the wire we can
+employ iron filings to delineate for us the form of the lines of
+magnetic force (fig. 4). In all cases a magnetic pole of strength M,
+placed in the field of an electric current, is urged along the lines of
+force with a mechanical force equal to MH, where H is the magnetic
+force. If then we carry a unit magnetic pole against the direction in
+which it would naturally move we do _work_. The lines of magnetic force
+embracing a current-carrying conductor are always loops or endless
+lines.
+
+  The work done in carrying a unit magnetic pole once round a circuit
+  conveying a current is called the "line integral of magnetic force"
+  along that path. If, for instance, we carry a unit pole in a circular
+  path of radius r once round an infinitely long straight filamentary
+  current I, the line integral is 4[pi]I. It is easy to prove that this
+  is a general law, and that if we have any currents flowing in a
+  conductor the line integral of magnetic force taken once round a path
+  linked with the current circuit is 4[pi] times the total current
+  flowing through the circuit. Let us apply this to the case of an
+  endless solenoid. If a copper wire insulated or covered with cotton or
+  silk is twisted round a thin rod so as to make a close spiral, this
+  forms a "solenoid," and if the solenoid is bent round so that its two
+  ends come together we have an endless solenoid. Consider such a
+  solenoid of mean length l and N turns of wire. If it is made endless,
+  the magnetic force H is the same everywhere along the central axis and
+  the line integral along the axis is Hl. If the current is denoted by
+  I, then NI is the total current, and accordingly 4[pi]NI = Hl, or H =
+  4[pi]NI/l. For a thin endless solenoid the axial magnetic force is
+  therefore 4[pi] times the current-turns per unit of length. This holds
+  good also for a long straight solenoid provided its length is large
+  compared with its diameter. It can be shown that if insulated wire is
+  wound round a sphere, the turns being all parallel to lines of
+  latitude, the magnetic force in the interior is constant and the lines
+  of force therefore parallel. The magnetic force at a point outside a
+  conductor conveying a current can by various means be measured or
+  compared with some other standard magnetic forces, and it becomes then
+  a means of measuring the current. Instruments called galvanometers and
+  ammeters for the most part operate on this principle.
+
+_Thermal Effects of Currents._--J.P. Joule proved that the heat produced
+by a constant current in a given time in a wire having a constant
+resistance is proportional to the square of the strength of the current.
+This is known as Joule's law, and it follows, as already shown, as an
+immediate consequence of Ohm's law and the fact that the power
+dissipated electrically in a conductor, when an electromotive force E is
+applied to its extremities, producing thereby a current I in it, is
+equal to EI.
+
+  If the current is alternating or periodic, the heat produced in any
+  time T is obtained by taking the sum at equidistant intervals of time
+  of all the values of the quantities Ri^2dt, where dt represents a small
+  interval of time and i is the current at that instant. The quantity
+           _
+          / T
+   T^(-1) |    i^2dt is called the mean-square-value of the variable
+         _/ 0
+
+  current, i being the instantaneous value of the current, that is, its
+  value at a particular instant or during a very small interval of time
+  dt. The square root of the above quantity, or
+     _        _      _
+    |        / T      | 1/2,
+    | T^(-1) |  i^2dt |
+    |_      _/ 0     _|
+
+  is called the root-mean-square-value, or the effective value of the
+  current, and is denoted by the letters R.M.S.
+
+Currents have equal heat-producing power in conductors of identical
+resistance when they have the same R.M.S. values. Hence periodic or
+alternating currents can be measured as regards their R.M.S. value by
+ascertaining the continuous current which produces in the same time the
+same heat in the same conductor as the periodic current considered.
+Current measuring instruments depending on this fact, called hot-wire
+ammeters, are in common use, especially for measuring alternating
+currents. The maximum value of the periodic current can only be
+determined from the R.M.S. value when we know the wave form of the
+current. The thermal effects of electric currents in conductors are
+dependent upon the production of a state of equilibrium between the heat
+produced electrically in the wire and the causes operative in removing
+it. If an ordinary round wire is heated by a current it loses heat, (1)
+by radiation, (2) by air convection or cooling, and (3) by conduction of
+heat out of the ends of the wire. Generally speaking, the greater part
+of the heat removal is effected by radiation and convection.
+
+  If a round sectioned metallic wire of uniform diameter d and length l
+  made of a material of resistivity [rho] has a current of A amperes
+  passed through it, the heat in watts produced in any time t seconds is
+  represented by the value of 4A^2[rho]lt/10^9[pi]d^2, where d and l
+  must be measured in centimetres and [rho] in absolute C.G.S.
+  electromagnetic units. The factor 10^9 enters because one ohm is 10^9
+  absolute electromagnetic C.G.S. units (see UNITS, PHYSICAL). If the
+  wire has an emissivity e, by which is meant that e units of heat
+  reckoned in joules or watt-seconds are radiated per second from unit
+  of surface, then the power removed by radiation in the time t is
+  expressed by [pi]dlet. Hence when thermal equilibrium is established
+  we have 4A^2[rho]lt/10^9[pi]d^2 = [pi]dlet, or A^2 =
+  10^9[pi]^2ed^3/4[rho]. If the diameter of the wire is reckoned in mils
+  (1 mil = .001 in.), and if we take e to have a value 0.1, an
+  emissivity which will generally bring the wire to about 60 deg. C., we
+  can put the above formula in the following forms for circular
+  sectioned copper, iron or platinoid wires, viz.
+
+    A = [root](d^3/500) for copper wires
+    A = [root](d^3/4000) for iron wires
+    A = [root](d^3/5000) for platinoid wires.
+
+  These expressions give the ampere value of the current which will
+  bring bare, straight or loosely coiled wires of d mils in diameter to
+  about 60 deg. C. when the steady state of temperature is reached. Thus,
+  for instance, a bare straight copper wire 50 mils in diameter (=0.05
+  in.) will be brought to a steady temperature of about 60 deg. C. if a
+  current of [root]50^3/500 = [root]250 = 16 amperes (nearly) is passed
+  through it, whilst a current of [root]25 = 5 amperes would bring a
+  platinoid wire to about the same temperature.
+
+A wire has therefore a certain safe current-carrying capacity which is
+determined by its specific resistance and emissivity, the latter being
+fixed by its form, surface and surroundings. The emissivity increases
+with the temperature, else no state of thermal equilibrium could be
+reached. It has been found experimentally that whilst for fairly thick
+wires from 8 to 60 mils in diameter the safe current varies
+approximately as the 1.5th power of the diameter, for fine wires of 1 to
+3 mils it varies more nearly as the diameter.
+
+_Action of one Current on Another._--The investigations of Ampere in
+connexion with electric currents are of fundamental importance in
+electrokinetics. Starting from the discovery of Oersted, Ampere made
+known the correlative fact that not only is there a mechanical action
+between a current and a magnet, but that two conductors conveying
+electric currents exert mechanical forces on each other. Ampere devised
+ingenious methods of making one portion of a circuit movable so that he
+might observe effects of attraction or repulsion between this circuit
+and some other fixed current. He employed for this purpose an astatic
+circuit B, consisting of a wire bent into a double rectangle round which
+a current flowed first in one and then in the opposite direction (fig.
+5). In this way the circuit was removed from the action of the earth's
+magnetic field, and yet one portion of it could be submitted to the
+action of any other circuit C. The astatic circuit was pivoted by
+suspending it in mercury cups q, p, one of which was in electrical
+connexion with the tubular support A, and the other with a strong
+insulated wire passing up it.
+
+[Illustration: FIG. 5.]
+
+Ampere devised certain crucial experiments, and the theory deduced from
+them is based upon four facts and one assumption.[2] He showed (1) that
+wire conveying a current bent back on itself produced no action upon a
+proximate portion of a movable astatic circuit; (2) that if the return
+wire was bent zig-zag but close to the outgoing straight wire the
+circuit produced no action on the movable one, showing that the effect
+of an element of the circuit was proportional to its projected length;
+(3) that a closed circuit cannot cause motion in an element of another
+circuit free to move in the direction of its length; and (4) that the
+action of two circuits on one and the same movable circuit was null if
+one of the two fixed circuits was n times greater than the other but n
+times further removed from the movable circuit. From this last
+experiment by an ingenious line of reasoning he proved that the action
+of an element of current on another element of current varies inversely
+as a square of their distance. These experiments enabled him to
+construct a mathematical expression of the law of action between two
+elements of conductors conveying currents. They also enabled him to
+prove that an element of current may be resolved like a force into
+components in different directions, also that the force produced by any
+element of the circuit on an element of any other circuit was
+perpendicular to the line joining the elements and inversely as the
+square of their distance. Also he showed that this force was an
+attraction if the currents in the elements were in the same direction,
+but a repulsion if they were in opposite directions. From these
+experiments and deductions from them he built up a complete formula for
+the action of one element of a current of length dS of one conductor
+conveying a current I upon another element dS' of another circuit
+conveying another current I' the elements being at a distance apart
+equal to r.
+
+  If [theta] and [theta]' are the angles the elements make with the line
+  joining them, and [phi] the angle they make with one another, then
+  Ampere's expression for the mechanical force f the elements exert on
+  one another is
+
+    f = 2II'r^(-2) {cos [phi] - (3/2)cos [theta] cos [theta]'}dSdS'.
+
+  This law, together with that of Laplace already mentioned, viz. that
+  the magnetic force due to an element of length dS of a current I at a
+  distance r, the element making an angle [theta] with the radius vector
+  o is IdS sin [theta]/r^2, constitute the fundamental laws of
+  electrokinetics.
+
+Ampere applied these with great mathematical skill to elucidate the
+mechanical actions of currents on each other, and experimentally
+confirmed the following deductions: (1) Currents in parallel circuits
+flowing in the same direction attract each other, but if in opposite
+directions repel each other. (2) Currents in wires meeting at an angle
+attract each other more into parallelism if both flow either to or from
+the angle, but repel each other more widely apart if they are in
+opposite directions. (3) A current in a small circular conductor exerts
+a magnetic force in its centre perpendicular to its plane and is in all
+respects equivalent to a magnetic shell or a thin circular disk of steel
+so magnetized that one face is a north pole and the other a south pole,
+the product of the area of the circuit and the current flowing in it
+determining the magnetic moment of the element. (4) A closely wound
+spiral current is equivalent as regards external magnetic force to a
+polar magnet, such a circuit being called a finite solenoid. (5) Two
+finite solenoid circuits act on each other like two polar magnets,
+exhibiting actions of attraction or repulsion between their ends.
+
+Ampere's theory was wholly built up on the assumption of action at a
+distance between elements of conductors conveying the electric currents.
+Faraday's researches and the discovery of the fact that the insulating
+medium is the real seat of the operations necessitates a change in the
+point of view from which we regard the facts discovered by Ampere.
+Maxwell showed that in any field of magnetic force there is a tension
+along the lines of force and a pressure at right angles to them; in
+other words, lines of magnetic force are like stretched elastic threads
+which tend to contract.[3] If, therefore, two conductors lie parallel
+and have currents in them in the same direction they are impressed by a
+certain number of lines of magnetic force which pass round the two
+conductors, and it is the tendency of these to contract which draws the
+circuits together. If, however, the currents are in opposite directions
+then the lateral pressure of the similarly contracted lines of force
+between them pushes the conductors apart. Practical application of
+Ampere's discoveries was made by W.E. Weber in inventing the
+electrodynamometer, and later Lord Kelvin devised ampere balances for
+the measurement of electric currents based on the attraction between
+coils conveying electric currents.
+
+_Induction of Electric Currents._--Faraday[4] in 1831 made the important
+discovery of the induction of electric currents (see ELECTRICITY). If
+two conductors are placed parallel to each other, and a current in one
+of them, called the primary, started or stopped or changed in strength,
+every such alteration causes a transitory current to appear in the other
+circuit, called the secondary. This is due to the fact that as the
+primary current increases or decreases, its own embracing magnetic field
+alters, and lines of magnetic force are added to or subtracted from its
+fields. These lines do not appear instantly in their place at a
+distance, but are propagated out from the wire with a velocity equal to
+that of light; hence in their outward progress they cut through the
+secondary circuit, just as ripples made on the surface of water in a
+lake by throwing a stone on to it expand and cut through a stick held
+vertically in the water at a distance from the place of origin of the
+ripples. Faraday confirmed this view of the phenomena by proving that
+the mere motion of a wire transversely to the lines of magnetic force of
+a permanent magnet gave rise to an induced electromotive force in the
+wire. He embraced all the facts in the single statement that if there
+be any circuit which by movement in a magnetic field, or by the creation
+or change in magnetic fields round it, experiences a change in the
+number of lines of force linked with it, then an electromotive force is
+set up in that circuit which is proportional at any instant to the rate
+at which the total magnetic flux linked with it is changing. Hence if Z
+represents the total number of lines of magnetic force linked with a
+circuit of N turns, then -N(dZ/dt) represents the electromotive force
+set up in that circuit. The operation of the induction coil (q.v.) and
+the transformer (q.v.) are based on this discovery. Faraday also found
+that if a copper disk A (fig. 6) is rotated between the poles of a
+magnet NO so that the disk moves with its plane perpendicular to the
+lines of magnetic force of the field, it has created in it an
+electromotive force directed from the centre to the edge or vice versa.
+The action of the dynamo (q.v.) depends on similar processes, viz. the
+cutting of the lines of magnetic force of a constant field produced by
+certain magnets by certain moving conductors called armature bars or
+coils in which an electromotive force is thereby created.
+
+[Illustration: FIG 6.]
+
+  In 1834 H.F.E. Lenz enunciated a law which connects together the
+  mechanical actions between electric circuits discovered by Ampere and
+  the induction of electric currents discovered by Faraday. It is as
+  follows: If a constant current flows in a primary circuit P, and if by
+  motion of P a secondary current is created in a neighbouring circuit
+  S, the direction of the secondary current will be such as to oppose
+  the relative motion of the circuits. Starting from this, F.E. Neumann
+  founded a mathematical theory of induced currents, discovering a
+  quantity M, called the "potential of one circuit on another," or
+  generally their "coefficient of mutual inductance." Mathematically M
+  is obtained by taking the sum of all such quantities as ff dSdS' cos
+  [phi]/r, where dS and dS' are the elements of length of the two
+  circuits, r is their distance, and [phi] is the angle which they make
+  with one another; the summation or integration must be extended over
+  every possible pair of elements. If we take pairs of elements in the
+  same circuit, then Neumann's formula gives us the coefficient of
+  self-induction of the circuit or the potential of the circuit on
+  itself. For the results of such calculations on various forms of
+  circuit the reader must be referred to special treatises.
+
+  H. von Helmholtz, and later on Lord Kelvin, showed that the facts of
+  induction of electric currents discovered by Faraday could have been
+  predicted from the electrodynamic actions discovered by Ampere
+  assuming the principle of the conservation of energy. Helmholtz takes
+  the case of a circuit of resistance R in which acts an electromotive
+  force due to a battery or thermopile. Let a magnet be in the
+  neighbourhood, and the potential of the magnet on the circuit be V, so
+  that if a current I existed in the circuit the work done on the magnet
+  in the time dt is I(dV/dt)dt. The source of electromotive force
+  supplies in the time dt work equal to EIdt, and according to Joule's
+  law energy is dissipated equal to RI^2dt. Hence, by the conservation
+  of energy,
+
+    EIdt = RI^2dt + I(dV/dt)dt.
+
+  If then E = 0, we have I = -(dV/dt)/R, or there will be a current due
+  to an induced electromotive force expressed by -dV/dt. Hence if the
+  magnet moves, it will create a current in the wire provided that such
+  motion changes the potential of the magnet with respect to the
+  circuit. This is the effect discovered by Faraday.[5]
+
+_Oscillatory Currents._--In considering the motion of electricity in
+conductors we find interesting phenomena connected with the discharge of
+a condenser or Leyden jar (q.v.). This problem was first mathematically
+treated by Lord Kelvin in 1853 (_Phil. Mag._, 1853, 5, p. 292).
+
+  If a conductor of capacity C has its terminals connected by a wire of
+  resistance R and inductance L, it becomes important to consider the
+  subsequent motion of electricity in the wire. If Q is the quantity of
+  electricity in the condenser initially, and q that at any time t after
+  completing the circuit, then the energy stored up in the condenser at
+  that instant is 1/2q^2/C, and the energy associated with the circuit
+  is 1/2L(dq/dt)^2, and the rate of dissipation of energy by resistance
+  is R(dq/dt)^2, since dq/dt = i is the discharge current. Hence we can
+  construct an equation of energy which expresses the fact that at any
+  instant the power given out by the condenser is partly stored in the
+  circuit and partly dissipated as heat in it. Mathematically this is
+  expressed as follows:--
+
+          _       _        _            _
+      d  |     q^2 |   d  |       /dq\^2 |      /dq\^2
+    - -- | 1/2 --- | = -- | 1/2L ( -- )  | + R ( -- )
+      dt |_     C _|   dt |_      \dt/  _|      \dt/
+
+  or
+
+    d^2q   R  dq   1
+    ---- + -- -- + -- q = 0.
+    dt^2   L  dt   LC
+
+  The above equation has two solutions according as R^2/4L^2 is greater
+  or less than 1/LC. In the first case the current i in the circuit can
+  be expressed by the equation
+
+         [alpha]^2+[beta]^2
+    i= Q ------------------ e^(-[alpha]t) [e^([beta]t) - e^(-[beta]t)],
+               2[beta]
+                                    ________
+                                   /R^2    1
+  where [alpha] = R/2L, [beta] =  / --- - --, Q is the value of q when
+                                \/  4L^2   LC
+
+  t = 0, and e is the base of Napierian logarithms; and in the second
+  case by the equation
+
+          [alpha]^2+[beta]^2
+    i = Q ------------------ e^(-[alpha]t) sin [beta]t
+                [beta]
+                                        _________
+                                       /1    R^2
+  where [alpha] = R/2L, and [beta] =  / -- - ----.
+                                    \/  LC   4L^2
+
+
+  These expressions show that in the first case the discharge current of
+  the jar is always in the same direction and is a transient
+  unidirectional current. In the second case, however, the current is an
+  oscillatory current gradually decreasing in amplitude, the frequency n
+  of the oscillation being given by the expression
+                  _________
+          1      /1    R^2
+    n = -----   / -- - ----.
+        2[pi] \/  LC   4L^2
+
+  In those cases in which the resistance of the discharge circuit is
+  very small, the expression for the frequency n and for the time period
+  of oscillation R take the simple forms n = 1, 2[pi][root]LC, or T =
+  1/n = 2[pi][root]LC.
+
+The above investigation shows that if we construct a circuit consisting
+of a condenser and inductance placed in series with one another, such
+circuit has a natural electrical time period of its own in which the
+electrical charge in it oscillates if disturbed. It may therefore be
+compared with a pendulum of any kind which when displaced oscillates
+with a time period depending on its inertia and on its restoring force.
+
+The study of these electrical oscillations received a great impetus
+after H.R. Hertz showed that when taking place in electric circuits of a
+certain kind they create electromagnetic waves (see ELECTRIC WAVES) in
+the dielectric surrounding the oscillator, and an additional interest
+was given to them by their application to telegraphy. If a Leyden jar
+and a circuit of low resistance but some inductance in series with it
+are connected across the secondary spark gap of an induction coil, then
+when the coil is set in action we have a series of bright noisy sparks,
+each of which consists of a train of oscillatory electric discharges
+from the jar. The condenser becomes charged as the secondary
+electromotive force of the coil is created at each break of the primary
+current, and when the potential difference of the condenser coatings
+reaches a certain value determined by the spark-ball distance a
+discharge happens. This discharge, however, is not a single movement of
+electricity in one direction but an oscillatory motion with gradually
+decreasing amplitude. If the oscillatory spark is photographed on a
+revolving plate or a rapidly moving film, we have evidence in the
+photograph that such a spark consists of numerous intermittent sparks
+gradually becoming feebler. As the coil continues to operate, these
+trains of electric discharges take place at regular intervals. We can
+cause a train of electric oscillations in one circuit to induce similar
+oscillations in a neighbouring circuit, and thus construct an
+oscillation transformer or high frequency induction coil.
+
+_Alternating Currents._--The study of alternating currents of
+electricity began to attract great attention towards the end of the 19th
+century by reason of their application in electrotechnics and
+especially to the transmission of power. A circuit in which a simple
+periodic alternating current flows is called a single phase circuit. The
+important difference between such a form of current flow and steady
+current flow arises from the fact that if the circuit has inductance
+then the periodic electric current in it is not in step with the
+terminal potential difference or electromotive force acting in the
+circuit, but the current lags behind the electromotive force by a
+certain fraction of the periodic time called the "phase difference." If
+two alternating currents having a fixed difference in phase flow in two
+connected separate but related circuits, the two are called a two-phase
+current. If three or more single-phase currents preserving a fixed
+difference of phase flow in various parts of a connected circuit, the
+whole taken together is called a polyphase current. Since an electric
+current is a vector quantity, that is, has direction as well as
+magnitude, it can most conveniently be represented by a line denoting
+its maximum value, and if the alternating current is a simple periodic
+current then the root-mean-square or effective value of the current is
+obtained by dividing the maximum value by [root]2. Accordingly when we
+have an electric circuit or circuits in which there are simple periodic
+currents we can draw a vector diagram, the lines of which represent the
+relative magnitudes and phase differences of these currents.
+
+  A vector can most conveniently be represented by a symbol such as a +
+  ib, where a stands for any length of a units measured horizontally and
+  b for a length b units measured vertically, and the symbol i is a sign
+  of perpendicularity, and equivalent analytically[6] to [root]-1.
+  Accordingly if E represents the periodic electromotive force (maximum
+  value) acting in a circuit of resistance R and inductance L and
+  frequency n, and if the current considered as a vector is represented
+  by I, it is easy to show that a vector equation exists between these
+  quantities as follows:--
+
+    E = RI + [iota]2[pi]nLI.
+
+  Since the absolute magnitude of a vector a + [iota]b is [root](a^2 +
+  b^2), it follows that considering merely magnitudes of current and
+  electromotive force and denoting them by symbols (E) (I), we have the
+  following equation connecting (I) and (E):--
+
+    (I) = (E)[root](R^2 + p^2L^2),
+
+  where p stands for 2[pi]n. If the above equation is compared with the
+  symbolic expression of Ohm's law, it will be seen that the quantity
+  [root](R^2 + p^2L^2) takes the place of resistance R in the expression
+  of Ohm. This quantity [root](R^2 + p^2L^2) is called the "impedance"
+  of the alternating circuit. The quantity pL is called the "reactance"
+  of the alternating circuit, and it is therefore obvious that the
+  current in such a circuit lags behind the electromotive force by an
+  angle, called the angle of lag, the tangent of which is pL/R.
+
+  _Currents in Networks of Conductors._--In dealing with problems
+  connected with electric currents we have to consider the laws which
+  govern the flow of currents in linear conductors (wires), in plane
+  conductors (sheets), and throughout the mass of a material
+  conductor.[7] In the first case consider the collocation of a number
+  of linear conductors, such as rods or wires of metal, joined at their
+  ends to form a network of conductors. The network consists of a number
+  of conductors joining certain points and forming meshes. In each
+  conductor a current may exist, and along each conductor there is a
+  fall of potential, or an active electromotive force may be acting in
+  it. Each conductor has a certain resistance. To find the current in
+  each conductor when the individual resistances and electromotive
+  forces are given, proceed as follows:--Consider any one mesh. The sum
+  of all the electromotive forces which exist in the branches bounding
+  that mesh must be equal to the sum of all the products of the
+  resistances into the currents flowing along them, or [Sigma](E) =
+  [Sigma](C.R.). Hence if we consider each mesh as traversed by
+  imaginary currents all circulating in the same direction, the real
+  currents are the sums or differences of these imaginary cyclic
+  currents in each branch. Hence we may assign to each mesh a cycle
+  symbol x, y, z, &c., and form a cycle equation. Write down the cycle
+  symbol for a mesh and prefix as coefficient the sum of all the
+  resistances which bound that cycle, then subtract the cycle symbols of
+  each adjacent cycle, each multiplied by the value of the bounding or
+  common resistances, and equate this sum to the total electromotive
+  force acting round the cycle. Thus if x y z are the cycle currents,
+  and a b c the resistances bounding the mesh x, and b and c those
+  separating it from the meshes y and z, and E an electromotive force in
+  the branch a, then we have formed the cycle equation x(a + b + c) -
+  by - cz = E. For each mesh a similar equation may be formed. Hence we
+  have as many linear equations as there are meshes, and we can obtain
+  the solution for each cycle symbol, and therefore for the current in
+  each branch. The solution giving the current in such branch of the
+  network is therefore always in the form of the quotient of two
+  determinants. The solution of the well-known problem of finding the
+  current in the galvanometer circuit of the arrangement of linear
+  conductors called Wheatstone's Bridge is thus easily obtained. For if
+  we call the cycles (see fig. 7) (x + y), y and z, and the resistances
+  P, Q, R, S, G and B, and if E be the electromotive force in the
+  battery circuit, we have the cycle equations
+
+    (P + G + R)(x + y) - Gy - Rz = 0,
+    (Q + G + S)y - G(x + y) - Sz = 0,
+    (R + S + B)z - R(x + y) - Sy = E.
+
+  [Illustration: FIG. 7.]
+
+  From these we can easily obtain the solution for (x + y) - y = x,
+  which is the current through the galvanometer circuit in the form
+
+    x = E(PS - RQ)[Delta].
+
+  where [Delta] is a certain function of P, Q, R, S, B and G.
+
+  _Currents in Sheets._--In the case of current flow in plane sheets, we
+  have to consider certain points called sources at which the current
+  flows into the sheet, and certain points called sinks at which it
+  leaves. We may investigate, first, the simple case of one source and
+  one sink in an infinite plane sheet of thickness [delta] and
+  conductivity k. Take any point P in the plane at distances R and r
+  from the source and sink respectively. The potential V at P is
+  obviously given by
+
+              Q            r1
+    V = -------------log_e --,
+        2[pi]k[delta]      r2
+
+  where Q is the quantity of electricity supplied by the source per
+  second. Hence the equation to the equipotential curve is r1r2 = a
+  constant.
+
+  If we take a point half-way between the sink and the source as the
+  origin of a system of rectangular co-ordinates, and if the distance
+  between sink and source is equal to p, and the line joining them is
+  taken as the axis of x, then the equation to the equipotential line is
+
+    y^2 + (x + p)^2
+    --------------- = a constant.
+    y^2 + (x - p)^2
+
+  This is the equation of a family of circles having the axis of y for a
+  common radical axis, one set of circles surrounding the sink and
+  another set of circles surrounding the source. In order to discover
+  the form of the stream of current lines we have to determine the
+  orthogonal trajectories to this family of coaxial circles. It is easy
+  to show that the orthogonal trajectory of the system of circles is
+  another system of circles all passing through the sink and the source,
+  and as a corollary of this fact, that the electric resistance of a
+  circular disk of uniform thickness is the same between any two points
+  taken anywhere on its circumference as sink and source. These
+  equipotential lines may be delineated experimentally by attaching the
+  terminals of a battery or batteries to small wires which touch at
+  various places a sheet of tinfoil. Two wires attached to a
+  galvanometer may then be placed on the tinfoil, and one may be kept
+  stationary and the other may be moved about, so that the galvanometer
+  is not traversed by any current. The moving terminal then traces out
+  an equipotential curve. If there are n sinks and sources in a plane
+  conducting sheet, and if r, r', r" be the distances of any point from
+  the sinks, and t, t', t" the distances of the sources, then
+
+    r r' r" ...
+    ----------- = a constant,
+    t t' t" ...
+
+  is the equation to the equipotential lines. The orthogonal
+  trajectories or stream lines have the equation
+
+    [Sigma]([theta] - [theta]') = a constant,
+
+  where [theta] and [theta]' are the angles which the lines drawn from
+  any point in the plane to the sink and corresponding source make with
+  the line joining that sink and source. Generally it may be shown that
+  if there are any number of sinks and sources in an infinite
+  plane-conducting sheet, and if r, [theta] are the polar co-ordinates
+  of any one, then the equation to the equipotential surfaces is given
+  by the equation
+
+    [Sigma](A log_er) = a constant,
+
+  where A is a constant; and the equation to the stream of current lines
+  is
+
+    [Sigma]([theta]) = a constant.
+
+  In the case of electric flow in three dimensions the electric
+  potential must satisfy Laplace's equation, and a solution is therefore
+  found in the form [Sigma](A/r) = a constant, as the equation to an
+  equipotential surface, where r is the distance of any point on that
+  surface from a source or sink.
+
+_Convection Currents._--The subject of convection electric currents has
+risen to great importance in connexion with modern electrical
+investigations. The question whether a statically electrified body in
+motion creates a magnetic field is of fundamental importance.
+Experiments to settle it were first undertaken in the year 1876 by H.A.
+Rowland, at a suggestion of H. von Helmholtz.[8] After preliminary
+experiments, Rowland's first apparatus for testing this hypothesis was
+constructed, as follows:--An ebonite disk was covered with radial strips
+of gold-leaf and placed between two other metal plates which acted as
+screens. The disk was then charged with electricity and set in rapid
+rotation. It was found to affect a delicately suspended pair of astatic
+magnetic needles hung in proximity to the disk just as would, by
+Oersted's rule, a circular electric current coincident with the
+periphery of the disk. Hence the statically-charged but rotating disk
+becomes in effect a circular electric current.
+
+The experiments were repeated and confirmed by W.C. Rontgen (_Wied.
+Ann._, 1888, 35, p. 264; 1890, 40, p. 93) and by F. Himstedt (_Wied.
+Ann._, 1889, 38, p. 560). Later V. Cremieu again repeated them and
+obtained negative results (_Com. rend._, 1900, 130, p. 1544, and 131,
+pp. 578 and 797; 1901, 132, pp. 327 and 1108). They were again very
+carefully reconducted by H. Pender (_Phil. Mag._, 1901, 2, p. 179) and
+by E.P. Adams (id. ib., 285). Pender's work showed beyond any doubt that
+electric convection does produce a magnetic effect. Adams employed
+charged copper spheres rotating at a high speed in place of a disk, and
+was able to prove that the rotation of such spheres produced a magnetic
+field similar to that due to a circular current and agreeing numerically
+with the theoretical value. It has been shown by J.J. Thomson (_Phil.
+Mag._, 1881, 2, p. 236) and O. Heaviside (_Electrical Papers_, vol. ii.
+p. 205) that an electrified sphere, moving with a velocity v and
+carrying a quantity of electricity q, should produce a magnetic force H,
+at a point at a distance [rho] from the centre of the sphere, equal to
+qv sin [theta]/[rho]^2, where [theta] is the angle between the direction
+of [rho] and the motion of the sphere. Adams found the field produced by
+a known electric charge rotating at a known speed had a strength not
+very different from that predetermined by the above formula. An
+observation recorded by R.W. Wood (_Phil. Mag._, 1902, 2, p. 659)
+provides a confirmatory fact. He noticed that if carbon-dioxide strongly
+compressed in a steel bottle is allowed to escape suddenly the cold
+produced solidifies some part of the gas, and the issuing jet is full of
+particles of carbon-dioxide snow. These by friction against the nozzle
+are electrified positively. Wood caused the jet of gas to pass through a
+glass tube 2.5 mm. in diameter, and found that these particles of
+electrified snow were blown through it with a velocity of 2000 ft. a
+second. Moreover, he found that a magnetic needle hung near the tube was
+deflected as if held near an electric current. Hence the positively
+electrified particles in motion in the tube create a magnetic field
+round it.
+
+_Nature of an Electric Current._--The question, What is an electric
+current? is involved in the larger question of the nature of
+electricity. Modern investigations have shown that negative electricity
+is identical with the electrons or corpuscles which are components of
+the chemical atom (see MATTER and ELECTRICITY). Certain lines of
+argument lead to the conclusion that a solid conductor is not only
+composed of chemical atoms, but that there is a certain proportion of
+free electrons present in it, the electronic density or number per unit
+of volume being determined by the material, its temperature and other
+physical conditions. If any cause operates to add or remove electrons at
+one point there is an immediate diffusion of electrons to re-establish
+equilibrium, and this electronic movement constitutes an electric
+current. This hypothesis explains the reason for the identity between
+the laws of diffusion of matter, of heat and of electricity.
+Electromotive force is then any cause making or tending to make an
+inequality of electronic density in conductors, and may arise from
+differences of temperature, i.e. thermoelectromotive force (see
+THERMOELECTRICITY), or from chemical action when part of the circuit is
+an electrolytic conductor, or from the movement of lines of magnetic
+force across the conductor.
+
+  BIBLIOGRAPHY.--For additional information the reader may be referred
+  to the following books: M. Faraday, _Experimental Researches in
+  Electricity_ (3 vols., London, 1839, 1844, 1855); J. Clerk Maxwell,
+  _Electricity and Magnetism_ (2 vols., Oxford, 1892); W. Watson and
+  S.H. Burbury, _Mathematical Theory of Electricity and Magnetism_, vol.
+  ii. (Oxford, 1889); E. Mascart and J. Joubert, _A Treatise on
+  Electricity and Magnetism_ (2 vols., London, 1883); A. Hay,
+  _Alternating Currents_ (London, 1905); W.G. Rhodes, _An Elementary
+  Treatise on Alternating Currents_ (London, 1902); D.C. Jackson and
+  J.P. Jackson, _Alternating Currents and Alternating Current Machinery_
+  (1896, new ed. 1903); S.P. Thompson, _Polyphase Electric Currents_
+  (London, 1900); _Dynamo-Electric Machinery_, vol. ii., "Alternating
+  Currents" (London, 1905); E.E. Fournier d'Albe, _The Electron Theory_
+  (London, 1906).     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] See J.A. Fleming, _The Alternate Current Transformer_, vol. i. p.
+    519.
+
+  [2] See Maxwell, _Electricity and Magnetism_, vol. ii. chap. ii.
+
+  [3] See Maxwell, _Electricity and Magnetism_, vol. ii. 642.
+
+  [4] _Experimental Researches_, vol. i. ser. 1.
+
+  [5] See Maxwell, _Electricity and Magnetism_, vol. ii. S 542, p. 178.
+
+  [6] See W.G. Rhodes, _An Elementary Treatise on Alternating Currents_
+    (London, 1902), chap. vii.
+
+  [7] See J.A. Fleming, "Problems on the Distribution of Electric
+    Currents in Networks of Conductors," _Phil. Mag_. (1885), or Proc.
+    Phys. Soc. Lond. (1885), 7; also Maxwell, _Electricity and Magnetism_
+    (2nd ed.), vol. i. p. 374, S 280, 282b.
+
+  [8] See _Berl. Acad. Ber._, 1876, p. 211; also H.A. Rowland and C.T.
+    Hutchinson, "On the Electromagnetic Effect of Convection Currents,"
+    _Phil. Mag._, 1889, 27, p. 445.
+
+
+
+
+ELECTROLIER, a fixture, usually pendent from the ceiling, for holding
+electric lamps. The word is analogous to chandelier, from which indeed
+it was formed.
+
+
+
+
+ELECTROLYSIS (formed from Gr. [Greek: lyein], to loosen). When the
+passage of an electric current through a substance is accompanied by
+definite chemical changes which are independent of the heating effects
+of the current, the process is known as _electrolysis_, and the
+substance is called an _electrolyte_. As an example we may take the case
+of a solution of a salt such as copper sulphate in water, through which
+an electric current is passed between copper plates. We shall then
+observe the following phenomena. (1) The bulk of the solution is
+unaltered, except that its temperature may be raised owing to the usual
+heating effect which is proportional to the square of the strength of
+the current. (2) The copper plate by which the current is said to enter
+the solution, i.e. the plate attached to the so-called positive terminal
+of the battery or other source of current, dissolves away, the copper
+going into solution as copper sulphate. (3) Copper is deposited on the
+surface of the other plate, being obtained from the solution. (4)
+Changes in concentration are produced in the neighbourhood of the two
+plates or electrodes. In the case we have chosen, the solution becomes
+stronger near the anode, or electrode at which the current enters, and
+weaker near the cathode, or electrode at which it leaves the solution.
+If, instead of using copper electrodes, we take plates of platinum,
+copper is still deposited on the cathode; but, instead of the anode
+dissolving, free sulphuric acid appears in the neighbouring solution,
+and oxygen gas is evolved at the surface of the platinum plate.
+
+With other electrolytes similar phenomena appear, though the primary
+chemical changes may be masked by secondary actions. Thus, with a dilute
+solution of sulphuric acid and platinum electrodes, hydrogen gas is
+evolved at the cathode, while, as the result of a secondary action on
+the anode, sulphuric acid is there re-formed, and oxygen gas evolved.
+Again, with the solution of a salt such as sodium chloride, the sodium,
+which is primarily liberated at the cathode, decomposes the water and
+evolves hydrogen, while the chlorine may be evolved as such, may
+dissolve the anode, or may liberate oxygen from the water, according to
+the nature of the plate and the concentration of the solution.
+
+_Early History of Electrolysis._--Alessandro Volta of Pavia discovered
+the electric battery in the year 1800, and thus placed the means of
+maintaining a steady electric current in the hands of investigators,
+who, before that date, had been restricted to the study of the isolated
+electric charges given by frictional electric machines. Volta's cell
+consists essentially of two plates of different metals, such as zinc and
+copper, connected by an electrolyte such as a solution of salt or acid.
+Immediately on its discovery intense interest was aroused in the new
+invention, and the chemical effects of electric currents were speedily
+detected. W. Nicholson and Sir A. Carlisle found that hydrogen and
+oxygen were evolved at the surfaces of gold and platinum wires connected
+with the terminals of a battery and dipped in water. The volume of the
+hydrogen was about double that of the oxygen, and, since this is the
+ratio in which these elements are combined in water, it was concluded
+that the process consisted essentially in the decomposition of water.
+They also noticed that a similar kind of chemical action went on in the
+battery itself. Soon afterwards, William Cruickshank decomposed the
+magnesium, sodium and ammonium chlorides, and precipitated silver and
+copper from their solutions--an observation which led to the process of
+electroplating. He also found that the liquid round the anode became
+acid, and that round the cathode alkaline. In 1804 W. Hisinger and J.J.
+Berzelius stated that neutral salt solutions could be decomposed by
+electricity, the acid appearing at one pole and the metal at the other.
+This observation showed that nascent hydrogen was not, as had been
+supposed, the primary cause of the separation of metals from their
+solutions, but that the action consisted in a direct decomposition into
+metal and acid. During the earliest investigation of the subject it was
+thought that, since hydrogen and oxygen were usually evolved, the
+electrolysis of solutions of acids and alkalis was to be regarded as a
+direct decomposition of water. In 1806 Sir Humphry Davy proved that the
+formation of acid and alkali when water was electrolysed was due to
+saline impurities in the water. He had shown previously that
+decomposition of water could be effected although the two poles were
+placed in separate vessels connected by moistened threads. In 1807 he
+decomposed potash and soda, previously considered to be elements, by
+passing the current from a powerful battery through the moistened
+solids, and thus isolated the metals potassium and sodium.
+
+The electromotive force of Volta's simple cell falls off rapidly when
+the cell is used, and this phenomenon was shown to be due to the
+accumulation at the metal plates of the products of chemical changes in
+the cell itself. This reverse electromotive force of polarization is
+produced in all electrolytes when the passage of the current changes the
+nature of the electrodes. In batteries which use acids as the
+electrolyte, a film of hydrogen tends to be deposited on the copper or
+platinum electrode; but, to obtain a constant electromotive force,
+several means were soon devised of preventing the formation of the film.
+Constant cells may be divided into two groups, according as their action
+is chemical (as in the bichromate cell, where the hydrogen is converted
+into water by an oxidizing agent placed in a porous pot round the carbon
+plate) or electrochemical (as in Daniell's cell, where a copper plate is
+surrounded by a solution of copper sulphate, and the hydrogen, instead
+of being liberated, replaces copper, which is deposited on the plate
+from the solution).
+
+[Illustration: FIG. 1.]
+
+_Faraday's Laws._--The first exact quantitative study of electrolytic
+phenomena was made about 1830 by Michael Faraday (_Experimental
+Researches_, 1833). When an electric current flows round a circuit,
+there is no accumulation of electricity anywhere in the circuit, hence
+the current strength is everywhere the same, and we may picture the
+current as analogous to the flow of an incompressible fluid. Acting on
+this view, Faraday set himself to examine the relation between the flow
+of electricity round the circuit and the amount of chemical
+decomposition. He passed the current driven by a voltaic battery ZnPt
+(fig. 1) through two branches containing the two electrolytic cells A
+and B. The reunited current was then led through another cell C, in
+which the strength of the current must be the sum of those in the arms A
+and B. Faraday found that the mass of substance liberated at the
+electrodes in the cell C was equal to the sum of the masses liberated in
+the cells A and B. He also found that, for the same current, the amount
+of chemical action was independent of the size of the electrodes and
+proportional to the time that the current flowed. Regarding the current
+as the passage of a certain amount of electricity per second, it will be
+seen that the results of all these experiments may be summed up in the
+statement that the amount of chemical action is proportional to the
+quantity of electricity which passes through the cell.
+
+Faraday's next step was to pass the same current through different
+electrolytes in series. He found that the amounts of the substances
+liberated in each cell were proportional to the chemical equivalent
+weights of those substances. Thus, if the current be passed through
+dilute sulphuric acid between hydrogen electrodes, and through a
+solution of copper sulphate, it will be found that the mass of hydrogen
+evolved in the first cell is to the mass of copper deposited in the
+second as 1 is to 31.8. Now this ratio is the same as that which gives
+the relative chemical equivalents of hydrogen and copper, for 1 gramme
+of hydrogen and 31.8 grammes of copper unite chemically with the same
+weight of any acid radicle such as chlorine or the sulphuric group, SO4.
+Faraday examined also the electrolysis of certain fused salts such as
+lead chloride and silver chloride. Similar relations were found to hold
+and the amounts of chemical change to be the same for the same electric
+transfer as in the case of solutions.
+
+We may sum up the chief results of Faraday's work in the statements
+known as Faraday's laws: The mass of substance liberated from an
+electrolyte by the passage of a current is proportional (1) to the total
+quantity of electricity which passes through the electrolyte, and (2) to
+the chemical equivalent weight of the substance liberated.
+
+Since Faraday's time his laws have been confirmed by modern research,
+and in favourable cases have been shown to hold good with an accuracy of
+at least one part in a thousand. The principal object of this more
+recent research has been the determination of the quantitative amount of
+chemical change associated with the passage for a given time of a
+current of strength known in electromagnetic units. It is found that the
+most accurate and convenient apparatus to use is a platinum bowl filled
+with a solution of silver nitrate containing about fifteen parts of the
+salt to one hundred of water. Into the solution dips a silver plate
+wrapped in filter paper, and the current is passed from the silver plate
+as anode to the bowl as cathode. The bowl is weighed before and after
+the passage of the current, and the increase gives the mass of silver
+deposited. The mean result of the best determinations shows that when a
+current of one ampere is passed for one second, a mass of silver is
+deposited equal to 0.001118 gramme. So accurate and convenient is this
+determination that it is now used conversely as a practical definition
+of the ampere, which (defined theoretically in terms of magnetic force)
+is defined practically as the current which in one second deposits 1.118
+milligramme of silver.
+
+Taking the chemical equivalent weight of silver, as determined by
+chemical experiments, to be 107.92, the result described gives as the
+electrochemical equivalent of an ion of unit chemical equivalent the
+value 1.036 X 10^(-5). If, as is now usual, we take the equivalent
+weight of oxygen as our standard and call it 16, the equivalent weight
+of hydrogen is 1.008, and its electrochemical equivalent is 1.044 X
+10^(-5). The electrochemical equivalent of any other substance, whether
+element or compound, may be found by multiplying its chemical equivalent
+by 1.036 X 10^(-5). If, instead of the ampere, we take the C.G.S.
+electromagnetic unit of current, this number becomes 1.036 X 10^(-4).
+
+_Chemical Nature of the Ions._--A study of the products of decomposition
+does not necessarily lead directly to a knowledge of the ions actually
+employed in carrying the current through the electrolyte. Since the
+electric forces are active throughout the whole solution, all the ions
+must come under its influence and therefore move, but their separation
+from the electrodes is determined by the electromotive force needed to
+liberate them. Thus, as long as every ion of the solution is present in
+the layer of liquid next the electrode, the one which responds to the
+least electromotive force will alone be set free. When the amount of
+this ion in the surface layer becomes too small to carry all the current
+across the junction, other ions must also be used, and either they or
+their secondary products will appear also at the electrode. In aqueous
+solutions, for instance, a few hydrogen (H) and hydroxyl (OH) ions
+derived from the water are always present, and will be liberated if the
+other ions require a higher decomposition voltage and the current be
+kept so small that hydrogen and hydroxyl ions can be formed fast enough
+to carry all the current across the junction between solution and
+electrode.
+
+The issue is also obscured in another way. When the ions are set free at
+the electrodes, they may unite with the substance of the electrode or
+with some constituent of the solution to form secondary products. Thus
+the hydroxyl mentioned above decomposes into water and oxygen, and the
+chlorine produced by the electrolysis of a chloride may attack the metal
+of the anode. This leads us to examine more closely the part played by
+water in the electrolysis of aqueous solutions. Distilled water is a
+very bad conductor, though, even when great care is taken to remove all
+dissolved bodies, there is evidence to show that some part of the trace
+of conductivity remaining is due to the water itself. By careful
+redistillation F. Kohlrausch has prepared water of which the
+conductivity compared with that of mercury was only 0.40 X 10^(-11) at
+18 deg. C. Even here some little impurity was present, and the
+conductivity of chemically pure water was estimated by thermodynamic
+reasoning as 0.36 X 10^(-11) at 18 deg. C. As we shall see later, the
+conductivity of very dilute salt solutions is proportional to the
+concentration, so that it is probable that, in most cases, practically
+all the current is carried by the salt. At the electrodes, however, the
+small quantity of hydrogen and hydroxyl ions from the water are
+liberated first in cases where the ions of the salt have a higher
+decomposition voltage. The water being present in excess, the hydrogen
+and hydroxyl are re-formed at once and therefore are set free
+continuously. If the current be so strong that new hydrogen and hydroxyl
+ions cannot be formed in time, other substances are liberated; in a
+solution of sulphuric acid a strong current will evolve sulphur dioxide,
+the more readily as the concentration of the solution is increased.
+Similar phenomena are seen in the case of a solution of hydrochloric
+acid. When the solution is weak, hydrogen and oxygen are evolved; but,
+as the concentration is increased, and the current raised, more and more
+chlorine is liberated.
+
+  An interesting example of secondary action is shown by the common
+  technical process of electroplating with silver from a bath of
+  potassium silver cyanide. Here the ions are potassium and the group
+  Ag(CN)2.[1] Each potassium ion as it reaches the cathode precipitates
+  silver by reacting with the solution in accordance with the chemical
+  equation
+
+    K + KAg(CN)2 = 2KCN + Ag,
+
+  while the anion Ag(CN)2 dissolves an atom of silver from the anode,
+  and re-forms the complex cyanide KAg(CN)2 by combining with the 2KCN
+  produced in the reaction described in the equation. If the anode
+  consist of platinum, cyanogen gas is evolved thereat from the anion
+  Ag(CN)2, and the platinum becomes covered with the insoluble silver
+  cyanide, AgCN, which soon stops the current. The coating of silver
+  obtained by this process is coherent and homogeneous, while that
+  deposited from a solution of silver nitrate, as the result of the
+  primary action of the current, is crystalline and easily detached.
+
+  In the electrolysis of a concentrated solution of sodium acetate,
+  hydrogen is evolved at the cathode and a mixture of ethane and carbon
+  dioxide at the anode. According to H. Jahn,[2] the processes at the
+  anode can be represented by the equations
+
+    2CH3.COO + H2O = 2CH3.COOH + O
+
+    2CH3.COOH + O = C2H6 + 2CO2 + H2O.
+
+  The hydrogen at the cathode is developed by the secondary action
+
+    2Na + 2H2O = 2NaOH + H2.
+
+  Many organic compounds can be prepared by taking advantage of
+  secondary actions at the electrodes, such as reduction by the cathodic
+  hydrogen, or oxidation at the anode (see ELECTROCHEMISTRY).
+
+  It is possible to distinguish between double salts and salts of
+  compound acids. Thus J.W. Hittorf showed that when a current was
+  passed through a solution of sodium platino-chloride, the platinum
+  appeared at the anode. The salt must therefore be derived from an
+  acid, chloroplatinic acid, H2PtCl6, and have the formula Na2PtCl6, the
+  ions being Na and PtCl6", for if it were a double salt it would
+  decompose as a mixture of sodium chloride and platinum chloride and
+  both metals would go to the cathode.
+
+_Early Theories of Electrolysis._--The obvious phenomena to be explained
+by any theory of electrolysis are the liberation of the products of
+chemical decomposition at the two electrodes while the intervening
+liquid is unaltered. To explain these facts, Theodor Grotthus
+(1785-1822) in 1806 put forward an hypothesis which supposed that the
+opposite chemical constituents of an electrolyte interchanged partners
+all along the line between the electrodes when a current passed. Thus,
+if the molecule of a substance in solution is represented by AB,
+Grotthus considered a chain of AB molecules to exist from one electrode
+to the other. Under the influence of an applied electric force, he
+imagined that the B part of the first molecule was liberated at the
+anode, and that the A part thus isolated united with the B part of the
+second molecule, which, in its turn, passed on its A to the B of the
+third molecule. In this manner, the B part of the last molecule of the
+chain was seized by the A of the last molecule but one, and the A part
+of the last molecule liberated at the surface of the cathode.
+
+Chemical phenomena throw further light on this question. If two
+solutions containing the salts AB and CD be mixed, double decomposition
+is found to occur, the salts AD and CB being formed till a certain part
+of the first pair of substances is transformed into an equivalent amount
+of the second pair. The proportions between the four salts AB, CD, AD
+and CB, which exist finally in solution, are found to be the same
+whether we begin with the pair AB and CD or with the pair AD and CB. To
+explain this result, chemists suppose that both changes can occur
+simultaneously, and that equilibrium results when the rate at which AB
+and CD are transformed into AD and CB is the same as the rate at which
+the reverse change goes on. A freedom of interchange is thus indicated
+between the opposite parts of the molecules of salts in solution, and it
+follows reasonably that with the solution of a single salt, say sodium
+chloride, continual interchanges go on between the sodium and chlorine
+parts of the different molecules.
+
+These views were applied to the theory of electrolysis by R.J.E.
+Clausius. He pointed out that it followed that the electric forces did
+not cause the interchanges between the opposite parts of the dissolved
+molecules but only controlled their direction. Interchanges must be
+supposed to go on whether a current passes or not, the function of the
+electric forces in electrolysis being merely to determine in what
+direction the parts of the molecules shall work their way through the
+liquid and to effect actual separation of these parts (or their
+secondary products) at the electrodes. This conclusion is supported also
+by the evidence supplied by the phenomena of electrolytic conduction
+(see CONDUCTION, ELECTRIC, S II.). If we eliminate the reverse
+electromotive forces of polarization at the two electrodes, the
+conduction of electricity through electrolytes is found to conform to
+Ohm's law; that is, once the polarization is overcome, the current is
+proportional to the electromotive force applied to the bulk of the
+liquid. Hence there can be no reverse forces of polarization inside the
+liquid itself, such forces being confined to the surface of the
+electrodes. No work is done in separating the parts of the molecules
+from each other. This result again indicates that the parts of the
+molecules are effectively separate from each other, the function of the
+electric forces being merely directive.
+
+_Migration of the Ions._--The opposite parts of an electrolyte, which
+work their way through the liquid under the action of the electric
+forces, were named by Faraday the ions--the travellers. The changes of
+concentration which occur in the solution near the two electrodes were
+referred by W. Hittorf (1853) to the unequal speeds with which he
+supposed the two opposite ions to travel. It is clear that, when two
+opposite streams of ions move past each other, equivalent quantities are
+liberated at the two ends of the system. If the ions move at equal
+rates, the salt which is decomposed to supply the ions liberated must be
+taken equally from the neighbourhood of the two electrodes. But if one
+ion, say the anion, travels faster through the liquid than the other,
+the end of the solution from which it comes will be more exhausted of
+salt than the end towards which it goes. If we assume that no other
+cause is at work, it is easy to prove that, with non-dissolvable
+electrodes, the ratio of salt lost at the anode to the salt lost at the
+cathode must be equal to the ratio of the velocity of the cation to the
+velocity of the anion. This result may be illustrated by fig. 2. The
+black circles represent one ion and the white circles the other. If the
+black ions move twice as fast as the white ones, the state of things
+after the passage of a current will be represented by the lower part of
+the figure. Here the middle part of the solution is unaltered and the
+number of ions liberated is the same at either end, but the amount of
+salt left at one end is less than that at the other. On the right,
+towards which the faster ion travels, five molecules of salt are left,
+being a loss of two from the original seven. On the left, towards which
+the slower ion moves, only three molecules remain--a loss of four. Thus,
+the ratio of the losses at the two ends is two to one--the same as the
+ratio of the assumed ionic velocities. It should be noted, however, that
+another cause would be competent to explain the unequal dilution of the
+two solutions. If either ion carried with it some of the unaltered salt
+or some of the solvent, concentration or dilution of the liquid would be
+produced where the ion was liberated. There is reason to believe that in
+certain cases such complex ions do exist, and interfere with the results
+of the differing ionic velocities.
+
+[Illustration: FIG. 2.]
+
+Hittorf and many other observers have made experiments to determine the
+unequal dilution of a solution round the two electrodes when a current
+passes. Various forms of apparatus have been used, the principle of them
+all being to secure efficient separation of the two volumes of solution
+in which the changes occur. In some cases porous diaphragms have been
+employed; but such diaphragms introduce a new complication, for the
+liquid as a whole is pushed through them by the action of the current,
+the phenomenon being known as electric endosmose. Hence experiments
+without separating diaphragms are to be preferred, and the apparatus may
+be considered effective when a considerable bulk of intervening solution
+is left unaltered in composition. It is usual to express the results in
+terms of what is called the migration constant of the anion, that is,
+the ratio of the amount of salt lost by the anode vessel to the whole
+amount lost by both vessels. Thus the statement that the migration
+constant or transport number for a decinormal solution of copper
+sulphate is 0.632 implies that of every gramme of copper sulphate lost
+by a solution containing originally one-tenth of a gramme equivalent per
+litre when a current is passed through it between platinum electrodes,
+0.632 gramme is taken from the cathode vessel and 0.368 gramme from the
+anode vessel. For certain concentrated solutions the transport number is
+found to be greater than unity; thus for a normal solution of cadmium
+iodide its value is 1.12. On the theory that the phenomena are wholly
+due to unequal ionic velocities this result would mean that the cation
+like the anion moved against the conventional direction of the current.
+That a body carrying a positive electric charge should move against the
+direction of the electric intensity is contrary to all our notions of
+electric forces, and we are compelled to seek some other explanation. An
+alternative hypothesis is given by the idea of complex ions. If some of
+the anions, instead of being simple iodine ions represented chemically
+by the symbol I, are complex structures formed by the union of iodine
+with unaltered cadmium iodide--structures represented by some such
+chemical formula as I(CdI2), the concentration of the solution round the
+anode would be increased by the passage of an electric current, and the
+phenomena observed would be explained. It is found that, in such cases
+as this, where it seems necessary to imagine the existence of complex
+ions, the transport number changes rapidly as the concentration of the
+original solution is changed. Thus, diminishing the concentration of the
+cadmium iodine solution from normal to one-twentieth normal changes the
+transport number from 1.12 to 0.64. Hence it is probable that in cases
+where the transport number keeps constant with changing concentration
+the hypothesis of complex ions is unnecessary, and we may suppose that
+the transport number is a true migration constant from which the
+relative velocities of the two ions may be calculated in the matter
+suggested by Hittorf and illustrated in fig. 2. This conclusion is
+confirmed by the results of the direct visual determination of ionic
+velocities (see CONDUCTION, ELECTRIC, S II.), which, in cases where the
+transport number remains constant, agree with the values calculated from
+those numbers. Many solutions in which the transport numbers vary at
+high concentration often become simple at greater dilution. For
+instance, to take the two solutions to which we have already referred,
+we have--
+
+  +----------------------------------+------+------+------+------+------+------+------+-----+-----------+
+  |Concentration                     | 2.0  | 1.5  | 1.0  | 0.5  | 0.2  | 0.1  | 0.05 | 0.02|0.01 normal|
+  |Copper sulphate transport numbers | 0.72 | 0.714| 0.696| 0.668| 0.643| 0.632| 0.626| 0.62|     ..    |
+  |Cadmium iodide     "         "    | 1.22 | 1.18 | 1.12 | 1.00 | 0.83 | 0.71 | 0.64 | 0.59|0.56       |
+  +----------------------------------+------+------+------+------+------+------+------+-----+-----------+
+
+It is probable that in both these solutions complex ions exist at fairly
+high concentrations, but gradually gets less in number and finally
+disappear as the dilution is increased. In such salts as potassium
+chloride the ions seem to be simple throughout a wide range of
+concentration since the transport numbers for the same series of
+concentrations as those used above run--
+
+  Potassium chloride--
+  0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.507, 0.506.
+
+The next important step in the theory of the subject was made by F.
+Kohlrausch in 1879. Kohlrausch formulated a theory of electrolytic
+conduction based on the idea that, under the action of the electric
+forces, the oppositely charged ions moved in opposite directions through
+the liquid, carrying their charges with them. If we eliminate the
+polarization at the electrodes, it can be shown that an electrolyte
+possesses a definite electric resistance and therefore a definite
+conductivity. The conductivity gives us the amount of electricity
+conveyed per second under a definite electromotive force. On the view of
+the process of conduction described above, the amount of electricity
+conveyed per second is measured by the product of the number of ions,
+known from the concentration of the solution, the charge carried by each
+of them, and the velocity with which, on the average, they move through
+the liquid. The concentration is known, and the conductivity can be
+measured experimentally; thus the average velocity with which the ions
+move past each other under the existent electromotive force can be
+estimated. The velocity with which the ions move past each other is
+equal to the sum of their individual velocities, which can therefore be
+calculated. Now Hittorf's transport number, in the case of simple salts
+in moderately dilute solution, gives us the ratio between the two ionic
+velocities. Hence the absolute velocities of the two ions can be
+determined, and we can calculate the actual speed with which a certain
+ion moves through a given liquid under the action of a given potential
+gradient or electromotive force. The details of the calculation are
+given in the article CONDUCTION, ELECTRIC, S II., where also will be
+found an account of the methods which have been used to measure the
+velocities of many ions by direct visual observation. The results go to
+show that, where the existence of complex ions is not indicated by
+varying transport numbers, the observed velocities agree with those
+calculated on Kohlrausch's theory.
+
+_Dissociation Theory._--The verification of Kohlrausch's theory of ionic
+velocity verifies also the view of electrolysis which regards the
+electric current as due to streams of ions moving in opposite directions
+through the liquid and carrying their opposite electric charges with
+them. There remains the question how the necessary migratory freedom of
+the ions is secured. As we have seen, Grotthus imagined that it was the
+electric forces which sheared the ions past each other and loosened the
+chemical bonds holding the opposite parts of each dissolved molecule
+together. Clausius extended to electrolysis the chemical ideas which
+looked on the opposite parts of the molecule as always changing partners
+independently of any electric force, and regarded the function of the
+current as merely directive. Still, the necessary freedom was supposed
+to be secured by interchanges of ions between molecules at the instants
+of molecular collision only; during the rest of the life of the ions
+they were regarded as linked to each other to form electrically neutral
+molecules.
+
+In 1887 Svante Arrhenius, professor of physics at Stockholm, put forward
+a new theory which supposed that the freedom of the opposite ions from
+each other was not a mere momentary freedom at the instants of molecular
+collision, but a more or less permanent freedom, the ions moving
+independently of each other through the liquid. The evidence which led
+Arrhenius to this conclusion was based on van 't Hoff's work on the
+osmotic pressure of solutions (see SOLUTION). If a solution, let us say
+of sugar, be confined in a closed vessel through the walls of which the
+solvent can pass but the solution cannot, the solvent will enter till a
+certain equilibrium pressure is reached. This equilibrium pressure is
+called the osmotic pressure of the solution, and thermodynamic theory
+shows that, in an ideal case of perfect separation between solvent and
+solute, it should have the same value as the pressure which a number of
+molecules equal to the number of solute molecules in the solution would
+exert if they could exist as a gas in a space equal to the volume of the
+solution, provided that the space was large enough (i.e. the solution
+dilute enough) for the intermolecular forces between the dissolved
+particles to be inappreciable. Van 't Hoff pointed out that measurements
+of osmotic pressure confirmed this value in the case of dilute solutions
+of cane sugar.
+
+Thermodynamic theory also indicates a connexion between the osmotic
+pressure of a solution and the depression of its freezing point and its
+vapour pressure compared with those of the pure solvent. The freezing
+points and vapour pressures of solutions of sugar are also in conformity
+with the theoretical numbers. But when we pass to solutions of mineral
+salts and acids--to solutions of electrolytes in fact--we find that the
+observed values of the osmotic pressures and of the allied phenomena are
+greater than the normal values. Arrhenius pointed out that these
+exceptions would be brought into line if the ions of electrolytes were
+imagined to be separate entities each capable of producing its own
+pressure effects just as would an ordinary dissolved molecule.
+
+Two relations are suggested by Arrhenius' theory. (1) In very dilute
+solutions of simple substances, where only one kind of dissociation is
+possible and the dissociation of the ions is complete, the number of
+pressure-producing particles necessary to produce the observed osmotic
+effects should be equal to the number of ions given by a molecule of the
+salt as shown by its electrical properties. Thus the osmotic pressure,
+or the depression of the freezing point of a solution of potassium
+chloride should, at extreme dilution, be twice the normal value, but of
+a solution of sulphuric acid three times that value, since the potassium
+salt contains two ions and the acid three. (2) As the concentration of
+the solutions increases, the ionization as measured electrically and the
+dissociation as measured osmotically might decrease more or less
+together, though, since the thermodynamic theory only holds when the
+solution is so dilute that the dissolved particles are beyond each
+other's sphere of action, there is much doubt whether this second
+relation is valid through any appreciable range of concentration.
+
+At present, measurements of freezing point are more convenient and
+accurate than those of osmotic pressure, and we may test the validity of
+Arrhenius' relations by their means. The theoretical value for the
+depression of the freezing point of a dilute solution per
+gramme-equivalent of solute per litre is 1.857 deg. C. Completely
+ionized solutions of salts with two ions should give double this number
+or 3.714 deg., while electrolytes with three ions should have a value of
+5.57 deg.
+
+The following results are given by H.B. Loomis for the concentration of
+0.01 gramme-molecule of salt to one thousand grammes of water. The salts
+tabulated are those of which the equivalent conductivity reaches a
+limiting value indicating that complete ionization is reached as
+dilution is increased. With such salts alone is a valid comparison
+possible.
+
+  _Molecular Depressions of the Freezing Point._
+
+  _Electrolytes with two Ions._
+
+  Potassium chloride  3.60
+  Sodium chloride     3.67
+  Potassium hydrate   3.71
+  Hydrochloric acid   3.61
+  Nitric acid         3.73
+  Potassium nitrate   3.46
+  Sodium nitrate      3.55
+  Ammonium nitrate    3.58
+
+  _Electrolytes with three Ions._
+
+  Sulphuric acid      4.49
+  Sodium sulphate     5.09
+  Calcium chloride    5.04
+  Magnesium chloride  5.08
+
+At the concentration used by Loomis the electrical conductivity
+indicates that the ionization is not complete, particularly in the case
+of the salts with divalent ions in the second list. Allowing for
+incomplete ionization the general concordance of these numbers with the
+theoretical ones is very striking.
+
+The measurements of freezing points of solutions at the extreme dilution
+necessary to secure complete ionization is a matter of great difficulty,
+and has been overcome only in a research initiated by E.H. Griffiths.[3]
+Results have been obtained for solutions of sugar, where the
+experimental number is 1.858, and for potassium chloride, which gives a
+depression of 3.720. These numbers agree with those indicated by theory,
+viz. 1.857 and 3.714, with astonishing exactitude. We may take
+Arrhenius' first relation as established for the case of potassium
+chloride.
+
+The second relation, as we have seen, is not a strict consequence of
+theory, and experiments to examine it must be treated as an
+investigation of the limits within which solutions are dilute within the
+thermodynamic sense of the word, rather than as a test of the soundness
+of the theory. It is found that divergence has begun before the
+concentration has become great enough to enable freezing points to be
+measured with any ordinary apparatus. The freezing point curve usually
+lies below the electrical one, but approaches it as dilution is
+increased.[4]
+
+Returning once more to the consideration of the first relation, which
+deals with the comparison between the number of ions and the number of
+pressure-producing particles in dilute solution, one caution is
+necessary. In simple substances like potassium chloride it seems evident
+that one kind of dissociation only is possible. The electrical phenomena
+show that there are two ions to the molecule, and that these ions are
+electrically charged. Corresponding with this result we find that the
+freezing point of dilute solutions indicates that two pressure-producing
+particles per molecule are present. But the converse relation does not
+necessarily follow. It would be possible for a body in solution to be
+dissociated into non-electrical parts, which would give osmotic pressure
+effects twice or three times the normal value, but, being uncharged,
+would not act as ions and impart electrical conductivity to the
+solution. L. Kahlenberg (_Jour. Phys. Chem._, 1901, v. 344, 1902, vi.
+43) has found that solutions of diphenylamine in methyl cyanide possess
+an excess of pressure-producing particles and yet are non-conductors of
+electricity. It is possible that in complicated organic substances we
+might have two kinds of dissociation, electrical and non-electrical,
+occurring simultaneously, while the possibility of the association of
+molecules accompanied by the electrical dissociation of some of them
+into new parts should not be overlooked. It should be pointed out that
+no measurements on osmotic pressures or freezing points can do more than
+tell us that an excess of particles is present; such experiments can
+throw no light on the question whether or not those particles are
+electrically charged. That question can only be answered by examining
+whether or not the particles move in an electric field.
+
+The dissociation theory was originally suggested by the osmotic pressure
+relations. But not only has it explained satisfactorily the electrical
+properties of solutions, but it seems to be the only known hypothesis
+which is consistent with the experimental relation between the
+concentration of a solution and its electrical conductivity (see
+CONDUCTION, ELECTRIC, S II., "Nature of Electrolytes"). It is probable
+that the electrical effects constitute the strongest arguments in favour
+of the theory. It is necessary to point out that the dissociated ions of
+such a body as potassium chloride are not in the same condition as
+potassium and chlorine in the free state. The ions are associated with
+very large electric charges, and, whatever their exact relations with
+those charges may be, it is certain that the energy of a system in such
+a state must be different from its energy when unelectrified. It is not
+unlikely, therefore, that even a compound as stable in the solid form as
+potassium chloride should be thus dissociated when dissolved. Again,
+water, the best electrolytic solvent known, is also the body of the
+highest specific inductive capacity (dielectric constant), and this
+property, to whatever cause it may be due, will reduce the forces
+between electric charges in the neighbourhood, and may therefore enable
+two ions to separate.
+
+This view of the nature of electrolytic solutions at once explains many
+well-known phenomena. Other physical properties of these solutions, such
+as density, colour, optical rotatory power, &c., like the
+conductivities, are _additive_, i.e. can be calculated by adding
+together the corresponding properties of the parts. This again suggests
+that these parts are independent of each other. For instance, the colour
+of a salt solution is the colour obtained by the superposition of the
+colours of the ions and the colour of any undissociated salt that may be
+present. All copper salts in dilute solution are blue, which is
+therefore the colour of the copper ion. Solid copper chloride is brown
+or yellow, so that its concentrated solution, which contains both ions
+and undissociated molecules, is green, but changes to blue as water is
+added and the ionization becomes complete. A series of equivalent
+solutions all containing the same coloured ion have absorption spectra
+which, when photographed, show identical absorption bands of equal
+intensity.[5] The colour changes shown by many substances which are used
+as indicators (q.v.) of acids or alkalis can be explained in a similar
+way. Thus para-nitrophenol has colourless molecules, but an intensely
+yellow negative ion. In neutral, and still more in acid solutions, the
+dissociation of the indicator is practically nothing, and the liquid is
+colourless. If an alkali is added, however, a highly dissociated salt of
+para-nitrophenol is formed, and the yellow colour is at once evident. In
+other cases, such as that of litmus, both the ion and the undissociated
+molecule are coloured, but in different ways.
+
+Electrolytes possess the power of coagulating solutions of colloids such
+as albumen and arsenious sulphide. The mean values of the relative
+coagulative powers of sulphates of mono-, di-, and tri-valent metals
+have been shown experimentally to be approximately in the ratios
+1:35:1023. The dissociation theory refers this to the action of electric
+charges carried by the free ions. If a certain minimum charge must be
+collected in order to start coagulation, it will need the conjunction of
+6n monovalent, or 3n divalent, to equal the effect of 2n tri-valent
+ions. The ratios of the coagulative powers can thus be calculated to be
+1:x:x^2, and putting x = 32 we get 1:32:1024, a satisfactory agreement
+with the numbers observed.[6]
+
+The question of the application of the dissociation theory to the case
+of fused salts remains. While it seems clear that the conduction in this
+case is carried on by ions similar to those of solutions, since
+Faraday's laws apply equally to both, it does not follow necessarily
+that semi-permanent dissociation is the only way to explain the
+phenomena. The evidence in favour of dissociation in the case of
+solutions does not apply to fused salts, and it is possible that, in
+their case, a series of molecular interchanges, somewhat like Grotthus's
+chain, may represent the mechanism of conduction.
+
+An interesting relation appears when the electrolytic conductivity of
+solutions is compared with their chemical activity. The readiness and
+speed with which electrolytes react are in sharp contrast with the
+difficulty experienced in the case of non-electrolytes. Moreover, a
+study of the chemical relations of electrolytes indicates that it is
+always the electrolytic ions that are concerned in their reactions. The
+tests for a salt, potassium nitrate, for example, are the tests not for
+KNO3, but for its ions K and NO3, and in cases of double decomposition
+it is always these ions that are exchanged for those of other
+substances. If an element be present in a compound otherwise than as an
+ion, it is not interchangeable, and cannot be recognized by the usual
+tests. Thus neither a chlorate, which contains the ion ClO3, nor
+monochloracetic acid, shows the reactions of chlorine, though it is, of
+course, present in both substances; again, the sulphates do not answer
+to the usual tests which indicate the presence of sulphur as sulphide.
+The chemical activity of a substance is a quantity which may be measured
+by different methods. For some substances it has been shown to be
+independent of the particular reaction used. It is then possible to
+assign to each body a specific coefficient of affinity. Arrhenius has
+pointed out that the coefficient of affinity of an acid is proportional
+to its electrolytic ionization.
+
+  The affinities of acids have been compared in several ways. W. Ostwald
+  (_Lehrbuch der allg. Chemie_, vol. ii., Leipzig, 1893) investigated
+  the relative affinities of acids for potash, soda and ammonia, and
+  proved them to be independent of the base used. The method employed
+  was to measure the changes in volume caused by the action. His results
+  are given in column I. of the following table, the affinity of
+  hydrochloric acid being taken as one hundred. Another method is to
+  allow an acid to act on an insoluble salt, and to measure the quantity
+  which goes into solution. Determinations have been made with calcium
+  oxalate, CaC2O4+H2O, which is easily decomposed by acids, oxalic acid
+  and a soluble calcium salt being formed. The affinities of acids
+  relative to that of oxalic acid are thus found, so that the acids can
+  be compared among themselves (column II.). If an aqueous solution of
+  methyl acetate be allowed to stand, a slow decomposition goes on. This
+  is much quickened by the presence of a little dilute acid, though the
+  acid itself remains unchanged. It is found that the influence of
+  different acids on this action is proportional to their specific
+  coefficients of affinity. The results of this method are given in
+  column III. Finally, in column IV. the electrical conductivities of
+  normal solutions of the acids have been tabulated. A better basis of
+  comparison would be the ratio of the actual to the limiting
+  conductivity, but since the conductivity of acids is chiefly due to
+  the mobility of the hydrogen ions, its limiting value is nearly the
+  same for all, and the general result of the comparison would be
+  unchanged.
+
+    +-----------------+---------+---------+---------+---------+
+    |      Acid.      |    I.   |   II.   |   III.  |   IV.   |
+    +-----------------+---------+---------+---------+---------+
+    | Hydrochloric    |  100    |  100    |  100    |  100    |
+    | Nitric          |  102    |  110    |   92    |   99.6  |
+    | Sulphuric       |   68    |   67    |   74    |   65.1  |
+    | Formic          |    4.0  |    2.5  |    1.3  |    1.7  |
+    | Acetic          |    1.2  |    1.0  |    0.3  |    0.4  |
+    | Propionic       |    1.1  |     ..  |    0.3  |    0.3  |
+    | Monochloracetic |    7.2  |    5.1  |    4.3  |    4.9  |
+    | Dichloracetic   |   34    |   18    |   23.0  |   25.3  |
+    | Trichloracetic  |   82    |   63    |   68.2  |   62.3  |
+    | Malic           |   3.0   |    5.0  |    1.2  |    1.3  |
+    | Tartaric        |   5.3   |    6.3  |    2.3  |    2.3  |
+    | Succinic        |   0.1   |    0.2  |    0.5  |    0.6  |
+    +-----------------+---------+---------+---------+---------+
+
+  It must be remembered that, the solutions not being of quite the same
+  strength, these numbers are not strictly comparable, and that the
+  experimental difficulties involved in the chemical measurements are
+  considerable. Nevertheless, the remarkable general agreement of the
+  numbers in the four columns is quite enough to show the intimate
+  connexion between chemical activity and electrical conductivity. We
+  may take it, then, that only that portion of these bodies is
+  chemically active which is electrolytically active--that ionization is
+  necessary for such chemical activity as we are dealing with here, just
+  as it is necessary for electrolytic conductivity.
+
+  The ordinary laws of chemical equilibrium have been applied to the
+  case of the dissociation of a substance into its ions. Let x be the
+  number of molecules which dissociate per second when the number of
+  undissociated molecules in unit volume is unity, then in a dilute
+  solution where the molecules do not interfere with each other, xp is
+  the number when the concentration is p. Recombination can only occur
+  when two ions meet, and since the frequency with which this will
+  happen is, in dilute solution, proportional to the square of the ionic
+  concentration, we shall get for the number of molecules re-formed in
+  one second yq^2 where q is the number of dissociated molecules in one
+  cubic centimetre. When there is equilibrium, xp = yq^2. If [mu] be the
+  molecular conductivity, and [mu]_([oo]) its value at infinite
+  dilution, the fractional number of molecules dissociated is
+  [mu]/[mu]_([oo]), which we may write as [alpha]. The number of
+  undissociated molecules is then 1 - [alpha], so that if V be the
+  volume of the solution containing 1 gramme-molecule of the dissolved
+  substance, we get
+
+    q = [alpha]/V and p = (1 - [alpha])/V,
+
+  hence   x(1 - [alpha])V = ya^2/V^2,
+
+           [alpha]^2     x
+  and   -------------- = -- = constant = k.
+        V(1 - [alpha])   y
+
+  This constant k gives a numerical value for the chemical affinity, and
+  the equation should represent the effect of dilution on the molecular
+  conductivity of binary electrolytes.
+
+  In the case of substances like ammonia and acetic acid, where the
+  dissociation is very small, 1 - [alpha] is nearly equal to unity, and
+  only varies slowly with dilution. The equation then becomes
+  [alpha]^2/V = k, or [alpha] = [root](Vk), so that the molecular
+  conductivity is proportional to the square root of the dilution.
+  Ostwald has confirmed the equation by observation on an enormous
+  number of weak acids (_Zeits. physikal. Chemie_, 1888, ii. p. 278;
+  1889, iii. pp. 170, 241, 369). Thus in the case of cyanacetic acid,
+  while the volume V changed by doubling from 16 to 1024 litres, the
+  values of k were 0.00 (376, 373, 374, 361, 362, 361, 368). The mean
+  values of k for other common acids were--formic, 0.0000214; acetic,
+  0.0000180; monochloracetic, 0.00155; dichloracetic, 0.051;
+  trichloracetic, 1.21; propionic, 0.0000134. From these numbers we can,
+  by help of the equation, calculate the conductivity of the acids for
+  any dilution. The value of k, however, does not keep constant so
+  satisfactorily in the case of highly dissociated substances, and
+  empirical formulae have been constructed to represent the effect of
+  dilution on them. Thus the values of the expressions [alpha]^2/(1 -
+  [alpha][root]V) (Rudolphi, _Zeits. physikal. Chemie_, 1895, vol. xvii.
+  p. 385) and [alpha]^3/(1 - [alpha])^2V (van 't Hoff, ibid., 1895, vol.
+  xviii. p. 300) are found to keep constant as V changes. Van 't Hoff's
+  formula is equivalent to taking the frequency of dissociation as
+  proportional to the square of the concentration of the molecules, and
+  the frequency of recombination as proportional to the cube of the
+  concentration of the ions. An explanation of the failure of the usual
+  dilution law in these cases may be given if we remember that, while
+  the electric forces between bodies like undissociated molecules, each
+  associated with equal and opposite charges, will vary inversely as the
+  fourth power of the distance, the forces between dissociated ions,
+  each carrying one charge only, will be inversely proportional to the
+  square of the distance. The forces between the ions of a strongly
+  dissociated solution will thus be considerable at a dilution which
+  makes forces between undissociated molecules quite insensible, and at
+  the concentrations necessary to test Ostwald's formula an electrolyte
+  will be far from dilute in the thermodynamic sense of the term, which
+  implies no appreciable intermolecular or interionic forces.
+
+  When the solutions of two substances are mixed, similar considerations
+  to those given above enable us to calculate the resultant changes in
+  dissociation. (See Arrhenius, loc. cit.) The simplest and most
+  important case is that of two electrolytes having one ion in common,
+  such as two acids. It is evident that the undissociated part of each
+  acid must eventually be in equilibrium with the free hydrogen ions,
+  and, if the concentrations are not such as to secure this condition,
+  readjustment must occur. In order that there should be no change in
+  the states of dissociation on mixing, it is necessary, therefore, that
+  the concentration of the hydrogen ions should be the same in each
+  separate solution. Such solutions were called by Arrhenius
+  "isohydric." The two solutions, then, will so act on each other when
+  mixed that they become isohydric. Let us suppose that we have one very
+  active acid like hydrochloric, in which dissociation is nearly
+  complete, another like acetic, in which it is very small. In order
+  that the solutions of these should be isohydric and the concentrations
+  of the hydrogen ions the same, we must have a very large quantity of
+  the feebly dissociated acetic acid, and a very small quantity of the
+  strongly dissociated hydrochloric, and in such proportions alone will
+  equilibrium be possible. This explains the action of a strong acid on
+  the salt of a weak acid. Let us allow dilute sodium acetate to react
+  with dilute hydrochloric acid. Some acetic acid is formed, and this
+  process will go on till the solutions of the two acids are isohydric:
+  that is, till the dissociated hydrogen ions are in equilibrium with
+  both. In order that this should hold, we have seen that a considerable
+  quantity of acetic acid must be present, so that a corresponding
+  amount of the salt will be decomposed, the quantity being greater the
+  less the acid is dissociated. This "replacement" of a "weak" acid by a
+  "strong" one is a matter of common observation in the chemical
+  laboratory. Similar investigations applied to the general case of
+  chemical equilibrium lead to an expression of exactly the same form as
+  that given by C.M. Guldberg and P. Waage, which is universally
+  accepted as an accurate representation of the facts.
+
+The temperature coefficient of conductivity has approximately the same
+value for most aqueous salt solutions. It decreases both as the
+temperature is raised and as the concentration is increased, ranging
+from about 3.5% per degree for extremely dilute solutions (i.e.
+practically pure water) at 0 deg. to about 1.5 for concentrated
+solutions at 18 deg. For acids its value is usually rather less than for
+salts at equivalent concentrations. The influence of temperature on the
+conductivity of solutions depends on (1) the ionization, and (2) the
+frictional resistance of the liquid to the passage of the ions, the
+reciprocal of which is called the ionic fluidity. At extreme dilution,
+when the ionization is complete, a variation in temperature cannot
+change its amount. The rise of conductivity with temperature, therefore,
+shows that the fluidity becomes greater when the solution is heated. As
+the concentration is increased and un-ionized molecules are formed, a
+change in temperature begins to affect the ionization as well as the
+fluidity. But the temperature coefficient of conductivity is now
+generally less than before; thus the effect of temperature on ionization
+must be of opposite sign to its effect on fluidity. The ionization of a
+solution, then, is usually diminished by raising the temperature, the
+rise in conductivity being due to the greater increase in fluidity.
+Nevertheless, in certain cases, the temperature coefficient of
+conductivity becomes negative at high temperatures, a solution of
+phosphoric acid, for example, reaching a maximum conductivity at 75 deg.
+C.
+
+The dissociation theory gives an immediate explanation of the fact that,
+in general, no heat-change occurs when two neutral salt solutions are
+mixed. Since the salts, both before and after mixture, exist mainly as
+dissociated ions, it is obvious that large thermal effects can only
+appear when the state of dissociation of the products is very different
+from that of the reagents. Let us consider the case of the
+neutralization of a base by an acid in the light of the dissociation
+theory. In dilute solution such substances as hydrochloric acid and
+potash are almost completely dissociated, so that, instead of
+representing the reaction as
+
+  HCl + KOH = KCl + H2O,
+
+we must write
+
+  +   -    +   -    +   -
+  H + Cl + K + OH = K + Cl + H2O.
+
+The ions K and Cl suffer no change, but the hydrogen of the acid and the
+hydroxyl (OH) of the potash unite to form water, which is only very
+slightly dissociated. The heat liberated, then, is almost exclusively
+that produced by the formation of water from its ions. An exactly
+similar process occurs when any strongly dissociated acid acts on any
+strongly dissociated base, so that in all such cases the heat evolution
+should be approximately the same. This is fully borne out by the
+experiments of Julius Thomsen, who found that the heat of neutralization
+of one gramme-molecule of a strong base by an equivalent quantity of a
+strong acid was nearly constant, and equal to 13,700 or 13,800 calories.
+In the case of weaker acids, the dissociation of which is less complete,
+divergences from this constant value will occur, for some of the
+molecules have to be separated into their ions. For instance, sulphuric
+acid, which in the fairly strong solutions used by Thomsen is only about
+half dissociated, gives a higher value for the heat of neutralization,
+so that heat must be evolved when it is ionized. The heat of formation
+of a substance from its ions is, of course, very different from that
+evolved when it is formed from its elements in the usual way, since the
+energy associated with an ion is different from that possessed by the
+atoms of the element in their normal state. We can calculate the heat of
+formation from its ions for any substance dissolved in a given liquid,
+from a knowledge of the temperature coefficient of ionization, by means
+of an application of the well-known thermodynamical process, which also
+gives the latent heat of evaporation of a liquid when the temperature
+coefficient of its vapour pressure is known. The heats of formation thus
+obtained may be either positive or negative, and by using them to
+supplement the heat of formation of water, Arrhenius calculated the
+total heats of neutralization of soda by different acids, some of them
+only slightly dissociated, and found values agreeing well with
+observation (_Zeits. physikal. Chemie_, 1889, 4, p. 96; and 1892, 9, p.
+339).
+
+_Voltaic Cells._--When two metallic conductors are placed in an
+electrolyte, a current will flow through a wire connecting them provided
+that a difference of any kind exists between the two conductors in the
+nature either of the metals or of the portions of the electrolyte which
+surround them. A current can be obtained by the combination of two
+metals in the same electrolyte, of two metals in different electrolytes,
+of the same metal in different electrolytes, or of the same metal in
+solutions of the same electrolyte at different concentrations. In
+accordance with the principles of energetics (q.v.), any change which
+involves a decrease in the total available energy of the system will
+tend to occur, and thus the necessary and sufficient condition for the
+production of electromotive force is that the available energy of the
+system should decrease when the current flows.
+
+In order that the current should be maintained, and the electromotive
+force of the cell remain constant during action, it is necessary to
+ensure that the changes in the cell, chemical or other, which produce
+the current, should neither destroy the difference between the
+electrodes, nor coat either electrode with a non-conducting layer
+through which the current cannot pass. As an example of a fairly
+constant cell we may take that of Daniell, which consists of the
+electrical arrangement--zinc | zinc sulphate solution | copper sulphate
+solution | copper,--the two solutions being usually separated by a pot
+of porous earthenware. When the zinc and copper plates are connected
+through a wire, a current flows, the conventionally positive electricity
+passing from copper to zinc in the wire and from zinc to copper in the
+cell. Zinc dissolves at the anode, an equal amount of zinc replaces an
+equivalent amount of copper on the other side of the porous partition,
+and the same amount of copper is deposited on the cathode. This process
+involves a decrease in the available energy of the system, for the
+dissolution of zinc gives out more energy than the separation of copper
+absorbs. But the internal rearrangements which accompany the production
+of a current do not cause any change in the original nature of the
+electrodes, fresh zinc being exposed at the anode, and copper being
+deposited on copper at the cathode. Thus as long as a moderate current
+flows, the only variation in the cell is the appearance of zinc sulphate
+in the liquid on the copper side of the porous wall. In spite of this
+appearance, however, while the supply of copper is maintained, copper,
+being more easily separated from the solution than zinc, is deposited
+alone at the cathode, and the cell remains constant.
+
+It is necessary to observe that the condition for change in a system is
+that the total available energy of the whole system should be decreased
+by the change. We must consider what change is allowed by the mechanism
+of the system, and deal with the sum of all the alterations in energy.
+Thus in the Daniell cell the dissolution of copper as well as of zinc
+would increase the loss in available energy. But when zinc dissolves,
+the zinc ions carry their electric charges with them, and the liquid
+tends to become positively electrified. The electric forces then soon
+stop further action unless an equivalent quantity of positive ions are
+removed from the solution. Hence zinc can only dissolve when some more
+easily separable substance is present in solution to be removed pari
+passu with the dissolution of zinc. The mechanism of such systems is
+well illustrated by an experiment devised by W. Ostwald. Plates of
+platinum and pure or amalgamated zinc are separated by a porous pot, and
+each surrounded by some of the same solution of a salt of a metal more
+oxidizable than zinc, such as potassium. When the plates are connected
+together by means of a wire, no current flows, and no appreciable amount
+of zinc dissolves, for the dissolution of zinc would involve the
+separation of potassium and a gain in available energy. If sulphuric
+acid be added to the vessel containing the zinc, these conditions are
+unaltered and still no zinc is dissolved. But, on the other hand, if a
+few drops of acid be placed in the vessel with the platinum, bubbles of
+hydrogen appear, and a current flows, zinc dissolving at the anode, and
+hydrogen being liberated at the cathode. In order that positively
+electrified ions may enter a solution, an equivalent amount of other
+positive ions must be removed or negative ions be added, and, for the
+process to occur spontaneously, the possible action at the two
+electrodes must involve a decrease in the total available energy of the
+system.
+
+Considered thermodynamically, voltaic cells must be divided into
+reversible and non-reversible systems. If the slow processes of
+diffusion be ignored, the Daniell cell already described may be taken as
+a type of a reversible cell. Let an electromotive force exactly equal to
+that of the cell be applied to it in the reverse direction. When the
+applied electromotive force is diminished by an infinitesimal amount,
+the cell produces a current in the usual direction, and the ordinary
+chemical changes occur. If the external electromotive force exceed that
+of the cell by ever so little, a current flows in the opposite
+direction, and all the former chemical changes are reversed, copper
+dissolving from the copper plate, while zinc is deposited on the zinc
+plate. The cell, together with this balancing electromotive force, is
+thus a reversible system in true equilibrium, and the thermodynamical
+reasoning applicable to such systems can be used to examine its
+properties.
+
+Now a well-known relation connects the available energy of a reversible
+system with the corresponding change in its total internal energy.
+
+  The available energy A is the amount of external work obtainable by an
+  infinitesimal, reversible change in the system which occurs at a
+  constant temperature T. If I be the change in the internal energy, the
+  relation referred to gives us the equation
+
+    A = I + T(dA/dT),
+
+  where dA/dT denotes the rate of change of the available energy of the
+  system per degree change in temperature. During a small electric
+  transfer through the cell, the external work done is Ee, where E is
+  the electromotive force. If the chemical changes which occur in the
+  cell were allowed to take place in a closed vessel without the
+  performance of electrical or other work, the change in energy would be
+  measured by the heat evolved. Since the final state of the system
+  would be the same as in the actual processes of the cell, the same
+  amount of heat must give a measure of the change in internal energy
+  when the cell is in action. Thus, if L denote the heat corresponding
+  with the chemical changes associated with unit electric transfer, Le
+  will be the heat corresponding with an electric transfer e, and will
+  also be equal to the change in internal energy of the cell. Hence we
+  get the equation
+
+    Ee = Le + Te(dE/dT) or E = L + T(dE/dT),
+
+  as a particular case of the general thermodynamic equation of
+  available energy. This equation was obtained in different ways by J.
+  Willard Gibbs and H. von Helmholtz.
+
+  It will be noticed that when dE/dT is zero, that is, when the
+  electromotive force of the cell does not change with temperature, the
+  electromotive force is measured by the heat of reaction per unit of
+  electrochemical change. The earliest formulation of the subject, due
+  to Lord Kelvin, assumed that this relation was true in all cases, and,
+  calculated in this way, the electromotive force of Daniell's cell,
+  which happens to possess a very small temperature coefficient, was
+  found to agree with observation.
+
+  When one gramme of zinc is dissolved in dilute sulphuric acid, 1670
+  thermal units or calories are evolved. Hence for the electrochemical
+  unit of zinc or 0.003388 gramme, the thermal evolution is 5.66
+  calories. Similarly, the heat which accompanies the dissolution of one
+  electrochemical unit of copper is 3.00 calories. Thus, the thermal
+  equivalent of the unit of resultant electrochemical change in
+  Daniell's cell is 5.66 - 3.00 = 2.66 calories. The dynamical
+  equivalent of the calorie is 4.18 X 10^7 ergs or C.G.S. units of work,
+  and therefore the electromotive force of the cell should be 1.112 X
+  10^8 C.G.S. units or 1.112 volts--a close agreement with the
+  experimental result of about 1.08 volts. For cells in which the
+  electromotive force varies with temperature, the full equation given
+  by Gibbs and Helmholtz has also been confirmed experimentally.
+
+As stated above, an electromotive force is set up whenever there is a
+difference of any kind at two electrodes immersed in electrolytes. In
+ordinary cells the difference is secured by using two dissimilar metals,
+but an electromotive force exists if two plates of the same metal are
+placed in solutions of different substances, or of the same substance at
+different concentrations. In the latter case, the tendency of the metal
+to dissolve in the more dilute solution is greater than its tendency to
+dissolve in the more concentrated solution, and thus there is a decrease
+in available energy when metal dissolves in the dilute solution and
+separates in equivalent quantity from the concentrated solution. An
+electromotive force is therefore set up in this direction, and, if we
+can calculate the change in available energy due to the processes of the
+cell, we can foretell the value of the electromotive force. Now the
+effective change produced by the action of the current is the
+concentration of the more dilute solution by the dissolution of metal in
+it, and the dilution of the originally stronger solution by the
+separation of metal from it. We may imagine these changes reversed in
+two ways. We may evaporate some of the solvent from the solution which
+has become weaker and thus reconcentrate it, condensing the vapour on
+the solution which had become stronger. By this reasoning Helmholtz
+showed how to obtain an expression for the work done. On the other hand,
+we may imagine the processes due to the electrical transfer to be
+reversed by an osmotic operation. Solvent may be supposed to be squeezed
+out from the solution which has become more dilute through a
+semi-permeable wall, and through another such wall allowed to mix with
+the solution which in the electrical operation had become more
+concentrated. Again, we may calculate the osmotic work done, and, if the
+whole cycle of operations be supposed to occur at the same temperature,
+the osmotic work must be equal and opposite to the electrical work of
+the first operation.
+
+  The result of the investigation shows that the electrical work Ee is
+  given by the equation
+          _
+         / p2
+    Ee = |   vdp,
+        _/ p1
+
+  where v is the volume of the solution used and p its osmotic pressure.
+  When the solutions may be taken as effectively dilute, so that the gas
+  laws apply to the osmotic pressure, this relation reduces to
+
+        nrRT               c1
+    E = ---- log_[epsilon] --
+         ey                c2
+
+  where n is the number of ions given by one molecule of the salt, r the
+  transport ratio of the anion, R the gas constant, T the absolute
+  temperature, y the total valency of the anions obtained from one
+  molecule, and c1 and c2 the concentrations of the two solutions.
+
+  If we take as an example a concentration cell in which silver plates
+  are placed in solutions of silver nitrate, one of which is ten times
+  as strong as the other, this equation gives
+
+    E = 0.060 X 10^8 C.G.S. units
+      = 0.060 volts.
+
+W. Nernst, to whom this theory is due, determined the electromotive
+force of this cell experimentally, and found the value 0.055 volt.
+
+The logarithmic formulae for these concentration cells indicate that
+theoretically their electromotive force can be increased to any extent
+by diminishing without limit the concentration of the more dilute
+solution, log c1/c2 then becoming very great. This condition may be
+realized to some extent in a manner that throws light on the general
+theory of the voltaic cell. Let us consider the arrangement--silver |
+silver chloride with potassium chloride solution | potassium nitrate
+solution | silver nitrate solution | silver. Silver chloride is a very
+insoluble substance, and here the amount in solution is still further
+reduced by the presence of excess of chlorine ions of the potassium
+salt. Thus silver, at one end of the cell in contact with many silver
+ions of the silver nitrate solution, at the other end is in contact with
+a liquid in which the concentration of those ions is very small indeed.
+The result is that a high electromotive force is set up, which has been
+calculated as 0.52 volt, and observed as 0.51 volt. Again, Hittorf has
+shown that the effect of a cyanide round a copper electrode is to
+combine with the copper ions. The concentration of the simple copper
+ions is then so much diminished that the copper plate becomes an anode
+with regard to zinc. Thus the cell--copper | potassium cyanide solution
+| potassium sulphate solution--zinc sulphate solution | zinc--gives a
+current which carries copper into solution and deposits zinc. In a
+similar way silver could be made to act as anode with respect to
+cadmium.
+
+It is now evident that the electromotive force of an ordinary chemical
+cell such as that of Daniell depends on the concentration of the
+solutions as well as on the nature of the metals. In ordinary cases
+possible changes in the concentrations only affect the electromotive
+force by a few parts in a hundred, but, by means such as those indicated
+above, it is possible to produce such immense differences in the
+concentrations that the electromotive force of the cell is not only
+changed appreciably but even reversed in direction. Once more we see
+that it is the total impending change in the available energy of the
+system which controls the electromotive force.
+
+Any reversible cell can theoretically be employed as an accumulator,
+though, in practice, conditions of general convenience are more sought
+after than thermodynamic efficiency. The effective electromotive force
+of the common lead accumulator (q.v.) is less than that required to
+charge it. This drop in the electromotive force has led to the belief
+that the cell is not reversible. F. Dolezalek, however, has attributed
+the difference to mechanical hindrances, which prevent the equalization
+of acid concentration in the neighbourhood of the electrodes, rather
+than to any essentially irreversible chemical action. The fact that the
+Gibbs-Helmholtz equation is found to apply also indicates that the lead
+accumulator is approximately reversible in the thermodynamic sense of
+the term.
+
+_Polarization and Contact Difference of Potential._--If we connect
+together in series a single Daniell's cell, a galvanometer, and two
+platinum electrodes dipping into acidulated water, no visible chemical
+decomposition ensues. At first a considerable current is indicated by
+the galvanometer; the deflexion soon diminishes, however, and finally
+becomes very small. If, instead of using a single Daniell's cell, we
+employ some source of electromotive force which can be varied as we
+please, and gradually raise its intensity, we shall find that, when it
+exceeds a certain value, about 1.7 volt, a permanent current of
+considerable strength flows through the solution, and, after the initial
+period, shows no signs of decrease. This current is accompanied by
+chemical decomposition. Now let us disconnect the platinum plates from
+the battery and join them directly with the galvanometer. A current will
+flow for a while in the reverse direction; the system of plates and
+acidulated water through which a current has been passed, acts as an
+accumulator, and will itself yield a current in return. These phenomena
+are explained by the existence of a reverse electromotive force at the
+surface of the platinum plates. Only when the applied electromotive
+force exceeds this reverse force of polarization, will a permanent
+steady current pass through the liquid, and visible chemical
+decomposition proceed. It seems that this reverse electromotive force of
+polarization is due to the deposit on the electrodes of minute
+quantities of the products of chemical decomposition. Differences
+between the two electrodes are thus set up, and, as we have seen above,
+an electromotive force will therefore exist between them. To pass a
+steady current in the direction opposite to this electromotive force of
+polarization, the applied electromotive force E must exceed that of
+polarization E', and the excess E - E' is the effective electromotive
+force of the circuit, the current being, in accordance with Ohm's law,
+proportional to the applied electromotive force and represented by (E -
+E')/R, where R is a constant called the resistance of the circuit.
+
+When we use platinum electrodes in acidulated water, hydrogen and oxygen
+are evolved. The opposing force of polarization is about 1.7 volt, but,
+when the plates are disconnected and used as a source of current, the
+electromotive force they give is only about 1.07 volt. This
+irreversibility is due to the work required to evolve bubbles of gas at
+the surface of bright platinum plates. If the plates be covered with a
+deposit of platinum black, in which the gases are absorbed as fast as
+they are produced, the minimum decomposition point is 1.07 volt, and the
+process is reversible. If secondary effects are eliminated, the
+deposition of metals also is a reversible process; the decomposition
+voltage is equal to the electromotive force which the metal itself gives
+when going into solution. The phenomena of polarization are thus seen to
+be due to the changes of surface produced, and are correlated with the
+differences of potential which exist at any surface of separation
+between a metal and an electrolyte.
+
+Many experiments have been made with a view of separating the two
+potential-differences which must exist in any cell made of two metals
+and a liquid, and of determining each one individually. If we regard the
+thermal effect at each junction as a measure of the potential-difference
+there, as the total thermal effect in the cell undoubtedly is of the sum
+of its potential-differences, in cases where the temperature coefficient
+is negligible, the heat evolved on solution of a metal should give the
+electrical potential-difference at its surface. Hence, if we assume
+that, in the Daniell's cell, the temperature coefficients are negligible
+at the individual contacts as well as in the cell as a whole, the sign
+of the potential-difference ought to be the same at the surface of the
+zinc as it is at the surface of the copper. Since zinc goes into
+solution and copper comes out, the electromotive force of the cell will
+be the difference between the two effects. On the other hand, it is
+commonly thought that the single potential-differences at the surface of
+metals and electrolytes have been determined by methods based on the use
+of the capillary electrometer and on others depending on what is called
+a dropping electrode, that is, mercury dropping rapidly into an
+electrolyte and forming a cell with the mercury at rest in the bottom of
+the vessel. By both these methods the single potential-differences found
+at the surfaces of the zinc and copper have opposite signs, and the
+effective electromotive force of a Daniell's cell is the sum of the two
+effects. Which of these conflicting views represents the truth still
+remains uncertain.
+
+_Diffusion of Electrolytes and Contact Difference of Potential between
+Liquids._--An application of the theory of ionic velocity due to W.
+Nernst[7] and M. Planck[8] enables us to calculate the diffusion
+constant of dissolved electrolytes. According to the molecular theory,
+diffusion is due to the motion of the molecules of the dissolved
+substance through the liquid. When the dissolved molecules are uniformly
+distributed, the osmotic pressure will be the same everywhere throughout
+the solution, but, if the concentration vary from point to point, the
+pressure will vary also. There must, then, be a relation between the
+rate of change of the concentration and the osmotic pressure gradient,
+and thus we may consider the osmotic pressure gradient as a force
+driving the solute through a viscous medium. In the case of
+non-electrolytes and of all non-ionized molecules this analogy
+completely represents the facts, and the phenomena of diffusion can be
+deduced from it alone. But the ions of an electrolytic solution can move
+independently through the liquid, even when no current flows, as the
+consequences of Ohm's law indicate. The ions will therefore diffuse
+independently, and the faster ion will travel quicker into pure water in
+contact with a solution. The ions carry their charges with them, and, as
+a matter of fact, it is found that water in contact with a solution
+takes with respect to it a positive or negative potential, according as
+the positive or negative ion travels the faster. This process will go on
+until the simultaneous separation of electric charges produces an
+electrostatic force strong enough to prevent further separation of ions.
+We can therefore calculate the rate at which the salt as a whole will
+diffuse by examining the conditions for a steady transfer, in which the
+ions diffuse at an equal rate, the faster one being restrained and the
+slower one urged forward by the electric forces. In this manner the
+diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3
+= 2.27, NaCl = 1.12), the unit of time being the day. By experiments on
+diffusion this constant has been found by Scheffer, and the numbers
+observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl =
+1.11).
+
+As we have seen above, when a solution is placed in contact with water
+the water will take a positive or negative potential with regard to the
+solution, according as the cation or anion has the greater specific
+velocity, and therefore the greater initial rate of diffusion. The
+difference of potential between two solutions of a substance at
+different concentrations can be calculated from the equations used to
+give the diffusion constants. The results give equations of the same
+logarithmic form as those obtained in a somewhat different manner in the
+theory of concentration cells described above, and have been verified by
+experiment.
+
+The contact differences of potential at the interfaces of metals and
+electrolytes have been co-ordinated by Nernst with those at the surfaces
+of separation between different liquids. In contact with a solvent a
+metal is supposed to possess a definite solution pressure, analogous to
+the vapour pressure of a liquid. Metal goes into solution in the form of
+electrified ions. The liquid thus acquires a positive charge, and the
+metal a negative charge. The electric forces set up tend to prevent
+further separation, and finally a state of equilibrium is reached, when
+no more ions can go into solution unless an equivalent number are
+removed by voltaic action. On the analogy between this case and that of
+the interface between two solutions, Nernst has arrived at similar
+logarithmic expressions for the difference of potential, which becomes
+proportional to log (P1/P2) where P2 is taken to mean the osmotic
+pressure of the cations in the solution, and P1 the osmotic pressure of
+the cations in the substance of the metal itself. On these lines the
+equations of concentration cells, deduced above on less hypothetical
+grounds, may be regained.
+
+_Theory of Electrons._--Our views of the nature of the ions of
+electrolytes have been extended by the application of the ideas of the
+relations between matter and electricity obtained by the study of
+electric conduction through gases. The interpretation of the phenomena
+of gaseous conduction was rendered possible by the knowledge previously
+acquired of conduction through liquids; the newer subject is now
+reaching a position whence it can repay its debt to the older.
+
+Sir J.J. Thomson has shown (see CONDUCTION, ELECTRIC, S III.) that the
+negative ions in certain cases of gaseous conduction are much more
+mobile than the corresponding positive ions, and possess a mass of about
+the one-thousandth part of that of a hydrogen atom. These negative
+particles or corpuscles seem to be the ultimate units of negative
+electricity, and may be identified with the electrons required by the
+theories of H.A. Lorentz and Sir J. Larmor. A body containing an excess
+of these particles is negatively electrified, and is positively
+electrified if it has parted with some of its normal number. An electric
+current consists of a moving stream of electrons. In gases the electrons
+sometimes travel alone, but in liquids they are always attached to
+matter, and their motion involves the movement of chemical atoms or
+groups of atoms. An atom with an extra corpuscle is a univalent negative
+ion, an atom with one corpuscle detached is a univalent positive ion. In
+metals the electrons can slip from one atom to the next, since a current
+can pass without chemical action. When a current passes from an
+electrolyte to a metal, the electron must be detached from the atom it
+was accompanying and chemical action be manifested at the electrode.
+
+  BIBLIOGRAPHY.--Michael Faraday, _Experimental Researches in
+  Electricity_ (London, 1844 and 1855); W. Ostwald, _Lehrbuch der
+  allgemeinen Chemie_, 2te Aufl. (Leipzig, 1891); _Elektrochemie_
+  (Leipzig, 1896); W Nernst, _Theoretische Chemie_, 3te Aufl.
+  (Stuttgart, 1900; English translation, London, 1904); F. Kohlrausch
+  and L. Holborn, _Das Leitvermogen der Elektrolyte_ (Leipzig, 1898);
+  W.C.D. Whetham, _The Theory of Solution and Electrolysis_ (Cambridge,
+  1902); M. Le Blanc, _Elements of Electrochemistry_ (Eng. trans.,
+  London, 1896); S. Arrhenius, _Text-Book of Electrochemistry_ (Eng.
+  trans., London, 1902); H.C. Jones, _The Theory of Electrolytic
+  Dissociation_ (New York, 1900); N. Munroe Hopkins, _Experimental
+  Electrochemistry_ (London, 1905); Luphe, _Grundzuge der Elektrochemie_
+  (Berlin, 1896).
+
+  Some of the more important papers on the subject have been reprinted
+  for Harper's _Series of Scientific Memoirs in Electrolytic Conduction_
+  (1899) and the _Modern Theory of Solution_ (1899). Several journals
+  are published specially to deal with physical chemistry, of which
+  electrochemistry forms an important part. Among them may be mentioned
+  the _Zeitschrift fur physikalische Chemie_ (Leipzig); and the _Journal
+  of Physical Chemistry_ (Cornell University). In these periodicals will
+  be found new work on the subject and abstracts of papers which appear
+  in other physical and chemical publications.     (W. C. D. W.)
+
+
+FOOTNOTES:
+
+  [1] See Hittorf, _Pogg. Ann._ cvi. 517 (1859).
+
+  [2] _Grundriss der Elektrochemie_ (1895), p. 292; see also F. Kaufler
+    and C. Herzog, _Ber._, 1909, 42, p. 3858.
+
+  [3] _Brit. Ass. Rep._, 1906, Section A, Presidential Address.
+
+  [4] See _Theory of Solution_, by W.C.D. Whetham (1902), p. 328.
+
+  [5] W. Ostwald, _Zeits. physikal. Chemie_, 1892, vol. IX. p. 579; T.
+    Ewan, _Phil. Mag._ (5), 1892, vol. xxxiii. p. 317; G.D. Liveing,
+    _Cambridge Phil. Trans._, 1900, vol. xviii. p. 298.
+
+  [6] See W.B. Hardy, _Journal of Physiology_, 1899, vol. xxiv. p. 288;
+    and W.C.D. Whetham, _Phil. Mag._, November 1899.
+
+  [7] _Zeits. physikal. Chem._ 2, p. 613.
+
+  [8] _Wied. Ann._, 1890, 40, p. 561.
+
+
+
+
+ELECTROMAGNETISM, that branch of physical science which is concerned
+with the interconnexion of electricity and magnetism, and with the
+production of magnetism by means of electric currents by devices called
+electromagnets.
+
+_History._--The foundation was laid by the observation first made by
+Hans Christian Oersted (1777-1851), professor of natural philosophy in
+Copenhagen, who discovered in 1820 that a wire uniting the poles or
+terminal plates of a voltaic pile has the property of affecting a
+magnetic needle[1] (see ELECTRICITY). Oersted carefully ascertained
+that the nature of the wire itself did not influence the result but saw
+that it was due to the electric conflict, as he called it, round the
+wire; or in modern language, to the magnetic force or magnetic flux
+round the conductor. If a straight wire through which an electric
+current is flowing is placed above and parallel to a magnetic compass
+needle, it is found that if the current is flowing in the conductor in a
+direction from south to north, the north pole of the needle under the
+conductor deviates to the left hand, whereas if the conductor is placed
+under the needle, the north pole deviates to the right hand; if the
+conductor is doubled back over the needle, the effects of the two sides
+of the loop are added together and the deflection is increased. These
+results are summed up in the mnemonic rule: _Imagine yourself swimming
+in the conductor with the current, that is, moving in the direction of
+the positive electricity, with your face towards the magnetic needle;
+the north pole will then deviate to your left hand._ The deflection of
+the magnetic needle can therefore reveal the existence of an electric
+current in a neighbouring circuit, and this fact was soon utilized in
+the construction of instruments called galvanometers (q.v.).
+
+Immediately after Oersted's discovery was announced, D.F.J. Arago and
+A.M. Ampere began investigations on the subject of electromagnetism. On
+the 18th of September 1820, Ampere read a paper before the Academy of
+Sciences in Paris, in which he announced that the voltaic pile itself
+affected a magnetic needle as did the uniting wire, and he showed that
+the effects in both cases were consistent with the theory that electric
+current was a circulation round a circuit, and equivalent in magnetic
+effect to a very short magnet with axis placed at right angles to the
+plane of the circuit. He then propounded his brilliant hypothesis that
+the magnetization of iron was due to molecular electric currents. This
+suggested to Arago that wire wound into a helix carrying electric
+current should magnetize a steel needle placed in the interior. In the
+_Ann. Chim._ (1820, 15, p. 94), Arago published a paper entitled
+"Experiences relatives a l'aimantation du fer et de l'acier par l'action
+du courant voltaique," announcing that the wire conveying the current,
+even though of copper, could magnetize steel needles placed across it,
+and if plunged into iron filings it attracted them. About the same time
+Sir Humphry Davy sent a communication to Dr W.H. Wollaston, read at the
+Royal Society on the 16th of November 1820 (reproduced in the _Annals of
+Philosophy_ for August 1821, p. 81), "On the Magnetic Phenomena produced
+by Electricity," in which he announced his independent discovery of the
+same fact. With a large battery of 100 pairs of plates at the Royal
+Institution, he found in October 1820 that the uniting wire became
+strongly magnetic and that iron filings clung to it; also that steel
+needles placed across the wire were permanently magnetized. He placed a
+sheet of glass over the wire and sprinkling iron filings on it saw that
+they arranged themselves in straight lines at right angles to the wire.
+He then proved that Leyden jar discharges could produce the same
+effects. Ampere and Arago then seem to have experimented together and
+magnetized a steel needle wrapped in paper which was enclosed in a
+helical wire conveying a current. All these facts were rendered
+intelligible when it was seen that a wire when conveying an electric
+current becomes surrounded by a magnetic field. If the wire is a long
+straight one, the lines of magnetic force are circular and concentric
+with centres on the wire axis, and if the wire is bent into a circle the
+lines of magnetic force are endless loops surrounding and linked with
+the electric circuit. Since a magnetic pole tends to move along a line
+of magnetic force it was obvious that it should revolve round a wire
+conveying a current. To exhibit this fact involved, however, much
+ingenuity. It was first accomplished by Faraday in October 1821 (_Exper.
+Res._ ii. p. 127). Since the action is reciprocal a current free to move
+tends to revolve round a magnetic pole. The fact is most easily shown by
+a small piece of apparatus made as follows: In a glass cylinder (see
+fig. 1) like a lamp chimney are fitted two corks. Through the bottom one
+is passed the north end of a bar magnet which projects up above a little
+mercury lying in the cork. Through the top cork is passed one end of a
+wire from a battery, and a piece of wire in the cylinder is flexibly
+connected to it, the lower end of this last piece just touching the
+mercury. When a current is passed in at the top wire and out at the
+lower end of the bar magnet, the loose wire revolves round the magnet
+pole. All text-books on physics contain in their chapters on
+electromagnetism full accounts of various forms of this experiment.
+
+[Illustration: FIG. 1.]
+
+In 1825 another important step forward was taken when William Sturgeon
+(1783-1850) of London produced the electromagnet. It consisted of a
+horseshoe-shaped bar of soft iron, coated with varnish, on which was
+wrapped a spiral coil of bare copper wire, the turns not touching each
+other. When a voltaic current was passed through the wire the iron
+became a powerful magnet, but on severing the connexion with the
+battery, the soft iron lost immediately nearly all its magnetism.[2]
+
+At that date Ohm had not announced his law of the electric circuit, and
+it was a matter of some surprise to investigators to find that
+Sturgeon's electromagnet could not be operated at a distance through a
+long circuit of wire with such good results as when close to the
+battery. Peter Barlow, in January 1825, published in the _Edinburgh
+Philosophical Journal_, a description of such an experiment made with a
+view of applying Sturgeon's electromagnet to telegraphy, with results
+which were unfavourable. Sturgeon's experiments, however, stimulated
+Joseph Henry (q.v.) in the United States, and in 1831 he gave a
+description of a method of winding electromagnets which at once put a
+new face upon matters (_Silliman's Journal_, 1831, 19, p. 400). Instead
+of insulating the iron core, he wrapped the copper wire round with silk
+and wound in numerous turns and many layers upon the iron horseshoe in
+such fashion that the current went round the iron always in the same
+direction. He then found that such an electromagnet wound with a long
+fine wire, if worked with a battery consisting of a large number of
+cells in series, could be operated at a considerable distance, and he
+thus produced what were called at that time _intensity electromagnets_,
+and which subsequently rendered the electric telegraph a possibility. In
+fact, Henry established in 1831, in Albany, U.S.A., an electromagnetic
+telegraph, and in 1835 at Princeton even used an earth return, thereby
+anticipating the discovery (1838) of C.A. Steinheil (1801-1870) of
+Munich.
+
+[Illustration: FIG. 2.]
+
+Inventors were then incited to construct powerful electromagnets as
+tested by the weight they could carry from their armatures. Joseph Henry
+made a magnet for Yale College, U.S.A., which lifted 3000 lb.
+(_Silliman's Journal_, 1831, 20, p. 201), and one for Princeton which
+lifted 3000 with a very small battery. Amongst others J.P. Joule, ever
+memorable for his investigations on the mechanical equivalent of heat,
+gave much attention about 1838-1840 to the construction of
+electromagnets and succeeded in devising some forms remarkable for their
+lifting power. One form was constructed by cutting a thick soft iron
+tube longitudinally into two equal parts. Insulated copper wire was then
+wound longitudinally over one of both parts (see fig. 2) and a current
+sent through the wire. In another form two iron disks with teeth at
+right angles to the disk had insulated wire wound zigzag between the
+teeth; when a current was sent through the wire, the teeth were so
+magnetized that they were alternately N. and S. poles. If two such
+similar disks were placed with teeth of opposite polarity in contact, a
+very large force was required to detach them, and with a magnet and
+armature weighing in all 11.575 lb. Joule found that a weight of 2718
+was supported. Joule's papers on this subject will be found in his
+_Collected Papers_ published by the Physical Society of London, and in
+_Sturgeon's Annals of Electricity_, 1838-1841, vols. 2-6.
+
+  _The Magnetic Circuit._--The phenomena presented by the electromagnet
+  are interpreted by the aid of the notion of the magnetic circuit. Let
+  us consider a thin circular sectioned ring of iron wire wound over
+  with a solenoid or spiral of insulated copper wire through which a
+  current of electricity can be passed. If the solenoid or wire windings
+  existed alone, a current having a strength A amperes passed through it
+  would create in the interior of the solenoid a magnetic force H,
+  numerically equal to 4[pi]/10 multiplied by the number of windings N
+  on the solenoid, and by the current in amperes A, and divided by the
+  mean length of the solenoid l, or H = 4[pi]AN/10l. The product AN is
+  called the "ampere-turns" on the solenoid. The product Hl of the
+  magnetic force H and the length l of the magnetic circuit is called
+  the "magnetomotive force" in the magnetic circuit, and from the above
+  formula it is seen that the magnetomotive force denoted by (M.M.F.) is
+  equal to 4[pi]/10 (= 1.25 nearly) times the ampere-turns (A.N.) on the
+  exciting coil or solenoid. Otherwise (A.N.) = 0.8(M.M.F.). The
+  magnetomotive force is regarded as creating an effect called magnetic
+  flux (Z) in the magnetic circuit, just as electromotive force E.M.F.
+  produces electric current (A) in the electric circuit, and as by Ohm's
+  law (see ELECTROKINETICS) the current varies as the E.M.F. and
+  inversely as a quality of the electric circuit called its
+  "resistance," so in the magnetic circuit the magnetic flux varies as
+  the magnetomotive force and inversely as a quality of the magnetic
+  circuit called its "reluctance." The great difference between the
+  electric circuit and the magnetic circuit lies in the fact that
+  whereas the electric resistance of a solid or liquid conductor is
+  independent of the current and affected only by the temperature, the
+  magnetic reluctance varies with the magnetic flux and cannot be
+  defined except by means of a curve which shows its value for different
+  flux densities. The quotient of the total magnetic flux, Z, in a
+  circuit by the cross section, S, of the circuit is called the mean
+  "flux density," and the reluctance of a magnetic circuit one
+  centimetre long and one square centimetre in cross section is called
+  the "reluctivity" of the material. The relation between reluctivity
+  [rho] = 1/[mu] magnetic force H, and flux density B, is defined by the
+  equation H = [rho]B, from which we have Hl = Z([rho]l/S) = M.M.F.
+  acting on the circuit. Again, since the ampere-turns (AN) on the
+  circuit are equal to 0.8 times the M.M.F., we have finally AN/l =
+  0.8(Z/[mu]S). This equation tells us the exciting force reckoned in
+  ampere-turns, AN, which must be put on the ring core to create a total
+  magnetic flux Z in it, the ring core having a mean perimeter l and
+  cross section S and reluctivity [rho] = 1/[mu] corresponding to a flux
+  density Z/S. Hence before we can make use of the equation for
+  practical purposes we need to possess a curve for the particular
+  material showing us the value of the reluctivity corresponding to
+  various values of the possible flux density. The reciprocal of [rho]
+  is usually called the "permeability" of the material and denoted by
+  [mu]. Curves showing the relation of 1/[rho] and ZS or [mu] and B, are
+  called "permeability curves." For air and all other non-magnetic
+  matter the permeability has the same value, taken arbitrarily as
+  unity. On the other hand, for iron, nickel and cobalt the permeability
+  may in some cases reach a value of 2000 or 2500 for a value of B =
+  5000 in C.G.S. measure (see UNITS, PHYSICAL). The process of taking
+  these curves consists in sending a current of known strength through a
+  solenoid of known number of turns wound on a circular iron ring of
+  known dimensions, and observing the time-integral of the secondary
+  current produced in a secondary circuit of known turns and resistance
+  R wound over the iron core N times. The secondary electromotive force
+  is by Faraday's law (see ELECTROKINETICS) equal to the time rate of
+  change of the total flux, or E = NdZ/dt. But by Ohm's law E = Rdq/dt,
+  where q is the quantity of electricity set flowing in the secondary
+  circuit by a change dZ in the co-linked total flux. Hence if 2Q
+  represents this total quantity of electricity set flowing in the
+  secondary circuit by suddenly reversing the direction of the magnetic
+  flux Z in the iron core we must have
+
+    RQ = NZ or Z = RQ/N.
+
+  The measurement of the total quantity of electricity Q can be made by
+  means of a ballistic galvanometer (q.v.), and the resistance R of the
+  secondary circuit includes that of the coil wound on the iron core and
+  the galvanometer as well. In this manner the value of the total flux Z
+  and therefore of Z/S = B or the flux density, can be found for a given
+  magnetizing force H, and this last quantity is determined when we know
+  the magnetizing current in the solenoid and its turns and dimensions.
+  The curve which delineates the relation of H and B is called the
+  magnetization curve for the material in question. For examples of
+  these curves see MAGNETISM.
+
+  The fundamental law of the non-homogeneous magnetic circuit traversed
+  by one and the same total magnetic flux Z is that the sum of all the
+  magnetomotive forces acting in the circuit is numerically equal to the
+  product of the factor 0.8, the total flux in the circuit, and the sum
+  of all the reluctances of the various parts of the circuit. If then
+  the circuit consists of materials of different permeability and it is
+  desired to know the ampere-turns required to produce a given total of
+  flux round the circuit, we have to calculate from the magnetization
+  curves of the material of each part the necessary magnetomotive forces
+  and add these forces together. The practical application of this
+  principle to the predetermination of the field windings of dynamo
+  magnets was first made by Drs J. and E. Hopkinson (_Phil. Trans._,
+  1886, 177, p. 331).
+
+  We may illustrate the principles of this predetermination by a simple
+  example. Suppose a ring of iron has a mean diameter of 10 cms. and a
+  cross section of 2 sq. cms., and a transverse cut on air gap made in
+  it 1 mm. wide. Let us inquire the ampere-turns to be put upon the ring
+  to create in it a total flux of 24,000 C.G.S. units. The total length
+  of the iron part of the circuit is (10[pi] - 0.1) cms., and its
+  section is 2 sq. cms., and the flux density in it is to be 12,000.
+  From Table II. below we see that the permeability of pure iron
+  corresponding to a flux density of 12,000 is 2760. Hence the
+  reluctance of the iron circuits is equal to
+
+    10[pi] - 0.1    220
+    ------------ = ----- C.G.S. units.
+      2760 X 2     38640
+
+  The length of the air gap is 0.1 cm., its section 2 sq. cms., and its
+  permeability is unity. Hence the reluctance of the air gap is
+
+     0.1     1
+    ----- = -- C.G.S. unit.
+    1 X 2   20
+
+  Accordingly the magnetomotive force in ampere-turns required to
+  produce the required flux is equal to
+
+                 / 1    220 \
+    0.8(24,000) ( -- + ----- ) = 1070 nearly.
+                 \20   38640/
+
+  It follows that the part of the magnetomotive force required to
+  overcome the reluctance of the narrow air gap is about nine times that
+  required for the iron alone.
+
+  In the above example we have for simplicity assumed that the flux in
+  passing across the air gap does not spread out at all. In dealing with
+  electromagnet design in dynamo construction we have, however, to take
+  into consideration the spreading as well as the leakage of flux across
+  the circuit (see DYNAMO). It will be seen, therefore, that in order
+  that we may predict the effect of a certain kind of iron or steel when
+  used as the core of an electromagnet, we must be provided with tables
+  or curves showing the reluctivity or permeability corresponding to
+  various flux densities or--which comes to the same thing--with (B, H)
+  curves for the sample.
+
+_Iron and Steel for Electromagnetic Machinery._--In connexion with the
+technical application of electromagnets such as those used in the field
+magnets of dynamos (q.v.), the testing of different kinds of iron and
+steel for magnetic permeability has therefore become very important.
+Various instruments called permeameters and hysteresis meters have been
+designed for this purpose, but much of the work has been done by means
+of a ballistic galvanometer and test ring as above described. The
+"hysteresis" of an iron or steel is that quality of it in virtue of
+which energy is dissipated as heat when the magnetization is reversed or
+carried through a cycle (see MAGNETISM), and it is generally measured
+either in ergs per cubic centimetre of metal per cycle of magnetization,
+or in watts per lb. per 50 or 100 cycles per second at or corresponding
+to a certain maximum flux density, say 2500 or 600 C.G.S. units. For the
+details of various forms of permeameter and hysteresis meter technical
+books must be consulted.[3]
+
+An immense number of observations have been carried out on the magnetic
+permeability of different kinds of iron and steel, and in the following
+tables are given some typical results, mostly from experiments made by
+J.A. Ewing (see _Proc. Inst. C.E._, 1896, 126, p. 185) in which the
+ballistic method was employed to determine the flux density
+corresponding to various magnetizing forces acting upon samples of iron
+and steel in the form of rings.
+
+  The figures under heading I. are values given in a paper by A.W.S.
+  Pocklington and F. Lydall (_Proc. Roy. Soc_., 1892-1893, 52, pp. 164
+  and 228) as the results of a magnetic test of an exceptionally pure
+  iron supplied for the purpose of experiment by Colonel Dyer, of the
+  Elswick Works. The substances other than iron in this sample were
+  stated to be: carbon, _trace_; silicon, _trace_; phosphorus, _none_;
+  sulphur, 0.013%; manganese, 0.1%. The other five specimens, II. to
+  VI., are samples of commercial iron or steel. No. II. is a sample of
+  Low Moor bar iron forged into a ring, annealed and turned. No. III. is
+  a steel forging furnished by Mr R. Jenkins as a sample of forged
+  ingot-metal for dynamo magnets. No. IV. is a steel casting for dynamo
+  magnets, unforged, made by Messrs Edgar Allen & Company by a special
+  pneumatic process under the patents of Mr A. Tropenas. No. V. is also
+  an unforged steel casting for dynamo magnets, made by Messrs Samuel
+  Osborne & Company by the Siemens process. No. VI. is also an unforged
+  steel casting for dynamo magnets, made by Messrs Fried. Krupp, of
+  Essen.
+
+    TABLE I.--_Magnetic Flux Density corresponding to various Magnetizing
+    Forces in the case of certain Samples of Iron and Steel_ (_Ewing_).
+
+    +------------+-----------------------------------------------------+
+    |Magnetizing |                                                     |
+    |   Force    |                                                     |
+    |  H (C.G.S. |       Magnetic Flux Density B (C.G.S. Units).       |
+    |   Units).  |                                                     |
+    +------------+--------+--------+--------+--------+--------+--------+
+    |            |   I.   |   II.  |  III.  |   IV.  |   V.   |   VI.  |
+    +------------+--------+--------+--------+--------+--------+--------+
+    |      5     | 12,700 | 10,900 | 12,300 |  4,700 |  9,600 | 10,900 |
+    |     10     | 14,980 | 13,120 | 14,920 | 12,250 | 13,050 | 13,320 |
+    |     15     | 15,800 | 14,010 | 15,800 | 14,000 | 14,600 | 14,350 |
+    |     20     | 16,300 | 14,580 | 16,280 | 15,050 | 15,310 | 14,950 |
+    |     30     | 16,950 | 15,280 | 16,810 | 16,200 | 16,000 | 15,660 |
+    |     40     | 17,350 | 15,760 | 17,190 | 16,800 | 16,510 | 16,150 |
+    |     50     |   ..   | 16,060 | 17,500 | 17,140 | 16,900 | 16,480 |
+    |     60     |   ..   | 16,340 | 17,750 | 17,450 | 17,180 | 16,780 |
+    |     70     |   ..   | 16,580 | 17,970 | 17,750 | 17,400 | 17,000 |
+    |     80     |   ..   | 16,800 | 18,180 | 18,040 | 17,620 | 17,200 |
+    |     90     |   ..   | 17,000 | 18,390 | 18,230 | 17,830 | 17,400 |
+    |    100     |   ..   | 17,200 | 18,600 | 18,420 | 18,030 | 17,600 |
+    +------------+--------+--------+--------+--------+--------+--------+
+
+  It will be seen from the figures and the description of the materials
+  that the steel forgings and castings have a remarkably high
+  permeability under small magnetizing force.
+
+Table II. shows the magnetic qualities of some of these materials as
+found by Ewing when tested with small magnetizing forces.
+
+  TABLE II.--_Magnetic Permeability of Samples of Iron and Steel under
+  Weak Magnetizing Forces._
+
+  +-----------------+-------------+----------------+---------------+
+  |  Magnetic Flux  |      I.     |      III.      |       VI.     |
+  |    Density B    |  Pure Iron. | Steel Forging. | Steel Casting.|
+  | (C.G.S. Units). |             |                |               |
+  +-----------------+-------------+----------------+---------------+
+  |                 |  H     [mu] |   H      [mu]  |  H      [mu]  |
+  |      2,000      | 0.90   2220 |  1.38    1450  | 1.18    1690  |
+  |      4,000      | 1.40   2850 |  1.91    2090  | 1.66    2410  |
+  |      6,000      | 1.85   3240 |  2.38    2520  | 2.15    2790  |
+  |      8,000      | 2.30   3480 |  2.92    2740  | 2.83    2830  |
+  |     10,000      | 3.10   3220 |  3.62    2760  | 4.05    2470  |
+  |     12,000      | 4.40   2760 |  4.80    2500  | 6.65    1810  |
+  +-----------------+-------------+----------------+---------------+
+
+The numbers I., III. and VI. in the above table refer to the samples
+mentioned in connexion with Table I.
+
+It is a remarkable fact that certain varieties of low carbon steel
+(commonly called mild steel) have a higher permeability than even
+annealed Swedish wrought iron under large magnetizing forces. The term
+_steel_, however, here used has reference rather to the mode of
+production than the final chemical nature of the material. In some of
+the mild-steel castings used for dynamo electromagnets it appears that
+the total foreign matter, including carbon, manganese and silicon, is
+not more than 0.3% of the whole, the material being 99.7% pure iron.
+This valuable magnetic property of steel capable of being cast is,
+however, of great utility in modern dynamo building, as it enables field
+magnets of very high permeability to be constructed, which can be
+fashioned into shape by casting instead of being built up as formerly
+out of masses of forged wrought iron. The curves in fig. 3 illustrate
+the manner in which the flux density or, as it is usually called, the
+magnetization curve of this mild cast steel crosses that of Swedish
+wrought iron, and enables us to obtain a higher flux density
+corresponding to a given magnetizing force with the steel than with the
+iron.
+
+From the same paper by Ewing we extract a number of results relating to
+permeability tests of thin sheet iron and sheet steel, such as is used
+in the construction of dynamo armatures and transformer cores.
+
+  No. VII. is a specimen of good transformer-plate, 0.301 millimetre
+  thick, rolled from Swedish iron by Messrs Sankey of Bilston. No. VIII.
+  is a specimen of specially thin transformer-plate rolled from scrap
+  iron. No. IX. is a specimen of transformer-plate rolled from
+  ingot-steel. No. X. is a specimen of the wire which was used by J.
+  Swinburne to form the core of his "hedgehog" transformers. Its
+  diameter was 0.602 millimetre. All these samples were tested in the
+  form of rings by the ballistic method, the rings of sheet-metal being
+  stamped or turned in the flat. The wire ring No. X. was coiled and
+  annealed after coiling.
+
+  [Illustration: FIG. 3.]
+
+    TABLE III.--_Permeability Tests of Transformer Plate and Wire_.
+
+    +---------+--------------+--------------+--------------+--------------+
+    |Magnetic |     VII.     |     VIII.    |      IX.     |      X.      |
+    |  Flux   | Transformer- | Transformer- | Transformer- | Transformer- |
+    |Density B|   plate of   |   plate of   |   plate of   |     wire.    |
+    | (C.G.S. | Swedish Iron.|  Scrap Iron. |   of Steel.  |              |
+    | Units). |              |              |              |              |
+    +---------+--------------+--------------+--------------+--------------+
+    |         |   H     [mu] |   H     [mu] |   H     [mu] |   H     [mu] |
+    |  1,000  |  0.81   1230 |  1.08    920 |  0.60   1470 |  1.71    590 |
+    |  2,000  |  1.05   1900 |  1.46   1370 |  0.90   2230 |  2.10    950 |
+    |  3,000  |  1.26   2320 |  1.77   1690 |  1.04   2880 |  2.30   1300 |
+    |  4,000  |  1.54   2600 |  2.10   1900 |  1.19   3360 |  2.50   1600 |
+    |  5,000  |  1.82   2750 |  2.53   1980 |  1.38   3620 |  2.70   1850 |
+    |  6,000  |  2.14   2800 |  3.04   1970 |  1.59   3770 |  2.92   2070 |
+    |  7,000  |  2.54   2760 |  3.62   1930 |  1.89   3700 |  3.16   2210 |
+    |  8,000  |  3.09   2590 |  4.37   1830 |  2.25   3600 |  3.43   2330 |
+    |  9,000  |  3.77   2390 |  5.3    1700 |  2.72   3310 |  3.77   2390 |
+    | 10,000  |  4.6    2170 |  6.5    1540 |  3.33   3000 |  4.17   2400 |
+    | 11,000  |  5.7    1930 |  7.9    1390 |  4.15   2650 |  4.70   2340 |
+    | 12,000  |  7.0    1710 |  9.8    1220 |  5.40   2220 |  5.45   2200 |
+    | 13,000  |  8.5    1530 | 11.9    1190 |  7.1    1830 |  6.5    2000 |
+    | 14,000  | 11.0    1270 | 15.0     930 | 10.0    1400 |  8.4    1670 |
+    | 15,000  | 15.1     990 | 19.5     770 |   ..     ..  | 11.9    1260 |
+    | 16,000  | 21.4     750 | 27.5     580 |   ..     ..  | 21.0     760 |
+    +---------+--------------+--------------+--------------+--------------+
+
+Some typical flux-density curves of iron and steel as used in dynamo and
+transformer building are given in fig. 4.
+
+[Illustration: FIG. 4.]
+
+The numbers in Table III. well illustrate the fact that the
+permeability, [mu] = B/H has a maximum value corresponding to a certain
+flux density. The tables are also explanatory of the fact that mild
+steel has gradually replaced iron in the manufacture of dynamo
+electromagnets and transformer-cores.
+
+Broadly speaking, the materials which are now employed in the
+manufacture of the cores of electromagnets for technical purposes of
+various kinds may be said to fall into three classes, namely, forgings,
+castings and stampings. In some cases the iron or steel core which is to
+be magnetized is simply a mass of iron hammered or pressed into shape by
+hydraulic pressure; in other cases it has to be fused and cast; and for
+certain other purposes it must be rolled first into thin sheets, which
+are subsequently stamped out into the required forms.
+
+[Illustration: FIG. 5.]
+
+For particular purposes it is necessary to obtain the highest possible
+magnetic permeability corresponding to a high, or the highest attainable
+flux density. This is generally the case in the electromagnets which are
+employed as the field magnets in dynamo machines. It may generally be
+said that whilst the best wrought iron, such as annealed Low Moor or
+Swedish iron, is more permeable for low flux densities than steel
+castings, the cast steel may surpass the wrought metal for high flux
+density. For most electro-technical purposes the best magnetic results
+are given by the employment of forged ingot-iron. This material is
+probably the most permeable throughout the whole scale of attainable
+flux densities. It is slightly superior to wrought iron, and it only
+becomes inferior to the highest class of cast steel when the flux
+density is pressed above 18,000 C.G.S. units (see fig. 5). For flux
+densities above 13,000 the forged ingot-iron has now practically
+replaced for electric engineering purposes the Low Moor or Swedish iron.
+Owing to the method of its production, it might in truth be called a
+soft steel with a very small percentage of combined carbon. The best
+description of this material is conveyed by the German term
+"Flusseisen," but its nearest British equivalent is "ingot-iron."
+Chemically speaking, the material is for all practical purposes very
+nearly pure iron. The same may be said of the cast steels now much
+employed for the production of dynamo magnet cores. The cast steel which
+is in demand for this purpose has a slightly lower permeability than the
+ingot-iron for low flux densities, but for flux densities above 16,000
+the required result may be more cheaply obtained with a steel casting
+than with a forging. When high tensile strength is required in addition
+to considerable magnetic permeability, it has been found advantageous to
+employ a steel containing 5% of nickel. The rolled sheet iron and sheet
+steel which is in request for the construction of magnet cores,
+especially those in which the exciting current is an alternating
+current, are, generally speaking, produced from Swedish iron. Owing to
+the mechanical treatment necessary to reduce the material to a thin
+sheet, the permeability at low flux densities is rather higher than,
+although at high flux densities it is inferior to, the same iron and
+steel when tested in bulk. For most purposes, however, where a laminated
+iron magnet core is required, the flux density is not pressed up above
+6000 units, and it is then more important to secure small hysteresis
+loss than high permeability. The magnetic permeability of cast iron is
+much inferior to that of wrought or ingot-iron, or the mild steels taken
+at the same flux densities.
+
+The following Table IV. gives the flux density and permeability of a
+typical cast iron taken by J.A. Fleming by the ballistic method:--
+
+  TABLE IV.--_Magnetic Permeability and Magnetization Curve of Cast
+  Iron._
+
+  +------+------+-----++-------+------+-----++--------+--------+-----+
+  |  H   |  B   | [mu]||   H   |  B   | [mu]||    H   |   B    | [mu]|
+  |  .19 |  27  | 139 ||  8.84 | 4030 | 456 ||  44.65 |  8,071 | 181 |
+  |  .41 |   62 | 150 || 10.60 | 4491 | 424 ||  56.57 |  8,548 | 151 |
+  | 1.11 |  206 | 176 || 12.33 | 4884 | 396 ||  71.98 |  9,097 | 126 |
+  | 2.53 |  768 | 303 || 13.95 | 5276 | 378 ||  88.99 |  9,600 | 108 |
+  | 3.41 | 1251 | 367 || 15.61 | 5504 | 353 || 106.35 | 10,066 |  95 |
+  | 4.45 | 1898 | 427 || 18.21 | 5829 | 320 || 120.60 | 10,375 |  86 |
+  | 5.67 | 2589 | 456 || 26.37 | 6814 | 258 || 140.37 | 10,725 |  76 |
+  | 7.16 | 3350 | 468 || 36.54 | 7580 | 207 || 152.73 | 10,985 |  72 |
+  +------+------+-----++-------+------+-----++--------+--------+-----+
+
+The metal of which the tests are given in Table IV. contained 2% of
+silicon, 2.85% of total carbon, and 0.5% of manganese. It will be seen
+that a magnetizing force of about 5 C.G.S. units is sufficient to impart
+to a wrought-iron ring a flux density of 18,000 C.G.S. units, but the
+same force hardly produces more than one-tenth of this flux density in
+cast iron.
+
+The testing of sheet iron and steel for magnetic hysteresis loss has
+developed into an important factory process, giving as it does a means
+of ascertaining the suitability of the metal for use in the manufacture
+of transformers and cores of alternating-current electromagnets.
+
+In Table V. are given the results of hysteresis tests by Ewing on
+samples of commercial sheet iron and steel. The numbers VII., VIII., IX.
+and X. refer to the same samples as those for which permeability results
+are given in Table III.
+
+  TABLE V.--_Hysteresis Loss in Transformer-iron._
+
+  +-------+------------------------------+-------------------------------+
+  |       |  Ergs per Cubic Centimetre   | Watts per lb. at a Frequency  |
+  |       |          per Cycle.          |            of 100.            |
+  |Maximum+-------+-------+-------+------+-------+-------+-------+-------+
+  | Flux  |  VII. | VIII. |  IX.  |  X.  |       |       |       |       |
+  |Density|Swedish| Forged| Ingot-| Soft |       |       |       |       |
+  |   B.  | Iron. |Scrap- | steel.| Iron |  VII. | VIII. |  IX.  |   X.  |
+  |       |       | iron. |       | Wire.|       |       |       |       |
+  +-------+-------+-------+-------+------+-------+-------+-------+-------+
+  | 2000  |  240  |  400  |  215  |  600 | 0.141 | 0.236 | 0.127 | 0.356 |
+  | 3000  |  520  |  790  |  430  | 1150 | 0.306 | 0.465 | 0.253 | 0.630 |
+  | 4000  |  830  | 1220  |  700  | 1780 | 0.490 | 0.720 | 0.410 | 1.050 |
+  | 5000  | 1190  | 1710  | 1000  | 2640 | 0.700 | 1.010 | 0.590 | 1.550 |
+  | 6000  | 1600  | 2260  | 1350  | 3360 | 0.940 | 1.330 | 0.790 | 1.980 |
+  | 7000  | 2020  | 2940  | 1730  | 4300 | 1.200 | 1.730 | 1.020 | 2.530 |
+  | 8000  | 2510  | 3710  | 2150  | 5300 | 1.480 | 2.180 | 1.270 | 3.120 |
+  | 9000  | 3050  | 4560  | 2620  | 6380 | 1.800 | 2.680 | 1.540 | 3.750 |
+  +-------+-------+-------+-------+------+-------+-------+-------+-------+
+
+In Table VI. are given the results of a magnetic test of some
+exceedingly good transformer-sheet rolled from Swedish iron.
+
+  TABLE VI.--_Hysteresis Loss in Strip of Transformer-plate rolled
+  Swedish Iron._
+
+  +------------+---------------------------+--------------------+
+  |Maximum Flux| Ergs per Cubic Centimetre | Watts per lb. at a |
+  |Density B.  |         per Cycle.        |  Frequency of 100. |
+  +------------+---------------------------+--------------------+
+  |    2000    |            220            |       0.129        |
+  |    3000    |            410            |       0.242        |
+  |    4000    |            640            |       0.376        |
+  |    5000    |            910            |       0.535        |
+  |    6000    |           1200            |       0.710        |
+  |    7000    |           1520            |       0.890        |
+  |    8000    |           1900            |       1.120        |
+  |    9000    |           2310            |       1.360        |
+  +------------+---------------------------+--------------------+
+
+In Table VII. are given some values obtained by Fleming for the
+hysteresis loss in the sample of cast iron, the permeability test of
+which is recorded in Table IV.
+
+  TABLE VII.--_Observations on the Magnetic Hysteresis of Cast Iron._
+
+  +------+---------+-----------------------------------+
+  |      |         |         Hysteresis Loss.          |
+  |      |         +-------------+---------------------+
+  | Loop.| B (max.)| Ergs per cc.|  Watts per lb. per. |
+  |      |         |  per Cycle. | 100 Cycles per sec. |
+  +------+---------+-------------+---------------------+
+  |   I. |  1475   |      466    |         .300        |
+  |  II. |  2545   |    1,288    |         .829        |
+  | III. |  3865   |    2,997    |        1.934        |
+  |  IV. |  5972   |    7,397    |        4.765        |
+  |   V. |  8930   |   13,423    |        8.658        |
+  +------+---------+-------------+---------------------+
+
+For most practical purposes the constructor of electromagnetic machinery
+requires his iron or steel to have some one of the following
+characteristics. If for dynamo or magnet making, it should have the
+highest possible permeability at a flux density corresponding to
+practically maximum magnetization. If for transformer or
+alternating-current magnet building, it should have the smallest
+possible hysteresis loss at a maximum flux density of 2500 C.G.S. units
+during the cycle. If required for permanent magnet making, it should
+have the highest possible coercivity combined with a high retentivity.
+Manufacturers of iron and steel are now able to meet these demands in a
+very remarkable manner by the commercial production of material of a
+quality which at one time would have been considered a scientific
+curiosity.
+
+It is usual to specify iron and steel for the first purpose by naming
+the minimum permeability it should possess corresponding to a flux
+density of 18,000 C.G.S. units; for the second, by stating the
+hysteresis loss in watts per lb. per 100 cycles per second,
+corresponding to a maximum flux density of 2500 C.G.S. units during the
+cycle; and for the third, by mentioning the coercive force required to
+reduce to zero magnetization a sample of the metal in the form of a long
+bar magnetized to a stated magnetization. In the cyclical reversal of
+magnetization of iron we have two modes to consider. In the first case,
+which is that of the core of the alternating transformer, the magnetic
+force passes through a cycle of values, the iron remaining stationary,
+and the direction of the magnetic force being always the same. In the
+other case, that of the dynamo armature core, the direction of the
+magnetic force in the iron is constantly changing, and at the same time
+undergoing a change in magnitude.
+
+It has been shown by F.G. Baily (_Proc. Roy. Soc._, 1896) that if a mass
+of laminated iron is rotating in a magnetic field which remains constant
+in direction and magnitude in any one experiment, the hysteresis loss
+rises to a maximum as the magnitude of the flux density in the iron is
+increased and then falls away again to nearly zero value. These
+observations have been confirmed by other observers. The question has
+been much debated whether the values of the hysteresis loss obtained by
+these two different methods are identical for magnetic cycles in which
+the flux density reaches the same maximum value. This question is also
+connected with another one, namely, whether the hysteresis loss per
+cycle is or is not a function of the speed with which the cycle is
+traversed. Early experiments by C.P. Steinmetz and others seemed to show
+that there was a difference between slow-speed and high-speed hysteresis
+cycles, but later experiments by J. Hopkinson and by A. Tanakadate,
+though not absolutely exhaustive, tend to prove that up to 400 cycles
+per second the hysteresis loss per cycle is practically unchanged.
+
+Experiments made in 1896 by R. Beattie and R.C. Clinker on magnetic
+hysteresis in rotating fields were partly directed to determine whether
+the hysteresis loss at moderate flux densities, such as are employed in
+transformer work, was the same as that found by measurements made with
+alternating-current fields on the same iron and steel specimens (see
+_The Electrician_, 1896, 37, p. 723). These experiments showed that
+over moderate ranges of induction, such as may be expected in
+electro-technical work, the hysteresis loss per cycle per cubic
+centimetre was practically the same when the iron was tested in an
+alternating field with a periodicity of 100, the field remaining
+constant in direction, and when the iron was tested in a rotating field
+giving the same maximum flux density.
+
+With respect to the variation of hysteresis loss in magnetic cycles
+having different maximum values for the flux density, Steinmetz found
+that the hysteresis loss (W), as measured by the area of the complete
+(B, H) cycle and expressed in ergs per centimetre-cube per cycle, varies
+proportionately to a constant called the _hysteretic constant_, and to
+the 1.6th power of the maximum flux density (B), or W = [eta]B^(1.6).
+
+The hysteretic constants ([eta]) for various kinds of iron and steel are
+given in the table below:--
+
+    Metal.                                  Hysteretic Constant.
+
+  Swedish wrought iron, well annealed         .0010 to .0017
+  Annealed cast steel of good quality; small
+    percentage of carbon                      .0017 to .0029
+  Cast Siemens-Martin steel                   .0019 to .0028
+  Cast ingot-iron                             .0021 to .0026
+  Cast steel, with higher percentages of
+    carbon, or inferior qualities of wrought
+    iron                                      .0031 to .0054
+
+Steinmetz's law, though not strictly true for very low or very high
+maximum flux densities, is yet a convenient empirical rule for obtaining
+approximately the hysteresis loss at any one maximum flux density and
+knowing it at another, provided these values fall within a range varying
+say from 1 to 9000 C.G.S. units. (See MAGNETISM.)
+
+The standard maximum flux density which is adopted in electro-technical
+work is 2500, hence in the construction of the cores of
+alternating-current electromagnets and transformers iron has to be
+employed having a known hysteretic constant at the standard flux
+density. It is generally expressed by stating the number of watts per
+lb. of metal which would be dissipated for a frequency of 100 cycles,
+and a maximum flux density (B max.) during the cycle of 2500. In the
+case of good iron or steel for transformer-core making, it should not
+exceed 1.25 watt per lb. per 100 cycles per 2500 B (maximum value).
+
+It has been found that if the sheet iron employed for cores of
+alternating electromagnets or transformers is heated to a temperature
+somewhere in the neighbourhood of 200 deg. C. the hysteresis loss is
+very greatly increased. It was noticed in 1894 by G.W. Partridge that
+alternating-current transformers which had been in use some time had a
+very considerably augmented core loss when compared with their initial
+condition. O.T. Blathy and W.M. Mordey in 1895 showed that this
+augmentation in hysteresis loss in iron was due to heating. H.F.
+Parshall investigated the effect up to moderate temperatures, such as
+140 deg. C., and an extensive series of experiments was made in 1898 by
+S.R. Roget (_Proc. Roy. Soc._, 1898, 63, p. 258, and 64, p. 150). Roget
+found that below 40 deg. C. a rise in temperature did not produce any
+augmentation in the hysteresis loss in iron, but if it is heated to
+between 40 deg. C. and 135 deg. C. the hysteresis loss increases
+continuously with time, and this increase is now called "ageing" of the
+iron. It proceeds more slowly as the temperature is higher. If heated to
+above 135 deg. C., the hysteresis loss soon attains a maximum, but then
+begins to decrease. Certain specimens heated to 160 deg. C. were found
+to have their hysteresis loss doubled in a few days. The effect seems to
+come to a maximum at about 180 deg. C. or 200 deg. C. Mere lapse of time
+does not remove the increase, but if the iron is reannealed the
+augmentation in hysteresis disappears. If the iron is heated to a higher
+temperature, say between 300 deg. C. and 700 deg. C., Roget found the
+initial rise of hysteresis happens more quickly, but that the metal soon
+settles down into a state in which the hysteresis loss has a small but
+still augmented constant value. The augmentation in value, however,
+becomes more nearly zero as the temperature approaches 700 deg. C.
+Brands of steel are now obtainable which do not age in this manner, but
+these _non-ageing_ varieties of steel have not generally such low
+initial hysteresis values as the "Swedish Iron," commonly considered
+best for the cores of transformers and alternating-current magnets.
+
+The following conclusions have been reached in the matter:--(1) Iron and
+mild steel in the annealed state are more liable to change their
+hysteresis value by heating than when in the harder condition; (2) all
+changes are removed by re-annealing; (3) the changes thus produced by
+heating affect not only the amount of the hysteresis loss, but also the
+form of the lower part of the (B, H) curve.
+
+_Forms of Electromagnet._--The form which an electromagnet must take
+will greatly depend upon the purposes for which it is to be used. A
+design or form of electromagnet which will be very suitable for some
+purposes will be useless for others. Supposing it is desired to make an
+electromagnet which shall be capable of undergoing very rapid changes of
+strength, it must have such a form that the coercivity of the material
+is overcome by a self-demagnetizing force. This can be achieved by
+making the magnet in the form of a short and stout bar rather than a
+long thin one. It has already been explained that the ends or poles of a
+polar magnet exert a demagnetizing power upon the mass of the metal in
+the interior of the bar. If then the electromagnet has the form of a
+long thin bar, the length of which is several hundred times its
+diameter, the poles are very far removed from the centre of the bar, and
+the demagnetizing action will be very feeble; such a long thin
+electromagnet, although made of very soft iron, retains a considerable
+amount of magnetism after the magnetizing force is withdrawn. On the
+other hand, a very thick bar very quickly demagnetizes itself, because
+no part of the metal is far removed from the action of the free poles.
+Hence when, as in many telegraphic instruments, a piece of soft iron,
+called an armature, has to be attracted to the poles of a
+horseshoe-shaped electromagnet, this armature should be prevented from
+quite touching the polar surfaces of the magnet. If a soft iron mass
+does quite touch the poles, then it completes the magnetic circuit and
+abolishes the free poles, and the magnet is to a very large extent
+deprived of its self-demagnetizing power. This is the explanation of the
+well-known fact that after exciting the electromagnet and then stopping
+the current, it still requires a good pull to detach the "keeper"; but
+when once the keeper has been detached, the magnetism is found to have
+nearly disappeared. An excellent form of electromagnet for the
+production of very powerful fields has been designed by H. du Bois (fig.
+6).
+
+[Illustration: FIG. 6.--Du Bois's Electromagnet.]
+
+Various forms of electromagnets used in connexion with dynamo machines
+are considered in the article DYNAMO, and there is, therefore, no
+necessity to refer particularly to the numerous different shapes and
+types employed in electrotechnics.
+
+  BIBLIOGRAPHY.--For additional information on the above subject the
+  reader may be referred to the following works and original papers:--
+
+  H. du Bois, _The Magnetic Circuit in Theory and Practice_; S.P.
+  Thompson, _The Electromagnet_; J.A. Fleming, _Magnets and Electric
+  Currents_; J.A. Ewing, _Magnetic Induction in Iron and other Metals_;
+  J.A. Fleming, "The Ferromagnetic Properties of Iron and Steel,"
+  _Proceedings of Sheffield Society of Engineers and Metallurgists_
+  (Oct. 1897); J.A. Ewing, "The Magnetic Testing of Iron and Steel,"
+  _Proc. Inst. Civ. Eng._, 1896, 126, p. 185; H.F. Parshall, "The
+  Magnetic Data of Iron and Steel," _Proc. Inst. Civ. Eng._, 1896, 126,
+  p. 220; J.A. Ewing, "The Molecular Theory of Induced Magnetism,"
+  _Phil. Mag._, Sept. 1890; W.M. Mordey, "Slow Changes in the
+  Permeability of Iron," _Proc. Roy. Soc._ 57, p. 224; J.A. Ewing,
+  "Magnetism," James Forrest Lecture, _Proc. Inst. Civ. Eng._ 138; S.P.
+  Thompson, "Electromagnetic Mechanism," _Electrician_, 26, pp. 238,
+  269, 293; J.A. Ewing, "Experimental Researches in Magnetism," _Phil.
+  Trans._, 1885, part ii.; Ewing and Klassen, "Magnetic Qualities of
+  Iron," _Proc. Roy. Soc._, 1893.     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] In the _Annals of Philosophy_ for November 1821 is a long article
+    entitled "Electromagnetism" by Oersted, in which he gives a detailed
+    account of his discovery. He had his thoughts turned to it as far
+    back as 1813, but not until the 20th of July 1820 had he actually
+    made his discovery. He seems to have been arranging a compass needle
+    to observe any deflections during a storm, and placed near it a
+    platinum wire through which a galvanic current was passed.
+
+  [2] See _Trans. Soc. Arts_, 1825, 43, p. 38, in which a figure of
+    Sturgeon's electromagnet is given as well as of other pieces of
+    apparatus for which the Society granted him a premium and a silver
+    medal.
+
+  [3] See S.P. Thompson, _The Electromagnet_ (London, 1891); J.A.
+    Fleming, _A Handbook for the Electrical Laboratory and Testing Room_,
+    vol. 2 (London, 1903); J.A. Ewing, _Magnetic Induction in Iron and
+    other Metals_ (London, 1903, 3rd ed.).
+
+
+
+
+ELECTROMETALLURGY. The present article, as explained under
+ELECTROCHEMISTRY, treats only of those processes in which electricity is
+applied to the production of chemical reactions or molecular changes at
+furnace temperatures. In many of these the application of heat is
+necessary to bring the substances used into the liquid state for the
+purpose of electrolysis, aqueous solutions being unsuitable. Among the
+earliest experiments in this branch of the subject were those of Sir H.
+Davy, who in 1807 (_Phil. Trans._, 1808, p. 1), produced the alkali
+metals by passing an intense current of electricity from a platinum wire
+to a platinum dish, through a mass of fused caustic alkali. The action
+was started in the cold, the alkali being slightly moistened to render
+it a conductor; then, as the current passed, heat was produced and the
+alkali fused, the metal being deposited in the liquid condition. Later,
+A. Matthiessen (_Quarterly Journ. Chem. Soc._ viii. 30) obtained
+potassium by the electrolysis of a mixture of potassium and calcium
+chlorides fused over a lamp. There are here foreshadowed two types of
+electrolytic furnace-operations: (a) those in which external heating
+maintains the electrolyte in the fused condition, and (b) those in which
+a current-density is applied sufficiently high to develop the heat
+necessary to effect this object unaided. Much of the earlier
+electro-metallurgical work was done with furnaces of the (a) type, while
+nearly all the later developments have been with those of class (b).
+There is a third class of operations, exemplified by the manufacture of
+calcium carbide, in which electricity is employed solely as a heating
+agent; these are termed _electrothermal_, as distinguished from
+_electrolytic_. In certain electrothermal processes (e.g. calcium
+carbide production) the heat from the current is employed in raising
+mixtures of substances to the temperature at which a desired chemical
+reaction will take place between them, while in others (e.g. the
+production of graphite from coke or gas-carbon) the heat is applied
+solely to the production of molecular or physical changes. In ordinary
+electrolytic work only the continuous current may of course be used, but
+in electrothermal work an alternating current is equally available.
+
+_Electric Furnaces._--Independently of the question of the application
+of external heating, the furnaces used in electrometallurgy may be
+broadly classified into (i.) arc furnaces, in which the intense heat of
+the electric arc is utilized, and (ii.) resistance and incandescence
+furnaces, in which the heat is generated by an electric current
+overcoming the resistance of an inferior conductor.
+
+
+  Arc furnaces.
+
+Excepting such experimental arrangements as that of C.M. Despretz
+(_C.R._, 1849, 29) for use on a small scale in the laboratory, Pichou in
+France and J.H. Johnson in England appear, in 1853, to have introduced
+the earliest practical form of furnace. In these arrangements, which
+were similar if not identical, the furnace charge was crushed to a fine
+powder and passed through two or more electric arcs in succession. When
+used for ore smelting, the reduced metal and the accompanying slag were
+to be caught, after leaving the arc and while still liquid, in a hearth
+fired with ordinary fuel. Although this primitive furnace could be made
+to act, its efficiency was low, and the use of a separate fire was
+disadvantageous. In 1878 Sir William Siemens patented a form of
+furnace[1] which is the type of a very large number of those designed by
+later inventors.
+
+  In the best-known form a plumbago crucible was used with a hole cut in
+  the bottom to receive a carbon rod, which was ground in so as to make
+  a tight joint. This rod was connected with the positive pole of the
+  dynamo or electric generator. The crucible was fitted with a cover in
+  which were two holes; one at the side to serve at once as sight-hole
+  and charging door, the other in the centre to allow a second carbon
+  rod to pass freely (without touching) into the interior. This rod was
+  connected with the negative pole of the generator, and was suspended
+  from one arm of a balance-beam, while from the other end of the beam
+  was suspended a vertical hollow iron cylinder, which could be moved
+  into or out of a wire coil or solenoid joined as a shunt across the
+  two carbon rods of the furnace. The solenoid was above the iron
+  cylinder, the supporting rod of which passed through it as a core.
+  When the furnace with this well-known regulating device was to be
+  used, say, for the melting of metals or other conductors of
+  electricity, the fragments of metal were placed in the crucible and
+  the positive electrode was brought near them. Immediately the current
+  passed through the solenoid it caused the iron cylinder to rise, and,
+  by means of its supporting rod, forced the end of the balance beam
+  upwards, so depressing the other end that the negative carbon rod was
+  forced downwards into contact with the metal in the crucible. This
+  action completed the furnace-circuit, and current passed freely from
+  the positive carbon through the fragments of metal to the negative
+  carbon, thereby reducing the current through the shunt. At once the
+  attractive force of the solenoid on the iron cylinder was
+  automatically reduced, and the falling of the latter caused the
+  negative carbon to rise, starting an arc between it and the metal in
+  the crucible. A counterpoise was placed on the solenoid end of the
+  balance beam to act against the attraction of the solenoid, the
+  position of the counterpoise determining the length of the arc in the
+  crucible. Any change in the resistance of the arc, either by
+  lengthening, due to the sinking of the charge in the crucible, or by
+  the burning of the carbon, affected the proportion of current flowing
+  in the two shunt circuits, and so altered the position of the iron
+  cylinder in the solenoid that the length of arc was, within limits,
+  automatically regulated. Were it not for the use of some such device
+  the arc would be liable to constant fluctuation and to frequent
+  extinction. The crucible was surrounded with a bad conductor of heat
+  to minimize loss by radiation. The positive carbon was in some cases
+  replaced by a water-cooled metal tube, or ferrule, closed, of course,
+  at the end inserted in the crucible. Several modifications were
+  proposed, in one of which, intended for the heating of non-conducting
+  substances, the electrodes were passed horizontally through
+  perforations in the upper part of the crucible walls, and the charge
+  in the lower part of the crucible was heated by radiation.
+
+The furnace used by Henri Moissan in his experiments on reactions at
+high temperatures, on the fusion and volatilization of refractory
+materials, and on the formation of carbides, silicides and borides of
+various metals, consisted, in its simplest form, of two superposed
+blocks of lime or of limestone with a central cavity cut in the lower
+block, and with a corresponding but much shallower inverted cavity in
+the upper block, which thus formed the lid of the furnace. Horizontal
+channels were cut on opposite walls, through which the carbon poles or
+electrodes were passed into the upper part of the cavity. Such a
+furnace, to take a current of 4 H.P. (say, of 60 amperes and 50 volts),
+measured externally about 6 by 6 by 7 in., and the electrodes were about
+0.4 in. in diameter, while for a current of 100 H.P. (say, of 746
+amperes and 100 volts) it measured about 14 by 12 by 14 in., and the
+electrodes were about 1.5 in. in diameter. In the latter case the
+crucible, which was placed in the cavity immediately beneath the arc,
+was about 3 in. in diameter (internally), and about 3-1/2 in. in height.
+The fact that energy is being used at so high a rate as 100 H.P. on so
+small a charge of material sufficiently indicates that the furnace is
+only used for experimental work, or for the fusion of metals which, like
+tungsten or chromium, can only be melted at temperatures attainable by
+electrical means. Moissan succeeded in fusing about 3/4 lb. of either of
+these metals in 5 or 6 minutes in a furnace similar to that last
+described. He also arranged an experimental tube-furnace by passing a
+carbon tube horizontally beneath the arc in the cavity of the lime
+blocks. When prolonged heating is required at very high temperatures it
+is found necessary to line the furnace-cavity with alternate layers of
+magnesia and carbon, taking care that the lamina next to the lime is of
+magnesia; if this were not done the lime in contact with the carbon
+crucible would form calcium carbide and would slag down, but magnesia
+does not yield a carbide in this way. Chaplet has patented a muffle or
+tube furnace, similar in principle, for use on a larger scale, with a
+number of electrodes placed above and below the muffle-tube. The arc
+furnaces now widely used in the manufacture of calcium carbide on a
+large scale are chiefly developments of the Siemens furnace. But
+whereas, from its construction, the Siemens furnace was intermittent in
+operation, necessitating stoppage of the current while the contents of
+the crucible were poured out, many of the newer forms are specially
+designed either to minimize the time required in effecting the
+withdrawal of one charge and the introduction of the next, or to ensure
+absolute continuity of action, raw material being constantly charged in
+at the top and the finished substance and by-products (slag, &c.)
+withdrawn either continuously or at intervals, as sufficient quantity
+shall have accumulated. In the King furnace, for example, the crucible,
+or lowest part of the furnace, is made detachable, so that when full it
+may be removed and an empty crucible substituted. In the United States a
+revolving furnace is used which is quite continuous in action.
+
+
+  Incandescence furnaces.
+
+The class of furnaces heated by electrically incandescent materials has
+been divided by Borchers into two groups: (1) those in which the
+substance is heated by contact with a substance offering a high
+resistance to the current passing through it, and (2) those in which the
+substance to be heated itself affords the resistance to the passage of
+the current whereby electric energy is converted into heat. Practically
+the first of these furnaces was that of Despretz, in which the mixture
+to be heated was placed in a carbon tube rendered incandescent by the
+passage of a current through its substance from end to end. In 1880 W.
+Borchers introduced his resistance-furnace, which, in one sense, is the
+converse of the Despretz apparatus. A thin carbon pencil, forming a
+bridge between two stout carbon rods, is set in the midst of the mixture
+to be heated. On passing a current through the carbon the small rod is
+heated to incandescence, and imparts heat to the surrounding mass. On a
+larger scale several pencils are used to make the connexions between
+carbon blocks which form the end walls of the furnace, while the side
+walls are of fire-brick laid upon one another without mortar. Many of
+the furnaces now in constant use depend mainly on this principle, a core
+of granular carbon fragments stamped together in the direct line between
+the electrodes, as in Acheson's carborundum furnace, being substituted
+for the carbon pencils. In other cases carbon fragments are mixed
+throughout the charge, as in E.H. and A.H. Cowles's zinc-smelting
+retort. In practice, in these furnaces, it is possible for small local
+arcs to be temporarily set up by the shifting of the charge, and these
+would contribute to the heating of the mass. In the remaining class of
+furnace, in which the electrical resistance of the charge itself is
+utilized, are the continuous-current furnaces, such as are used for the
+smelting of aluminium, and those alternating-current furnaces, (e.g. for
+the production of calcium carbide) in which a portion of the charge is
+first actually fused, and then maintained in the molten condition by the
+current passing through it, while the reaction between further portions
+of the charge is proceeding.
+
+
+  Uses and advantages.
+
+For ordinary metallurgical work the electric furnace, requiring as it
+does (excepting where waterfalls or other cheap sources of power are
+available) the intervention of the boiler and steam-engine, or of the
+gas or oil engine, with a consequent loss of energy, has not usually
+proved so economical as an ordinary direct fired furnace. But in some
+cases in which the current is used for electrolysis and for the
+production of extremely high temperatures, for which the calorific
+intensity of ordinary fuel is insufficient, the electric furnace is
+employed with advantage. The temperature of the electric furnace,
+whether of the arc or incandescence type, is practically limited to
+that at which the least easily vaporized material available for
+electrodes is converted into vapour. This material is carbon, and as its
+vaporizing point is (estimated at) over 3500 deg. C., and less than 4000
+deg. C., the temperature of the electric furnace cannot rise much above
+3500 deg. C. (6330 deg. F.); but H. Moissan showed that at this
+temperature the most stable of mineral combinations are dissociated, and
+the most refractory elements are converted into vapour, only certain
+borides, silicides and metallic carbides having been found to resist the
+action of the heat. It is not necessary that all electric furnaces shall
+be run at these high temperatures; obviously, those of the incandescence
+or resistance type may be worked at any convenient temperature below the
+maximum. The electric furnace has several advantages as compared with
+some of the ordinary types of furnace, arising from the fact that the
+heat is generated from within the mass of material operated upon, and
+(unlike the blast-furnace, which presents the same advantage) without a
+large volume of gaseous products of combustion and atmospheric nitrogen
+being passed through it. In ordinary reverberatory and other heating
+furnaces the burning fuel is without the mass, so that the vessel
+containing the charge, and other parts of the plant, are raised to a
+higher temperature than would otherwise be necessary, in order to
+compensate for losses by radiation, convection and conduction. This
+advantage is especially observed in some cases in which the charge of
+the furnace is liable to attack the containing vessel at high
+temperatures, as it is often possible to maintain the outer walls of the
+electric furnace relatively cool, and even to keep them lined with a
+protecting crust of unfused charge. Again, the construction of electric
+furnaces may often be exceedingly crude and simple; in the carborundum
+furnace, for example, the outer walls are of loosely piled bricks, and
+in one type of furnace the charge is simply heaped on the ground around
+the carbon resistance used for heating, without containing-walls of any
+kind. There is, however, one (not insuperable) drawback in the use of
+the electric furnace for the smelting of pure metals. Ordinarily carbon
+is used as the electrode material, but when carbon comes in contact at
+high temperatures with any metal that is capable of forming a carbide a
+certain amount of combination between them is inevitable, and the carbon
+thus introduced impairs the mechanical properties of the ultimate
+metallic product. Aluminium, iron, platinum and many other metals may
+thus take up so much carbon as to become brittle and unforgeable. It is
+for this reason that Siemens, Borchers and others substituted a hollow
+water-cooled metal block for the carbon cathode upon which the melted
+metal rests while in the furnace. Liquid metal coming in contact with
+such a surface forms a crust of solidified metal over it, and this crust
+thickens up to a certain point, namely, until the heat from within the
+furnace just overbalances that lost by conduction through the solidified
+crust and the cathode material to the flowing water. In such an
+arrangement, after the first instant, the melted metal in the furnace
+does not come in contact with the cathode material.
+
+
+  Aluminium alloys.
+
+_Electrothermal Processes._--In these processes the electric current is
+used solely to generate heat, either to induce chemical reactions
+between admixed substances, or to produce a physical (allotropic)
+modification of a given substance. Borchers predicted that, at the high
+temperatures available with the electric furnace, every oxide would
+prove to be reducible by the action of carbon, and this prediction has
+in most instances been justified. Alumina and lime, for example, which
+cannot be reduced at ordinary furnace temperatures, readily give up
+their oxygen to carbon in the electric furnace, and then combine with an
+excess of carbon to form metallic carbides. In 1885 the brothers Cowles
+patented a process for the electrothermal reduction of oxidized ores by
+exposure to an intense current of electricity when admixed with carbon
+in a retort. Later in that year they patented a process for the
+reduction of aluminium by carbon, and in 1886 an electric furnace with
+sliding carbon rods passed through the end walls to the centre of a
+rectangular furnace. The impossibility of working with just sufficient
+carbon to reduce the alumina, without using any excess which would be
+free to form at least so much carbide as would suffice, when diffused
+through the metal, to render it brittle, practically restricts the use
+of such processes to the production of aluminium alloys. Aluminium
+bronze (aluminium and copper) and ferro-aluminium (aluminium and iron)
+have been made in this way; the latter is the more satisfactory product,
+because a certain proportion of carbon is expected in an alloy of this
+character, as in ferromanganese and cast iron, and its presence is not
+objectionable. The furnace is built of fire-brick, and may measure
+(internally) 5 ft. in length by 1 ft. 8 in. in width, and 3 ft. in
+height. Into each end wall is built a short iron tube sloping downwards
+towards the centre, and through this is passed a bundle of five 3-in.
+carbon rods, bound together at the outer end by being cast into a head
+of cast iron for use with iron alloys, or of cast copper for aluminium
+bronze. This head slides freely in the cast iron tubes, and is connected
+by a copper rod with one of the terminals of the dynamo supplying the
+current. The carbons can thus, by the application of suitable mechanism,
+be withdrawn from or plunged into the furnace at will. In starting the
+furnace, the bottom is prepared by ramming it with charcoal-powder that
+has been soaked in milk of lime and dried, so that each particle is
+coated with a film of lime, which serves to reduce the loss of current
+by conduction through the lining when the furnace becomes hot. A sheet
+iron case is then placed within the furnace, and the space between it
+and the walls rammed with limed charcoal; the interior is filled with
+fragments of the iron or copper to be alloyed, mixed with alumina and
+coarse charcoal, broken pieces of carbon being placed in position to
+connect the electrodes. The iron case is then removed, the whole is
+covered with charcoal, and a cast iron cover with a central flue is
+placed above all. The current, either continuous or alternating, is then
+started, and continued for about 1 to 1-1/2 hours, until the operation
+is complete, the carbon rods being gradually withdrawn as the action
+proceeds. In such a furnace a continuous current, for example, of 3000
+amperes, at 50 to 60 volts, may be used at first, increasing to 5000
+amperes in about half an hour. The reduction is not due to electrolysis,
+but to the action of carbon on alumina, a part of the carbon in the
+charge being consumed and evolved as carbon monoxide gas, which burns at
+the orifice in the cover so long as reduction is taking place. The
+reduced aluminium alloys itself immediately with the fused globules of
+metal in its midst, and as the charge becomes reduced the globules of
+alloy unite until, in the end, they are run out of the tap-hole after
+the current has been diverted to another furnace. It was found in
+practice (in 1889) that the expenditure of energy per pound of reduced
+aluminium was about 23 H.P.-hours, a number considerably in excess of
+that required at the present time for the production of pure aluminium
+by the electrolytic process described in the article ALUMINIUM. Calcium
+carbide, graphite (q.v.), phosphorus (q.v.) and carborundum (q.v.) are
+now extensively manufactured by the operations outlined above.
+
+_Electrolytic Processes._--The isolation of the metals sodium and
+potassium by Sir Humphry Davy in 1807 by the electrolysis of the fused
+hydroxides was one of the earliest applications of the electric current
+to the extraction of metals. This pioneering work showed little
+development until about the middle of the 19th century. In 1852
+magnesium was isolated electrolytically by R. Bunsen, and this process
+subsequently received much attention at the hands of Moissan and
+Borchers. Two years later Bunsen and H.E. Sainte Claire Deville working
+independently obtained aluminium (q.v.) by the electrolysis of the fused
+double sodium aluminium chloride. Since that date other processes have
+been devised and the electrolytic processes have entirely replaced the
+older methods of reduction with sodium. Methods have also been
+discovered for the electrolytic manufacture of calcium (q.v.), which
+have had the effect of converting a laboratory curiosity into a product
+of commercial importance. Barium and strontium have also been produced
+by electro-metallurgical methods, but the processes have only a
+laboratory interest at present. Lead, zinc and other metals have also
+been reduced in this manner.
+
+  For further information the following books, in addition to those
+  mentioned at the end of the article ELECTROCHEMISTRY, may be
+  consulted: Borchers, _Handbuch der Elektrochemie_; _Electric Furnaces_
+  (Eng. trans. by H.G. Solomon, 1908); Moissan, _The Electric Furnace_
+  (1904); J. Escard, _Fours electriques_ (1905); _Les Industries
+  electrochimiques_ (1907).     (W. G. M.)
+
+
+FOOTNOTE:
+
+  [1] Cf. Siemens's account of the use of this furnace for experimental
+    purposes in _British Association Report_ for 1882.
+
+
+
+
+ELECTROMETER, an instrument for measuring difference of potential, which
+operates by means of electrostatic force and gives the measurement
+either in arbitrary or in absolute units (see UNITS, PHYSICAL). In the
+last case the instrument is called an absolute electrometer. Lord Kelvin
+has classified electrometers into (1) Repulsion, (2) Attracted disk, and
+(3) Symmetrical electrometers (see W. Thomson, _Brit. Assoc. Report_,
+1867, or _Reprinted Papers on Electrostatics and Magnetization_, p.
+261).
+
+_Repulsion Electrometers._--The simplest form of repulsion electrometer
+is W. Henley's pith ball electrometer (_Phil. Trans._, 1772, 63, p. 359)
+in which the repulsion of a straw ending in a pith ball from a fixed
+stem is indicated on a graduated arc (see ELECTROSCOPE). A double pith
+ball repulsion electrometer was employed by T. Cavallo in 1777.
+
+  It may be pointed out that such an arrangement is not merely an
+  arbitrary electrometer, but may become an absolute electrometer within
+  certain rough limits. Let two spherical pith balls of radius r and
+  weight W, covered with gold-leaf so as to be conducting, be suspended
+  by parallel silk threads of length l so as just to touch each other.
+  If then the balls are both charged to a potential V they will repel
+  each other, and the threads will stand out at an angle 2[theta], which
+  can be observed on a protractor. Since the electrical repulsion of the
+  balls is equal to C^2V^24l^2 sin^2[theta] dynes, where C = r is the
+  capacity of either ball, and this force is balanced by the restoring
+  force due to their weight, Wg dynes, where g is the acceleration of
+  gravity, it is easy to show that we have
+
+        2l sin [theta] [root](Wg tan [theta])
+    V = -------------------------------------
+                         r
+
+  as an expression for their common potential V, provided that the balls
+  are small and their distance sufficiently great not sensibly to
+  disturb the uniformity of electric charge upon them. Observation of
+  [theta] with measurement of the value of l and r reckoned in
+  centimetres and W in grammes gives us the potential difference of the
+  balls in absolute C.G.S. or electrostatic units. The gold-leaf
+  electroscope invented by Abraham Bennet (see ELECTROSCOPE) can in like
+  manner, by the addition of a scale to observe the divergence of the
+  gold-leaves, be made a repulsion electrometer.
+
+[Illustration: FIG. 1.--Snow-Harris's Disk Electrometer.]
+
+_Attracted Disk Electrometers._--A form of attracted disk absolute
+electrometer was devised by A. Volta. It consisted of a plane conducting
+plate forming one pan of a balance which was suspended over another
+insulated plate which could be electrified. The attraction between the
+two plates was balanced by a weight put in the opposite pan. A similar
+electric balance was subsequently devised by Sir W. Snow-Harris,[1] one
+of whose instruments is shown in fig. 1. C is an insulated disk over
+which is suspended another disk attached to the arm of a balance. A
+weight is put in the opposite scale pan and a measured charge of
+electricity is given to the disk C just sufficient to tip over the
+balance. Snow-Harris found that this charge varied as the square root of
+the weight in the opposite pan, thus showing that the attraction
+between the disks at given distance apart varies as the square of their
+difference of potential.
+
+The most important improvements in connexion with electrometers are due,
+however, to Lord Kelvin, who introduced the guard plate and used gravity
+or the torsion of a wire as a means for evaluating the electrical
+forces.
+
+[Illustration: FIG. 2.--Kelvin's Portable Electrometer.]
+
+[Illustration: FIG. 3.]
+
+  His portable electrometer is shown in fig. 2. H H (see fig. 3) is a
+  plane disk of metal called the guard plate, fixed to the inner coating
+  of a small Leyden jar (see fig. 2). At F a square hole is cut out of H
+  H, and into this fits loosely without touching, like a trap door, a
+  square piece of aluminium foil having a projecting tail, which carries
+  at its end a stirrup L, crossed by a fine hair (see fig. 3). The
+  square piece of aluminium is pivoted round a horizontal stretched
+  wire. If then another horizontal disk G is placed over the disk H H
+  and a difference of potential made between G and H H, the movable
+  aluminium trap door F will be attracted by the fixed plate G. Matters
+  are so arranged by giving a torsion to the wire carrying the aluminium
+  disk F that for a certain potential difference between the plates H
+  and G, the movable part F comes into a definite sighted position,
+  which is observed by means of a small lens. The plate G (see fig. 2)
+  is moved up and down, parallel to itself, by means of a screw. In
+  using the instrument the conductor, whose potential is to be tested,
+  is connected to the plate G. Let this potential be denoted by V, and
+  let v be the potential of the guard plate and the aluminium flap. This
+  last potential is maintained constant by guard plate and flap being
+  part of the interior coating of a charged Leyden jar. Since the
+  distribution of electricity may be considered to be constant over the
+  surface S of the attracted disk, the mechanical force f on it is given
+  by the expression,[2]
+
+        S(V - v)^2
+    f = ----------,
+         8[pi]d^2
+
+  where d is the distance between the two plates. If this distance is
+  varied until the attracted disk comes into a definite sighted position
+  as seen by observing the end of the index through the lens, then since
+  the force f is constant, being due to the torque applied by the wire
+  for a definite angle of twist, it follows that the difference of
+  potential of the two plates varies as their distance. If then two
+  experiments are made, first with the upper plate connected to earth,
+  and secondly, connected to the object being tested, we get an
+  expression for the potential V of this conductor in the form
+
+    V = A(d' - d),
+
+  where d and d' are the distances of the fixed and movable plates from
+  one another in the two cases, and A is some constant. We thus find V
+  in terms of the constant and the difference of the two screw readings.
+
+  [Illustration: FIG. 4.--Kelvin's Absolute Electrometer.]
+
+  Lord Kelvin's absolute electrometer (fig. 4) involves the same
+  principle. There is a certain fixed guard disk B having a hole in it
+  which is loosely occupied by an aluminium trap door plate, shielded by
+  D and suspended on springs, so that its surface is parallel with that
+  of the guard plate. Parallel to this is a second movable plate A, the
+  distances between the two being measurable by means of a screw. The
+  movable plate can be drawn down into a definite sighted position when
+  a difference of potential is made between the two plates. This
+  sighted position is such that the surface of the trap door plate is
+  level with that of the guard plate, and is determined by observations
+  made with the lenses H and L. The movable plate can be thus depressed
+  by placing on it a certain standard weight W grammes.
+
+  Suppose it is required to measure the difference of potentials V and
+  V' of two conductors. First one and then the other conductor is
+  connected with the electrode of the lower or movable plate, which is
+  moved by the screw until the index attached to the attracted disk
+  shows it to be in the sighted position. Let the screw readings in the
+  two cases be d and d'. If W is the weight required to depress the
+  attracted disk into the same sighted position when the plates are
+  unelectrified and g is the acceleration of gravity, then the
+  difference of potentials of the conductors tested is expressed by the
+  formula
+                         _______
+                        /8[pi]gW
+    V - V' = (d - d')  / -------,
+                     \/     S
+
+  where S denotes the area of the attracted disk.
+
+  The difference of potentials is thus determined in terms of a weight,
+  an area and a distance, in absolute C.G.S. measure or electrostatic
+  units.
+
+[Illustration: FIG. 5.]
+
+_Symmetrical Electrometers_ include the dry pile electrometer and
+Kelvin's quadrant electrometer. The principle underlying these
+instruments is that we can measure differences of potential by means of
+the motion of an electrified body in a symmetrical field of electric
+force. In the dry pile electrometer a single gold-leaf is hung up
+between two plates which are connected to the opposite terminals of a
+dry pile so that a certain constant difference of potential exists
+between these plates. The original inventor of this instrument was
+T.G.B. Behrens (_Gilb. Ann._, 1806, 23), but it generally bears the name
+of J.G.F. von Bohnenberger, who slightly modified its form. G.T. Fechner
+introduced the important improvement of using only one pile, which he
+removed from the immediate neighbourhood of the suspended leaf. W.G.
+Hankel still further improved the dry pile electrometer by giving a slow
+motion movement to the two plates, and substituted a galvanic battery
+with a large number of cells for the dry pile, and also employed a
+divided scale to measure the movements of the gold-leaf (_Pogg. Ann._,
+1858, 103). If the gold-leaf is unelectrified, it is not acted upon by
+the two plates placed at equal distances on either side of it, but if
+its potential is raised or lowered it is attracted by one disk and
+repelled by the other, and the displacement becomes a measure of its
+potential.
+
+[Illustration: FIG. 6.--Kelvin's Quadrant Electrometer.]
+
+A vast improvement in this instrument was made by the invention of the
+quadrant electrometer by Lord Kelvin, which is the most sensitive form
+of electrometer yet devised. In this instrument (see fig. 5) a flat
+paddle-shaped needle of aluminium foil U is supported by a bifilar
+suspension consisting of two cocoon fibres. This needle is suspended in
+the interior of a glass vessel partly coated with tin-foil on the
+outside and inside, forming therefore a Leyden jar (see fig. 6). In the
+bottom of the vessel is placed some sulphuric acid, and a platinum wire
+attached to the suspended needle dips into this acid. By giving a charge
+to this Leyden jar the needle can thus be maintained at a certain
+constant high potential. The needle is enclosed by a sort of flat box
+divided into four insulated quadrants A, B, C, D (fig. 5), whence the
+name. The opposite quadrants are connected together by thin platinum
+wires. These quadrants are insulated from the needle and from the case,
+and the two pairs are connected to two electrodes. When the instrument
+is to be used to determine the potential difference between two
+conductors, they are connected to the two opposite pairs of quadrants.
+The needle in its normal position is symmetrically placed with regard to
+the quadrants, and carries a mirror by means of which its displacement
+can be observed in the usual manner by reflecting the ray of light from
+it. If the two quadrants are at different potentials, the needle moves
+from one quadrant towards the other, and the image of a spot of light on
+the scale is therefore displaced. Lord Kelvin provided the instrument
+with two necessary adjuncts, viz. a replenisher or rotating
+electrophorus (q.v.), by means of which the charge of the Leyden jar
+which forms the enclosing vessel can be increased or diminished, and
+also a small aluminium balance plate or gauge, which is in principle the
+same as the attracted disk portable electrometer by means of which the
+potential of the inner coating of the Leyden jar is preserved at a known
+value.
+
+  According to the mathematical theory of the instrument,[3] if V and V'
+  are the potentials of the quadrants and v is the potential of the
+  needle, then the torque acting upon the needle to cause rotation is
+  given by the expression,
+
+    C(V - V') {v - 1/2(V + V')},
+
+  where C is some constant. If v is very large compared with the mean
+  value of the potentials of the two quadrants, as it usually is, then
+  the above expression indicates that the couple varies as the
+  difference of the potentials between the quadrants.
+
+  Dr J. Hopkinson found, however, before 1885, that the above formula
+  does not agree with observed facts (_Proc. Phys. Soc. Lond._, 1885, 7,
+  p. 7). The formula indicates that the sensibility of the instrument
+  should increase with the charge of the Leyden jar or needle, whereas
+  Hopkinson found that as the potential of the needle was increased by
+  working the replenisher of the jar, the deflection due to three volts
+  difference between the quadrants first increased and then diminished.
+  He found that when the potential of the needle exceeded a certain
+  value, of about 200 volts, for the particular instrument he was using
+  (made by White of Glasgow), the above formula did not hold good. W.E.
+  Ayrton, J. Perry and W.E. Sumpner, who in 1886 had noticed the same
+  fact as Hopkinson, investigated the matter in 1891 (_Proc. Roy. Soc._,
+  1891, 50, p. 52; _Phil. Trans._, 1891, 182, p. 519). Hopkinson had
+  been inclined to attribute the anomaly to an increase in the tension
+  of the bifilar threads, owing to a downward pull on the needle, but
+  they showed that this theory would not account for the discrepancy.
+  They found from observations that the particular quadrant electrometer
+  they used might be made to follow one or other of three distinct laws.
+  If the quadrants were near together there were certain limits between
+  which the potential of the needle might vary without producing more
+  than a small change in the deflection corresponding with the fixed
+  potential difference of the quadrants. For example, when the quadrants
+  were about 2.5 mm. apart and the suspended fibres near together at the
+  top, the deflection produced by a P.D. of 1.45 volts between the
+  quadrants only varied about 11% when the potential of the needle
+  varied from 896 to 3586 volts. When the fibres were far apart at the
+  top a similar flatness was obtained in the curve with the quadrants
+  about 1 mm. apart. In this case the deflection of the needle was
+  practically quite constant when its potential varied from 2152 to 3227
+  volts. When the quadrants were about 3.9 mm. apart, the deflection for
+  a given P.D. between the quadrants was almost directly proportional to
+  the potential of the needle. In other words, the electrometer nearly
+  obeyed the theoretical law. Lastly, when the quadrants were 4 mm. or
+  more apart, the deflection increased much more rapidly than the
+  potential, so that a maximum sensibility bordering on instability was
+  obtained. Finally, these observers traced the variation to the fact
+  that the wire supporting the aluminium needle as well as the wire
+  which connects the needle with the sulphuric acid in the Leyden jar in
+  the White pattern of Leyden jar is enclosed in a metallic guard tube
+  to screen the wire from external action. In order that the needle may
+  project outside the guard tube, openings are made in its two sides;
+  hence the moment the needle is deflected each half of it becomes
+  unsymmetrically placed relatively to the two metallic pieces which
+  join the upper and lower half of the guard tube. Guided by these
+  experiments, Ayrton, Perry and Sumpner constructed an improved
+  unifilar quadrant electrometer which was not only more sensitive than
+  the White pattern, but fulfilled the theoretical law of working. The
+  bifilar suspension was abandoned, and instead a new form of adjustable
+  magnetic control was adopted. All the working parts of the instrument
+  were supported on the base, so that on removing a glass shade which
+  serves as a Leyden jar they can be got at and adjusted in position.
+  The conclusion to which the above observers came was that any quadrant
+  electrometer made in any manner does not necessarily obey a law of
+  deflection making the deflections proportional to the potential
+  difference of the quadrants, but that an electrometer can be
+  constructed which does fulfil the above law.
+
+  The importance of this investigation resides in the fact that an
+  electrometer of the above pattern can be used as a wattmeter (q.v.),
+  provided that the deflection of the needle is proportional to the
+  potential difference of the quadrants. This use of the instrument was
+  proposed simultaneously in 1881 by Professors Ayrton and G.F.
+  Fitzgerald and M.A. Potier. Suppose we have an inductive and a
+  non-inductive circuit in series, which is traversed by a periodic
+  current, and that we desire to know the power being absorbed to the
+  inductive circuit. Let v1, v2, v3 be the instantaneous potentials of
+  the two ends and middle of the circuit; let a quadrant electrometer be
+  connected first with the quadrants to the two ends of the inductive
+  circuit and the needle to the far end of the non-inductive circuit,
+  and then secondly with the needle connected to one of the quadrants
+  (see fig. 5). Assuming the electrometer to obey the above-mentioned
+  theoretical law, the first reading is proportional to
+
+             /     v1 + v2\
+    v1 - v2 ( v3 - ------- )
+             \        2   /
+
+  and the second to
+
+             /     v1 + v2\
+    v1 - v2 ( v2 - ------- ).
+             \        2   /
+
+  The difference of the readings is then proportional to
+
+    (v1 - v2)(v2 - v3).
+
+  But this last expression is proportional to the instantaneous power
+  taken up in the inductive circuit, and hence the difference of the two
+  readings of the electrometer is proportional to the mean power taken
+  up in the circuit (_Phil. Mag._, 1891, 32, p. 206). Ayrton and Perry
+  and also P.R. Blondlot and P. Curie afterwards suggested that a single
+  electrometer could be constructed with two pairs of quadrants and a
+  duplicate needle on one stem, so as to make two readings
+  simultaneously and produce a deflection proportional at once to the
+  power being taken up in the inductive circuit.
+
+[Illustration: FIG. 7.--Quadrant Electrometer. Dolezalek Pattern.]
+
+Quadrant electrometers have also been designed especially for measuring
+extremely small potential differences. An instrument of this kind has
+been constructed by Dr. F. Dolezalek (fig. 7). The needle and quadrants
+are of small size, and the electrostatic capacity is correspondingly
+small. The quadrants are mounted on pillars of amber which afford a very
+high insulation. The needle, a piece of paddle-shaped paper thinly
+coated with silver foil, is suspended by a quartz fibre, its extreme
+lightness making it possible to use a very feeble controlling force
+without rendering the period of oscillation unduly great. The resistance
+offered by the air to a needle of such light construction suffices to
+render the motion nearly dead-beat. Throughout a wide range the
+deflections are proportional to the potential difference producing them.
+The needle is charged to a potential of 50 to 200 volts by means of a
+dry pile or voltaic battery, or from a lighting circuit. To facilitate
+the communication of the charge to the needle, the quartz fibre and its
+attachments are rendered conductive by a thin film of solution of
+hygroscopic salt such as calcium chloride. The lightness of the needle
+enables the instrument to be moved without fear of damaging the
+suspension. The upper end of the quartz fibre is rotated by a torsion
+head, and a metal cover serves to screen the instrument from stray
+electrostatic fields. With a quartz fibre 0.009 mm. thick and 60 mm.
+long, the needle being charged to 110 volts, the period and swing of the
+needle was 18 seconds. With the scale at a distance of two metres, a
+deflection of 130 mm. was produced by an electromotive force of 0.1
+volt. By using a quartz fibre of about half the above diameter the
+sensitiveness was much increased. An instrument of this form is valuable
+in measuring small alternating currents by the fall of potential
+produced down a known resistance. In the same way it may be employed to
+measure high potentials by measuring the fall of potential down a
+fraction of a known non-inductive resistance. In this last case,
+however, the capacity of the electrometer used must be small, otherwise
+an error is introduced.[4]
+
+  See, in addition to references already given, A. Gray, _Absolute
+  Measurements in Electricity and Magnetism_ (London, 1888), vol. i. p.
+  254; A. Winkelmann, _Handbuch der Physik_ (Breslau, 1905), pp. 58-70,
+  which contains a large number of references to original papers on
+  electrometers.     (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] It is probable that an experiment of this kind had been made as
+    far back as 1746 by Daniel Gralath, of Danzig, who has some claims to
+    have suggested the word "electrometer" in connexion with it. See Park
+    Benjamin, _The Intellectual Rise in Electricity_ (London, 1895), p.
+    542.
+
+  [2] See Maxwell, _Treatise on Electricity and Magnetism_ (2nd ed.),
+    i. 308.
+
+  [3] See Maxwell, _Electricity and Magnetism_ (2nd ed., Oxford, 1881),
+    vol. i. p. 311.
+
+  [4] See J.A. Fleming, _Handbook for the Electrical Laboratory and
+    Testing Room_, vol. i. p. 448 (London, 1901).
+
+
+
+
+ELECTRON, the name suggested by Dr G. Johnstone Stoney in 1891 for the
+natural unit of electricity to which he had drawn attention in 1874, and
+subsequently applied to the ultra-atomic particles carrying negative
+charges of electricity, of which Professor Sir J.J. Thomson proved in
+1897 that the cathode rays consisted. The electrons, which Thomson at
+first called corpuscles, are point charges of negative electricity,
+their inertia showing them to have a mass equal to about 1/2000 that
+of the hydrogen atom. They are apparently derivable from all kinds of
+matter, and are believed to be components at any rate of the chemical
+atom. The electronic theory of the chemical atom supposes, in fact, that
+atoms are congeries of electrons in rapid orbital motion. The size of
+the electron is to that of an atom roughly in the ratio of a pin's head
+to the dome of St Paul's cathedral. The electron is always associated
+with the unit charge of negative electricity, and it has been suggested
+that its inertia is wholly electrical. For further details see the
+articles on ELECTRICITY; MAGNETISM; MATTER; RADIOACTIVITY; CONDUCTION,
+ELECTRIC; _The Electron Theory_, E. Fournier d'Albe (London, 1907); and
+the original papers of Dr G. Johnstone Stoney, _Proc. Brit. Ass._
+(Belfast, August 1874), "On the Physical Units of Nature," and _Trans.
+Royal Dublin Society_ (1891), 4, p. 583.
+
+
+
+
+ELECTROPHORUS, an instrument invented by Alessandro Volta in 1775, by
+which mechanical work is transformed into electrostatic charge by the
+aid of a small initial charge of electricity. The operation depends on
+the facts of electrostatic induction discovered by John Canton in 1753,
+and, independently, by J.K. Wilcke in 1762 (see ELECTRICITY). Volta, in
+a letter to J. Priestley on the 10th of June 1775 (see _Collezione dell'
+opere_, ed. 1816, vol. i. p. 118), described the invention of a device
+he called an _elettroforo perpetuo_, based on the fact that a conductor
+held near an electrified body and touched by the finger was found, when
+withdrawn, to possess an electric charge of opposite sign to that of the
+electrified body. His electrophorus in one form consisted of a disk of
+non-conducting material, such as pitch or resin, placed between two
+metal sheets, one being provided with an insulating handle. For the
+pitch or resin may be substituted a sheet of glass, ebonite,
+india-rubber or any other good dielectric placed upon a metallic sheet,
+called the sole-plate. To use the apparatus the surface of the
+dielectric is rubbed with a piece of warm flannel, silk or catskin, so
+as to electrify it, and the upper metal plate is then placed upon it.
+Owing to the irregularities in the surfaces of the dielectric and upper
+plate the two are only in contact at a few points, and owing to the
+insulating quality of the dielectric its surface electrical charge
+cannot move over it. It therefore acts inductively upon the upper plate
+and induces on the adjacent surface an electric charge of opposite sign.
+Suppose, for instance, that the dielectric is a plate of resin rubbed
+with catskin, it will then be negatively electrified and will act by
+induction on the upper plate across the film of air separating the upper
+resin surface and lower surface of the upper metal plate. If the upper
+plate is touched with the finger or connected to earth for a moment, a
+negative charge will escape from the metal plate to earth at that
+moment. The arrangement thus constitutes a condenser; the upper plate on
+its under surface carries a charge of positive electricity and the resin
+plate a charge of negative electricity on its upper surface, the air
+film between them being the dielectric of the condenser. If, therefore,
+the upper plate is elevated, mechanical work has to be done to separate
+the two electric charges. Accordingly on raising the upper plate, the
+charge on it, in old-fashioned nomenclature, becomes _free_ and can be
+communicated to any other insulated conductor at a lower potential, the
+upper plate thereby becoming more or less discharged. On placing the
+upper plate again on the resin and touching it for a moment, the process
+can be repeated, and so at the expense of mechanical work done in
+lifting the upper plate against the mutual attraction of two electric
+charges of opposite sign, an indefinitely large electric charge can be
+accumulated and given to any other suitable conductor. In course of
+time, however, the surface charge of the resin becomes dissipated and it
+then has to be again excited. To avoid the necessity for touching the
+upper plate every time it is put down on the resin, a metal pin may be
+brought through the insulator from the sole-plate so that each time that
+the upper plate is put down on the resin it is automatically connected
+to earth. We are thus able by a process of merely lifting the upper
+plate repeatedly to convey a large electrical charge to some conductor
+starting from the small charge produced by friction on the resin. The
+above explanation does not take into account the function of the
+sole-plate, which is important. The sole-plate serves to increase the
+electrical capacity of the upper plate when placed down upon the resin
+or excited insulator. Hence when so placed it takes a larger charge.
+When touched by the finger the upper plate is brought to zero potential.
+If then the upper plate is lifted by its insulating handle its capacity
+becomes diminished. Since, however, it carries with it the charge it had
+when resting on the resin, its potential becomes increased as its
+capacity becomes less, and it therefore rises to a high potential, and
+will give a spark if the knuckle is approached to it when it is lifted
+after having been touched and raised.
+
+The study of Volta's electrophorus at once suggested the performance of
+these cyclical operations by some form of rotation instead of elevation,
+and led to the invention of various forms of doubler or multiplier. The
+instrument was thus the first of a long series of machines for
+converting mechanical work into electrostatic energy, and the
+predecessor of the modern type of influence machine (see ELECTRICAL
+MACHINE). Volta himself devised a double and reciprocal electrophorus
+and also made mention of the subject of multiplying condensers in a
+paper published in the _Phil. Trans._ for 1782 (p. 237, and appendix, p.
+vii.). He states, however, that the use of a condenser in connexion with
+an electrophorus to make evident and multiply weak charges was due to T.
+Cavallo (_Phil. Trans._, 1788).
+
+  For further information see S.P. Thompson, "The Influence Machine from
+  1788 to 1888," _Journ. Inst. Tel. Eng._, 1888, 17, p. 569. Many
+  references to original papers connected with the electrophorus will be
+  found in A. Winkelmann's _Handbuch der Physik_ (Breslau, 1905), vol.
+  iv. p. 48.     (J. A. F.)
+
+
+
+
+ELECTROPLATING, the art of depositing metals by the electric current. In
+the article ELECTROLYSIS it is shown how the passage of an electric
+current through a solution containing metallic ions involves the
+deposition of the metal on the cathode. Sometimes the metal is deposited
+in a pulverulent form, at others as a firm tenacious film, the nature of
+the deposit being dependent upon the particular metal, the concentration
+of the solution, the difference of potential between the electrodes, and
+other experimental conditions. As the durability of the
+electro-deposited coat on plated wares of all kinds is of the utmost
+importance, the greatest care must be taken to ensure its complete
+adhesion. This can only be effected if the surface of the metal on which
+the deposit is to be made is chemically clean. Grease must be removed by
+potash, whiting or other means, and tarnish by an acid or potassium
+cyanide, washing in plenty of water being resorted to after each
+operation. The vats for depositing may be of enamelled iron, slate,
+glazed earthenware, glass, lead-lined wood, &c. The current densities
+and potential differences frequently used for some of the commoner
+metals are given in the following table, taken from M'Millan's _Treatise
+on Electrometallurgy_. It must be remembered, however, that variations
+in conditions modify the electromotive force required for any given
+process. For example, a rise in temperature of the bath causes an
+increase in its conductivity, so that a lower E.M.F. will suffice to
+give the required current density; on the other hand, an abnormally
+great distance between the electrodes, or a diminution in acidity of an
+acid bath, or in the strength of the solution used, will increase the
+resistance, and so require the application of a higher E.M.F.
+
+  +----------------------+------------------------------------+---------------+
+  |                      |               Amperes.             |               |
+  |                      +-------------------+----------------+ Volts between |
+  |        Metal.        | Per sq. decimetre | Per sq. in. of |   Anode and   |
+  |                      |    of Cathode     |    Cathode     |    Cathode.   |
+  |                      |      Surface.     |    Surface.    |               |
+  +----------------------+-------------------+----------------+---------------+
+  | Antimony             |      0.4-0.5      |    0.02-0.03   |    1.0-1.2    |
+  | Brass                |      0.5-0.8      |    0.03-0.05   |    3.0-4.0    |
+  | Copper, acid bath    |      1.0-1.5      |   0.065-0.10   |    0.5-1.5    |
+  |   "     alkaline bath|      0.3-0.5      |    0.02-0.03   |    3.0-5.0    |
+  | Gold                 |        0.1        |     0.006      |    0.5-4.0    |
+  | Iron                 |        0.5        |      0.03      |      1.0      |
+  | Nickel, at first     |      1.4-1.5      |    0.09-0.10   |      5.0      |
+  |   "     after        |      0.2-0.3      |   0.015-0.02   |    1.5-2.0    |
+  |   "     on zinc      |        0.4        |     0.025      |    4.0-5.0    |
+  | Silver               |      0.2-0.5      |   0.015-0.03   |   0.75-1.0    |
+  | Zinc                 |      0.3-0.6      |    0.02-0.04   |    2.5-3.0    |
+  +----------------------+-------------------+----------------+---------------+
+
+Large objects are suspended in the tanks by hooks or wires, care being
+taken to shift their position and so avoid wire-marks. Small objects are
+often heaped together in perforated trays or ladles, the cathode
+connecting-rod being buried in the midst of them. These require constant
+shifting because the objects are in contact at many points, and because
+the top ones shield those below from the depositing action of the
+current. Hence processes have been patented in which the objects to be
+plated are suspended in revolving drums between the anodes, the rotation
+of the drum causing the constant renewal of surfaces and affording a
+burnishing action at the same time. Care must be taken not to expose
+goods in the plating-bath to too high a current density, else they may
+be "burnt"; they must never be exposed one at a time to the full anode
+surface, with the current flowing in an empty bath, but either one piece
+at a time should be replaced, or some of the anodes should be
+transferred temporarily to the place of the cathodes, in order to
+distribute the current over a sufficient cathode-area. Burnt deposits
+are dark-coloured, or even pulverulent and useless. The strength of the
+current may also be regulated by introducing lengths of German silver or
+iron wire, carbon rod, or other inferior conductors in the path of the
+current, and a series of such resistances should always be provided
+close to the tanks. Ammeters to measure the volume, and voltmeters to
+determine the pressure of current supplied to the baths, should also be
+provided. Very irregular surfaces may require the use of specially
+shaped anodes in order that the distance between the electrodes may be
+fairly uniform, otherwise the portion of the cathode lying nearest to
+the anode may receive an undue share of the current, and therefore a
+greater thickness of coat. Supplementary anodes are sometimes used in
+difficult cases of this kind. Large metallic surfaces (especially
+external surfaces) are sometimes plated by means of a "doctor," which,
+in its simplest form, is a brush constantly wetted with the electrolyte,
+with a wire anode buried amid the hairs or bristles; this brush is
+painted slowly over the surface of the metal to be coated, which must be
+connected to the negative terminal of the electrical generator. Under
+these conditions electrolysis of the solution in the brush takes place.
+Iron ships' plates have recently been coated with copper in sections (to
+prevent the adhesion of barnacles), by building up a temporary trough
+against the side of the ship, making the thoroughly cleansed plate act
+both as cathode and as one side of the trough. Decorative plating-work
+in several colours (e.g. "parcel-gilding") is effected by painting a
+portion of an object with a stopping-out (i.e. a non-conducting)
+varnish, such as copal varnish, so that this portion is not coated. The
+varnish is then removed, a different design stopped out, and another
+metal deposited. By varying this process, designs in metals of different
+colours may readily be obtained.
+
+Reference must be made to the textbooks (see ELECTROCHEMISTRY) for a
+fuller account of the very varied solutions and methods employed for
+electroplating with silver, gold, copper, iron and nickel. It should be
+mentioned here, however, that solutions which would deposit their metal
+on any object by simple immersion should not be generally used for
+electroplating that object, as the resulting deposit is usually
+non-adhesive. For this reason the acid copper-bath is not used for iron
+or zinc objects, a bath containing copper cyanide or oxide dissolved in
+potassium cyanide being substituted. This solution, being an inferior
+conductor of electricity, requires a much higher electromotive force to
+drive the current through it, and is therefore more costly in use. It
+is, however, commonly employed hot, whereby its resistance is reduced.
+_Zinc_ is commonly deposited by electrolysis on iron or steel goods
+which would ordinarily be "galvanized," but which for any reason may not
+conveniently be treated by the method of immersion in fused zinc. The
+zinc cyanide bath may be used for small objects, but for heavy goods the
+sulphate bath is employed. Sherard Cowper-Coles patented a process in
+which, working with a high current density, a lead anode is used, and
+powdered zinc is kept suspended in the solution to maintain the
+proportion of zinc in the electrolyte, and so to guard against the
+gradual acidification of the bath. _Cobalt_ is deposited by a method
+analogous to that used for its sister-metal nickel. _Platinum_,
+_palladium_ and _tin_ are occasionally deposited for special purposes.
+In the deposition of _gold_ the colour of the deposit is influenced by
+the presence of impurities in the solution; when copper is present, some
+is deposited with the gold, imparting to it a reddish colour, whilst a
+little silver gives it a greenish shade. Thus so-called coloured-gold
+deposits may be produced by the judicious introduction of suitable
+impurities. Even pure gold, it may be noted, is darker or lighter in
+colour according as a stronger or a weaker current is used. The
+electro-deposition of _brass_--mainly on iron ware, such as bedstead
+tubes--is now very widely practised, the bath employed being a mixture
+of copper, zinc and potassium cyanides, the proportions of which vary
+according to the character of the brass required, and to the mode of
+treatment. The colour depends in part upon the proportion of copper and
+zinc, and in part upon the current density, weaker currents tending to
+produce a redder or yellower metal. Other alloys may be produced, such
+as bronze, or German silver, by selecting solutions (usually cyanides)
+from which the current is able to deposit the constituent metals
+simultaneously.
+
+Electrolysis has in a few instances been applied to processes of
+manufacture. For example, Wilde produced copper printing surfaces for
+calico printing-rollers and the like by immersing rotating iron
+cylinders as cathodes in a copper bath. Elmore, Dumoulin, Cowper-Coles
+and others have prepared copper cylinders and plates by depositing
+copper on rotating mandrels with special arrangements. Others have
+arranged a means of obtaining high conductivity wire from cathode-copper
+without fusion, by depositing the metal in the form of a spiral strip on
+a cylinder, the strip being subsequently drawn down in the usual way; at
+present, however, the ordinary methods of wire production are found to
+be cheaper. J.W. Swan (_Journ. Inst. Elec. Eng._, 1898, vol. xxvii. p.
+16) also worked out, but did not proceed with, a process in which a
+copper wire whilst receiving a deposit of copper was continuously passed
+through the draw-plate, and thus indefinitely extended in length.
+Cowper-Coles (_Journ. Inst. Elec. Eng._, 1898, 27, p. 99) very
+successfully produced true parabolic reflectors for projectors, by
+depositing copper upon carefully ground and polished glass surfaces
+rendered conductive by a film of deposited silver.
+
+
+
+
+ELECTROSCOPE, an instrument for detecting differences of electric
+potential and hence electrification. The earliest form of scientific
+electroscope was the _versorium_ or electrical needle of William Gilbert
+(1544-1603), the celebrated author of the treatise _De magnete_ (see
+ELECTRICITY). It consisted simply of a light metallic needle balanced on
+a pivot like a compass needle. Gilbert employed it to prove that
+numerous other bodies besides amber are susceptible of being electrified
+by friction.[1] In this case the visible indication consisted in the
+attraction exerted between the electrified body and the light pivoted
+needle which was acted upon and electrified by induction. The next
+improvement was the invention of simple forms of repulsion electroscope.
+Two similarly electrified bodies repel each other. Benjamin Franklin
+employed the repulsion of two linen threads, C.F. de C. du Fay, J.
+Canton, W. Henley and others devised the pith ball, or double straw
+electroscope (fig. 1). T. Cavallo about 1770 employed two fine silver
+wires terminating in pith balls suspended in a glass vessel having
+strips of tin-foil pasted down the sides (fig. 2). The object of the
+thimble-shaped dome was to keep moisture from the stem from which the
+pith balls were supported, so that the apparatus could be used in the
+open air even in the rainy weather. Abraham Bennet (_Phil. Trans._,
+1787, 77, p. 26) invented the modern form of gold-leaf electroscope.
+Inside a glass shade he fixed to an insulated wire a pair of strips of
+gold-leaf (fig. 3). The wire terminated in a plate or knob outside the
+vessel. When an electrified body was held near or in contact with the
+knob, repulsion of the gold leaves ensued. Volta added the condenser
+(_Phil. Trans._, 1782), which greatly increased the power of the
+instrument. M. Faraday, however, showed long subsequently that to bestow
+upon the indications of such an electroscope definite meaning it was
+necessary to place a cylinder of metallic gauze connected to the earth
+inside the vessel, or better still, to line the glass shade with
+tin-foil connected to the earth and observe through a hole the
+indications of the gold leaves (fig. 4). Leaves of aluminium foil may
+with advantage be substituted for gold-leaf, and a scale is sometimes
+added to indicate the angular divergence of the leaves.
+
+[Illustration: FIG. 1.--Henley's Electroscope.]
+
+[Illustration: FIG. 2.--Cavallo's Electroscope.]
+
+[Illustration: FIG. 3.--Bennet's Electroscope.]
+
+The uses of an electroscope are, first, to ascertain if any body is in a
+state of electrification, and secondly, to indicate the sign of that
+charge. In connexion with the modern study of radioactivity, the
+electroscope has become an instrument of great usefulness, far
+outrivalling the spectroscope in sensibility. Radio-active bodies are
+chiefly recognized by the power they possess of rendering the air in
+their neighbourhood conductive; hence the electroscope detects the
+presence of a radioactive body by losing an electric charge given to it
+more quickly than it would otherwise do. A third great use of the
+electroscope is therefore to detect electric conductivity either in the
+air or in any other body.
+
+[Illustration: FIG. 4.--Gold-Leaf Electroscope.]
+
+To detect electrification it is best to charge the electroscope by
+induction. If an electrified body is held near the gold-leaf
+electroscope the leaves diverge with electricity of the same sign as
+that of the body being tested. If, without removing the electrified
+body, the plate or knob of the electroscope is touched, the leaves
+collapse. If the electroscope is insulated once more and the electrified
+body removed, the leaves again diverge with electricity of the opposite
+sign to that of the body being tested. The sign of charge is then
+determined by holding near the electroscope a glass rod rubbed with silk
+or a sealing-wax rod rubbed with flannel. If the approach of the glass
+rod causes the leaves in their final state to collapse, then the charge
+in the rod was positive, but if it causes them to expand still more the
+charge was negative, and vice versa for the sealing-wax rod. When
+employing a Volta condensing electroscope, the following is the method
+of procedure:--The top of the electroscope consists of a flat, smooth
+plate of lacquered brass on which another plate of brass rests,
+separated from it by three minute fragments of glass or shellac, or a
+film of shellac varnish. If the electrified body is touched against the
+upper plate whilst at the same time the lower plate is put to earth, the
+condenser formed of the two plates and the film of air or varnish
+becomes charged with positive electricity on the one plate and negative
+on the other. On insulating the lower plate and raising the upper plate
+by the glass handle, the capacity of the condenser formed by the plates
+is vastly decreased, but since the charge on the lower plate including
+the gold leaves attached to it remains the same, as the capacity of the
+system is reduced the potential is raised and therefore the gold leaves
+diverge widely. Volta made use of such an electroscope in his celebrated
+experiments (1790-1800) to prove that metals placed in contact with one
+another are brought to different potentials, in other words to prove the
+existence of so-called contact electricity. He was assisted to detect
+the small potential differences then in question by the use of a
+multiplying condenser or revolving doubler (see ELECTRICAL MACHINE). To
+employ the electroscope as a means of detecting radioactivity, we have
+first to test the leakage quality of the electroscope itself. Formerly
+it was usual to insulate the rod of the electroscope by passing it
+through a hole in a cork or mass of sulphur fixed in the top of the
+glass vessel within which the gold leaves were suspended. A further
+improvement consisted in passing the metal wire to which the gold leaves
+were attached through a glass tube much wider than the rod, the latter
+being fixed concentrically in the glass tube by means of solid shellac
+melted and run in. This insulation, however, is not sufficiently good
+for an electroscope intended for the detection of radioactivity; for
+this purpose it must be such that the leaves will remain for hours or
+days in a state of steady divergence when an electrical charge has been
+given to them.
+
+In their researches on radioactivity M. and Mme P. Curie employed an
+electroscope made as follows:--A metal case (fig. 5), having two holes
+in its sides, has a vertical brass strip B attached to the inside of the
+lid by a block of sulphur SS or any other good insulator. Joined to the
+strip is a transverse wire terminating at one end in a knob C, and at
+the other end in a condenser plate P'. The strip B carries also a strip
+of gold-leaf L, and the metal case is connected to earth. If a charge is
+given to the electroscope, and if any radioactive material is placed on
+a condenser plate P attached to the outer case, then this substance
+bestows conductivity on the air between the plates P and P', and the
+charge of the electroscope begins to leak away. The collapse of the
+gold-leaf is observed through an aperture in the case by a microscope,
+and the time taken by the gold-leaf to fall over a certain distance is
+proportional to the ionizing current, that is, to the intensity of the
+radioactivity of the substance.
+
+[Illustration: FIG. 5.--Curie's Electroscope.]
+
+A very similar form of electroscope was employed by J.P.L.J. Elster and
+H.F.K. Geitel (fig. 6), and also by C.T.R. Wilson (see _Proc. Roy.
+Soc._, 1901, 68, p. 152). A metal box has a metal strip B suspended from
+a block or insulator by means of a bit of sulphur or amber S, and to it
+is fastened a strip of gold-leaf L. The electroscope is provided with a
+charging rod C. In a dry atmosphere sulphur or amber is an early perfect
+insulator, and hence if the air in the interior of the box is kept dry
+by calcium chloride, the electroscope will hold its charge for a long
+time. Any divergence or collapse of the gold-leaf can be viewed by a
+microscope through an aperture in the side of the case.
+
+[Illustration: FIG. 6.--Elster and Geitel Electroscope.]
+
+[Illustration: FIG. 7.--Wilson's Electroscope.]
+
+Another type of sensitive electroscope is one devised by C.T.R. Wilson
+(_Proc. Cam. Phil. Soc._, 1903, 12, part 2). It consists of a metal box
+placed on a tilting stand (fig. 7). At one end is an insulated plate P
+kept at a potential of 200 volts or so above the earth by a battery. At
+the other end is an insulated metal wire having attached to it a thin
+strip of gold-leaf L. If the plate P is electrified it attracts the
+strip which stretches out towards it. Before use the strip is for one
+moment connected to the case, and the arrangement is then tilted until
+the strip extends at a certain angle. If then the strip of gold-leaf is
+raised or lowered in potential it moves to or from the plate P, and its
+movement can be observed by a microscope through a hole in the side of
+the box. There is a particular angle of tilt of the case which gives a
+maximum sensitiveness. Wilson found that with the plate electrified to
+207 volts and with a tilt of the case of 30 deg., if the gold-leaf was
+raised one volt in potential above the case, it moved over 200 divisions
+of the micrometer scale in the eye-piece of the microscope, 54 divisions
+being equal to one millimetre. In using the instrument the insulated rod
+to which the gold-leaf is attached is connected to the conductor, the
+potential of which is being examined. In the use of all these
+electroscopic instruments it is essential to bear in mind (as first
+pointed out by Lord Kelvin) that what a gold-leaf electroscope really
+indicates is the difference of potential between the gold-leaf and the
+solid walls enclosing the air space in which they move.[2] If these
+enclosing walls are made of anything else than perfectly conducting
+material, then the indications of the instrument may be uncertain and
+meaningless. As already mentioned, Faraday remedied this defect by
+coating the inside of the glass vessel in which the gold-leaves were
+suspended to form an electroscope with tinfoil (see fig. 4). In spite of
+these admonitions all but a few instrument makers have continued to make
+the vicious type of instrument consisting of a pair of gold-leaves
+suspended within a glass shade or bottle, no means being provided for
+keeping the walls of the vessel continually at zero potential.
+
+  See J. Clerk Maxwell, _Treatise on Electricity and Magnetism_, vol. i.
+  p. 300 (2nd ed., Oxford, 1881); H.M. Noad, _A Manual of Electricity_,
+  vol. i. p. 25 (London, 1855); E. Rutherford, _Radioactivity_.
+       (J. A. F.)
+
+
+FOOTNOTES:
+
+  [1] See the English translation by the Gilbert Club of Gilbert's _De
+    magnete_, p. 49 (London, 1900).
+
+  [2] See Lord Kelvin, "Report on Electrometers and Electrostatic
+    Measurements," _Brit. Assoc. Report_ for 1867, or Lord Kelvin's
+    _Reprint of Papers on Electrostatics and Magnetism_, p. 260.
+
+
+
+
+
+
+
+
+End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th
+Edition, Volume 9, Slice 2, by Various
+
+*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 9 SL 2 ***
+
+***** This file should be named 35092.txt or 35092.zip *****
+This and all associated files of various formats will be found in:
+        https://www.gutenberg.org/3/5/0/9/35092/
+
+Produced by Marius Masi, Don Kretz and the Online
+Distributed Proofreading Team at https://www.pgdp.net
+
+
+Updated editions will replace the previous one--the old editions
+will be renamed.
+
+Creating the works from public domain print editions means that no
+one owns a United States copyright in these works, so the Foundation
+(and you!) can copy and distribute it in the United States without
+permission and without paying copyright royalties.  Special rules,
+set forth in the General Terms of Use part of this license, apply to
+copying and distributing Project Gutenberg-tm electronic works to
+protect the PROJECT GUTENBERG-tm concept and trademark.  Project
+Gutenberg is a registered trademark, and may not be used if you
+charge for the eBooks, unless you receive specific permission.  If you
+do not charge anything for copies of this eBook, complying with the
+rules is very easy.  You may use this eBook for nearly any purpose
+such as creation of derivative works, reports, performances and
+research.  They may be modified and printed and given away--you may do
+practically ANYTHING with public domain eBooks.  Redistribution is
+subject to the trademark license, especially commercial
+redistribution.
+
+
+
+*** START: FULL LICENSE ***
+
+THE FULL PROJECT GUTENBERG LICENSE
+PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK
+
+To protect the Project Gutenberg-tm mission of promoting the free
+distribution of electronic works, by using or distributing this work
+(or any other work associated in any way with the phrase "Project
+Gutenberg"), you agree to comply with all the terms of the Full Project
+Gutenberg-tm License (available with this file or online at
+https://gutenberg.org/license).
+
+
+Section 1.  General Terms of Use and Redistributing Project Gutenberg-tm
+electronic works
+
+1.A.  By reading or using any part of this Project Gutenberg-tm
+electronic work, you indicate that you have read, understand, agree to
+and accept all the terms of this license and intellectual property
+(trademark/copyright) agreement.  If you do not agree to abide by all
+the terms of this agreement, you must cease using and return or destroy
+all copies of Project Gutenberg-tm electronic works in your possession.
+If you paid a fee for obtaining a copy of or access to a Project
+Gutenberg-tm electronic work and you do not agree to be bound by the
+terms of this agreement, you may obtain a refund from the person or
+entity to whom you paid the fee as set forth in paragraph 1.E.8.
+
+1.B.  "Project Gutenberg" is a registered trademark.  It may only be
+used on or associated in any way with an electronic work by people who
+agree to be bound by the terms of this agreement.  There are a few
+things that you can do with most Project Gutenberg-tm electronic works
+even without complying with the full terms of this agreement.  See
+paragraph 1.C below.  There are a lot of things you can do with Project
+Gutenberg-tm electronic works if you follow the terms of this agreement
+and help preserve free future access to Project Gutenberg-tm electronic
+works.  See paragraph 1.E below.
+
+1.C.  The Project Gutenberg Literary Archive Foundation ("the Foundation"
+or PGLAF), owns a compilation copyright in the collection of Project
+Gutenberg-tm electronic works.  Nearly all the individual works in the
+collection are in the public domain in the United States.  If an
+individual work is in the public domain in the United States and you are
+located in the United States, we do not claim a right to prevent you from
+copying, distributing, performing, displaying or creating derivative
+works based on the work as long as all references to Project Gutenberg
+are removed.  Of course, we hope that you will support the Project
+Gutenberg-tm mission of promoting free access to electronic works by
+freely sharing Project Gutenberg-tm works in compliance with the terms of
+this agreement for keeping the Project Gutenberg-tm name associated with
+the work.  You can easily comply with the terms of this agreement by
+keeping this work in the same format with its attached full Project
+Gutenberg-tm License when you share it without charge with others.
+
+1.D.  The copyright laws of the place where you are located also govern
+what you can do with this work.  Copyright laws in most countries are in
+a constant state of change.  If you are outside the United States, check
+the laws of your country in addition to the terms of this agreement
+before downloading, copying, displaying, performing, distributing or
+creating derivative works based on this work or any other Project
+Gutenberg-tm work.  The Foundation makes no representations concerning
+the copyright status of any work in any country outside the United
+States.
+
+1.E.  Unless you have removed all references to Project Gutenberg:
+
+1.E.1.  The following sentence, with active links to, or other immediate
+access to, the full Project Gutenberg-tm License must appear prominently
+whenever any copy of a Project Gutenberg-tm work (any work on which the
+phrase "Project Gutenberg" appears, or with which the phrase "Project
+Gutenberg" is associated) is accessed, displayed, performed, viewed,
+copied or distributed:
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+1.E.2.  If an individual Project Gutenberg-tm electronic work is derived
+from the public domain (does not contain a notice indicating that it is
+posted with permission of the copyright holder), the work can be copied
+and distributed to anyone in the United States without paying any fees
+or charges.  If you are redistributing or providing access to a work
+with the phrase "Project Gutenberg" associated with or appearing on the
+work, you must comply either with the requirements of paragraphs 1.E.1
+through 1.E.7 or obtain permission for the use of the work and the
+Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or
+1.E.9.
+
+1.E.3.  If an individual Project Gutenberg-tm electronic work is posted
+with the permission of the copyright holder, your use and distribution
+must comply with both paragraphs 1.E.1 through 1.E.7 and any additional
+terms imposed by the copyright holder.  Additional terms will be linked
+to the Project Gutenberg-tm License for all works posted with the
+permission of the copyright holder found at the beginning of this work.
+
+1.E.4.  Do not unlink or detach or remove the full Project Gutenberg-tm
+License terms from this work, or any files containing a part of this
+work or any other work associated with Project Gutenberg-tm.
+
+1.E.5.  Do not copy, display, perform, distribute or redistribute this
+electronic work, or any part of this electronic work, without
+prominently displaying the sentence set forth in paragraph 1.E.1 with
+active links or immediate access to the full terms of the Project
+Gutenberg-tm License.
+
+1.E.6.  You may convert to and distribute this work in any binary,
+compressed, marked up, nonproprietary or proprietary form, including any
+word processing or hypertext form.  However, if you provide access to or
+distribute copies of a Project Gutenberg-tm work in a format other than
+"Plain Vanilla ASCII" or other format used in the official version
+posted on the official Project Gutenberg-tm web site (www.gutenberg.org),
+you must, at no additional cost, fee or expense to the user, provide a
+copy, a means of exporting a copy, or a means of obtaining a copy upon
+request, of the work in its original "Plain Vanilla ASCII" or other
+form.  Any alternate format must include the full Project Gutenberg-tm
+License as specified in paragraph 1.E.1.
+
+1.E.7.  Do not charge a fee for access to, viewing, displaying,
+performing, copying or distributing any Project Gutenberg-tm works
+unless you comply with paragraph 1.E.8 or 1.E.9.
+
+1.E.8.  You may charge a reasonable fee for copies of or providing
+access to or distributing Project Gutenberg-tm electronic works provided
+that
+
+- You pay a royalty fee of 20% of the gross profits you derive from
+     the use of Project Gutenberg-tm works calculated using the method
+     you already use to calculate your applicable taxes.  The fee is
+     owed to the owner of the Project Gutenberg-tm trademark, but he
+     has agreed to donate royalties under this paragraph to the
+     Project Gutenberg Literary Archive Foundation.  Royalty payments
+     must be paid within 60 days following each date on which you
+     prepare (or are legally required to prepare) your periodic tax
+     returns.  Royalty payments should be clearly marked as such and
+     sent to the Project Gutenberg Literary Archive Foundation at the
+     address specified in Section 4, "Information about donations to
+     the Project Gutenberg Literary Archive Foundation."
+
+- You provide a full refund of any money paid by a user who notifies
+     you in writing (or by e-mail) within 30 days of receipt that s/he
+     does not agree to the terms of the full Project Gutenberg-tm
+     License.  You must require such a user to return or
+     destroy all copies of the works possessed in a physical medium
+     and discontinue all use of and all access to other copies of
+     Project Gutenberg-tm works.
+
+- You provide, in accordance with paragraph 1.F.3, a full refund of any
+     money paid for a work or a replacement copy, if a defect in the
+     electronic work is discovered and reported to you within 90 days
+     of receipt of the work.
+
+- You comply with all other terms of this agreement for free
+     distribution of Project Gutenberg-tm works.
+
+1.E.9.  If you wish to charge a fee or distribute a Project Gutenberg-tm
+electronic work or group of works on different terms than are set
+forth in this agreement, you must obtain permission in writing from
+both the Project Gutenberg Literary Archive Foundation and Michael
+Hart, the owner of the Project Gutenberg-tm trademark.  Contact the
+Foundation as set forth in Section 3 below.
+
+1.F.
+
+1.F.1.  Project Gutenberg volunteers and employees expend considerable
+effort to identify, do copyright research on, transcribe and proofread
+public domain works in creating the Project Gutenberg-tm
+collection.  Despite these efforts, Project Gutenberg-tm electronic
+works, and the medium on which they may be stored, may contain
+"Defects," such as, but not limited to, incomplete, inaccurate or
+corrupt data, transcription errors, a copyright or other intellectual
+property infringement, a defective or damaged disk or other medium, a
+computer virus, or computer codes that damage or cannot be read by
+your equipment.
+
+1.F.2.  LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right
+of Replacement or Refund" described in paragraph 1.F.3, the Project
+Gutenberg Literary Archive Foundation, the owner of the Project
+Gutenberg-tm trademark, and any other party distributing a Project
+Gutenberg-tm electronic work under this agreement, disclaim all
+liability to you for damages, costs and expenses, including legal
+fees.  YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
+LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
+PROVIDED IN PARAGRAPH 1.F.3.  YOU AGREE THAT THE FOUNDATION, THE
+TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
+LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
+INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
+DAMAGE.
+
+1.F.3.  LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
+defect in this electronic work within 90 days of receiving it, you can
+receive a refund of the money (if any) you paid for it by sending a
+written explanation to the person you received the work from.  If you
+received the work on a physical medium, you must return the medium with
+your written explanation.  The person or entity that provided you with
+the defective work may elect to provide a replacement copy in lieu of a
+refund.  If you received the work electronically, the person or entity
+providing it to you may choose to give you a second opportunity to
+receive the work electronically in lieu of a refund.  If the second copy
+is also defective, you may demand a refund in writing without further
+opportunities to fix the problem.
+
+1.F.4.  Except for the limited right of replacement or refund set forth
+in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER
+WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
+WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE.
+
+1.F.5.  Some states do not allow disclaimers of certain implied
+warranties or the exclusion or limitation of certain types of damages.
+If any disclaimer or limitation set forth in this agreement violates the
+law of the state applicable to this agreement, the agreement shall be
+interpreted to make the maximum disclaimer or limitation permitted by
+the applicable state law.  The invalidity or unenforceability of any
+provision of this agreement shall not void the remaining provisions.
+
+1.F.6.  INDEMNITY - You agree to indemnify and hold the Foundation, the
+trademark owner, any agent or employee of the Foundation, anyone
+providing copies of Project Gutenberg-tm electronic works in accordance
+with this agreement, and any volunteers associated with the production,
+promotion and distribution of Project Gutenberg-tm electronic works,
+harmless from all liability, costs and expenses, including legal fees,
+that arise directly or indirectly from any of the following which you do
+or cause to occur: (a) distribution of this or any Project Gutenberg-tm
+work, (b) alteration, modification, or additions or deletions to any
+Project Gutenberg-tm work, and (c) any Defect you cause.
+
+
+Section  2.  Information about the Mission of Project Gutenberg-tm
+
+Project Gutenberg-tm is synonymous with the free distribution of
+electronic works in formats readable by the widest variety of computers
+including obsolete, old, middle-aged and new computers.  It exists
+because of the efforts of hundreds of volunteers and donations from
+people in all walks of life.
+
+Volunteers and financial support to provide volunteers with the
+assistance they need are critical to reaching Project Gutenberg-tm's
+goals and ensuring that the Project Gutenberg-tm collection will
+remain freely available for generations to come.  In 2001, the Project
+Gutenberg Literary Archive Foundation was created to provide a secure
+and permanent future for Project Gutenberg-tm and future generations.
+To learn more about the Project Gutenberg Literary Archive Foundation
+and how your efforts and donations can help, see Sections 3 and 4
+and the Foundation web page at https://www.pglaf.org.
+
+
+Section 3.  Information about the Project Gutenberg Literary Archive
+Foundation
+
+The Project Gutenberg Literary Archive Foundation is a non profit
+501(c)(3) educational corporation organized under the laws of the
+state of Mississippi and granted tax exempt status by the Internal
+Revenue Service.  The Foundation's EIN or federal tax identification
+number is 64-6221541.  Its 501(c)(3) letter is posted at
+https://pglaf.org/fundraising.  Contributions to the Project Gutenberg
+Literary Archive Foundation are tax deductible to the full extent
+permitted by U.S. federal laws and your state's laws.
+
+The Foundation's principal office is located at 4557 Melan Dr. S.
+Fairbanks, AK, 99712., but its volunteers and employees are scattered
+throughout numerous locations.  Its business office is located at
+809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email
+business@pglaf.org.  Email contact links and up to date contact
+information can be found at the Foundation's web site and official
+page at https://pglaf.org
+
+For additional contact information:
+     Dr. Gregory B. Newby
+     Chief Executive and Director
+     gbnewby@pglaf.org
+
+
+Section 4.  Information about Donations to the Project Gutenberg
+Literary Archive Foundation
+
+Project Gutenberg-tm depends upon and cannot survive without wide
+spread public support and donations to carry out its mission of
+increasing the number of public domain and licensed works that can be
+freely distributed in machine readable form accessible by the widest
+array of equipment including outdated equipment.  Many small donations
+($1 to $5,000) are particularly important to maintaining tax exempt
+status with the IRS.
+
+The Foundation is committed to complying with the laws regulating
+charities and charitable donations in all 50 states of the United
+States.  Compliance requirements are not uniform and it takes a
+considerable effort, much paperwork and many fees to meet and keep up
+with these requirements.  We do not solicit donations in locations
+where we have not received written confirmation of compliance.  To
+SEND DONATIONS or determine the status of compliance for any
+particular state visit https://pglaf.org
+
+While we cannot and do not solicit contributions from states where we
+have not met the solicitation requirements, we know of no prohibition
+against accepting unsolicited donations from donors in such states who
+approach us with offers to donate.
+
+International donations are gratefully accepted, but we cannot make
+any statements concerning tax treatment of donations received from
+outside the United States.  U.S. laws alone swamp our small staff.
+
+Please check the Project Gutenberg Web pages for current donation
+methods and addresses.  Donations are accepted in a number of other
+ways including including checks, online payments and credit card
+donations.  To donate, please visit: https://pglaf.org/donate
+
+
+Section 5.  General Information About Project Gutenberg-tm electronic
+works.
+
+Professor Michael S. Hart was the originator of the Project Gutenberg-tm
+concept of a library of electronic works that could be freely shared
+with anyone.  For thirty years, he produced and distributed Project
+Gutenberg-tm eBooks with only a loose network of volunteer support.
+
+
+Project Gutenberg-tm eBooks are often created from several printed
+editions, all of which are confirmed as Public Domain in the U.S.
+unless a copyright notice is included.  Thus, we do not necessarily
+keep eBooks in compliance with any particular paper edition.
+
+
+Most people start at our Web site which has the main PG search facility:
+
+     https://www.gutenberg.org
+
+This Web site includes information about Project Gutenberg-tm,
+including how to make donations to the Project Gutenberg Literary
+Archive Foundation, how to help produce our new eBooks, and how to
+subscribe to our email newsletter to hear about new eBooks.
diff --git a/35092.zip b/35092.zip
new file mode 100644
index 0000000..9d0bcc7
--- /dev/null
+++ b/35092.zip
diff --git a/LICENSE.txt b/LICENSE.txt
new file mode 100644
index 0000000..6312041
--- /dev/null
+++ b/LICENSE.txt
@@ -0,0 +1,11 @@
+This eBook, including all associated images, markup, improvements,
+metadata, and any other content or labor, has been confirmed to be
+in the PUBLIC DOMAIN IN THE UNITED STATES.
+
+Procedures for determining public domain status are described in
+the "Copyright How-To" at https://www.gutenberg.org.
+
+No investigation has been made concerning possible copyrights in
+jurisdictions other than the United States. Anyone seeking to utilize
+this eBook outside of the United States should confirm copyright
+status under the laws that apply to them.
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..a240654
--- /dev/null
+++ b/README.md
@@ -0,0 +1,2 @@
+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #35092 (https://www.gutenberg.org/ebooks/35092)