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diff --git a/old/65359-0.txt b/old/65359-0.txt deleted file mode 100644 index ecae725..0000000 --- a/old/65359-0.txt +++ /dev/null @@ -1,7806 +0,0 @@ -The Project Gutenberg eBook, James Clerk Maxwell and Modern Physics, by -Richard Glazebrook - - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world 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. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - - - - -Title: James Clerk Maxwell and Modern Physics - - -Author: Richard Glazebrook - - - -Release Date: May 16, 2021 [eBook #65359] - -Language: English - -Character set encoding: UTF-8 - - -***START OF THE PROJECT GUTENBERG EBOOK JAMES CLERK MAXWELL AND MODERN -PHYSICS*** - - -E-text prepared by Fay Dunn, Charlie Howard, and the Online Distributed -Proofreading Team (http://www.pgdp.net) from page images generously made -available by Internet Archive (https://archive.org) - - - -Note: Project Gutenberg also has an HTML version of this - file which includes the original illustrations. - See 65359-h.htm or 65359-h.zip: - (http://www.gutenberg.org/files/65359/65359-h/65359-h.htm) - or - (http://www.gutenberg.org/files/65359/65359-h.zip) - - - Images of the original pages are available through - Internet Archive. See - https://archive.org/details/jamesclerkmaxwel00glaziala - - -Transcriber’s note: - - Text enclosed by underscores is in italics (_italics_). - - Superscripts that cannot be represented directly are - enclosed by curly brackets immediately after a caret - character (example: n^{th}). - - - Some characters might not display properly in this UTF-8 - text file (e.g., empty squares). If so, the reader should - consult the html version or the original page images noted - above. - - - - - -[Illustration: (cover)] - - -_The Century Science Series_ - -Edited by Sir Henry E. Roscoe, D.C.L., LL.D., F.R.S. - - -JAMES CLERK MAXWELL AND MODERN PHYSICS - - - * * * * * * - -The Century Science Series. - -EDITED BY - -SIR HENRY E. ROSCOE, D.C.L., F.R.S., M.P. - - - John Dalton and the Rise of Modern Chemistry. - By Sir HENRY E. ROSCOE, F.R.S. - - Major Rennell, F.R.S., and the Rise of English Geography. - By CLEMENTS R. MARKHAM, C.B., F.R.S., President of the Royal - Geographical Society. - - Justus von Liebig: his Life and Work (1803–1873). - By W. A. SHENSTONE, F.I.C., Lecturer on Chemistry in Clifton - College. - - The Herschels and Modern Astronomy. - By AGNES M. CLERKE, Author of “A Popular History of Astronomy - during the 19th Century,” &c. - - Charles Lyell and Modern Geology. - By Rev. Professor T. G. BONNEY, F.R.S. - - James Clerk Maxwell and Modern Physics. - By R. T. GLAZEBROOK, F.R.S., Fellow of Trinity College, - Cambridge. - - - _In Preparation._ - - Michael Faraday: his Life and Work. - By Professor SILVANUS P. THOMPSON, F.R.S. - - Humphry Davy. - By T. E. THORPE, F.R.S., Principal Chemist of the Government - Laboratories. - - Pasteur: his Life and Work. - By M. ARMAND RUFFER, M.D., Director of the British Institute of - Preventive Medicine. - - Charles Darwin and the Origin of Species. - By EDWARD B. POULTON, M.A., F.R.S., Hope Professor of Zoology - in the University of Oxford. - - Hermann von Helmholtz. - By A. W. RÜCKER, F.R.S., Professor of Physics in the Royal - College of Science, London. - -CASSELL & COMPANY, LIMITED, _London_; _Paris_ & _Melbourne_. - - * * * * * * - - -[Illustration: J. Clerk Maxwell - -(_From a Photograph of the Picture by G. Lowes Dickinson, Esq., in the -Hall of Trinity College, Cambridge._)] - - -The Century Science Series - -JAMES CLERK MAXWELL AND MODERN PHYSICS - -by - -R. T. GLAZEBROOK, F.R.S. - -Fellow of Trinity College, Cambridge -University Lecturer in Mathematics, and Assistant Director of the -Cavendish Laboratory - - - - - - -Cassell and Company, Limited -London, Paris & Melbourne -1896 -All Rights Reserved - -[Illustration] - - - - -PREFACE. - - -The task of giving some account of Maxwell’s work--of describing the -share that he has taken in the advance of Physical Science during the -latter half of this nineteenth century--has proved no light labour. -The problems which he attacked are of such magnitude and complexity, -that the attempt to explain them and their importance, satisfactorily, -without the aid of symbols, is almost foredoomed to failure. However, -the attempt has been made, in the belief that there are many who, -though they cannot follow the mathematical analysis of Maxwell’s work, -have sufficient general knowledge of physical ideas and principles to -make an account of Maxwell and of the development of the truths that he -discovered, subjects of intelligent interest. - -Maxwell’s life was written in 1882 by two of those who were most -intimately connected with him, Professor Lewis Campbell and Dr. -Garnett. Many of the biographical details of the earlier part of this -book are taken from their work. My thanks are due to them and to their -publishers, Messrs. Macmillan, for permission to use any of the letters -which appear in their biography. I trust that my brief account may -be sufficient to induce many to read Professor Campbell’s “Life and -Letters,” with a view of learning more of the inner thoughts of one who -has left so strong an imprint on all he undertook, and was so deeply -loved by all who knew him. - - R. T. G. - - _Cambridge, - December, 1895._ - - - - -CONTENTS. - - - CHAPTER PAGE - I. EARLY LIFE 9 - - II. UNDERGRADUATE LIFE AT CAMBRIDGE 28 - - III. EARLY RESEARCHES--PROFESSOR AT ABERDEEN 38 - - IV. PROFESSOR AT KING’S COLLEGE, LONDON--LIFE AT GLENLAIR 54 - - V. CAMBRIDGE--PROFESSOR OR PHYSICS 60 - - VI. CAMBRIDGE--THE CAVENDISH LABORATORY 73 - - VII. SCIENTIFIC WORK--COLOUR VISION 93 - - VIII. SCIENTIFIC WORK--MOLECULAR THEORY 108 - - IX. SCIENTIFIC WORK--ELECTRICAL THEORIES 148 - - X. DEVELOPMENT OF MAXWELL’S THEORY 202 - - - - -JAMES CLERK MAXWELL - -AND MODERN PHYSICS. - - - - -CHAPTER I. - -EARLY LIFE. - - -“One who has enriched the inheritance left by Newton and has -consolidated the work of Faraday--one who impelled the mind of -Cambridge to a fresh course of real investigation--has clearly earned -his place in human memory.” It was thus that Professor Lewis Campbell -and Mr. Garnett began in 1882 their life of James Clerk Maxwell. The -years which have passed, since that date, have all tended to strengthen -the belief in the greatness of Maxwell’s work and in the fertility -of his genius, which has inspired the labours of those who, not in -Cambridge only, but throughout the world, have aided in developing the -seeds sown by him. My object in the following pages will be to give -some very brief account of his life and writings, in a form which may, -I hope, enable many to realise what Physical Science owes to one who -was to me a most kind friend as well as a revered master. - -The Clerks of Penicuik, from whom Clerk Maxwell was descended, were -a distinguished family. Sir John Clerk, the great-great-grandfather -of Clerk Maxwell, was a Baron of the Exchequer in Scotland from -1707 to 1755; he was also one of the Commissioners of the Union, -and was in many ways an accomplished scholar. His second son George -married a first cousin, Dorothea Maxwell, the heiress of Middlebie in -Dumfriesshire, and took the name of Maxwell. By the death of his elder -brother James in 1782 George Clerk Maxwell succeeded to the baronetcy -and the property of Penicuik. Before this time he had become involved -in mining and manufacturing speculations, and most of the Middlebie -property had been sold to pay his debts. - -The property of Sir George Clerk Maxwell descended in 1798 to his two -grandsons, Sir George Clerk and Mr. John Clerk Maxwell. It had been -arranged that the younger of the two was to take the remains of the -Middlebie property and to assume with it the name of Maxwell. Sir -George Clerk was member for Midlothian, and held office under Sir -Robert Peel. John Clerk Maxwell was the father of James Clerk Maxwell, -the subject of this sketch.[1] - -John Clerk Maxwell lived with his widowed mother in Edinburgh until her -death in 1824. He was a lawyer, and from time to time did some little -business in the courts. At the same time he maintained an interest in -scientific pursuits, especially those of a practical nature. Professor -Campbell tells us of an endeavour to devise a bellows which would give -a continuous draught of air. In 1831 he contributed to the _Edinburgh -Medical and Philosophical Journal_ a paper entitled “Outlines of a Plan -for combining Machinery with the Manual Printing Press.” - -In 1826 John Clerk Maxwell married Miss Frances Cay, of North Charlton, -Northumberland. For the first few years of their married life their -home was in Edinburgh. The old estate of Middlebie had been greatly -reduced in extent, and there was not a house on it in which the laird -could live. However, soon after his marriage, John Clerk Maxwell -purchased the adjoining property of Glenlair and built a mansion-house -for himself and his wife. Mr. Maxwell superintended the building work. -The actual working plans for some further additions made in 1843 -were his handiwork. A garden was laid out and planted, and a dreary -stony waste was converted into a pleasant home. For some years after -he settled at Glenlair the house in Edinburgh was retained by Mr. -Maxwell, and here, on June 13, 1831, was born his only son, James Clerk -Maxwell. A daughter, born earlier, died in infancy. Glenlair, however, -was his parents’ home, and nearly all the reminiscences we have of -his childhood are connected with it. The laird devoted himself to his -estates and to the education of his son, taking, however, from time to -time his full share in such county business as fell to him. Glenlair in -1830 was very much in the wilds; the journey from Edinburgh occupied -two days. “Carriages in the modern sense were hardly known to the Vale -of Urr. A sort of double gig with a hood was the best apology for a -travelling coach, and the most active mode of locomotion was in a kind -of rough dog-cart known in the family speech as a hurly.”[2] - -Mrs. Maxwell writes thus[3], when the boy was nearly three years old, -to her sister, Miss Jane Cay:-- - - “He is a very happy man, and has improved much since the - weather got moderate. He has great work with doors, locks, - keys, etc., and ‘Show me how it doos’ is never out of his - mouth. He also investigates the hidden course of streams and - bell-wires--the way the water gets from the pond through the - wall and a pend or small bridge and down a drain into Water - Orr, then past the smiddy and down to the sea, where Maggy’s - ships sail. As to the bells, they will not rust; he stands - sentry in the kitchen and Mag runs through the house ringing - them all by turns, or he rings and sends Bessy to see and shout - to let him know; and he drags papa all over to show him the - holes where the wires go through.” - -To discover “how it doos” was thus early his aim. His cousin, Mrs. -Blackburn, tells us that throughout his childhood his constant question -was, “What’s the go of that? What does it do?” And if the answer were -too vague or inconclusive, he would add, “But what’s the _particular_ -go of that?” - -Professor Campbell’s most interesting account of these early years is -illustrated by a number of sketches of episodes in his life. In one -Maxwell is absorbed in watching the fiddler at a country dance; in -another he is teaching his dog some tricks; in a third he is helping a -smaller boy in his efforts to build a castle. Together with his cousin, -Miss Wedderburn, he devised a number of figures for a toy known as a -magic disc, which afterwards developed into the zoetrope or wheel of -life, and in which, by means of an ingenious contrivance of mirrors, -the impression of a continuous movement was produced. - -This happy life went on until his mother’s death in December, 1839; she -died, at the age of forty-eight, of the painful disease to which her -son afterwards succumbed. When James, being then eight years old, was -told that she was now in heaven, he said: “Oh, I’m so glad! Now she’ll -have no more pain.” - -After this his aunt, Miss Jane Cay, took a mother’s place. The problem -of his education had to be faced, and the first attempts were not -successful. A tutor had been engaged during Mrs. Maxwell’s last -illness, and he, it seems, tried to coerce Clerk Maxwell into learning; -but such treatment failed, and in 1841, when ten years old, he began -his school-life at the Edinburgh Academy. - -School-life at first had its hardships. Maxwell’s appearance, his -first day at school, in Galloway home-spun and square-toed shoes with -buckles, was more than his fellows could stand. “Who made those shoes?” -they asked[4]; and the reply they received was-- - - “Div ye ken ’twas a man, - And he lived in a house, - In whilk was a mouse.” - -He returned to Heriot Row that afternoon, says Professor Campbell, -“with his tunic in rags and wanting the skirt, his neat frill rumpled -and torn--himself excessively amused by his experiences and showing not -the slightest sign of irritation.” - -No. 31, Heriot Row, was the house of his widowed aunt, Mrs. Wedderburn, -Mr. Maxwell’s sister; and this, with occasional intervals when he -was with Miss Cay, was his home for the next eight or nine years. -Mr. Maxwell himself, during this period, spent much of his time in -Edinburgh, living with his sister during most of the winter and -returning to Glenlair for the spring and summer. - -Much of what we know of Clerk Maxwell’s life during this period comes -from the letters which passed between him and his father. They tell -us of the close intimacy and affection which existed between the two, -of the boy’s eager desire to please and amuse his father in the dull -solitude of Glenlair, and his father’s anxiety for his welfare and -progress. - -Professor Campbell was his schoolfellow, and records events of those -years in which he shared, which bring clearly before us what Clerk -Maxwell was like. Thus he writes[5]:-- - - “He came to know Swift and Dryden, and after a while Hobbes, - and Butler’s ‘Hudibras.’ Then, if his father was in Edinburgh, - they walked together, especially on the Saturday half-holiday, - and ‘viewed’ Leith Fort, or the preparations for the Granton - railway, or the stratification of Salisbury Crags--always - learning something new, and winning ideas for imagination to - feed upon. One Saturday, February 12, 1842, he had a special - treat, being taken ‘to see electro-magnetic machines.’” - -And again, speaking of his school-life:-- - - “But at school also he gradually made his way. He soon - discovered that Latin was worth learning, and the Greek - Delectus interested him when we got so far. And there were two - subjects in which he at once took the foremost place, when he - had a fair chance of doing so; these were Scripture Biography - and English. In arithmetic as well as in Latin his comparative - want of readiness kept him down. - - “On the whole he attained a measure of success which helped - to secure for him a certain respect; and, however strange he - sometimes seemed to his companions, he had three qualities - which they could not fail to understand--agile strength - of limb, imperturbable courage, and profound good-nature. - Professor James Muirhead remembers him as ‘a friendly boy, - though never quite amalgamating with the rest.’ And another old - class-fellow, the Rev. W. Macfarlane of Lenzie, records the - following as his impression:--‘Clerk Maxwell, when he entered - the Academy, was somewhat rustic and somewhat eccentric. Boys - called him “Dafty,” and used to try to make fun of him. On one - occasion I remember he turned with tremendous vigour, with a - kind of demonic force, on his tormentors. I think he was let - alone after that, and gradually won the respect even of the - most thoughtless of his schoolfellows.’” - -The first reference to mathematical studies occurs, says Professor -Campbell, in a letter to his father written soon after his thirteenth -birthday.[6] - - “After describing the Virginian Minstrels, and betwixt - inquiries after various pets at Glenlair, he remarks, as if it - were an ordinary piece of news, ‘I have made a tetrahedron, a - dodecahedron, and two other hedrons, whose names I don’t know.’ - We had not yet begun geometry, and he had certainly not at this - time learnt the definitions in Euclid; yet he had not merely - realised the nature of the five regular solids sufficiently to - construct them out of pasteboard with approximate accuracy, but - had further contrived other symmetrical polyhedra derived from - them, specimens of which (as improved in 1848) may be still - seen at the Cavendish Laboratory. - - “Who first called his attention to the pyramid, cube, etc., I - do not know. He may have seen an account of them by chance in a - book. But the fact remains that at this early time his fancy, - like that of the old Greek geometers, was arrested by these - types of complete symmetry; and his imagination so thoroughly - mastered them that he proceeded to make them with his own - hand. That he himself attached more importance to this moment - than the letter indicates is proved by the care with which he - has preserved these perishable things, so that they (or those - which replaced them in 1848) are still in existence after - thirty-seven years.” - -The summer holidays were spent at Glenlair. His cousin, Miss Jemima -Wedderburn, was with him, and shared his play. Her skilled pencil -has left us many amusing pictures of the time, some of which are -reproduced by Professor Campbell. There were expeditions and picnics of -all sorts, and a new toy known as “the devil on two sticks” afforded -infinite amusement. The winter holidays usually found him at Penicuik, -or occasionally at Glasgow, with Professor Blackburne or Professor -W. Thomson (now Lord Kelvin). In October, 1844, Maxwell was promoted -to the rector’s class-room. John Williams, afterwards Archdeacon of -Cardigan, a distinguished Baliol man, was rector, and the change was -in many ways an important one for Maxwell. He writes to his father: “I -like P---- better than B----. We have lots of jokes, and he speaks a -great deal, and we have not so much monotonous parsing. In the English -Milton is better than the History of Greece....” - -P---- was the boys’ nickname for the rector; B---- for Mr. Carmichael, -the second master. This[7] is the account of Maxwell’s first interview -with the rector:-- - -_Rector_: “What part of Galloway do you come from?” - -_J. C. M._: “From the Vale of Urr. Ye spell it o, err, err, or oo, err, -err.” - -The study of geometry was begun, and in the mathematical master, Mr. -Gloag, Maxwell found a teacher with a real gift for his task. It was -here that Maxwell’s vast superiority to many who were his companions -at once showed itself. “He seemed,” says Professor Campbell, “to be in -the heart of the subject when they were only at the boundary; but the -boyish game of contesting point by point with such a mind was a most -wholesome stimulus, so that the mere exercise of faculty was a pure -joy. With Maxwell the first lessons of geometry branched out at once -into inquiries which became fruitful.” - -In July, 1845, he writes:-- - - “I have got the 11th prize for Scholarship, the 1st for - English, the prize for English verses, and the Mathematical - Medal. I tried for Scripture knowledge, and Hamilton in the 7th - has got it. We tried for the Medal on Thursday. I had done them - all, and got home at half-past two; but Campbell stayed till - four. I was rather tired with writing exercises from nine till - half-past two. - - “Campbell and I went ‘once more unto the b(r)each’ to-day at - Portobello. I can swim a little now. Campbell has got 6 prizes. - He got a letter written too soon, congratulating him upon _my_ - medal; but there is no rivalry betwixt us, as B---- Carmichael - says.” - -After a summer spent chiefly at Glenlair, he returned with his father -to Edinburgh for the winter, and began, at the age of fourteen, to go -to the meetings of the Royal Society of Edinburgh. At the Society of -Arts he met Mr. R. D. Hay, the decorative painter, who had interested -himself in the attempt to reduce beauty in form and colour to -mathematical principles. Clerk Maxwell was interested in the question -how to draw a perfect oval, and devised a method of drawing oval curves -which was referred by his father to Professor Forbes for his criticism -and suggestions. After discussing the matter with Professor Kelland, -Professor Forbes wrote as follows[8]:-- - - “MY DEAR SIR,--I am glad to find to-day, from Professor - Kelland, that his opinion of your son’s paper agrees with - mine, namely, that it is most ingenious, most creditable to - him, and, we believe, a new way of considering higher curves - with reference to foci. Unfortunately, these ovals appear - to be curves of a very high and intractable order, so that - possibly the elegant method of description may not lead to a - corresponding simplicity in investigating their properties. But - that is not the present point. If you wish it, I think that - the simplicity and elegance of the method would entitle it to - be brought before the Royal Society.--Believe me, my dear sir, - yours truly, - - “JAMES D. FORBES.” - -In consequence of this, Clerk Maxwell’s first published paper was -communicated to the Royal Society of Edinburgh on April 6th, 1846, -when its author was barely fifteen. Its title is as follows: “On the -Description of Oval Curves and those having a Plurality of Foci. By Mr. -Clerk Maxwell, Junior. With Remarks by Professor Forbes. Communicated -by Professor Forbes.” - -The notice in his father’s diary runs: “M. 6 [Ap., 1846.] Royal Society -with Jas. Professor Forbes gave acct. of James’s Ovals. Met with very -great attention and approbation generally.” - -This was the beginning of the lifelong friendship between Maxwell and -Forbes. - -The curves investigated by Maxwell have the property that the sum found -by adding to the distance of any point on the curve from one focus a -constant multiple of the distance of the same point from a second focus -is always constant. - -The curves are of great importance in the theory of light, for if this -constant factor expresses the refractive index of any medium, then -light diverging from one focus without the medium and refracted at a -surface bounding the medium, and having the form of one of Maxwell’s -ovals, will be refracted so as to converge to the second focus. - -About the same time he was busy with some investigations on the -properties of jelly and gutta-percha, which seem to have been suggested -by Forbes’ “Theory of Glaciers.” - -He failed to obtain the Mathematical Medal in 1846--possibly on account -of these researches--but he continued at school till 1847, when he -left, being then first in mathematics and in English, and nearly first -in Latin. - -In 1847 he was working at magnetism and the polarisation of light. -Some time in that year he was taken by his uncle, Mr. John Cay, to see -William Nicol, the inventor of the polarising prism, who showed him the -colours exhibited by polarised light after passing through unannealed -glass. On his return, he made a polariscope with a glass reflector. -The framework of the first instrument was of cardboard, but a superior -article was afterwards constructed of wood. Small lenses mounted on -cardboard were employed when a conical pencil was needed. By means -of this instrument he examined the figures exhibited by pieces of -unannealed glass, which he prepared himself; and, with a camera lucida -and box of colours, he reproduced these figures on paper, taking care -to sketch no outlines, but to shade each coloured band imperceptibly -into the next. Some of these coloured drawings he forwarded to Nicol, -and was more than repaid by the receipt shortly afterwards of a pair of -prisms prepared by Nicol himself. These prisms were always very highly -prized by Maxwell. Once, when at Trinity, the little box containing -them was carried off by his bed-maker during a vacation, and destined -for destruction. The bed-maker died before term commenced, and it -was only by diligent search among her effects that the prisms were -recovered.[9] After this they were more carefully guarded, and they -are now, together with the wooden polariscope, the bits of unannealed -glass, and the water-colour drawings, in one of the showcases at the -Cavendish Laboratory. - -About this time, Professor P. G. Tait and he were schoolfellows at the -Academy, acknowledged as the two best mathematicians in the school. It -was thought desirable, says Professor Campbell, that “we should have -lessons in physical science, so one of the classical masters gave them -out of a text-book.... The only thing I distinctly remember about these -hours is that Maxwell and P. G. Tait seemed to know much more about the -subject than our teacher did.” - -An interesting account of these days is given by Professor Tait in an -obituary notice on Maxwell printed in the “Proceedings of the Royal -Society of Edinburgh, 1879–80,” from which the following is taken:-- - - “When I first made Clerk Maxwell’s acquaintance, about - thirty-five years ago, at the Edinburgh Academy, he was a year - before me, being in the fifth class, while I was in the fourth. - - “At school he was at first regarded as shy and rather dull. - He made no friendships, and he spent his occasional holidays - in reading old ballads, drawing curious diagrams, and making - rude mechanical models. This absorption in such pursuits, - totally unintelligible to his schoolfellows (who were then - quite innocent of mathematics), of course procured him a not - very complimentary nickname, which I know is still remembered - by many Fellows of this Society. About the middle of his school - career, however, he surprised his companions by suddenly - becoming one of the most brilliant among them, gaining - high, and sometimes the highest, prizes for scholarships, - mathematics, and English verse composition. From this time - forward I became very intimate with him, and we discussed - together, with schoolboy enthusiasm, numerous curious - problems, among which I remember particularly the various plane - sections of a ring or tore, and the form of a cylindrical - mirror which should show one his own image unperverted. I - still possess some of the MSS. we exchanged in 1846 and early - in 1847. Those by Maxwell are on ‘The Conical Pendulum,’ - ‘Descartes’ Ovals,’ ‘Meloid and Apioid,’ and ‘Trifocal Curves.’ - All are drawn up in strict geometrical form and divided into - consecutive propositions. The three latter are connected with - his first published paper, communicated by Forbes to this - society and printed in our ‘Proceedings,’ vol. ii., under the - title, ‘On the Description of Oval Curves and those having a - Plurality of Foci’ (1846). At the time when these papers were - written he had received no instruction in mathematics beyond a - few books of Euclid and the merest elements of algebra.” - -In November, 1847, Clerk Maxwell entered the University of Edinburgh, -learning mathematics from Kelland, natural philosophy from J. D. -Forbes, and logic from Sir W. R. Hamilton. At this time, according to -Professor Campbell[10]-- - - “he still occasioned some concern to the more conventional - amongst his friends by the originality and simplicity of his - ways. His replies in ordinary conversation were indirect and - enigmatical, often uttered with hesitation and in a monotonous - key. While extremely neat in his person, he had a rooted - objection to the vanities of starch and gloves. He had a pious - horror of destroying anything, even a scrap of writing-paper. - He preferred travelling by the third class in railway journeys, - saying he liked a hard seat. When at table he often seemed - abstracted from what was going on, being absorbed in observing - the effects of refracted light in the finger-glasses, or in - trying some experiment with his eyes--seeing round a corner, - making invisible stereoscopes, and the like. Miss Cay used - to call his attention by crying, ‘Jamsie, you’re in a prop.’ - He never tasted wine; and he spoke to gentle and simple in - exactly the same tone. On the other hand, his teachers--Forbes - above all--had formed the highest opinion of his intellectual - originality and force; and a few experienced observers, in - watching his devotion to his father, began to have some inkling - of his heroic singleness of heart. To his college companions, - whom he could now select at will, his quaint humour was an - endless delight. His chief associates, after I went to the - University of Glasgow, were my brother, Robert Campbell (still - at the Academy), P. G. Tait, and Allan Stewart. Tait went - to Peterhouse, Cambridge, in 1848, after one session of the - University of Edinburgh; Stewart to the same college in 1849; - Maxwell did not go up until 1850.” - -During this period he wrote two important papers. The one, on “Rolling -Curves,” was read to the Royal Society of Edinburgh by Professor -Kelland--(“it was not thought proper for a boy in a round jacket to -mount the rostrum”)--in February, 1849; the other, on “The Equilibrium -of Elastic Solids,” appeared in the spring of 1850. - -The vacations were spent at Glenlair, and we learn from letters to -Professor Campbell and others how the time was passed. - -“On Saturday,” he writes[11]--April 26th, 1848, just after his -arrival home--“the natural philosophers ran up Arthur’s Seat with the -barometer. The Professor set it down at the top.... He did not set it -straight, and made the hill grow fifty feet; but we got it down again.” - -In a letter of July in the same year he describes his laboratory:-- - - “I have regularly set up shop now above the wash-house at the - gate, in a garret. I have an old door set on two barrels, and - two chairs, of which one is safe, and a skylight above which - will slide up and down. - - “On the door (or table) there is a lot of bowls, jugs, plates, - jam pigs, etc., containing water, salt, soda, sulphuric acid, - blue vitriol, plumbago ore; also broken glass, iron, and copper - wire, copper and zinc plate, bees’ wax, sealing wax, clay, - rosin, charcoal, a lens, a Smee’s galvanic apparatus, and a - countless variety of little beetles, spiders, and wood lice, - which fall into the different liquids and poison themselves. I - intend to get up some more galvanism in jam pigs; but I must - first copper the interiors of the pigs, so I am experimenting - on the best methods of electrotyping. So I am making copper - seals with the device of a beetle. First, I thought a beetle - was a good conductor, so I embedded one in wax (not at all - cruel, because I slew him in boiling water, in which he never - kicked), leaving his back out; but he would not do. Then I took - a cast of him in sealing wax, and pressed wax into the hollow, - and blackleaded it with a brush; but neither would that do. So - at last I took my fingers and rubbed it, which I find the best - way to use the blacklead. Then it coppered famously. I melt out - the wax with the lens, that being the cleanest way of getting a - strong heat, so I do most things with it that need heat. To-day - I astonished the natives as follows. I took a crystal of blue - vitriol and put the lens to it, and so drove off the water, - leaving a white powder. Then I did the same to some washing - soda, and mixed the two white powders together, and made a - small native spit on them, which turned them green by a mutual - exchange, thus:--1. Sulphate of copper and carbonate of soda. - 2. Sulphate of soda and carbonate of copper (blue or green).” - -Of his reading he says:--“I am reading Herodotus’ ‘Euterpe,’ having -taken the turn--that is to say that sometimes I can do props., read -Diff. and Int. Calc., Poisson, Hamilton’s dissertation, etc.” - -In September he was busy with polarised light. “We were at Castle -Douglas yesterday, and got crystals of saltpetre, which I have been -cutting up into plates to-day in hopes to see rings.” - -In July, 1849, he writes[12]:-- - - “I have set up the machine for showing the rings in crystals, - which I planned during your visit last year. It answers very - well. I also made some experiments on compressed jellies in - illustration of my props. on that subject. The principal one - was this:--The jelly is poured while hot into the annular space - contained between a paper cylinder and a cork; then, when cold, - the cork is twisted round and the jelly exposed to polarised - light, when a transverse cross, X, not +, appears, with rings - as the inverse square of the radius, all which is fully - verified. Hip! etc. _Q.E.D._” - -And again on March 22nd, 1850:-- - - “At Practical Mechanics I have been turning Devils of sorts. - For private studies I have been reading Young’s ‘Lectures,’ - Willis’s ‘Principles of Mechanism,’ Moseley’s ‘Engineering - and Mechanics,’ Dixon on ‘Heat,’ and Moigno’s ‘Répertoire - d’Optique.’ This last is a very complete analysis of all that - has been done in the optical way from Fresnel to the end of - 1849, and there is another volume a-coming which will complete - the work. There is in it, besides common optics, all about the - other things which accompany light, as heat, chemical action, - photographic rays, action on vegetables, etc. - - “My notions are rather few, as I do not _entertain_ them just - now. I have a notion for the torsion of wires and rods, not - to be made till the vacation; of experiments on the action of - compression on glass, jelly, etc., numerically done up; of - papers for the Physico-Mathematical Society (which is to revive - in earnest next session!); on the relations of optical and - mechanical constants, their desirableness, etc.; and suspension - bridges, and catenaries, and elastic curves. Alex. Campbell, - Agnew, and I are appointed to read up the subject of periodical - shooting stars, and to prepare a list of the phenomena to be - observed on the 9th August and 13th November. The society’s - barometer is to be taken up Arthur’s Seat at the end of the - session, when Forbes goes up, and All students are invited to - attend, so that the existence of the society may be recognised.” - -It was at last settled that he was to go up to Cambridge. Tait had been -at Peterhouse for two years, while Allan Stewart had joined him there -in 1849, and after much discussion it was arranged that Maxwell should -enter at the same college. - -Of this period of his life Tait writes as follows:-- - - “The winter of 1847 found us together in the classes of Forbes - and Kelland, where he highly distinguished himself. With the - former he was a particular favourite, being admitted to the - free use of the class apparatus for original experiments. He - lingered here behind most of his former associates, having - spent three years at the University of Edinburgh, working - (without any assistance or supervision) with physical and - chemical apparatus, and devouring all sorts of scientific - works in the library. During this period he wrote two valuable - papers, which are published in our ‘Transactions,’ on ‘The - Theory of Rolling Curves’ and on ‘The Equilibrium of Elastic - Solids.’ Thus he brought to Cambridge, in the autumn of 1850, a - mass of knowledge which was really immense for so young a man, - but in a state of disorder appalling to his methodical private - tutor. Though that tutor was William Hopkins, the pupil to a - great extent took his own way, and it may safely be said that - no high wrangler of recent years ever entered the Senate House - more imperfectly trained to produce ‘paying’ work than did - Clerk Maxwell. But by sheer strength of intellect, though with - the very minimum of knowledge how to use it to advantage under - the conditions of the examination, he obtained the position - of Second Wrangler, and was bracketed equal with the Senior - Wrangler in the higher ordeal of the Smith’s Prizes. His name - appears in the Cambridge ‘Calendar’ as Maxwell of Trinity, - but he was originally entered at Peterhouse, and kept his - first term there, in that small but most ancient foundation - which has of late furnished Scotland with the majority of the - professors of mathematics and natural philosophy in her four - universities.” - -While W. D. Niven, in his preface to Maxwell’s collected works (p. -xii.), says:-- - - “It may readily be supposed that his preparatory training for - the Cambridge course was far removed from the ordinary type. - There had indeed for some time been practically no restraint - upon his plan of study, and his mind had been allowed to follow - its natural bent towards science, though not to an extent - so absorbing as to withdraw him from other pursuits. Though - he was not a sportsman--indeed, sport so-called was always - repugnant to him--he was yet exceedingly fond of a country - life. He was a good horseman and a good swimmer. Whence, - however, he derived his chief enjoyment may be gathered from - the account which Mr. Campbell gives of the zest with which he - quoted on one occasion the lines of Burns which describe the - poet finding inspiration while wandering along the banks of a - stream in the free indulgence of his fancies. Maxwell was not - only a lover of poetry, but himself a poet, as the fine pieces - gathered together by Mr. Campbell abundantly testify. He saw, - however, that his true calling was science, and never regarded - these poetical efforts as other than mere pastime. Devotion - to science, already stimulated by successful endeavour; - a tendency to ponder over philosophical problems; and an - attachment to English literature, particularly to English - poetry--these tastes, implanted in a mind of singular strength - and purity, may be said to have been the endowments with which - young Maxwell began his Cambridge career. Besides this, his - scientific reading, as we may gather from his papers to the - Royal Society of Edinburgh referred to above, was already - extensive and varied. He brought with him, says Professor Tait, - a mass of knowledge which was really immense for so young a - man, but in a state of disorder appalling to his methodical - private tutor.” - - - - -CHAPTER II. - -UNDERGRADUATE LIFE AT CAMBRIDGE. - - -Maxwell did not remain long at Peterhouse; before the end of his -first term he migrated to Trinity, and was entered under Dr. Thompson -December 14th, 1850. He appeared to the tutor a shy and diffident -youth, but presently surprised Dr. Thompson by producing a bundle -of papers--copies, probably, of those he had already published--and -remarking, “Perhaps these may show that I am not unfit to enter at your -College.” - -The change was pressed upon him by many friends, the grounds of the -advice being that, from the large number of high wranglers recently -at Peterhouse and the smallness of the foundation, the chances of a -Fellowship there for a mathematical man were less than at Trinity. It -was a step he never regretted; the prospect of a Fellowship had but -little influence on his mind. He found, however, at the larger college -ampler opportunities for self-improvement, and it was possible for him -to select his friends from among men whom he otherwise would never have -known. - -The record of his undergraduate life is not very full; his letters to -his father have, unfortunately, been lost, but we have enough in the -recollections of friends still living to picture what it was like. At -first he lodged in King’s Parade with an old Edinburgh schoolfellow, -C. H. Robertson. He attended the College lectures on mathematics, -though they were somewhat elementary, and worked as a private pupil -with Porter, of Peterhouse. His father writes to him, November, 1850: -“Have you called on Professors Sedgwick, at Trin., and Stokes, at -Pembroke? If not, you should do both. Stokes will be most in your line, -if he takes you in hand at all. Sedgwick is also a great Don in his -line, and, if you were entered in geology, would be a most valuable -acquaintance.” - -In his second year he became a pupil of Hopkins, the great coach; he -also attended Stokes’ lectures, and the friendship which lasted till -his death was thus begun. In April, 1852, he was elected a scholar, -and obtained rooms in College (G, Old Court). In June, 1852, he came -of age. “I trust you will be as discreet when major as you have been -while minor,” writes his father the day before. The next academic -year, October, 1852, to June, 1853, was a very busy one; hard grind -for the Tripos occupied his time, and he seems to have been thoroughly -overstrained. He was taken ill while staying near Lowestoft with the -Rev. C. B. Tayler, the uncle of a College friend. His own account of -the illness is given in a letter to Professor Campbell[13], dated July -14th, 1853. - - “You wrote just in time for your letter to reach me as I - reached Cambridge. After examination, I went to visit the - Rev. C. B. Tayler (uncle to a Tayler whom I think you have - seen under the name of _Freshman_, etc., and author of many - tracts and other didactic works). We had little expedites and - walks, and things parochial and educational, and domesticity. - I intended to return on the 18th June, but on the 17th I felt - unwell, and took measures accordingly to be well again--_i.e._ - went to bed, and made up my mind to recover. But it lasted more - than a fortnight, during which time I was taken care of beyond - expectation (not that I did not expect much before). When I - was perfectly useless and could not sit up without fainting, - Mr. Tayler did everything for me in such a way that I had no - fear of giving trouble. So did Mrs. Tayler; and the two nephews - did all they could. So they kept me in great happiness all the - time, and detained me till I was able to walk about and got - back strength. I returned on the 4th July. - - “The consequence of all this is that I correspond with Mr. - Tayler, and have entered into bonds with the nephews, of all of - whom more hereafter. Since I came here I have been attending - Hop., but, with his approval, did not begin full swing. I - am getting on, though, and the work is not grinding on the - prepared brain.” - -During this period he wrote some papers for the _Cambridge and Dublin -Mathematical Journal_ which will be referred to again later. He was -also a member of a discussion society known as the “Apostles,” and some -of the essays contributed by him are preserved by Professor Campbell. -Mr. Niven, in his preface to the collected edition of Maxwell’s works, -suggests that the composition of these essays laid the foundation of -that literary finish which is one of the characteristics of Maxwell’s -scientific writings. - -Among his friends at the time were Tait, Charles Mackenzie of Caius, -the missionary bishop of Central Africa, Henry and Frank Mackenzie of -Trinity, Droop, third Wrangler in 1854; Gedge, Isaac Taylor, Blakiston, -F. W. Farrar,[14] H. M. Butler,[15] Hort, V. Lushington, Cecil Munro, -G. W. H. Tayler, and W. N. Lawson. Some of these who survived him have -given to Professor Campbell their recollections of these undergraduate -days, which are full of interest. - -Thus Mr. Lawson writes[16]:-- - - “There must be many of his quaint verses about, if one could - lay hands on them, for Maxwell was constantly producing - something of the sort and bringing it round to his friends, - with a sly chuckle at the humour, which, though his own, no one - enjoyed more than himself. - - “I remember Maxwell coming to me one morning with a copy of - verses beginning, ‘Gin a body meet a body going through the - air,’ in which he had twisted the well-known song into a - description of the laws of impact of solid bodies. - - “There was also a description which Maxwell wrote of some - University ceremony--I forget what--in which somebody ‘went - before’ and somebody ‘followed after,’ and ‘in the midst were - the wranglers, playing with the symbols.’ - - “These last words, however meant, were, in fact, a description - of his own wonderful power. I remember, one day in lecture, - our lecturer had filled the black-board three times with - the investigation of some hard problem in Geometry of Three - Dimensions, and was not at the end of it, when Maxwell came up - with a question whether it would not come out geometrically, - and showed how, with a figure, and in a few lines, there was - the solution at once. - - “Maxwell was, I daresay you remember, very fond of a talk upon - almost anything. He and I were pupils (at an enormous distance - apart) of Hopkins, and I well recollect how, when I had been - working the night before and all the morning at Hopkins’s - problems, with little or no result, Maxwell would come in for a - gossip, and talk on while I was wishing him far away, till at - last, about half an hour or so before our meeting at Hopkins’s, - he would say, ‘Well, I must go to old Hop.’s problems’; and, by - the time we met there, they were all done. - - “I remember Hopkins telling me, when speaking of Maxwell, - either just before or just after his degree, ‘It is not - possible for that man to think incorrectly on physical - subjects’; and Hopkins, as you know, had had, perhaps, more - experience of mathematical minds than any man of his time.” - -The last clause is part of a quotation from a diary kept by Mr. Lawson -at Cambridge, in which, under the date July 15th, 1853, he writes:-- - - “He (Hopkins) was talking to me this evening about Maxwell. - He says he is unquestionably the most extraordinary man he - has met with in the whole range of his experience; he says - it appears impossible for Maxwell to think incorrectly on - physical subjects; that in his analysis, however, he is far - more deficient. He looks upon him as a great genius with all - its eccentricities, and prophesies that one day he will shine - as a light in physical science--a prophecy in which all his - fellow-students strenuously unite.” - -How many who have struggled through the “Electricity and Magnetism” -have realised the truth of the remark about the correctness of his -physical intuitions and the deficiency at times of his analysis! - -Dr. Butler, a friend of these early days, preached the University -sermon on November 16th, 1879, ten days after Maxwell’s death, and -spoke thus:-- - - “It is a solemn thing--even the least thoughtful is touched - by it--when a great intellect passes away into the silence - and we see it no more. Such a loss, such a void, is present, - I feel certain, to many here to-day. It is not often, even - in this great home of thought and knowledge, that so bright - a light is extinguished as that which is now mourned by many - illustrious mourners, here chiefly, but also far beyond this - place. I shall be believed when I say in all simplicity that I - wish it had fallen to some more competent tongue to put into - words those feelings of reverent affection which are, I am - persuaded, uppermost in many hearts on this Sunday. My poor - words shall be few, but believe me they come from the heart. - You know, brethren, with what an eager pride we follow the - fortunes of those whom we have loved and reverenced in our - undergraduate days. We may see them but seldom, few letters may - pass between us, but their names are never common names. They - never become to us only what other men are. When I came up to - Trinity twenty-eight years ago, James Clerk Maxwell was just - beginning his second year. His position among us--I speak in - the presence of many who remember that time--was unique. He was - the one acknowledged man of genius among the undergraduates. We - understood even then that, though barely of age, he was in his - own line of inquiry not a beginner but a master. His name was - already a familiar name to men of science. If he lived, it was - certain that he was one of that small but sacred band to whom - it would be given to enlarge the bounds of human knowledge. - It was a position which might have turned the head of a - smaller man; but the friend of whom we were all so proud, and - who seemed, as it were, to link us thus early with the great - outside world of the pioneers of knowledge, had one of those - rich and lavish natures which no prosperity can impoverish, - and which make faith in goodness easy for others. I have often - thought that those who never knew the grand old Adam Sedgwick - and the then young and ever-youthful Clerk Maxwell had yet to - learn the largeness and fulness of the moulds in which some - choice natures are framed. Of the scientific greatness of our - friend we were most of us unable to judge; but anyone could - see and admire the boy-like glee, the joyous invention, the - wide reading, the eager thirst for truth, the subtle thought, - the perfect temper, the unfailing reverence, the singular - absence of any taint of the breath of worldliness in any of its - thousand forms. - - “Brethren, you may know such men now among your college - friends, though there can be but few in any year, or indeed in - any century, that possess the rare genius of the man whom we - deplore. If it be so, then, if you will accept the counsel of - a stranger, thank God for His gift. Believe me when I tell you - that few such blessings will come to you in later life. There - are blessings that come once in a lifetime. One of these is the - reverence with which we look up to greatness and goodness in - a college friend--above us, beyond us, far out of our mental - or moral grasp, but still one of us, near to us, our own. You - know, in part at least, how in this case the promise of youth - was more than fulfilled, and how the man who, but a fortnight - ago, was the ornament of the University, and--shall I be - wrong in saying it?--almost the discoverer of a new world of - knowledge, was even more loved than he was admired, retaining - after twenty years of fame that mirth, that simplicity, that - child-like delight in all that is fresh and wonderful which we - rejoice to think of as some of the surest accompaniment of true - scientific genius. - - “You know, also, that he was a devout as well as thoughtful - Christian. I do not note this in the triumphant spirit of a - controversialist. I will not for a moment assume that there is - any natural opposition between scientific genius and simple - Christian faith. I will not compare him with others who have - had the genius without the faith. Christianity, though she - thankfully welcomes and deeply prizes them, does not need - now, any more than when St. Paul first preached the Cross at - Corinth, the speculations of the subtle or the wisdom of the - wise. If I wished to show men, especially young men, the living - force of the Gospel, I would take them not so much to a learned - and devout Christian man to whom all stores of knowledge were - familiar, but to some country village where for fifty years - there had been devout traditions and devout practice. There - they would see the Gospel lived out; truths, which other men - spoke of, seen and known; a spirit not of this world, visibly, - hourly present; citizenship in heaven daily assumed and daily - realised. Such characters I believe to be the most convincing - preachers to those who ask whether Revelation is a fable - and God an unknowable. Yes, in most cases--not, I admit, in - all--simple faith, even peradventure more than devout genius, - is mighty for removing doubts and implanting fresh conviction. - But having said this, we may well give thanks to God that our - friend was what he was, a firm Christian believer, and that his - powerful mind, after ranging at will through the illimitable - spaces of Creation and almost handling what he called ‘the - foundation-stones of the material universe,’ found its true - rest and happiness in the love and the mercy of Him whom the - humblest Christian calls his Father. Of such a man it may be - truly said that he had his citizenship in heaven, and that he - looked for, as a Saviour, the Lord Jesus Christ, through whom - the unnumbered worlds were made, and in the likeness of whose - image our new and spiritual body will be fashioned.” - -The Tripos came in January, 1854. “You will need to get muffetees for -the Senate Room. Take your plaid or rug to wrap round your feet and -legs,” was his father’s advice--advice which will appeal to many who -can remember the Senate House as it felt on a cold January morning. - -Maxwell had been preparing carefully for this examination. Thus to -his aunt, Miss Cay, in June, 1853, he writes:--“If anyone asks how I -am getting on in mathematics, say that I am busy arranging everything -so as to be able to express all distinctly, so that examiner may be -satisfied now and pupils edified hereafter. It is pleasant work and -very strengthening, but not nearly finished.” - -Still, the illness of July, 1853, had left some effect. Professor -Baynes states that he said that on entering the Senate House for the -first paper he felt his mind almost a blank, but by-and-by his mental -vision became preternaturally clear. - -The moderators were Mackenzie of Caius, whose advice had been mainly -instrumental in leading him to migrate to Trinity, Wm. Walton of -Trinity, Wolstenholme of Christ’s, and Percival Frost of St. John’s. - -When the lists were published, Routh of Peterhouse was senior, Maxwell -second. The examination for the Smith’s Prizes followed in a few days, -and then Routh and Maxwell were declared equal. - -In a letter to Miss Cay[17] of January 13th, while waiting for the -three days’ list, he writes:-- - - “All my correspondents have been writing to me, which is kind, - and have not been writing questions, which is kinder. So I - answer you now, while I am slacking speed to get up steam, - leaving Lewis and Stewart, etc., till next week, when I will - give an account of the _five days_. There are a good many up - here at present, and we get on very jolly on the whole; but - some are not well, and some are going to be plucked or gulphed, - as the case may be, and others are reading so hard that they - are invisible. I go to-morrow to breakfast with shaky men, and - after food I am to go and hear the list read out, and whether - they are through, and bring them word. When the honour list - comes out the poll men act as messengers. Bob Campbell comes - in occasionally of an evening now, to discuss matters and vary - sports. During examination I have had men at night working with - gutta-percha, magnets, etc. It is much better than reading - novels or talking after 5½ hours’ hard writing.” - -His father, on hearing the news, wrote from Edinburgh:-- - - “I heartily congratulate you on your place in the list. I - suppose it is higher than the speculators would have guessed, - and quite as high as Hopkins reckoned on. I wish you success - in the Smith’s Prizes; be sure to write me the result. I will - see Mrs. Morrieson, and I think I will call on Dr. Gloag to - congratulate him. He has at least three pupils gaining honours.” - -His friends in Edinburgh were greatly pleased. “I get congratulations -on all hands,” his father writes,[18] “including Professor Kelland -and Sandy Fraser and all others competent.... To-night or on Monday -I shall expect to hear of the Smith’s Prizes.” And again, February -6th, 1854:--“George Wedderburn came into my room at 2 a.m. yesterday -morning, having seen the Saturday _Times_, received by the express -train.... As you are equal to the Senior in the champion trial, you are -very little behind him.” - -Or again, March 5th, 1854:-- - - “Aunt Jane stirred me up to sit for my picture, as she said you - wished for it and were entitled to ask for it _qua_ Wrangler. I - have had four sittings to Sir John Watson Gordon, and it is now - far advanced; I think it is very like. It is kitcat size, to be - a companion to Dyce’s picture of your mother and self, which - Aunt Jane says she is to leave to you.” - -And now the long years of preparation were nearly over. The cunning -craftsman was fitted with his tools; he could set to work to unlock the -secrets of Nature; he was free to employ his genius and his knowledge -on those tasks for which he felt most fitted. - - - - -CHAPTER III. - -EARLY RESEARCHES.--PROFESSOR AT ABERDEEN. - - -From this time on Maxwell’s life becomes a record of his writings -and discoveries. It will, however, probably be clearest to separate -as far as possible biographical details from a detailed account of -his scientific work, leaving this for consecutive treatment in later -chapters, and only alluding to it so far as may prove necessary to -explain references in his letters. - -He continued in Cambridge till the Long Vacation of 1854, reading -Mill’s “Logic.” “I am experiencing the effects of Mill,” he writes, -March 25th, 1854, “but I take him slowly. I do not think him the last -of his kind. I think more is wanted to bring the connexion of sensation -with science to light, and to show what it is not.” He also read -Berkeley on “The Theory of Vision” and “greatly admired it.” - -About the same time he devised an ophthalmoscope.[19] - - “I have made an instrument for seeing into the eye through - the pupil. The difficulty is to throw the light in at that - small hole and look in at the same time; but that difficulty - is overcome, and I can see a large part of the back of the eye - quite distinctly with the image of the candle on it. People - find no inconvenience in being examined, and I have got dogs - to sit quite still and keep their eyes steady. Dogs’ eyes are - very beautiful behind--a copper-coloured ground, with glorious - bright patches and networks of blue, yellow, and green, with - blood-vessels great and small.” - -After the vacation he returned to Cambridge, and the letters refer to -the colour-top. Thus to Miss Cay, November 24th, 1854, p. 208:-- - - “I have been very busy of late with various things, and am just - beginning to make papers for the examination at Cheltenham, - which I have to conduct about the 11th of December. I have - also to make papers to polish off my pups. with. I have been - spinning colours a great deal, and have got most accurate - results, proving that ordinary people’s eyes are all made - alike, though some are better than others, and that other - people see two colours instead of three; but all those who do - so agree amongst themselves. I have made a triangle of colours - by which you may make out everything. - - “If you can find out any people in Edinburgh who do not see - colours (I know the Dicksons don’t), pray drop a hint that - I would like to see them. I have put one here up to a dodge - by which he distinguishes colours without fail. I have also - constructed a pair of squinting spectacles, and am beginning - operations on a squinting man.” - -A paper written for his own use originally some time in 1854, but -communicated as a parting gift to his friend Farrar, who was about to -become a master at Marlborough, gives us some insight into his view of -life at the age of twenty-three. - - “He that would enjoy life and act with freedom must have the - work of the day continually before his eyes. Not yesterday’s - work, lest he fall into despair; nor to-morrow’s, lest he - become a visionary--not that which ends with the day, which is - a worldly work; nor yet that only which remains to eternity, - for by it he cannot shape his actions. - - “Happy is the man who can recognise in the work of to-day a - connected portion of the work of life and an embodiment of - the work of Eternity. The foundations of his confidence are - unchangeable, for he has been made a partaker of Infinity. He - strenuously works out his daily enterprises because the present - is given him for a possession. - - “Thus ought Man to be an impersonation of the divine process - of nature, and to show forth the union of the infinite with - the finite, not slighting his temporal existence, remembering - that in it only is individual action possible; nor yet shutting - out from his view that which is eternal, knowing that Time is - a mystery which man cannot endure to contemplate until eternal - Truth enlighten it.” - -His father was unwell in the Christmas vacation of that year, and he -could not return to Cambridge at the beginning of the Lent term. “My -steps,” he writes[20] to C. J. Munro from Edinburgh, February 19th, -1855, “will be no more by the reedy and crooked till Easter term.... I -should like to know how many kept bacalaurean weeks go to each of these -terms, and when they begin and end. Overhaul the Calendar, and when -found make note of.” - -He was back in Cambridge for the May term, working at the motion -of fluids and at his colour-top. A paper on “Experiments on Colour -as Perceived by the Eye” was communicated to the Royal Society of -Edinburgh on March 19th, 1855. The experiments were shown to the -Cambridge Philosophical Society in May following, and the results are -thus described in two letters[21] to his father, Saturday, May 5th, -1855: - - “The Royal Society have been very considerate in sending me my - paper on ‘Colours’ just when I wanted it for the Philosophical - here. I am to let them see the tricks on Monday evening, - and I have been there preparing their experiments in the - gaslight. There is to be a meeting in my rooms to-night to - discuss Adam Smith’s ‘Theory of Moral Sentiments,’ so I must - clear up my litter presently. I am working away at electricity - again, and have been working my way into the views of heavy - German writers. It takes a long time to reduce to order all - the notions one gets from these men, but I hope to see my way - through the subject and arrive at something intelligible in the - way of a theory.... - - “The colour trick came off on Monday, 7th. I had the - proof-sheets of my paper, and was going to read; but I changed - my mind and talked instead, which was more to the purpose. - There were sundry men who thought that blue and yellow make - green, so I had to undeceive them. I have got Hay’s book of - colours out of the Univ. Library, and am working through the - specimens, matching them with the top. I have a new trick of - stretching the string horizontally above the top, so as to - touch the upper part of the axis. The motion of the axis sets - the string a-vibrating in the same time with the revolutions of - the top, and the colours are seen in the haze produced by the - vibration. Thomson has been spinning the top, and he finds my - diagram of colours agrees with his experiments, but he doubts - about browns, what is their composition. I have got colcothar - brown, and can make white with it, and blue and green; also, - by mixing red with a little blue and green and a great deal of - black, I can match colcothar exactly. - - “I have been perfecting my instrument for looking into the eye. - Ware has a little beast like old Ask, which sits quite steady - and seems to like being looked at, and I have got several men - who have large pupils and do not wish to let me look in. I - have seen the image of the candle distinctly in all the eyes I - have tried, and the veins of the retina were visible in some; - but the dogs’ eyes showed all the ramifications of veins, with - glorious blue and green network, so that you might copy down - everything. I have shown lots of men the image in my own eye by - shutting off the light till the pupil dilated and then letting - it on. - - “I am reading Electricity and working at Fluid Motion, and have - got out the condition of a fluid being able to flow the same - way for a length of time and not wriggle about.” - -The British Association met at Glasgow in September, 1855, and Maxwell -was present, and showed his colour-top at Professor Ramsay’s house to -some of those interested. Letters[22] to his father about this time -describe some of the events of the meeting and his own plans for the -term. - - “We had a paper from Brewster on ‘The theory of three colours - in the spectrum,’ in which he treated Whewell with philosophic - pity, commending him to the care of Prof. Wartman of Geneva, - who was considered the greatest authority in cases of his - kind--cases, in fact, of colour-blindness. Whewell was in the - room, but went out and avoided the quarrel; and Stokes made a - few remarks, stating the case not only clearly but courteously. - However, Brewster did not seem to see that Stokes admitted - his experiments to be correct, and the newspapers represented - Stokes as calling in question the accuracy of the experiments. - - “I am getting my electrical mathematics into shape, and I see - through some parts which were rather hazy before; but I do not - find very much time for it at present, because I am reading - about heat and fluids, so as not to tell lies in my lectures. - I got a note from the Society of Arts about the platometer, - awarding thanks and offering to defray the expenses to the - extent of £10, on the machine being produced in working order. - When I have arranged it in my head, I intend to write to James - Bryson about it. - - “I got a long letter from Thomson about colours and - electricity. He is beginning to believe in my theory about all - colours being capable of reference to three standard ones, and - he is very glad that I should poach on his electrical preserves. - - “... It is difficult to keep up one’s interest in intellectual - matters when friends of the intellectual kind are scarce. - However, there are plenty friends not intellectual who serve - to bring out the active and practical habits of mind, which - overly-intellectual people seldom do. Wherefore, if I am to be - up this term, I intend to addict myself rather to the working - men who are getting up classes than to pups., who are in - the main a vexation. Meanwhile, there is the examination to - consider. - - “You say Dr. Wilson has sent his book. I will write and thank - him. I suppose it is about colour-blindness. I intend to begin - Poisson’s papers on electricity and magnetism to-morrow. I have - got them out of the library. My reading hitherto has been of - novels--‘Shirley’ and ‘The Newcomes,’ and now ‘Westward Ho.’ - - “Macmillan proposes to get up a book of optics with my - assistance, and I feel inclined for the job. There is great - bother in making a mathematical book, especially on a subject - with which you are familiar, for in correcting it you do as - you would to pups.--look if the principle and result is right, - and forget to look out for small errors in the course of the - work. However, I expect the work will be salutary, as involving - hard work, and in the end much abuse from coaches and students, - and certainly no vain fame, except in Macmillan’s puffs. But, - if I have rightly conceived the plan of an educational book - on optics, it will be very different in manner, though not in - matter, from those now used.” - -The examination referred to was that for a Fellowship at Trinity, and -Maxwell was elected on October 10th, 1855. - -He was immediately asked to lecture for the College, on hydrostatics -and optics, to the upper division of the third year, and to set papers -for the questionists. In consequence, he declined to take pupils, in -order to have time for reading and doing private mathematics, and for -seeing the men who attended his lectures. - -In November he writes: “I have been lecturing two weeks now, and the -class seems improving; and they come and ask questions, which is a good -sign. I have been making curves to show the relations of pressure and -volume in gases, and they make the subject easier.” - -Still, he found time to attend Professor Willis’s lectures on mechanism -and to continue his reading. “I have been reading,” he writes, “old -books on optics, and find many things in them far better than what is -new. The foreign mathematicians are discovering for themselves methods -which were well known at Cambridge in 1720, but are now forgotten.” - -The “Poisson” was read to help him with his own views on electricity, -which were rapidly maturing, and the first of that great series of -works which has revolutionised the science was published on December -10th, 1855, when his paper on “Faraday’s Lines of Force” was read to -the Cambridge Philosophical Society. - -The next term found him back in Cambridge at work on his lectures, full -of plans for a new colour top and other matters. Early in February -he received a letter from Professor Forbes, telling him that the -Professorship of Natural Philosophy in Marischal College, Aberdeen, was -vacant, and suggesting that he should apply. - -He decided to be a candidate if his father approved. “For my own part,” -he writes, “I think the sooner I get into regular work the better, -and that the best way of getting into such work is to profess one’s -readiness by applying for it.” On the 20th of February he writes: -“However, wisdom is of many kinds, and I do not know which dwells -with wise counsellors most, whether scientific, practical, political, -or ecclesiastical. I hear there are candidates of all kinds relying -on the predominance of one or other of these kinds of wisdom in the -constitution of the Government.” - -The second part of the paper on “Faraday’s Lines of Force” was read -during the term. Writing on the 4th of March, he expresses the hope -soon to be able to write out fully the paper. “I have done nothing -in that way this term,” he says, “but am just beginning to feel the -electrical state come on again.” - -His father was working at Edinburgh in support of his candidature for -Aberdeen, and when, in the middle of March, he returned North, he -found everything well prepared. The two returned to Glenlair together -after a few days in Edinburgh, and Maxwell was preparing to go back to -Cambridge, when, on the 2nd of April, his father died suddenly. - -Writing to Mrs. Blackburn, he says: “My father died suddenly to-day at -twelve o’clock. He had been giving directions about the garden, and he -said he would sit down and rest a little, as usual. After a few minutes -I asked him to lie down on the sofa, and he did not seem inclined to do -so; and then I got him some ether, which had helped him before. Before -he could take any he had a slight struggle, and all was over. He hardly -breathed afterwards.” - -Almost immediately after this, Maxwell was appointed to Aberdeen. His -father’s death had frustrated some at least of the intentions with -which he had applied for the post. He knew the old man would be glad -to see him the occupant of a Scotch chair. He hoped, too, to be able to -live with his father at Glenlair for one half the year; but this was -not to be. No doubt the laboratory and the freedom of the post, when -compared with the routine work of preparing men for the Tripos, had -their inducements; still, it may be doubted if the choice was a wise -one for him. The work of drilling classes, composed, for the most part, -of raw untrained lads, in the elements of physics and mechanics was, as -Niven says in his preface to the collected works, not that for which -he was best fitted; while at Cambridge, had he stayed, he must always -have had among his pupils some of the best mathematicians of the time; -and he might have founded some ten or fifteen years before he did that -Cambridge School of Physicists which looks back with so much pride to -him as their master. - -Leave-taking at Trinity was a sad task. He writes[23] thus, June 4th, -to Mr. R. B. Litchfield:-- - - “On Thursday evening I take the North-Western route to the - North. I am busy looking over immense rubbish of papers, etc., - for some things not to be burnt lie among much combustible - matter, and some is soft and good for packing. - - “It is not pleasant to go down to live solitary, but it would - not be pleasant to stay up either, when all one had to do lay - elsewhere. The transition state from a man into a Don must come - at last, and it must be painful, like gradual outrooting of - nerves. When it is done there is no more pain, but occasional - reminders from some suckers, tap-roots, or other remnants of - the old nerves, just to show what was there and what might have - been.” - -The summer of 1856 was spent at Glenlair, where various friends were -his guests--Lushington, MacLennan, the two cousins Cay, and others. -He continued to work at optics, electricity, and magnetism, and in -October was busy with “a solemn address or manifesto to the Natural -Philosophers of the North, which needed coffee and anchovies and a -roaring hot fire and spread coat-tails to make it natural.” This was -his inaugural lecture. - -In November he was at Aberdeen. Letters[24] to Miss Cay, Professor -Campbell, and C. J. Munro tell of the work of the session. The last is -from Glenlair, dated May 20th, 1857, after work was over. - - “The session went off smoothly enough. I had Sun, all the - beginning of optics, and worked off all the experimental part - up to Fraunhofer’s lines, which were glorious to see with a - water-prism I have set up in the form of a cubical box, five - inch side.... - - “I succeeded very well with heat. The experiments on latent - heat came out very accurate. That was my part, and the class - could explain and work out the results better than I expected. - Next year I intend to mix experimental physics with mechanics, - devoting Tuesday and THURSDAY (what would Stokes say?) to the - science of experimenting accurately.... - - “Last week I brewed chlorophyll (as the chemists word it), a - green liquor, which turns the invisible light red.... - - “My last grind was the reduction of equations of colour which I - made last year. The result was eminently satisfactory.” - -Another letter,[25] June 5th, 1857, also to Munro, refers to the work -of the University Commission and the new statutes. - - “I have not seen Article 7, but I agree with your dissent from - it entirely. On the vested interest principle, I think the - men who intended to keep their fellowships by celibacy and - ordination, and got them on that footing, should not be allowed - to desert the virgin choir or neglect the priestly office, - but on those principles should be allowed to live out their - days, provided the whole amount of souls cured annually does - not amount to £20 in the King’s Book. But my doctrine is that - the various grades of College officers should be set on such a - basis that, although chance lecturers might be sometimes chosen - from among fresh fellows who are going away soon, the reliable - assistant tutors, and those that have a plain calling that - way, should, after a few years, be elected permanent officers - of the College, and be tutors and deans in their time, and - seniors also, with leave to marry, or, rather, never prohibited - or asked any questions on that head, and with leave to retire - after so many years’ service as seniors. As for the men of the - world, we should have a limited term of existence, and that - independent of marriage or ‘parsonage.’” - -It was more than twenty years before the scheme outlined in the above -letter came to anything; but, at the time of Maxwell’s death in 1879, -another Commission was sitting, and the plan suggested by Maxwell -became the basis of the statutes of nearly all the colleges. - -For the winter session of 1857–58 he was again at Aberdeen. - -The Adams Prize had been established in 1848 by some members of -St. John’s College, and connected by them with the name of Adams -“in testimony of their sense of the honour he had conferred upon -his College and the University by having been the first among the -mathematicians of Europe to determine from perturbations the unknown -place of a disturbing planet exterior to Uranus.” Professor Challis, -Dr. Parkinson, and Sir William Thomson, the examiners, had selected -as the subject for the prize to be awarded in 1857 the “Motions of -Saturn’s Rings.” For this Maxwell had decided to compete, and his -letters at the end of 1857 tell of the progress of the task. Thus, -writing[26] to Lewis Campbell from Glenlair on August 28th, he says:-- - - “I have been battering away at Saturn, returning to the charge - every now and then. I have effected several breaches in the - solid ring, and now I am splash into the fluid one, amid a - clash of symbols truly astounding. When I reappear it will be - in the dusky ring, which is something like the state of the - air supposing the siege of Sebastopol conducted from a forest - of guns 100 miles one way, and 30,000 miles the other, and the - shot never to stop, but go spinning away round a circle, radius - 170,000 miles.” - -And again[27] to Miss Cay on the 28th of November:-- - - “I have been pretty steady at work since I came. The class - is small and not bright, but I am going to give them plenty - to do from the first, and I find it a good plan. I have a - large attendance of my old pupils, who go on with the higher - subjects. This is not part of the College course, so they - come merely from choice, and I have begun with the least - amusing part of what I intend to give them. Many had been - reading in summer, for they did very good papers for me on - the old subjects at the beginning of the month. Most of my - spare time I have been doing Saturn’s rings, which is getting - on now, but lately I have had a great many long letters to - write--some to Glenlair, some to private friends, and some all - about science.... I have had letters from Thomson and Challis - about Saturn--from Hayward, of Durham University, about the - brass top, of which he wants one. He says that the earth has - been really found to change its axis regularly in the way I - supposed. Faraday has also been writing about his own subjects. - I have had also to write Forbes a long report on colours; so - that for every note I have got I have had to write a couple of - sheets in reply, and reporting progress takes a deal of writing - and spelling.” - -He devised a model (now at the Cavendish Laboratory) to exhibit the -motions of the satellites in a disturbed ring, “for the edification of -sensible image-worshippers.” - -The essay was awarded the prize, and secured for its author great -credit among scientific men. - -In another letter, written during the same session, he says: “I find my -principal work here is teaching my men to avoid vague expressions, as -‘a certain force,’ meaning uncertain; _may_ instead of _must_; _will -be_ instead of _is_; _proportional_ instead of _equal_.” - -The death, during the autumn, of his College friend Pomeroy, from fever -in India, was a great blow to him; his letters at the time show the -depth of his feelings and his beliefs. - -The question of the fusion of the two Colleges at Aberdeen, King’s -College and the Marischal College, was coming to the fore. “Know -all men,” he says, in a letter to Professor Campbell, “that I am a -Fusionist.” - -In February, 1858, he was still engaged on Saturn’s rings, while hard -at work during the same time with his classes. He had established a -voluntary class for his students of the previous year, and was reading -with them Newton’s “Lunar Theory and Astronomy.” This was followed by -“Electricity and Magnetism,” Faraday’s book being the backbone of -everything, “as he himself is the nucleus of everything electric since -1830.” - -In February, 1858, he announced his engagement to Katherine Mary Dewar, -the daughter of the Principal of Marischal College. - - “Dear Aunt” (he says,[28] February 18th, 1858), “this comes to - tell you that I am going to have a wife.... - - “Don’t be afraid; she is not mathematical, but there are other - things besides that, and she certainly won’t stop mathematics. - The only one that can speak as an eye-witness is Johnnie, - and he only saw her when we were both trying to act the - indifferent. We have been trying it since, but it would not do, - and it was not good for either.” - -The wedding took place early in June. Professor Campbell has preserved -some of the letters written by Maxwell to Miss Dewar, and these -contain “the record of feelings which in the years that followed were -transfused in action and embodied in a married life which can only be -spoken of as one of unexampled devotion.” - -The project for the fusion of the two Colleges, to which reference has -been made, went on, and the scheme was completed in 1860. - -The two Colleges were united to form the University of Aberdeen, and -the new chair of Natural Philosophy thus created was filled by the -appointment of David Thomson, Professor of Natural Philosophy in King’s -College, and Maxwell’s senior. Mr. W. D. Niven, in his preface to -Maxwell’s works, when dealing with this appointment, writes:-- - - “Professor Thomson, though not comparable to Maxwell as - a physicist, was nevertheless a remarkable man. He was - distinguished by singular force of character and great - administrative faculty, and he had been prominent in bringing - about the fusion of the Colleges. He was also an admirable - lecturer and teacher, and had done much to raise the standard - of scientific education in the north of Scotland. Thus the - choice made by the Commissioners, though almost inevitable, - had the effect of making it appear that Maxwell failed as a - teacher. There seems, however, to be no evidence to support - such an inference. On the contrary, if we may judge from the - number of voluntary students attending his classes in his last - College session, he would seem to have been as popular as a - professor as he was personally estimable.” - -The question whether Maxwell was a great teacher has sometimes been -discussed. I trust that the following pages will give an answer to -it. He was not a prominent lecturer. As Professor Campbell says,[29] -“Between his students’ ignorance and his vast knowledge it was -difficult to find a common measure. The advice which he once gave -to a friend whose duty it was to preach to a country congregation, -‘Why don’t you give it them thinner?’ must often have been applicable -to himself.... Illustrations of _ignotum per ignotius_, or of the -abstruse by some unobserved property of the familiar, were multiplied -with dazzling rapidity. Then the spirit of indirectness and paradox, -though he was aware of its dangers, would often take possession of him -against his will, and, either from shyness or momentary excitement, or -the despair of making himself understood, would land him in ‘chaotic -statements,’ breaking off with some quirk of ironical humour.” - -But teaching is not all done by lecturing. His books and papers are -vast storehouses of suggestions and ideas which the ablest minds of the -past twenty years have been since developing. To talk with him for an -hour was to gain inspiration for a year’s work; to see his enthusiasm -and to win his praise or commendation were enough to compensate for -many weary struggles over some stubborn piece of apparatus which would -not go right, or some small source of error which threatened to prove -intractable and declined to submit itself to calculation. The sure -judgment of posterity will confirm the verdict that Clerk Maxwell was a -great teacher, though lecturing to a crowd of untrained undergraduates -was a task for which others were better fitted than he. - - - - -CHAPTER IV. - -PROFESSOR AT KING’S COLLEGE, LONDON.--LIFE AT GLENLAIR. - - -In 1860 Forbes resigned the chair of Natural Philosophy at Edinburgh. -Maxwell and Tait were candidates, and Tait was appointed. In the -summer of the same year Maxwell obtained the vacant Professorship of -Natural Philosophy at King’s College, London. This he held to 1865, -and this period of his life is distinguished by the appearance of -some of his most important papers. The work was arduous; the College -course extended over nine months of the year; there were as well -evening lectures to artisans as part of his regular duties. His life in -London was useful to him in the opportunities it gave him for becoming -personally acquainted with Faraday and others. He also renewed his -intimacy with various Cambridge friends. - -He was at the celebrated Oxford meeting of the British Association in -1860, where he exhibited his colour-box for mixing the colours of the -spectrum. In 1859, at the meeting at Aberdeen, he had read to Section -A his first paper on the “Dynamical Theory of Gases,” published in the -_Philosophical Magazine_ for January, 1860. The second part of the -paper, dealing with the conduction of heat and other phenomena in a -gas, was published in July, 1860, after the Oxford meeting. - -A paper on the “Theory of Compound Colours” was communicated to -the Royal Society by Professor Stokes in January, 1860. It contains -the account of his colour-box in the form finally adopted (most of -the important parts of the apparatus are still at the Cavendish -Laboratory), and a number of observations by Mrs. Maxwell and himself, -which will be more fully described later. - -In November, 1860, he received for this work the Rumford medal of the -Royal Society. - -The next year, 1861, is of great importance in the history of -electrical science. The British Association met at Manchester, and a -Committee was appointed on Standards of Electrical Resistance. Maxwell -was not a member. The committee reported at the Cambridge meeting in -1862, and were reappointed with extended duties. Maxwell’s name, among -others, was added, and he took a prominent part in the deliberations -of the committee, which, as their Report[30] presented in 1863 states, -came to the opinion, “after mature consideration, that the system -of so-called absolute electrical units, based on purely mechanical -measurements, is not only the best system yet proposed, but is the -only one consistent with our present knowledge both of the relations -existing between the various electrical phenomena and of the connection -between these and the fundamental measurements of time, space, and -mass.” - -Appendix C of this Report, “On the Elementary Relations between -Electrical Measurements,” bears the names of Clerk Maxwell and Fleeming -Jenkin, and is the foundation of everything that has been done in the -way of absolute electrical measurement since that date; while Appendix -D gives an account by the same two workers of the experiments on the -absolute unit of electrical resistance made in the laboratory of King’s -College by Maxwell, Fleeming Jenkin, and Balfour Stewart. Further -experiments are described in the report for 1864. The work thus begun -was consummated during the year 1894 by the legalisation throughout -the civilised world of a system of electrical units based on those -described in these reports. - -Meanwhile, Maxwell’s views on electro-magnetic theory were quietly -developing. Papers on “Physical Lines of Force,” which appeared in the -_Philosophical Magazine_ during 1861 and 1862, contain the germs of -his theory--expressed at that time, it is true, in a somewhat material -form. In the paper published January, 1862, the now well-known relation -between the ratio of the electric units and the velocity of light was -established, and his correspondence with Fleeming Jenkin and C. J. -Munro about this time relates in part to the experimental verification -of this relation. His experiments on this matter were published in the -“Philosophical Transactions” for 1868. - -This electrical theory occupied his mind mainly during 1863 and 1864. -In September of the latter year he writes[31] from Glenlair to C. -Hockin, who had taken Balfour Stewart’s place during the second series -of experiments on the measurement of resistance. - - “I have been doing several electrical problems. I have got a - theory of ‘electric absorption,’ _i.e._, residual charge, etc., - and I very much want determinations of the specific induction, - electric resistance, and absorption of good dielectrics, such - as glass, shell-lac, gutta-percha, ebonite, sulphur, etc. - - “I have also cleared the electromagnetic theory of light from - all unwarrantable assumption, so that we may safely determine - the velocity of light by measuring the attraction between - bodies kept at a given difference of potential, the value of - which is known in electromagnetic measure. - - “I hope there will be resistance coils at the British - Association.” - -This work resulted in his greatest electrical paper, “A Dynamical -Theory of the Electromagnetic Field,” read to the Royal Society -December 8th, 1864. - -But the molecular theory of gases was still prominently before his mind. - -In 1862, writing[32] to H. R. Droop, he says:-- - - “Some time ago, when investigating Bernoulli’s theory of gases, - I was surprised to find that the internal friction of a gas (if - it depends on the collision of particles) should be independent - of the density. - - “Stokes has been examining Graham’s experiments on the rate - of flow of gases through fine tubes, and he finds that the - friction, if independent of density, accounts for Graham’s - results; but, if taken proportional to density, differs from - those results very much. This seems rather a curious result, - and an additional phenomenon, explained by the ‘collision of - particles’ theory of gases. Still one phenomenon goes against - that theory--the relation between specific heat at constant - pressure and at constant volume, which is in air = 1·408, while - it ought to be 1·333.” - -And again[33] in the same year, 21st April, 1862, to Lewis Campbell:-- - - “Herr Clausius of Zürich, one of the heat philosophers, has - been working at the theory of gases being little bodies flying - about, and has found some cases in which he and I don’t tally. - So I am working it out again. Several experimental results have - turned up lately rather confirmatory than otherwise of that - theory. - - “I hope you enjoy the absence of pupils. I find the division of - them into smaller classes is a great help to me and to them; - but the total oblivion of them for definite intervals is a - necessary condition for doing them justice at the proper time.” - -The experiments on the viscosity of gases, which formed the Bakerian -Lecture to the Royal Society read on February 8th, 1866, were the -outcome of this work. His house in 8, Palace Gardens, Kensington, -contained a large garret running the complete length. - -“To maintain the proper temperature a large fire was for some days kept -up in the room in the midst of very hot weather. Kettles were kept on -the fire and large quantities of steam allowed to flow into the room. -Mrs. Maxwell acted as stoker, which was very exhausting work when -maintained for several consecutive hours. After this the room was kept -cool for subsequent experiments by the employment of a considerable -amount of ice.” - -Next year, May, 1866, was read his paper on the “Dynamical Theory of -Gases,” in which errors in his former papers, which had been pointed -out by Clausius, were corrected. - -Meanwhile he had resigned his London Professorship at the end of the -Session of 1865, and had been succeeded by Professor W. G. Adams. - -For the next four years he lived chiefly at Glenlair, working at his -theory of electricity, occasionally, as we shall see, visiting London -and Cambridge, and taking an active interest in the affairs of his -own neighbourhood. In 1865 he had a serious illness, through which he -was nursed with great care by Mrs. Maxwell. His correspondence was -considerable, and absorbed much of his time. Much also was given to the -study of English literature; he was fond of reading Chaucer, Milton, or -Shakespeare aloud to Mrs. Maxwell. - -He also read much theological and philosophical literature, and all he -read helped only to strengthen that firm faith in the fundamentals of -Christianity in which he lived and died. - -In 1867 he and Mrs. Maxwell paid a visit to Italy, which was a source -of great pleasure to both. - -His chief scientific work was the preparation of his “Electricity and -Magnetism,” which did not appear till 1873; the time was in the main -one of quiet thought and preparation for his next great task, the -foundation of the School of Physics in Cambridge. - -In 1868 the principalship of the United College in the University of -St. Andrews was vacant by the resignation of Forbes, and Maxwell was -invited by several of the professors to stand. He, however, declined to -submit his name to the Crown. - - - - -CHAPTER V. - -CAMBRIDGE.--PROFESSOR OF PHYSICS. - - -During his retirement at Glenlair from 1865 to 1870 Maxwell was -frequently at Cambridge. He examined in the Mathematical Tripos in 1866 -and 1867, and again in 1869 and 1870. - -The regulations for the Tripos had been in force practically unchanged -since 1848, and it was felt by many that the range of subjects included -was not sufficiently extensive, and that changes were urgently needed -if Cambridge were to retain its position as the centre of mathematical -teaching. Natural Philosophy was mentioned in the Schedule, but Natural -Philosophy included only Dynamics and Astronomy, Hydrostatics and -Physical Optics, with some simple Hydrodynamics and Sound. - -The subjects of Heat, Electricity and Magnetism, the Theory of Elastic -Solids and Vibrations, Vortex-Motion in Hydrodynamics, and much else, -were practically new since 1848. Stokes, Thomson, and Maxwell in -England, and Helmholtz in Germany, had created them. - -Accordingly in June, 1868, a new plan of examinations was sanctioned -by the Senate to come into force in January, 1873, and these various -subjects were explicitly included. - -Mr. Niven, who was one of those examined by Maxwell in 1866, writes in -the preface to the collected works:-- - - “For some years previous to 1866, when Maxwell returned to - Cambridge as Moderator in the Mathematical Tripos, the studies - in the University had lost touch with the great scientific - movements going on outside her walls. It was said that some - of the subjects most in vogue had but little interest for the - present generation, and loud complaints began to be heard - that while such branches of knowledge as Heat, Electricity, - and Magnetism were left out of the Tripos examination, the - candidates were wasting their time and energy upon mathematical - trifles barren of scientific interest and of practical results. - Into the movement for reform Maxwell entered warmly. By his - questions in 1866, and subsequent years, he infused new life - into the examination; he took an active part in drafting the - new scheme introduced in 1873; but most of all by his writings - he exerted a powerful influence on the younger members of the - University, and was largely instrumental in bringing about the - change which has been now effected.” - -But the University possessed no means of teaching these subjects, and a -Syndicate or Committee was appointed, November 25th, 1868, “to consider -the best means of giving instruction to students in Physics, especially -in Heat, Electricity and Magnetism, and the methods of providing -apparatus for this purpose.” - -Dr. Cookson, Master of St. Peter’s College, took an active part in the -work of the Syndicate. Professor Stokes, Professor Liveing, Professor -Humphry, Dr. Phear, and Dr. Routh were among the members. Maxwell -himself was in Cambridge that winter, as Examiner for the Tripos, and -his work as Moderator and Examiner in the two previous years had done -much to show the necessity of alterations and to indicate the direction -which changes should take. - -The Syndicate reported February 27th, 1869. They called attention to -the Report of the Royal Commission of 1850. The Commissioners had -“prominently urged the importance of cultivating a knowledge of the -great branches of Experimental Physics in the University”; and in -page 118 of their Report, after commending the manner in which the -subject of Physical Optics is studied in the University, and pointing -out that “there is, perhaps, no public institution where it is better -represented or prosecuted with more zeal and success in the way of -original research,” they had stated that “no reason can be assigned -why other great branches of Natural Science should not become equally -objects of attention, or why Cambridge should not become a great school -of physical and experimental, as it is already of mathematical and -classical, instruction.” - -And again the Commissioners remark: “In a University so thoroughly -imbued with the mathematical spirit, physical study might be expected -to assume within its precincts its highest and severest tone, be -studied under more abstract forms, with more continual reference to -mathematical laws, and therefore with better hope of bringing them one -by one under the domain of mathematical investigation than elsewhere.” - -After calling attention to these statements the Report of the Syndicate -then continues:-- - -“In the scheme of Examination for Honours in the Mathematical Tripos -approved by Grace of the Senate on the 2nd of June, 1868, Heat, -Electricity and Magnetism, if not introduced for the first time, had a -much greater degree of importance assigned to them than at any previous -period, and these subjects will henceforth demand a corresponding -amount of attention from the candidates for Mathematical Honours. The -Syndicate have limited their attention almost entirely to the question -of providing public instruction in Heat, Electricity and Magnetism. -They recognise the importance and advantage of tutorial instruction in -these subjects in the several colleges, but they are also alive to the -great impulse given to studies of this kind, and to the large amount of -additional training which students may receive through the instruction -of a public Professor, and by knowledge gained in a well-appointed -laboratory.” - -“In accordance with these views, and at an early period in their -deliberations, they requested the Professors[34] of the University, who -are engaged in teaching Mathematical and Physical Science, to confer -together upon the present means of teaching Experimental Physics, -especially Heat, Electricity and Magnetism, and to inform them how the -increased requirements of the University in this respect could be met -by them.” - -“The Professors, so consulted, favoured the Syndicate with a report -on the subject, which the Syndicate now beg leave to lay before the -Senate. It points out how the requirements of the University might -be “partially met,” but the Professors state distinctly that they -“do not think that they are able to meet the want of an extensive -course of lectures on Physics treated as such, and in great measure -experimentally. As Experimental Physics may fairly be considered -to come within the province of one or more of the above-mentioned -Professors, the Syndicate have considered whether now or at some -future time some arrangement might not be made to secure the effective -teaching of this branch of science, without having resort to the -services of an additional Professor. They are, however, of opinion that -such an arrangement cannot be made at the present time, and that the -exigencies of the case may be best met by founding a new professorship -which shall terminate with the tenure of office of the Professor first -elected. The services of a man of the highest attainments in science, -devoting his life to public teaching as such Professor, and engaged in -original research, would be of incalculable benefit to the University.” - -The Report goes on to point out that a laboratory would be necessary, -and also apparatus. It is estimated that £5,000 would cover the cost -of the laboratory, and £1,300 the necessary apparatus. Provision is -also made for a demonstrator and a laboratory assistant, and the Report -closes with a recommendation that a special Syndicate of Finance should -be appointed to consider the means of raising the funds. - -The Professors in their Report to the Syndicate point out that teaching -in Experimental Physics is needed for the Mathematical Tripos, the -Natural Sciences Tripos, certain Special examinations, and the first -examination for the degree of M.B. It appeared to them clear that there -was work for a new Professor. - -In May, 1869, the Financial Syndicate recommended by the above Report -was appointed “to consider the means of raising the necessary funds for -establishing a professor and demonstrator of Experimental Physics, and -for providing buildings and apparatus required for that department of -science, and further to consider other wants of the University, and the -sources from which those wants may be supplied.” - -The Syndicate endeavoured to meet the expenditure by inquiry from the -several Colleges whether they would be willing to make contributions -from their corporate funds, but without success. - -“The answers of the Colleges indicated such a want of concurrence -in any proposal to raise contributions from the corporate funds of -Colleges by any kind of direct taxation that the Syndicate felt -obliged to abandon the notion of obtaining the necessary funds from -this source, and accordingly to limit the number of objects which they -should recommend the Senate to accomplish.” - -External authority was necessary before the colleges would submit -to taxation for University purposes, and it was left to the Royal -Commission of 1877 to carry into effect many of the suggestions -made by the Syndicate. Meanwhile they contented themselves with -recommending means for raising an annual stipend of £660 for the -professor, demonstrator, and assistant, and a capital sum of £5,000, or -thereabouts, for the expenses of a building. - -The Syndicate’s Report was issued in an amended form in the May term of -1870, and before any decision was taken on it the Vice-Chancellor, Dr. -Atkinson, on October 13th, 1870, published “the following munificent -offer of his grace the Duke of Devonshire, the Chancellor of the -University,” who had been chairman of the Commission on Scientific -Education. - - “Holker Hall, Grange, Lancashire. - - “MY DEAR MR. VICE-CHANCELLOR,--I have the honour to address you - for the purpose of making an offer to the University, which, if - you see no objection, I shall be much obliged to you to submit - in such manner as you may think fit for the consideration of - the Council and the University. - - “I find in the report dated February 29th, 1869, of the - Physical Science Syndicate, recommending the establishment of - a Professor and Demonstrator of Experimental Physics, that the - buildings and apparatus required for this department of science - are estimated to cost £6,300. - - “I am desirous to assist the University in carrying this - recommendation into effect, and shall accordingly be prepared - to provide the funds required for the building and apparatus as - soon as the University shall have in other respects completed - its arrangements for teaching Experimental Physics, and shall - have approved the plan of the building. - - “I remain, my dear Mr. Vice-Chancellor, - “Yours very faithfully, - “DEVONSHIRE.” - -By his generous action the University was relieved from all expense -connected with the building. A Grace establishing a Professorship of -Experimental Physics was confirmed by the Senate February 9th, 1871, -and March 8th was fixed for the election. - -Meanwhile who was to be Professor? Sir W. Thomson’s name had been -mentioned, but he, it was known, would not accept the post. Maxwell -was then applied to, and at first he was unwilling to leave Glenlair. -Professor Stokes, the Hon. J. W. Strutt (Lord Rayleigh), Mr. Blore -of Trinity, and others wrote to him. Lord Rayleigh’s letter[35] is as -follows: - - “Cambridge, 14th February, 1871. - - “When I came here last Friday I found everyone talking about - the new professorship, and hoping that you would come. Thomson, - it seems, has definitely declined.... There is no one here in - the least fit for the post. What is wanted by most who know - anything about it is not so much a lecturer as a mathematician - who has actual experience in experimenting, and who might - direct the energies of the younger Fellows and bachelors into - a proper channel. There must be many who would be willing to - work under a competent man, and who, while learning themselves, - would materially assist him.... I hope you may be induced to - come; if not, I don’t know who it is to be. Do not trouble to - answer me about this, as I believe others have written to you - about it.” - -On the 15th of February, Maxwell wrote to Mr. Blore:-- - - “I had no intention of applying for the post when I got your - letter, and I have none now, unless I come to see that I can do - some good by it.” The letter continues:--“The class of Physical - Investigations, which might be undertaken with the help of men - of Cambridge education, and which would be creditable to the - University, demand in general a considerable amount of dull - labour, which may or may not be attractive to the pupils.” - -However, on the 24th of February, Mr. Blore wrote to the Electoral -Roll:-- - -“I am authorised to give notice that Mr. John (_sic_) Clerk Maxwell, -F.R.S., formerly Professor of Natural Philosophy at Aberdeen, and -at King’s College, London, is a candidate for the professorship of -Experimental Physics.” - -Maxwell was elected without opposition. Writing[36] to his wife from -Cambridge, 20th March, 1871, he says:-- - - “There are two parties about the professorship. One wants - popular lectures, and the other cares more for experimental - work. I think there should be a gradation--popular lectures and - rough experiments for the masses; real experiments for real - students; and laborious experiments for first-rate men like - Trotter and Stuart and Strutt.” - -While in a letter[37] from Glenlair to C. J. Munro, dated March 15th, -1871, he writes:--“The Experimental Physics at Cambridge is not built -yet, but we are going to try. The desideratum is to set a Don and a -Freshman to observe and register (say) the vibrations of a magnet -together, or the Don to turn a watch and the Freshman to observe and -govern him.” - -In October he delivered his Introductory Lecture. A few quotations will -show the spirit in which he approached his task. - - “In a course of Experimental Physics we may consider either - the Physics or the Experiments as the leading feature. We may - either employ the experiments to illustrate the phenomena of - a particular branch of Physics, or we may make some physical - research in order to exemplify a particular experimental - method. In the order of time, we should begin, in the Lecture - Room, with a course of lectures on some branch of Physics - aided by experiments of illustration, and conclude, in the - Laboratory, with a course of experiments of research. - - “Let me say a few words on these two classes of - experiments--Experiments of Illustration and Experiments of - Research. The aim of an experiment of illustration is to throw - light upon some scientific idea so that the student may be - enabled to grasp it. The circumstances of the experiment are - so arranged that the phenomenon which we wish to observe or to - exhibit is brought into prominence, instead of being obscured - and entangled among other phenomena, as it is when it occurs - in the ordinary course of nature. To exhibit illustrative - experiments, to encourage others to make them, and to cultivate - in every way the ideas on which they throw light, forms an - important part of our duty. The simpler the materials of an - illustrative experiment, and the more familiar they are to the - student, the more thoroughly is he likely to acquire the idea - which it is meant to illustrate. The educational value of such - experiments is often inversely proportional to the complexity - of the apparatus. The student who uses home-made apparatus, - which is always going wrong, often learns more than one who has - the use of carefully adjusted instruments, to which he is apt - to trust, and which he dares not take to pieces. - - “It is very necessary that those who are trying to learn from - books the facts of physical science should be enabled by the - help of a few illustrative experiments to recognise these facts - when they meet with them out of doors. Science appears to us - with a very different aspect after we have found out that it is - not in lecture-rooms only, and by means of the electric light - projected on a screen, that we may witness physical phenomena, - but that we may find illustrations of the highest doctrines of - science in games and gymnastics, in travelling by land and by - water, in storms of the air and of the sea, and wherever there - is matter in motion. - - “If, therefore, we desire, for our own advantage and for the - honour of our University, that the Devonshire Laboratory should - be successful, we must endeavour to maintain it in living union - with the other organs and faculties of our learned body. We - shall therefore first consider the relation in which we stand - to those mathematical studies which have so long flourished - among us, which deal with our own subjects, and which differ - from our experimental studies only in the mode in which they - are presented to the mind. - - “There is no more powerful method for introducing knowledge - into the mind than that of presenting it in as many different - ways as we can. When the ideas, after entering through - different gateways, effect a junction in the citadel of the - mind, the position they occupy becomes impregnable. Opticians - tell us that the mental combination of the views of an object - which we obtain from stations no further apart than our two - eyes is sufficient to produce in our minds an impression of the - solidity of the object seen; and we find that this impression - is produced even when we are aware that we are really looking - at two flat pictures placed in a stereoscope. It is therefore - natural to expect that the knowledge of physical science - obtained by the combined use of mathematical analysis and - experimental research will be of a more solid, available, and - enduring kind than that possessed by the mere mathematician or - the mere experimenter. - - “But what will be the effect on the University if men pursuing - that course of reading which has produced so many distinguished - Wranglers turn aside to work experiments? Will not their - attendance at the Laboratory count not merely as time withdrawn - from their more legitimate studies, but as the introduction of - a disturbing element, tainting their mathematical conceptions - with material imagery, and sapping their faith in the formulæ - of the text-books? Besides this, we have already heard - complaints of the undue extension of our studies, and of the - strain put upon our questionists by the weight of learning - which they try to carry with them into the Senate-House. If we - now ask them to get up their subjects not only by books and - writing, but at the same time by observation and manipulation, - will they not break down altogether? The Physical Laboratory, - we are told, may perhaps be useful to those who are going out - in Natural Science, and who do not take in Mathematics, but - to attempt to combine both kinds of study during the time of - residence at the University is more than one mind can bear. - - “No doubt there is some reason for this feeling. Many of us - have already overcome the initial difficulties of mathematical - training. When we now go on with our study, we feel that it - requires exertion and involves fatigue, but we are confident - that if we only work hard our progress will be certain. - - “Some of us, on the other hand, may have had some experience - of the routine of experimental work. As soon as we can read - scales, observe times, focus telescopes, and so on, this kind - of work ceases to require any great mental effort. We may, - perhaps, tire our eyes and weary our backs, but we do not - greatly fatigue our minds. - - “It is not till we attempt to bring the theoretical part of - our training into contact with the practical that we begin to - experience the full effect of what Faraday has called ‘mental - inertia’--not only the difficulty of recognising, among the - concrete objects before us, the abstract relation which we have - learned from books, but the distracting pain of wrenching the - mind away from the symbols to the objects, and from the objects - back to the symbols. This, however, is the price we have to pay - for new ideas. - - “But when we have overcome these difficulties, and successfully - bridged over the gulph between the abstract and the concrete, - it is not a mere piece of knowledge that we have obtained; we - have acquired the rudiment of a permanent mental endowment. - When, by a repetition of efforts of this kind, we have more - fully developed the scientific faculty, the exercise of this - faculty in detecting scientific principles in nature, and in - directing practice by theory, is no longer irksome, but becomes - an unfailing source of enjoyment, to which we return so often - that at last even our careless thoughts begin to run in a - scientific channel. - - “Our principal work, however, in the Laboratory must be to - acquaint ourselves with all kinds of scientific methods, to - compare them and to estimate their value. It will, I think, - be a result worthy of our University, and more likely to be - accomplished here than in any private laboratory, if, by the - free and full discussion of the relative value of different - scientific procedures, we succeed in forming a school of - scientific criticism and in assisting the development of the - doctrine of method. - - “But admitting that a practical acquaintance with the methods - of Physical Science is an essential part of a mathematical - and scientific education, we may be asked whether we are not - attributing too much importance to science altogether as part - of a liberal education. - - “Fortunately, there is no question here whether the University - should continue to be a place of liberal education, or - should devote itself to preparing young men for particular - professions. Hence, though some of us may, I hope, see reason - to make the pursuit of science the main business of our lives, - it must be one of our most constant aims to maintain a living - connexion between our work and the other liberal studies of - Cambridge, whether literary, philological, historical, or - philosophical. - - “There is a narrow professional spirit which may grow up among - men of science just as it does among men who practise any other - special business. But surely a University is the very place - where we should be able to overcome this tendency of men to - become, as it were, granulated into small worlds, which are - all the more worldly for their very smallness? We lose the - advantage of having men of varied pursuits collected into one - body if we do not endeavour to imbibe some of the spirit even - of those whose special branch of learning is different from our - own.” - -Another expression of his views on the position of Physics at the time -will be found in his address to Section A of the British Association, -when President at the Liverpool meeting of 1870. - - - - -CHAPTER VI. - -CAMBRIDGE--THE CAVENDISH LABORATORY. - - -But the laboratory was not yet built. A Syndicate, of which Maxwell -was a member, was appointed to consider the question of a site, to -take professional advice, and to obtain plans and estimates. Professor -Maxwell and Mr. Trotter visited various laboratories at home and -abroad for the purpose of ascertaining the best arrangements. Mr. W. -M. Fawcett was appointed architect; the tender of Mr. John Loveday, -of Kebworth, for the building at a cost of £8,450, exclusive of gas, -water, and heating, was accepted in March, 1872, and the building[38] -was begun during the summer. - -In the meantime Maxwell began to lecture, finding a home where he could. - - “Lectures begin 24th,” he writes from Glenlair, October 19th, - 1872. “Laboratory rising, I hear, but I have no place to erect - my chair, but move about like the cuckoo, depositing my notions - in the Chemical Lecture-room 1st term; in the Botanical in - Lent, and in Comparative Anatomy in Easter.” - -It was not till June, 1874, that the building was complete, and on -the 16th the Chancellor formally presented his gift of the Cavendish -Laboratory to the University. In the correspondence previous to this -time it was spoken of as the Devonshire Laboratory. The name Cavendish -commemorated the work of the great physicist of a century earlier, -whose writings Maxwell was shortly to edit, as well as the generosity -of the Chancellor. - -In their letter of thanks to the Duke of Devonshire the University -write:-- - -“Unde vero conventius poterat illis artibus succurri quam e tua domo -quæ in ipsis jam pridem inclaruerat. Notum est Henricum Cavendish quem -secutus est Coulombius primum ita docuisse, quæ sit vis electrica ut -eam numerorum modulis illustraret; adhibitis rationibus quas hodie -veras esse constat.” And they suggest the name as suitable for the -building. To this the Chancellor replied, after referring to the work -of Henry Cavendish: “Quod pono in officinâ ipsâ nuncupandâ nomen ejus -commemorare dignati sitis, id grato animo accepi.” - -The building had cost far more than the original estimate, but the -Chancellor’s generosity was not limited, and on July 21st, 1874, he -wrote to the Vice-Chancellor:-- - -“It is my wish to provide all instruments for the Cavendish Laboratory -which Professor Maxwell may consider to be immediately required, either -in his lectures or otherwise.” - -Maxwell prepared a list, but explained while doing it that time and -thought were necessary to secure the best form of instruments; and he -continues, writing to the Vice-Chancellor: “I think the Duke fully -understood from what I said to him that to furnish the Laboratory -will be a matter of several years’ duration. I shall consider myself, -however,” he says, “at liberty to contribute to the Laboratory any -instruments which I have had constructed in former years, and which -may be found still useful, and also from time to time to procure others -for special researches.” - -In 1877 in his annual report Professor Maxwell announced that the -Chancellor[39] had now “completed his gift to the University by -furnishing the Cavendish Laboratory with apparatus suited to the -present state of science.” - -The stock of apparatus, however, was still small, although Maxwell in -the most generous manner himself spent large sums in adding to it; -for the Professor was most particular in procuring only expensive -instruments by the best makers, with such additional improvements as he -could himself suggest. - -In March, 1874, a Demonstratorship of Physics had been established, and -Mr. Garnett of St. John’s College was appointed. - -Work began in the laboratory in October, 1874. At first the number of -students was small. Only seventeen names appear in the Natural Sciences -Tripos[40] list for 1874, and few of those did Physics. - -The fear alluded to by the Professor in his introductory lecture, -that men reading for the Mathematical Tripos would not find -time for attendance at the laboratory, was justified. One of the -weaknesses of our Cambridge plan has been the divorce between -Mathematics and experimental work, encouraged by our system of -examinations. Experimental knowledge is supposed not to be needed for -the Mathematical Tripos; the Mathematics permitted in the Natural -Sciences Tripos are very simple; thus it came about that few men while -reading for the Mathematical Tripos attended the laboratory, and this -unfortunate result was intensified by the action of the University in -1877–78, when the regulations for the Mathematical Tripos were again -altered.[41] - -Still there were pupils eager and willing to work, though they were -chiefly men who had already taken their B.A. degree, and who wished -to continue Physical reading and research, even though it involved “a -considerable amount of dull labour not altogether attractive.” My own -work there began in 1876, and it may be interesting if I recall my -reminiscences of that time. - -The first experiments I can recollect related to the measurement -of electrical resistance. I well remember Maxwell explaining the -principle of Wheatstone’s bridge, and my own wish at the time that I -had come to the laboratory before the Tripos, instead of afterwards. -Lord Rayleigh had, during the examination, set an easy question which -I failed to do for want of some slight experimental knowledge, and the -first few words of Maxwell’s talk showed me the solution. - -I did not attend his lectures regularly--they were given, I think, at -an hour which I was obliged to devote to teaching; besides, there was -his book, the “Electricity and Magnetism,” into which I had just dipped -before the Tripos, to work at. - -Chrystal and Saunder were then busy at their verification of Ohm’s law. -They were using a number of the Thomson form of tray Daniell’s cells, -and Maxwell was anxious for tests of various kinds to be made on these -cells; these I undertook, and spent some time over various simple -measurements on them. He then set me to work at some of the properties -of a stratified dielectric, consisting, if I remember rightly, of -sheets of paraffin paper and mica. By this means I became acquainted -with various pieces of apparatus. There were no regular classes and no -set drill of demonstrations arranged for examination purposes; these -came later. In Maxwell’s time those who wished to work had the use of -the laboratory and assistance and help from him, but they were left -pretty much to themselves to find out about the apparatus and the best -methods of using it. - -Rather later than this Schuster came and did some of his spectroscope -work. J. E. H. Gordon was busy with the preliminary observations -for his determination of Verdet’s constant, and Niven had various -electrical experiments on hand; while Fleming was at work on the B. A. -resistance coils. - -My own tastes lay in the direction of optics. Maxwell was anxious that -I should investigate the properties of certain crystals. I think they -were the chlorate of potash crystals, about which Stokes and Rayleigh -have since written; but these crystals were to be grown, a slow process -which would, he supposed, take years; and as I wished to produce a -dissertation for the Trinity Fellowship examination in 1877, that work -had to be laid aside. - -Eventually I selected as a subject the form of the wave surface in -a biaxial crystal, and set to work in a room assigned to me. The -Professor used to come in on most days to see how I was getting on. -Generally he brought his dog, which sometimes was shut up in the next -room while he went to college. Dogs were not allowed in college, and -Maxwell had an amusing way of describing how Toby once wandered into -Trinity, and by some doggish instinct discovered immediately, to his -intense amazement, that he was in a place where no dogs had been since -the college was. Toby was not always quiet in his master’s absence, and -his presence in the next room was somewhat disturbing. - -When difficulties occurred Maxwell was always ready to listen. Often -the answer did not come at once, but it always did come after a little -time. I remember one day, when I was in a serious dilemma, I told him -my long tale, and he said:-- - -“Well, Chrystal has been talking to me, and Garnett and Schuster have -been asking questions, and all this has formed a good thick crust round -my brain. What you have said will take some time to soak through, but -we will see about it.” In a few days he came back with--“I have been -thinking over what you said the other day, and if you do so-and-so it -will be all right.” - -My dissertation was referred to him, and on the day of the election, -when returning to Cambridge for the admission, I met him at Bletchley -station, and well remember his kind congratulations and words of warm -encouragement. - -For the next year and a half I was working regularly at the laboratory -and saw him almost daily during term time. - -Of these last years there really is but little to tell. His own -scientific work went on. The “Electricity and Magnetism” was written -mostly at Glenlair. About the time of his return to Cambridge, in -October, 1872, he writes[42] to Lewis Campbell:-- - - “I am continually engaged in stirring up the Clarendon Press, - but they have been tolerably regular for two months. I find - nine sheets in thirteen weeks is their average. Tait gives me - great help in detecting absurdities. I am getting converted to - quaternions, and have put some in my book.” - -The book was published in 1873. The Text-book of Heat was written -during the same period, while “Matter and Motion,” “a small book on a -great subject,” was published in 1876. - -In 1873 and 1874 he was one of the examiners for the Natural Sciences -Tripos, and in 1873 he was the first additional examiner for the -Mathematical Tripos, in accordance with the scheme which he had done so -much to promote in 1868. - -Many of his shorter papers were written about the same time. The -ninth edition of the _Encyclopædia Britannica_ was being published, -and Professor Baynes had enlisted his aid in the work. The articles -“Atom,” “Attraction,” “Capillary Action,” “Constitution of Bodies,” -“Diffusion,” “Ether,” “Faraday,” and others are by him. - -He also wrote a number of papers for _Nature_. Some of these are -reviews of books or accounts of scientific men, such as the notices -of Faraday and Helmholtz, which appeared with their portraits; others -again are original contributions to science. Among the latter many have -reference to the molecular constitution of bodies. Two lectures--the -first on “Molecules,” delivered before the British Association at -Bradford in 1873; the second on the “Dynamical Evidence of the -Molecular Constitution of Bodies,” delivered before the Chemical -Society in 1875--were of special importance. The closing sentences of -the first lecture have been often quoted. They run as follow:-- - - “In the heavens we discover by their light, and by their light - alone, stars so distant from each other that no material thing - can ever have passed from one to another; and yet this light, - which is to us the sole evidence of the existence of these - distant worlds, tells us also that each of them is built up of - molecules of the same kinds as those which we find on earth. - A molecule of hydrogen, for example, whether in Sirius or in - Arcturus, executes its vibrations in precisely the same time. - - “Each molecule therefore throughout the universe bears - impressed upon it the stamp of a metric system, as distinctly - as does the metre of the Archives at Paris, or the double royal - cubit of the temple of Karnac. - - “No theory of evolution can be formed to account for the - similarity of molecules, for evolution necessarily implies - continuous change, and the molecule is incapable of growth or - decay, of generation or destruction. - - “None of the processes of Nature, since the time when Nature - began, have produced the slightest difference in the properties - of any molecule. We are therefore unable to ascribe either the - existence of the molecules or the identity of their properties - to any of the causes which we call natural. - - “On the other hand, the exact equality of each molecule to all - others of the same kind gives it, as Sir John Herschel has well - said, the essential character of a manufactured article, and - precludes the idea of its being eternal and self-existent. - - “Thus we have been led along a strictly scientific path, - very near to the point at which Science must stop--not that - Science is debarred from studying the internal mechanism of a - molecule which she cannot take to pieces any more than from - investigating an organism which she cannot put together. But in - tracing back the history of matter, Science is arrested when - she assures herself, on the one hand, that the molecule has - been made, and, on the other, that it has not been made by any - of the processes we call natural. - - “Science is incompetent to reason upon the creation of matter - itself out of nothing. We have reached the utmost limits of our - thinking faculties when we have admitted that because matter - cannot be eternal and self-existent, it must have been created. - - “It is only when we contemplate, not matter in itself, but the - form in which it actually exists, that our mind finds something - on which it can lay hold. - - “That matter, as such, should have certain fundamental - properties, that it should exist in space and be capable of - motion, that its motion should be persistent, and so on, are - truths which may, for anything we know, be of the kind which - metaphysicians call necessary. We may use our knowledge of - such truths for purposes of deduction, but we have no data for - speculating as to their origin. - - “But that there should be exactly so much matter and no more - in every molecule of hydrogen is a fact of a very different - order. We have here a particular distribution of matter--a - _collocation_, to use the expression of Dr. Chalmers, of things - which we have no difficulty in imagining to have been arranged - otherwise. - - “The form and dimensions of the orbits of the planets, for - instance, are not determined by any law of nature, but depend - upon a particular collocation of matter. The same is the case - with respect to the size of the earth, from which the standard - of what is called the metrical system has been derived. But - these astronomical and terrestrial magnitudes are far inferior - in scientific importance to that most fundamental of all - standards which forms the base of the molecular system. Natural - causes, as we know, are at work which tend to modify, if they - do not at length destroy, all the arrangements and dimensions - of the earth and the whole solar system. But though in the - course of ages catastrophes have occurred and may yet occur in - the heavens, though ancient systems may be dissolved and new - systems evolved out of their ruins, the molecules out of which - these systems are built--the foundation stones of the material - universe--remain unbroken and unworn. They continue this day as - they were created--perfect in number and measure and weight; - and from the ineffaceable characters impressed on them we may - learn that those aspirations after accuracy in measurement, and - justice in action, which we reckon among our noblest attributes - as men, are ours because they are essential constituents of the - image of Him who in the beginning created, not only the heaven - and the earth, but the materials of which heaven and earth - consist.” - -This was criticised in _Nature_ by Mr. C. J. Munro, and at a later time -by Clifford in one of his essays. - -Some correspondence with the Bishop of Gloucester and Bristol on the -authority for the comparison of molecules to manufactured articles is -given by Professor Campbell, and in it Maxwell points out that the -latter part of the article “Atom” in the _Encyclopædia_ is intended to -meet Mr. Munro’s criticism. - -In 1874 the British Association met at Belfast, under the presidency of -Tyndall. Maxwell was present, and published afterwards in _Blackwood’s -Magazine_ an amusing paraphrase of the president’s address. This, with -some other verses written at about the same time, may be quoted here. -Professor Campbell has collected a number of verses written by Maxwell -at various times, which illustrate in an admirable manner both the -grave and the gay side of his character. - - -BRITISH ASSOCIATION, 1874. - -_Notes of the President’s Address._ - - In the very beginnings of science, the parsons, who managed - things then, - Being handy with hammer and chisel, made gods in the likeness - of men; - Till commerce arose, and at length some men of exceptional power - Supplanted both demons and gods by the atoms, which last - to this hour. - Yet they did not abolish the gods, but they sent them well - out of the way, - With the rarest of nectar to drink, and blue fields of - nothing to sway. - From nothing comes nothing, they told us--naught happens by - chance, but by fate; - There is nothing but atoms and void, all else is mere whims - out of date! - Then why should a man curry favour with beings who cannot exist, - To compass some petty promotion in nebulous kingdoms of mist? - But not by the rays of the sun, nor the glittering shafts of the - day, - Must the fear of the gods be dispelled, but by words, and their - wonderful play. - So treading a path all untrod, the poet-philosopher sings - Of the seeds of the mighty world--the first-beginnings of things; - How freely he scatters his atoms before the beginning of years; - How he clothes them with force as a garment, those small - incompressible spheres! - Nor yet does he leave them hard-hearted--he dowers them with love - and with hate, - Like spherical small British Asses in infinitesimal state; - Till just as that living Plato, whom foreigners nickname - Plateau,[43] - Drops oil in his whisky-and-water (for foreigners sweeten it so); - Each drop keeps apart from the other, enclosed in a flexible skin, - Till touched by the gentle emotion evolved by the prick of a pin: - Thus in atoms a simple collision excites a sensational thrill, - Evolved through all sorts of emotion, as sense, understanding, - and will - (For by laying their heads all together, the atoms, as - councillors do, - May combine to express an opinion to every one of them new). - There is nobody here, I should say, has felt true indignation at - all, - Till an indignation meeting is held in the Ulster Hall; - Then gathers the wave of emotion, then noble feelings arise, - Till you all pass a resolution which takes every man by surprise. - Thus the pure elementary atom, the unit of mass and of thought, - By force of mere juxtaposition to life and sensation is brought; - So, down through untold generations, transmission of structureless - gorms - Enables our race to inherit the thoughts of beasts, fishes, and - worms. - We honour our fathers and mothers, grandfathers and grandmothers - too; - But how shall we honour the vista of ancestors now in our view? - First, then, let us honour the atom, so lively, so wise, - and so small; - The atomists next let us praise, Epicurus, Lucretius, and all. - Let us damn with faint praise Bishop Butler, in whom many - atoms combined - To form that remarkable structure it pleased him to call--his mind. - Last, praise we the noble body to which, for the time, we belong, - Ere yet the swift whirl of the atoms has hurried us, ruthless, - along, - The British Association--like Leviathan worshipped by Hobbes, - The incarnation of wisdom, built up of our witless nobs, - Which will carry on endless discussions when I, and probably you, - Have melted in infinite azure--in English, till all is blue. - - -MOLECULAR EVOLUTION. - -_Belfast, 1874._ - - At quite uncertain times and places, - The atoms left their heavenly path, - And by fortuitous embraces - Engendered all that being hath. - And though they seem to cling together, - And form “associations” here, - Yet, soon or late, they burst their tether, - And through the depths of space career. - - So we who sat, oppressed with science, - As British Asses, wise and grave, - Are now transformed to wild Red Lions,[44] - As round our prey we ramp and rave. - Thus, by a swift metamorphōsis, - Wisdom turns wit, and science joke, - Nonsense is incense to our noses, - For when Red Lions speak they smoke. - - Hail, Nonsense! dry nurse of Red Lions,[45] - From thee the wise their wisdom learn; - From thee they cull those truths of science, - Which into thee again they turn. - What combinations of ideas - Nonsense alone can wisely form! - What sage has half the power that she has, - To take the towers of Truth by storm? - - Yield, then, ye rules of rigid reason! - Dissolve, thou too, too solid sense! - Melt into nonsense for a season, - Then in some nobler form condense. - Soon, all too soon, the chilly morning - This flow of soul will crystallise; - Then those who Nonsense now are scorning - May learn, too late, where wisdom lies. - - -TO THE COMMITTEE OF THE CAYLEY PORTRAIT FUND. - -1874. - - O wretched race of men, to space confined! - What honour can ye pay to him, whose mind - To that which lies beyond hath penetrated? - The symbols he hath formed shall sound his praise, - And lead him on through unimagined ways - To conquests new, in worlds not yet created. - - First, ye Determinants! in ordered row - And massive column ranged, before him go, - To form a phalanx for his safe protection. - Ye powers of the _n^{th}_ roots of -1! - Around his head in ceaseless[46] cycles run, - As unembodied spirits of direction. - - And you, ye undevelopable scrolls! - Above the host wave your emblazoned rolls, - Ruled for the record of his bright inventions. - Ye cubic surfaces! by threes and nines - Draw round his camp your seven-and-twenty lines-- - The seal of Solomon in three dimensions. - - March on, symbolic host! with step sublime, - Up to the flaming bounds of Space and Time! - There pause, until by Dickinson depicted, - In two dimensions, we the form may trace - Of him whose soul, too large for vulgar space, - In _n_ dimensions flourished unrestricted. - - -IN MEMORY OF EDWARD WILSON, - -_Who repented of what was in his mind to write after section._ - -RIGID BODY (_sings_). - - GIN a body meet a body - Flyin’ through the air, - Gin a body hit a body, - Will it fly? and where? - Ilka impact has its measure, - Ne’er a ane hae I; - Yet a’ the lads they measure me, - Or, at least, they try. - - Gin a body meet a body - Altogether free, - How they travel afterwards - We do not always see. - Ilka problem has its method - By analytics high; - For me, I ken na ane o’ them, - But what the waur am I? - -Another task, which occupied much time, from 1874 to 1879, was the -edition of the works of Henry Cavendish. Cavendish, who was great-uncle -to the Chancellor, had published only two electrical papers, but he had -left some twenty packets of manuscript on Mathematical and Experimental -Electricity. These were placed in Maxwell’s hands in 1874 by the Duke -of Devonshire. - -Niven, in his preface to the collected papers dealing with this book, -writes thus:-- - - “This work, published in 1879, has had the effect of increasing - the reputation of Cavendish, disclosing as it does the - unsuspected advances which that acute physicist had made in - the Theory of Electricity, especially in the measurement of - electrical quantities. The work is enriched by a variety of - valuable notes, in which Cavendish’s views and results are - examined by the light of modern theory and methods. Especially - valuable are the methods applied to the determination of the - electrical capacities of conductors and condensers, a subject - in which Cavendish himself showed considerable skill both of a - mathematical and experimental character. - - “The importance of the task undertaken by Maxwell in connection - with Cavendish’s papers will be understood from the following - extract from his introduction to them:-- - - “‘It is somewhat difficult to account for the fact that - though Cavendish had prepared a complete description of his - experiments on the charges of bodies, and had even taken the - trouble to write out a fair copy, and though all this seems - to have been done before 1774, and he continued to make - experiments in electricity till 1781, and lived on till 1810, - he kept his manuscript by him and never published it. - - “‘Cavendish cared more for investigation than for publication. - He would undertake the most laborious researches in order to - clear up a difficulty which no one but himself could appreciate - or was even aware of, and we cannot doubt that the result of - his enquiries, when successful, gave him a certain degree of - satisfaction. But it did not excite in him that desire to - communicate the discovery to others, which in the case of - ordinary men of science generally ensures the publication of - their results. How completely these researches of Cavendish - remained unknown to other men of science is shown by the - external history of electricity.’ - - “It will probably be thought a matter of some difficulty to - place oneself in the position of a physicist of a century - ago, and to ascertain the exact bearing of his experiments. - But Maxwell entered upon this undertaking with the utmost - enthusiasm, and succeeded in identifying himself with - Cavendish’s methods. He showed that Cavendish had really - anticipated several of the discoveries in electrical science - which have been made since his time. Cavendish was the first to - form the conception of and to measure Electrostatic Capacity - and Specific Inductive Capacity; he also anticipated Ohm’s law.” - -During the last years of his life Mrs. Maxwell had a serious and -prolonged illness, and Maxwell’s work was much increased by his duties -as sick nurse. On one occasion he did not sleep in a bed for three -weeks, but conducted his lectures and experiments at the laboratory as -usual. - -About this time some of those who had been “Apostles” in 1853–57 -revived the habit of meeting together for discussion. The club, which -included Professors Lightfoot, Hort and Westcott, was christened -the “Eranus,” and three of Maxwell’s contributions to it have been -preserved and are printed by Professor Campbell. - -After the Cavendish papers were finished, Maxwell had more time for his -own original researches, and two important papers were published in -1879. The one on “Stresses in Rarefied Gases arising from Inequalities -of Temperature” was printed in the Royal Society’s Transactions, and -deals with the Theory of the Radiometer; the other on “Boltzmann’s -Theorem” appears in the Transactions of the Cambridge Philosophical -Society. In the previous year he had delivered the Rede lecture on “The -Telephone.” He also began to prepare a second edition of “Electricity -and Magnetism.” - -His health gave way during the Easter term of 1879; indeed for two -years previously he had been troubled with dyspeptic symptoms, but had -consulted no one on the subject. He left Cambridge as usual in June, -hoping that he would quickly recover at Glenlair, but he grew worse -instead. In October he was told by Dr. Sanders of Edinburgh that he had -not a month to live. He returned to Cambridge in order to be under the -care of Dr. Paget, who was able in some measure to relieve his most -severe suffering but the disease, of which his mother had died at the -same age, continued its progress, and he died on November 5th. His one -care during his last illness was for those whom he left behind. Mrs. -Maxwell was an invalid dependent on him for everything, and the thought -of her helplessness was the one thing which in these last days troubled -him. - -A funeral service took place in the chapel at Trinity College, and -afterwards his remains were conveyed to Scotland and interred in the -family burying-place at Corsock, Kirkcudbright. - -A memorial edition of his works was issued by the Cambridge University -Press in 1890. A portrait by Lowes Dickinson hangs in the hall of -Trinity College, and there is a bust by Boehm in the laboratory. - -After his death Mrs. Maxwell gave his scientific library to the -Cavendish Laboratory, and on her death she left a sum of about £6,000 -to found a scholarship in Physics, to be held at the laboratory. - - * * * * * - -The preceding pages contain some account of Clerk Maxwell’s life as -a man of science. His character had other sides, and any life of him -would be incomplete without some brief reference to these. His letters -to his wife and to other intimate friends show throughout his life -the depth of his religious convictions. The high purpose evidenced -in the paper given to the present Dean of Canterbury when leaving -Cambridge, animated him continually, and appears from time to time in -his writings. The student’s evening hymn, composed in 1853 when still -an undergraduate, expresses the same feelings-- - - Through the creatures Thou hast made - Show the brightness of Thy glory, - Be eternal truth displayed - In their substance transitory, - Till green earth and ocean hoary, - Massy rock and tender blade, - Tell the same unending story, - “We are Truth in form arrayed.” - - Teach me so Thy works to read - That my faith, new strength accruing, - May from world to world proceed, - Wisdom’s fruitful search pursuing, - Till Thy breath my mind imbuing, - I proclaim the eternal creed, - Oft the glorious theme renewing, - God our Lord is God indeed. - -His views on the relation of Science to Faith are given in his -letter[47] to Bishop Ellicott already referred to-- - - “But I should be very sorry if an interpretation founded - on a most conjectural scientific hypothesis were to get - fastened to the text in Genesis, even if by so doing it got - rid of the old statement of the commentators which has long - ceased to be intelligible. The rate of change of scientific - hypothesis is naturally much more rapid than that of Biblical - interpretations, so that if an interpretation is founded on - such an hypothesis, it may help to keep the hypothesis above - ground long after it ought to be buried and forgotten. - - “At the same time I think that each individual man should do - all he can to impress his own mind with the extent, the order, - and the unity of the universe, and should carry these ideas - with him as he reads such passages as the 1st chapter of the - Epistle to Colossians (_see_ ‘Lightfoot on Colossians,’ p. - 182), just as enlarged conceptions of the extent and unity of - the world of life may be of service to us in reading Psalm - viii., Heb. ii. 6, etc.” - -And again in his letter[48] to the secretary of the Victoria Institute -giving his reasons for declining to become a member-- - - “I think men of science as well as other men need to learn from - Christ, and I think Christians whose minds are scientific are - bound to study science, that their view of the glory of God - may be as extensive as their being is capable of. But I think - that the results which each man arrives at in his attempts to - harmonise his science with his Christianity ought not to be - regarded as having any significance except to the man himself, - and to him only for a time, and should not receive the stamp of - a society.” - -Professor Campbell and Mr. Garnett have given us the evidence of those -who were with him in his last days, as to the strength of his own -faith. On his death bed he said that he had been occupied in trying to -gain truth; that it is but little of truth that man can acquire, but it -is something to know in whom we have believed. - - - - -CHAPTER VII. - -SCIENTIFIC WORK--COLOUR VISION. - - -Fifteen years only have passed since the death of Clerk Maxwell, and it -is almost too soon to hope to form a correct estimate of the value of -his work and its relation to that of others who have laboured in the -same field. - -Thus Niven, at the close of his obituary notice in the Proceedings of -the Royal Society, says: “It is seldom that the faculties of invention -and exposition, the attachment to physical science and capability of -developing it mathematically, have been found existing in one mind -to the same degree. It would, however, require powers somewhat akin -to Maxwell’s own to describe the more delicate features of the works -resulting from this combination, every one of which is stamped with the -subtle but unmistakable impress of genius.” And again in the preface -to Maxwell’s works, issued in 1890, he wrote: “Nor does it appear to -the present editor that the time has yet arrived when the quickening -influence of Maxwell’s mind on modern scientific thought can be duly -estimated.” - -It is, however, the object of the present series to attempt to give -some account of the work of men of science of the last hundred years, -and to show how each has contributed his share to our present stock -of knowledge. This task, then, remains to be done. While attempting -it I wish to express my indebtedness to others who have already -written about Maxwell’s scientific work, especially to Mr. W. D. -Niven, whose preface to the Maxwell papers has been so often referred -to; to Mr. Garnett, the author of Part II. of the “Life of Maxwell,” -which deals with his contributions to science; and to Professor Tait, -who in _Nature_ for February 5th, 1880, gave an account of Clerk -Maxwell’s work, “necessarily brief, but sufficient to let even the -non-mathematical reader see how very great were his contributions to -modern science”--an account all the more interesting because, again to -quote from Professor Tait, “I have been intimately acquainted with him -since we were schoolboys together.” - -Maxwell’s main contributions to science may be classified under three -heads--“Colour Perception,” “Molecular Physics,” and “Electrical -Theories.” In addition to these there were other papers of the highest -interest and importance, such as the essay on “Saturn’s Rings,” the -paper on the “Equilibrium of Elastic Solids,” and various memoirs on -pure geometry and questions of mechanics, which would, if they stood -alone, have secured for their author a distinguished position as a -physicist and mathematician, but which are not the works by which his -name will be mostly remembered. - -The work on “Colour Perception” was begun at an early date. We have -seen Maxwell while still at Edinburgh interested in the discussions -about Hay’s theories. - -His first published paper on the subject was a letter to Dr. G. -Wilson, printed in the Transactions of the Royal Society of Arts for -1855; but he had been mixing colours by means of his top for some -little time previously, and the results of these experiments are given -in a paper entitled “Experiments on Colour,” communicated to the Royal -Society of Edinburgh by Dr. Gregory, and printed in their Transactions, -vol. xxi. - -In the paper on “The Theory of Compound Colours,” printed in the -Philosophical Transactions for 1860, Maxwell gives a history of the -theory as it was known to him. - -He points out first the distinction between the _optical_ properties -and the _chromatic_ properties of a beam of light. “The optical -properties are those which have reference to its origin and propagation -through media until it falls on the sensitive organ of vision;” -they depend on the periods and amplitudes of the ether vibrations -which compose the beam. “The chromatic properties are those which -have reference to its power of exciting certain sensations of colour -perceived through the organ of vision.” It is possible for two beams to -be optically very different and chromatically alike. The converse is -not true; two beams which are optically alike are also chromatically -alike. - -The foundation of the theory of compound colours was laid by Newton. -He first shewed that “by the mixture of homogeneal light colours may -be produced which are like to the colours of homogeneal light as to -the appearance of colour, but not as to the immutability of colour and -constitution of light.” Two beams which differ optically may yet be -alike chromatically; it is possible by mixing red and yellow to obtain -an orange colour chromatically similar to the orange of the spectrum, -but optically different to that orange, for the compound orange can be -analysed by a prism into its component red and yellow; the spectrum -orange is incapable of further resolution. - -Newton also solves the following problem:-- - -_In a mixture of primary colours, the quantity and quality of each -being given to know the colour of the compound_ (Optics, Book 1, Part -2, Prop. 6), and his solution is the following:--He arranges the seven -colours of the spectrum round the circumference of a circle, the length -occupied by each colour being proportional to the musical interval to -which, in Newton’s views, the colour corresponded. At the centre of -gravity of each of these arcs he supposes a weight placed proportional -to the number of rays of the corresponding colour which enter into the -mixture under consideration. The position of the centre of gravity of -these weights indicates the nature of the resultant colour. A radius -drawn through this centre of gravity points out the colour of the -spectrum which it most resembles; the distance of the centre of gravity -from the centre gives the fulness of the colour. The centre itself is -white. Newton gives no proof of this rule; he merely says, “This rule I -conceive to be accurate enough for practice, though not mathematically -accurate.” - -Maxwell proved that Newton’s method of finding the centre of gravity of -the component colours was confirmed by his observations, and that it -involves mathematically the theory of three elements of colour; but -the disposition of the colours on the circle was only a provisional -arrangement; the true relations of the colours could only be determined -by direct experiment. - -Thomas Young appears to have been the next, after Newton, to work -at the theory of colour sensation. He made observations by spinning -coloured discs much in the same way as that which was afterwards -adopted by Maxwell, and he developed the theory that three different -primary sensations may be excited in the eye by light, while the colour -of any beam depends on the proportions in which these three sensations -are excited. He supposes the three primary sensations to correspond -to red, green, and violet. A blue ray is capable of exciting both the -green and the violet; a yellow ray excites the red and the green. Any -colour, according to Young’s theory, may be matched by a mixture of -these three primary colours taken in proper proportion; the quality -of the colour depends on the proportion of the intensities of the -components; its brightness depends on the sum of these intensities. - -Maxwell’s experiments were undertaken with the object of proving or -disproving the physical part of Young’s theory. He does not consider -the question whether there are three distinct sensations corresponding -to the three primary colours; that is a physiological inquiry, and one -to which no completely satisfactory answer has yet been given. He does -show that by a proper mixture of any three arbitrarily chosen standard -colours it is possible to match any other colour; the words “proper -mixture,” however, need, as will appear shortly, some development. - -We may with advantage compare the problem with one in acoustics. - -When a compound musical note consisting of a pure tone and its -overtones is sounded, the trained ear can distinguish the various -overtones and analyse the sound into its simple components. The same -sensation cannot be excited in two different ways. The eye has no such -corresponding power. A given yellow may be a pure spectral yellow, -corresponding to a pure tone in music, or it may be a mixture of a -number of other pure tones; in either case it can be matched by a -proper combination of three standard colours--this Maxwell proved. -It may be, as Young supposed, that if the three standard colours be -properly selected they correspond exactly to three primary sensations -of the brain. Maxwell’s experiments do not afford any light on this -point, which still remains more than doubtful. - -When Maxwell began his work the theory of colours was exciting -considerable interest. Sir David Brewster had recently developed a -new theory of colour sensation which had formed the basis of some -discussions, and in 1852 von Helmholtz published his first paper -on the subject. According to Brewster, the three primitive colours -were red, yellow and blue, and he supposed that they corresponded to -three different kinds of objective light. Helmholtz pointed out that -experiments up to that date had been conducted by mixing pigments, with -the exception of those in which the rotating disc was used, and that -it is necessary to make them on the rays of the spectrum itself. He -then describes a method of mixing the light from two spectra so as to -obtain the combination of every two of the simple prismatic rays in all -degrees of relative strength. - -From these experiments results, which at the time were unexpected, but -some of which must have been known to Young, were obtained. Among them -it was shown that a mixture of red and green made yellow, while one of -green and violet produced blue. - -In a later paper (_Philosophical Magazine_, 1854) Helmholtz described -a method for ascertaining the various pairs of complementary -colours--colours, that is, which when mixed will give white--which had -been shown by Grassman to exist if Newton’s theory were true. He also -gave a provisional diagram of the curve formed by the spectrum, which -ought to take the place of the circle in Newton’s diagram; for this, -however, his experiments did not give the complete data. - -Such was the state of the question when Maxwell began. His first -colour-box was made in 1852. Others were designed in 1855 and 1856, -and the final paper appeared in 1860. But before that time he had -established important results by means of his rotatory discs and colour -top. In his own description of this he says: “The coloured paper is -cut into the form of disc, each with a hole in the centre and divided -along a radius so as to admit of several of them being placed on the -same axis, so that part of each is exposed. By slipping one disc over -another we can expose any given portion of each colour. These discs -are placed on a top or teetotum, which is spun rapidly. The axis of the -top passes through the centre of the discs, and the quantity of each -colour exposed is measured by graduations on the rim of the top, which -is divided into 100 parts. When the top is spun sufficiently rapidly, -the impressions due to each colour separately follow each other in -quick succession at each point of the retina, and are blended together; -the strength of the impression due to each colour is, as can be shown -experimentally, the same as when the three kinds of light in the same -relative proportions enter the eye simultaneously. These relative -proportions are measured by the areas of the various discs which are -exposed. Two sets of discs of different radius are used; the largest -discs are put on first, then the smaller, so that the centre portion -of the top shows the colour arising from the mixture of those of the -smaller discs; the outer portion, that of the larger discs.” - -In experimenting, six discs of each size are used, black, white, red, -green, yellow and blue. It is found by experiment that a match can be -arranged between any five of these. Thus three of the larger discs are -placed on the top--say black, yellow and blue--and two of the smaller -discs, red and green, are placed above these. Then it is found that it -is possible so to adjust the amount exposed of each disc that the two -parts of the top appear when it is spun to be of the same tint. In one -series of experiments the chromatic effect of 46·8 parts of black, 29·1 -of yellow, and 24·1 of blue was found to be the same as that of 66·6 -of red and 33·4 of green; each set of discs has a dirty yellow tinge. - -Now, in this experiment, black is not a colour; practically no light -reaches the eye from a dead black. We have, however, to fill up -the circumference of the top in some way which will not affect the -impression on the retina arising from the mixture of the blue and -yellow; this we can do by using the black disc. - -Thus we have shown that 66·6 parts of red and 33·4 parts of green -produce the same chromatic effect as 29·1 of yellow and 24·1 of -blue. Similarly in this manner a match can be arranged between any -four colours and black, the black being necessary to complete the -circumference of the discs. - -Thus using A, B, C, D to denote the various colours, _a_, _b_, _c_, -_d_ the amounts of each colour taken, we can get a series of results -expressed as follows: _a_ parts of A together with _b_ parts of B match -_c_ parts of C together with _d_ parts of D; or we may write this as an -equation thus:-- - - _a_ A + _b_ B = _c_ C + _d_ D, - -where the + stands for “combined with,” and the = for “matches in tint.” - -We may also write the above-- - - _d_ D = _a_ A + _b_ B - _c_ C, - -or _d_ parts of D can be matched by a _proper_ combination of colours -A, B, C. The sign - shows that in order to make the match we have to -combine the colour C with D; the combination then matches a mixture of -A and B. - -In this way we can form a number of equations for all possible colours, -and if we like to take any three colours A, B, C as standards, we -obtain a result which may be written generally-- - - _x_ X = _a_ A + _b_ B + _c_ C, - -or _x_ parts of X can be matched by _a_ parts of A, combined with _b_ -parts of B and _c_ parts of C. If the sign of one of the quantities -_a_, _b_, or _c_ is negative, it indicates that that colour must be -combined with X to match the other two. - -Now Maxwell was able to show that, if A, B, C be properly selected, -nearly every other colour can be matched by positive combinations of -these three. These three colours, then, are primary colours, and nearly -every other colour can be matched by a combination of the three primary -colours. - -Experiments, however, with coloured discs, such as were undertaken by -Young, Forbes and Maxwell, were not capable of giving satisfactory -results. The colours of the discs were not pure spectrum colours, and -varied to some extent with the nature of the incident light. It was for -this reason that Helmholtz in 1852 experimented with the spectrum, and -that Maxwell about the same time invented his colour box. - -The principle of the latter was very simple. Suppose we have a slit -S, and some arrangement for forming a pure spectrum on a screen. Let -there now be a slit R placed in the red part of the spectrum on the -screen. When light falls on the slit S, only the red rays can reach -R, and hence conversely, if the white source be placed at the other -end of the apparatus, so that R is illuminated with white light, only -red rays will reach S. Similarly, if another slit be placed in the -green at G, and this be illuminated by white light, only the green -rays will reach S, while from a third slit V in the violet, violet -light only can arrive at S. Thus by opening the three slits at V, G -and R simultaneously, and looking through S, the retina receives the -impression of the three different colours. The amount of light of each -colour will depend on the breadth to which the corresponding slit is -opened, and the relative intensities of the three different components -can be compared by comparing the breadths of the three slits. Any other -colour which is allowed by some suitable contrivance to enter the eye -simultaneously can now be matched, provided the red, green and violet -are primary colours. - -By means of experiments with the colour box Maxwell showed conclusively -that a match could be obtained between any four colours; the -experiments could not be carried out in quite the simple manner -suggested by the above description of the principle of the box. -An account of the method will be found in Maxwell’s own paper. It -consisted in matching a standard white by various combinations of other -colours. - -The main object of his research, however, was to examine the chromatic -properties of the different parts of the spectrum, and to determine the -form of the curve which ought to replace the circle in Newton’s diagram -of colour. - -Maxwell adopted as his three standard colours: red, of about wave -length 6,302; green, wave length 5,281; and violet, 4,569 tenth metres. -On the scale of Maxwell’s instrument these are represented by the -numbers 24, 44 and 68. - -Let us take three points A, B, C at the corners of an equilateral -triangle to represent on a diagram these three colours. The position -of any other colour on the diagram will be found by taking weights -proportional to the amounts of the colours A, B, C required to make the -match between A, B, C and the given colour; these weights are placed at -A, B, C respectively; the position of their centre of gravity is the -point required. Thus the position of white is given by the equation-- - - W = 18·6 (24) + 31·4 (44) + 30·5 (68) - -which means that weights proportional to 18·6, 31·4 and 30·5 are to be -placed at A, B, C respectively, and their centre of gravity is to be -found. The point so found is the position of white. Any other colour is -given by the equation-- - - X = _a_ (24) + _b_ (44) + _c_ (68). - -Again, the position on the diagram for all colours for which _a_, -_b_, _c_ are all positive lies within the triangle A B C. If one of -the coefficients, say _c_, is negative the same construction applies, -but the weight applied at C must be treated as acting in the opposite -direction to those at A and B. A mixture of the given colour and C -matches a mixture of A and B. It is clear that the point corresponding -to X will then lie outside the triangle A B C. Maxwell showed that, -with his standards, nearly all colours could be represented by points -inside the triangle. The colours he had selected as standards were very -close to primary colours. - -Again, he proved that any spectrum colour between red and green, when -combined with a very slight admixture of violet, could be matched, in -the case of either Mrs. Maxwell or himself, by a proper mixture of -the red and green. The positions, therefore, of the spectrum colours -between red and green lie just outside the triangle A B C, being very -close to the line A B, while for the colours between green and violet -Maxwell obtained a curve lying rather further outside the side B C. -Any spectrum colour between green and violet, together with a slight -admixture of red, can be matched by a proper mixture of green and -violet. - -Thus the circle of Newton’s diagram should be replaced by a curve, -which coincides very nearly with the two sides A B and B C of Maxwell’s -figure. Strictly, according to his observations, the curve lies just -outside these two sides. The purples of the spectrum lie nearly along -the third side, C A, of the triangle, being obtained approximately by -mixing the violet and the red. - -To find the point on the diagram corresponding to the colour obtained -by mixing any two or more spectrum colours we must, in accordance -with Newton’s rule, place weights at the points corresponding to the -selected colours, and find the centre of gravity of these weights. - -This, then, was the outcome of Maxwell’s work on colour. It verified -the essential part of Newton’s construction, and obtained for the first -time the true form of the spectrum curve on the diagram. - -The form of this curve will of course depend on the eye of the -individual observer. Thus Maxwell and Mrs. Maxwell both made -observations, and distinct differences were found in their eyes. It -appears, however, that a large majority of persons have normal vision, -and that matches made by one such person are accepted by most others -as satisfactory. Some people, however, are colour blind, and Maxwell -examined a few such. In the case of those whom he examined it appeared -as though vision was dichromatic, the red sensation seemed to be -absent; nearly all colours could be matched by combinations of green -and violet. The colour diagram was reduced to the straight line B C. -Other forms of colour blindness have since been investigated. - -In awarding to Maxwell the Rumford medal in 1860, Major-General -Sabine, vice-president of the Royal Society, after explaining the -theory of colour vision and the possible method of verifying it, said: -“Professor Maxwell has subjected the theory to this verification, and -thereby raised the composition of colours to the rank of a branch of -mathematical physics,” and he continues: “The researches for which -the Rumford medal is awarded lead to the remarkable result that to a -very near degree of approximation all the colours of the spectrum, and -therefore all colours in nature which are only mixtures of these, can -be perfectly imitated by mixtures of three actually attainable colours, -which are the red, green and blue belonging respectively to three -particular parts of the spectrum.” - -It should be noticed in concluding our remarks on this part of -Maxwell’s work that his results are purely physical. They are not -inconsistent with the physiological part of Young’s theory, viz., that -there are three primary sensations of colour which can be transmitted -to the brain, and that the colour of any object depends on the relative -proportions in which these sensations are excited, but they do not -prove that theory. Any physiological theory which can be accepted as -true must explain Maxwell’s observations, and Young’s theory does this; -but it is, of course, possible that other theories may explain them -equally well, and be more in accordance with physiological observations -than Young’s. Maxwell has given us the physical facts which have to be -explained; it is for the physiologists to do the rest. - - - - -CHAPTER VIII. - -SCIENTIFIC WORK--MOLECULAR THEORY. - - -Maxwell in his article “Atom,” in the ninth edition of the -_Encyclopædia Britannica_, has given some account of Modern Molecular -Science, and in particular of the molecular theory of gases. Of this -science, Clausius and Maxwell are the founders, though to their names -it has recently been shown that a third, that of Waterston, must be -added. In the present chapter it is intended to give an outline of -Maxwell’s contributions to molecular science, and to explain the -advances due to him. - -The doctrine that bodies are composed of small particles in rapid -motion is very ancient. Democritus was its founder, Lucretius--de Rerum -Naturâ--explained its principles. The atoms do not fill space; there is -void between. - - “Quapropter locus est intactus inane vacansque, - Quod si non esset, nullâ ratione moveri - Res possent; namque officium quod corporis extat - Officere atque obstare, id in omni tempore adesset - Omnibus. Haud igitur quicquam procedere posset - Principium quoniam cedendi nulla daret res.” - -According to Boscovitch an atom is an indivisible point, having -position in space, capable of motion, and possessing mass. It is also -endowed with the power of exerting force, so that two atoms attract -or repel each other with a force depending on their distance apart. -It has no parts or dimensions: it is a mere geometrical point without -extension in space; it has not the property of impenetrability, for two -atoms can, it is supposed, exist at the same point. - -In modern molecular science according to Maxwell, “we begin by assuming -that bodies are made up of parts each of which is capable of motion, -and that these parts act on each other in a manner consistent with the -principle of the conservation of energy. In making these assumptions -we are justified by the facts that bodies may be divided into -smaller parts, and that all bodies with which we are acquainted are -conservative systems, which would not be the case unless their parts -were also conservative systems. - -“We may also assume that these small parts are in motion. This is the -most general assumption we can make, for it includes as a particular -case the theory that the small parts are at rest. The phenomena of the -diffusion of gases and liquids through each other show that there may -be a motion of the small parts of a body which is not perceptible to us. - -“We make no assumption with respect to the nature of the small -parts--whether they are all of one magnitude. We do not even assume -them to have extension and figure. Each of them must be measured by its -mass, and any two of them must, like visible bodies, have the power -of acting on one another when they come near enough to do so. The -properties of the body or medium are determined by the configuration of -its parts.” - -These small particles are called molecules, and a molecule in its -physical aspect was defined by Maxwell in the following terms:-- - - “A molecule of a substance is a small body, such that if, on - the one hand, a number of similar molecules were assembled - together, they would form a mass of that substance; while on - the other hand, if any portion of this molecule were removed, - it would no longer be able, along with an assemblage of other - molecules similarly treated, to make up a mass of the original - substance.” - -We are to look upon a gas as an assemblage of molecules flying about -in all directions. The path of any molecule is a straight line, except -during the time when it is under the action of a neighbouring molecule; -this time is usually small compared with that during which it is free. - -The simplest theory we could formulate would be that the molecules -behaved like elastic spheres, and that the action between any two was -a collision following the laws which we know apply to the collision of -elastic bodies. If the average distance between two molecules be great -compared with their dimensions, the time during which any molecule -is in collision will be small compared with the interval between the -collisions, and this is in accordance with the fundamental assumption -just mentioned. It is not, however, necessary to suppose an encounter -between two molecules to be a collision. One molecule may act on -another with a force, which depends on the distance between them, of -such a character that the force is insensible except when the molecules -are extremely close together. - -It is not difficult to see how the pressure exerted by a gas on the -sides of a vessel which contains it may be accounted for on this -assumption. Each molecule as it strikes the side has its momentum -reversed--the molecules are here assumed to be perfectly elastic. - -Thus each molecule of the gas is continually gaining momentum from -the sides of the vessel, while it gives up to the vessel the momentum -which it possessed before the impact. The rate at which this change of -momentum proceeds across a given area measures the force exerted on -that area; the pressure of the gas is the rate of change of momentum -per unit of area of the surface. - -Again, it can be shown that this pressure is proportional to the -product of the mass of each molecule, the number of molecules in a unit -of volume, and the square of the velocity of the molecules. - -Let us consider in the first instance the case of a jet of sand or -water of unit cross section which is playing against a surface. Suppose -for the present that all the molecules which strike the surface have -the same velocity. - -Then the number of molecules which strike the surface per second, will -be proportional to this velocity. If the particles are moving quickly -they can reach the surface in one second from a greater distance than -is possible if they be moving slowly. Again, the number reaching the -surface will be proportional to the number of molecules per unit of -volume. Hence, if we call _v_ the velocity of each particle, and N -the number of particles per unit of volume, the number which strike -the surface in one second will be N _v_; if _m_ be the mass of each -molecule, the mass which strikes the surface per second is N _m_ _v_; -the velocity of each particle of this mass is _v_, therefore the -momentum destroyed per second by the impact is N _m_ _v_ × _v_, or N -_m_ _v_², and this measures the pressure. - -Hence in this case if _p_ be the pressure - - _p_ = N _m_ _v_². - -In the above we assume that _all_ the molecules in the jet are moving -with velocity _v_ perpendicular to the surface. In the case of a crowd -of molecules flying about in a closed space this is clearly not true. -The molecules may strike the surface in any direction; they will not -all be moving normal to the surface. To simplify the case, consider a -cubical box filled with gas. The box has three pairs of equal faces at -right angles. We may suppose one-third of the particles to be moving at -right angles to each face, and in this case the number per unit volume -which we have to consider is not N, but ⅓ N. Hence the formula becomes -_p_ = ⅓ N _m_ _v_². - -Moreover, if _ρ_ be the density of the gas--that is, the mass of -unit volume--then N_m_ is equal to _ρ_, for _m_ is the mass of each -particle, and there are N particles in a unit of volume. - -Hence, finally, _p_ = ⅓ _ρ_ _v_². - -Or, again, if V be the volume of unit mass of the gas, then _ρ_ V is -unity, or ρ is equal to 1/V. - -Hence _p_V = ⅓_v_². - -Formulæ equivalent to these appear first to have been obtained by -Herapath about the year 1816 (Thomson’s “Annals of Philosophy,” 1816). -The results only, however, were stated in that year. A paper which -attempted to establish them was presented to the Royal Society in 1820. -It gave rise to very considerable correspondence, and was withdrawn -by the author before being read. It is printed in full in Thomson’s -“Annals of Philosophy” for 1821, vol. i., pp. 273, 340, 401. The -arguments of the author are no doubt open to criticism, and are in many -points far from sound. Still, by considering the problem of the impact -of a large number of hard bodies, he arrived at a formula connecting -the pressure and volume of a given mass of gas equivalent to that just -given. These results are contained in Propositions viii. and ix. of -Herapath’s paper. - -In his next step, however, Herapath, as we know now, was wrong. One -of his fundamental assumptions is that the temperature of a gas is -measured by the momentum of each of its particles. Hence, assuming -this, we have T = _m_ _v_, if T represents the temperature: and - - _p_ = ⅓ N _m_ _v_² = ⅓ (N/_m_) (_m_ _v_)². - -Or, again-- - - _p_ = ⅓ N·T·_v_ = ⅓·(N/_m_)·T². - -These results are practically given in Proposition viii., Corr. (1) -and (2), and Proposition ix.[49] The temperature as thus defined by -Herapath is an absolute temperature, and he calculates the absolute -zero of temperature at which the gas would have no volume from the -above results. The actual calculation is of course wrong, for, as -we know now by experiment, the pressure is proportional to the -temperature, and not to its square, as Herapath supposed. It will be -seen, however, that Herapath’s formula gives Boyle’s law; for if the -temperature is constant, the formula is equivalent to - - _p_ V = a constant. - -Herapath somewhat extended his work in his “Mathematical Physics” -published in 1847, and applied his principles to explain diffusion, the -relation between specific heat and atomic weight, and other properties -of bodies. He still, however, retained his erroneous supposition -that temperature is to be measured by the momentum of the individual -particles. - -The next step in the theory was made by Waterston. His paper was read -to the Royal Society on March 5th, 1846. It was most unfortunately -committed to the Archives of the Society, and was only disinterred by -Lord Rayleigh in 1892 and printed in the Transactions for that year. - -In the account just given of the theory, it has been supposed that all -the particles move with the same velocity. This is clearly not the -case in a gas. If at starting all the particles had the same velocity, -the collisions would change this state of affairs. Some particles will -be moving quickly, some slowly. We may, however, still apply the -theory by splitting up the particles into groups, and, supposing that -each group has a constant velocity, the particles in this group will -contribute to the pressure an amount--_p_₁--equal to ⅓ N₁ _m_ _v_₁², -where _v_₁ is the velocity of the group and N₁ the number of particles -having that velocity. The whole pressure will be found by adding that -due to the various groups, and will be given as before by _p_ = ⅓ N _m_ -_v_², where _v_ is not now the actual velocity of the particles, but a -mean velocity given by the equation - - N _v_² = N₁ _v_₁² + N₂ _v_₂² + ....., - -which will produce the same pressure as arises from the actual impacts. -This quantity v² is known as the _mean square_ of the molecular -velocity, and is so used by Waterston. - -In a paper in the _Philosophical Magazine_ for 1858 Waterston gives an -account of his own paper of 1846 in the following terms:--“Mr. Herapath -unfortunately assumed heat or temperature to be represented by the -simple ratio of the velocity instead of the square of the velocity, -being in this apparently led astray by the definition of motion -generally received, and thus was baffled in his attempts to reconcile -his theory with observation. If we make this change in Mr. Herapath’s -definition of heat or temperature--viz., that it is proportional -to the vis-viva or square velocity of the moving particle, not to -the momentum or simple ratio of the velocity--we can without much -difficulty deduce not only the primary laws of elastic fluids, but also -the other physical properties of gases enumerated above in the third -objection to Newton’s hypothesis. [The paper from which the quotation -is taken is on ‘The Theory of Sound.’] In the Archives of the Royal -Society for 1845–46 there is a paper on ‘The Physics of Media that -consist of perfectly “Elastic Molecules in a State of Motion,”’ which -contains the synthetical reasoning on which the demonstration of these -matters rests.... This theory does not take account of the size of the -molecules. It assumes that no time is lost at the impact, and that if -the impacts produce rotatory motion, the vis viva thus invested bears -a constant ratio to the rectilineal vis viva, so as not to require -separate consideration. It does, also, not take account of the probable -internal motion of composite molecules; yet the results so closely -accord with observation in every part of the subject as to leave no -doubt that Mr. Herapath’s idea of the physical constitution of gases -approximates closely to the truth.” - -In his introduction to Waterston’s paper (Phil. Trans., 1892) Lord -Rayleigh writes:--“Impressed with the above passage, and with the -general ingenuity and soundness of Waterston’s views, I took the first -opportunity of consulting the Archives, and saw at once that the memoir -justified the large claims made for it, and that it marks an immense -advance in the direction of the now generally received theory.” - -In the first section of the paper Waterston’s great advance consisted -in the statement that the mean square of the kinetic energy of each -molecule measures the temperature. - -According to this we are thus to put in the pressure equation--½ _m_ -_v_² = T, the temperature, and we have at once--_p_ V = ⅔ N · T. - -Now this equation expresses, as we know, the laws of Boyle and Gay -Lussac. - -The second section discusses the properties of media, consisting of -two or more gases, and arrives at the result that “in mixed media -the mean square molecular velocity is inversely proportional to the -specific weights of the molecules.” This was the great law rediscovered -by Maxwell fifteen years later. With modern notation it may be put -thus:--If _m_₁, _m_₂ be the masses of each molecule of two different -sets of molecules mixed together, then, when a steady state has been -reached, since the temperature is the same throughout, _m_₁ _v_₁² is -equal to _m_₂ _v_₂². The average kinetic energy of each molecule is the -same. - -From this Avogadros’ law follows at once--for if _p_₁, _p_₂ be the -pressures, N₁, N₂ the numbers of molecules per unit volume-- - - _p_₁ = ⅓ N₁ _m_₁ _v_₁², - _p_₂ = ⅓ N₂ _m_₂ _v_₂². - -Hence, if _p_₁, is equal to _p_₂, since _m_₁ _v_₁² is equal to _m_₂ -_v_₂², we must have N₁ equal to N₂, or the number of molecules in equal -volumes of two gases at the same pressure and temperature is the same. -The proof of this proposition given by Waterston is not satisfactory. -On this point, however, we shall have more to say. The third section of -the paper deals with adiabatic expansion, and in it there is an error -in calculation which prevented correct results from being attained. - -At the meeting of the British Association at Ipswich, in 1851, a paper -by J. J. Waterston of Bombay, on “The General Theory of Gases,” was -read. The following is an extract from the Proceedings:-- - -The author “conceives that the atoms of a gas, being perfectly elastic, -are in continual motion in all directions, being constrained within -a limited space by their collisions with each other, and with the -particles of surrounding bodies. - -“The vis viva of these motions in a given portion of a gas constitutes -the quantity of heat contained in it. - -“He shows that the result of this state of motion must be to give the -gas an elasticity proportional to the mean square of the velocity of -the molecular motions, and to the total mass of the atoms contained in -unity of bulk” (unit of volume)--that is to say, to the density of the -medium. - -“The elasticity in a given gas is the measure of temperature. -Equilibrium of pressure and heat between two gases takes place when the -number of atoms in unit of volume is equal and the vis viva of each -atom equal. Temperature, therefore, in all gases is proportional to the -mass of one atom multiplied by the mean square of the velocity of the -molecular motions, being measured from an absolute zero 491° below the -zero of Fahrenheit’s thermometer.” - -It appears, therefore, from these extracts that the discovery of the -laws that temperature is measured by the mean kinetic energy of a -single molecule, and that in a mixture of gases the mean kinetic energy -of each molecule is the same for each gas, is due to Waterston. They -were contained in his paper of 1846, and published by him in 1851. Both -these papers, however, appear to have been unnoticed by all subsequent -writers until 1892. - -Meanwhile, in 1848, Joule’s attention was called by his experiments -to the question, and he saw that Herapath’s result gave a means of -calculating the mean velocity of the molecules of a gas. For according -to the result given above, _p_ = ⅓ _ρ v_²; thus _v_² = 3 _p/ρ_, and _p_ -and _ρ_ being known, we find _v_². Thus for hydrogen at freezing-point -and atmospheric pressure Joule obtains for _v_ the value 6,055 feet per -second, or, roughly, six times the velocity of sound in air. - -Clausius was the next writer of importance on the subject. His first -paper is in “Poggendorff’s Annalen,” vol. c., 1857, “On the Kind -of Motion we call Heat.” It gives an exposition of the theory, and -establishes the fact that the kinetic energy of the translatory motion -of a molecule does not represent the whole of the heat it contains. If -we look upon a molecule as a small solid we must consider the energy it -possesses in consequence of its rotation about its centre of gravity, -as well as the energy due to the motion of translation of the whole. - -Clausius’ second paper appeared in 1859. In it he considers the average -length of the path of a molecule during the interval between two -collisions. He determines this path in terms of the average distance -between the molecules and the distance between the centres of two -molecules at the time when a collision is taking place. - -These two papers appear to have attracted Maxwell’s attention to the -matter, and his first paper, entitled “Illustrations of the Dynamical -Theory of Gases,” was read to the British Association at Aberdeen and -Oxford in 1859 and 1860, and appeared in the _Philosophical Magazine_, -January and July, 1860. - -In the introduction to this paper Maxwell points out, while there was -then no means of measuring the quantities which occurred in Clausius’ -expression for the mean free path, “the phenomena of the internal -friction of gases, the conduction of heat through a gas, and the -diffusion of one gas through another, seem to indicate the possibility -of determining accurately the mean length of path which a particle -describes between two collisions. In order, therefore, to lay the -foundation of such investigations on strict mechanical principles,” he -continues, “I shall demonstrate the laws of motion of an indefinite -number of small, hard and perfectly elastic spheres acting on one -another only during impact.” - -Maxwell then proceeds to consider in the first case the impact of two -spheres. - -But a gas consists of an indefinite number of molecules. Now it is -impossible to deal with each molecule individually, to trace its -history and follow its path. In order, therefore, to avoid this -difficulty Maxwell introduced the statistical method of dealing with -such problems, and this introduction is the first great step in -molecular theory with which his name is connected. - -He was led to this method by his investigation into the theory of -Saturn’s rings, which had been completed in 1856, and in which he -had shown that the conditions of stability required the supposition -that the rings are composed of an indefinite number of free particles -revolving round the planet, with velocities depending on their -distances from the centre. These particles may either be arranged in -separate rings, or their motion may be such that they are continually -coming into collision with each other. - -As an example of the statistical method, let us consider a crowd -of people moving along a street. Taken as a whole the crowd moves -steadily forwards. Any individual in the crowd, however, is jostled -backwards and forwards and from side to side; if a line were drawn -across the street we should find people crossing it in both directions. -In a considerable interval more people would cross it, going in the -direction in which the crowd is moving, than in the other, and the -velocity of the crowd might be estimated by counting the number which -crossed the line in a given interval. This velocity so found would -differ greatly from the velocity of any individual, which might have -any value within limits, and which is continually changing. If we knew -the velocity of each individual and the number of individuals we could -calculate the average velocity, and this would agree with the value -found by counting the resultant number of people who cross the line in -a given interval. - -Again, the people in the crowd will naturally fall into groups -according to their velocities. At any moment there will be a certain -number of people whose velocities are all practically equal, or, to be -more accurate, do not differ among themselves by more than some small -quantity. The number of people at any moment in each of these groups -will be very different. The number in any group, which has a velocity -not differing greatly from the mean velocity of the whole, will be -large; comparatively few will have either a very large or a very small -velocity. - -Again, at any moment, individuals are changing from one group to -another; a man is brought to a stop by some obstruction, and his -velocity is considerably altered--he passes from one group to a -different one; but while this is so, if the mean velocity remains -constant, and the size of the crowd be very great, the number of people -at any moment in a given group remains unchanged. People pass from that -group into others, but during any interval the same number pass back -again into that group. - -It is clear that if this condition is satisfied the distribution is -a steady one, and the crowd will continue to move on with the same -uniform mean velocity. - -Now, Maxwell applies these considerations to a crowd of perfectly -elastic spheres, moving anyhow in a closed space, acting upon each -other only when in contact. He shows that they may be divided into -groups according to their velocities, and that, when the steady state -is reached, the number in each group will remain the same, although the -individuals change. Moreover, it is shown that, if A and B represent -any two groups, the state will only be steady when the numbers which -pass from the group A to the group B are equal to the numbers which -pass back from the group B to the group A. This condition, combined -with the fact that the total kinetic energy of the motion remains -unchanged, enables him to calculate the number of particles in any -group in terms of the whole number of particles, the mean velocity, and -the actual velocity of the group. - -From this an accurate expression can be found for the pressure of the -gas, and it is proved that the value found by others, on the assumption -that all the particles were moving with a common velocity, is correct. -Previous to this paper of Maxwell’s it had been realised that the -velocities could not be uniform throughout. There had been no attempt -to determine the distribution of velocity, or to submit the problem to -calculation, making allowance for the variations in velocity. - -Maxwell’s mathematical methods are, in their generality and elegance, -far in advance of anything previously attempted in the subject. - -So far it has been assumed that the particles in the vessel are all -alike. Maxwell next takes the case of a mixture of two kinds of -particles, and inquires what relation must exist between the average -velocities of these different particles, in order that the state may be -steady. - -Now, it can be shown that when two elastic spheres impinge the effect -of the impact is always such as to reduce the difference between their -kinetic energies. - -Hence, after a very large number of impacts the kinetic energies of the -two balls must be the same; the steady state, then, will be reached -when each ball has the same kinetic energy. - -Thus if _m_₁, _m_₂ be the masses of the particles in the two sets -respectively, _v_₁, _v_₂ their mean velocities we must have finally-- - - ½ _m_₁ _v_₁² = ½ _m_₂ _v_₂² - -This is the second of the two great laws enunciated by Waterston in -1845 and 1851, but which, as we have seen, had remained unknown until -1859, when it was again given by Maxwell. - -Now, when gases are mixed their temperatures become equal. Hence we -conclude, in Maxwell’s words, “that the physical condition which -determines that the temperature of two gases shall be the same, is that -the mean kinetic energy of agitation of the individual molecules of the -two gases are equal.” - -Thus, as the result of Maxwell’s more exact researches on the motion of -a system of spherical particles, we find that we again can obtain the -equations-- - - T = ½ _mv_² - _p_ = ⅓ N _mv_² = ⅔ NT = ⅔ _ρ_ T/_m_ - -From these results we obtain as before the laws of Boyle, Charles and -Avrogadro. - -Again if _σ_ be the specific heat of the gas at constant volume, the -quantity of heat required to raise a single molecule of mass _m_ one -degree will be _σ_ _m_. - -Thus, when a molecule is heated, the kinetic energy must increase by -this amount. But the increase of temperature, which in this case is 1°, -is measured by the increase of kinetic energy of the single molecule. -Hence the amount of heat required to raise the temperature of a single -molecule of all gases 1° is the same. Thus the quantity _σ_ _m_ is the -same for all gases; or, in other words, the specific heat of a gas is -inversely proportional to the mass of its individual molecules. The -density of a gas--since the number of molecules per unit volume at -a given pressure and temperature is the same for all gases--is also -proportional to the mass of each individual molecule. Thus the specific -heats of all gases are inversely proportional to their densities. -This is the law discovered experimentally by Dulong and Petit to be -approximately true for a large number of substances. - - * * * * * - -In the next part of the paper Maxwell proceeded to determine the -average number of collisions in a given time, and hence, knowing the -velocities, to determine, in terms of the size of the particles and -their numbers, the mean free path of a particle; the result so found -differed somewhat from that already obtained by Clausius. - -Having done this he showed how, by means of experiments on the -viscosity of gases, the length of the mean free path could be -determined. - -An illustration due to Professor Balfour Stewart will perhaps make this -clear. Let us suppose we have two trains running with uniform speed in -opposite directions on parallel lines, and, further, that the engines -continue to work at the same rate, developing just sufficient energy to -overcome the resistance of the line, etc., and to maintain the speed -constant. Now suppose passengers commence to jump across from one train -to the other. Each man carries with him his own momentum, which is in -the opposite direction to that of the train into which he jumps; the -result is that the momentum of each train is reduced by the process; -the velocities of the two decrease; it appears as though a frictional -force were acting between the two. Maxwell suggests that a similar -process will account for the apparent viscosity of gases. - -Consider two streams of gas, moving in opposite directions one over -the other; it is found that in each case the layers of gas near the -separating surface move more slowly than those in the interior of -the streams; there is apparently a frictional force between the two -streams along this surface, tending to reduce their relative velocity. -Maxwell’s explanation of this is that at the common surface particles -from the one stream enter the other, and carry with them their own -momentum; thus near this surface the momentum of each stream is -reduced, just as the momentum of the trains is reduced by the people -jumping across. Internal friction or viscosity is due to the diffusion -of momentum across this common surface. The effect does not penetrate -far into the gas, for the particles soon acquire the velocity of the -stream to which they have come. - -Now, the rate at which the momentum is diffused will measure the -frictional force, and will depend on the mean free path of the -particles. If this is considerable, so that on the average a particle -can penetrate a considerable distance into the second gas before a -collision takes place and its motion is changed, the viscosity will be -considerable; if, on the other hand, the mean free path is small, the -reverse will be true. Thus it is possible to obtain a relation between -the mean free path and the coefficient of viscosity, and from this, if -the coefficient of viscosity be known, a value for the mean free path -can be found. - -Maxwell, in the paper under discussion, was the first to do this, -and, using a value found by Professor Stokes for the coefficient of -viscosity, obtained as the length of the mean free path of molecules -of air 1/447000 of an inch, while the number of collisions per second -experienced by each molecule is found to be about 8,077,200,000. - -Moreover, it appeared from his theory that the coefficient of viscosity -should be independent of the number of molecules of gas present, so -that it is not altered by varying the density. This result Maxwell -characterises as startling, and he instituted an elaborate series of -experiments a few years later with a view of testing it. The reason -for this result will appear if we remember that, when the density is -decreased, the mean free path is increased; relatively, then, to the -total number of molecules present, the number which cross the surface -in a given time is increased. And it appears from Maxwell’s result that -this relative increase is such that the total number crossing remains -unchanged. Hence the momentum conveyed across each unit area per second -remains the same, in spite of the decrease in density. - -Another consequence of the same investigation is that the coefficient -of viscosity is proportional to the mean velocity of the molecules. -Since the absolute temperature is proportional to the square of the -velocity, it follows that the coefficient of viscosity is proportional -to the square root of the absolute temperature. - -The second part of the paper deals with the process of diffusion of two -or more kinds of moving particles among one another. - -If two different gases are placed in two vessels separated by a porous -diaphragm such as a piece of unglazed earthenware, or connected by -means of a narrow tube, Graham had shewn that, after sufficient time -has elapsed, the two are mixed together. The same process takes place -when two gases of different density are placed together in the same -vessel. At first the denser gas may be at the bottom, the less dense -above, but after a time the two are found to be uniformly distributed -throughout. - -Maxwell attempted to calculate from his theory the rate at which -the diffusion takes place in these cases. The conditions of most of -Graham’s experiments were too complicated to admit of direct comparison -with the theory, from which it appeared that there is a relation -between the mean free path and the rate of diffusion. One experiment, -however, was found, the conditions of which could be made the subject -of calculation, and from it Maxwell obtained as the value of the mean -free path in air 1/389000 of an inch. - -The number was close enough to that found from the viscosity to afford -some confirmation of his theory. - -However, a few years later Clausius criticised the details of this -part of the paper, and Maxwell, in his memoir of 1866, admits the -calculation to have been erroneous. The main principles remained -unaffected, the molecules pass from one gas to the other, and this -constitutes diffusion. - -Now, suppose we have two sets of particles in contact of such a nature -that the mean kinetic energy of the one set is different from that of -the other; the temperatures of the two will then be different. These -two sets will diffuse into each other, and the diffusing particles will -carry with them their kinetic energy, which will gradually pass from -those which have the greater energy to those which have the less, until -the average kinetic energy is equalised throughout. But the kinetic -energy of translation is the heat of the particles. This diffusion of -kinetic energy is a diffusion of heat by conduction, and we have here -the mechanical theory of the conduction of heat in a gas. - -Maxwell obtained an expression, which, however, he afterwards modified, -for the conductivity of a gas in terms of the mean free path. It -followed from this that the conductivity of air was only about 1/7000 -of that of copper. - -Thus the diffusion of gases, the viscosity of gases, and the conduction -of heat in gases, are all connected with the diffusion of the particles -carrying with them their momenta and their energy; while values of the -mean free path can be obtained from observations on any one of these -properties. - -In the third part of his paper Maxwell considers the consequences -of supposing the particles not to be spherical. In this case the -impacts would tend to set up a motion of rotation in the particles. -The direction of the force acting on any particle at impact would not -necessarily pass through its centre; thus by impact the velocity of its -centre would be changed, and in addition the particles would be made to -spin. Some part, therefore, of the energy of the particles will appear -in the form of the translational energy of their centres, while the -rest will take the form of rotational energy of each particle about its -centre. - -It follows from Maxwell’s work that for each particle the average value -of these two portions of energy would be equal. The total energy will -be half translational and half rotational. - -This theorem, in a more general form which was afterwards given to -it, has led to much discussion, and will be again considered later. -For the present we will assume it to be true. Clausius had already -called attention to the fact that some of the energy must be rotational -unless the molecules be smooth spheres, and had given some reasons -for supposing that the ratio of the whole energy to the energy of -translation is in a steady state a constant. Maxwell shows that for -rigid bodies this constant is 2. Let us denote it for the present by -the symbol β. Thus, if the translational energy of a molecule is ½ _m_ -_v_², its whole energy is ½ β _m_ _v_². - -The temperature is still measured by the translational energy, or ½ _m_ -_v_²; the heat depends on the whole energy. Hence if H represent the -amount of heat--measured as energy--contained by a single molecule, -and T its temperature, we have-- - - H = βT - -From this it can be shewn[50] that if γ represent the ratio of the -specific heat of a gas at constant pressure to the specific heat at -constant volume, then-- - - β = ⅔ 1/(γ-1) - -For air and some other gases the value of γ has been shown to be 1·408. -From this it follows that β = 1·634. Now, Maxwell’s theory required -that for smooth hard particles, approximately spherical in shape, β -should be 2, and hence he concludes “we have shown that a system of -such particles could not possibly satisfy the known relation between -the two specific heats of all gases.” - -Since this statement was made many more experiments on the value of γ -have been undertaken; it is not equal to 1·408 for _all_ gases. Hence -the value of β is different for various gases. - -It is of some importance to notice that the value of β just found for -air is very approximately 1·66 or 5/3. - -For mercury vapour the value of γ has been shown by Kundt to be 1·33 -or 1⅓, and hence β is equal to 1. Thus all the energy of a particle of -mercury vapour is translational, and its behaviour in this respect is -consistent with the assumption that a particle of mercury vapour is a -smooth sphere. - -The two results of this theory which seemed to lend themselves most -readily to experimental verification were (1) that the viscosity of -a gas is independent of its density, and (2) that it is proportional -to the square root of the absolute temperature. The next piece -of work connected with the theory was an attempt to test these -consequences, and a description of the experiments was published in the -“Philosophical Transactions” for 1865, in a paper on the “Viscosity -or Internal Friction of Air and other Gases,” and forms the Bakerian -lecture for that year. - -The first result was completely proved. It is shewn that the value of -the coefficient[51] of viscosity “is the same for air at 0·5 inch and -at 30 inches pressure, provided that the temperature remains the same.” - -It was clear also that the viscosity depended on the temperature, -and the results of the experiments seemed to show that it was nearly -proportional to the absolute temperature. Thus for two temperatures, -185° Fah. and 51° Fah., the ratio of the two coefficients found was -1·2624; the ratio of the two temperatures, each measured from absolute -zero, is 1·2605. - -This result, then, does not agree with the hypothesis that a gas -consists of spherical molecules acting only on each other by a kind of -impact, for, if this were so, the coefficient would, as we have seen, -depend on the square root of the absolute temperature. But Maxwell’s -result, connecting viscosity with the first power of the absolute -temperature, has not been confirmed by other investigators. According -to it we should have as the relation between μ, the coefficient of -viscosity at t° and μ₀, that at zero the equation-- - - μ = μ₀ (1 + .00365 t). - -The most recent results of Professor Holman (_Philosophical Magazine_, -Vol. xxi., p. 212) give-- - - μ = μ₀ (1 + .00275 t - .00000034 t²). - -And results similar to this are given by O. E. Meyer, Puluj, and -Obermeyer. Maxwell’s coefficient ·00365 is too large, but ·00182, the -coefficient obtained by supposing the viscosity proportional to the -square root of the temperature, would be too small. - -It still remains true, therefore, that the laws of the viscosity of -gases cannot be explained by the hypothesis of the impact of hard -spheres; but some deductions drawn by Maxwell in his next paper from -his supposed law of proportionality to the first power of the absolute -temperature require modification. - -It was clear from his experiments just described that the simple -hypothesis of the impact of elastic bodies would not account for all -the phenomena observed. Accordingly, in 1866, Maxwell took up the -problem in a more general form in his paper on the “Dynamical Theory of -Gases,” Phil. Trans., 1866. - -In it he considered the molecules of the gas not as elastic spheres -of definite radius, but as small bodies, or groups of smaller -molecules, repelling one another with a force whose direction always -passes very nearly through the centre of gravity of the molecules, -and whose magnitude is represented very nearly by some function of -the distance of the centres of gravity. “I have made,” he continues, -“this modification of the theory in consequence of the results of my -experiments on the viscosity of air at different temperatures, and I -have deduced from these experiments that the repulsion is inversely as -the fifth power of the distance.” - -Since more recent observation has shown that the numerical results of -Maxwell’s work connecting viscosity and temperature are erroneous, this -last deduction does not hold; the inverse fifth power law of force -will not give the correct relation between viscosity and temperature. -Maxwell himself at a later date, “On the Stresses in Rarefied Gases,” -Phil. Trans., 1879, realised this; but even in this last paper he -adhered to the fifth power law because it leads to an important -simplification in the equations to be dealt with. - -The paper of 1866 is chiefly important because it contains for the -first time the application of general dynamical methods to molecular -problems. The law of the distribution of velocities among the molecules -is again investigated, and a result practically identical with that -found for the elastic spheres is arrived at. In obtaining this -conclusion, however, it is assumed that the distribution of velocities -is uniform in all directions about any point, whatever actions may be -taking place in the gas. If, for example, the temperature is different -at different points, then, for a given velocity, all directions are not -equally probable. Maxwell’s expression, therefore, for the number of -molecules which at any moment have a given velocity only applies to the -permanent state in which the distribution of temperature is uniform. -When dealing, for example, with the conduction of heat, a modification -of the expression is necessary. This was pointed out by Boltzmann.[52] - -In the paper of 1866, Maxwell applies his generalised results to the -final distribution of two gases under the action of gravity, the -equilibrium of temperature between two gases, and the distribution of -temperature in a vertical column. These results are, as he states, -independent of the law of force between the molecules. The dynamical -causes of diffusion viscosity and conduction of heat are dealt with, -and these involve the law of force. - -It follows also from the investigation that, on the hypotheses assumed -as its basis, if two kinds of gases be mixed, the difference between -the average kinetic energies of translation of the gases of each kind -diminishes rapidly in consequence of the action between the two. The -average kinetic energy of translation, therefore, tends to become the -same for each kind of gas, and as before, it is this average energy of -translation which measures the temperature. - -A molecule in the theory is a portion of a gas which moves about as a -single body. It may be a mere point, a centre of force having inertia, -capable of doing work while losing velocity. There may be also in each -molecule systems of several such centres of force bound together by -their mutual actions. Again, a molecule may be a small solid body of -determinate form; but in this case we must, as Maxwell points out, -introduce a new set of forces binding together the parts of each -molecule: we must have a molecular theory of the second order. In any -case, the most general supposition made is that a molecule consists of -a series of parts which stick together, but are capable of relative -motion among each other. - -In this case the kinetic energy of the molecule consists of the energy -of its centre of gravity, together with the energy of its component -parts, relative to its centre of gravity.[53] - -Now Clausius had, as we have seen, given reasons for believing that the -ratio of the whole energy of a molecule to the energy of translation of -its centre of gravity tends to become constant. We have already used β -to denote this constant. Thus, while the temperature is measured by the -average kinetic energy of translation of the centre of gravity of each -molecule, the heat contained in a molecule is its whole energy, and is -β times this quantity. Thus the conclusions as to specific heat, etc., -already given on page 130, apply in this case, and in particular we -have the result that if γ be the ratio of the specific heat at constant -pressure to that at constant volume, then-- - - β = ⅔ 1/(γ-1) - -Maxwell’s theorem of the distribution of kinetic energy among a system -of molecules applied, as he gave it in 1866, to the kinetic energy of -translation of the centre of gravity of each molecule. Two years later -Dr. Boltzmann, in the paper we have already referred to, extended -it (under certain limitations) to the parts of which a molecule is -composed. According to Maxwell the average kinetic energy of the centre -of gravity of each molecule tends to become the same. According to -Boltzmann the average kinetic energy of each part of the molecule tends -to become the same. - -Maxwell, in the last paper he wrote on the subject (“On Boltzmann’s -Theorem on the Average Distribution of Energy in a System of -Material Points,” Camb. Phil. Trans., XII.), took up this problem. -Watson had given a proof of it in 1876 differing from Boltzmann’s, -but still limited by the stipulation that the time, during which a -particle is encountering other particles, is very small compared with -the time during which there is no sensible action between it and -other particles, and also that the time during which a particle is -simultaneously within the distance of more than one other particle may -be neglected. - -Maxwell claims that his proof is free from any such limitation. The -material points may act on each other at all distances, and according -to any law which is consistent with the conservation of energy; they -may also be acted on by forces external to the system, provided these -are consistent with that law. - -The only assumption which is necessary for the direct proof is that -the system, if left to itself in its actual state of motion, will -sooner or later pass through every phase which is consistent with the -conservation of energy. - -In this paper Maxwell finds in a very general manner an expression for -the number of molecules which at any time have a given velocity, and -this, when simplified by the assumptions of the former papers, reduces -to the form already found. He also shows that the average kinetic -energy corresponding to any one of the variables which define his -system is the same for every one of the variables of his system. - -Thus, according to this theorem, if each molecule be a single small -solid body, six variables will be required to determine the position -of each, three variables will give us the position of the centre of -gravity of the molecule, while three others will determine the position -of the body relative to its centre of gravity. If the six variables -be properly chosen, the kinetic energy can be expressed as a sum of -six squares, one square corresponding to each variable. According to -the theorem the part of the kinetic energy depending on each square is -the same. Thus, the whole energy is six times as great as that which -arises from any one of the variables. The kinetic energy of translation -is three times as great as that arising from each variable, for it -involves the three variables which determine the position of the centre -of gravity. Hence, if we denote by K the kinetic energy due to one -variable, the whole energy is 6 K, and the translational energy is 3 K; -thus, for this case-- - - β = 6K/3K = 2 - -Or, again, if we suppose that the molecule is such that _m_ variables -are required to determine its position relatively to its centre of -gravity, since 3 are needed to fix the centre of gravity, the total -number of variables defining the position of the molecule is _m_ + 3, -and it is said to have _m_ + 3 degrees of freedom. Hence, in this case, -its total energy is (_m_ + 3) K and its energy of translation is 3 K, -thus we find-- - - β = (_m_ + 3)/3 - - Hence γ = 1 + 2/(_m_ + 3) = 1 + 2/_n_ - -if _n_ be the number of degrees of freedom of the molecule. - -Thus, if this Boltzmann-Maxwell theorem be true, the specific heat of a -gas will depend solely on the number of degrees of freedom of each of -its molecules. For hard rigid bodies we should have _n_ equal to 6, and -hence γ = 1·333. Now the fact that this is not the value of γ for any -of the known gases is a fundamental difficulty in the way of accepting -the complete theory. - -Boltzmann has called attention to the fact that if _n_ be equal to -five, then γ has the value 1·40. And this agrees fairly with the value -found by experiment for air, oxygen, nitrogen, and various other gases. -We will, however, return to this point shortly. - -There is, perhaps, no result in the domain of physical science in -recent years which has been more discussed than the two fundamental -theorems of the molecular theory which we owe to Maxwell and to -Boltzmann. - -The two results in question are (1) the expression for the number of -molecules which at any moment will have a given velocity, and (2) the -proposition that the kinetic energy is ultimately equally divided -among all the variables which determine the system. - -With regard to (1) Maxwell showed that his error law was one possible -condition of permanence. If at any moment the velocities are -distributed according to the error law, that distribution will be a -permanent one. He did not prove that such a distribution is the only -one which can satisfy all the conditions of the problem. - -The proof that this law is a necessary, as well as a sufficient, -condition of permanence was first given by Boltzmann, for a single -monatomic gas in 1872, for a mixture of such gases in 1886, and for a -polyatomic gas in 1887. Other proofs have been given since by Watson -and Burbury. It would be quite beyond the limits of this book to go -into the question of the completeness or sufficiency of the proofs. The -discussion of the question is still in progress. - -The British Association Report for 1894 contains an important -contribution to the question, in the shape of a report by Mr. G. H. -Bryan, and the discussion he started at Oxford by reading this report -has been continued in the pages of _Nature_ and elsewhere since that -time. - -Mr. Bryan shows in the first place what may be the nature of the -systems of molecules to which the results will apply, and discusses -various points of difficulty in the proof. - -The theorem in question, from which the result (1) follows as a simple -deduction, has been thus stated by Dr. Larmor.[54] - -“There exists a positive function belonging to a group of molecules -which, as they settle themselves into a steady state--on the average -derived from a great number of configurations--maintains a steady -downward trend. The Maxwell-Boltzmann steady state is the one in which -this function has finally attained its minimum value, and is thus a -unique steady state, it still being borne in mind that this is only a -proposition of averages derived from a great number of instances in -which nothing is conserved in encounters, except the energy, and that -exceptional circumstances may exist, comparatively very few in number, -in which the trend is, at any rate, temporarily the other way.” - -This theorem, when applied to cases of motion, such as that of a gas at -constant temperature enclosed in a rigid envelope impermeable to heat, -appears to be proved. For such a case, therefore, the Maxwell-Boltzmann -law is the only one possible. - -But whether this be so or not, the law first introduced by Maxwell is -one of those possible, and the advance in molecular science due to its -introduction is enormous. - -We come now to the second result, the equal partition of the energy -among all the degrees of freedom of each molecule. Lord Kelvin -has pointed out a flaw in Maxwell’s proof, but Boltzmann showed -(_Philosophical Magazine_, March, 1893) how this flaw can easily -be corrected, and it may be said that in all cases in which the -Boltzmann-Maxwell law of the distribution of velocities holds, -Maxwell’s law of the equal partition of energy holds also. - -Three cases are considered by Mr. Bryan, in which the law of -distribution fails for rigid molecules: the first is when the molecules -have all, in addition to their velocities of agitation, a common -velocity of translation in a fixed direction; the second is when the -gas has a motion of uniform rotation about a fixed axis; while the -third is when each molecule has an axis of symmetry. In this last case -the forces acting during a collision necessarily pass through the -axis of symmetry, the angular velocity, therefore, of any molecule -about this axis remains constant, the number of molecules having a -given angular velocity will remain the same throughout the motion, -and the part of the kinetic energy which depends on this component of -the motion will remain fixed, and will not come into consideration -when dealing with the equal partition of the energy among the various -degrees of freedom. - -Such a molecule has five, and not six, degrees of freedom; three -quantities are needed to determine the position of its centre of -gravity, and two to fix the position of the axis of symmetry. - -In this case, then, as Boltzmann points out, in the expression for the -ratio of the specific heats, we must have _n_ equal to 5, and hence - - γ = 1 + 2/_n_ = 1 + 2/5 = 1·4 - -agreeing fairly with the value found for air and various other -permanent gases. - -For cases, then, in which we consider each atom as a single rigid body, -the Boltzmann-Maxwell theorem appears to give a unique solution, -and the Maxwell law of the distribution of the energy to be in fair -accordance with the results of observation.[55] - -If we can never go further--and it must be admitted that the -difficulties in the way of further advance are enormous--it may, -I think, be claimed for Maxwell that the progress already made is -greatly due to him. Both these laws, for the case of elastic spheres, -are contained in his first paper of 1860; and while it is to the -genius of Boltzmann that we owe their earliest generalisation, and in -particular the proof of the uniqueness of the solution under proper -restrictions, Maxwell’s last paper contributed in no small degree to -the security of the position. Not merely the foundations, but much of -the superstructure of molecular science is his work. - -The difficulties in the way of advance are, as we have said, enormous. -Boltzmann, in one of his papers, has considered the properties of a -complex molecule of a gas, consisting maybe of a number of atoms and -possibly of ether atoms bound with them, and he concludes that such a -molecule will behave in its progressive motion, and in its collisions -with other molecules, nearly like a rigid body. But to quote from Mr. -Bryan: “The case of a polyatomic molecule, whose atoms are capable of -vibrating relative to one another, affords an interesting field for -investigation and speculation. Is the Boltzmann distribution still -unique, or do other permanent distributions exist in which the kinetic -energy is unequally divided?” - -Again, the spectroscope reveals to us vibrations of the ether, which -are connected in some way with the vibrations of the molecules of -gas, whose spectrum we are observing. It seems clear that the law of -equal partition does not apply to these, and yet, if we are to suppose -that the ether vibrations are due to actual vibrations of the atoms -which constitute a molecule, why does it not apply? Where does the -condition come in which leads to failure in the proof? Or, again, -is it, as has been suggested, the fact that the complex spectrum -of a gas represents the terms of a Fourier Series, into which some -elaborate vibration of the atoms is resolved by the ether? or is the -spectrum due simply to electro-magnetic vibrations on the surface of -the molecules--vibrations whose period is determined chiefly by the -size and shape of the molecule, but in which the atoms of which it is -composed take part? There are grave difficulties in the way of either -of these explanations, but we must not let our dread of the task which -remains to be done blind our eyes to the greatness of Maxwell’s work. - -One other important paper, and a number of shorter articles, remain to -be mentioned. - -The Boltzmann-Maxwell law applies only to cases in which the -temperature is uniform throughout. In a paper published in the -Philosophical Transactions for 1879, on “Stresses in Rarefied Gases -Arising from Inequalities of Temperature,” Maxwell deals, among other -matters, with the theory of the radiometer. He shows that the observed -motions will not take place unless gas, in contact with a solid, can -slide along the surface of the solid with a finite velocity between -places where the temperature is different; and in an appendix he proves -that, on certain assumptions regarding the nature of the contact of the -solid and the gas, there will be, even when the pressure is constant, a -flow of gas along the surface from the colder to the hotter parts. - -Among his less important papers bearing on molecular theory must be -mentioned a lecture on “Molecules” to the British Association at its -Bradford meeting; “Scientific Papers of Clerk Maxwell,” vol. ii., p. -361; and another on “The Molecular Constitution of Bodies,” Scientific -Papers, vol. ii., p. 418. - -In this latter, and also in a review in _Nature_ of Van der Waals’ -book on “The Continuity of the Gaseous and Liquid States,”[56] he -explains and discusses Clausius’ virial equation, by means of which the -variations of the permanent gases from Boyle’s law are explained. The -lecture gives a clear account, in Maxwell’s own inimitable style, of -the advances made in the kinetic theory up to the date at which it was -delivered, and puts clearly the difficulties it has to meet. Maxwell -thought that those arising from the known values of the ratio of the -specific heats were the most serious. - -In the articles, “Atomic Constitution of Bodies” and “Diffusion,” in -the ninth edition of the _Encyclopædia Britannica_, we have Maxwell’s -later views on the fundamental assumptions of the molecular theory. - -The text-book on “Heat” contains some further developments of the -theory. In particular he shows how the conclusions of the second law -of thermo-dynamics are connected with the fact that the coarseness of -our faculties will not allow us to grapple with individual molecules. - -The work described in the foregoing chapters would have been sufficient -to secure to Maxwell a distinguished place among those who have -advanced our knowledge; it remains still to describe his greatest work, -his theory of Electricity and Magnetism. - - - - -CHAPTER IX. - -SCIENTIFIC WORK.--ELECTRICAL THEORIES. - - -Clerk Maxwell’s first electrical paper--that on Faraday’s “Lines of -Force”--was read to the Cambridge Philosophical Society on December -10th, 1855, and Part II. on February 11th, 1856. The author was then a -Bachelor of Arts, only twenty-three years in age, and of less than one -year’s standing from the time of taking his degree. - -The opening words of the paper are as follows (Scientific Papers, vol. -i., p. 155):-- - - “The present state of electrical science seems peculiarly - unfavourable to speculation. The laws of the distribution of - electricity on the surface of conductors have been analytically - deduced from experiment; some parts of the mathematical - theory of magnetism are established, while in other parts the - experimental data are wanting; the theory of the conduction of - galvanism, and that of the mutual attraction of conductors, - have been reduced to mathematical formulæ, but have not - fallen into relation with the other parts of the science. No - electrical theory can now be put forth, unless it shows the - connection, not only between electricity at rest and current - electricity, but between the attractions and inductive effects - of electricity in both states. Such a theory must accurately - satisfy those laws, the mathematical form of which is known, - and must afford the means of calculating the effects in the - limiting cases where the known formulæ are inapplicable. - In order, therefore, to appreciate the requirements of the - science, the student must make himself familiar with a - considerable body of most intricate mathematics, the mere - retention of which in the memory materially interferes with - further progress. The first process, therefore, in the - effectual study of the science, must be one of simplification - and reduction of the results of previous investigation to a - form in which the mind can grasp them. The results of this - simplification may take the form of a purely mathematical - formula or of a physical hypothesis. In the first case we - entirely lose sight of the phenomena to be explained; and - though we may trace out the consequences of given laws, we can - never obtain more extended views of the connections of the - subject. If, on the other hand, we adopt a physical hypothesis, - we see the phenomena only through a medium, and are liable - to that blindness to facts and rashness in assumption which - a partial explanation encourages. We must therefore discover - some method of investigation which allows the mind at every - step to lay hold of a clear physical conception, without being - committed to any theory founded on the physical science from - which that conception is borrowed, so that it is neither drawn - aside from the subject in pursuit of analytical subtleties, nor - carried beyond the truth by a favourite hypothesis. - - “In order to obtain physical ideas without adopting a physical - theory we must make ourselves familiar with the existence of - physical analogies. By a physical analogy I mean that partial - similarity between the laws of one science and those of another - which makes each of them illustrate the other. Thus all the - mathematical sciences are founded on relations between physical - laws and laws of numbers, so that the aim of exact science - is to reduce the problems of Nature to the determination of - quantities by operations with members. Passing from the most - universal of all analogies to a very partial one, we find the - same resemblance in mathematical form between two different - phenomena giving rise to a physical theory of light. - - “The changes of direction which light undergoes in passing from - one medium to another are identical with the deviations of the - path of a particle in moving through a narrow space in which - intense forces act. This analogy, which extends only to the - direction, and not to the velocity of motion, was long believed - to be the true explanation of the refraction of light; and we - still find it useful in the solution of certain problems, in - which we employ it without danger as an artificial method. The - other analogy, between light and the vibrations of an elastic - medium, extends much farther, but, though its importance and - fruitfulness cannot be over-estimated, we must recollect that - it is founded only on a resemblance _in form_ between the - laws of light and those of vibrations. By stripping it of its - physical dress and reducing it to a theory of ‘transverse - alternations,’ we might obtain a system of truth strictly - founded on observation, but probably deficient both in the - vividness of its conceptions and the fertility of its method. - I have said thus much on the disputed questions of optics, as - a preparation for the discussion of the almost universally - admitted theory of attraction at a distance. - - “We have all acquired the mathematical conception of these - attractions. We can reason about them and determine their - appropriate forms or formulæ. These formulæ have a distinct - mathematical significance, and their results are found to be - in accordance with natural phenomena. There is no formula - in applied mathematics more consistent with Nature than the - formula of attractions, and no theory better established in - the minds of men than that of the action of bodies on one - another at a distance. The laws of the conduction of heat in - uniform media appear at first sight among the most different in - their physical relations from those relating to attractions. - The quantities which enter into them are _temperature_, _flow - of heat_, _conductivity_. The word _force_ is foreign to the - subject. Yet we find that the mathematical laws of the uniform - motion of heat in homogeneous media are identical in form - with those of attractions varying inversely as the square of - the distance. We have only to substitute _source of heat_ for - _centre of attraction_, _flow of heat_ for _accelerating effect - of attraction_ at any point, and _temperature_ for _potential_, - and the solution of a problem in attractions is transformed - into that of a problem in heat. - - “This analogy between the formulæ of heat and attraction was, I - believe, first pointed out by Professor William Thomson in the - _Cambridge Mathematical Journal_, Vol. III. - - “Now the conduction of heat is supposed to proceed by an - action between contiguous parts of a medium, while the force - of attraction is a relation between distant bodies, and yet, - if we knew nothing more than is expressed in the mathematical - formulæ, there would be nothing to distinguish between the one - set of phenomena and the other. - - “It is true that, if we introduce other considerations and - observe additional facts, the two subjects will assume very - different aspects, but the mathematical resemblance of some - of their laws will remain, and may still be made useful in - exciting appropriate mathematical ideas. - - “It is by the use of analogies of this kind that I have - attempted to bring before the mind, in a convenient and - manageable form, those mathematical ideas which are necessary - to the study of the phenomena of electricity. The methods are - generally those suggested by the processes of reasoning which - are found in the researches of Faraday, and which, though they - have been interpreted mathematically by Professor Thomson and - others, are very generally supposed to be of an indefinite and - unmathematical character, when compared with those employed by - the professed mathematicians. By the method which I adopt, I - hope to render it evident that I am not attempting to establish - any physical theory of a science in which I have hardly made - a single experiment, and that the limit of my design is to - show how, by a strict application of the ideas and methods - of Faraday, the connection of the very different orders of - phenomena which he has discovered may be clearly placed before - the mathematical mind. I shall therefore avoid as much as I can - the introduction of anything which does not serve as a direct - illustration of Faraday’s methods, or of the mathematical - deductions which may be made from them. In treating the simpler - parts of the subject I shall use Faraday’s mathematical methods - as well as his ideas. When the complexity of the subject - requires it, I shall use analytical notation, still confining - myself to the development of ideas originated by the same - philosopher. - - “I have in the first place to explain and illustrate the idea - of ‘lines of force.’ - - “When a body is electrified in any manner, a small body - charged with positive electricity, and placed in any given - position, will experience a force urging it in a certain - direction. If the small body be now negatively electrified, it - will be urged by an equal force in a direction exactly opposite. - - “The same relations hold between a magnetic body and the north - or south poles of a small magnet. If the north pole is urged - in one direction, the south pole is urged in the opposite - direction. - - “In this way we might find a line passing through any point - of space, such that it represents the direction of the - force acting on a positively electrified particle, or on an - elementary north pole, and the reverse direction of the force - on a negatively electrified particle or an elementary south - pole. Since at every point of space such a direction may be - found, if we commence at any point and draw a line so that, - as we go along it, its direction at any point shall always - coincide with that of the resultant force at that point, this - curve will indicate the direction of that force for every point - through which it passes, and might be called on that account a - _line of force_. We might in the same way draw other lines of - force, till we had filled all space with curves indicating by - their direction that of the force at any assigned point. - - “We should thus obtain a geometrical model of the physical - phenomena, which would tell us the _direction_ of the force, - but we should still require some method of indicating the - _intensity_ of the force at any point. If we consider these - curves not as mere lines, but as fine tubes of variable section - carrying an incompressible fluid, then, since the velocity of - the fluid is inversely as the section of the tube, we may make - the velocity vary according to any given law, by regulating the - section of the tube, and in this way we might represent the - intensity of the force as well as its direction by the motion - of the fluid in these tubes. This method of representing the - intensity of a force by the velocity of an imaginary fluid in - a tube is applicable to any conceivable system of forces, but - it is capable of great simplification in the case in which - the forces are such as can be explained by the hypothesis of - attractions varying inversely as the square of the distance, - such as those observed in electrical and magnetic phenomena. - In the case of a perfectly arbitrary system of forces, there - will generally be interstices between the tubes; but in the - case of electric and magnetic forces it is possible to arrange - the tubes so as to leave no interstices. The tubes will then be - mere surfaces, directing the motion of a fluid filling up the - whole space. It has been usual to commence the investigation of - the laws of these forces by at once assuming that the phenomena - are due to attractive or repulsive forces acting between - certain points. We may, however, obtain a different view of the - subject, and one more suited to our more difficult inquiries, - by adopting for the definition of the forces of which we treat, - that they may be represented in magnitude and direction by the - uniform motion of an incompressible fluid. - - “I propose, then, first to describe a method by which the - motion of such a fluid can be clearly conceived; secondly - to trace the consequences of assuming certain conditions of - motion, and to point out the application of the method to some - of the less complicated phenomena of electricity, magnetism, - and galvanism; and lastly, to show how by an extension of these - methods, and the introduction of another idea due to Faraday, - the laws of the attractions and inductive actions of magnets - and currents may be clearly conceived, without making any - assumptions as to the physical nature of electricity, or adding - anything to that which has been already proved by experiment. - - “By referring everything to the purely geometrical idea of the - motion of an imaginary fluid, I hope to attain generality and - precision, and to avoid the dangers arising from a premature - theory professing to explain the cause of the phenomena. - If the results of mere speculation which I have collected - are found to be of any use to experimental philosophers, in - arranging and interpreting their results, they will have served - their purpose, and a mature theory, in which physical facts - will be physically explained, will be formed by those who by - interrogating Nature herself can obtain the only true solution - of the questions which the mathematical theory suggests.” - -The idea was a bold one: for a youth of twenty-three to explain, by -means of the motions of an incompressible fluid, some of the less -complicated phenomena of electricity and magnetism, to show how -the laws of the attractions of magnets and currents may be clearly -conceived without making any assumption as to the physical nature of -electricity, or adding anything to that which has already been proved -by experiment. - -It may be useful to review in a very few words the position of -electrical theory[57] in 1855. - -Coulomb’s experiments had established the fundamental facts of -electrostatic attraction and repulsion, and Coulomb himself, about -1785, had stated a theory based on these experiments which could “only -be attacked by proving his experimental results to be inaccurate.”[58] - -Coulomb supposes the existence of two electric fluids, the theory -developed previously by Franklin, but says-- - - “Je préviens pour mettre la théorie qui va suivre à l’abri de - toute dispute systématique, que dans la supposition de deux - fluides électriques, je n’ai autre intention que de présenter - avec le moins d’éléments possible les résultats du calcul et - de l’expérience, et non d’indiquer les véritables causes de - l’électricité.” - -Cavendish was working in England about the same time as Coulomb, but -he published very little, and the value and importance of his work -was not recognised until the appearance in 1879 of the “Electrical -Researches of Henry Cavendish,” edited by Clerk Maxwell. - -Early in the present century the application of mathematical analysis -to electrical problems was begun by Laplace, who investigated the -distribution of electricity on spheroids, and about 1811 Poisson’s -great work on the distribution of electricity on two spheres placed -at any given distance apart was published. Meanwhile the properties -of the electric current were being investigated. Galvani’s discovery -of the muscular contraction in a frog’s leg, caused by the contact of -dissimilar metals, was made in 1790. Volta invented the voltaic pile in -1800, and Oersted in 1820 discovered that an electric current produced -magnetic force in its neighbourhood. On this Ampère laid the foundation -of his theory of electro-dynamics, in which he showed how to calculate -the forces between circuits carrying currents from an assumed law of -force between each pair of elements of the circuits. His experiments -proved that the consequences which follow from this law are consistent -with all the observed facts. They do not prove that Ampère’s law alone -can explain the facts. - -Maxwell, writing on this subject in the “Electricity an Magnetism,” -vol. ii., p. 162, says-- - - “The experimental investigation by which Ampère established the - laws of the mechanical action between electric currents is one - of the most brilliant achievements in science. - - “The whole, theory and experiment, seems as if it had leaped - full grown and full armed from the brain of the ‘Newton - of Electricity.’ It is perfect in form and unassailable in - accuracy, and it is summed up in a formula from which all the - phenomena may be deduced, and which must always remain the - cardinal formula of electro-dynamics. - - “The method of Ampère, however, though cast into an inductive - form, does not allow us to trace the formation of the ideas - which guided it. We can scarcely believe that Ampère really - discovered the law of action by means of the experiments which - he describes. We are led to suspect, what, indeed, he tells us - himself, that he discovered the law by some process which he - has not shown us, and that when he had afterwards built up a - perfect demonstration, he removed all traces of the scaffolding - by which he had built it.” - -The experimental evidence for Ampère’s theory, so far, at least, as -it was possible to obtain it from experiments on closed circuits, was -rendered unimpeachable by W. Weber about 1846, while in the previous -year Grassman and F. E. Neumann both published laws for the attraction -between two elements of current which differ from that of Ampère, but -lead to the same result for closed circuits. In a paper published in -1846 Weber announced his hypothesis connecting together electrostatic -and electro-dynamic action. In this paper he supposed that the force -between two particles of electricity depends on the motion of the -particles as well as on their distance apart. A somewhat similar -theory was proposed by Gauss and published after his death in his -collected works. It has been shown, however, that Gauss’ theory is -inconsistent with the conservation of energy. Weber’s theory avoids -this inconsistency and leads, for closed circuits, to the same results -as Ampère. It has been proved, however, by Von Helmholtz, that, under -certain circumstances, according to it, a body would behave as though -its mass were negative--it would move in a direction opposite to that -of the force.[59] - -Since 1846 many other theories have been proposed to explain Ampère’s -laws. Meanwhile, in 1821, Faraday observed that under certain -circumstances a wire carrying a current could be kept in continuous -rotation in a magnetic field by the action between the magnets and -the current. In 1824 Arago observed the motion of a magnet caused by -rotating a copper disc in its neighbourhood, while in 1831 Faraday -began his experimental researches into electro-magnetic induction. -About the same period Joseph Henry, of Washington, was making, -independently of Faraday, experiments of fundamental importance on -electro-magnetic induction, but sufficient attention was not called to -his work until comparatively recent years. - -In 1833 Lenz made some important researches, which led him to discover -the connection between the direction of the induced currents and -Ampère’s laws, summed up in his rule that the direction of the induced -current is always such as to oppose by its electro-magnetic action the -motion which induces it. - -In 1845 F. E. Neumann developed from this law the mathematical theory -of electro-magnetic induction, and about the same time W. Weber showed -how it might be deduced from his elementary law of electrical action. - -The great name of Von Helmholtz first appears in connection with this -subject in 1851, but of his writings we shall have more to say at a -later stage. - -Meanwhile, during the same period, various writers, Murphy, Plana, -Charles, Sturm, and Gauss, extended Poisson’s work on electrostatics, -treating the questions which arose as problems in the distribution of -an attracting fluid, attracting or repelling according to Newton’s law, -though here again the greatest advances were made by a self-taught -Nottingham shoemaker, George Green by name, in his paper “On the -Application of Mathematical Analysis to the Theories of Electricity and -Magnetism,” 1828. - -Green’s researches, Lord Kelvin writes, “have led to the elementary -proposition which must constitute the legitimate foundation of every -perfect mathematical structure that is to be made from the materials -furnished by the experimental laws of Coulomb.” - -Green, it may be remarked, was the inventor of the term Potential. -His essay, however, lay neglected from 1828, until Lord Kelvin called -attention to it in 1845. Meanwhile, some of its most important results -had been re-discovered by Gauss and Charles and Thomson himself. - -Until about 1845, the experimental work on which these mathematical -researches in electrostatics were based was that of Coulomb. An -electrified body is supposed to have a charge of some imponderable -fluid “electricity.” Particles of electricity repel each other -according to a certain law, and the fluid distributes itself in -equilibrium over the surface of any charged conductor in accordance -with this law. There are on this theory two opposite kinds of electric -fluid, positive and negative, two charges of the same kind repel, two -charges of opposite kinds attract; the repulsion or attraction is -proportional to the product of the charges, and inversely proportional -to the square of the distance between them. - -The action between two charges is action at a distance taking place -across the space which separates the two. - -Faraday, in 1837, in the eleventh series of his “Experimental -Researches,” published his first paper on “Electrostatic Induction.” -He showed--as indeed Cavendish had proved long previously, though the -result remained unpublished--that the force between two charged bodies -will depend on the insulating medium which surrounds them, not merely -on their shape and position. Induction, as he expresses it, takes place -along curved lines, and is an action of contiguous particles; these -curved lines he calls the “lines of force.” - -Discussing these researches in 1845, Lord Kelvin writes[60]:-- - - “Mr. Faraday’s researches ... were undertaken with a view to - test an idea which he had long possessed that the forces of - attraction and repulsion exercised by free electricity are not - the resultants of actions exercised at a distance, but are - propagated by means of molecular action among the contiguous - particles of the insulating medium surrounding the electrified - bodies, which he therefore calls the dielectric. By this idea - he has been led to some very remarkable views upon induction, - or, in fact, upon electrical action in general. As it is - impossible that the phenomena observed by Faraday can be - incompatible with the results of experiment which constitute - Coulomb’s theory, it is to be expected that the difference - of his ideas from those of Coulomb must arise solely from a - different method of stating and interpreting physically the - same laws; and further, it may, I think, be shown that either - method of viewing this subject, when carried sufficiently - far, may be made the foundation of a mathematical theory - which would lead to the elementary principles of the other as - consequences. This theory would, accordingly, be the expression - of the ultimate law of the phenomena, independently of any - physical hypothesis we might from other circumstances be led - to adopt. That there are necessarily two distinct elementary - ways of viewing the theory of electricity may be seen from the - following considerations....” - -In the pages which follow, Lord Kelvin develops the consequences of an -analogy between the conduction of heat and electrostatic action, which -he had pointed out three years earlier (1842), in his paper on “The -Uniform Motion of Heat in Homogeneous Solid Bodies,” and discusses its -connection with the mathematical theory of electricity. - -The problem of distributing sources of heat in a given homogeneous -conductor of heat, so as to produce a definite steady temperature at -each point on the conductor is shewn to be _mathematically_ identical -with that of distributing electricity in equilibrium, so as to produce -at each point an electrical potential having the same value as the -temperature. - -Thus the fundamental laws of the conduction of heat may be made the -basis of the mathematical theory of electricity, but the physical -idea which they suggest is that of the propagation of some effect by -means of the mutual action of contiguous particles, rather than that -of material particles attracting or repelling at a distance, which -naturally follows from the statement of Coulomb’s law. - -Lord Kelvin continues:-- - - “All the views which Faraday has brought forward and - illustrated, as demonstrated by experiment, lead to this method - of establishing the mathematical theory, and, as far as the - analysis is concerned, it would in most _general_ propositions - be more simple, if possible, than that of Coulomb. Of course - the analysis of _particular_ problems would be identical in the - two methods. It is thus that Faraday arrives at a knowledge of - some of the most important of the mathematical theorems which - from their nature seemed destined never to be perceived except - as mathematical truths.” - -Lord Kelvin’s papers on “The Mathematical Theory of Electricity,” -published from 1848 to 1850, his “Propositions on the Theory of -Attraction” (1842), his “Theory of Electrical Images” (1847), and his -paper on “The Mathematical Theory of Magnetism” (1849), contain a -statement of the most important results achieved in the mathematical -sciences of Electrostatics and Magnetism up to the time of Maxwell’s -first paper. - -The opening sentences of that paper have already been quoted. In the -preface to the “Electricity and Magnetism” Maxwell writes thus:-- - - “Before I began the study of electricity I resolved to read - no mathematics on the subject till I had first read through - ‘Experimental Researches on Electricity.’ I was aware that - there was supposed to be a difference between Faraday’s way of - conceiving phenomena and that of the mathematicians, so that - neither he nor they were satisfied with each other’s language. - I had also the conviction that this discrepancy did not arise - from either party being wrong. I was first convinced of this by - Sir William Thomson, to whose advice and assistance, as well as - to his published papers, I owe most of what I have learned on - the subject. - - “As I proceeded with the study of Faraday, I perceived that his - method of conceiving the phenomena was also a mathematical - one, though not exhibited in the conventional form of - mathematical symbols. I also found that these methods were - capable of being expressed in the ordinary mathematical forms, - and thus compared with those of the professed mathematicians. - - “For instance, Faraday, in his mind’s eye, saw lines of force - traversing all space where the mathematicians saw centres of - force attracting at a distance. Faraday saw a medium where - they saw nothing but distance. Faraday sought the seat of the - phenomena in real actions going on in the medium. They were - satisfied that they had found it in a power of action at a - distance impressed on the electric fluids.” - -Now, Maxwell saw an analogy between electrostatics and the steady -motion of an incompressible fluid like water, and it is this analogy -which he develops in the first part of his paper. The water flows along -definite lines; a surface which consists wholly of such lines of flow -will have the property that no water ever crosses it. In any stream -of water we can imagine a number of such surfaces drawn, dividing it -up into a series of tubes; each of these will be a tube of flow, each -of these tubes remain always filled with water. Hence, the quantity -of water which crosses per second any section of a tube of flow -perpendicular to its length is always the same. Thus, from the form of -the tube, we can obtain information as to the direction and strength of -the flow, for where the tube is wide the flow will be proportionately -small, and _vice versâ_. - -Again, we can draw in the fluid a number of surfaces, over each of -which the pressure is the same; these surfaces will cut the tubes -of flow at right angles. Let us suppose they are drawn so that the -difference of pressure between any two consecutive surfaces is unity, -then the surfaces will be close together at points at which the -pressure changes rapidly; where the variation of pressure is slow, the -distance between two consecutive surfaces will be considerable. - -If, then, in any case of motion, we can draw the pressure surfaces, -and the tubes of flow, we can determine the motion of the fluid -completely. Now, the same mathematical expressions which appear in -the hydro-dynamical theory occur also in the theory of electricity, -the meaning only of the symbols is changed. For velocity of fluid we -have to write electrical force. For difference of fluid pressure we -substitute work done, or difference of electrical potential or pressure. - -The surfaces and tubes, drawn as the solution of any hydro-dynamical -problem, give us also the solution of an electrical problem; the -tubes of flow are Faraday’s tubes of force, or tubes of induction, -the surfaces of constant pressure are surfaces of equal electrical -potential. Induction may take place in curved lines just as the tubes -of flow may be bent and curved; the analogy between the two is a -complete one. - -But, as Maxwell shows, the analogy reaches further still. An electric -current flowing along a wire had been recognised as having many -properties similar to those of a current of liquid in a tube. When a -steady current is passing through any solid conductor, there are formed -in the conductor tubes of electrical flow and surfaces of constant -pressure. These tubes and surfaces are the same as those formed by the -flow of liquid through a solid whose boundary surface is the same -as that of the conductor, provided the flow of liquid is properly -proportioned to the flow of electricity. - -These analogies refer to steady currents in which, therefore, the flow -at any point of the conductor does not depend on the time. In Part -II. of his paper Maxwell deals with Faraday’s electro-tonic state. -Faraday had found that when _changes_ are produced in the magnetic -phenomena surrounding a conductor, an electric current is set up in -the conductor, which continues so long as the magnetic changes are in -progress, but which ceases when the magnetic state becomes steady. - - “Considerations of this kind led Professor Faraday to connect - with his discovery of the induction of electric currents the - conception of a state into which all bodies are thrown by the - presence of magnets and currents. This state does not manifest - itself by any known phenomena as long as it is undisturbed, - but any change in this state is indicated by a current or - tendency towards a current. To this state he gave the name of - the ‘Electro-tonic State,’ and although he afterwards succeeded - in explaining the phenomena which suggested it by means of less - hypothetical conceptions, he has on several occasions hinted at - the probability that some phenomena might be discovered which - would render the electro-tonic state an object of legitimate - induction. These speculations, into which Faraday had been - led by the study of laws which he has well established, and - which he abandoned only for want of experimental data for the - direct proof of the unknown state, have not, I think, been - made the subject of mathematical investigation. Perhaps it - may be thought that the quantitative determinations of the - various phenomena are not sufficiently rigorous to be made - the basis of a mathematical theory. Faraday, however, has not - contented himself with simply stating the numerical results - of his experiments and leaving the law to be discovered by - calculation. Where he has perceived a law he has at once stated - it, in terms as unambiguous as those of pure mathematics, - and if the mathematician, receiving this as a physical - truth, deduces from it other laws capable of being tested by - experiment, he has merely assisted the physicist in arranging - his own ideas, which is confessedly a necessary step in - scientific induction. - - “In the following investigation, therefore, the laws - established by Faraday will be assumed as true, and it will - be shown that by following out his speculations other and - more general laws can be deduced from them. If it should, - then, appear that these laws, originally devised to include - one set of phenomena, may be generalised so as to extend to - phenomena of a different class, these mathematical connections - may suggest to physicists the means of establishing physical - connections, and thus mere speculation may be turned to account - in experimental science.” - -Maxwell shows how to obtain a mathematical expression for Faraday’s -electro-tonic state. In his “Electricity and Magnetism,” this -electro-tonic state receives a new name. It is known as the Vector -Potential,[61] and the paper under consideration contains, though -in an incomplete form, his first statement of those equations of the -electric field which are so indissolubly bound up with Maxwell’s name. - -The great advance in theory made in the paper is the distinct -recognition of certain mathematical functions as representing Faraday’s -electrotonic-state, and their use in solving electro-magnetic problems. - -The paper contains no new physical theory of electricity, but in a -few years one appeared. In his later writings Maxwell adopted a more -general view of the electro-magnetic field than that contained in his -early papers on “Physical Lines of Force.” It must, therefore, not be -supposed that the somewhat gross conception of cog-wheels and pulleys, -which we are about to describe, were anything more to their author than -a model, which enabled him to realise how the changes, which occur when -a current of electricity passes through a wire, might be represented by -the motion of actual material particles. - -The problem before him was to devise a physical theory of electricity, -which would explain the forces exerted on electrified bodies by means -of action between the contiguous parts of the medium in the space -surrounding these bodies, rather than by direct action across the -distance which separates them. A similar question, still unanswered, -had arisen in the case of gravitation. Astronomers have determined the -forces between attracting bodies; they do not know how those forces -arise. - -Maxwell’s fondness for models has already been alluded to; it had led -him to construct his top to illustrate the dynamics of a rigid body -rotating about a fixed point, and his model of Saturn’s rings (now in -the Cavendish Laboratory) to illustrate the motion of the satellites -in the rings. He had explained many of the gaseous laws by means of -the impact of molecules, and now his fertile ingenuity was to imagine -a mechanical model of the state of the electro-magnetic field near a -system of conductors carrying currents. - -Faraday, as we have seen, looked upon electrostatic and magnetic -induction as taking place along curved lines of force. He pictures -these lines as ropes of molecules starting from a charged conductor, or -a magnet, as the case may be, and acting on other bodies near. These -ropes of molecules tend to shorten, and at the same time to swell -outwards laterally. Thus the charged conductor tends to draw other -bodies to itself, there is a tension along the lines of force, while -at the same time each tube of molecules pushes its neighbours aside; a -pressure at right angles to the lines of force is combined with this -tension. Assuming for a moment this pressure and tension to exist, can -we devise a mechanism to account for it? Maxwell himself has likened -the lines of force to the fibres of a muscle. As the fibres contract, -causing the limb to which they are attached to move, they swell -outwards, and the muscle thickens. - -Again, from another point of view, we might consider a line of force -as consisting of a string of small cells of some flexible material -each filled with fluid. If we then suppose this series of cells caused -to rotate rapidly about the direction of the line of force, the cells -will expand laterally and contract longitudinally; there will again be -tension along the lines of force and pressure at right angles to them. -It was this last idea, as we shall see shortly, of which Maxwell made -use-- - - “I propose now” [he writes (“On Physical Lines of Force,” - _Phil. Mag._, vol. xxi.)] “to examine magnetic phenomena from - a mechanical point of view, and to determine what tensions in, - or motions of, a medium are capable of producing the mechanical - phenomena observed. If by the same hypothesis we can connect - the phenomena of magnetic attraction with electro-magnetic - phenomena, and with those of induced currents, we shall have - found a theory which, if not true, can only be proved to be - erroneous by experiments, which will greatly enlarge our - knowledge of this part of physics.” - -Lord Kelvin had in 1847 given a mechanical representation of electric, -magnetic and galvanic forces by means of the displacements of an -elastic solid in a state of strain. The angular displacement at each -point of the solid was taken as proportional to the magnetic force, and -from this the relation between the various other electric quantities -and the motion of the solid was developed. But Lord Kelvin did not -attempt to explain the origin of the observed forces by the effects due -to these strains, but merely made use of the mathematical analogy to -assist the imagination in the study of both. - -Maxwell considered magnetic action as existing in the form of pressure -or tension, or more generally, of some stress in some medium. The -existence of a medium capable of exerting force on material bodies and -of withstanding considerable stress, both pressure and tension, is -thus a fundamental hypothesis with him; this medium is to be capable -of motion, and electro-magnetic forces arise from its motion and its -stresses. - -Now, Maxwell’s fundamental supposition is that, in a magnetic field, -there is a rotation of the molecules continually in progress about the -lines of magnetic force. Consider now the case of a uniform magnetic -field, whose direction is perpendicular to the paper; we are to look -upon the lines of force as parallel strings of molecules, the axes of -these strings being perpendicular to the paper. Each string is supposed -to be rotating in the same direction about its axis, and the angular -velocity of rotation is a measure of the magnetic force. In consequence -of this rotation there will be differences of pressure in different -directions in the medium; the pressure along the axes of the strings -will be less than it would be if the medium were at rest, that in the -directions at right angles to the axes will be greater, the medium will -behave as though it were under tension along the axes of the molecules -under pressure at right angles to them. Moreover, it can be shown that -the pressure and the tension are both proportional to the square of the -angular velocity--the square, that is, of the magnetic force--and this -result is in accordance with the consequences of experiment. - -More elaborate calculation shows that this statement is true generally. -If we draw the lines of force in any magnetic field, and then suppose -the molecules of the medium set in rotation about these lines of force -as axes, with velocities which at each point are proportional to the -magnetic force, the distribution of pressure throughout is that which -we know actually to exist in the magnetic field. - -According to this hypothesis, then, a permanent bar magnet has the -power of setting the medium round it into continuous molecular rotation -about the lines of force as axes. The molecules which are set in -rotation we may consider as spherical, or nearly spherical, cells -filled with a fluid, or an elastic solid substance, and surrounded by a -kind of membrane, or sack, holding the contents together. - -So far the model does not give any account of electrical actions which -go on in the magnetic field. - -The energy is wholly rotational, and the forces wholly magnetic. - -Consider, however, any two contiguous strings of molecules. Let them -cut the paper as shown in the two circles in Fig. 1:-- - -[Illustration: Fig. 1. - -Fig. 2.] - -Then these cells are both rotating in the same direction, hence at C, -where they touch, their points of contact will be moving in opposite -directions, as shown by the arrow heads, and it is difficult to imagine -how such motion can continue; it would require the surfaces of the -cells to be perfectly smooth, and if this were so they would lose the -power of transmitting action from one cell to the next. - -The cells A and B may be compared to two cog-wheels placed close -together, which we wish to turn in the same direction. If the cogs can -interlock, as in Fig. 2, this is impossible: consecutive wheels in the -train must move in opposite directions. - -[Illustration: Fig. 3.] - -But in many machines the desired end is attained by inserting between -the two wheels A and B a third idle wheel C, as shewn in Fig. 3. This -may be very small, its only function is to transmit the motion of A to -B in such a way that A and B may both turn in the same direction. It is -not necessary that there should be cogs on the wheels; if the surfaces -be perfectly rough, so that no slipping can take place, the same result -follows without the cogs. - -Guided by this analogy Maxwell extended his model by supposing each -cell coated with a number of small particles which roll on its surface. -These particles play the part of the idle wheels in the machine, and by -their rolling merely enable the adjacent parts of two cells to move in -opposite directions. - -Consider now a number of such cells and their idle wheels lying in a -plane, that of the paper, and suppose each cell is rotating with the -same uniform angular velocity about an axis at right angles to that -plane, each idle wheel will be acted on by two equal and opposite -forces at the ends of the diameter in which it is touched by the -adjacent cells; it will therefore be set in rotation, but there will be -no force tending to drive it onwards; it does not matter whether the -axis on which it rotates is free to move or fixed, in either case the -idle wheel simply rotates. But suppose now the adjacent cells are not -rotating at the same rate. In addition to its rotation the idle wheel -will be urged onward with a velocity which depends on the difference -between the rotations, and, if it can move freely, it will move on from -between the two cells. Imagine now that the interstices between the -cells are fitted with a string of idle wheels. So long as the adjacent -cells move with different velocity there will be a continual stream of -rolling particles or idle wheels between them. Maxwell in the paper -considered these rolling particles to be particles of electricity. -Their motion constitutes an electric current. In a uniform magnetic -field there is no electric current; if the strength of the field -varies, the idle wheels are set in motion and there may be a current. - -These particles are very small compared with the magnetic vortices. -The mass of all the particles is inappreciable compared with the mass -of the vortices, and a great many vortices with their surrounding -particles are contained in a molecule of the medium; the particles -roll on the vortices without touching each other, so that so long as -they remain within the same molecule there is no loss of energy by -resistance. When, however, there is a current or general transference -of particles in one direction they must pass from one molecule to -another, and in doing so may experience resistance and generate heat. - -Maxwell states that the conception of a particle, having its motion -connected with that of a vortex by perfect rolling contact, may appear -somewhat awkward. “I do not bring it forward,” he writes, “as a mode of -connection existing in Nature, or even as that which I would willingly -assent to as an electrical hypothesis. It is, however, a mode of -connection which is mechanically conceivable and easily investigated, -and it serves to bring out the actual mechanical connections between -the known electro-magnetic phenomena, so that I venture to say that -anyone who understands the provisional and temporary character of this -hypothesis will find himself rather helped than hindered by it in his -search after the true interpretation of the phenomena.” - -The first part of the paper deals with the theory of magnetism; in the -second part the hypothesis is applied to the phenomena of electric -currents, and it is shown how the known laws of steady currents and -of electro-magnetic induction can be deduced from it. In Part III., -published January and February, 1862, the theory of molecular vortices -is applied to statical electricity. - -The distinction between a conductor and an insulator or dielectric -is supposed to be that in the former the particles of electricity -can pass with more or less freedom from molecule to molecule. In the -latter such transference is impossible, the particles can only be -displaced within the molecule with which they are connected; the cells -or vortices of the medium are supposed to be elastic, and to resist by -their elasticity the displacement of the particles within them. When -electrical force acts on the medium this displacement of the particles -within each molecule takes place until the stresses due to the elastic -reaction of the vortices balance the electrical force; the medium -behaves like an elastic body yielding to pressure until the pressure is -balanced by the elastic stress. When the electric force is removed the -cells or vortices recover their form, the electricity returns to its -former position. - -In a medium such as this waves of periodic displacement could be -set up, and would travel with a velocity depending on its electric -properties. The value for this velocity can be obtained from electrical -observations, and Maxwell showed that this velocity, so found, was, -within the limits of experimental error, the same as that of light. -Moreover, the electrical oscillations take place, like those of light, -in the front of the wave. Hence, he concludes, “the elasticity of the -magnetic medium in air is the same as that of the luminiferous medium, -if these two coexistent, coextensive, and equally elastic media are not -rather one medium.” - -The paper thus contains the first germs of the electro-magnetic theory -of light. Moreover, it is shown that the attraction between two small -bodies charged with given quantities of electricity depends on the -medium in which they are placed, while the specific inductive capacity -is found to be proportional to the square of the refractive index. - -The fourth and final part of the paper investigates the propagation of -light in a magnetic field. - -Faraday had shown that the direction of vibration in a wave of -polarised light travelling parallel to the lines of force in a magnetic -field is rotated by its passage through the field. The numerical laws -of this relation had been investigated by Verdet, and Maxwell showed -how his hypothesis of molecular vortices led to laws which agree in the -main with those found by Verdet. - -He points out that the connection between magnetism and electricity -has the same mathematical form as that between certain other pairs -of phenomena, one of which has a _linear_ and the other a _rotatory_ -character; and, further, that an analogy may be worked out assuming -either the linear character for magnetism and the rotatory character -for electricity, or the reverse. He alludes to Prof. Challis’ theory, -according to which magnetism is to consist in currents in a fluid -whose directions correspond with the lines of magnetic force, while -electric currents are supposed to be accompanied by, if not dependent -upon, a rotatory motion of the fluid about the axis of the current; -and to Von Helmholtz’s theory of a somewhat similar character. He then -gives his own reasons--agreeing with those of Sir W. Thomson (Lord -Kelvin)--for supposing that there must be a real rotation going on in -a magnetic field in order to account for the rotation of the plane of -polarisation, and, accepting these reasons as valid, he develops the -consequences of his theory with the results stated above. - -His own verdict on the theory is given in the “Electricity and -Magnetism” (vol. ii., § 831, first edition, p. 416):-- - - “A theory of molecular vortices, which I worked out at - considerable length, was published in the _Phil. Mag._ for - March, April, and May, 1861; Jan. and Feb., 1862. - - “I think we have good evidence for the opinion that some - phenomenon of rotation is going on in the magnetic field, that - this rotation is performed by a great number of very small - portions of matter, each rotating on its own axis, this axis - being parallel to the direction of the magnetic force, and that - the rotations of these different vortices are made to depend on - one another by means of some kind of mechanism connecting them. - - “The attempt which I then made to imagine a working model of - this mechanism must be taken for no more than it really is, - a demonstration that mechanism may be imagined capable of - producing a connection mechanically equivalent to the actual - connection of the parts of the electro-magnetic field. The - problem of determining the mechanism required to establish a - given species of connection between the motions of the parts of - a system always admits of an infinite number of solutions. Of - these, some may be more clumsy or more complex than others, but - all must satisfy the conditions of mechanism in general. - - “The following results of the theory, however, are of higher - value:-- - - “(1) Magnetic force is the effect of the centrifugal force of - the vortices. - - “(2) Electro-magnetic induction of currents is the effect of - the forces called into play when the velocity of the vortices - is changing. - - “(3) Electromotive force arises from the stress on the - connecting mechanism. - - “(4) Electric displacement arises from the elastic yielding of - the connecting mechanism.” - -In studying this part of Maxwell’s work, it must clearly be remembered -that he did not look upon the ether as a series of cog-wheels with -idle wheels between, or anything of the kind. He devised a mechanical -model of such cogs and idle wheels, the properties of which would in -some respects closely resemble those of the ether; from this model he -deduced, among other things, the important fact that electric waves -would travel outwards with the velocity of light. Other such models -have been devised since his time to illustrate the same laws. Prof. -Fitzgerald has actually constructed one of wheels connected together by -elastic bands, which shows clearly the kind of processes which Maxwell -supposed to go on in a dielectric when under electric force. Professor -Lodge, in his book, “Modern Views of Electricity,” has very fully -developed a somewhat different arrangement of cog-wheels to attain the -same result. - -Maxwell’s predictions as to the propagation of electric waves have -in recent days received their full verification in the brilliant -experiments of Hertz and his followers; it remains for us, before -dealing with these, to trace their final development in his hands. - -The papers we have been discussing were perhaps too material to receive -the full attention they deserved; the ether is not a series of cogs, -and electricity is something different from material idle wheels. In -his paper on “The Dynamical Theory of the Electro-magnetic Field,” -_Phil. Trans._, 1864, Maxwell treats the same questions in a more -general manner. On a former occasion he says, “I have attempted to -describe a particular kind of motion and a particular kind of strain -so arranged as to account for the phenomena. In the present paper I -avoid any hypothesis of this kind; and in using such words as electric -momentum and electric elasticity in reference to the known phenomena of -the induction of currents and the polarisation of dielectrics, I wish -merely to direct the mind of the reader to mechanical phenomena, which -will assist him in understanding the electrical ones. All such phrases -in the present paper are to be considered as illustrative and not as -explanatory.” He then continues:-- - - “In speaking of the energy of the field, however, I wish to - be understood literally. All energy is the same as mechanical - energy, whether it exists in the form of motion or in that of - elasticity, or in any other form. - - “The energy in electro-magnetic phenomena is mechanical energy. - The only question is, Where does it reside? - - “On the old theories it resides in the electrified bodies, - conducting circuits, and magnets, in the form of an unknown - quality called potential energy, or the power of producing - certain effects at a distance. On our theory it resides in - the electro-magnetic field, in the space surrounding the - electrified and magnetic bodies, as well as in those bodies - themselves, and is in two different forms, which may be - described without hypothesis as magnetic polarisation and - electric polarisation, or, according to a very probable - hypothesis, as the motion and the strain of one and the same - medium. - - “The conclusions arrived at in the present paper are - independent of this hypothesis, being deduced from experimental - facts of three kinds:-- - - “(1) The induction of electric currents by the increase or - diminution of neighbouring currents according to the changes in - the lines of force passing through the circuit. - - “(2) The distribution of magnetic intensity according to the - variations of a magnetic potential. - - “(3) The induction (or influence) of statical electricity - through dielectrics. - - “We may now proceed to demonstrate from these principles the - existence and laws of the mechanical forces, which act upon - electric currents, magnets, and electrified bodies placed in - the electro-magnetic field.” - -In his introduction to the paper, he discusses in a general way the -various explanations of electric phenomena which had been given, and -points out that-- - - “It appears, therefore, that certain phenomena in electricity - and magnetism lead to the same conclusion as those of optics, - namely, that there is an ætherial medium pervading all bodies, - and modified only in degree by their presence; that the parts - of this medium are capable of being set in motion by electric - currents and magnets; that this motion is communicated from - one part of the medium to another by forces arising from the - connection of those parts; that under the action of these - forces there is a certain yielding depending on the elasticity - of these connections; and that, therefore, energy in two - different forms may exist in the medium, the one form being - the actual energy of motion of its parts, and the other being - the potential energy stored up in the connections in virtue of - their elasticity. - - “Thus, then, we are led to the conception of a complicated - mechanism capable of a vast variety of motion, but at the - same time so connected that the motion of one part depends, - according to definite relations, on the motion of other parts, - these motions being communicated by forces arising from the - relative displacement of the connected parts, in virtue of - their elasticity. Such a mechanism must be subject to the - general laws of dynamics, and we ought to be able to work out - all the consequences of its motion, provided we know the form - of the relation between the motions of the parts.” - -These general laws of dynamics, applicable to the motion of any -connected system, had been developed by Lagrange, and are expressed -in his generalised equations of motion. It is one of Maxwell’s chief -claims to fame that he saw in the electric field a connected system to -which Lagrange’s equations could be applied, and that he was able to -deduce the mechanical and electrical actions which take place by means -of fundamental propositions of dynamics. - -The methods of the paper now under discussion were developed further -in the “Treatise on Electricity and Magnetism,” published in 1873; in -endeavouring to give some slight account of Maxwell’s work, we shall -describe it in the form it ultimately took. - -The task which Maxwell set himself was a double one; he had first to -express in symbols, in as general a form as possible, the fundamental -laws of electro-magnetism as deduced from experiments, chiefly -the experiments of Faraday, and the relations between the various -quantities involved; when this was done he had to show how these laws -could be deduced from the general dynamical laws applicable to any -system of moving bodies. - -There are two classes of phenomena, electric and magnetic, which have -been known from very early times, and which are connected together. -When a piece of sealing-wax is rubbed it is found to attract other -bodies, it is said to exert electric force throughout the space -surrounding it; when two different metals are dipped in slightly -acidulated water and connected by a wire, certain changes take place -in the plates, the water, the wire, and the space round the wire, -electric force is again exerted and a current of electricity is said -to flow in the wire. Again, certain bodies, such as the lodestone, or -pieces of iron and steel which have been treated in a certain manner, -exhibit phenomena of action at a distance: they are said to exert -magnetic force, and it is found that this magnetic force exists in the -neighbourhood of an electric current and is connected with the current. - -Again, when electric force is applied to a body, the effects may be in -part electrical, in part mechanical; the electrical state of the body -is in general changed, while in addition, mechanical forces tending to -move the body are set up. Experiment must teach us how the electrical -state depends on the electric force, and what is the connection -between this electric force and the magnetic forces which may, under -certain circumstances, be observed. Now, in specifying the electric -and magnetic conditions of the system, various other quantities, in -addition to the electric force, will have to be introduced; the first -step is to formulate the necessary quantities, and to determine the -relations between them and the electric force. - -Consider now a wire connecting the two poles of an electric battery--in -its simplest form, a piece of zinc and a piece of copper in a vessel -of dilute acid--electric force is produced at each point of the wire. -Let us suppose this force known; an electric current depending on the -material and the size of the wire flows along it, its value can be -determined at each point of the wire in terms of the electric force -by Ohm’s law. If we take either this current or the electric force -as known, we can determine by known laws the electric and magnetic -conditions elsewhere. If we suppose the wire to be straight and very -long, then, so long as the current is steady and we neglect the small -effect due to the electrostatic charge on the wire, there is no -electric force outside the wire. There is, however, magnetic force, -and it is found that the lines of magnetic force are circles round the -wire. It is found also that the work done in travelling once completely -round the wire against the magnetic force is measured by the current -flowing through the wire, and is obtained in the system of units -usually adopted by multiplying the current by 4π. This last result then -gives us one of the necessary relations, that between the magnetic -force due to a current and the strength of the current. - -Again, consider a steady current flowing in a conductor of any form or -shape, the total flow of current across any section of the conductor -can be measured in various ways, and it is found that at any time this -total flow is the same for each section of the conductor. In this -respect the flow of a current resembles that of an incompressible -fluid through a pipe; where the pipe is narrow the velocity of flow -is greater than it is where the pipe is broad, but the total quantity -crossing each section at any given instant is the same. - -Consider now two conducting bodies, two spheres, or two flat plates -placed near together but insulated. Let each conductor be connected -to one of the poles of the battery by a conducting wire. Then, for a -very short interval after the contact is made, it is found that there -is a current in each wire which rapidly dies away to zero. In the -neighbourhood of the balls there is electric force; the balls are said -to be charged with electricity, and the lines of force are curved lines -running from one ball to the other. It is found that the balls slightly -attract each other, and the space between them is now in a different -condition from what it was before the balls were charged. According -to Maxwell, _Electric Displacement_ has been produced in this space, -and the electric displacement at each point is proportional to the -electric force at that point. - -Thus, (i) when electric force acts on a conductor, it produces a -current, the current being by Ohm’s law proportional to the force: -(ii) when it acts on an insulator it produces electric displacement, -and the displacement is proportional to the force; while (iii) there -is magnetic force in the neighbourhood of the current, and the work -done in carrying a magnetic pole round any complete circuit linked -with the current is proportional to the current. The first two of -these principles give us two sets of equations connecting together the -electric force and the current in a conductor or the displacement in a -dielectric respectively; the third connects the magnetic force and the -current. - -Now let us go back to the variable period when the current is flowing -in the wires; and to make ideas precise, let the two conductors be two -equal large flat plates placed with their faces parallel, and at some -small distance apart. In this case, when the plates are charged, and -the current has ceased, the electric displacement and the force are -confined almost entirely to the space between the plates. During the -variable period the total flow at any instant across each section of -the wire is the same, but in the ordinary sense of the word there is no -flow of electricity across the insulating medium between the plates. -In this space, however, the electric displacement is continuously -changing, rising from zero initially to its final steady value when the -current ceases. It is a fundamental part of Maxwell’s theory that this -variation of electric displacement is equivalent in all respects to a -current. The current at any point in a dielectric is measured by the -rate of change of displacement at that point. - -Moreover, it is also an essential point that if we consider any section -of the dielectric between the two plates, the rate of change of the -total displacement across this section is at each moment equal to the -total flow of current across each section of the conducting wire. - -Currents of electricity, therefore, including displacement -currents, always flow in closed circuits, and obey the laws of an -incompressible fluid in that the total flow across each section of the -circuit--conducting or dielectric--is at any moment the same. - -It should be clearly remembered that this fundamental hypothesis of -Maxwell’s theory is an assumption only to be justified by experiment. -Von Helmholtz, in his paper on “The Equations of Motion of Electricity -for Bodies at Rest,” formed his equations in an entirely different -manner from Maxwell, and arrived at results of a more general -character, which do not require us to suppose that currents flow always -in closed circuits, but permit of the condensation of electricity at -points in the circuit where the conductors end and the non-conducting -part of the circuit begins. We leave for the present the question which -of the two theories, if either, represents the facts. - -We have obtained above three fundamental relations--(i) that between -electric force and electric current in a conductor; (ii) that between -electric force and electric displacement in a dielectric; (iii) that -between magnetic force and the current which gives rise to it. And -we have seen that an electric current--_i.e._ in a dielectric the -variation of the strength of an electric field of force--gives rise -to magnetic force. Now, magnetic force acting on a medium produces -“magnetic displacement,” or magnetic induction, as it is called. In -all media except iron, nickel, cobalt, and a few other substances, the -magnetic induction is proportional to the magnetic force, and the ratio -between the magnetic induction produced by a given force and the force -is found to be very nearly the same for all such media. This ratio is -known as the permeability, and is generally denoted by the symbol μ. - -A relation reciprocal to that given in (iii) above might be -anticipated, and was, in fact, discovered by Faraday. Changes in a -field of magnetic induction give rise to electric force, and hence to -displacement currents in a dielectric or to conduction currents in a -conductor. In considering the relation between these changes and the -electric force, it is simplest at first not to deal with magnetic -matter such as iron, nickel, or cobalt; and then we may say that (iv) -the work which at any instant would be done in carrying a unit quantity -of electricity round a closed circuit in a magnetic field against the -electric forces due to the field is equal to the rate at which the -total magnetic induction which threads the circuit is being decreased. -This law, summing up Faraday’s experiments on electro-magnetic -induction, gives a fourth principle, leading to a fourth series of -equations connecting together the electric and magnetic quantities -involved. - -The equations deduced from the above four principles, together with the -condition implied in the continuity of an electric current, constitute -Maxwell’s equations of the electro-magnetic field. - -If we are dealing only with a dielectric medium, the reciprocal -relation between the third and fourth principle may be made more clear -by the following statement:-- - -(A) The work done at any moment in carrying a unit quantity of -magnetism round a closed circuit in a field in which electric -displacement is varying, is equal to the rate of change of the total -electric displacement through the circuit multiplied by 4 π.[62] - -(B) The work done at any moment in carrying a unit quantity of -electricity round a circuit in a field in which the magnetic induction -is varying, is equal to the rate of change of the total magnetic -induction through the circuit. - -From these two principles, combined with the laws connecting electric -force and displacement, magnetic force and induction, and with the -condition of continuity, Maxwell obtained his equations of the field. - -Faraday’s experiments on electro-magnetic induction afford the proof of -the truth of the fourth principle. It follows from those experiments -that when the number of lines of magnetic induction which are linked -with any closed circuit are made to vary, an induced electromotive -force is brought into play round that circuit. This electromotive force -is, according to Faraday’s results, measured by the rate of decrease -in the number of lines of magnetic induction which thread the circuit. -Maxwell applies this principle to all circuits, whether conducting or -not. - -In obtaining equations to express in symbols the results of the fourth -principle just enunciated, Maxwell introduces a new quantity, to which -he gives the name of the “vector potential.” This quantity appears in -his analysis, and its physical meaning is not at first quite clear. -Professor Poynting has, however, put Maxwell’s principles in a slightly -different form, which enables us to see definitely the meaning of the -vector potential, and to deduce Maxwell’s equations more readily from -the fundamental statements. - -We are dealing with a circuit with which lines of magnetic induction -are linked, while the number of such lines linked with the circuit is -varying. Now, let us suppose the variation to take place in consequence -of the lines of induction moving outwards or inwards, as the case may -be, so as to cut the circuit. Originally there are none linked with -the circuit. As the magnetic field has grown to its present strength -lines of magnetic induction have moved inwards. Each little element of -the circuit has been cut by some, and the total number linked with the -circuit can be found by adding together those cut by each element. Now, -Professor Poynting’s statement of Maxwell’s fourth principle is that -the electrical force in the direction of any element of the circuit is -found by dividing by the length of the element the number of lines of -magnetic induction which are cut in one second by it. - -Moreover, the total number of lines of magnetic induction which have -been cut by an element of unit length is defined as the component -of the vector potential in the direction of the element; hence the -electrical force in any direction is the rate of decrease of the -component of the vector potential in that direction. We have thus a -physical meaning for the vector potential, and shall find that in the -dynamical theory this quantity is of great importance. - -Professor Poynting has modified Maxwell’s third principle in a similar -manner; he looks upon the variation in the electric displacement as -due to the motion of tubes of electric induction,[63] and the magnetic -force along any circuit is equal to the number of tubes of electric -induction cutting or cut by unit length of the circuit per second, -multiplied by 4π. - -From the equations of the field, as found by Maxwell, it is possible -to derive two sets of symmetrical equations. The one set connects the -rate of change of the electric force with quantities depending on the -magnetic force; the other set connects in a similar manner the rate of -change of the magnetic force with quantities depending on the electric -force. Several writers in recent years adopt these equations as the -fundamental relations of the field, establishing them by the argument -that they lead to consequences which are found to be in accordance with -experiment. - -We have endeavoured to give some account of Maxwell’s historical -method, according to which the equations are deduced from the laws of -electric currents and of electro-magnetic induction derived directly -from experiment. - -While the manner in which Maxwell obtained his equations is all his -own, he was not alone in stating and discussing general equations -of the electro-magnetic field. The next steps which we are about to -consider are, however, in a special manner due to him. An electrical -or magnetic system is the seat of energy; this energy is partly -electrical, partly magnetic, and various expressions can be found for -it. In Maxwell’s theory it is a fundamental assumption that energy has -position. “The electric and magnetic energies of any electro-magnetic -system,” says Professor Poynting, “reside, therefore, somewhere in the -field.” It follows from this that they are present wherever electric -and magnetic force can be shown to exist. Maxwell showed that all the -electric energy is accounted for by supposing that in the neighbourhood -of a point at which the electric force is R there is an amount of -energy per unit of volume equal to KR²/8π, K being the inductive -capacity of the medium, while in the neighbourhood of a point at which -the magnetic force is H, the magnetic energy per unit of volume is -μH²/8π, μ being the permeability. He supposes, then, that at each point -of an electro-magnetic system energy is stored according to these -laws. It follows, then, that the electro-magnetic field resembles a -dynamical system in which energy is stored. Can we discover more of -the mechanism by which the actions in the field are maintained? Now -the motion of any point of a connected system depends on that of other -points of the system; there are generally, in any machine, a certain -number of points called driving-points, the motion of which controls -the motion of all other parts of the machine; if the motion of the -driving-points be known, that of any other point can be determined. -Thus in a steam engine the motion of a point on the fly-wheel can be -found if the motion of the piston and the connections between the -piston and the wheel be known. - -In order to determine the force which is acting on any part of the -machine we must find its momentum, and then calculate the rate at -which this momentum is being changed. This rate of change will give us -the force. The method of calculation which it is necessary to employ -was first given by Lagrange, and afterwards developed, with some -modifications, by Hamilton. It is usually referred to as Hamilton’s -principle; when the equations in the original form are used they are -known as Lagrange’s equations. - -Now Maxwell showed how these methods of calculation could be applied -to the electro-magnetic field. The energy of a dynamical system is -partly kinetic, partly potential. Maxwell supposes that the magnetic -energy of the field is kinetic energy, the electric energy potential. -When the kinetic energy of a system is known, the momentum of any -part of the system can be calculated by recognised processes. Thus if -we consider a circuit in an electro-magnetic field we can calculate -the energy of the field, and hence obtain the momentum corresponding -to this circuit. If we deal with a simple case in which the conducting -circuits are fixed in position, and only the current in each circuit is -allowed to vary, the rate of change of momentum corresponding to any -circuit will give the force in that circuit. The momentum in question -is electric momentum, and the force is electric force. Now we have -already seen that the electric force at any point of a conducting -circuit is given by the rate of change of the vector potential in the -direction considered. Hence we are led to identify the vector potential -with the electric momentum of our dynamical system; and, referring to -the original definition of vector potential, we see that the electric -momentum of a circuit is measured by the number of lines of magnetic -induction which are interlinked with it. - -Again, the kinetic energy of a dynamical system can be expressed in -terms of the squares and products of the velocities of its several -parts. It can also be expressed by multiplying the velocity of each -driving-point by the momentum corresponding to that driving-point, and -taking half the sum of the products. Suppose, now, we are dealing with -a system consisting of a number of wire circuits in which currents are -running, and let us suppose that we may represent the current in each -wire as the velocity of a driving-point in our dynamical system. We can -also express in terms of these currents the electric momentum of each -wire circuit; let this be done, and let half the sum of the products of -the corresponding velocities and momenta be formed. - -In maintaining the currents in the wires energy is needed to supply -the heat which is produced in each wire; but in starting the currents -it is found that more energy is needed than is requisite for the -supply of this heat. This excess of energy can be calculated, and when -the calculation is made it is found that the excess is equal to half -the sum of the products of the currents and corresponding momenta. -Moreover, if this sum be expressed in terms of the magnetic force, it -is found to be equal to μ H²/8 π, which is the magnetic energy of the -field. Now, when a dynamical system is set in motion against known -forces, more energy is supplied than is needed to do the work against -the forces; this excess of energy measures the kinetic energy acquired -by the system. - -Hence, Maxwell was justified in taking the magnetic energy of the field -as the kinetic energy of the mechanical system, and if the strengths -of the currents in the wires be taken to represent the velocities of -the driving-points, this energy is measured in terms of the electrical -velocities and momenta in exactly the same way as the energy of a -mechanical system is measured in terms of the velocities and momenta of -its driving-points. - -The mechanical system in which, according to Maxwell, the energy is -stored is the ether. A state of motion or of strain is set up in the -ether of the field. The electric forces which drive the currents, and -also the mechanical forces acting on the conductors carrying the -currents, are due to this state of motion, or it may be of strain, in -the ether. It must not be supposed that the term electric displacement -in Maxwell’s mind meant an actual bodily displacement of the particles -of the ether; it is in some way connected with such a material -displacement. In his view, without motion of the ether particles -there would be no electric action, but he does not identify electric -displacement and the displacement of an ether particle. - -His mechanical theory, however, does account for the electro-magnetic -forces between conductors carrying currents. The energy of the system -depends on the relative positions of the currents which form part of -it. Now, any conservative mechanical system tends to set itself in -such a position that its potential energy is least, its kinetic energy -greatest. The circuits of the system, then, will tend to set themselves -so that the electro-kinetic energy of the system may be as large as -possible; forces will be needed to hold them in any position in which -this condition is not satisfied. - -We have another proof of the correctness of the value found for the -energy of the field in that the forces calculated from this value agree -with those which are determined by direct experiment. - -Again, the forces applied at the various driving-points are transmitted -to other points by the connections of the machine; the connections -are thrown into a state of strain; stress exists throughout their -substance. When we see the piston-rod and the shaft of an engine -connected by the crank and the connecting-rod, we recognise that the -work done on the piston is transmitted thus to the shaft. So, too, in -the electro-magnetic field, the ether forms the connection between the -various circuits in the field; the forces with which those circuits -act on each other are transmitted from one circuit to another by the -stresses set up in the ether. - -To take another instance, consider the electrostatic attraction between -two charged bodies. Let us suppose the bodies charged by connecting -each to the opposite pole of a battery; a current flows from the -battery setting up electric displacement in the space between the -bodies, and throwing the ether into a state of strain. As the strain -increases the current gets less; the reaction resulting from the strain -tends to stop it, until at last this reaction is so great that the -current is stopped. When this is the case the wires to the battery may -be removed, provided this is done without destroying the insulation of -the bodies; the state of strain will remain and shows itself in the -attraction between the balls. - -Looking at the problem in this manner, we are face to face with two -great questions--the one, What is the state of strain in the ether -which will enable it to produce the observed electrostatic attractions -and repulsions between charged bodies? and the other, What is the -mechanical structure of the ether which would give rise to such a state -of strain as will account for the observed forces? Maxwell gives one -answer to the first question; it is not the only answer which could -be given, but it does account for the facts. He failed to answer the -second. He says (“Electricity and Magnetism,” vol. i. p. 132):-- - - “It must be carefully borne in mind that we have made only - one step in the theory of the action of the medium. We have - supposed it to be in a state of stress, but have not in - any way accounted for this stress, or explained how it is - maintained.... I have not been able to make the next step, - namely, to account by mechanical considerations for these - stresses in the dielectric.” - -Faraday had pointed out that the inductive action between two bodies -takes place along the lines of force, which tend to shorten along their -length and to spread outwards in other directions. Maxwell compares -them to the fibres of a muscle, which contracts and at the same time -thickens when exerting force. In the electric field there is, on -Maxwell’s theory, a tension along the lines of electric force and a -pressure at right angles to those lines. Maxwell proved that a tension -K R²/8 π along the lines of force, combined with an equal pressure -in perpendicular directions, would maintain the equilibrium of the -field, and would give rise to the observed attractions or repulsions -between electrified bodies. Other distributions of stress might be -found which would lead to the same result. The one just stated will -always be connected with Maxwell’s name. It will be noticed that the -tension along the lines of force and the pressure at right angles to -them are each numerically equal to the potential energy stored per unit -of volume in the field. The value of each of the three quantities is K -R²/8 π. - -In the same way, in a magnetic field, there is a state of stress, and -on Maxwell’s theory this, too, consists of a tension along the lines -of force and an equal pressure at right angles to them, the values of -the tension and the pressure being each equal to that of the magnetic -energy per unit of volume, or μH²/8π. - -In a case in which both electric and magnetic force exists, these two -states of stress are superposed. The total energy per unit of volume -is KR²/8π + μH²/8π; the total stress is made up of tensions KR²/8π and -μH²/8π along the lines of electric and magnetic force respectively, and -equal pressures at right angles to these lines. - -We see, then, from Maxwell’s theory, that electric force produced at -any given point in space is transmitted from that point by the action -of the ether. The question suggests itself, Does the transmission take -time, and if so, does it proceed with a definite velocity depending on -the nature of the medium through which the change is proceeding? - -According to the molecular-vortex theory, we have seen that waves of -electric force are transmitted with a definite velocity. The more -general theory developed in the “Electricity and Magnetism” leads to -the same result. Electric force produced at any point travels outwards -from that point with a velocity given by 1/√(Kμ). At a distant point -the force is zero, until the disturbance reaches it. If the disturbance -last only for a limited interval, its effects will at any future time -be confined to the space within a spherical shell of constant thickness -depending on the interval; the radii of this shell increase with -uniform speed 1/√(Kμ). - -If the initial disturbance be periodic, periodic waves of electric -force will travel out from the centre, just as waves of sound travel -out from a bell, or waves of light from a candle flame. A wire carrying -an alternating current may be such a source of periodic disturbance, -and from the wire waves travel outwards into space. - -Now, it is known that in a sound wave the displacements of the air -particles take place in the direction in which the wave is travelling; -they lie at right angles to the wave front, and are spoken of as -longitudinal. In light waves, on the other hand, the displacements are, -as Fresnel proved, in the wave front, at right angles, that is, to the -direction of propagation; they are transverse. - -Theory shows that in general both these waves may exist in an elastic -solid body, and that they travel with different velocities. Of which -nature are the waves of electric displacement in a dielectric? It -can be shewn to follow as a necessary consequence of Maxwell’s views -as to the closed character of all electric currents, that waves of -electric displacement are transverse. Electric vibrations, like those -of light, are in the wave front and at right angles to the direction -of propagation; they depend on the rigidity or quasi-rigidity of the -medium through which they travel, not on its resistance to compression. - -Again, an electric current, whether due to variation of displacement -in a dielectric or to conduction in a conductor, is accompanied by -magnetic force. A wave of periodic electric displacement, then, will be -also a wave of periodic magnetic force travelling at the same rate; -and Maxwell shewed that the direction of this magnetic force also -lies in the wave front, and is always at right angles to the electric -displacement. In the ordinary theory of light the wave of linear -displacement is accompanied by a wave of periodic angular twist about -a direction lying in the wave front and perpendicular to the linear -displacement. - -In many respects, then, waves of electric displacement resemble waves -of light, and, indeed, as we proceed we shall find closer connections -still. Hence comes Maxwell’s electro-magnetic theory of light. - -It is only in dielectric media that electric force is propagated by -wave motion. In conductors, although the third and fourth of Maxwell’s -principles given on page 185 still are true, the relation between -the electric force and the electric current differs from that which -holds in a dielectric. Hence the equations satisfied by the force are -different. The laws of its propagation resemble those of the conduction -of heat rather than those of the transmission of light. - -Again, light travels with different velocities in different transparent -media. The velocity of electric waves, as has been stated, is equal to -1/√(μK); but in making this statement it is assumed that the simple -laws which hold where there is no gross matter--or, rather, where -air is the only dielectric with which we are concerned--hold also in -solid or liquid dielectrics. In a solid or a liquid, as in vacuo, the -waves are propagated by the ether. We assume, as a first step towards -a complete theory, that so far as the electric waves are concerned -the sole effect produced by the matter shews itself in a change of -inductive capacity or of permeability. It is not likely that such a -supposition should be the whole truth, and we may, therefore, expect -results deduced from it to be only approximation to the true result. - -Now, electro-magnetic experiments show that, excluding magnetic -substances, the permeability of all bodies is very nearly the same, -and differs very slightly from that of air. The inductive capacity, -however, of different bodies is different, and hence the velocity with -which electro-magnetic waves travel differs in different bodies. - -But the refraction of waves of light depends on the fact that light -travels with different velocities in different media; hence we should -expect to have waves of electric displacement reflected and refracted -when they pass from one dielectric, such as air, to another, such as -glass or gutta-percha; moreover, for light the refractive index of -a medium such as glass is the ratio of the velocity in air to the -velocity in the glass. - -Thus the electrical refractive index of glass is the ratio of the -velocity of electric waves in air to their velocity in glass. - -Now let K₀ be the inductive capacity of air, K₁ that of glass, taking -the permeability of air and glass to be the same, we have the result -that-- - - Electrical refractive index = √(K₁/K₀). - -But the ratio of the inductive capacity of glass to that of air is -known as the specific inductive capacity of glass. - -Hence, the specific inductive capacity of any medium is equal to the -square of the electrical refractive index of that medium. - -Since Maxwell’s time the mathematical laws of the reflexion and -refraction of electric waves have been investigated by various writers, -and it has been shewn that they agree exactly with those enunciated by -Fresnel for light. - -Hitherto we have been discussing the propagation of electric waves -in an isotropic medium, one which has identical properties in all -directions about a point. Let us now consider how these laws are -modified if the dielectric be crystalline in structure. - -Maxwell assumes that the crystalline character of the dielectric can -be sufficiently represented by supposing the inductive capacity to -be different in different directions; experiments have since shewn -that this is true for crystals such as Iceland Spar and Aragonite; -he assumes also, and this, too, is justified by experiment, that the -magnetic permeability does not depend on the direction. It follows -from these assumptions that a crystal will produce double refraction -and polarisation of electric waves which fall upon it, and, further, -that the laws of double refraction will be those given by Fresnel for -light waves in a doubly refracting medium. There will be two waves in -the crystal. The disturbance in each of these will be plane polarised; -their velocity and the position of their plane of polarisation can be -found from the direction in which they are travelling by Fresnel’s -construction exactly. - -Maxwell’s theory, then, would appear to indicate some close connection -between electric waves and those of light. Faraday’s experiments on -the rotation of the plane of polarisation by magnetic force shew one -phenomenon in which the two are connected, and Maxwell endeavoured to -apply his theory to explain this. Here, however, it became necessary -to introduce an additional hypothesis--there must be some connection -between the motion of the ether to which magnetic force is due and that -which constitutes light. It is impossible to give a mechanical account -of the rotation of the plane of polarisation without some assumption as -to the relation between these two kinds of motion. Maxwell, therefore, -supposes the linear displacements of a point in the ether to be those -which give rise to light, while the components of the magnetic force -are connected with these in the same way as the components of a vortex -in a liquid in vortex motion are connected with the displacements of -the liquid. He further assumes the existence of a term of special form -in the expression for the kinetic energy, and from these assumptions he -deduces the laws of the propagation of polarised light in a magnetic -field. These laws agree in the main with the results of Verdet’s -experiments. - - - - -CHAPTER X. - -DEVELOPMENT OF MAXWELL’S THEORY. - - -We have endeavoured in the preceding pages to give some account of -Maxwell’s contributions to electrical theory and the physics of the -ether. We must now consider very briefly what evidence there is to -support these views. At Maxwell’s death such evidence, though strong, -was indirect. His supporters were limited to some few English-speaking -pupils, young and enthusiastic, who were convinced, it may be, in no -small measure, by the affection and reverence with which they regarded -their master. Abroad his views had made very little way. - -In the last words of his book he writes, speaking of various -distinguished workers-- - - “There appears to be in the minds of these eminent men some - prejudice, or _à priori_ objection, against the hypothesis - of a medium in which the phenomena of radiation of light and - heat, and the electric actions at a distance, take place. It - is true that, at one time, those who speculated as to the - causes of physical phenomena were in the habit of accounting - for each kind of action at a distance by means of a special - ætherial fluid, whose function and property it was to produce - these actions. They filled all space three and four times over - with æthers of different kinds, the properties of which were - invented merely to ‘save appearances,’ so that more rational - enquirers were willing rather to accept not only Newton’s - definite law of attraction at a distance, but even the dogma - of Cotes,[64] that action at a distance is one of the primary - properties of matter, and that no explanation can be more - intelligible than this fact. Hence the undulatory theory of - light has met with much opposition, directed not against its - failure to explain the phenomena, but against its assumption of - the existence of a medium in which light is propagated. - - “We have seen that the mathematical expression for - electro-dynamic action led, in the mind of Gauss, to the - conviction that a theory of the propagation of electric - action in time would be found to be the very key-stone of - electro-dynamics. Now we are unable to conceive of propagation - in time, except either as the flight of a material substance - through space, or as the propagation of a condition of motion, - or stress, in a medium already existing in space. - - “In the theory of Neumann, the mathematical conception called - potential, which we are unable to conceive as a material - substance, is supposed to be projected from one particle to - another in a manner which is quite independent of a medium, - and which, as Neumann has himself pointed out, is extremely - different from that of the propagation of light. - - “In the theories of Riemann and Betti it would appear that the - action is supposed to be propagated in a manner somewhat more - similar to that of light. - - “But in all of these theories the question naturally - occurs:--If something is transmitted from one particle to - another at a distance, what is its condition after it has - left one particle and before it has reached the other? If - this something is the potential energy of the two particles, - as in Neumann’s theory, how are we to conceive this energy - as existing in a point of space, coinciding neither with the - one particle nor with the other? In fact, whenever energy is - transmitted from one body to another in time, there must be - a medium or substance in which the energy exists after it - leaves one body and before it reaches the other, for energy, - as Torricelli[65] remarked, ‘is a quintessence of so subtle a - nature that it cannot be contained in any vessel except the - inmost substance of material things.’ Hence all these theories - lead to a conception of a medium in which the propagation takes - place, and if we admit this medium as an hypothesis, I think - it ought to occupy a prominent place in our investigations, - and that we ought to endeavour to construct a mental - representation of all the details of its action, and this has - been my constant aim in this treatise.” - -Let us see, then, what were the experimental grounds in Maxwell’s day -for accepting as true his views on electrical action, and how since -then, by the genius of Heinrich Hertz and the labours of his followers, -those grounds have been rendered so sure that nearly the whole progress -of electrical science during the last twenty years has consisted in -the development of ideas which are to be found in the “Treatise on -Electricity and Magnetism.” - -The purely electrical consequences of Maxwell’s theory were of course -in accord with all known electrical observations. The equations of the -field accounted for the electro-magnetic forces observed in various -experiments, and from them the laws of electro-magnetic induction -could be correctly deduced; but there was nothing very special in -this. Similar equations had been obtained from the theory of action at -a distance by various writers; in fact, Helmholtz’s theory, based on -the most general form of expression for the force between two elements -of current consistent with certain experiments of Ampère’s, was more -general in its character than Maxwell’s. The destructive features of -Maxwell’s theory were: - -(1) The assumption that all currents flow in closed circuits. - -(2) The idea of energy residing throughout the electro-magnetic -field in consequence of the strains and stresses set up in the -electro-magnetic medium by the actions to which it was subject. - -(3) The identification of this electro-magnetic medium with the -luminiferous ether, and the consequent view that light is an -electro-magnetic phenomena. - -(4) The view that electro-magnetic forces arise entirely from strains -and stresses set up in the ether; the electrostatic charge of an -insulated conductor being one of the forms in which the ether strain is -manifested to us. - -(5) A dielectric under the action of electric force is said to -become polarised, and, according to Maxwell (vol. i. p. 133), all -electrification is the residual effect of the polarisation of the -dielectric. - -Now it must, I think, be admitted that in Maxwell’s day there was -direct proof of very few of these propositions. No one has even yet so -measured the displacement currents in a dielectric as to show that the -total flow across every section of a circuit is at any given moment -the same, though there are other experiments of an indirect character -which have now completely justified Maxwell’s hypothesis. Experiments -by Schiller and Von Helmholtz prove it is true that some action in -the dielectric must be taken into consideration in any satisfactory -theory; they therefore upset various theories based on direct action at -a distance, “but they tell us nothing as to whether any special form -of the dielectric theory, such as Maxwell’s or Helmholtz’s, is true or -not.” (J. J. Thomson, “Report on Electrical Theories,” B.A. Report, -1885, p. 149.) - -When Maxwell died there had been little if any experimental evidence -as to the stresses set up in a body by electric force. Fontana, Govi, -and Duter had all observed that changes take place in the volume of -the dielectric of a condenser when it is charged. Quincke had taken -up the work, and the first of his classic papers on this subject was -published in 1880, the year following Maxwell’s death. Maxwell himself -was fond of shewing an experiment in which a charged insulated sphere -was brought near to the surface of paraffin; the stress on the surface -causes a heaping up of the paraffin under the sphere. - -Kerr had shewn in 1875 that many substances become doubly refracting -under electric stress; his complete determination of the laws of this -action was published at a later date. - -As to direct measurements on electric waves, there were none; the value -of the velocity with which, if Maxwell’s theory were true, they must -travel had been determined from electrical observations of quite a -different character. Weber and Kohlrausch had measured the value of K -for air, for which μ is unity, and from their observations it follows -that the value of the wave velocity for electro-magnetic waves is about -31 × 10⁹ centimetres per second. The velocity of light was known, from -the experiments of Fizeau and Foucault, to have about this value, and -it was the near coincidence of these two values which led Maxwell to -write in 1864:-- - -“The agreement of the results seems to show that light and magnetism -are affections of the same substance, and that light is an -electro-magnetic disturbance propagated through the field according to -electro-magnetic laws.” - -By the time the first edition of the “Electricity and Magnetism” -was published, Maxwell and Thomson (Lord Kelvin) had both made -determinations of K, and had shewn that for air at least the resulting -value for the velocity of electro-magnetic waves was very nearly that -of light. - -For other substances at that date the observations were fewer still. -Gibson and Barclay had determined the specific inductive capacity -of paraffin, and found that its square root was 1·405, while its -refractive index for long waves is 1·422. Maxwell himself thought -that if a similar agreement could be shewn to hold for a number of -substances, we should be warranted in concluding that “the square root -of K, though it may not be the complete expression for the index of -refraction, is at least the most important term in it.” - -Between this time and Maxwell’s death enough had been done to more -than justify this statement. It was clear from the observations of -Boltzmann, Silow, Hopkinson, and others that there were many substances -for which the square root of the specific inductive capacity was very -nearly indeed equal to the refractive index, and good reason had been -given why in some cases there should be a considerable difference -between the two. - -Hopkinson found that in the case of glass the differences were very -large, and they have since been found to be considerable for most -solids examined, with the exception of paraffin and sulphur. For -petroleum oil, benzine, toluene, carbon-bisulphide, and some other -liquids the agreement between Maxwell’s theory and experiment is -close. For the fatty oils, such as castor oil, olive oil, sperm oil, -neatsfoot oil, and also for ether, the differences are considerable. - -It seems probable that the reason for this difference lies in the -fact that, in the light waves, we are dealing with the wave velocity -of a disturbance of an extremely short period. Now, we know that the -substances mentioned shew optical dispersion, and we have at present -no completely satisfactory theory from which we can calculate, from -experiments on very short waves, what the velocity for very long -waves will be. In most cases Cauchy’s formula has been used to obtain -the numbers given. The value of K, however, as found by experiment, -corresponds to these infinitely long waves, and to quote Professor -J. J. Thomson’s words, “the marvel is not that there should not be -substances for which the relation K = μ² does not hold, but that there -should be any for which it does.”[66] - -It has been shewn, moreover, both by Professor J. J. Thomson himself -and by Blondlot, that when the value of K is measured under very -rapidly varying electrifications, changing at the rate of about -25,000,000 to the second, the value of the inductive capacity for glass -is reduced from about 6·8 or 7 to about 2·7; the square root of this is -1·6, which does not differ much from its refractive index. The values -of the inductive capacity of paraffin and sulphur, which it will be -remembered agree fairly with Maxwell’s theory, were found to be not -greatly different in the steady and in the rapidly varying field. - -On the other hand, some experiments of Arons and Rubens in rapidly -varying fields lead to values which do not differ greatly from those -given by other methods. The theory, however, of these experiments seems -open to criticism. - -To attempt anything like a complete account of modern verifications -of Maxwell’s views and modern developments of his theory is a task -beyond our limits, but an account of Maxwell written in 1895 would be -incomplete without a reference to the work of Heinrich Hertz. - -Maxwell told us what the properties of electro-magnetic waves in air -must be. Hertz[67] in 1887 enabled us to measure those properties, and -the measurements have verified completely Maxwell’s views. - -The method of producing electrical oscillations in a conductor had -long been known. Thomson and Von Helmholtz had both pointed it out. -Schiller had examined such oscillations in 1874, and had determined the -inductive capacity of glass by their means, using oscillations whose -period varied from ·000056 to ·00012 of a second. - -These oscillations were produced by discharging a condenser through a -coil of wire having self-induction. If the electrical resistance of the -coil be not too great, the charge oscillates backwards and forwards -between the plates of the condenser until its energy is dissipated in -the heat produced in the wire, and in the electro-magnetic radiations -which leave it. - -The period of these oscillations under proper conditions is given by -the formula T = 2π√(CL) where L, the coefficient of self induction, -and _C_ the capacity of the condenser. These quantities can be -calculated, and hence the time of an oscillation is known. From such -an arrangement waves radiate out into space. If we could measure -by any method the length of such a wave we could determine its -velocity by dividing the wave length by the period. But it is clear -that since the velocity is comparable with that of light the wave -length will be enormous, unless the period is very short. Thus, a -wave, travelling with the velocity of light, whose period was ·0001 -second, such as the waves Schiller worked with, would have a length of -·0001 × 30,000,000,000 or 3,000,000 centimetres, and would be quite -unmeasurable. Before measurements on electric waves could be made it -was necessary (1) to produce waves of sufficiently rapid period, (2) to -devise means to detect them. This is what Hertz did. - -The wave length of the electrical oscillations can be reduced by -reducing either the electrical capacity of the system, or the -coefficient of self-induction of the wire. Hertz adopted both these -expedients. His vibrator, in some of his more important experiments, -consisted of two square brass plates 40 cm. in the side. To each of -these is attached a piece of copper wire about 30 cm. in length, and -each wire ends in a small highly-polished brass ball. The plates are -placed so that the wires lie in the same straight line, the brass -balls being separated by a very small air gap. The two plates are then -charged, the one positively the other negatively, until the insulation -resistance of the air gap breaks down and a discharge passes across. -Under these conditions the discharge is oscillatory. It does not -consist of a single spark, but of a series of sparks, which pass -and repass in opposite directions, until the energy of the original -charge is radiated into space or dissipated as heat; the plates are -then recharged and the process repeated. In Hertz’s experiments the -oscillator was charged by being connected to the secondary terminals of -an induction coil. - -In 1883 Professor Fitzgerald had called attention to this method of -producing electric waves in air, and had given two metres as the -minimum wave length which might be attained. In 1870 Herr von Bezold -had actually made observations on the propagation and reflection of -electrical oscillations, but his work, published as a preliminary -communication, had attracted little notice. Hertz was the first to -undertake in 1887 in a systematic manner the investigation of the -electric waves in air which proceed from such an oscillator with a view -to testing various theories of electro-magnetic action. - -It remained, however, necessary to devise an apparatus for detecting -the waves. When the waves are incident on a conductor, electric -surgings are set up in the conductor, and may, under proper conditions, -be observed as tiny sparks. Hertz used as his detector a loop of wire, -the ends of which terminated in two small brass balls. The wire was -bent so that the balls were very close together, and the sparks could -be seen passing across the tiny air gap which separated them. Such -a wire will have a definite period of its own for oscillations of -electricity with which it may be charged, and if the frequency of the -electric waves which fall on it agrees with that of the waves which -it can itself emit, the oscillations which are set up in the wire will -be stronger than under other conditions, the sparks seen will be more -brilliant.[68] Hertz’s resonator was a circle of wire thirty-five -centimetres in radius, the period for such a resonator would, he -calculated, be the same as that of his vibrator. - -There is, however, very considerable difficulty in determining the -period of an electric oscillator from its dimensions, and the value -obtained from calculation for that of Hertz’s radiator is not very -trustworthy. The complete period is, however, comparable with two -one hundredth millionths of a second; in his original papers, Hertz, -through an error, gave a value greater than this. - -With these arrangements Hertz was able to detect the presence of -electrical radiation at considerable distances from the radiator; he -was also able to measure its wave length. In the case of sound waves -the existence of nodes and loops formed under proper conditions is -well known. When waves are directly reflected from a flat surface, -interference takes place between the incident and reflected waves, -stationary vibrations are set up, and nodes and loops--places, that -is, of minimum and of maximum motion respectively--are formed. The -position of these nodes and loops can be determined by the aid of -suitable apparatus, and it can be shewn that the distance between two -consecutive nodes is half the wave length. - -Similarly when electrical vibrations fall on a reflector, a large -flat surface of metal, for example, stationary vibrations due to the -interference between the incident and reflected waves are produced, and -these give rise to electrical nodes and loops. The position of such -nodes and loops can be found by the use of Hertz’s apparatus, or in -other ways, and hence the length of the electrical waves can be found. -The existence of the nodes and loops shews that the electric effects -are propagated by wave motion. The length of the waves is found to be -definite, since the nodes and loops recur at equal intervals apart. - -If it be assumed that the frequency is known, the velocity of wave -propagation can be determined. Hertz found from his experiments that -in air the waves travelled with the velocity of light. It appears, -however, that there were two errors in the calculation which happened -to correct each other, so that neither the value of the frequency given -in Hertz’s paper nor the wave length observed is correct. - -By modifying the apparatus it was possible to measure the wave length -of the waves transmitted along a copper wire, and hence, again -assuming the period of oscillation, to calculate the velocity of wave -propagation along the wire. Hertz made the experiment, and found from -his first observations that the waves were propagated along the wire -with a finite velocity, but that the velocity differed from that in -air. The half-wave length in the wire was only about 2·8 metres; that -in air was about 4·5 metres. - -Now, this experiment afforded a crucial test between the theories of -Maxwell and Von Helmholtz. According to the former, the waves do not -travel in the wire at all; they travel through the air alongside the -wire, and the wave length observed by Hertz ought to have been the same -as in air. According to Von Helmholtz, the two velocities observed -by Hertz should have been different, as, indeed, they were, and the -experiment appeared to prove that Maxwell’s theory was insufficient and -that a more general one, such as that of Von Helmholtz, was necessary. -But other experiments have not led to the same result. Hertz himself, -using more rapid oscillations in some later measurements, found that -the wave length of the electric waves from a given oscillator was the -same whether they were transmitted through free space or conducted -along a wire.[69] Lecher and J. J. Thomson have arrived at the same -result; but the most complete experiments on this point are those of -Sarasin and De la Rive. - -It may be taken, then, as established that Maxwell’s theory is -sufficient, and that the greater generality of Von Helmholtz is -unnecessary. - -In a later paper Hertz showed that electric waves could be reflected -and refracted, polarised and analysed, just like light waves. In his -introduction to his “Collected Papers” he writes (p. 19):-- - - “Casting now a glance backwards, we see that by the experiments - above sketched the propagation in time of a supposed action - at a distance is for the first time proved. This fact forms - the philosophic result of the experiments, and indeed, in a - certain sense, the most important result. The proof includes - a recognition of the fact that the electric forces can - disentangle themselves from material bodies, and can continue - to subsist as conditions or changes in the state of space. The - details of the experiments further prove that the particular - manner in which the electric force is propagated exhibits the - closest analogy[70] with the propagation of light; indeed, that - it corresponds almost completely to it. The hypothesis that - light is an electrical phenomenon is thus made highly probable. - To give a strict proof of this hypothesis would logically - require experiments upon light itself. - - “What we here indicate as having been accomplished by the - experiments is accomplished independently of the correctness - of particular theories. Nevertheless, there is an obvious - connection between the experiments and the theory in connection - with which they were really undertaken. Since the year 1861 - science has been in possession of a theory which Maxwell - constructed upon Faraday’s views, and which we therefore call - the Faraday-Maxwell theory. This theory affirms the possibility - of the class of phenomena here discovered just as positively - as the remaining electrical theories are compelled to deny - it. From the outset Maxwell’s theory excelled all others in - elegance and in the abundance of the relations between the - various phenomena which it included. - - “The probability of this theory, and therefore the number of - its adherents, increased from year to year. But as long as - Maxwell’s theory depended solely upon the probability of its - results, and not on the certainty of its hypotheses, it could - not completely displace the theories which were opposed to it. - - “The fundamental hypotheses of Maxwell’s theory contradicted - the usual views, and did not rest upon the evidence of decisive - experiments. In this connection we can best characterise the - object and the result of our experiments by saying: The object - of these experiments was to test the fundamental hypotheses of - the Faraday-Maxwell theory, and the result of the experiments - is to confirm the fundamental hypotheses of the theory.” - -Since Maxwell’s death volumes have been written on electrical -questions, which have all been inspired by his work. The standpoint -from which electrical theory is regarded has been entirely changed. The -greatest masters of mathematical physics have found, in the development -of Maxwell’s views, a task that called for all their powers, and the -harvest of new truths which has been garnered has proved most rich. But -while this is so, the question is still often asked, What is Maxwell’s -theory? Hertz himself concludes the introduction just referred to with -his most interesting answer to this question. Prof. Boltzmann has made -the theory the subject of an important course of lectures. Poincaré, -in the introduction to his “Lectures on Maxwell’s Theories and the -Electro-magnetic Theory of Light,” expresses the difficulty, which many -feel, in understanding what the theory is. “The first time,” he says, -“that a French reader opens Maxwell’s book a feeling of uneasiness, -often even of distrust, is mingled with his admiration. It is only -after prolonged study, and at the cost of many efforts, that this -feeling is dissipated. Some great minds retain it always.” And again -he writes: “A French _savant_, one of those who have most completely -fathomed Maxwell’s meaning, said to me once, ‘I understand everything -in the book except what is meant by a body charged with electricity.’” - -In considering this question, Poincaré’s own remark--“Maxwell does -not give a mechanical explanation of electricity and magnetism, he is -only concerned to show that such an explanation is possible”--is most -important. - -We cannot find in the “Electricity” an answer to the question--What is -an electric charge? Maxwell did not pretend to know, and the attempt to -give too great definiteness to his views on this point is apt to lead -to a misconception of what those views were. - -On the old theories of action at a distance and of electric and -magnetic fluids attracting according to known laws, it was easy to be -mechanical. It was only necessary to investigate the manner in which -such fluids could distribute themselves so as to be in equilibrium, -and to calculate the forces arising from the distribution. The problem -of assigning such a mechanical structure to the ether as will permit -of its exerting the action which occurs in an electro-magnetic field -is a harder one to solve, and till it is solved the question--What is -an electric charge?--must remain unanswered. Still, in order to grasp -Maxwell’s theory this knowledge is not necessary. - -The properties of ether in dielectrics and in conductors must be quite -different. In a dielectric the ether has the power of storing energy by -some change in its configuration or its structure; in a conductor this -power is absent, owing probably to the action of the matter of which -the conductor is composed. - -When we are said to charge an insulated conductor we really act on the -ether in the neighbourhood of the body so as to store it with energy; -if there be another conductor in the field we cannot store energy in -the ether it contains. As, then, we pass from the outside of this -conductor to its interior there is a sudden change in some mechanical -quantity connected with the ether, and this change shows itself as a -force of attraction between the two conductors. Maxwell called the -change in structure, or in property, which occurs when a dielectric -is thus stored with electrostatic energy, _Electric Displacement_; if -we denote it by D, then the electric force R is equal to 4πD/K, and -hence the energy in a unit of volume is 2πD²/K, where K is a quantity -depending on the insulator. - -Now, D, the electric displacement, is a quantity which has direction -as well as magnitude. Its value, therefore, at any point can be -represented by a straight line in the usual way; inside a conductor it -is zero. The total change in D, which takes place all over the surface -of a conductor as we enter it from the outside measures, according -to Maxwell, the total charge on the conductor. At points at which -the lines representing D enter the conductor the charge is negative; -at points at which they leave it the charge is positive; along the -lines of the displacement there exists throughout the ether a tension -measured by 2πD²/K; at right angles to these lines there is a pressure -of the same amount. - -In addition to the above the components of the displacement D must -satisfy certain relations which can only be expressed in mathematical -form, the physical meaning of which it is difficult to state in -non-mathematical language. - -When these relations are so expressed the problem of finding the value -of the displacement at all points of space becomes determinate, and -the forces acting on the conductors can be obtained. Moreover, the -total change of displacement on entering or leaving a conductor can be -calculated, and this gives the quantity which is known as the total -electrical charge on the conductor. The forces obtained by the above -method are exactly the same as those which would exist if we supposed -each conductor to be charged in the ordinary sense with the quantities -just found, and to attract or repel according to the ordinary laws. - -If, then, we define electric displacement as that change which takes -place in a dielectric when it becomes the seat of electrostatic -energy, and if, further, we suppose that the change, whatever it -be mechanically, satisfies certain well-known laws, and that in -consequence certain pressures and tensions exist in the dielectric, -electrostatic problems can be solved without reference to a charge of -electricity residing on the conductors. - -Something such as this, it appears to me, is Maxwell’s theory of -electricity as applied to electrostatics. It is not necessary, in order -to understand it, to know what change in the ether constitutes electric -displacement, or what is an electric charge, though, of course, such -knowledge would render our views more definite, and would make the -theory a mechanical one. - -When we turn to magnetism and electro-magnetism, Maxwell’s theory -develops itself naturally. Experiment proves that magnetic induction is -connected with the rate of change of electric displacement, according -to the laws already given. If, then, we knew the nature of the change -to which the name “electric displacement” has been given, the nature -of magnetic induction would be known. The difficulties in the way of -any mechanical explanation are, it is true, very great; assuming, -however, that some mechanical conception of “electric displacement” -is possible, Maxwell’s theory gives a consistent account of the other -phenomena of electro-magnetism. - -Again, we have, it is true, an electro-magnetic theory of light, but -we do not know the nature of the change in the ether which affects -our eyes with the sensation of light. Is it the same as electric -displacement, or as magnetic induction, or since, when electric -displacement is varying, magnetic induction always accompanies it, is -the sensation of light due to the combined effect of the two? - -These questions remain unanswered. It may be that light is neither -electric displacement nor magnetic induction, but some quite different -periodic change of structure of the ether, which travels through the -ether at the same rate as these quantities, and obeys many of the same -laws. - -In this respect there is a material difference between the ordinary -theory of light and the electro-magnetic theory. The former is a -mechanical theory; it starts from the assumption that the periodic -change which constitutes light is the ordinary linear displacement of a -medium--the ether--having certain mechanical properties, and from those -properties it deduces the laws of optics with more or less success. - -Lord Kelvin, in his labile ether, has devised a medium which could -exist and which has the necessary mechanical properties. The periodic -linear displacements of the labile ether would obey the laws of -light, and from the fundamental hypotheses of the theory, a mechanical -explanation, reasonably satisfactory in its main features, can be given -of most purely optical phenomena. The relations between light and -electricity, or light and magnetism, are not, however, touched by this -theory; indeed, they cannot be touched without making some assumption -as to what electric displacement is. - -In recent years various suggestions have been made as to the nature -of the change which constitutes electric displacement. One theory, -due to Von Helmholtz, supposes that the electro-kinetic momentum, or -vector potential of Maxwell, is actually the momentum of the moving -ether; according to another, suggested, it would appear originally -in a crude form by Challis, and developed within the last few months -in very satisfactory detail by Larmor, the velocity of the ether is -magnetic force; others have been devised, but we are still waiting for -a second Newton to give us a theory of the ether which shall include -the facts of electricity and magnetism, luminous radiation, and it may -be gravitation.[71] - -Meanwhile we believe that Maxwell has taken the first steps towards -this discovery, and has pointed out the lines along which the future -discoverer must direct his search, and hence we claim for him a -foremost place among the leaders of this century of science. - - - - -FOOTNOTES - - -[1] A full biographical account of the Clerk and Maxwell families is -given in a note by Miss Isabella Clerk in the “Life of James Clerk -Maxwell,” and from this the above brief statement has been taken. - -[2] “Life of J. C. Maxwell,” p. 26. - -[3] “Life of J. C. Maxwell,” p. 27. - -[4] “Life of J. C. Maxwell,” p. 49. - -[5] “Life of J. C. Maxwell,” p. 52. - -[6] “Life of J. C. Maxwell,” p. 56. - -[7] “Life of J. C. Maxwell,” p. 67. - -[8] “Life of J. C. Maxwell,” p. 75. - -[9] Professor Garnett in _Nature_, November 13th, 1879. - -[10] “Life of J. C. Maxwell,” p. 105. - -[11] “Life of J. C. Maxwell,” p. 116. - -[12] “Life of J. C. Maxwell,” pp. 123–129. - -[13] “Life of J. C. Maxwell,” p. 190. - -[14] Dean of Canterbury. - -[15] Master of Trinity. - -[16] “Life of J. C. Maxwell,” p. 174. - -[17] “Life of J. C. Maxwell,” p. 195. - -[18] “Life of J. C. Maxwell,” p. 207. - -[19] “Life of J. C. Maxwell,” p. 208. - -[20] “Life of J. C. Maxwell,” p. 210. - -[21] “Life of J. C. Maxwell,” p. 211. - -[22] “Life of J. C. Maxwell,” p. 216. - -[23] “Life of J. C. Maxwell,” p. 256. - -[24] “Life of J. C. Maxwell,” p. 267. - -[25] “Life of J. C. Maxwell,” p. 269. - -[26] “Life of J. C. Maxwell,” p. 278. - -[27] “Life of J. C. Maxwell,” p. 292. - -[28] “Life of J. C. Maxwell,” p. 303. - -[29] “Life of J. C. Maxwell,” p. 259. - -[30] B.A. Report, Newcastle, 1863. - -[31] “Life of J. C. Maxwell,” p. 340. - -[32] “Life of J. C. Maxwell,” p. 332. - -[33] “Life of J. C. Maxwell,” p. 336. - -[34] The Professors who were consulted were Challis, Willis, Stokes, -Cayley, Adams, and Liveing. - -[35] “Life of J. C. Maxwell,” p. 349. - -[36] “Life of J. C. Maxwell,” p. 381. - -[37] “Life of J. C. Maxwell,” p. 379. - -[38] An account of the laboratory is given in _Nature_, vol. x., p. 139. - -[39] The Chancellor continued to take to the end of his life a warm -interest in the work at the laboratory. In 1887, the Jubilee year, as -Proctor--at the same time I held the office of Demonstrator--it was -my duty to accompany the Chancellor and other officers to Windsor to -present an address from the University to Her Majesty. I was introduced -to the Chancellor at Paddington, and he at once began to question me -closely about the progress of the laboratory, the number of students, -and the work being done there, showing himself fully acquainted with -recent progress. - -[40] In 1894 the list contained, in Part II., sixteen names, and in -Part I., one hundred and three names. - -[41] Under the new regulations Physics was removed from the first part -of the Tripos and formed, with the more advanced parts of Astronomy -and Pure Mathematics, a part by itself, to which only the Wranglers -were admitted. Thus the number of men encouraged to read Physics was -very limited. This pernicious system was altered in the regulations -at present in force, which came into action in 1892. Part I. of the -Mathematical Tripos now contains Heat, Elementary Hydrodynamics -and Sound, and the simpler parts of Electricity and Magnetism, and -candidates for this examination do come to the laboratory, though not -in very large numbers. The more advanced parts both of Mathematics and -Physics are included in Part II. - -[42] “Life of J. C. Maxwell,” p. 383. - -[43] “Statique Expérimentale et Théorique des Liquides soumis aux -seules Forces Moléculaires.” Par J. Plateau, Professeur à l’Université -de Gaud. - -[44] The “Red Lions” are a club formed by Members of the British -Association to meet for relaxation after the graver labours of the day. - -[45] “Leonum arida nutrix.”--_Horace._ - -[46] _v.r._, endless. - -[47] “Life of J. C. Maxwell,” p. 394. - -[48] “Life of J. C. Maxwell,” p. 404. - -[49] In his “Hydrodynamics,” published in 1738, Daniel Bernouilli -had discussed the constitution of a gas, and had proved from general -considerations that the pressure, if it arose from the impact of a -number of moving particles, must be proportional to the square of their -velocity. (_See_ “Pogg. Ann.,” Bd. 107, 1859, p. 490.) - -[50] The proof is as follows:-- - -If σ be the specific heat at constant volume, σ′ at constant pressure, -and consider a unit of mass of gas at pressure p and volume v, let the -volume increase by an amount dv, while the temperature dy. - - Thus σ′dT = σdT + pdv - - But pv = ⅔T/m - - Hence p being constant, - - pdv = ⅔ dT/m - Therefore σ′ = σ + ⅔ 1/m - -Now suppose an amount of heat, dH, is given to a single molecule and -that its temperature is T. Its specific heat is σ, and - - dH = σmdT - But dH = βdT - Therefore β = σm - - Hence 1/m = σ/β - - Thus σ′ = σ(1 + 2/(3β)) - - And σ′/σ = γ - - Therefore γ = 1 + 2/(3β) - - Or β = 2/(3(γ-1)) - - -[51] Owing to an error of calculation the actual value obtained by -Maxwell from these observations for the coefficient of viscosity is too -great. More recent observers have found lower values than those given -by him; the difference is thus explained. - -[52] Studien über das Gleichgewicht der lebendigen Kraft zwischen -bewegten materiellen Punkten Sitz d. k. Akad Wien, Band LVIII., 1868. - -[53] Another supposition which might be made, and which is necessary -in order to explain various actions observed in a compound gas under -electric force, is that the parts of which a molecule is composed are -continually changing. Thus a molecule of steam consists of two parts of -hydrogen, one of oxygen, but a given molecule of oxygen is not always -combined with the same two molecules of hydrogen; the particles are -continually changed. In Maxwell’s paper an hypothesis of this kind is -not dealt with. - -[54] _Nature_, vol. 1., p. 152 (December 13th, 1894). - -[55] See papers by Mr. Capstick, _Phil. Trans._, vols. 185–186. - -[56] _Nature_, vol. x. - -[57] An historical account of the development of the science of -electricity will be found in the article “Electricity” in the -_Encyclopædia Britannica_, ninth edition, by Professor Chrystal. - -[58] Thomson (Lord Kelvin), “Papers on Electrostatics and Magnetism,” -p. 15. - -[59] J. J. Thomson, B.A., Report, 1885, pp. 109, 113, Report on -Electrical Theories. - -[60] Papers on “Electrostatics,” etc., p. 26. - -[61] It is difficult to explain without analysis exactly what is -measured by Maxwell’s Vector Potential. Its rate of change at any -point of space measures the electromotive force at that point, so far -as it is due to variations of the electric current in neighbouring -conductors; the magnetic induction depends on the first differential -coefficients of the components of the electro-tonic state; the -electric current is related to their second differential coefficients -in the same manner as the density of attracting matter is related -to the potential it produces. In language which is now frequently -used in mathematical physics, the electromotive force at a point -due to magnetic induction is proportioned to the rate of change of -the Vector Potential, the magnetic induction depends on the “curl” -of the Vector Potential, while the electric current is measured by -the “concentration” of the Vector Potential. From a knowledge of the -Vector Potential these other quantities can be obtained by processes of -differentiation. - -[62] The 4 π is introduced because of the system of units usually -employed to measure electrical quantities. If we adopted Mr. Oliver -Heaviside’s “rational units,” it would disappear, as it does in (B). - -[63] For an exact statement as to the relation between the directions -of the lines of electric displacement and of the magnetic force, -reference must be made to Professor Poynting’s paper, _Phil. Trans._, -1885, Part II., pp. 280, 281. The ideas are further developed in a -series of articles in the _Electrician_, September, 1895. Reference -should also be made to J. J. Thomson’s “Recent Researches in -Electricity and Magnetism.” - -[64] Preface to Newton’s “Principia,” 2nd edition. - -[65] “Lezioni Accademiche” (Firenze, 1715), p. 25. - -[66] In his sentence μ stands for the refractive index. - -[67] Hertz’s papers have been translated into English by D. E. Jones, -and are published under the title of _Electric Waves_. - -[68] Some of the consequences of this electrical resonance have been -very strikingly shown by Professor Oliver Lodge. _See_ _Nature_, -February 20th, 1890. - -[69] Hertz’s original results were no doubt affected by waves reflected -from the walls and floor of the room in which he worked. An iron -stove also, which was near his apparatus, may have had a disturbing -influence; but for all this, it is to his genius and his brilliant -achievements that the complete establishment of Maxwell’s theory is due. - -[70] The analogy does not consist only in the agreement between the -more or less accurately measured velocities. The approximately equal -velocity is only one element among many others. - -[71] For a very suggestive account of some possible theories, -reference should be made to the presidential address of Professor W. M. -Hicks to Section A of the British Association at Ipswich in 1895. - - - - -INDEX. - - - Aberdeen, Maxwell elected Professor at, 45; - formation of University of, 51 - - Adams, W. G., succeeds Maxwell as Professor at King’s College, - London, 58 - - Adams Prize, The, 48; - gained by Maxwell, 50 - - Ampère, 155, 204 - - Ampère’s Law, 155, 156 - - _Annals of Philosophy_, Thomson’s, 112, 113 - - “Apostles,” club so called, 30, 89 - - Arago, 157 - - Aragonite, 200 - - Atom, article by Maxwell in _Encyclopædia Britannica_, 108 - - Avogadros’ Law, 117, 124 - - - Bakerian Lecture, delivered by Maxwell, 58 - - Berkeley on the Theory of Vision, 38 - - Bernouilli, D., 113 - - Blackburne, Professor, 16 - - Blore, Rev. E. W., 67 - - Boehm, Bust of Maxwell by, 90 - - Boltzmann, Dr., 135, 137, 138, 144, 216 - - Boltzmann-Maxwell Theory, The, 140, 145 - - Boscovitch on Atoms, 108, 109 - - Boyle’s Law, 114, 117, 124 - - Brewster, Sir David, on Colour Sensation, 99 - - British Association, Maxwell and, 42,54; - Lecture before, 80–82; - Lines on President’s address, 83, 84 - - Butler, Dr. H. M., extract from sermon on Maxwell, 32–35 - - Bryan, G. H., 141, 143 - - - Cambridge, Maxwell at, 28–46; - Mathematical Tripos at, 60; - Foundation of Professorship of Experimental Physics at, 66 - - _Cambridge and Dublin Mathematical Journal_, Papers by Maxwell in, 30 - - Campbell, Professor L., 9, 10, 12, 14, 22, 52, 57, 79 - - Cauchy’s Formula, 208 - - Cavendish, Henry, 73, 74; - Works of, edited by Maxwell, 87, 154, 155 - - Cavendish Laboratory, built and presented to University of - Cambridge, 73, 74 - - Cay, Miss Frances, 11 - - Cayley Portrait Fund, lines to Committee, 86 - - Challis, Professor, 49 - - Charles’ Law, 124 - - Chemical Society, Maxwell’s lecture before, 80–82 - - Clausius, on kinetic theory of gases, 119, 129, 130, 137 - - Clerks of Penicuik, The, 9, 10 - - Colour Perception, 94 - - Colour Sensation, Young on, 97, 98; - Sir D. Brewster on, 99 - - Colours, paper by Maxwell, on, 40, 41; - Helmholtz on, 99 - - Conductors and Insulators, Distinction between, 173 - - Cookson, Dr., 61 - - Corsock, Maxwell buried at, 90 - - Cotes, 202 - - Coulomb, 154 - - Curves, investigated by Maxwell, 19 - - - Daniell’s cells, 77 - - Democritus, 108 - - Demonstrator of Physics, W. Garnett appointed, 75 - - Description of Oval Curves, first paper by Maxwell, 19 - - Devonshire, Duke of, Cavendish Laboratory built by, 73, 74; - Letter of Thanks from University of Cambridge, 74 - - Dewar, Miss K. M., her marriage to Maxwell, 51 - - Dickinson, Lowes; Portrait of Maxwell by, 90 - - Diffusion of gases, 128 - - Discs for colour experiments, 99–101 - - Droop, H. R., 57 - - Dynamical Theory of the Electro-magnetic Field, Maxwell on, 57, 177 - - Dynamical Theory of Gases, Maxwell on, 58, 134 - - - Edinburgh Academy, Maxwell’s school-life at, 13–18 - - Edinburgh, Royal Society of, Maxwell at meetings of, 18 - - Edinburgh, University of, Maxwell at, 22 - - Elastic Spheres, 144 - - Electric Displacement, 218, 219, 220 - - Electrical Theories, 94, 154, 155 - - Electricity and Magnetism, Maxwell’s book on, 59, 77, 79, 147, 155, - 156, 176, 180–201; - papers by Lord Kelvin on, 161–2; - Application of Mathematical Analysis to, paper by G. Green, 158 - - Electricity, Modern Views of, by Professor Lodge, 177 - - Electro-kinetic Momentum, 221 - - Electro-magnetic Field, Dynamical Theory of, Maxwell on, 57, 177 - - Electro-magnetic Induction, 157 - - Electro-magnetic Theory of Light, 174 - - Electro-tonic State, 164 - - Electrostatic Induction, Faraday on, 159 - - _Encyclopædia Britannica_, articles by Maxwell in, 80, 108, 146 - - Ether, labile, 220 - - Experimental Physics, foundation of Professorship at Cambridge, 66; - Election of Maxwell, 68 - - - Faraday on electrical science, 157; - on electrostatic induction, 159 - - Faraday’s Lines of Force, paper by Maxwell on, 44, 45, 148–153 - - Fawcett, W. M., architect of Cavendish Laboratory, 73 - - Fitzgerald, Professor, 177, 211 - - Forbes, Professor J. D., 18, 44, 54; - friendship with Maxwell, 19; - paper on Theory of Glaciers, 19; - resigns Professorship at Edinburgh, 54 - - - Galvani, 155 - - Garnett, W., appointed Demonstrator of Physics at Cambridge, 75; - Life of Maxwell by, 94 - - Gases, Molecular theory of, 57, 108; - Waterston on general theory of, 118; - Clausius on, 119; - diffusion of, 128 - - Gauss’ Theory, 156 - - Gay Lussac’s Law, 117 - - General Theory of Gases, Waterston on, 118; - Clausius on, 119 - - Glenlair, home of Maxwell, 11, 23; - laboratory at, 24; - Maxwell’s life at, 58, 59; - “Electricity and Magnetism” written at, 79 - - Gordon, J. E. H., 77, 78 - - Green, G., of Nottingham, paper on electricity and magnetism, 158; - inventor of term “Potential,” 158 - - - Hamilton, Sir W. R., 22 - - Hamilton’s Principle, 190 - - Heat, Text-book on, by Maxwell, 79 - - Helmholtz, 99, 156, 157, 175, 221 - - Henry, J., of Washington, on electro-magnetic induction, 157 - - Herapath on molecules, 112–116 - - Hertz, Heinrich, 204, 209–213 - - Hicks, W. M., 221 - - Hockin, C., 56 - - Holman, Professor, 133 - - - Iceland Spar, 200 - - Insulators and Conductors, Distinction between, 173 - - - Jenkin, Fleeming, 55, 56 - - - Kelland, Professor, 22 - - Kelvin, Lord, 16, 142, 158, 159, 160, 168; - on the Uniform Motion of Heat, 160; - papers on Electricity and Magnetism, 161, 162 - - Kinetic energy, 124, 129, 136, 139, 191 - - King’s College, London, Maxwell elected Professor at, 54 - - Kohlrausch, 206 - - Kundt, 132 - - - Labile Ether, 220 - - Laboratory at Glenlair, 24 - - Lagrange, 179 - - Lagrange’s Equations, 179, 190 - - Laplace, 155 - - Larmor, J., 141, 142 - - Lecher, 214 - - Lenz, 157 - - Litchfield, R. B., 46 - - Light, Electro-magnetic Theory of, 174; - Waves of, 198, 199 - - Lodge, Professor, book on Modern Views of Electricity, 177 - - Lucretius, 108 - - Luminous Radiation, 221 - - - Mathematical Tripos at Cambridge, subjects, 60; - Maxwell an examiner for, 60, 80; - experimental work in, 76 - - Matter and Motion, Maxwell on, 79 - - Maxwell, James Clerk, parentage and birthplace, 10, 11; - childhood and school-days, 12–18; - his mother’s death, 13; - first lessons in geometry, 17; - attends meetings of Royal Society of Edinburgh, 18; - his first published paper, 19; - friendship with Professor Forbes, 19; - his polariscope, 20; - enters the University of Edinburgh, 22; - papers on Rolling Curves and Elastic Solids, 23; - vacations at Glenlair, 23; - laboratory at Glenlair, 24; - undergraduate life at Cambridge, 28–36; - elected scholar of Trinity, 29; - illness at Lowestoft, 29; - his friends at Cambridge, 30; - Tripos and degree, 35–37; - early researches, 38–44; - paper on Colours, 40, 41; - elected Fellow of Trinity, 43; - Lecturer at Trinity, 43; - Professor at Aberdeen, 45; - his father’s death, 45; - gains the Adams Prize, 50; - marriage, 51; - powers as teacher and lecturer, 52, 53; - Professor at King’s College, London, 54; - gains the Rumford Medal, 55; - delivers Bakerian lecture, 58; - resigns Professorship at King’s College, London, 58; - life at Glenlair, 58, 59; - visit to Italy, 59; - Examiner for Mathematical Tripos, 60, 80; - elected Professor of Experimental Physics at Cambridge, 68; - Introductory Lecture, 68–72; - Examiner for Natural Sciences Tripos, 79; - articles in _Encyclopædia Britannica_, 80, 118, 146; - papers in Nature, 80; - lectures before British Association and Chemical Society, 80–82; - humorous poems, 83–87; - delivers Rede Lecture on the Telephone, 89; - last illness and death, 89, 90; - buried at Corsock, 90; - bust and portrait, 90; - religious views, 91, 92 - - Maxwell, John Clerk, 10, 11 - - Meyer, O. E., 133 - - Mill’s Logic, 38 - - Molecular Evolution, Lines on, 85 - - ---- Physics, 94 - - ---- Constitution of Bodies, Maxwell on, 146 - - ---- Theory of Gases, 57, 108 - - Molecules, 109, 110; - Herapath on, 112–116; - lecture by Maxwell on, 146 - - Motion of Saturn’s Rings, subject for Adams Prize, 49 - - Munro, J. C., 40, 56, 68, 82 - - - Natural Sciences Tripos, Maxwell Examiner for, 79 - - _Nature_, papers by Maxwell in, 80 - - Neumann, F. E., 156, 157 - - Newton’s Lunar Theory and Astronomy, 50 - - ---- Principia, 202 - - Nicol, Wm., inventor of the polarising prism, 20 - - Niven, W. D., 27, 46, 51, 52, 60, 78, 87, 88, 93 - - - Obermeyer, 134 - - Ohm’s Law, 77 - - Ophthalmoscope devised by Maxwell, 83 - - Oval Curves, Description of, Maxwell’s first paper, 19 - - - Parkinson, Dr., 49 - - _Philosophical Magazine_, 56, 99, 115, 120, 133, 142 - - _Philosophical Transactions_, 56, 89, 132, 145 - - Physical Lines of Force, Maxwell on, 56, 158 - - Physics, Instruction in, at Cambridge, 61; - Report of Syndicate on, 62–64; - Demonstrator appointed, 75 - - Poincaré, 216 - - Poisson, 44; - on distribution of electricity, 155 - - Polariscope, made by Maxwell, 20 - - “Potential,” term invented by G. Green, 158; - the Vector, 165, 221 - - Poynting, Professor, 187–189 - - Puluj, 134 - - - Quincke, 206 - - - Radiation, Luminous, 221 - - Rarefied Gases, Stresses in, paper by Maxwell, 135, 145 - - Rayleigh, Lord, 67, 77 - - Rede Lecture on the Telephone, delivered by Maxwell, 89 - - Report on Electrical Theories, J. J. Thomson, 204 - - ---- of Syndicate as to instruction in Physics at Cambridge, 62–64 - - Robertson, C. H., 28 - - Rolling Curves, Maxwell on, 23 - - Royal Society, The, Maxwell and, 55; - Transactions of, 89 - - Rumford Medal gained by Maxwell, 55, 106 - - - Sabine, Major-General, Vice-President of Royal Society, 106 - - Smith’s Prizes, 36 - - Standards of Electrical Resistance, Committee on, 55 - - Stewart, Balfour, 56, 125 - - Stresses in Rarefied Gases, Maxwell on, 135, 155 - - - Tait, Professor P. G., 21, 26, 94 - - Tayler, Rev. C. B., 29 - - Telephone, Rede Lecture by Maxwell on, 89 - - Theory of Glaciers, Prof. Forbes on, 19 - - Thomson, J. J., 157, 208; - Report on Electrical Theories, 205 - - Thomson’s _Annals of Philosophy_, 112, 113 - - - Uniform Motion of Heat in Homogeneous Solid Bodies, paper by Lord - Kelvin, 160, 161 - - University Commission, 47, 48, 62 - - Urr, Vale of, 11 - - - Vector Potential, The, 165, 221 - - Viscosity of Gases, Experiments on, 58, 125, 132 - - Volta, Inventor of voltaic pile, 155 - - - Waterston, J. J., on molecular theory of gases, 114, 115; - on general theory of gases, 118 - - Waves of Light, 198, 199 - - Weber, W., 156, 206 - - Wedderburn, Mrs., 14 - - Wheatstone’s Bridge, 77 - - Williams, J., Archdeacon of Cardigan, 16 - - Willis, Professor, 44 - - Wilson, E., lines in memory of, 86, 87 - - - Young, T., on colour sensation, 97, 98 - - -PRINTED BY CASSELL & COMPANY, LIMITED, LA BELLE SAUVAGE, LONDON, E.C. - - - - - * * * * * * - - - - -Transcriber’s note: - -Punctuation, hyphenation, and spelling were made consistent when a -predominant preference was found in the original book; otherwise they -were not changed. - -Simple typographical errors were corrected; unpaired quotation -marks were remedied when the change was obvious, and otherwise left -unpaired. - -Illustrations in this eBook have been positioned between paragraphs -and outside quotations. - -Footnotes, originally at the bottoms of pages, have been collected, -renumbered, and placed just before the Index. - -The Index was not checked for proper alphabetization or correct page -references. - -Some values in the original book are known today to be incorrect, but -have not been changed here. - -Page 133: The last equation on the page, - - μ = μ₀ (1 + .00275 t - .00000034 t²) - -was misprinted as - - μ = μ₀ {1 + .00275 t .00000034 t²}. - -It is shown here with corrections based on its cited source: - - https://archive.org/details/s05philosophicalmag21londuoft/page/212 - -Page 144: “possibly of ether atoms bound with them” was printed that -way, but “ether” may be a misprint for “other”. - -Page 170: “hence at C, where they touch” was printed as “A”, but Figure -1 at that point is labelled “C”. - - - -***END OF THE PROJECT GUTENBERG EBOOK JAMES CLERK MAXWELL AND MODERN -PHYSICS*** - - -******* This file should be named 65359-0.txt or 65359-0.zip ******* - - -This and all associated files of various formats will be found in: -http://www.gutenberg.org/dirs/6/5/3/5/65359 - - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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