THE CENTURY SCIENCE SERIES JAMES CLERK MAXWELL MODERN PHYSICS GLAZEBROOK THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES THE CENTURY SCIENCE SERIES EDITED BY SIR HENRY E. ROSCOE, U.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. Roscos, F.R.S. Major Rennell, F.R.S. , and the Rise of English Geography. By CLKMBNTS 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. SHBNSTONB, 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 igth Century," &c. Charles Lyell and Modern Geology. By Rev. Professor T. G. BONNEY, F.R.S. James Clerk Maxwell and Modern Physics. B> 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. RUCKER, F.R.S., Professor of Physics in the Royal College of Science, London. CASSELL & COMPANY, LIMITED, London; Paris&r Melbou>nc. (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 R T. GLAZEBROOK, F.R.S. Fellow of Trinity College, Cambridge University Lecturer in Mathematics, and Assistant Director of the Cavendish Latmratnrv CASSELL AND COMPANY, LIMITED LONDON, PARIS $ MELBOURNE 189G ALL RIGHTS RESKKVElJ AM 6-4 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 halt 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 dis- covered, subjects of intelligent interest. Maxwell's life was written in 1882 by two of those who were most intimately connected with him, Pro- fessor 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 653510 VI PREFACE. 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 learn- ing 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. PACK CHAPTER I. EAKLY LIFE 9 ,, II. UNDKB.ORADUATE LIKE AT CAMBRIDGE . . '28 III. EARLY RESEARCHES- PROFESSOR AT AHKRDF.EN . 38 IV. PROFESSOR AT KING'S COLLEGE, LONDON Ln i: AT (JLEM.AIU .">! ,, V. CAMBRIDGE PROFESSOR OF PHYM< . . . i>o ,, VI. CAMBRIDGE THE CAVENDISH LABORATORY . . 73 VII. SCIENTIFIC WORK COLOUR VISION . . .93 VIII. SCIENTIFIC WORK MOLECULAR THEORY . . 108 ,, IX. SCIENTIFIC WORK ELECTRICAL THEORIES . . 118 X. DEVELOPMENT OF MAXWELL'S THEORY . 20'J 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. (Jarnett 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 de- veloping 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, 10 JAMES 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 Dum- friesshire, 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 specu- lations, and most of the Middlebie property had been sold to pay his debts. The property of Sir George Clerk Maxwell de- scended 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.* 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 main- tained 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 * 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. AND MODERN PHYSICS. 11 contributed to the Edinburgh Medical and Philosoph- ical Journal a paper entitled "Outlines of a Plan for combining Machinery with the Manual Printing Press." In 182G 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 super- intended the building work. The actual working plans for some further additions made in 1848 were his handiwork. A garden was laid out and planted, and a dreary stony waste Avas 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 18, 1881, 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 wo have of his childhood are connected with it. The laird devoted himself to his estates and to the educa- tion 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 jour- ney 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 12 JAMES CLERK MAXWELL mode of locomotion was in a kind of rough dog-cart known in the family speech as a hurly." * Mrs. Maxwell writes thusf, 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 * Life of J. C. Maxwell," p. 26. t " Life of J. C. Maxwell," p. 27. AND MODERN PHYSICS. 13 toy known as a magic disc, which afterwards de- veloped 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. I 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*; 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 * "Life of J. C. Maxwell," p. 49. 14 JAMES CLERK MAXWELL 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 be- tween 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 * : "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 im- agination to feed upon. One Saturday, February 12, 1842, lie had a .special treat, being taken 'to see electro-magnetic machines.' " * " Life of J. C. Maxwell," p. 52. AKD MODERN PHYSICS. 15 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. Hoys called him "Dafty,"and used to try to make fun of him. On one occasion I remember lie turned with tremendous vigour, with a kind of demonic force. on his tormentors. I think lie was let alone after that, and gradually won the respect even of the most thoughtless <>l hi^ schoolfellows.'" The first reference to mathematical studies occurs, says Professor Campbell, in a letter to his father written soon after his thirteenth birthday.* "After describing the Virginian Minstrels, and betwixt inquiries after various pets at Ulenlair, lie 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 * "Life of J. C. Maxwell," p 56. 16 JAMES CLERK MAXWELL not merely realised the nature of the five regular solids sufficiently to construct them out of pasteboard with ap- proximate accuracy, but had further contrived other sym- metrical 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 su 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 AND MODERN PHYSICS. 17 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* is the account of Maxwell's first interview with the rector : Rector : " What part of Galloway do you come from ? " ./. C. *][. : " 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 rirst lessons of geometry branched out at once into inquiries which became fruitful." In July, 1H45, he writes : "I have got the llth prize for Scholar>hip, the l.-t 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)eacli * " Life of J. <_'. Maxwell," p. 07. 18 JAMES CLERK MAXWELL 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 lather 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 in- terested 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 * : " 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 corre- sponding 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 truly, ' JAMES D. FORBES.' In consequence of this, Clerk Maxwell's first * "Life of J. C. Maxwell," p. 75. AM) MODERN I'HYSICS. 19 published paper was communicated to the Royal Society of Edinburgh on April 6th, 1840, 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 ex- presses 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 he 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 u -2 20 JAMES CLERK MAXWELL 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 card- board, 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 after- wards 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.* After this they were more carefully guarded, and they are now, together with the wooden polariscope, the bits of unannealed glass, * Professor Garnctt in Nature, November 13th, 1879. AND MODERN' PHYSICS. 21 and the water-colour drawings, in one of the show- cases 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 tin 1 fourth. "At school he was at first regarded as shy and rather dull. Ue 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 scholar- ships, mathematics, and English verse composition. From this time forward I became very intimate with him, and we discussed together, with schoolboy enthusiasm, numerous 22 JAMES CLERK MAXWELL 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, communi- cated by Forbes to this society and printed in our ' Proceed- ings,' 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 \V. R. Hamilton. At this time, accord- ing to Professor Campbell* "he still occasioned some concern to the more conven- tional 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 * "Life of J. C. Maxwell," p. 10.}. AND MODERN' PHYSICS. 23 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. O. Tait, and Allan Stewart. Tait went to Peterhouse, Cambridge, in 184S, after one session of the University of Edinburgh ; Stewart to the same college in 1841) ; Maxwell did not go up until IS "><>." During this period he wrote two important papers. The one, on " Rolling Curves," was read to the Royal Society of Edinburgh by 1'rofessor Kelland (" it was not thought proper for a boy in a round jacket to mount the rostrum") in February. 1S4M: the other, on "The Equilibrium of Elastic Solids. appeared in the spring of lSf>0. The vacations were spent at ( Jlenlair, and we It am from letters to Professor Campbell and others liou the time was passed. " On Saturday," he writes* April 2(Jth, ls4s, 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, * " Lifn of ,1. C. Maxwell," p. 11(J. 24 JAMES CLERK MAXWELL and two chairs, of which one is sate, 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 experiment- ing 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 AND MODERN PHYSICS. 25 crystals of saltpetre, which I have been cutting up into plates to-day in hopes to see rings." In July, 1849, he writes * :- " 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 com- pressed 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 ivading Young's 'Lectures,' Willis's 'Principles of Mechanism; Moseley's ' Engineering and Mechanics,' Dixon on 'Heat.' and Moiguo's ' Repertoire d'Optique.' This last is a very complete analysis of all that has been done in the optical way from 1-Vesnel 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 li^lit, as heat, chemical action, photographic rays, action on vegetables, etc. "My notions are rather few, as I do not ers 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 sus- pension bridges, and catenaries, and el.istic 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 * "Life of .1. ('. Maxwell," pp. 1 -JIM '-!). 26 JAMES CLERK MAXWELL 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 Torbes 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 \\orks in the library. 1 Miring this period he wrote two valuable papers, which are published in our 'Transaction?,' 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 examina- tion, 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 AND MODERN PHYSICS. 27 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. I). Niven, in his preface to Maxwell's collected works (p. xii.), says : "It may readily l>e supposed that his preparatory training for the Cambridge course was far removed from the ordinary tyie. There had indeed for some time been practically no restraint upon his plan of study, and his mind had born 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 ond 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 \\hil-- wandering along the banks of a stream in the fiv.- indnlgi-nc.- of his fancies. .Maxwell was not only a lo\er of portry, but himself a poet, as the line pieces gathered together by Mr. Campbell abundantly testily. He saw, however, that his true calling was science, and never regarded these poetical ell'orts as other than mere pastime. Devotion to science, already stimulated by successful endeavour; a tendency to ponder over philosophical problems; and an attachment to Knglish literature, particularly to Knglish poetry these tastes, im- planted 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 Jtoyal Society of Kdinburgh 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." 28 JAMES CLERK MAXWELL 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 mam- 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 Edin- burgh schoolfellow, C. H. Robertson. He attended the AND MODERN PHYSICS. 29 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 ((, Old Court). In 'June, 1852, he came of age. " 1 trust you will IK- as discreet when major as you have been while- minor." writes his father the day before. The next academic year, October, 1852, to .lime, 185:{, 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 Lowest oft. with tin Rev. C. B. Tayler, the uncle of a Collrge friend. His own account of the illness is given in a letter to Professor Campbell*, dated July 14th, 1S5-S. " You wrote just in time for your let tor to reach me as I reached Cambridge. After examination, I went to visit the Hev. C. B. Tayler (uncle to a Tayler whom I think you havr seen under the name of Freshman, ete., 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 lth June, l.ut on the 17th I felt * Lift- of J. C 1 . Maxwrll," p. lo. 30 JAMES CLERK MAXWELL unwell, and took measures accordingly to be well again -i.e. Avent to bed, and made up ray 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 founda- tion 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 Cains, the missionary bishop of Central Africa, Henry and Frank Mackenzie of Trinity, Droop, third Wrangler in 1854 ; Gedge, Isaac Taylor, Blakiston, F. W. Farrar,* H. M. Butler,f Hort, V. Lushington, Cecil Munro, G. W. H. Tayler, and W. X. Lawson. Some of these who survived him have * Dean of Canterbury. f Master of Trinity. AND MODERN PHYSICS. 31 given to Professor Campbell their recollections of these undergraduate days, which are full of interest. Thus Mr. Lawson writes * : " 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, '(iin 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 descrip- tion of his own wonderful power. I remember, one day in lecture, our lecturer had filled the Mack-hoard three times with the investigation of some hard problem in ( Jeometry 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 loud of a talk upon almost anything. He and 1 were pupils i.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 * " Life of J. C. Maxwell," i>. 174. 32 JAMES CLERK MAXWELL 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 extra- ordinary 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 oue 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, 1i 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 kiteat 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 titled 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 lie felt most fitted. * " Life of J. C. Maxwell," p. 207. 38 JAMES CLERK MAXWELL 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 con- nexion 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 ophthalmo- scope.* " 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 * " Life of J. C. Maxwell," p. 208. AND MODERN PHYSICS. 39 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 llth 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. [ have made a tii uule of colours by which you may make out everything. " If you can find out any people in Kdinburgh 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. [ have also constructed a pair of squinting spectacle", 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-throe. " He that would enjoy life and act with freedom must have the work of the day continually before his eyes. Not yester- day's work, lest he fall into despair ; nor to-morrowV, 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 40 JAMES CLERK MAXWELL 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, remem- bering 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 Christinas vacation of that year, and he could not return to Cambridge at the beginning of the Lent term. " My steps," he writes* 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 lettersf 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 * " Life of J. C. Maxwell," p. 210. t " Life of J. C. Maxwell," p. 211. \ AND MODERN PHYSICS. 41 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 (Jerman writers. It takes a long time to reduce to order all the notions one gets from these men, but 1 hope to see my way through the subject and arrive at some- thing 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 1 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, 1 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. 42 JAMES CLERK MAXWELL "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 Sep- tember, 1855, and Maxwell was present, and showed his colour-top at Professor Ramsay's house to some ot those interested. Letters* 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. Wart- man 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 news- papers 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 ex- penses 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 intel- * "Life of J. C. Maxwell," p. 216. AND. MODERN PHYSICS. 43 lectual 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 examina- tion to consider. 4i 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 groat 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, 1 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 havo 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. 44 JAMES CLERK MAXWELL 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 dis- covering 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 w r ork is to profess one's readiness by applying for it." On the AND MODERN PHYSICS. 45 20th of February ho 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 ot 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 lie able to write out fully the paper. " I have done nothing in that way this term," he says, " but am just begin- ning to feel the electrical state come on again." His lather was working at Edinburgh in support of his candidature for Aberdeen, and when, in the middle of March, he returned North, he found every- thing well prepared. The two returned to (ilenlair 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. Ho had been giving directions about the garden, and he said he would sit down and rest a little, as usual. Alter 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 46 JAMES CLERK MAXWELL 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 induce- ments ; 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* 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." * Life of J. C. Maxwell," p. 256. AND MODERN PHYSICS. 47 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 corVee 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* 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 sec- 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 satis- factory." Another letter,! June 5th, 1857, also to Munro, refers to the work of the University Commission and the new statutes. * " Lift- of J. C. Maxwell," p. 207. t " Life of J. C. Maxwell," p. 269. 48 JAMES CLERK MAXWELL " 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 some- times 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 pro- hibited 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 1 848 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 AND MODERN PHYSICS. 49 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 1S57 tell of the progress of the task. Thus, writing* to Lewis Campbell from Olenlair on August 2y 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 Max- well's time those who wished to work had the use of the laboratory and assistance and help from him, but they were left pretty riiuch 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 tho preliminary observations for his 78 JAMES CLERK MAXWELL 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 some- what 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 ine, and AND MODERN PHYSICS. 79 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 Ulonlair. About the time of his return to Cambridge, in October, 1872, he writes* to Lewis Campbell : " I am continually engaged in stirring up the Clarendon Press, but they have been tolerably regular for two months. I lind 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 1870. In 1873 and 1874 he was one of the examiners for the Natural Sciences Tripos, and in 1873 he was the * Life of J. C. Maxwell," p. 383. 80 JAMES CLERK MAXWELL 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 Encyclopaedia Britannica was being published, and Professor Baynes had enlisted his aid in the work. The articles " Atom," " Attraction," " Capillary Action," " Constitu- tion 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 AND MODERN PHYSICS. 81 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 con- tinuous change, and the molecule is incapable of growth or decay, of generation or destruction. "None of the processes of Xature, since the time when Nature began, have produced the slightest difference in the properties of any molecule. We are therefore unable to ascribe cither 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, us Sir John Ilerschel 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 wlien she assures herself, on the one hind, 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 some- thing 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 F 82 JAMES CLERK MAXWELL 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 aspira- tions 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 Nuture by Mr. C. J. Munro, and at a later time by Clifford in one of his essays. Some correspondence with the Bishop of Glou- cester and Bristol on the authority for the com- parison of molecules to manufactured articles is AND MODERN PHYSICS. 83 given by Professor Campbell, and in it Maxwell points out that the latter part of the article " Atom " in the Encyclopaedia is intended to meet Mr. Munro's criticism. In 1874 the British Association met at Belfast, under the presidency of Tyndall. Maxwell was pre- sent, and published afterwards in Blackwood's Maga- zine 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. Xotes 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 likenoss 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 currv 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. P 2 84 JAMES CLERK MAXWELL 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 incom- pressible 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,* 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, do wn through untold generations, transmission of structureless germs 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 wo honour the vista of ancestors now in our view ? First, then, lot us honour the atom, so lively, so wise, and so small ; The atornists 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. * "Statique Expenmentale et ThSorique des Liquides souinis aux seulea Forces Moleculaires." Par J. Plateau, Professeur a 1'Uuiversite de Gaud. AND MODERN PHYSICS. 85 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,* As round our proy wo ramp and rave. Thus, by a swift metamorphosis, 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,f From thee the wise their wisdom learn ; From thec 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. * The "Red Lions" arc a club formed by Members of the British Association to meet for relaxation after the graver lalxmrs of the day. f "Leonum arida nutrix." Horace. 86 JAMES CLERK MAXWELL 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 * 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 naming 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). Gi.v a body meet a body Flyin' through the air, Gin a body hit a body, Will it fly? and where? * v.r.. endless. AND MODERN PHYSICS. 87 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 Wo do not always see. Ilka problem has its method By analytics high ; For me, I ken na anc 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 measure- ment 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 con- siderable skill both of a mathematical and experimental character. 83 JAMES CLERK MAXWELL " 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 experi- ments 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 publica- tion. 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 publica- tion 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 ut- most 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, AND MODERN PHYSICS. 89 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 chris- tened the " Eranus," and three of Maxwell's contribu- tions to it have been preserved and are printed by Professor Campbell. After the Cavendish papers were finished, Max- well 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 Cam- bridge Philosophical Society. In the previous year he had delivered the Rede lecture on " The Tele- phone." 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 con- suited 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 90 JAMES CLERK MAXWELL 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 con- veyed 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 AND MODERN PHYSICS. 91 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* 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 fas- tened 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 interpre- tations, 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." * " Life of J. C. Maxwell," p. 394. 92 JAMES CLERK MAXWELL And again in his letter* 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 arc 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. * " Life of J. C. Maxwell," p. 401. AND MODERN PHYSICS. 93 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 Nivcn, at the close of his obituary notice in the Proceedings of the Royal Society, says : " It is seldom that the faculties of invention and exposi- tion, the attachment to physical science and capa- bility 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 unmistak- able 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. 94 JAMES CLERK MAXWELL While attempting it I wish to express my indebted- ness to others who have already written about Max- well'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 con- tributions 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 Avhich 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 AND MODERN PHYSICS. 95 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 chroma- tically 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 pro- duced 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 96 JAMES CLERK MAXWELL beams which differ optically may yet be alike chroma- tically ; 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. 0), and his solution is the following : He arranges the seven colours of the spectrum round the circumfer- ence 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 mathe- matically 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 AND MODERN PHYSICS. 97 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 rulour depends on the proportion of the intensities of the compon- ents; 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 corre- sponding 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 98 JAMES CLERK MAXWELL 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, corre- sponding 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 Brewstcr had recently developed a new theory of colour sensation which had formed the basis of some discussions, and in 1852 von Helmholtx published his first paper on the subject. According to Brewster, the three primitive colours were rod, 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 con- ducted by mixing pigments, with the exception of those in which the rotating disc was used, and that it is AND MODERN PHYSICS. 99 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, 185-i) 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 I860. 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. G 2 100 JAMES CLERK MAXWELL 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 im- pression 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 GG'G of AND MODERN PHYSICS. 101 red and 334 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'(5 parts of red and 33'4 parts of green produce the same chromatic effect as 29'1 of yellow and 241 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, 0, 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 13 match c parts of C together with d parts of D ; or we may write this as an equation thus : a A + b B = r C + d D, where the -I- stands for " combined with," and the = for " matches in tint." We may also write the above rfI)=aA + 6B < 4) + ft (44) + c ((58). Again, the position on the diagram tor all colours for which , c, are all positive lies within the triangle A B I'. If one of the co-efficients, sav <\ is negative the same construction applies, but, the weight applied at ( must be treated as acting in the opposite direction to those at A and 15. A mixture of the given colour and ( ' matches a mixture of A and B. It is clear that the point corresponding to X will then lie outside the triangle AND MODERN PHYSICS. 105 A H 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 mix- ture 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 mix- ture 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 New- ton'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 106 JAMES CLERK MAXWELL colour. If 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 Max- well 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 satis- factory. 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 blind- ness 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 remark- able result that to a very near degree of approxi- mation 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 MODERN PHYSICS. 107 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 tor the physiologists to do the rest. 108 JAMES CLERK MAXWELL CHAPTER VIII. SCIENTIFIC WORK MOLECULAR THEORY. MAXWELL in his article "Atom," in the ninth edition of the Encyclopaedia Britannica, has given some account of Modern Molecular Science, and in particular of the molecular theory of gases. Of this sciencCi Clausius and Maxwell are the founders, tKough 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 contri- butions 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 Natura ex- plained its principles. The atoms do not till space ; there is void between. " Quapropter locus est intactus inane vacansque, Quod si non esset, nuM ratione mover! Res possent ; namque officium quod corporis extat Officere atquo obstare, id in omni tenipore adesset Omnibus. Hand 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 AND MODERN PHYSICS. 100 apart. It has no parts or dimensions : it is a mere geometrical point without extension in space; it lias 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 arc 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 maybe 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 110 .JAMES CLEKK MAXWELL 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 follow- ing 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 funda- mental assumption just mentioned. Tt 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 AND MODERN PHYSICS. Ill 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 gaming 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 pro- portional 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 ; 112 JAMES CLERK MAXWELL if ni be the mass of each molecule, the mass which strikes the surface per second is X m v ; the velocity of each particle of this mass is r, therefore the momentum destroyed per second by the impact is N m v x v, or N m v*, and this measures the pressure. Hence in this case if p be the pressure 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 ?, X. Hence the formula becomes p = i X T m c~. Moreover, if p be the density of the gas that is, the mass of unit volume then Nm is equal to p, for m is the mass of each particle, and there are N particles in a unit of volume. Hence, finally, p = J p v 2 . Or, again, if V be the volume of unit mass of the gas, then p V is unity, or p is equal to \JV. Hence ^>V = v 2 . Formulae equivalent to these appear first to have been obtained by Herapath about the year 1810 (Thomson's "Annals of Philosophy," 1810). The AND MODERN PHYSICS. 113 results only, however, were stated in that year. A paper which attempted to establish them was pre- sented 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 Proposi- tions 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 = /// i\ if T represents the tempera- ture: and Or, again These results are practically given in Proposition viii., Corr. (1) and (2), and Proposition ix.* The tempera- * In his " Hydrodynamics, " published in 1738, Daniel liornouilli had discussed the constitution of a ga.s, 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 <>f their velocity. (See " Pogg. Ann.," Bel. 107, 18o9, p. 490.) 114 JAMES CLERK MAXWELL ture 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 '/> 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, AND MODERN PHYSICS. 115 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^ equal to I N, in v* t where r, is the velocity of the group and ]S\ 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 l> = I N m v 2 , where v is not now the actual velocity of the particles, but a mean velocity given by the equation N ^ = N, v* + N 2 *v + , which will produce the same pressure as arises from the actual impacts. This quantity v- 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 1840 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 re- ceived, 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 116 JAMES CLERK MAXWELL 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 in- genuity 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. AND MODERN PHYSIOS. 117 According to this we are thus to put in the pres- sure equation i m v- - T, the temperature, and we have at once p \ = -- 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 , in, be the masses of each molecule of two dif- ferent sets of molecules mixed together, then, when a steady state has been reached, since the temporal mv is the same throughout, m, v? is equal to '///., >.,-. The average kinetic energy of each molecule is the same. From this Avogadros' law follows at once for if y>,, p. 2 be the pressures, X,, X, the numbers of molecules per unit volume Hence, if /> k is equal to y>.,, since //;, /*,- is equal to in., v. 2 ~, we must have N\ equal to N.,, 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, wo shall have more to say. The third section of the paper deals with adiabatic expansion, and in it there is an error in calcula- tion which prevented correct rcsultsfrom being attained. 118 JAMES CLERK MAXWELL 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 ther- mometer." 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 AND MOIlEHX PHYSICS. 119 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 ac- cording to the result given above, p = i p r- : thus v- = 3 pfp, and p and p being known, we rind ?-. Thus for hydrogen at freezing-point and atmospheric pros- sure 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 tin- subject. His first paper is in " PoggendorfTs Annu- len," 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. 120 JAMES OLE11K MAXWELL These two papers appear to have attracted Max- well's attention to the matter, and his tirst paper, entitled "Illustrations of the Dynamical Theory of Gases," was read to the British Association at Aber- deen 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 founda- tion of such investigations on strict mechanical prin- ciples," 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 Avas led to this method by his investigation into the theory of Saturn's rings, which had been com- AX1) MODEHX PHYSICS. 121 pletcd in 1850, 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 back- wards 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 in- terval more people would cross it, going in the direc- tion in which the crowd is moving, than in die 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 in- terval. 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 122 JAMES CLERK MAXWELL more accurate, do not dift'er 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 con- siderably 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 AN' I) MODERN PHYSICS. 128 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 hud 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 lt m* be the masses of the particles in 124 .JAMES CLERK MAXWELL the two sets respectively, r,, v., their mean velocities we must have finally 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 re- searches on the motion of a system of spherical particles, we find that we again can obtain the equations T = i mv* p = I N,//>' 2 = | NT = * P T From these results we obtain as before the laws of Boyle, Charles and Avrogadro. Again if a 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 a 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 AND MODERN PHYSICS. 125 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 a 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 in- dividual 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 tho 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 IK>\V, by means of experiments on the viscosity of gases, the length of the mean free path could be determined. An illustration due to Professor Hal four Stewart will perhaps make this clear. Lot 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 126 JAMES CLERK MAXWELL 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 sur- face 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 explana- tion 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 consider- able, so that on the average a particle can penetrate a considerable distance into the second gas before a AND MODERN PHYSICS. 127 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( .^, 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 co- efficient 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 in- crease 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 128 JAMES CLERK MAXWELL 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 experi- ments were too complicated to admit of direct com- parison 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 ^ of an inch. The number was close enough to that found from the viscosity to afford some confirmation of his theory. AND MODERN PHYSICS. 129 However, a few years later Clausius criticised tlio 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 tho other; the temperatures of the two will then be dif- ferent. 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 ef 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 .,; 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 130 JAMES CLERK MAXWELL 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 par- ticle the average value of these two portions of energy would be equal. The total energy will be half trans- lational 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. Max- well shows that for rigid bodies this constant is 2. Let us denote it for the present by the symbol @. Thus, if the translational energy of a molecule is m v~, its whole energy is $ m v~. The temperature is still measured by the trans- lational energy, or \ m v* ; the heat depends on the whole energy. Hence if H represent the amount of AND MODERN PHYSICS. 131 heat measured as energy contained by a single molecule, and T its temperature, we have H == /3T From this it can be shewn* that if 7 represent the ratio of the specific heat of a gas at constant pressure to the specific heat at constant volume, then For air and some other gases the value of 7 has been shown to be T408. From this- it follows that * The proof is as follows : If a be the specific heat at constant volume, ut Max- well'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 p, the coefficient of viscosity at t and /* 0) that at zero the equation p = ^(1 +.00365 t). The most recent results of Professor Holinan (Philosophical Magazine, Vol. xxi., p. 212) give p = ^ {i + .00275 t .00000034 t-}. And results similar to this are given by 0. E. Meyer * 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. 134 JAMES CLERK MAXWELL 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 sup- posed 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 18G6, 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 ot 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 AND MODERN PHYSICS. Ic5 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 Liter date, " On the Stresses in Rarefied Gases," Phil. Trans., 1879, realised this ; but even in this last paper ho 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 tempera- ture 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 dis- tribution of temperature is uniform. When dealing, for example, with the conduction of heat, a modifi- cation of the expression is necessary. This was pointed out by Boltzmann.* In the paper of 1866, Maxwell applies his gener- alised results to the final distribution of two gases * Studien uber das Gleichgewicht dcr lebendigen. Kraft zwisclien bewegten materiellcn Punkten Sitz d. k. Akad Wien, Band LVIIl, 136 JAMES CLERK MAXWELL under the action of gravity, the equilibrium of tem- perature 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 tem- perature. 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. AND MODERN PHYSICS. 137 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.* 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 ft to denote this constant. Thus, while the tem- perature is measured by the average kinetic energy of translation of the centre of gravity of each mole- cule, the heat contained in a molecule is its whole energy, and is ft times this quantity. Thus the con- clusions as to specific heat, etc., already given on page 130, apply in this case, and in particular we have the result that if 7 be the ratio of the specific heat at constant pressure to that at constant volume, then Maxwell's theorem of the distribution of kinetic energy among a system of molecules applied, as he gave it in 18GG, 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 * 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. 138 JAMES CLERK MAXWELL 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 Distri- bution of Energy in a System of Material Points," Camb. Phil. Trans., XII.), took up this probleai. Watson had given a proof of it in 1876 differing from B jltzmann'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 AND MODERN PHYSICS. 139 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 re- quired 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 deter- mine 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 ft - GK = 2 ~ 3K Or, again, if we suppose that the molecule is such that ra 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 140 JAMES CLERK MAXWELL 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 Hence y = 1 + m ~s = l + if 7i 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 7=1-333. Now the fact that this is not the value of 7 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 7i be equal to five, then 7 has the value 140. 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 AND MODERN PHYSICS. 141 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 188G, 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 dis- cussion he started at Oxford by reading this report has been continued in the pages of Nature and else- where since that time. Mr. Bryan shows in the first place what may bo 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.* * Nature, vol. 1., p. 152 (December 13th, 1894). 142 JAMES CLERK MAXWELL " 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 pro- position 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 en- closed in a rigid envelope impermeable to heat, appears to be proved. For such a case, therefore, the Maxwell-Boltzrnann law is the only one possible. But whether this be so or not, the kw first intro- duced 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,]fi.a,rch, 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. AND MODERN PHYSICS. 143 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 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 144 JAMES CLERK 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.* 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 super- structure 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 mole- cule, whose atoms are capable of vibrating relative to one another, affords an interesting field for investi- gation and speculation. Is the Boltzmann distribu- tion still unique, or do other permanent distribu- tions exist in which the kinetic energy is unequally divided ? " * Sec papers by Mr. Capstick/PAiJ. Trans , vols. 185-180, AND MODERN PHYSICS, 145 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 con- stitute 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 ex- planations, but we must not let our dread of the task which remains to be done blind our eyes to the great- ness of Maxwell's work. One other important paper, and a number of shorter articles, remain to be mentioned. The Boltzniann-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 14G JAMES CLERK MAXWELL 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 re- garding the nature of the contact of the solid and the gas, there will be, even when the pressure is con- stant, 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 Waal's book on " The Continuity of the Gaseous and Liquid States,"* he explains and dis- cusses 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 Encyclo- paedia 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 * Xatitre, vol. x. AND MODERN PHYSICS. 147 how the conclusions of the second law of thermo-dyna- mics 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. 148 JAMES CLEilK MAXWELL CHAPTER IX. SCIENTIFIC WORK. ELECTRICAL THEORIES. CLERK MAXWELL'S first electrical paper that on Faraday's " Lines of Force " was read to the Cam- bridge Philosophical Society on December 10th, 1855, and Part II. on February llth, 185G. 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 formulae, 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 formuhe are inapplicable. In order, therefore, to appreciate the requirements of the science, the student must make himself familiar with a consider- able body of most intricate mathematics, the mere retention of which iu the memory materially interferes with further AND MODERN PHYSICS. 149 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 com- mitted 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 ; 150 JAMES CLERK MAXWELL 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 import- ance 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 formulae. These formula? 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, %ow of heat for accelerating eject of attraction at any point, and temperature {or potential, and the solution of a problem in attractions is transformed into that of a problem in heat. "This analogy between the for muke of heat and attraction was, I believe, first pointed out by Professor William Thomson in the Camlriilye Mathematical Journal, Vol. III. " Now the conduction of heat is supposed to proceed by an AND MODERN PHYSICS. 151 action between contiguous parts of a me Jium, while the force of attraction is a relation between distant bodies, and yet, if we knew nothing more than is expressed in the mathematical formulae, 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 at- tempted to bring before the mind, in a convenient and manage- able form, those mathematical ideas which are necessary to the study of the phenomena of electricity. The methods are gener- ally 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, ore 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 com- plexity 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 152 JAMES CLERK MAXWELL 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 polo 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 a3 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 AND MODERN PHYSICS. 153 observed in electrical and magnetic phenomena. In the case of a perfectly arbitrary system of forces, there will generally bo 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 whit-h 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 pre- mature 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 philo- sophers, 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." 154 JAMES CLERK MAXWELL 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 as- sumption 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* in 1855. Coulomb's experiments had established the funda- mental facts of electrostatic attraction and repulsion, and Coulomb himself, about 1785, had stated a theory based on these experiments Avhich could " only be attacked by proving his experimental results to be inaccurate."f Coulomb supposes the existence of two electric fluids, the theory developed previously by Franklin, but says " Jc previens pour mettre la theorie ut 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 con- tradicted the usual views, and did not rest upon the evidence of decisive experiments. In this connection \\e can best characterise the object and the result of our experiments by * 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. 216 JAMES CLERK MAXWELL 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 in- teresting answer to this question. Prof. Boltzmann has made the theory the subject of an important course of lectures. Poincare, 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, Poincare's own AND MODERN PHYSICS. 217 remark " Maxwell does not give a mechanical ex- planation 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 equi- librium, 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 con- ductors 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 arc 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 218 JAMES CLERK MAXWELL 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 electro- static energy, Electric Displacement; if we denote it by D, then the electric force R is equal to 47rl)/K, and hence the energy in a unit of volume is 27rD~/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 2?rD 2 /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 AND MODE11X 1MIVSIOS. 211 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 scat 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 Max- well'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 displace- ment, 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-mag- netism, Maxwell's theory develops itself naturally. Experiment proves that magnetic induction is con- nected with the rate of change of electric displace- ment, according to the laws already given. If, then, we knew the nature of the change to which the name 220 JAMES CLERK MAXWELL " 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 displace- ment, 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 be- tween 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 dis- placement 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 AND MODERN PHYSICS. 221 displacements of the labile ether would obey the laws of light, and from the fundamental hypotheses of the theory, a mechanical explanation, reasonably satis- factory 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 Yon Helm- holtz, supposes that the electro-kinetic momentum, or vector potential of Maxwell, is actually the momen- tum of the moving ether; according to another, sug- gested, it would appear originally in a crude form by Challis, and developed within the last few months in very satisfactory detail by l,:irmor, the velocity of the ether is magnetic force: others have been devised, but we are still waiting for a second Xewtoii to give us a theory of the ether which sh;ill include the facts of electricity and magnetism, luminous radi- ation, and it may be gravitation.* Meanwhile we believe that Maxwell has taken the Jirst steps towards this discovery, and has pointed out the lines along which the future discoverer must direct his search, and hence AVC claim for him a foremost place among the leaders of this century of science. * Fora very suggestive account of some poxsiUe theories, reference should be made to the presidential address of Professor W. M. Hicks to .Section A of the British Association at Ipswich in ISO.',. I^DEX. Aberdeen, Maxwell elected Professor at, 45 ; formation of University of, 51 Clausius, on kinetic theory of gases, 119, 12!, 130, 137 Adams, W. G., succeeds Maxwell as Pro- fessor at King's College, London, 58 Adams Prize, The, 48 ; gained by Max- Clerks of Penicuik, The, 9, 10 Colour Perception, 94 Colour Sensation, Young on, 9V, 98 ; well, 50 Sir D. Brewster on, 99 Ampere, 155, 204 Ampere's Law, 155, 156 Colours, paper by Maxwell, on, 40, 41 ; Helmholtz on, 99 Annals of Philosophy, Thomson's, 112, 113 Conductors and Insulators, Distinction between, 173 " Apostles," club so called, 30, 89 Cookson, Dr., 61 Arago, 157 Corsoek, Maxwell buried at, 90 Arragonite, 200 Cotes, 202 Atom, article by Maxwell in Encyclo- Coulomb, 154 pwlitt. Uritannica, 108 Curves, investigated by Maxwell, 19 Avogadros' Law, 117, 124 Daniell s cells. 77 Bakerian Lecture, delivered bv Max- Democritus, 108 well, 58 Demonstrator of Physics, W. Garmtt Berkeley on the Theory of Vision, 38 Bernoulli, D., 113 Blackburne, PWcssor, 16 appointed. 75 Description of Oval Curves, lirst paper by Maxwell 19 Blore, Kev. E. W., 67 Devonshire, Duke of, Cavendish La- Boehm, Bust of Maxwell by, 90 boratory built by, 73, 74 ; Letter of Boltzmann, Dr., 135, 137,138, 144, 21(5 Thanks Irom University of Cam- Boltzmann-Maxwell Theorv, The, 140, 145 bridge, 74 Dewar, Miss K. M., her marriage to Boscovitch on Atoms, 10S, lOii Maxwell, 51 Boyle's Ijiw, 114, 117, 124 Dickinson, Lowes; Portrait o| Maxwell bv *K) tion, !>9 Diffusion of gases, 12S British Association, Maxwell and, 42, Discs for colour experiments, !'.i-l(U 54 ; Lecture In-fore, 80-82 ; Lines on Droop, II. H., 57 President's address, S3, 84 Dynamical Theorv of the Electromag- Butler, Dr. H. M., extract from sermon netic Field. Maxwell on, 57, 177 on Maxwell, 32-:i5 Dynamical Theory of Gases, Maxwell Bryan, G. H., 141, 143 on, . r .s, 134 Cambridge, Maxwell at, 28-4L ; Mathe- Edinburgh Academy, Maxwell's school- matical Tripos at, 60; Foundation life at, 13-18 " of Professorship of Experimental Edinburgh, Royal Society of, Maxwell Phvsics at, 66 at meetings" of, 18 On.hrt".l.je and D Ilia Mathematical Edinbiirgh.University of, Maxwellat, 20 Journal, Papers by Maxwell in, 30 Elastic Spheres, 144 Campbell, Professor L., 9, 10, 12,14, 22, Electric Displacement, 218, 219, 220 52, 57, 79 Electrical Theories, 94, 154, 155 Cauehy's Formula, 208 Electricity and Magnetism, Maxwell's Cavendish, Henry, 73, 74 ; Works of, edited by Maxwell, 87, 154, 155 bnok on, 59, 77, 79, 147, 155, 156, 176, 180-201 ; papers bv Lord Kelvin Cavendish Laboratory, built and pre- sented to University of Cambridge, on, Kil-2; Application of Mathe- matical Analysis to, paper by G, 73,74 Green, 158 Cay, Miss Frances, 11 Electricity, Modern Views of, by Pro- Cayley Portrait Fund, lines to Com- mittee, 86 fessor Lodge, 177 Electro-kinetic Momentum, 221 Challis, Professor, 49 Electro-magnetic Field, Dynamical Charles' Law, 124 Theory of, Maxwell on, 57, 177 Chemical Societv, Maxwell's lecture Electro-magnetic Induction, 157 before, 80-82 Electro-magnetic Theorv of Light, 174 INDEX. 223 Electro-tonic State, 164 Electrostatic Induction, Faraday on, 159 Encyclopedia Britannica, articles by Maxwell in, SO, 108, 14ti Ether, labile, 220 Experimental Physics, foundation of Professorship at Cambridge, papers on Electricity and Mag- netism, 161, 162 Kinetic energy, 124, 120, 136, 139, 191 King's College, London, Maxwell elected Professor at, 54 Kohlrausch, 206 Kundt, 132 Election of Maxwell, 68 Faradav 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. I)., IS, 44, 54; friendship with Maxwell, 1! ; paper on Theory of Glaciers, 19 ; resigns Professorship at Edinburgh, 54 Galvani, 1'.5 Garnett, \V., appointed Demonstrator 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 of Maxwell hv, 91 Gases, Molecular theory of, 57, IDS; \Vaterston on general theory of,l IS ; subjects, lid; Maxwell an examiner for,' 60, so ; experimental work in. 76 Matter and Motion, Maxwell on, 79 Gauss' Theory, l.Vi (iay Lussac's law, 117 birthplace, 10, 11 ; childhood and 118; Clausiiison, ll'.t Glenlair, home of Maxwell, 11. 23; laboratory at, 24 ; Maxwell's life at, 17; attends meetings of Royal Society of Edinburgh, Is ; his firs! ism" written at. 7'.' Gordon, ,1. E. 1L, 77. 7S scope, 20; enters the University of inventor of term ' Potential/' 10s' Hamilton, Sir W. K., 22 Hamilton's Principle. P.'O Meat, Text-book on, by Maxwell, 79 Helmholtz, '."0, 156, 15", 175, 221 Henry, J., of Washington, on electro- magnetic induction, 107 Hcrapath on molecules, 112-116 Hertz, Heinrich, 204, 209-213 Hicks, W.M., 221 Hockin, C., 56 Uolman, Professor, 133 Iceland Spar, 200 Insulators and Conductors, Distinction between, 173 .Ic-nkin, Fleeming, 55, 56 Kelland, Professor, 22 Kelvin, Lord, 1C., 142, 108, 159, 160, 10S ; on the Uniform Motion of Heat, 160; of Trinity. 29; illness at Lowe.-itoft, 29 : his 'friends at Cambridge, :',<>; 40, 41 ; elected' Fellow of Trinity,' 4:! ; Lecturer at Trinity, 43 ; Pro- fessor at Aberdeen, 40 ; his father's death, 40 ; gains the Adams Prize, 50 ; marriage, 01 ; powers as teacher King's College, "London, 54; gains the Rmuford Medal, 00; delivers Bakerian lecture, 58 ; resigns Pro- fessorship at King's College, Lon- don, OS ; life at Glenlair, OS, 09 ; visit to Italy, 09; Examiner for Mathematical Tripos, 60, SO ; elected Professor of Experimental Physics at Cambridge, uS ; Introductory Lecture, 08-72 ; Examiner for Natural Sciences Tripos, 79 ; articles 224 INDEX. in Encyclopaedia I)ritannica,SQ, IIS, 146 ; papers in Nature, 80 ; lectures before British Association and Chemical Society, 80-82 ; humorous poems, 83-87 ; delivers Rede Lec- ture 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, 140 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 Ex- aminer for, 79 Nature, papers by Maxwell in, 80 Neumann, F. E., 150, 157 Newton's Lunar Theory and Astronomy, 50 Principia, 202 Nicol, Win., inventor of the polarising prism, 20 Niven, W. D., 27, 46, 51, 52, 60, 78, 87, 88, 93 Oliermeyor, 134 Ohm's Law, 77 Ophthalmoscope devised by M;ixwell,83 Oval Curves, Description of, Maxwell's first paper, 1'J Parkinson, Dr., 49 Philosophical Magazine, 56, 99, 115, 120, 133, 142 Philosophical Trajwiclions, 56, 89, 132, Physical Lines of Force, Maxwell on, 56, 158 Physics, Instruction in, at Cambridge, 61 ; Rei>ort of Syndicate on, 02-64 ; Demonstrator appointed, 75 Poineure, 216 Poisson, 44 ; on distribution of elec- tricity, 155 Polariseope, made by Maxwell, 20 "Potential," term invented by G. Green, 158; the Vector, 165, 221 Poynting, Professor, 187-189 Puluj, 134 Quiucke, 206 Radiation, Luminous, 221 Rarefied Gases, Stresses in, paper by Maxwell, 135, 145 Rayleigh, Lord, 67, 77 Rede Lecture on the Telephone, de- livered 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 Homo- geneous Solid Bodies, paper by Lord Kelvin, 100, 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 BT CASSELL & COMPANY, LIMITED, LA BELI.E SAUVAGE, LONDON, B.C. Selections from Cassell S; Company's Publications. Illustrated, Jine-^rt, antr rrtber Volumes. Abbeys and Churches of England and Wales, The: Descriptive, Historical, Pictorial. Series II. 2is. Adventure, The World of. Fully Illustrated. In Three Vols. gs. each. Africa and its Explorers, The Story of. By DR. ROBERT BROWN, F.L.S. Illustrated. Complete in 4 Vols., 75. 6d. each. Animals, Popular History of. By HENRY SCHERRKN, F.Z.S. With la Coloured Plates and other Illustrations. 73. 6d. Arabian Nights Entertainments, Cassell's Pictorial, ics. 6d. Architectural Drawing. By R. PHF.N& SPIERS. Illustrated. 103. 6d. 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