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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. 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