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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..4b4396c --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #65359 (https://www.gutenberg.org/ebooks/65359) diff --git a/old/65359-0.txt b/old/65359-0.txt deleted file mode 100644 index ecae725..0000000 --- a/old/65359-0.txt +++ /dev/null @@ -1,7806 +0,0 @@ -The Project Gutenberg eBook, James Clerk Maxwell and Modern Physics, by -Richard Glazebrook - - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - - - - -Title: James Clerk Maxwell and Modern Physics - - -Author: Richard Glazebrook - - - -Release Date: May 16, 2021 [eBook #65359] - -Language: English - -Character set encoding: UTF-8 - - -***START OF THE PROJECT GUTENBERG EBOOK JAMES CLERK MAXWELL AND MODERN -PHYSICS*** - - -E-text prepared by Fay Dunn, Charlie Howard, and the Online Distributed -Proofreading Team (http://www.pgdp.net) from page images generously made -available by Internet Archive (https://archive.org) - - - -Note: Project Gutenberg also has an HTML version of this - file which includes the original illustrations. - See 65359-h.htm or 65359-h.zip: - (http://www.gutenberg.org/files/65359/65359-h/65359-h.htm) - or - (http://www.gutenberg.org/files/65359/65359-h.zip) - - - Images of the original pages are available through - Internet Archive. See - https://archive.org/details/jamesclerkmaxwel00glaziala - - -Transcriber’s note: - - Text enclosed by underscores is in italics (_italics_). - - Superscripts that cannot be represented directly are - enclosed by curly brackets immediately after a caret - character (example: n^{th}). - - - Some characters might not display properly in this UTF-8 - text file (e.g., empty squares). If so, the reader should - consult the html version or the original page images noted - above. - - - - - -[Illustration: (cover)] - - -_The Century Science Series_ - -Edited by Sir Henry E. Roscoe, D.C.L., LL.D., F.R.S. - - -JAMES CLERK MAXWELL AND MODERN PHYSICS - - - * * * * * * - -The Century Science Series. - -EDITED BY - -SIR HENRY E. ROSCOE, D.C.L., F.R.S., M.P. - - - John Dalton and the Rise of Modern Chemistry. - By Sir HENRY E. ROSCOE, F.R.S. - - Major Rennell, F.R.S., and the Rise of English Geography. - By CLEMENTS R. MARKHAM, C.B., F.R.S., President of the Royal - Geographical Society. - - Justus von Liebig: his Life and Work (1803–1873). - By W. A. SHENSTONE, F.I.C., Lecturer on Chemistry in Clifton - College. - - The Herschels and Modern Astronomy. - By AGNES M. CLERKE, Author of “A Popular History of Astronomy - during the 19th Century,” &c. - - Charles Lyell and Modern Geology. - By Rev. Professor T. G. BONNEY, F.R.S. - - James Clerk Maxwell and Modern Physics. - By R. T. GLAZEBROOK, F.R.S., Fellow of Trinity College, - Cambridge. - - - _In Preparation._ - - Michael Faraday: his Life and Work. - By Professor SILVANUS P. THOMPSON, F.R.S. - - Humphry Davy. - By T. E. THORPE, F.R.S., Principal Chemist of the Government - Laboratories. - - Pasteur: his Life and Work. - By M. ARMAND RUFFER, M.D., Director of the British Institute of - Preventive Medicine. - - Charles Darwin and the Origin of Species. - By EDWARD B. POULTON, M.A., F.R.S., Hope Professor of Zoology - in the University of Oxford. - - Hermann von Helmholtz. - By A. W. RÜCKER, F.R.S., Professor of Physics in the Royal - College of Science, London. - -CASSELL & COMPANY, LIMITED, _London_; _Paris_ & _Melbourne_. - - * * * * * * - - -[Illustration: J. Clerk Maxwell - -(_From a Photograph of the Picture by G. Lowes Dickinson, Esq., in the -Hall of Trinity College, Cambridge._)] - - -The Century Science Series - -JAMES CLERK MAXWELL AND MODERN PHYSICS - -by - -R. T. GLAZEBROOK, F.R.S. - -Fellow of Trinity College, Cambridge -University Lecturer in Mathematics, and Assistant Director of the -Cavendish Laboratory - - - - - - -Cassell and Company, Limited -London, Paris & Melbourne -1896 -All Rights Reserved - -[Illustration] - - - - -PREFACE. - - -The task of giving some account of Maxwell’s work--of describing the -share that he has taken in the advance of Physical Science during the -latter half of this nineteenth century--has proved no light labour. -The problems which he attacked are of such magnitude and complexity, -that the attempt to explain them and their importance, satisfactorily, -without the aid of symbols, is almost foredoomed to failure. However, -the attempt has been made, in the belief that there are many who, -though they cannot follow the mathematical analysis of Maxwell’s work, -have sufficient general knowledge of physical ideas and principles to -make an account of Maxwell and of the development of the truths that he -discovered, subjects of intelligent interest. - -Maxwell’s life was written in 1882 by two of those who were most -intimately connected with him, Professor Lewis Campbell and Dr. -Garnett. Many of the biographical details of the earlier part of this -book are taken from their work. My thanks are due to them and to their -publishers, Messrs. Macmillan, for permission to use any of the letters -which appear in their biography. I trust that my brief account may -be sufficient to induce many to read Professor Campbell’s “Life and -Letters,” with a view of learning more of the inner thoughts of one who -has left so strong an imprint on all he undertook, and was so deeply -loved by all who knew him. - - R. T. G. - - _Cambridge, - December, 1895._ - - - - -CONTENTS. - - - CHAPTER PAGE - I. EARLY LIFE 9 - - II. UNDERGRADUATE LIFE AT CAMBRIDGE 28 - - III. EARLY RESEARCHES--PROFESSOR AT ABERDEEN 38 - - IV. PROFESSOR AT KING’S COLLEGE, LONDON--LIFE AT GLENLAIR 54 - - V. CAMBRIDGE--PROFESSOR OR PHYSICS 60 - - VI. CAMBRIDGE--THE CAVENDISH LABORATORY 73 - - VII. SCIENTIFIC WORK--COLOUR VISION 93 - - VIII. SCIENTIFIC WORK--MOLECULAR THEORY 108 - - IX. SCIENTIFIC WORK--ELECTRICAL THEORIES 148 - - X. DEVELOPMENT OF MAXWELL’S THEORY 202 - - - - -JAMES CLERK MAXWELL - -AND MODERN PHYSICS. - - - - -CHAPTER I. - -EARLY LIFE. - - -“One who has enriched the inheritance left by Newton and has -consolidated the work of Faraday--one who impelled the mind of -Cambridge to a fresh course of real investigation--has clearly earned -his place in human memory.” It was thus that Professor Lewis Campbell -and Mr. Garnett began in 1882 their life of James Clerk Maxwell. The -years which have passed, since that date, have all tended to strengthen -the belief in the greatness of Maxwell’s work and in the fertility -of his genius, which has inspired the labours of those who, not in -Cambridge only, but throughout the world, have aided in developing the -seeds sown by him. My object in the following pages will be to give -some very brief account of his life and writings, in a form which may, -I hope, enable many to realise what Physical Science owes to one who -was to me a most kind friend as well as a revered master. - -The Clerks of Penicuik, from whom Clerk Maxwell was descended, were -a distinguished family. Sir John Clerk, the great-great-grandfather -of Clerk Maxwell, was a Baron of the Exchequer in Scotland from -1707 to 1755; he was also one of the Commissioners of the Union, -and was in many ways an accomplished scholar. His second son George -married a first cousin, Dorothea Maxwell, the heiress of Middlebie in -Dumfriesshire, and took the name of Maxwell. By the death of his elder -brother James in 1782 George Clerk Maxwell succeeded to the baronetcy -and the property of Penicuik. Before this time he had become involved -in mining and manufacturing speculations, and most of the Middlebie -property had been sold to pay his debts. - -The property of Sir George Clerk Maxwell descended in 1798 to his two -grandsons, Sir George Clerk and Mr. John Clerk Maxwell. It had been -arranged that the younger of the two was to take the remains of the -Middlebie property and to assume with it the name of Maxwell. Sir -George Clerk was member for Midlothian, and held office under Sir -Robert Peel. John Clerk Maxwell was the father of James Clerk Maxwell, -the subject of this sketch.[1] - -John Clerk Maxwell lived with his widowed mother in Edinburgh until her -death in 1824. He was a lawyer, and from time to time did some little -business in the courts. At the same time he maintained an interest in -scientific pursuits, especially those of a practical nature. Professor -Campbell tells us of an endeavour to devise a bellows which would give -a continuous draught of air. In 1831 he contributed to the _Edinburgh -Medical and Philosophical Journal_ a paper entitled “Outlines of a Plan -for combining Machinery with the Manual Printing Press.” - -In 1826 John Clerk Maxwell married Miss Frances Cay, of North Charlton, -Northumberland. For the first few years of their married life their -home was in Edinburgh. The old estate of Middlebie had been greatly -reduced in extent, and there was not a house on it in which the laird -could live. However, soon after his marriage, John Clerk Maxwell -purchased the adjoining property of Glenlair and built a mansion-house -for himself and his wife. Mr. Maxwell superintended the building work. -The actual working plans for some further additions made in 1843 -were his handiwork. A garden was laid out and planted, and a dreary -stony waste was converted into a pleasant home. For some years after -he settled at Glenlair the house in Edinburgh was retained by Mr. -Maxwell, and here, on June 13, 1831, was born his only son, James Clerk -Maxwell. A daughter, born earlier, died in infancy. Glenlair, however, -was his parents’ home, and nearly all the reminiscences we have of -his childhood are connected with it. The laird devoted himself to his -estates and to the education of his son, taking, however, from time to -time his full share in such county business as fell to him. Glenlair in -1830 was very much in the wilds; the journey from Edinburgh occupied -two days. “Carriages in the modern sense were hardly known to the Vale -of Urr. A sort of double gig with a hood was the best apology for a -travelling coach, and the most active mode of locomotion was in a kind -of rough dog-cart known in the family speech as a hurly.”[2] - -Mrs. Maxwell writes thus[3], when the boy was nearly three years old, -to her sister, Miss Jane Cay:-- - - “He is a very happy man, and has improved much since the - weather got moderate. He has great work with doors, locks, - keys, etc., and ‘Show me how it doos’ is never out of his - mouth. He also investigates the hidden course of streams and - bell-wires--the way the water gets from the pond through the - wall and a pend or small bridge and down a drain into Water - Orr, then past the smiddy and down to the sea, where Maggy’s - ships sail. As to the bells, they will not rust; he stands - sentry in the kitchen and Mag runs through the house ringing - them all by turns, or he rings and sends Bessy to see and shout - to let him know; and he drags papa all over to show him the - holes where the wires go through.” - -To discover “how it doos” was thus early his aim. His cousin, Mrs. -Blackburn, tells us that throughout his childhood his constant question -was, “What’s the go of that? What does it do?” And if the answer were -too vague or inconclusive, he would add, “But what’s the _particular_ -go of that?” - -Professor Campbell’s most interesting account of these early years is -illustrated by a number of sketches of episodes in his life. In one -Maxwell is absorbed in watching the fiddler at a country dance; in -another he is teaching his dog some tricks; in a third he is helping a -smaller boy in his efforts to build a castle. Together with his cousin, -Miss Wedderburn, he devised a number of figures for a toy known as a -magic disc, which afterwards developed into the zoetrope or wheel of -life, and in which, by means of an ingenious contrivance of mirrors, -the impression of a continuous movement was produced. - -This happy life went on until his mother’s death in December, 1839; she -died, at the age of forty-eight, of the painful disease to which her -son afterwards succumbed. When James, being then eight years old, was -told that she was now in heaven, he said: “Oh, I’m so glad! Now she’ll -have no more pain.” - -After this his aunt, Miss Jane Cay, took a mother’s place. The problem -of his education had to be faced, and the first attempts were not -successful. A tutor had been engaged during Mrs. Maxwell’s last -illness, and he, it seems, tried to coerce Clerk Maxwell into learning; -but such treatment failed, and in 1841, when ten years old, he began -his school-life at the Edinburgh Academy. - -School-life at first had its hardships. Maxwell’s appearance, his -first day at school, in Galloway home-spun and square-toed shoes with -buckles, was more than his fellows could stand. “Who made those shoes?” -they asked[4]; and the reply they received was-- - - “Div ye ken ’twas a man, - And he lived in a house, - In whilk was a mouse.” - -He returned to Heriot Row that afternoon, says Professor Campbell, -“with his tunic in rags and wanting the skirt, his neat frill rumpled -and torn--himself excessively amused by his experiences and showing not -the slightest sign of irritation.” - -No. 31, Heriot Row, was the house of his widowed aunt, Mrs. Wedderburn, -Mr. Maxwell’s sister; and this, with occasional intervals when he -was with Miss Cay, was his home for the next eight or nine years. -Mr. Maxwell himself, during this period, spent much of his time in -Edinburgh, living with his sister during most of the winter and -returning to Glenlair for the spring and summer. - -Much of what we know of Clerk Maxwell’s life during this period comes -from the letters which passed between him and his father. They tell -us of the close intimacy and affection which existed between the two, -of the boy’s eager desire to please and amuse his father in the dull -solitude of Glenlair, and his father’s anxiety for his welfare and -progress. - -Professor Campbell was his schoolfellow, and records events of those -years in which he shared, which bring clearly before us what Clerk -Maxwell was like. Thus he writes[5]:-- - - “He came to know Swift and Dryden, and after a while Hobbes, - and Butler’s ‘Hudibras.’ Then, if his father was in Edinburgh, - they walked together, especially on the Saturday half-holiday, - and ‘viewed’ Leith Fort, or the preparations for the Granton - railway, or the stratification of Salisbury Crags--always - learning something new, and winning ideas for imagination to - feed upon. One Saturday, February 12, 1842, he had a special - treat, being taken ‘to see electro-magnetic machines.’” - -And again, speaking of his school-life:-- - - “But at school also he gradually made his way. He soon - discovered that Latin was worth learning, and the Greek - Delectus interested him when we got so far. And there were two - subjects in which he at once took the foremost place, when he - had a fair chance of doing so; these were Scripture Biography - and English. In arithmetic as well as in Latin his comparative - want of readiness kept him down. - - “On the whole he attained a measure of success which helped - to secure for him a certain respect; and, however strange he - sometimes seemed to his companions, he had three qualities - which they could not fail to understand--agile strength - of limb, imperturbable courage, and profound good-nature. - Professor James Muirhead remembers him as ‘a friendly boy, - though never quite amalgamating with the rest.’ And another old - class-fellow, the Rev. W. Macfarlane of Lenzie, records the - following as his impression:--‘Clerk Maxwell, when he entered - the Academy, was somewhat rustic and somewhat eccentric. Boys - called him “Dafty,” and used to try to make fun of him. On one - occasion I remember he turned with tremendous vigour, with a - kind of demonic force, on his tormentors. I think he was let - alone after that, and gradually won the respect even of the - most thoughtless of his schoolfellows.’” - -The first reference to mathematical studies occurs, says Professor -Campbell, in a letter to his father written soon after his thirteenth -birthday.[6] - - “After describing the Virginian Minstrels, and betwixt - inquiries after various pets at Glenlair, he remarks, as if it - were an ordinary piece of news, ‘I have made a tetrahedron, a - dodecahedron, and two other hedrons, whose names I don’t know.’ - We had not yet begun geometry, and he had certainly not at this - time learnt the definitions in Euclid; yet he had not merely - realised the nature of the five regular solids sufficiently to - construct them out of pasteboard with approximate accuracy, but - had further contrived other symmetrical polyhedra derived from - them, specimens of which (as improved in 1848) may be still - seen at the Cavendish Laboratory. - - “Who first called his attention to the pyramid, cube, etc., I - do not know. He may have seen an account of them by chance in a - book. But the fact remains that at this early time his fancy, - like that of the old Greek geometers, was arrested by these - types of complete symmetry; and his imagination so thoroughly - mastered them that he proceeded to make them with his own - hand. That he himself attached more importance to this moment - than the letter indicates is proved by the care with which he - has preserved these perishable things, so that they (or those - which replaced them in 1848) are still in existence after - thirty-seven years.” - -The summer holidays were spent at Glenlair. His cousin, Miss Jemima -Wedderburn, was with him, and shared his play. Her skilled pencil -has left us many amusing pictures of the time, some of which are -reproduced by Professor Campbell. There were expeditions and picnics of -all sorts, and a new toy known as “the devil on two sticks” afforded -infinite amusement. The winter holidays usually found him at Penicuik, -or occasionally at Glasgow, with Professor Blackburne or Professor -W. Thomson (now Lord Kelvin). In October, 1844, Maxwell was promoted -to the rector’s class-room. John Williams, afterwards Archdeacon of -Cardigan, a distinguished Baliol man, was rector, and the change was -in many ways an important one for Maxwell. He writes to his father: “I -like P---- better than B----. We have lots of jokes, and he speaks a -great deal, and we have not so much monotonous parsing. In the English -Milton is better than the History of Greece....” - -P---- was the boys’ nickname for the rector; B---- for Mr. Carmichael, -the second master. This[7] is the account of Maxwell’s first interview -with the rector:-- - -_Rector_: “What part of Galloway do you come from?” - -_J. C. M._: “From the Vale of Urr. Ye spell it o, err, err, or oo, err, -err.” - -The study of geometry was begun, and in the mathematical master, Mr. -Gloag, Maxwell found a teacher with a real gift for his task. It was -here that Maxwell’s vast superiority to many who were his companions -at once showed itself. “He seemed,” says Professor Campbell, “to be in -the heart of the subject when they were only at the boundary; but the -boyish game of contesting point by point with such a mind was a most -wholesome stimulus, so that the mere exercise of faculty was a pure -joy. With Maxwell the first lessons of geometry branched out at once -into inquiries which became fruitful.” - -In July, 1845, he writes:-- - - “I have got the 11th prize for Scholarship, the 1st for - English, the prize for English verses, and the Mathematical - Medal. I tried for Scripture knowledge, and Hamilton in the 7th - has got it. We tried for the Medal on Thursday. I had done them - all, and got home at half-past two; but Campbell stayed till - four. I was rather tired with writing exercises from nine till - half-past two. - - “Campbell and I went ‘once more unto the b(r)each’ to-day at - Portobello. I can swim a little now. Campbell has got 6 prizes. - He got a letter written too soon, congratulating him upon _my_ - medal; but there is no rivalry betwixt us, as B---- Carmichael - says.” - -After a summer spent chiefly at Glenlair, he returned with his father -to Edinburgh for the winter, and began, at the age of fourteen, to go -to the meetings of the Royal Society of Edinburgh. At the Society of -Arts he met Mr. R. D. Hay, the decorative painter, who had interested -himself in the attempt to reduce beauty in form and colour to -mathematical principles. Clerk Maxwell was interested in the question -how to draw a perfect oval, and devised a method of drawing oval curves -which was referred by his father to Professor Forbes for his criticism -and suggestions. After discussing the matter with Professor Kelland, -Professor Forbes wrote as follows[8]:-- - - “MY DEAR SIR,--I am glad to find to-day, from Professor - Kelland, that his opinion of your son’s paper agrees with - mine, namely, that it is most ingenious, most creditable to - him, and, we believe, a new way of considering higher curves - with reference to foci. Unfortunately, these ovals appear - to be curves of a very high and intractable order, so that - possibly the elegant method of description may not lead to a - corresponding simplicity in investigating their properties. But - that is not the present point. If you wish it, I think that - the simplicity and elegance of the method would entitle it to - be brought before the Royal Society.--Believe me, my dear sir, - yours truly, - - “JAMES D. FORBES.” - -In consequence of this, Clerk Maxwell’s first published paper was -communicated to the Royal Society of Edinburgh on April 6th, 1846, -when its author was barely fifteen. Its title is as follows: “On the -Description of Oval Curves and those having a Plurality of Foci. By Mr. -Clerk Maxwell, Junior. With Remarks by Professor Forbes. Communicated -by Professor Forbes.” - -The notice in his father’s diary runs: “M. 6 [Ap., 1846.] Royal Society -with Jas. Professor Forbes gave acct. of James’s Ovals. Met with very -great attention and approbation generally.” - -This was the beginning of the lifelong friendship between Maxwell and -Forbes. - -The curves investigated by Maxwell have the property that the sum found -by adding to the distance of any point on the curve from one focus a -constant multiple of the distance of the same point from a second focus -is always constant. - -The curves are of great importance in the theory of light, for if this -constant factor expresses the refractive index of any medium, then -light diverging from one focus without the medium and refracted at a -surface bounding the medium, and having the form of one of Maxwell’s -ovals, will be refracted so as to converge to the second focus. - -About the same time he was busy with some investigations on the -properties of jelly and gutta-percha, which seem to have been suggested -by Forbes’ “Theory of Glaciers.” - -He failed to obtain the Mathematical Medal in 1846--possibly on account -of these researches--but he continued at school till 1847, when he -left, being then first in mathematics and in English, and nearly first -in Latin. - -In 1847 he was working at magnetism and the polarisation of light. -Some time in that year he was taken by his uncle, Mr. John Cay, to see -William Nicol, the inventor of the polarising prism, who showed him the -colours exhibited by polarised light after passing through unannealed -glass. On his return, he made a polariscope with a glass reflector. -The framework of the first instrument was of cardboard, but a superior -article was afterwards constructed of wood. Small lenses mounted on -cardboard were employed when a conical pencil was needed. By means -of this instrument he examined the figures exhibited by pieces of -unannealed glass, which he prepared himself; and, with a camera lucida -and box of colours, he reproduced these figures on paper, taking care -to sketch no outlines, but to shade each coloured band imperceptibly -into the next. Some of these coloured drawings he forwarded to Nicol, -and was more than repaid by the receipt shortly afterwards of a pair of -prisms prepared by Nicol himself. These prisms were always very highly -prized by Maxwell. Once, when at Trinity, the little box containing -them was carried off by his bed-maker during a vacation, and destined -for destruction. The bed-maker died before term commenced, and it -was only by diligent search among her effects that the prisms were -recovered.[9] After this they were more carefully guarded, and they -are now, together with the wooden polariscope, the bits of unannealed -glass, and the water-colour drawings, in one of the showcases at the -Cavendish Laboratory. - -About this time, Professor P. G. Tait and he were schoolfellows at the -Academy, acknowledged as the two best mathematicians in the school. It -was thought desirable, says Professor Campbell, that “we should have -lessons in physical science, so one of the classical masters gave them -out of a text-book.... The only thing I distinctly remember about these -hours is that Maxwell and P. G. Tait seemed to know much more about the -subject than our teacher did.” - -An interesting account of these days is given by Professor Tait in an -obituary notice on Maxwell printed in the “Proceedings of the Royal -Society of Edinburgh, 1879–80,” from which the following is taken:-- - - “When I first made Clerk Maxwell’s acquaintance, about - thirty-five years ago, at the Edinburgh Academy, he was a year - before me, being in the fifth class, while I was in the fourth. - - “At school he was at first regarded as shy and rather dull. - He made no friendships, and he spent his occasional holidays - in reading old ballads, drawing curious diagrams, and making - rude mechanical models. This absorption in such pursuits, - totally unintelligible to his schoolfellows (who were then - quite innocent of mathematics), of course procured him a not - very complimentary nickname, which I know is still remembered - by many Fellows of this Society. About the middle of his school - career, however, he surprised his companions by suddenly - becoming one of the most brilliant among them, gaining - high, and sometimes the highest, prizes for scholarships, - mathematics, and English verse composition. From this time - forward I became very intimate with him, and we discussed - together, with schoolboy enthusiasm, numerous curious - problems, among which I remember particularly the various plane - sections of a ring or tore, and the form of a cylindrical - mirror which should show one his own image unperverted. I - still possess some of the MSS. we exchanged in 1846 and early - in 1847. Those by Maxwell are on ‘The Conical Pendulum,’ - ‘Descartes’ Ovals,’ ‘Meloid and Apioid,’ and ‘Trifocal Curves.’ - All are drawn up in strict geometrical form and divided into - consecutive propositions. The three latter are connected with - his first published paper, communicated by Forbes to this - society and printed in our ‘Proceedings,’ vol. ii., under the - title, ‘On the Description of Oval Curves and those having a - Plurality of Foci’ (1846). At the time when these papers were - written he had received no instruction in mathematics beyond a - few books of Euclid and the merest elements of algebra.” - -In November, 1847, Clerk Maxwell entered the University of Edinburgh, -learning mathematics from Kelland, natural philosophy from J. D. -Forbes, and logic from Sir W. R. Hamilton. At this time, according to -Professor Campbell[10]-- - - “he still occasioned some concern to the more conventional - amongst his friends by the originality and simplicity of his - ways. His replies in ordinary conversation were indirect and - enigmatical, often uttered with hesitation and in a monotonous - key. While extremely neat in his person, he had a rooted - objection to the vanities of starch and gloves. He had a pious - horror of destroying anything, even a scrap of writing-paper. - He preferred travelling by the third class in railway journeys, - saying he liked a hard seat. When at table he often seemed - abstracted from what was going on, being absorbed in observing - the effects of refracted light in the finger-glasses, or in - trying some experiment with his eyes--seeing round a corner, - making invisible stereoscopes, and the like. Miss Cay used - to call his attention by crying, ‘Jamsie, you’re in a prop.’ - He never tasted wine; and he spoke to gentle and simple in - exactly the same tone. On the other hand, his teachers--Forbes - above all--had formed the highest opinion of his intellectual - originality and force; and a few experienced observers, in - watching his devotion to his father, began to have some inkling - of his heroic singleness of heart. To his college companions, - whom he could now select at will, his quaint humour was an - endless delight. His chief associates, after I went to the - University of Glasgow, were my brother, Robert Campbell (still - at the Academy), P. G. Tait, and Allan Stewart. Tait went - to Peterhouse, Cambridge, in 1848, after one session of the - University of Edinburgh; Stewart to the same college in 1849; - Maxwell did not go up until 1850.” - -During this period he wrote two important papers. The one, on “Rolling -Curves,” was read to the Royal Society of Edinburgh by Professor -Kelland--(“it was not thought proper for a boy in a round jacket to -mount the rostrum”)--in February, 1849; the other, on “The Equilibrium -of Elastic Solids,” appeared in the spring of 1850. - -The vacations were spent at Glenlair, and we learn from letters to -Professor Campbell and others how the time was passed. - -“On Saturday,” he writes[11]--April 26th, 1848, just after his -arrival home--“the natural philosophers ran up Arthur’s Seat with the -barometer. The Professor set it down at the top.... He did not set it -straight, and made the hill grow fifty feet; but we got it down again.” - -In a letter of July in the same year he describes his laboratory:-- - - “I have regularly set up shop now above the wash-house at the - gate, in a garret. I have an old door set on two barrels, and - two chairs, of which one is safe, and a skylight above which - will slide up and down. - - “On the door (or table) there is a lot of bowls, jugs, plates, - jam pigs, etc., containing water, salt, soda, sulphuric acid, - blue vitriol, plumbago ore; also broken glass, iron, and copper - wire, copper and zinc plate, bees’ wax, sealing wax, clay, - rosin, charcoal, a lens, a Smee’s galvanic apparatus, and a - countless variety of little beetles, spiders, and wood lice, - which fall into the different liquids and poison themselves. I - intend to get up some more galvanism in jam pigs; but I must - first copper the interiors of the pigs, so I am experimenting - on the best methods of electrotyping. So I am making copper - seals with the device of a beetle. First, I thought a beetle - was a good conductor, so I embedded one in wax (not at all - cruel, because I slew him in boiling water, in which he never - kicked), leaving his back out; but he would not do. Then I took - a cast of him in sealing wax, and pressed wax into the hollow, - and blackleaded it with a brush; but neither would that do. So - at last I took my fingers and rubbed it, which I find the best - way to use the blacklead. Then it coppered famously. I melt out - the wax with the lens, that being the cleanest way of getting a - strong heat, so I do most things with it that need heat. To-day - I astonished the natives as follows. I took a crystal of blue - vitriol and put the lens to it, and so drove off the water, - leaving a white powder. Then I did the same to some washing - soda, and mixed the two white powders together, and made a - small native spit on them, which turned them green by a mutual - exchange, thus:--1. Sulphate of copper and carbonate of soda. - 2. Sulphate of soda and carbonate of copper (blue or green).” - -Of his reading he says:--“I am reading Herodotus’ ‘Euterpe,’ having -taken the turn--that is to say that sometimes I can do props., read -Diff. and Int. Calc., Poisson, Hamilton’s dissertation, etc.” - -In September he was busy with polarised light. “We were at Castle -Douglas yesterday, and got crystals of saltpetre, which I have been -cutting up into plates to-day in hopes to see rings.” - -In July, 1849, he writes[12]:-- - - “I have set up the machine for showing the rings in crystals, - which I planned during your visit last year. It answers very - well. I also made some experiments on compressed jellies in - illustration of my props. on that subject. The principal one - was this:--The jelly is poured while hot into the annular space - contained between a paper cylinder and a cork; then, when cold, - the cork is twisted round and the jelly exposed to polarised - light, when a transverse cross, X, not +, appears, with rings - as the inverse square of the radius, all which is fully - verified. Hip! etc. _Q.E.D._” - -And again on March 22nd, 1850:-- - - “At Practical Mechanics I have been turning Devils of sorts. - For private studies I have been reading Young’s ‘Lectures,’ - Willis’s ‘Principles of Mechanism,’ Moseley’s ‘Engineering - and Mechanics,’ Dixon on ‘Heat,’ and Moigno’s ‘Répertoire - d’Optique.’ This last is a very complete analysis of all that - has been done in the optical way from Fresnel to the end of - 1849, and there is another volume a-coming which will complete - the work. There is in it, besides common optics, all about the - other things which accompany light, as heat, chemical action, - photographic rays, action on vegetables, etc. - - “My notions are rather few, as I do not _entertain_ them just - now. I have a notion for the torsion of wires and rods, not - to be made till the vacation; of experiments on the action of - compression on glass, jelly, etc., numerically done up; of - papers for the Physico-Mathematical Society (which is to revive - in earnest next session!); on the relations of optical and - mechanical constants, their desirableness, etc.; and suspension - bridges, and catenaries, and elastic curves. Alex. Campbell, - Agnew, and I are appointed to read up the subject of periodical - shooting stars, and to prepare a list of the phenomena to be - observed on the 9th August and 13th November. The society’s - barometer is to be taken up Arthur’s Seat at the end of the - session, when Forbes goes up, and All students are invited to - attend, so that the existence of the society may be recognised.” - -It was at last settled that he was to go up to Cambridge. Tait had been -at Peterhouse for two years, while Allan Stewart had joined him there -in 1849, and after much discussion it was arranged that Maxwell should -enter at the same college. - -Of this period of his life Tait writes as follows:-- - - “The winter of 1847 found us together in the classes of Forbes - and Kelland, where he highly distinguished himself. With the - former he was a particular favourite, being admitted to the - free use of the class apparatus for original experiments. He - lingered here behind most of his former associates, having - spent three years at the University of Edinburgh, working - (without any assistance or supervision) with physical and - chemical apparatus, and devouring all sorts of scientific - works in the library. During this period he wrote two valuable - papers, which are published in our ‘Transactions,’ on ‘The - Theory of Rolling Curves’ and on ‘The Equilibrium of Elastic - Solids.’ Thus he brought to Cambridge, in the autumn of 1850, a - mass of knowledge which was really immense for so young a man, - but in a state of disorder appalling to his methodical private - tutor. Though that tutor was William Hopkins, the pupil to a - great extent took his own way, and it may safely be said that - no high wrangler of recent years ever entered the Senate House - more imperfectly trained to produce ‘paying’ work than did - Clerk Maxwell. But by sheer strength of intellect, though with - the very minimum of knowledge how to use it to advantage under - the conditions of the examination, he obtained the position - of Second Wrangler, and was bracketed equal with the Senior - Wrangler in the higher ordeal of the Smith’s Prizes. His name - appears in the Cambridge ‘Calendar’ as Maxwell of Trinity, - but he was originally entered at Peterhouse, and kept his - first term there, in that small but most ancient foundation - which has of late furnished Scotland with the majority of the - professors of mathematics and natural philosophy in her four - universities.” - -While W. D. Niven, in his preface to Maxwell’s collected works (p. -xii.), says:-- - - “It may readily be supposed that his preparatory training for - the Cambridge course was far removed from the ordinary type. - There had indeed for some time been practically no restraint - upon his plan of study, and his mind had been allowed to follow - its natural bent towards science, though not to an extent - so absorbing as to withdraw him from other pursuits. Though - he was not a sportsman--indeed, sport so-called was always - repugnant to him--he was yet exceedingly fond of a country - life. He was a good horseman and a good swimmer. Whence, - however, he derived his chief enjoyment may be gathered from - the account which Mr. Campbell gives of the zest with which he - quoted on one occasion the lines of Burns which describe the - poet finding inspiration while wandering along the banks of a - stream in the free indulgence of his fancies. Maxwell was not - only a lover of poetry, but himself a poet, as the fine pieces - gathered together by Mr. Campbell abundantly testify. He saw, - however, that his true calling was science, and never regarded - these poetical efforts as other than mere pastime. Devotion - to science, already stimulated by successful endeavour; - a tendency to ponder over philosophical problems; and an - attachment to English literature, particularly to English - poetry--these tastes, implanted in a mind of singular strength - and purity, may be said to have been the endowments with which - young Maxwell began his Cambridge career. Besides this, his - scientific reading, as we may gather from his papers to the - Royal Society of Edinburgh referred to above, was already - extensive and varied. He brought with him, says Professor Tait, - a mass of knowledge which was really immense for so young a - man, but in a state of disorder appalling to his methodical - private tutor.” - - - - -CHAPTER II. - -UNDERGRADUATE LIFE AT CAMBRIDGE. - - -Maxwell did not remain long at Peterhouse; before the end of his -first term he migrated to Trinity, and was entered under Dr. Thompson -December 14th, 1850. He appeared to the tutor a shy and diffident -youth, but presently surprised Dr. Thompson by producing a bundle -of papers--copies, probably, of those he had already published--and -remarking, “Perhaps these may show that I am not unfit to enter at your -College.” - -The change was pressed upon him by many friends, the grounds of the -advice being that, from the large number of high wranglers recently -at Peterhouse and the smallness of the foundation, the chances of a -Fellowship there for a mathematical man were less than at Trinity. It -was a step he never regretted; the prospect of a Fellowship had but -little influence on his mind. He found, however, at the larger college -ampler opportunities for self-improvement, and it was possible for him -to select his friends from among men whom he otherwise would never have -known. - -The record of his undergraduate life is not very full; his letters to -his father have, unfortunately, been lost, but we have enough in the -recollections of friends still living to picture what it was like. At -first he lodged in King’s Parade with an old Edinburgh schoolfellow, -C. H. Robertson. He attended the College lectures on mathematics, -though they were somewhat elementary, and worked as a private pupil -with Porter, of Peterhouse. His father writes to him, November, 1850: -“Have you called on Professors Sedgwick, at Trin., and Stokes, at -Pembroke? If not, you should do both. Stokes will be most in your line, -if he takes you in hand at all. Sedgwick is also a great Don in his -line, and, if you were entered in geology, would be a most valuable -acquaintance.” - -In his second year he became a pupil of Hopkins, the great coach; he -also attended Stokes’ lectures, and the friendship which lasted till -his death was thus begun. In April, 1852, he was elected a scholar, -and obtained rooms in College (G, Old Court). In June, 1852, he came -of age. “I trust you will be as discreet when major as you have been -while minor,” writes his father the day before. The next academic -year, October, 1852, to June, 1853, was a very busy one; hard grind -for the Tripos occupied his time, and he seems to have been thoroughly -overstrained. He was taken ill while staying near Lowestoft with the -Rev. C. B. Tayler, the uncle of a College friend. His own account of -the illness is given in a letter to Professor Campbell[13], dated July -14th, 1853. - - “You wrote just in time for your letter to reach me as I - reached Cambridge. After examination, I went to visit the - Rev. C. B. Tayler (uncle to a Tayler whom I think you have - seen under the name of _Freshman_, etc., and author of many - tracts and other didactic works). We had little expedites and - walks, and things parochial and educational, and domesticity. - I intended to return on the 18th June, but on the 17th I felt - unwell, and took measures accordingly to be well again--_i.e._ - went to bed, and made up my mind to recover. But it lasted more - than a fortnight, during which time I was taken care of beyond - expectation (not that I did not expect much before). When I - was perfectly useless and could not sit up without fainting, - Mr. Tayler did everything for me in such a way that I had no - fear of giving trouble. So did Mrs. Tayler; and the two nephews - did all they could. So they kept me in great happiness all the - time, and detained me till I was able to walk about and got - back strength. I returned on the 4th July. - - “The consequence of all this is that I correspond with Mr. - Tayler, and have entered into bonds with the nephews, of all of - whom more hereafter. Since I came here I have been attending - Hop., but, with his approval, did not begin full swing. I - am getting on, though, and the work is not grinding on the - prepared brain.” - -During this period he wrote some papers for the _Cambridge and Dublin -Mathematical Journal_ which will be referred to again later. He was -also a member of a discussion society known as the “Apostles,” and some -of the essays contributed by him are preserved by Professor Campbell. -Mr. Niven, in his preface to the collected edition of Maxwell’s works, -suggests that the composition of these essays laid the foundation of -that literary finish which is one of the characteristics of Maxwell’s -scientific writings. - -Among his friends at the time were Tait, Charles Mackenzie of Caius, -the missionary bishop of Central Africa, Henry and Frank Mackenzie of -Trinity, Droop, third Wrangler in 1854; Gedge, Isaac Taylor, Blakiston, -F. W. Farrar,[14] H. M. Butler,[15] Hort, V. Lushington, Cecil Munro, -G. W. H. Tayler, and W. N. Lawson. Some of these who survived him have -given to Professor Campbell their recollections of these undergraduate -days, which are full of interest. - -Thus Mr. Lawson writes[16]:-- - - “There must be many of his quaint verses about, if one could - lay hands on them, for Maxwell was constantly producing - something of the sort and bringing it round to his friends, - with a sly chuckle at the humour, which, though his own, no one - enjoyed more than himself. - - “I remember Maxwell coming to me one morning with a copy of - verses beginning, ‘Gin a body meet a body going through the - air,’ in which he had twisted the well-known song into a - description of the laws of impact of solid bodies. - - “There was also a description which Maxwell wrote of some - University ceremony--I forget what--in which somebody ‘went - before’ and somebody ‘followed after,’ and ‘in the midst were - the wranglers, playing with the symbols.’ - - “These last words, however meant, were, in fact, a description - of his own wonderful power. I remember, one day in lecture, - our lecturer had filled the black-board three times with - the investigation of some hard problem in Geometry of Three - Dimensions, and was not at the end of it, when Maxwell came up - with a question whether it would not come out geometrically, - and showed how, with a figure, and in a few lines, there was - the solution at once. - - “Maxwell was, I daresay you remember, very fond of a talk upon - almost anything. He and I were pupils (at an enormous distance - apart) of Hopkins, and I well recollect how, when I had been - working the night before and all the morning at Hopkins’s - problems, with little or no result, Maxwell would come in for a - gossip, and talk on while I was wishing him far away, till at - last, about half an hour or so before our meeting at Hopkins’s, - he would say, ‘Well, I must go to old Hop.’s problems’; and, by - the time we met there, they were all done. - - “I remember Hopkins telling me, when speaking of Maxwell, - either just before or just after his degree, ‘It is not - possible for that man to think incorrectly on physical - subjects’; and Hopkins, as you know, had had, perhaps, more - experience of mathematical minds than any man of his time.” - -The last clause is part of a quotation from a diary kept by Mr. Lawson -at Cambridge, in which, under the date July 15th, 1853, he writes:-- - - “He (Hopkins) was talking to me this evening about Maxwell. - He says he is unquestionably the most extraordinary man he - has met with in the whole range of his experience; he says - it appears impossible for Maxwell to think incorrectly on - physical subjects; that in his analysis, however, he is far - more deficient. He looks upon him as a great genius with all - its eccentricities, and prophesies that one day he will shine - as a light in physical science--a prophecy in which all his - fellow-students strenuously unite.” - -How many who have struggled through the “Electricity and Magnetism” -have realised the truth of the remark about the correctness of his -physical intuitions and the deficiency at times of his analysis! - -Dr. Butler, a friend of these early days, preached the University -sermon on November 16th, 1879, ten days after Maxwell’s death, and -spoke thus:-- - - “It is a solemn thing--even the least thoughtful is touched - by it--when a great intellect passes away into the silence - and we see it no more. Such a loss, such a void, is present, - I feel certain, to many here to-day. It is not often, even - in this great home of thought and knowledge, that so bright - a light is extinguished as that which is now mourned by many - illustrious mourners, here chiefly, but also far beyond this - place. I shall be believed when I say in all simplicity that I - wish it had fallen to some more competent tongue to put into - words those feelings of reverent affection which are, I am - persuaded, uppermost in many hearts on this Sunday. My poor - words shall be few, but believe me they come from the heart. - You know, brethren, with what an eager pride we follow the - fortunes of those whom we have loved and reverenced in our - undergraduate days. We may see them but seldom, few letters may - pass between us, but their names are never common names. They - never become to us only what other men are. When I came up to - Trinity twenty-eight years ago, James Clerk Maxwell was just - beginning his second year. His position among us--I speak in - the presence of many who remember that time--was unique. He was - the one acknowledged man of genius among the undergraduates. We - understood even then that, though barely of age, he was in his - own line of inquiry not a beginner but a master. His name was - already a familiar name to men of science. If he lived, it was - certain that he was one of that small but sacred band to whom - it would be given to enlarge the bounds of human knowledge. - It was a position which might have turned the head of a - smaller man; but the friend of whom we were all so proud, and - who seemed, as it were, to link us thus early with the great - outside world of the pioneers of knowledge, had one of those - rich and lavish natures which no prosperity can impoverish, - and which make faith in goodness easy for others. I have often - thought that those who never knew the grand old Adam Sedgwick - and the then young and ever-youthful Clerk Maxwell had yet to - learn the largeness and fulness of the moulds in which some - choice natures are framed. Of the scientific greatness of our - friend we were most of us unable to judge; but anyone could - see and admire the boy-like glee, the joyous invention, the - wide reading, the eager thirst for truth, the subtle thought, - the perfect temper, the unfailing reverence, the singular - absence of any taint of the breath of worldliness in any of its - thousand forms. - - “Brethren, you may know such men now among your college - friends, though there can be but few in any year, or indeed in - any century, that possess the rare genius of the man whom we - deplore. If it be so, then, if you will accept the counsel of - a stranger, thank God for His gift. Believe me when I tell you - that few such blessings will come to you in later life. There - are blessings that come once in a lifetime. One of these is the - reverence with which we look up to greatness and goodness in - a college friend--above us, beyond us, far out of our mental - or moral grasp, but still one of us, near to us, our own. You - know, in part at least, how in this case the promise of youth - was more than fulfilled, and how the man who, but a fortnight - ago, was the ornament of the University, and--shall I be - wrong in saying it?--almost the discoverer of a new world of - knowledge, was even more loved than he was admired, retaining - after twenty years of fame that mirth, that simplicity, that - child-like delight in all that is fresh and wonderful which we - rejoice to think of as some of the surest accompaniment of true - scientific genius. - - “You know, also, that he was a devout as well as thoughtful - Christian. I do not note this in the triumphant spirit of a - controversialist. I will not for a moment assume that there is - any natural opposition between scientific genius and simple - Christian faith. I will not compare him with others who have - had the genius without the faith. Christianity, though she - thankfully welcomes and deeply prizes them, does not need - now, any more than when St. Paul first preached the Cross at - Corinth, the speculations of the subtle or the wisdom of the - wise. If I wished to show men, especially young men, the living - force of the Gospel, I would take them not so much to a learned - and devout Christian man to whom all stores of knowledge were - familiar, but to some country village where for fifty years - there had been devout traditions and devout practice. There - they would see the Gospel lived out; truths, which other men - spoke of, seen and known; a spirit not of this world, visibly, - hourly present; citizenship in heaven daily assumed and daily - realised. Such characters I believe to be the most convincing - preachers to those who ask whether Revelation is a fable - and God an unknowable. Yes, in most cases--not, I admit, in - all--simple faith, even peradventure more than devout genius, - is mighty for removing doubts and implanting fresh conviction. - But having said this, we may well give thanks to God that our - friend was what he was, a firm Christian believer, and that his - powerful mind, after ranging at will through the illimitable - spaces of Creation and almost handling what he called ‘the - foundation-stones of the material universe,’ found its true - rest and happiness in the love and the mercy of Him whom the - humblest Christian calls his Father. Of such a man it may be - truly said that he had his citizenship in heaven, and that he - looked for, as a Saviour, the Lord Jesus Christ, through whom - the unnumbered worlds were made, and in the likeness of whose - image our new and spiritual body will be fashioned.” - -The Tripos came in January, 1854. “You will need to get muffetees for -the Senate Room. Take your plaid or rug to wrap round your feet and -legs,” was his father’s advice--advice which will appeal to many who -can remember the Senate House as it felt on a cold January morning. - -Maxwell had been preparing carefully for this examination. Thus to -his aunt, Miss Cay, in June, 1853, he writes:--“If anyone asks how I -am getting on in mathematics, say that I am busy arranging everything -so as to be able to express all distinctly, so that examiner may be -satisfied now and pupils edified hereafter. It is pleasant work and -very strengthening, but not nearly finished.” - -Still, the illness of July, 1853, had left some effect. Professor -Baynes states that he said that on entering the Senate House for the -first paper he felt his mind almost a blank, but by-and-by his mental -vision became preternaturally clear. - -The moderators were Mackenzie of Caius, whose advice had been mainly -instrumental in leading him to migrate to Trinity, Wm. Walton of -Trinity, Wolstenholme of Christ’s, and Percival Frost of St. John’s. - -When the lists were published, Routh of Peterhouse was senior, Maxwell -second. The examination for the Smith’s Prizes followed in a few days, -and then Routh and Maxwell were declared equal. - -In a letter to Miss Cay[17] of January 13th, while waiting for the -three days’ list, he writes:-- - - “All my correspondents have been writing to me, which is kind, - and have not been writing questions, which is kinder. So I - answer you now, while I am slacking speed to get up steam, - leaving Lewis and Stewart, etc., till next week, when I will - give an account of the _five days_. There are a good many up - here at present, and we get on very jolly on the whole; but - some are not well, and some are going to be plucked or gulphed, - as the case may be, and others are reading so hard that they - are invisible. I go to-morrow to breakfast with shaky men, and - after food I am to go and hear the list read out, and whether - they are through, and bring them word. When the honour list - comes out the poll men act as messengers. Bob Campbell comes - in occasionally of an evening now, to discuss matters and vary - sports. During examination I have had men at night working with - gutta-percha, magnets, etc. It is much better than reading - novels or talking after 5½ hours’ hard writing.” - -His father, on hearing the news, wrote from Edinburgh:-- - - “I heartily congratulate you on your place in the list. I - suppose it is higher than the speculators would have guessed, - and quite as high as Hopkins reckoned on. I wish you success - in the Smith’s Prizes; be sure to write me the result. I will - see Mrs. Morrieson, and I think I will call on Dr. Gloag to - congratulate him. He has at least three pupils gaining honours.” - -His friends in Edinburgh were greatly pleased. “I get congratulations -on all hands,” his father writes,[18] “including Professor Kelland -and Sandy Fraser and all others competent.... To-night or on Monday -I shall expect to hear of the Smith’s Prizes.” And again, February -6th, 1854:--“George Wedderburn came into my room at 2 a.m. yesterday -morning, having seen the Saturday _Times_, received by the express -train.... As you are equal to the Senior in the champion trial, you are -very little behind him.” - -Or again, March 5th, 1854:-- - - “Aunt Jane stirred me up to sit for my picture, as she said you - wished for it and were entitled to ask for it _qua_ Wrangler. I - have had four sittings to Sir John Watson Gordon, and it is now - far advanced; I think it is very like. It is kitcat size, to be - a companion to Dyce’s picture of your mother and self, which - Aunt Jane says she is to leave to you.” - -And now the long years of preparation were nearly over. The cunning -craftsman was fitted with his tools; he could set to work to unlock the -secrets of Nature; he was free to employ his genius and his knowledge -on those tasks for which he felt most fitted. - - - - -CHAPTER III. - -EARLY RESEARCHES.--PROFESSOR AT ABERDEEN. - - -From this time on Maxwell’s life becomes a record of his writings -and discoveries. It will, however, probably be clearest to separate -as far as possible biographical details from a detailed account of -his scientific work, leaving this for consecutive treatment in later -chapters, and only alluding to it so far as may prove necessary to -explain references in his letters. - -He continued in Cambridge till the Long Vacation of 1854, reading -Mill’s “Logic.” “I am experiencing the effects of Mill,” he writes, -March 25th, 1854, “but I take him slowly. I do not think him the last -of his kind. I think more is wanted to bring the connexion of sensation -with science to light, and to show what it is not.” He also read -Berkeley on “The Theory of Vision” and “greatly admired it.” - -About the same time he devised an ophthalmoscope.[19] - - “I have made an instrument for seeing into the eye through - the pupil. The difficulty is to throw the light in at that - small hole and look in at the same time; but that difficulty - is overcome, and I can see a large part of the back of the eye - quite distinctly with the image of the candle on it. People - find no inconvenience in being examined, and I have got dogs - to sit quite still and keep their eyes steady. Dogs’ eyes are - very beautiful behind--a copper-coloured ground, with glorious - bright patches and networks of blue, yellow, and green, with - blood-vessels great and small.” - -After the vacation he returned to Cambridge, and the letters refer to -the colour-top. Thus to Miss Cay, November 24th, 1854, p. 208:-- - - “I have been very busy of late with various things, and am just - beginning to make papers for the examination at Cheltenham, - which I have to conduct about the 11th of December. I have - also to make papers to polish off my pups. with. I have been - spinning colours a great deal, and have got most accurate - results, proving that ordinary people’s eyes are all made - alike, though some are better than others, and that other - people see two colours instead of three; but all those who do - so agree amongst themselves. I have made a triangle of colours - by which you may make out everything. - - “If you can find out any people in Edinburgh who do not see - colours (I know the Dicksons don’t), pray drop a hint that - I would like to see them. I have put one here up to a dodge - by which he distinguishes colours without fail. I have also - constructed a pair of squinting spectacles, and am beginning - operations on a squinting man.” - -A paper written for his own use originally some time in 1854, but -communicated as a parting gift to his friend Farrar, who was about to -become a master at Marlborough, gives us some insight into his view of -life at the age of twenty-three. - - “He that would enjoy life and act with freedom must have the - work of the day continually before his eyes. Not yesterday’s - work, lest he fall into despair; nor to-morrow’s, lest he - become a visionary--not that which ends with the day, which is - a worldly work; nor yet that only which remains to eternity, - for by it he cannot shape his actions. - - “Happy is the man who can recognise in the work of to-day a - connected portion of the work of life and an embodiment of - the work of Eternity. The foundations of his confidence are - unchangeable, for he has been made a partaker of Infinity. He - strenuously works out his daily enterprises because the present - is given him for a possession. - - “Thus ought Man to be an impersonation of the divine process - of nature, and to show forth the union of the infinite with - the finite, not slighting his temporal existence, remembering - that in it only is individual action possible; nor yet shutting - out from his view that which is eternal, knowing that Time is - a mystery which man cannot endure to contemplate until eternal - Truth enlighten it.” - -His father was unwell in the Christmas vacation of that year, and he -could not return to Cambridge at the beginning of the Lent term. “My -steps,” he writes[20] to C. J. Munro from Edinburgh, February 19th, -1855, “will be no more by the reedy and crooked till Easter term.... I -should like to know how many kept bacalaurean weeks go to each of these -terms, and when they begin and end. Overhaul the Calendar, and when -found make note of.” - -He was back in Cambridge for the May term, working at the motion -of fluids and at his colour-top. A paper on “Experiments on Colour -as Perceived by the Eye” was communicated to the Royal Society of -Edinburgh on March 19th, 1855. The experiments were shown to the -Cambridge Philosophical Society in May following, and the results are -thus described in two letters[21] to his father, Saturday, May 5th, -1855: - - “The Royal Society have been very considerate in sending me my - paper on ‘Colours’ just when I wanted it for the Philosophical - here. I am to let them see the tricks on Monday evening, - and I have been there preparing their experiments in the - gaslight. There is to be a meeting in my rooms to-night to - discuss Adam Smith’s ‘Theory of Moral Sentiments,’ so I must - clear up my litter presently. I am working away at electricity - again, and have been working my way into the views of heavy - German writers. It takes a long time to reduce to order all - the notions one gets from these men, but I hope to see my way - through the subject and arrive at something intelligible in the - way of a theory.... - - “The colour trick came off on Monday, 7th. I had the - proof-sheets of my paper, and was going to read; but I changed - my mind and talked instead, which was more to the purpose. - There were sundry men who thought that blue and yellow make - green, so I had to undeceive them. I have got Hay’s book of - colours out of the Univ. Library, and am working through the - specimens, matching them with the top. I have a new trick of - stretching the string horizontally above the top, so as to - touch the upper part of the axis. The motion of the axis sets - the string a-vibrating in the same time with the revolutions of - the top, and the colours are seen in the haze produced by the - vibration. Thomson has been spinning the top, and he finds my - diagram of colours agrees with his experiments, but he doubts - about browns, what is their composition. I have got colcothar - brown, and can make white with it, and blue and green; also, - by mixing red with a little blue and green and a great deal of - black, I can match colcothar exactly. - - “I have been perfecting my instrument for looking into the eye. - Ware has a little beast like old Ask, which sits quite steady - and seems to like being looked at, and I have got several men - who have large pupils and do not wish to let me look in. I - have seen the image of the candle distinctly in all the eyes I - have tried, and the veins of the retina were visible in some; - but the dogs’ eyes showed all the ramifications of veins, with - glorious blue and green network, so that you might copy down - everything. I have shown lots of men the image in my own eye by - shutting off the light till the pupil dilated and then letting - it on. - - “I am reading Electricity and working at Fluid Motion, and have - got out the condition of a fluid being able to flow the same - way for a length of time and not wriggle about.” - -The British Association met at Glasgow in September, 1855, and Maxwell -was present, and showed his colour-top at Professor Ramsay’s house to -some of those interested. Letters[22] to his father about this time -describe some of the events of the meeting and his own plans for the -term. - - “We had a paper from Brewster on ‘The theory of three colours - in the spectrum,’ in which he treated Whewell with philosophic - pity, commending him to the care of Prof. Wartman of Geneva, - who was considered the greatest authority in cases of his - kind--cases, in fact, of colour-blindness. Whewell was in the - room, but went out and avoided the quarrel; and Stokes made a - few remarks, stating the case not only clearly but courteously. - However, Brewster did not seem to see that Stokes admitted - his experiments to be correct, and the newspapers represented - Stokes as calling in question the accuracy of the experiments. - - “I am getting my electrical mathematics into shape, and I see - through some parts which were rather hazy before; but I do not - find very much time for it at present, because I am reading - about heat and fluids, so as not to tell lies in my lectures. - I got a note from the Society of Arts about the platometer, - awarding thanks and offering to defray the expenses to the - extent of £10, on the machine being produced in working order. - When I have arranged it in my head, I intend to write to James - Bryson about it. - - “I got a long letter from Thomson about colours and - electricity. He is beginning to believe in my theory about all - colours being capable of reference to three standard ones, and - he is very glad that I should poach on his electrical preserves. - - “... It is difficult to keep up one’s interest in intellectual - matters when friends of the intellectual kind are scarce. - However, there are plenty friends not intellectual who serve - to bring out the active and practical habits of mind, which - overly-intellectual people seldom do. Wherefore, if I am to be - up this term, I intend to addict myself rather to the working - men who are getting up classes than to pups., who are in - the main a vexation. Meanwhile, there is the examination to - consider. - - “You say Dr. Wilson has sent his book. I will write and thank - him. I suppose it is about colour-blindness. I intend to begin - Poisson’s papers on electricity and magnetism to-morrow. I have - got them out of the library. My reading hitherto has been of - novels--‘Shirley’ and ‘The Newcomes,’ and now ‘Westward Ho.’ - - “Macmillan proposes to get up a book of optics with my - assistance, and I feel inclined for the job. There is great - bother in making a mathematical book, especially on a subject - with which you are familiar, for in correcting it you do as - you would to pups.--look if the principle and result is right, - and forget to look out for small errors in the course of the - work. However, I expect the work will be salutary, as involving - hard work, and in the end much abuse from coaches and students, - and certainly no vain fame, except in Macmillan’s puffs. But, - if I have rightly conceived the plan of an educational book - on optics, it will be very different in manner, though not in - matter, from those now used.” - -The examination referred to was that for a Fellowship at Trinity, and -Maxwell was elected on October 10th, 1855. - -He was immediately asked to lecture for the College, on hydrostatics -and optics, to the upper division of the third year, and to set papers -for the questionists. In consequence, he declined to take pupils, in -order to have time for reading and doing private mathematics, and for -seeing the men who attended his lectures. - -In November he writes: “I have been lecturing two weeks now, and the -class seems improving; and they come and ask questions, which is a good -sign. I have been making curves to show the relations of pressure and -volume in gases, and they make the subject easier.” - -Still, he found time to attend Professor Willis’s lectures on mechanism -and to continue his reading. “I have been reading,” he writes, “old -books on optics, and find many things in them far better than what is -new. The foreign mathematicians are discovering for themselves methods -which were well known at Cambridge in 1720, but are now forgotten.” - -The “Poisson” was read to help him with his own views on electricity, -which were rapidly maturing, and the first of that great series of -works which has revolutionised the science was published on December -10th, 1855, when his paper on “Faraday’s Lines of Force” was read to -the Cambridge Philosophical Society. - -The next term found him back in Cambridge at work on his lectures, full -of plans for a new colour top and other matters. Early in February -he received a letter from Professor Forbes, telling him that the -Professorship of Natural Philosophy in Marischal College, Aberdeen, was -vacant, and suggesting that he should apply. - -He decided to be a candidate if his father approved. “For my own part,” -he writes, “I think the sooner I get into regular work the better, -and that the best way of getting into such work is to profess one’s -readiness by applying for it.” On the 20th of February he writes: -“However, wisdom is of many kinds, and I do not know which dwells -with wise counsellors most, whether scientific, practical, political, -or ecclesiastical. I hear there are candidates of all kinds relying -on the predominance of one or other of these kinds of wisdom in the -constitution of the Government.” - -The second part of the paper on “Faraday’s Lines of Force” was read -during the term. Writing on the 4th of March, he expresses the hope -soon to be able to write out fully the paper. “I have done nothing -in that way this term,” he says, “but am just beginning to feel the -electrical state come on again.” - -His father was working at Edinburgh in support of his candidature for -Aberdeen, and when, in the middle of March, he returned North, he -found everything well prepared. The two returned to Glenlair together -after a few days in Edinburgh, and Maxwell was preparing to go back to -Cambridge, when, on the 2nd of April, his father died suddenly. - -Writing to Mrs. Blackburn, he says: “My father died suddenly to-day at -twelve o’clock. He had been giving directions about the garden, and he -said he would sit down and rest a little, as usual. After a few minutes -I asked him to lie down on the sofa, and he did not seem inclined to do -so; and then I got him some ether, which had helped him before. Before -he could take any he had a slight struggle, and all was over. He hardly -breathed afterwards.” - -Almost immediately after this, Maxwell was appointed to Aberdeen. His -father’s death had frustrated some at least of the intentions with -which he had applied for the post. He knew the old man would be glad -to see him the occupant of a Scotch chair. He hoped, too, to be able to -live with his father at Glenlair for one half the year; but this was -not to be. No doubt the laboratory and the freedom of the post, when -compared with the routine work of preparing men for the Tripos, had -their inducements; still, it may be doubted if the choice was a wise -one for him. The work of drilling classes, composed, for the most part, -of raw untrained lads, in the elements of physics and mechanics was, as -Niven says in his preface to the collected works, not that for which -he was best fitted; while at Cambridge, had he stayed, he must always -have had among his pupils some of the best mathematicians of the time; -and he might have founded some ten or fifteen years before he did that -Cambridge School of Physicists which looks back with so much pride to -him as their master. - -Leave-taking at Trinity was a sad task. He writes[23] thus, June 4th, -to Mr. R. B. Litchfield:-- - - “On Thursday evening I take the North-Western route to the - North. I am busy looking over immense rubbish of papers, etc., - for some things not to be burnt lie among much combustible - matter, and some is soft and good for packing. - - “It is not pleasant to go down to live solitary, but it would - not be pleasant to stay up either, when all one had to do lay - elsewhere. The transition state from a man into a Don must come - at last, and it must be painful, like gradual outrooting of - nerves. When it is done there is no more pain, but occasional - reminders from some suckers, tap-roots, or other remnants of - the old nerves, just to show what was there and what might have - been.” - -The summer of 1856 was spent at Glenlair, where various friends were -his guests--Lushington, MacLennan, the two cousins Cay, and others. -He continued to work at optics, electricity, and magnetism, and in -October was busy with “a solemn address or manifesto to the Natural -Philosophers of the North, which needed coffee and anchovies and a -roaring hot fire and spread coat-tails to make it natural.” This was -his inaugural lecture. - -In November he was at Aberdeen. Letters[24] to Miss Cay, Professor -Campbell, and C. J. Munro tell of the work of the session. The last is -from Glenlair, dated May 20th, 1857, after work was over. - - “The session went off smoothly enough. I had Sun, all the - beginning of optics, and worked off all the experimental part - up to Fraunhofer’s lines, which were glorious to see with a - water-prism I have set up in the form of a cubical box, five - inch side.... - - “I succeeded very well with heat. The experiments on latent - heat came out very accurate. That was my part, and the class - could explain and work out the results better than I expected. - Next year I intend to mix experimental physics with mechanics, - devoting Tuesday and THURSDAY (what would Stokes say?) to the - science of experimenting accurately.... - - “Last week I brewed chlorophyll (as the chemists word it), a - green liquor, which turns the invisible light red.... - - “My last grind was the reduction of equations of colour which I - made last year. The result was eminently satisfactory.” - -Another letter,[25] June 5th, 1857, also to Munro, refers to the work -of the University Commission and the new statutes. - - “I have not seen Article 7, but I agree with your dissent from - it entirely. On the vested interest principle, I think the - men who intended to keep their fellowships by celibacy and - ordination, and got them on that footing, should not be allowed - to desert the virgin choir or neglect the priestly office, - but on those principles should be allowed to live out their - days, provided the whole amount of souls cured annually does - not amount to £20 in the King’s Book. But my doctrine is that - the various grades of College officers should be set on such a - basis that, although chance lecturers might be sometimes chosen - from among fresh fellows who are going away soon, the reliable - assistant tutors, and those that have a plain calling that - way, should, after a few years, be elected permanent officers - of the College, and be tutors and deans in their time, and - seniors also, with leave to marry, or, rather, never prohibited - or asked any questions on that head, and with leave to retire - after so many years’ service as seniors. As for the men of the - world, we should have a limited term of existence, and that - independent of marriage or ‘parsonage.’” - -It was more than twenty years before the scheme outlined in the above -letter came to anything; but, at the time of Maxwell’s death in 1879, -another Commission was sitting, and the plan suggested by Maxwell -became the basis of the statutes of nearly all the colleges. - -For the winter session of 1857–58 he was again at Aberdeen. - -The Adams Prize had been established in 1848 by some members of -St. John’s College, and connected by them with the name of Adams -“in testimony of their sense of the honour he had conferred upon -his College and the University by having been the first among the -mathematicians of Europe to determine from perturbations the unknown -place of a disturbing planet exterior to Uranus.” Professor Challis, -Dr. Parkinson, and Sir William Thomson, the examiners, had selected -as the subject for the prize to be awarded in 1857 the “Motions of -Saturn’s Rings.” For this Maxwell had decided to compete, and his -letters at the end of 1857 tell of the progress of the task. Thus, -writing[26] to Lewis Campbell from Glenlair on August 28th, he says:-- - - “I have been battering away at Saturn, returning to the charge - every now and then. I have effected several breaches in the - solid ring, and now I am splash into the fluid one, amid a - clash of symbols truly astounding. When I reappear it will be - in the dusky ring, which is something like the state of the - air supposing the siege of Sebastopol conducted from a forest - of guns 100 miles one way, and 30,000 miles the other, and the - shot never to stop, but go spinning away round a circle, radius - 170,000 miles.” - -And again[27] to Miss Cay on the 28th of November:-- - - “I have been pretty steady at work since I came. The class - is small and not bright, but I am going to give them plenty - to do from the first, and I find it a good plan. I have a - large attendance of my old pupils, who go on with the higher - subjects. This is not part of the College course, so they - come merely from choice, and I have begun with the least - amusing part of what I intend to give them. Many had been - reading in summer, for they did very good papers for me on - the old subjects at the beginning of the month. Most of my - spare time I have been doing Saturn’s rings, which is getting - on now, but lately I have had a great many long letters to - write--some to Glenlair, some to private friends, and some all - about science.... I have had letters from Thomson and Challis - about Saturn--from Hayward, of Durham University, about the - brass top, of which he wants one. He says that the earth has - been really found to change its axis regularly in the way I - supposed. Faraday has also been writing about his own subjects. - I have had also to write Forbes a long report on colours; so - that for every note I have got I have had to write a couple of - sheets in reply, and reporting progress takes a deal of writing - and spelling.” - -He devised a model (now at the Cavendish Laboratory) to exhibit the -motions of the satellites in a disturbed ring, “for the edification of -sensible image-worshippers.” - -The essay was awarded the prize, and secured for its author great -credit among scientific men. - -In another letter, written during the same session, he says: “I find my -principal work here is teaching my men to avoid vague expressions, as -‘a certain force,’ meaning uncertain; _may_ instead of _must_; _will -be_ instead of _is_; _proportional_ instead of _equal_.” - -The death, during the autumn, of his College friend Pomeroy, from fever -in India, was a great blow to him; his letters at the time show the -depth of his feelings and his beliefs. - -The question of the fusion of the two Colleges at Aberdeen, King’s -College and the Marischal College, was coming to the fore. “Know -all men,” he says, in a letter to Professor Campbell, “that I am a -Fusionist.” - -In February, 1858, he was still engaged on Saturn’s rings, while hard -at work during the same time with his classes. He had established a -voluntary class for his students of the previous year, and was reading -with them Newton’s “Lunar Theory and Astronomy.” This was followed by -“Electricity and Magnetism,” Faraday’s book being the backbone of -everything, “as he himself is the nucleus of everything electric since -1830.” - -In February, 1858, he announced his engagement to Katherine Mary Dewar, -the daughter of the Principal of Marischal College. - - “Dear Aunt” (he says,[28] February 18th, 1858), “this comes to - tell you that I am going to have a wife.... - - “Don’t be afraid; she is not mathematical, but there are other - things besides that, and she certainly won’t stop mathematics. - The only one that can speak as an eye-witness is Johnnie, - and he only saw her when we were both trying to act the - indifferent. We have been trying it since, but it would not do, - and it was not good for either.” - -The wedding took place early in June. Professor Campbell has preserved -some of the letters written by Maxwell to Miss Dewar, and these -contain “the record of feelings which in the years that followed were -transfused in action and embodied in a married life which can only be -spoken of as one of unexampled devotion.” - -The project for the fusion of the two Colleges, to which reference has -been made, went on, and the scheme was completed in 1860. - -The two Colleges were united to form the University of Aberdeen, and -the new chair of Natural Philosophy thus created was filled by the -appointment of David Thomson, Professor of Natural Philosophy in King’s -College, and Maxwell’s senior. Mr. W. D. Niven, in his preface to -Maxwell’s works, when dealing with this appointment, writes:-- - - “Professor Thomson, though not comparable to Maxwell as - a physicist, was nevertheless a remarkable man. He was - distinguished by singular force of character and great - administrative faculty, and he had been prominent in bringing - about the fusion of the Colleges. He was also an admirable - lecturer and teacher, and had done much to raise the standard - of scientific education in the north of Scotland. Thus the - choice made by the Commissioners, though almost inevitable, - had the effect of making it appear that Maxwell failed as a - teacher. There seems, however, to be no evidence to support - such an inference. On the contrary, if we may judge from the - number of voluntary students attending his classes in his last - College session, he would seem to have been as popular as a - professor as he was personally estimable.” - -The question whether Maxwell was a great teacher has sometimes been -discussed. I trust that the following pages will give an answer to -it. He was not a prominent lecturer. As Professor Campbell says,[29] -“Between his students’ ignorance and his vast knowledge it was -difficult to find a common measure. The advice which he once gave -to a friend whose duty it was to preach to a country congregation, -‘Why don’t you give it them thinner?’ must often have been applicable -to himself.... Illustrations of _ignotum per ignotius_, or of the -abstruse by some unobserved property of the familiar, were multiplied -with dazzling rapidity. Then the spirit of indirectness and paradox, -though he was aware of its dangers, would often take possession of him -against his will, and, either from shyness or momentary excitement, or -the despair of making himself understood, would land him in ‘chaotic -statements,’ breaking off with some quirk of ironical humour.” - -But teaching is not all done by lecturing. His books and papers are -vast storehouses of suggestions and ideas which the ablest minds of the -past twenty years have been since developing. To talk with him for an -hour was to gain inspiration for a year’s work; to see his enthusiasm -and to win his praise or commendation were enough to compensate for -many weary struggles over some stubborn piece of apparatus which would -not go right, or some small source of error which threatened to prove -intractable and declined to submit itself to calculation. The sure -judgment of posterity will confirm the verdict that Clerk Maxwell was a -great teacher, though lecturing to a crowd of untrained undergraduates -was a task for which others were better fitted than he. - - - - -CHAPTER IV. - -PROFESSOR AT KING’S COLLEGE, LONDON.--LIFE AT GLENLAIR. - - -In 1860 Forbes resigned the chair of Natural Philosophy at Edinburgh. -Maxwell and Tait were candidates, and Tait was appointed. In the -summer of the same year Maxwell obtained the vacant Professorship of -Natural Philosophy at King’s College, London. This he held to 1865, -and this period of his life is distinguished by the appearance of -some of his most important papers. The work was arduous; the College -course extended over nine months of the year; there were as well -evening lectures to artisans as part of his regular duties. His life in -London was useful to him in the opportunities it gave him for becoming -personally acquainted with Faraday and others. He also renewed his -intimacy with various Cambridge friends. - -He was at the celebrated Oxford meeting of the British Association in -1860, where he exhibited his colour-box for mixing the colours of the -spectrum. In 1859, at the meeting at Aberdeen, he had read to Section -A his first paper on the “Dynamical Theory of Gases,” published in the -_Philosophical Magazine_ for January, 1860. The second part of the -paper, dealing with the conduction of heat and other phenomena in a -gas, was published in July, 1860, after the Oxford meeting. - -A paper on the “Theory of Compound Colours” was communicated to -the Royal Society by Professor Stokes in January, 1860. It contains -the account of his colour-box in the form finally adopted (most of -the important parts of the apparatus are still at the Cavendish -Laboratory), and a number of observations by Mrs. Maxwell and himself, -which will be more fully described later. - -In November, 1860, he received for this work the Rumford medal of the -Royal Society. - -The next year, 1861, is of great importance in the history of -electrical science. The British Association met at Manchester, and a -Committee was appointed on Standards of Electrical Resistance. Maxwell -was not a member. The committee reported at the Cambridge meeting in -1862, and were reappointed with extended duties. Maxwell’s name, among -others, was added, and he took a prominent part in the deliberations -of the committee, which, as their Report[30] presented in 1863 states, -came to the opinion, “after mature consideration, that the system -of so-called absolute electrical units, based on purely mechanical -measurements, is not only the best system yet proposed, but is the -only one consistent with our present knowledge both of the relations -existing between the various electrical phenomena and of the connection -between these and the fundamental measurements of time, space, and -mass.” - -Appendix C of this Report, “On the Elementary Relations between -Electrical Measurements,” bears the names of Clerk Maxwell and Fleeming -Jenkin, and is the foundation of everything that has been done in the -way of absolute electrical measurement since that date; while Appendix -D gives an account by the same two workers of the experiments on the -absolute unit of electrical resistance made in the laboratory of King’s -College by Maxwell, Fleeming Jenkin, and Balfour Stewart. Further -experiments are described in the report for 1864. The work thus begun -was consummated during the year 1894 by the legalisation throughout -the civilised world of a system of electrical units based on those -described in these reports. - -Meanwhile, Maxwell’s views on electro-magnetic theory were quietly -developing. Papers on “Physical Lines of Force,” which appeared in the -_Philosophical Magazine_ during 1861 and 1862, contain the germs of -his theory--expressed at that time, it is true, in a somewhat material -form. In the paper published January, 1862, the now well-known relation -between the ratio of the electric units and the velocity of light was -established, and his correspondence with Fleeming Jenkin and C. J. -Munro about this time relates in part to the experimental verification -of this relation. His experiments on this matter were published in the -“Philosophical Transactions” for 1868. - -This electrical theory occupied his mind mainly during 1863 and 1864. -In September of the latter year he writes[31] from Glenlair to C. -Hockin, who had taken Balfour Stewart’s place during the second series -of experiments on the measurement of resistance. - - “I have been doing several electrical problems. I have got a - theory of ‘electric absorption,’ _i.e._, residual charge, etc., - and I very much want determinations of the specific induction, - electric resistance, and absorption of good dielectrics, such - as glass, shell-lac, gutta-percha, ebonite, sulphur, etc. - - “I have also cleared the electromagnetic theory of light from - all unwarrantable assumption, so that we may safely determine - the velocity of light by measuring the attraction between - bodies kept at a given difference of potential, the value of - which is known in electromagnetic measure. - - “I hope there will be resistance coils at the British - Association.” - -This work resulted in his greatest electrical paper, “A Dynamical -Theory of the Electromagnetic Field,” read to the Royal Society -December 8th, 1864. - -But the molecular theory of gases was still prominently before his mind. - -In 1862, writing[32] to H. R. Droop, he says:-- - - “Some time ago, when investigating Bernoulli’s theory of gases, - I was surprised to find that the internal friction of a gas (if - it depends on the collision of particles) should be independent - of the density. - - “Stokes has been examining Graham’s experiments on the rate - of flow of gases through fine tubes, and he finds that the - friction, if independent of density, accounts for Graham’s - results; but, if taken proportional to density, differs from - those results very much. This seems rather a curious result, - and an additional phenomenon, explained by the ‘collision of - particles’ theory of gases. Still one phenomenon goes against - that theory--the relation between specific heat at constant - pressure and at constant volume, which is in air = 1·408, while - it ought to be 1·333.” - -And again[33] in the same year, 21st April, 1862, to Lewis Campbell:-- - - “Herr Clausius of Zürich, one of the heat philosophers, has - been working at the theory of gases being little bodies flying - about, and has found some cases in which he and I don’t tally. - So I am working it out again. Several experimental results have - turned up lately rather confirmatory than otherwise of that - theory. - - “I hope you enjoy the absence of pupils. I find the division of - them into smaller classes is a great help to me and to them; - but the total oblivion of them for definite intervals is a - necessary condition for doing them justice at the proper time.” - -The experiments on the viscosity of gases, which formed the Bakerian -Lecture to the Royal Society read on February 8th, 1866, were the -outcome of this work. His house in 8, Palace Gardens, Kensington, -contained a large garret running the complete length. - -“To maintain the proper temperature a large fire was for some days kept -up in the room in the midst of very hot weather. Kettles were kept on -the fire and large quantities of steam allowed to flow into the room. -Mrs. Maxwell acted as stoker, which was very exhausting work when -maintained for several consecutive hours. After this the room was kept -cool for subsequent experiments by the employment of a considerable -amount of ice.” - -Next year, May, 1866, was read his paper on the “Dynamical Theory of -Gases,” in which errors in his former papers, which had been pointed -out by Clausius, were corrected. - -Meanwhile he had resigned his London Professorship at the end of the -Session of 1865, and had been succeeded by Professor W. G. Adams. - -For the next four years he lived chiefly at Glenlair, working at his -theory of electricity, occasionally, as we shall see, visiting London -and Cambridge, and taking an active interest in the affairs of his -own neighbourhood. In 1865 he had a serious illness, through which he -was nursed with great care by Mrs. Maxwell. His correspondence was -considerable, and absorbed much of his time. Much also was given to the -study of English literature; he was fond of reading Chaucer, Milton, or -Shakespeare aloud to Mrs. Maxwell. - -He also read much theological and philosophical literature, and all he -read helped only to strengthen that firm faith in the fundamentals of -Christianity in which he lived and died. - -In 1867 he and Mrs. Maxwell paid a visit to Italy, which was a source -of great pleasure to both. - -His chief scientific work was the preparation of his “Electricity and -Magnetism,” which did not appear till 1873; the time was in the main -one of quiet thought and preparation for his next great task, the -foundation of the School of Physics in Cambridge. - -In 1868 the principalship of the United College in the University of -St. Andrews was vacant by the resignation of Forbes, and Maxwell was -invited by several of the professors to stand. He, however, declined to -submit his name to the Crown. - - - - -CHAPTER V. - -CAMBRIDGE.--PROFESSOR OF PHYSICS. - - -During his retirement at Glenlair from 1865 to 1870 Maxwell was -frequently at Cambridge. He examined in the Mathematical Tripos in 1866 -and 1867, and again in 1869 and 1870. - -The regulations for the Tripos had been in force practically unchanged -since 1848, and it was felt by many that the range of subjects included -was not sufficiently extensive, and that changes were urgently needed -if Cambridge were to retain its position as the centre of mathematical -teaching. Natural Philosophy was mentioned in the Schedule, but Natural -Philosophy included only Dynamics and Astronomy, Hydrostatics and -Physical Optics, with some simple Hydrodynamics and Sound. - -The subjects of Heat, Electricity and Magnetism, the Theory of Elastic -Solids and Vibrations, Vortex-Motion in Hydrodynamics, and much else, -were practically new since 1848. Stokes, Thomson, and Maxwell in -England, and Helmholtz in Germany, had created them. - -Accordingly in June, 1868, a new plan of examinations was sanctioned -by the Senate to come into force in January, 1873, and these various -subjects were explicitly included. - -Mr. Niven, who was one of those examined by Maxwell in 1866, writes in -the preface to the collected works:-- - - “For some years previous to 1866, when Maxwell returned to - Cambridge as Moderator in the Mathematical Tripos, the studies - in the University had lost touch with the great scientific - movements going on outside her walls. It was said that some - of the subjects most in vogue had but little interest for the - present generation, and loud complaints began to be heard - that while such branches of knowledge as Heat, Electricity, - and Magnetism were left out of the Tripos examination, the - candidates were wasting their time and energy upon mathematical - trifles barren of scientific interest and of practical results. - Into the movement for reform Maxwell entered warmly. By his - questions in 1866, and subsequent years, he infused new life - into the examination; he took an active part in drafting the - new scheme introduced in 1873; but most of all by his writings - he exerted a powerful influence on the younger members of the - University, and was largely instrumental in bringing about the - change which has been now effected.” - -But the University possessed no means of teaching these subjects, and a -Syndicate or Committee was appointed, November 25th, 1868, “to consider -the best means of giving instruction to students in Physics, especially -in Heat, Electricity and Magnetism, and the methods of providing -apparatus for this purpose.” - -Dr. Cookson, Master of St. Peter’s College, took an active part in the -work of the Syndicate. Professor Stokes, Professor Liveing, Professor -Humphry, Dr. Phear, and Dr. Routh were among the members. Maxwell -himself was in Cambridge that winter, as Examiner for the Tripos, and -his work as Moderator and Examiner in the two previous years had done -much to show the necessity of alterations and to indicate the direction -which changes should take. - -The Syndicate reported February 27th, 1869. They called attention to -the Report of the Royal Commission of 1850. The Commissioners had -“prominently urged the importance of cultivating a knowledge of the -great branches of Experimental Physics in the University”; and in -page 118 of their Report, after commending the manner in which the -subject of Physical Optics is studied in the University, and pointing -out that “there is, perhaps, no public institution where it is better -represented or prosecuted with more zeal and success in the way of -original research,” they had stated that “no reason can be assigned -why other great branches of Natural Science should not become equally -objects of attention, or why Cambridge should not become a great school -of physical and experimental, as it is already of mathematical and -classical, instruction.” - -And again the Commissioners remark: “In a University so thoroughly -imbued with the mathematical spirit, physical study might be expected -to assume within its precincts its highest and severest tone, be -studied under more abstract forms, with more continual reference to -mathematical laws, and therefore with better hope of bringing them one -by one under the domain of mathematical investigation than elsewhere.” - -After calling attention to these statements the Report of the Syndicate -then continues:-- - -“In the scheme of Examination for Honours in the Mathematical Tripos -approved by Grace of the Senate on the 2nd of June, 1868, Heat, -Electricity and Magnetism, if not introduced for the first time, had a -much greater degree of importance assigned to them than at any previous -period, and these subjects will henceforth demand a corresponding -amount of attention from the candidates for Mathematical Honours. The -Syndicate have limited their attention almost entirely to the question -of providing public instruction in Heat, Electricity and Magnetism. -They recognise the importance and advantage of tutorial instruction in -these subjects in the several colleges, but they are also alive to the -great impulse given to studies of this kind, and to the large amount of -additional training which students may receive through the instruction -of a public Professor, and by knowledge gained in a well-appointed -laboratory.” - -“In accordance with these views, and at an early period in their -deliberations, they requested the Professors[34] of the University, who -are engaged in teaching Mathematical and Physical Science, to confer -together upon the present means of teaching Experimental Physics, -especially Heat, Electricity and Magnetism, and to inform them how the -increased requirements of the University in this respect could be met -by them.” - -“The Professors, so consulted, favoured the Syndicate with a report -on the subject, which the Syndicate now beg leave to lay before the -Senate. It points out how the requirements of the University might -be “partially met,” but the Professors state distinctly that they -“do not think that they are able to meet the want of an extensive -course of lectures on Physics treated as such, and in great measure -experimentally. As Experimental Physics may fairly be considered -to come within the province of one or more of the above-mentioned -Professors, the Syndicate have considered whether now or at some -future time some arrangement might not be made to secure the effective -teaching of this branch of science, without having resort to the -services of an additional Professor. They are, however, of opinion that -such an arrangement cannot be made at the present time, and that the -exigencies of the case may be best met by founding a new professorship -which shall terminate with the tenure of office of the Professor first -elected. The services of a man of the highest attainments in science, -devoting his life to public teaching as such Professor, and engaged in -original research, would be of incalculable benefit to the University.” - -The Report goes on to point out that a laboratory would be necessary, -and also apparatus. It is estimated that £5,000 would cover the cost -of the laboratory, and £1,300 the necessary apparatus. Provision is -also made for a demonstrator and a laboratory assistant, and the Report -closes with a recommendation that a special Syndicate of Finance should -be appointed to consider the means of raising the funds. - -The Professors in their Report to the Syndicate point out that teaching -in Experimental Physics is needed for the Mathematical Tripos, the -Natural Sciences Tripos, certain Special examinations, and the first -examination for the degree of M.B. It appeared to them clear that there -was work for a new Professor. - -In May, 1869, the Financial Syndicate recommended by the above Report -was appointed “to consider the means of raising the necessary funds for -establishing a professor and demonstrator of Experimental Physics, and -for providing buildings and apparatus required for that department of -science, and further to consider other wants of the University, and the -sources from which those wants may be supplied.” - -The Syndicate endeavoured to meet the expenditure by inquiry from the -several Colleges whether they would be willing to make contributions -from their corporate funds, but without success. - -“The answers of the Colleges indicated such a want of concurrence -in any proposal to raise contributions from the corporate funds of -Colleges by any kind of direct taxation that the Syndicate felt -obliged to abandon the notion of obtaining the necessary funds from -this source, and accordingly to limit the number of objects which they -should recommend the Senate to accomplish.” - -External authority was necessary before the colleges would submit -to taxation for University purposes, and it was left to the Royal -Commission of 1877 to carry into effect many of the suggestions -made by the Syndicate. Meanwhile they contented themselves with -recommending means for raising an annual stipend of £660 for the -professor, demonstrator, and assistant, and a capital sum of £5,000, or -thereabouts, for the expenses of a building. - -The Syndicate’s Report was issued in an amended form in the May term of -1870, and before any decision was taken on it the Vice-Chancellor, Dr. -Atkinson, on October 13th, 1870, published “the following munificent -offer of his grace the Duke of Devonshire, the Chancellor of the -University,” who had been chairman of the Commission on Scientific -Education. - - “Holker Hall, Grange, Lancashire. - - “MY DEAR MR. VICE-CHANCELLOR,--I have the honour to address you - for the purpose of making an offer to the University, which, if - you see no objection, I shall be much obliged to you to submit - in such manner as you may think fit for the consideration of - the Council and the University. - - “I find in the report dated February 29th, 1869, of the - Physical Science Syndicate, recommending the establishment of - a Professor and Demonstrator of Experimental Physics, that the - buildings and apparatus required for this department of science - are estimated to cost £6,300. - - “I am desirous to assist the University in carrying this - recommendation into effect, and shall accordingly be prepared - to provide the funds required for the building and apparatus as - soon as the University shall have in other respects completed - its arrangements for teaching Experimental Physics, and shall - have approved the plan of the building. - - “I remain, my dear Mr. Vice-Chancellor, - “Yours very faithfully, - “DEVONSHIRE.” - -By his generous action the University was relieved from all expense -connected with the building. A Grace establishing a Professorship of -Experimental Physics was confirmed by the Senate February 9th, 1871, -and March 8th was fixed for the election. - -Meanwhile who was to be Professor? Sir W. Thomson’s name had been -mentioned, but he, it was known, would not accept the post. Maxwell -was then applied to, and at first he was unwilling to leave Glenlair. -Professor Stokes, the Hon. J. W. Strutt (Lord Rayleigh), Mr. Blore -of Trinity, and others wrote to him. Lord Rayleigh’s letter[35] is as -follows: - - “Cambridge, 14th February, 1871. - - “When I came here last Friday I found everyone talking about - the new professorship, and hoping that you would come. Thomson, - it seems, has definitely declined.... There is no one here in - the least fit for the post. What is wanted by most who know - anything about it is not so much a lecturer as a mathematician - who has actual experience in experimenting, and who might - direct the energies of the younger Fellows and bachelors into - a proper channel. There must be many who would be willing to - work under a competent man, and who, while learning themselves, - would materially assist him.... I hope you may be induced to - come; if not, I don’t know who it is to be. Do not trouble to - answer me about this, as I believe others have written to you - about it.” - -On the 15th of February, Maxwell wrote to Mr. Blore:-- - - “I had no intention of applying for the post when I got your - letter, and I have none now, unless I come to see that I can do - some good by it.” The letter continues:--“The class of Physical - Investigations, which might be undertaken with the help of men - of Cambridge education, and which would be creditable to the - University, demand in general a considerable amount of dull - labour, which may or may not be attractive to the pupils.” - -However, on the 24th of February, Mr. Blore wrote to the Electoral -Roll:-- - -“I am authorised to give notice that Mr. John (_sic_) Clerk Maxwell, -F.R.S., formerly Professor of Natural Philosophy at Aberdeen, and -at King’s College, London, is a candidate for the professorship of -Experimental Physics.” - -Maxwell was elected without opposition. Writing[36] to his wife from -Cambridge, 20th March, 1871, he says:-- - - “There are two parties about the professorship. One wants - popular lectures, and the other cares more for experimental - work. I think there should be a gradation--popular lectures and - rough experiments for the masses; real experiments for real - students; and laborious experiments for first-rate men like - Trotter and Stuart and Strutt.” - -While in a letter[37] from Glenlair to C. J. Munro, dated March 15th, -1871, he writes:--“The Experimental Physics at Cambridge is not built -yet, but we are going to try. The desideratum is to set a Don and a -Freshman to observe and register (say) the vibrations of a magnet -together, or the Don to turn a watch and the Freshman to observe and -govern him.” - -In October he delivered his Introductory Lecture. A few quotations will -show the spirit in which he approached his task. - - “In a course of Experimental Physics we may consider either - the Physics or the Experiments as the leading feature. We may - either employ the experiments to illustrate the phenomena of - a particular branch of Physics, or we may make some physical - research in order to exemplify a particular experimental - method. In the order of time, we should begin, in the Lecture - Room, with a course of lectures on some branch of Physics - aided by experiments of illustration, and conclude, in the - Laboratory, with a course of experiments of research. - - “Let me say a few words on these two classes of - experiments--Experiments of Illustration and Experiments of - Research. The aim of an experiment of illustration is to throw - light upon some scientific idea so that the student may be - enabled to grasp it. The circumstances of the experiment are - so arranged that the phenomenon which we wish to observe or to - exhibit is brought into prominence, instead of being obscured - and entangled among other phenomena, as it is when it occurs - in the ordinary course of nature. To exhibit illustrative - experiments, to encourage others to make them, and to cultivate - in every way the ideas on which they throw light, forms an - important part of our duty. The simpler the materials of an - illustrative experiment, and the more familiar they are to the - student, the more thoroughly is he likely to acquire the idea - which it is meant to illustrate. The educational value of such - experiments is often inversely proportional to the complexity - of the apparatus. The student who uses home-made apparatus, - which is always going wrong, often learns more than one who has - the use of carefully adjusted instruments, to which he is apt - to trust, and which he dares not take to pieces. - - “It is very necessary that those who are trying to learn from - books the facts of physical science should be enabled by the - help of a few illustrative experiments to recognise these facts - when they meet with them out of doors. Science appears to us - with a very different aspect after we have found out that it is - not in lecture-rooms only, and by means of the electric light - projected on a screen, that we may witness physical phenomena, - but that we may find illustrations of the highest doctrines of - science in games and gymnastics, in travelling by land and by - water, in storms of the air and of the sea, and wherever there - is matter in motion. - - “If, therefore, we desire, for our own advantage and for the - honour of our University, that the Devonshire Laboratory should - be successful, we must endeavour to maintain it in living union - with the other organs and faculties of our learned body. We - shall therefore first consider the relation in which we stand - to those mathematical studies which have so long flourished - among us, which deal with our own subjects, and which differ - from our experimental studies only in the mode in which they - are presented to the mind. - - “There is no more powerful method for introducing knowledge - into the mind than that of presenting it in as many different - ways as we can. When the ideas, after entering through - different gateways, effect a junction in the citadel of the - mind, the position they occupy becomes impregnable. Opticians - tell us that the mental combination of the views of an object - which we obtain from stations no further apart than our two - eyes is sufficient to produce in our minds an impression of the - solidity of the object seen; and we find that this impression - is produced even when we are aware that we are really looking - at two flat pictures placed in a stereoscope. It is therefore - natural to expect that the knowledge of physical science - obtained by the combined use of mathematical analysis and - experimental research will be of a more solid, available, and - enduring kind than that possessed by the mere mathematician or - the mere experimenter. - - “But what will be the effect on the University if men pursuing - that course of reading which has produced so many distinguished - Wranglers turn aside to work experiments? Will not their - attendance at the Laboratory count not merely as time withdrawn - from their more legitimate studies, but as the introduction of - a disturbing element, tainting their mathematical conceptions - with material imagery, and sapping their faith in the formulæ - of the text-books? Besides this, we have already heard - complaints of the undue extension of our studies, and of the - strain put upon our questionists by the weight of learning - which they try to carry with them into the Senate-House. If we - now ask them to get up their subjects not only by books and - writing, but at the same time by observation and manipulation, - will they not break down altogether? The Physical Laboratory, - we are told, may perhaps be useful to those who are going out - in Natural Science, and who do not take in Mathematics, but - to attempt to combine both kinds of study during the time of - residence at the University is more than one mind can bear. - - “No doubt there is some reason for this feeling. Many of us - have already overcome the initial difficulties of mathematical - training. When we now go on with our study, we feel that it - requires exertion and involves fatigue, but we are confident - that if we only work hard our progress will be certain. - - “Some of us, on the other hand, may have had some experience - of the routine of experimental work. As soon as we can read - scales, observe times, focus telescopes, and so on, this kind - of work ceases to require any great mental effort. We may, - perhaps, tire our eyes and weary our backs, but we do not - greatly fatigue our minds. - - “It is not till we attempt to bring the theoretical part of - our training into contact with the practical that we begin to - experience the full effect of what Faraday has called ‘mental - inertia’--not only the difficulty of recognising, among the - concrete objects before us, the abstract relation which we have - learned from books, but the distracting pain of wrenching the - mind away from the symbols to the objects, and from the objects - back to the symbols. This, however, is the price we have to pay - for new ideas. - - “But when we have overcome these difficulties, and successfully - bridged over the gulph between the abstract and the concrete, - it is not a mere piece of knowledge that we have obtained; we - have acquired the rudiment of a permanent mental endowment. - When, by a repetition of efforts of this kind, we have more - fully developed the scientific faculty, the exercise of this - faculty in detecting scientific principles in nature, and in - directing practice by theory, is no longer irksome, but becomes - an unfailing source of enjoyment, to which we return so often - that at last even our careless thoughts begin to run in a - scientific channel. - - “Our principal work, however, in the Laboratory must be to - acquaint ourselves with all kinds of scientific methods, to - compare them and to estimate their value. It will, I think, - be a result worthy of our University, and more likely to be - accomplished here than in any private laboratory, if, by the - free and full discussion of the relative value of different - scientific procedures, we succeed in forming a school of - scientific criticism and in assisting the development of the - doctrine of method. - - “But admitting that a practical acquaintance with the methods - of Physical Science is an essential part of a mathematical - and scientific education, we may be asked whether we are not - attributing too much importance to science altogether as part - of a liberal education. - - “Fortunately, there is no question here whether the University - should continue to be a place of liberal education, or - should devote itself to preparing young men for particular - professions. Hence, though some of us may, I hope, see reason - to make the pursuit of science the main business of our lives, - it must be one of our most constant aims to maintain a living - connexion between our work and the other liberal studies of - Cambridge, whether literary, philological, historical, or - philosophical. - - “There is a narrow professional spirit which may grow up among - men of science just as it does among men who practise any other - special business. But surely a University is the very place - where we should be able to overcome this tendency of men to - become, as it were, granulated into small worlds, which are - all the more worldly for their very smallness? We lose the - advantage of having men of varied pursuits collected into one - body if we do not endeavour to imbibe some of the spirit even - of those whose special branch of learning is different from our - own.” - -Another expression of his views on the position of Physics at the time -will be found in his address to Section A of the British Association, -when President at the Liverpool meeting of 1870. - - - - -CHAPTER VI. - -CAMBRIDGE--THE CAVENDISH LABORATORY. - - -But the laboratory was not yet built. A Syndicate, of which Maxwell -was a member, was appointed to consider the question of a site, to -take professional advice, and to obtain plans and estimates. Professor -Maxwell and Mr. Trotter visited various laboratories at home and -abroad for the purpose of ascertaining the best arrangements. Mr. W. -M. Fawcett was appointed architect; the tender of Mr. John Loveday, -of Kebworth, for the building at a cost of £8,450, exclusive of gas, -water, and heating, was accepted in March, 1872, and the building[38] -was begun during the summer. - -In the meantime Maxwell began to lecture, finding a home where he could. - - “Lectures begin 24th,” he writes from Glenlair, October 19th, - 1872. “Laboratory rising, I hear, but I have no place to erect - my chair, but move about like the cuckoo, depositing my notions - in the Chemical Lecture-room 1st term; in the Botanical in - Lent, and in Comparative Anatomy in Easter.” - -It was not till June, 1874, that the building was complete, and on -the 16th the Chancellor formally presented his gift of the Cavendish -Laboratory to the University. In the correspondence previous to this -time it was spoken of as the Devonshire Laboratory. The name Cavendish -commemorated the work of the great physicist of a century earlier, -whose writings Maxwell was shortly to edit, as well as the generosity -of the Chancellor. - -In their letter of thanks to the Duke of Devonshire the University -write:-- - -“Unde vero conventius poterat illis artibus succurri quam e tua domo -quæ in ipsis jam pridem inclaruerat. Notum est Henricum Cavendish quem -secutus est Coulombius primum ita docuisse, quæ sit vis electrica ut -eam numerorum modulis illustraret; adhibitis rationibus quas hodie -veras esse constat.” And they suggest the name as suitable for the -building. To this the Chancellor replied, after referring to the work -of Henry Cavendish: “Quod pono in officinâ ipsâ nuncupandâ nomen ejus -commemorare dignati sitis, id grato animo accepi.” - -The building had cost far more than the original estimate, but the -Chancellor’s generosity was not limited, and on July 21st, 1874, he -wrote to the Vice-Chancellor:-- - -“It is my wish to provide all instruments for the Cavendish Laboratory -which Professor Maxwell may consider to be immediately required, either -in his lectures or otherwise.” - -Maxwell prepared a list, but explained while doing it that time and -thought were necessary to secure the best form of instruments; and he -continues, writing to the Vice-Chancellor: “I think the Duke fully -understood from what I said to him that to furnish the Laboratory -will be a matter of several years’ duration. I shall consider myself, -however,” he says, “at liberty to contribute to the Laboratory any -instruments which I have had constructed in former years, and which -may be found still useful, and also from time to time to procure others -for special researches.” - -In 1877 in his annual report Professor Maxwell announced that the -Chancellor[39] had now “completed his gift to the University by -furnishing the Cavendish Laboratory with apparatus suited to the -present state of science.” - -The stock of apparatus, however, was still small, although Maxwell in -the most generous manner himself spent large sums in adding to it; -for the Professor was most particular in procuring only expensive -instruments by the best makers, with such additional improvements as he -could himself suggest. - -In March, 1874, a Demonstratorship of Physics had been established, and -Mr. Garnett of St. John’s College was appointed. - -Work began in the laboratory in October, 1874. At first the number of -students was small. Only seventeen names appear in the Natural Sciences -Tripos[40] list for 1874, and few of those did Physics. - -The fear alluded to by the Professor in his introductory lecture, -that men reading for the Mathematical Tripos would not find -time for attendance at the laboratory, was justified. One of the -weaknesses of our Cambridge plan has been the divorce between -Mathematics and experimental work, encouraged by our system of -examinations. Experimental knowledge is supposed not to be needed for -the Mathematical Tripos; the Mathematics permitted in the Natural -Sciences Tripos are very simple; thus it came about that few men while -reading for the Mathematical Tripos attended the laboratory, and this -unfortunate result was intensified by the action of the University in -1877–78, when the regulations for the Mathematical Tripos were again -altered.[41] - -Still there were pupils eager and willing to work, though they were -chiefly men who had already taken their B.A. degree, and who wished -to continue Physical reading and research, even though it involved “a -considerable amount of dull labour not altogether attractive.” My own -work there began in 1876, and it may be interesting if I recall my -reminiscences of that time. - -The first experiments I can recollect related to the measurement -of electrical resistance. I well remember Maxwell explaining the -principle of Wheatstone’s bridge, and my own wish at the time that I -had come to the laboratory before the Tripos, instead of afterwards. -Lord Rayleigh had, during the examination, set an easy question which -I failed to do for want of some slight experimental knowledge, and the -first few words of Maxwell’s talk showed me the solution. - -I did not attend his lectures regularly--they were given, I think, at -an hour which I was obliged to devote to teaching; besides, there was -his book, the “Electricity and Magnetism,” into which I had just dipped -before the Tripos, to work at. - -Chrystal and Saunder were then busy at their verification of Ohm’s law. -They were using a number of the Thomson form of tray Daniell’s cells, -and Maxwell was anxious for tests of various kinds to be made on these -cells; these I undertook, and spent some time over various simple -measurements on them. He then set me to work at some of the properties -of a stratified dielectric, consisting, if I remember rightly, of -sheets of paraffin paper and mica. By this means I became acquainted -with various pieces of apparatus. There were no regular classes and no -set drill of demonstrations arranged for examination purposes; these -came later. In Maxwell’s time those who wished to work had the use of -the laboratory and assistance and help from him, but they were left -pretty much to themselves to find out about the apparatus and the best -methods of using it. - -Rather later than this Schuster came and did some of his spectroscope -work. J. E. H. Gordon was busy with the preliminary observations -for his determination of Verdet’s constant, and Niven had various -electrical experiments on hand; while Fleming was at work on the B. A. -resistance coils. - -My own tastes lay in the direction of optics. Maxwell was anxious that -I should investigate the properties of certain crystals. I think they -were the chlorate of potash crystals, about which Stokes and Rayleigh -have since written; but these crystals were to be grown, a slow process -which would, he supposed, take years; and as I wished to produce a -dissertation for the Trinity Fellowship examination in 1877, that work -had to be laid aside. - -Eventually I selected as a subject the form of the wave surface in -a biaxial crystal, and set to work in a room assigned to me. The -Professor used to come in on most days to see how I was getting on. -Generally he brought his dog, which sometimes was shut up in the next -room while he went to college. Dogs were not allowed in college, and -Maxwell had an amusing way of describing how Toby once wandered into -Trinity, and by some doggish instinct discovered immediately, to his -intense amazement, that he was in a place where no dogs had been since -the college was. Toby was not always quiet in his master’s absence, and -his presence in the next room was somewhat disturbing. - -When difficulties occurred Maxwell was always ready to listen. Often -the answer did not come at once, but it always did come after a little -time. I remember one day, when I was in a serious dilemma, I told him -my long tale, and he said:-- - -“Well, Chrystal has been talking to me, and Garnett and Schuster have -been asking questions, and all this has formed a good thick crust round -my brain. What you have said will take some time to soak through, but -we will see about it.” In a few days he came back with--“I have been -thinking over what you said the other day, and if you do so-and-so it -will be all right.” - -My dissertation was referred to him, and on the day of the election, -when returning to Cambridge for the admission, I met him at Bletchley -station, and well remember his kind congratulations and words of warm -encouragement. - -For the next year and a half I was working regularly at the laboratory -and saw him almost daily during term time. - -Of these last years there really is but little to tell. His own -scientific work went on. The “Electricity and Magnetism” was written -mostly at Glenlair. About the time of his return to Cambridge, in -October, 1872, he writes[42] to Lewis Campbell:-- - - “I am continually engaged in stirring up the Clarendon Press, - but they have been tolerably regular for two months. I find - nine sheets in thirteen weeks is their average. Tait gives me - great help in detecting absurdities. I am getting converted to - quaternions, and have put some in my book.” - -The book was published in 1873. The Text-book of Heat was written -during the same period, while “Matter and Motion,” “a small book on a -great subject,” was published in 1876. - -In 1873 and 1874 he was one of the examiners for the Natural Sciences -Tripos, and in 1873 he was the first additional examiner for the -Mathematical Tripos, in accordance with the scheme which he had done so -much to promote in 1868. - -Many of his shorter papers were written about the same time. The -ninth edition of the _Encyclopædia Britannica_ was being published, -and Professor Baynes had enlisted his aid in the work. The articles -“Atom,” “Attraction,” “Capillary Action,” “Constitution of Bodies,” -“Diffusion,” “Ether,” “Faraday,” and others are by him. - -He also wrote a number of papers for _Nature_. Some of these are -reviews of books or accounts of scientific men, such as the notices -of Faraday and Helmholtz, which appeared with their portraits; others -again are original contributions to science. Among the latter many have -reference to the molecular constitution of bodies. Two lectures--the -first on “Molecules,” delivered before the British Association at -Bradford in 1873; the second on the “Dynamical Evidence of the -Molecular Constitution of Bodies,” delivered before the Chemical -Society in 1875--were of special importance. The closing sentences of -the first lecture have been often quoted. They run as follow:-- - - “In the heavens we discover by their light, and by their light - alone, stars so distant from each other that no material thing - can ever have passed from one to another; and yet this light, - which is to us the sole evidence of the existence of these - distant worlds, tells us also that each of them is built up of - molecules of the same kinds as those which we find on earth. - A molecule of hydrogen, for example, whether in Sirius or in - Arcturus, executes its vibrations in precisely the same time. - - “Each molecule therefore throughout the universe bears - impressed upon it the stamp of a metric system, as distinctly - as does the metre of the Archives at Paris, or the double royal - cubit of the temple of Karnac. - - “No theory of evolution can be formed to account for the - similarity of molecules, for evolution necessarily implies - continuous change, and the molecule is incapable of growth or - decay, of generation or destruction. - - “None of the processes of Nature, since the time when Nature - began, have produced the slightest difference in the properties - of any molecule. We are therefore unable to ascribe either the - existence of the molecules or the identity of their properties - to any of the causes which we call natural. - - “On the other hand, the exact equality of each molecule to all - others of the same kind gives it, as Sir John Herschel has well - said, the essential character of a manufactured article, and - precludes the idea of its being eternal and self-existent. - - “Thus we have been led along a strictly scientific path, - very near to the point at which Science must stop--not that - Science is debarred from studying the internal mechanism of a - molecule which she cannot take to pieces any more than from - investigating an organism which she cannot put together. But in - tracing back the history of matter, Science is arrested when - she assures herself, on the one hand, that the molecule has - been made, and, on the other, that it has not been made by any - of the processes we call natural. - - “Science is incompetent to reason upon the creation of matter - itself out of nothing. We have reached the utmost limits of our - thinking faculties when we have admitted that because matter - cannot be eternal and self-existent, it must have been created. - - “It is only when we contemplate, not matter in itself, but the - form in which it actually exists, that our mind finds something - on which it can lay hold. - - “That matter, as such, should have certain fundamental - properties, that it should exist in space and be capable of - motion, that its motion should be persistent, and so on, are - truths which may, for anything we know, be of the kind which - metaphysicians call necessary. We may use our knowledge of - such truths for purposes of deduction, but we have no data for - speculating as to their origin. - - “But that there should be exactly so much matter and no more - in every molecule of hydrogen is a fact of a very different - order. We have here a particular distribution of matter--a - _collocation_, to use the expression of Dr. Chalmers, of things - which we have no difficulty in imagining to have been arranged - otherwise. - - “The form and dimensions of the orbits of the planets, for - instance, are not determined by any law of nature, but depend - upon a particular collocation of matter. The same is the case - with respect to the size of the earth, from which the standard - of what is called the metrical system has been derived. But - these astronomical and terrestrial magnitudes are far inferior - in scientific importance to that most fundamental of all - standards which forms the base of the molecular system. Natural - causes, as we know, are at work which tend to modify, if they - do not at length destroy, all the arrangements and dimensions - of the earth and the whole solar system. But though in the - course of ages catastrophes have occurred and may yet occur in - the heavens, though ancient systems may be dissolved and new - systems evolved out of their ruins, the molecules out of which - these systems are built--the foundation stones of the material - universe--remain unbroken and unworn. They continue this day as - they were created--perfect in number and measure and weight; - and from the ineffaceable characters impressed on them we may - learn that those aspirations after accuracy in measurement, and - justice in action, which we reckon among our noblest attributes - as men, are ours because they are essential constituents of the - image of Him who in the beginning created, not only the heaven - and the earth, but the materials of which heaven and earth - consist.” - -This was criticised in _Nature_ by Mr. C. J. Munro, and at a later time -by Clifford in one of his essays. - -Some correspondence with the Bishop of Gloucester and Bristol on the -authority for the comparison of molecules to manufactured articles is -given by Professor Campbell, and in it Maxwell points out that the -latter part of the article “Atom” in the _Encyclopædia_ is intended to -meet Mr. Munro’s criticism. - -In 1874 the British Association met at Belfast, under the presidency of -Tyndall. Maxwell was present, and published afterwards in _Blackwood’s -Magazine_ an amusing paraphrase of the president’s address. This, with -some other verses written at about the same time, may be quoted here. -Professor Campbell has collected a number of verses written by Maxwell -at various times, which illustrate in an admirable manner both the -grave and the gay side of his character. - - -BRITISH ASSOCIATION, 1874. - -_Notes of the President’s Address._ - - In the very beginnings of science, the parsons, who managed - things then, - Being handy with hammer and chisel, made gods in the likeness - of men; - Till commerce arose, and at length some men of exceptional power - Supplanted both demons and gods by the atoms, which last - to this hour. - Yet they did not abolish the gods, but they sent them well - out of the way, - With the rarest of nectar to drink, and blue fields of - nothing to sway. - From nothing comes nothing, they told us--naught happens by - chance, but by fate; - There is nothing but atoms and void, all else is mere whims - out of date! - Then why should a man curry favour with beings who cannot exist, - To compass some petty promotion in nebulous kingdoms of mist? - But not by the rays of the sun, nor the glittering shafts of the - day, - Must the fear of the gods be dispelled, but by words, and their - wonderful play. - So treading a path all untrod, the poet-philosopher sings - Of the seeds of the mighty world--the first-beginnings of things; - How freely he scatters his atoms before the beginning of years; - How he clothes them with force as a garment, those small - incompressible spheres! - Nor yet does he leave them hard-hearted--he dowers them with love - and with hate, - Like spherical small British Asses in infinitesimal state; - Till just as that living Plato, whom foreigners nickname - Plateau,[43] - Drops oil in his whisky-and-water (for foreigners sweeten it so); - Each drop keeps apart from the other, enclosed in a flexible skin, - Till touched by the gentle emotion evolved by the prick of a pin: - Thus in atoms a simple collision excites a sensational thrill, - Evolved through all sorts of emotion, as sense, understanding, - and will - (For by laying their heads all together, the atoms, as - councillors do, - May combine to express an opinion to every one of them new). - There is nobody here, I should say, has felt true indignation at - all, - Till an indignation meeting is held in the Ulster Hall; - Then gathers the wave of emotion, then noble feelings arise, - Till you all pass a resolution which takes every man by surprise. - Thus the pure elementary atom, the unit of mass and of thought, - By force of mere juxtaposition to life and sensation is brought; - So, down through untold generations, transmission of structureless - gorms - Enables our race to inherit the thoughts of beasts, fishes, and - worms. - We honour our fathers and mothers, grandfathers and grandmothers - too; - But how shall we honour the vista of ancestors now in our view? - First, then, let us honour the atom, so lively, so wise, - and so small; - The atomists next let us praise, Epicurus, Lucretius, and all. - Let us damn with faint praise Bishop Butler, in whom many - atoms combined - To form that remarkable structure it pleased him to call--his mind. - Last, praise we the noble body to which, for the time, we belong, - Ere yet the swift whirl of the atoms has hurried us, ruthless, - along, - The British Association--like Leviathan worshipped by Hobbes, - The incarnation of wisdom, built up of our witless nobs, - Which will carry on endless discussions when I, and probably you, - Have melted in infinite azure--in English, till all is blue. - - -MOLECULAR EVOLUTION. - -_Belfast, 1874._ - - At quite uncertain times and places, - The atoms left their heavenly path, - And by fortuitous embraces - Engendered all that being hath. - And though they seem to cling together, - And form “associations” here, - Yet, soon or late, they burst their tether, - And through the depths of space career. - - So we who sat, oppressed with science, - As British Asses, wise and grave, - Are now transformed to wild Red Lions,[44] - As round our prey we ramp and rave. - Thus, by a swift metamorphōsis, - Wisdom turns wit, and science joke, - Nonsense is incense to our noses, - For when Red Lions speak they smoke. - - Hail, Nonsense! dry nurse of Red Lions,[45] - From thee the wise their wisdom learn; - From thee they cull those truths of science, - Which into thee again they turn. - What combinations of ideas - Nonsense alone can wisely form! - What sage has half the power that she has, - To take the towers of Truth by storm? - - Yield, then, ye rules of rigid reason! - Dissolve, thou too, too solid sense! - Melt into nonsense for a season, - Then in some nobler form condense. - Soon, all too soon, the chilly morning - This flow of soul will crystallise; - Then those who Nonsense now are scorning - May learn, too late, where wisdom lies. - - -TO THE COMMITTEE OF THE CAYLEY PORTRAIT FUND. - -1874. - - O wretched race of men, to space confined! - What honour can ye pay to him, whose mind - To that which lies beyond hath penetrated? - The symbols he hath formed shall sound his praise, - And lead him on through unimagined ways - To conquests new, in worlds not yet created. - - First, ye Determinants! in ordered row - And massive column ranged, before him go, - To form a phalanx for his safe protection. - Ye powers of the _n^{th}_ roots of -1! - Around his head in ceaseless[46] cycles run, - As unembodied spirits of direction. - - And you, ye undevelopable scrolls! - Above the host wave your emblazoned rolls, - Ruled for the record of his bright inventions. - Ye cubic surfaces! by threes and nines - Draw round his camp your seven-and-twenty lines-- - The seal of Solomon in three dimensions. - - March on, symbolic host! with step sublime, - Up to the flaming bounds of Space and Time! - There pause, until by Dickinson depicted, - In two dimensions, we the form may trace - Of him whose soul, too large for vulgar space, - In _n_ dimensions flourished unrestricted. - - -IN MEMORY OF EDWARD WILSON, - -_Who repented of what was in his mind to write after section._ - -RIGID BODY (_sings_). - - GIN a body meet a body - Flyin’ through the air, - Gin a body hit a body, - Will it fly? and where? - Ilka impact has its measure, - Ne’er a ane hae I; - Yet a’ the lads they measure me, - Or, at least, they try. - - Gin a body meet a body - Altogether free, - How they travel afterwards - We do not always see. - Ilka problem has its method - By analytics high; - For me, I ken na ane o’ them, - But what the waur am I? - -Another task, which occupied much time, from 1874 to 1879, was the -edition of the works of Henry Cavendish. Cavendish, who was great-uncle -to the Chancellor, had published only two electrical papers, but he had -left some twenty packets of manuscript on Mathematical and Experimental -Electricity. These were placed in Maxwell’s hands in 1874 by the Duke -of Devonshire. - -Niven, in his preface to the collected papers dealing with this book, -writes thus:-- - - “This work, published in 1879, has had the effect of increasing - the reputation of Cavendish, disclosing as it does the - unsuspected advances which that acute physicist had made in - the Theory of Electricity, especially in the measurement of - electrical quantities. The work is enriched by a variety of - valuable notes, in which Cavendish’s views and results are - examined by the light of modern theory and methods. Especially - valuable are the methods applied to the determination of the - electrical capacities of conductors and condensers, a subject - in which Cavendish himself showed considerable skill both of a - mathematical and experimental character. - - “The importance of the task undertaken by Maxwell in connection - with Cavendish’s papers will be understood from the following - extract from his introduction to them:-- - - “‘It is somewhat difficult to account for the fact that - though Cavendish had prepared a complete description of his - experiments on the charges of bodies, and had even taken the - trouble to write out a fair copy, and though all this seems - to have been done before 1774, and he continued to make - experiments in electricity till 1781, and lived on till 1810, - he kept his manuscript by him and never published it. - - “‘Cavendish cared more for investigation than for publication. - He would undertake the most laborious researches in order to - clear up a difficulty which no one but himself could appreciate - or was even aware of, and we cannot doubt that the result of - his enquiries, when successful, gave him a certain degree of - satisfaction. But it did not excite in him that desire to - communicate the discovery to others, which in the case of - ordinary men of science generally ensures the publication of - their results. How completely these researches of Cavendish - remained unknown to other men of science is shown by the - external history of electricity.’ - - “It will probably be thought a matter of some difficulty to - place oneself in the position of a physicist of a century - ago, and to ascertain the exact bearing of his experiments. - But Maxwell entered upon this undertaking with the utmost - enthusiasm, and succeeded in identifying himself with - Cavendish’s methods. He showed that Cavendish had really - anticipated several of the discoveries in electrical science - which have been made since his time. Cavendish was the first to - form the conception of and to measure Electrostatic Capacity - and Specific Inductive Capacity; he also anticipated Ohm’s law.” - -During the last years of his life Mrs. Maxwell had a serious and -prolonged illness, and Maxwell’s work was much increased by his duties -as sick nurse. On one occasion he did not sleep in a bed for three -weeks, but conducted his lectures and experiments at the laboratory as -usual. - -About this time some of those who had been “Apostles” in 1853–57 -revived the habit of meeting together for discussion. The club, which -included Professors Lightfoot, Hort and Westcott, was christened -the “Eranus,” and three of Maxwell’s contributions to it have been -preserved and are printed by Professor Campbell. - -After the Cavendish papers were finished, Maxwell had more time for his -own original researches, and two important papers were published in -1879. The one on “Stresses in Rarefied Gases arising from Inequalities -of Temperature” was printed in the Royal Society’s Transactions, and -deals with the Theory of the Radiometer; the other on “Boltzmann’s -Theorem” appears in the Transactions of the Cambridge Philosophical -Society. In the previous year he had delivered the Rede lecture on “The -Telephone.” He also began to prepare a second edition of “Electricity -and Magnetism.” - -His health gave way during the Easter term of 1879; indeed for two -years previously he had been troubled with dyspeptic symptoms, but had -consulted no one on the subject. He left Cambridge as usual in June, -hoping that he would quickly recover at Glenlair, but he grew worse -instead. In October he was told by Dr. Sanders of Edinburgh that he had -not a month to live. He returned to Cambridge in order to be under the -care of Dr. Paget, who was able in some measure to relieve his most -severe suffering but the disease, of which his mother had died at the -same age, continued its progress, and he died on November 5th. His one -care during his last illness was for those whom he left behind. Mrs. -Maxwell was an invalid dependent on him for everything, and the thought -of her helplessness was the one thing which in these last days troubled -him. - -A funeral service took place in the chapel at Trinity College, and -afterwards his remains were conveyed to Scotland and interred in the -family burying-place at Corsock, Kirkcudbright. - -A memorial edition of his works was issued by the Cambridge University -Press in 1890. A portrait by Lowes Dickinson hangs in the hall of -Trinity College, and there is a bust by Boehm in the laboratory. - -After his death Mrs. Maxwell gave his scientific library to the -Cavendish Laboratory, and on her death she left a sum of about £6,000 -to found a scholarship in Physics, to be held at the laboratory. - - * * * * * - -The preceding pages contain some account of Clerk Maxwell’s life as -a man of science. His character had other sides, and any life of him -would be incomplete without some brief reference to these. His letters -to his wife and to other intimate friends show throughout his life -the depth of his religious convictions. The high purpose evidenced -in the paper given to the present Dean of Canterbury when leaving -Cambridge, animated him continually, and appears from time to time in -his writings. The student’s evening hymn, composed in 1853 when still -an undergraduate, expresses the same feelings-- - - Through the creatures Thou hast made - Show the brightness of Thy glory, - Be eternal truth displayed - In their substance transitory, - Till green earth and ocean hoary, - Massy rock and tender blade, - Tell the same unending story, - “We are Truth in form arrayed.” - - Teach me so Thy works to read - That my faith, new strength accruing, - May from world to world proceed, - Wisdom’s fruitful search pursuing, - Till Thy breath my mind imbuing, - I proclaim the eternal creed, - Oft the glorious theme renewing, - God our Lord is God indeed. - -His views on the relation of Science to Faith are given in his -letter[47] to Bishop Ellicott already referred to-- - - “But I should be very sorry if an interpretation founded - on a most conjectural scientific hypothesis were to get - fastened to the text in Genesis, even if by so doing it got - rid of the old statement of the commentators which has long - ceased to be intelligible. The rate of change of scientific - hypothesis is naturally much more rapid than that of Biblical - interpretations, so that if an interpretation is founded on - such an hypothesis, it may help to keep the hypothesis above - ground long after it ought to be buried and forgotten. - - “At the same time I think that each individual man should do - all he can to impress his own mind with the extent, the order, - and the unity of the universe, and should carry these ideas - with him as he reads such passages as the 1st chapter of the - Epistle to Colossians (_see_ ‘Lightfoot on Colossians,’ p. - 182), just as enlarged conceptions of the extent and unity of - the world of life may be of service to us in reading Psalm - viii., Heb. ii. 6, etc.” - -And again in his letter[48] to the secretary of the Victoria Institute -giving his reasons for declining to become a member-- - - “I think men of science as well as other men need to learn from - Christ, and I think Christians whose minds are scientific are - bound to study science, that their view of the glory of God - may be as extensive as their being is capable of. But I think - that the results which each man arrives at in his attempts to - harmonise his science with his Christianity ought not to be - regarded as having any significance except to the man himself, - and to him only for a time, and should not receive the stamp of - a society.” - -Professor Campbell and Mr. Garnett have given us the evidence of those -who were with him in his last days, as to the strength of his own -faith. On his death bed he said that he had been occupied in trying to -gain truth; that it is but little of truth that man can acquire, but it -is something to know in whom we have believed. - - - - -CHAPTER VII. - -SCIENTIFIC WORK--COLOUR VISION. - - -Fifteen years only have passed since the death of Clerk Maxwell, and it -is almost too soon to hope to form a correct estimate of the value of -his work and its relation to that of others who have laboured in the -same field. - -Thus Niven, at the close of his obituary notice in the Proceedings of -the Royal Society, says: “It is seldom that the faculties of invention -and exposition, the attachment to physical science and capability of -developing it mathematically, have been found existing in one mind -to the same degree. It would, however, require powers somewhat akin -to Maxwell’s own to describe the more delicate features of the works -resulting from this combination, every one of which is stamped with the -subtle but unmistakable impress of genius.” And again in the preface -to Maxwell’s works, issued in 1890, he wrote: “Nor does it appear to -the present editor that the time has yet arrived when the quickening -influence of Maxwell’s mind on modern scientific thought can be duly -estimated.” - -It is, however, the object of the present series to attempt to give -some account of the work of men of science of the last hundred years, -and to show how each has contributed his share to our present stock -of knowledge. This task, then, remains to be done. While attempting -it I wish to express my indebtedness to others who have already -written about Maxwell’s scientific work, especially to Mr. W. D. -Niven, whose preface to the Maxwell papers has been so often referred -to; to Mr. Garnett, the author of Part II. of the “Life of Maxwell,” -which deals with his contributions to science; and to Professor Tait, -who in _Nature_ for February 5th, 1880, gave an account of Clerk -Maxwell’s work, “necessarily brief, but sufficient to let even the -non-mathematical reader see how very great were his contributions to -modern science”--an account all the more interesting because, again to -quote from Professor Tait, “I have been intimately acquainted with him -since we were schoolboys together.” - -Maxwell’s main contributions to science may be classified under three -heads--“Colour Perception,” “Molecular Physics,” and “Electrical -Theories.” In addition to these there were other papers of the highest -interest and importance, such as the essay on “Saturn’s Rings,” the -paper on the “Equilibrium of Elastic Solids,” and various memoirs on -pure geometry and questions of mechanics, which would, if they stood -alone, have secured for their author a distinguished position as a -physicist and mathematician, but which are not the works by which his -name will be mostly remembered. - -The work on “Colour Perception” was begun at an early date. We have -seen Maxwell while still at Edinburgh interested in the discussions -about Hay’s theories. - -His first published paper on the subject was a letter to Dr. G. -Wilson, printed in the Transactions of the Royal Society of Arts for -1855; but he had been mixing colours by means of his top for some -little time previously, and the results of these experiments are given -in a paper entitled “Experiments on Colour,” communicated to the Royal -Society of Edinburgh by Dr. Gregory, and printed in their Transactions, -vol. xxi. - -In the paper on “The Theory of Compound Colours,” printed in the -Philosophical Transactions for 1860, Maxwell gives a history of the -theory as it was known to him. - -He points out first the distinction between the _optical_ properties -and the _chromatic_ properties of a beam of light. “The optical -properties are those which have reference to its origin and propagation -through media until it falls on the sensitive organ of vision;” -they depend on the periods and amplitudes of the ether vibrations -which compose the beam. “The chromatic properties are those which -have reference to its power of exciting certain sensations of colour -perceived through the organ of vision.” It is possible for two beams to -be optically very different and chromatically alike. The converse is -not true; two beams which are optically alike are also chromatically -alike. - -The foundation of the theory of compound colours was laid by Newton. -He first shewed that “by the mixture of homogeneal light colours may -be produced which are like to the colours of homogeneal light as to -the appearance of colour, but not as to the immutability of colour and -constitution of light.” Two beams which differ optically may yet be -alike chromatically; it is possible by mixing red and yellow to obtain -an orange colour chromatically similar to the orange of the spectrum, -but optically different to that orange, for the compound orange can be -analysed by a prism into its component red and yellow; the spectrum -orange is incapable of further resolution. - -Newton also solves the following problem:-- - -_In a mixture of primary colours, the quantity and quality of each -being given to know the colour of the compound_ (Optics, Book 1, Part -2, Prop. 6), and his solution is the following:--He arranges the seven -colours of the spectrum round the circumference of a circle, the length -occupied by each colour being proportional to the musical interval to -which, in Newton’s views, the colour corresponded. At the centre of -gravity of each of these arcs he supposes a weight placed proportional -to the number of rays of the corresponding colour which enter into the -mixture under consideration. The position of the centre of gravity of -these weights indicates the nature of the resultant colour. A radius -drawn through this centre of gravity points out the colour of the -spectrum which it most resembles; the distance of the centre of gravity -from the centre gives the fulness of the colour. The centre itself is -white. Newton gives no proof of this rule; he merely says, “This rule I -conceive to be accurate enough for practice, though not mathematically -accurate.” - -Maxwell proved that Newton’s method of finding the centre of gravity of -the component colours was confirmed by his observations, and that it -involves mathematically the theory of three elements of colour; but -the disposition of the colours on the circle was only a provisional -arrangement; the true relations of the colours could only be determined -by direct experiment. - -Thomas Young appears to have been the next, after Newton, to work -at the theory of colour sensation. He made observations by spinning -coloured discs much in the same way as that which was afterwards -adopted by Maxwell, and he developed the theory that three different -primary sensations may be excited in the eye by light, while the colour -of any beam depends on the proportions in which these three sensations -are excited. He supposes the three primary sensations to correspond -to red, green, and violet. A blue ray is capable of exciting both the -green and the violet; a yellow ray excites the red and the green. Any -colour, according to Young’s theory, may be matched by a mixture of -these three primary colours taken in proper proportion; the quality -of the colour depends on the proportion of the intensities of the -components; its brightness depends on the sum of these intensities. - -Maxwell’s experiments were undertaken with the object of proving or -disproving the physical part of Young’s theory. He does not consider -the question whether there are three distinct sensations corresponding -to the three primary colours; that is a physiological inquiry, and one -to which no completely satisfactory answer has yet been given. He does -show that by a proper mixture of any three arbitrarily chosen standard -colours it is possible to match any other colour; the words “proper -mixture,” however, need, as will appear shortly, some development. - -We may with advantage compare the problem with one in acoustics. - -When a compound musical note consisting of a pure tone and its -overtones is sounded, the trained ear can distinguish the various -overtones and analyse the sound into its simple components. The same -sensation cannot be excited in two different ways. The eye has no such -corresponding power. A given yellow may be a pure spectral yellow, -corresponding to a pure tone in music, or it may be a mixture of a -number of other pure tones; in either case it can be matched by a -proper combination of three standard colours--this Maxwell proved. -It may be, as Young supposed, that if the three standard colours be -properly selected they correspond exactly to three primary sensations -of the brain. Maxwell’s experiments do not afford any light on this -point, which still remains more than doubtful. - -When Maxwell began his work the theory of colours was exciting -considerable interest. Sir David Brewster had recently developed a -new theory of colour sensation which had formed the basis of some -discussions, and in 1852 von Helmholtz published his first paper -on the subject. According to Brewster, the three primitive colours -were red, yellow and blue, and he supposed that they corresponded to -three different kinds of objective light. Helmholtz pointed out that -experiments up to that date had been conducted by mixing pigments, with -the exception of those in which the rotating disc was used, and that -it is necessary to make them on the rays of the spectrum itself. He -then describes a method of mixing the light from two spectra so as to -obtain the combination of every two of the simple prismatic rays in all -degrees of relative strength. - -From these experiments results, which at the time were unexpected, but -some of which must have been known to Young, were obtained. Among them -it was shown that a mixture of red and green made yellow, while one of -green and violet produced blue. - -In a later paper (_Philosophical Magazine_, 1854) Helmholtz described -a method for ascertaining the various pairs of complementary -colours--colours, that is, which when mixed will give white--which had -been shown by Grassman to exist if Newton’s theory were true. He also -gave a provisional diagram of the curve formed by the spectrum, which -ought to take the place of the circle in Newton’s diagram; for this, -however, his experiments did not give the complete data. - -Such was the state of the question when Maxwell began. His first -colour-box was made in 1852. Others were designed in 1855 and 1856, -and the final paper appeared in 1860. But before that time he had -established important results by means of his rotatory discs and colour -top. In his own description of this he says: “The coloured paper is -cut into the form of disc, each with a hole in the centre and divided -along a radius so as to admit of several of them being placed on the -same axis, so that part of each is exposed. By slipping one disc over -another we can expose any given portion of each colour. These discs -are placed on a top or teetotum, which is spun rapidly. The axis of the -top passes through the centre of the discs, and the quantity of each -colour exposed is measured by graduations on the rim of the top, which -is divided into 100 parts. When the top is spun sufficiently rapidly, -the impressions due to each colour separately follow each other in -quick succession at each point of the retina, and are blended together; -the strength of the impression due to each colour is, as can be shown -experimentally, the same as when the three kinds of light in the same -relative proportions enter the eye simultaneously. These relative -proportions are measured by the areas of the various discs which are -exposed. Two sets of discs of different radius are used; the largest -discs are put on first, then the smaller, so that the centre portion -of the top shows the colour arising from the mixture of those of the -smaller discs; the outer portion, that of the larger discs.” - -In experimenting, six discs of each size are used, black, white, red, -green, yellow and blue. It is found by experiment that a match can be -arranged between any five of these. Thus three of the larger discs are -placed on the top--say black, yellow and blue--and two of the smaller -discs, red and green, are placed above these. Then it is found that it -is possible so to adjust the amount exposed of each disc that the two -parts of the top appear when it is spun to be of the same tint. In one -series of experiments the chromatic effect of 46·8 parts of black, 29·1 -of yellow, and 24·1 of blue was found to be the same as that of 66·6 -of red and 33·4 of green; each set of discs has a dirty yellow tinge. - -Now, in this experiment, black is not a colour; practically no light -reaches the eye from a dead black. We have, however, to fill up -the circumference of the top in some way which will not affect the -impression on the retina arising from the mixture of the blue and -yellow; this we can do by using the black disc. - -Thus we have shown that 66·6 parts of red and 33·4 parts of green -produce the same chromatic effect as 29·1 of yellow and 24·1 of -blue. Similarly in this manner a match can be arranged between any -four colours and black, the black being necessary to complete the -circumference of the discs. - -Thus using A, B, C, D to denote the various colours, _a_, _b_, _c_, -_d_ the amounts of each colour taken, we can get a series of results -expressed as follows: _a_ parts of A together with _b_ parts of B match -_c_ parts of C together with _d_ parts of D; or we may write this as an -equation thus:-- - - _a_ A + _b_ B = _c_ C + _d_ D, - -where the + stands for “combined with,” and the = for “matches in tint.” - -We may also write the above-- - - _d_ D = _a_ A + _b_ B - _c_ C, - -or _d_ parts of D can be matched by a _proper_ combination of colours -A, B, C. The sign - shows that in order to make the match we have to -combine the colour C with D; the combination then matches a mixture of -A and B. - -In this way we can form a number of equations for all possible colours, -and if we like to take any three colours A, B, C as standards, we -obtain a result which may be written generally-- - - _x_ X = _a_ A + _b_ B + _c_ C, - -or _x_ parts of X can be matched by _a_ parts of A, combined with _b_ -parts of B and _c_ parts of C. If the sign of one of the quantities -_a_, _b_, or _c_ is negative, it indicates that that colour must be -combined with X to match the other two. - -Now Maxwell was able to show that, if A, B, C be properly selected, -nearly every other colour can be matched by positive combinations of -these three. These three colours, then, are primary colours, and nearly -every other colour can be matched by a combination of the three primary -colours. - -Experiments, however, with coloured discs, such as were undertaken by -Young, Forbes and Maxwell, were not capable of giving satisfactory -results. The colours of the discs were not pure spectrum colours, and -varied to some extent with the nature of the incident light. It was for -this reason that Helmholtz in 1852 experimented with the spectrum, and -that Maxwell about the same time invented his colour box. - -The principle of the latter was very simple. Suppose we have a slit -S, and some arrangement for forming a pure spectrum on a screen. Let -there now be a slit R placed in the red part of the spectrum on the -screen. When light falls on the slit S, only the red rays can reach -R, and hence conversely, if the white source be placed at the other -end of the apparatus, so that R is illuminated with white light, only -red rays will reach S. Similarly, if another slit be placed in the -green at G, and this be illuminated by white light, only the green -rays will reach S, while from a third slit V in the violet, violet -light only can arrive at S. Thus by opening the three slits at V, G -and R simultaneously, and looking through S, the retina receives the -impression of the three different colours. The amount of light of each -colour will depend on the breadth to which the corresponding slit is -opened, and the relative intensities of the three different components -can be compared by comparing the breadths of the three slits. Any other -colour which is allowed by some suitable contrivance to enter the eye -simultaneously can now be matched, provided the red, green and violet -are primary colours. - -By means of experiments with the colour box Maxwell showed conclusively -that a match could be obtained between any four colours; the -experiments could not be carried out in quite the simple manner -suggested by the above description of the principle of the box. -An account of the method will be found in Maxwell’s own paper. It -consisted in matching a standard white by various combinations of other -colours. - -The main object of his research, however, was to examine the chromatic -properties of the different parts of the spectrum, and to determine the -form of the curve which ought to replace the circle in Newton’s diagram -of colour. - -Maxwell adopted as his three standard colours: red, of about wave -length 6,302; green, wave length 5,281; and violet, 4,569 tenth metres. -On the scale of Maxwell’s instrument these are represented by the -numbers 24, 44 and 68. - -Let us take three points A, B, C at the corners of an equilateral -triangle to represent on a diagram these three colours. The position -of any other colour on the diagram will be found by taking weights -proportional to the amounts of the colours A, B, C required to make the -match between A, B, C and the given colour; these weights are placed at -A, B, C respectively; the position of their centre of gravity is the -point required. Thus the position of white is given by the equation-- - - W = 18·6 (24) + 31·4 (44) + 30·5 (68) - -which means that weights proportional to 18·6, 31·4 and 30·5 are to be -placed at A, B, C respectively, and their centre of gravity is to be -found. The point so found is the position of white. Any other colour is -given by the equation-- - - X = _a_ (24) + _b_ (44) + _c_ (68). - -Again, the position on the diagram for all colours for which _a_, -_b_, _c_ are all positive lies within the triangle A B C. If one of -the coefficients, say _c_, is negative the same construction applies, -but the weight applied at C must be treated as acting in the opposite -direction to those at A and B. A mixture of the given colour and C -matches a mixture of A and B. It is clear that the point corresponding -to X will then lie outside the triangle A B C. Maxwell showed that, -with his standards, nearly all colours could be represented by points -inside the triangle. The colours he had selected as standards were very -close to primary colours. - -Again, he proved that any spectrum colour between red and green, when -combined with a very slight admixture of violet, could be matched, in -the case of either Mrs. Maxwell or himself, by a proper mixture of -the red and green. The positions, therefore, of the spectrum colours -between red and green lie just outside the triangle A B C, being very -close to the line A B, while for the colours between green and violet -Maxwell obtained a curve lying rather further outside the side B C. -Any spectrum colour between green and violet, together with a slight -admixture of red, can be matched by a proper mixture of green and -violet. - -Thus the circle of Newton’s diagram should be replaced by a curve, -which coincides very nearly with the two sides A B and B C of Maxwell’s -figure. Strictly, according to his observations, the curve lies just -outside these two sides. The purples of the spectrum lie nearly along -the third side, C A, of the triangle, being obtained approximately by -mixing the violet and the red. - -To find the point on the diagram corresponding to the colour obtained -by mixing any two or more spectrum colours we must, in accordance -with Newton’s rule, place weights at the points corresponding to the -selected colours, and find the centre of gravity of these weights. - -This, then, was the outcome of Maxwell’s work on colour. It verified -the essential part of Newton’s construction, and obtained for the first -time the true form of the spectrum curve on the diagram. - -The form of this curve will of course depend on the eye of the -individual observer. Thus Maxwell and Mrs. Maxwell both made -observations, and distinct differences were found in their eyes. It -appears, however, that a large majority of persons have normal vision, -and that matches made by one such person are accepted by most others -as satisfactory. Some people, however, are colour blind, and Maxwell -examined a few such. In the case of those whom he examined it appeared -as though vision was dichromatic, the red sensation seemed to be -absent; nearly all colours could be matched by combinations of green -and violet. The colour diagram was reduced to the straight line B C. -Other forms of colour blindness have since been investigated. - -In awarding to Maxwell the Rumford medal in 1860, Major-General -Sabine, vice-president of the Royal Society, after explaining the -theory of colour vision and the possible method of verifying it, said: -“Professor Maxwell has subjected the theory to this verification, and -thereby raised the composition of colours to the rank of a branch of -mathematical physics,” and he continues: “The researches for which -the Rumford medal is awarded lead to the remarkable result that to a -very near degree of approximation all the colours of the spectrum, and -therefore all colours in nature which are only mixtures of these, can -be perfectly imitated by mixtures of three actually attainable colours, -which are the red, green and blue belonging respectively to three -particular parts of the spectrum.” - -It should be noticed in concluding our remarks on this part of -Maxwell’s work that his results are purely physical. They are not -inconsistent with the physiological part of Young’s theory, viz., that -there are three primary sensations of colour which can be transmitted -to the brain, and that the colour of any object depends on the relative -proportions in which these sensations are excited, but they do not -prove that theory. Any physiological theory which can be accepted as -true must explain Maxwell’s observations, and Young’s theory does this; -but it is, of course, possible that other theories may explain them -equally well, and be more in accordance with physiological observations -than Young’s. Maxwell has given us the physical facts which have to be -explained; it is for the physiologists to do the rest. - - - - -CHAPTER VIII. - -SCIENTIFIC WORK--MOLECULAR THEORY. - - -Maxwell in his article “Atom,” in the ninth edition of the -_Encyclopædia Britannica_, has given some account of Modern Molecular -Science, and in particular of the molecular theory of gases. Of this -science, Clausius and Maxwell are the founders, though to their names -it has recently been shown that a third, that of Waterston, must be -added. In the present chapter it is intended to give an outline of -Maxwell’s contributions to molecular science, and to explain the -advances due to him. - -The doctrine that bodies are composed of small particles in rapid -motion is very ancient. Democritus was its founder, Lucretius--de Rerum -Naturâ--explained its principles. The atoms do not fill space; there is -void between. - - “Quapropter locus est intactus inane vacansque, - Quod si non esset, nullâ ratione moveri - Res possent; namque officium quod corporis extat - Officere atque obstare, id in omni tempore adesset - Omnibus. Haud igitur quicquam procedere posset - Principium quoniam cedendi nulla daret res.” - -According to Boscovitch an atom is an indivisible point, having -position in space, capable of motion, and possessing mass. It is also -endowed with the power of exerting force, so that two atoms attract -or repel each other with a force depending on their distance apart. -It has no parts or dimensions: it is a mere geometrical point without -extension in space; it has not the property of impenetrability, for two -atoms can, it is supposed, exist at the same point. - -In modern molecular science according to Maxwell, “we begin by assuming -that bodies are made up of parts each of which is capable of motion, -and that these parts act on each other in a manner consistent with the -principle of the conservation of energy. In making these assumptions -we are justified by the facts that bodies may be divided into -smaller parts, and that all bodies with which we are acquainted are -conservative systems, which would not be the case unless their parts -were also conservative systems. - -“We may also assume that these small parts are in motion. This is the -most general assumption we can make, for it includes as a particular -case the theory that the small parts are at rest. The phenomena of the -diffusion of gases and liquids through each other show that there may -be a motion of the small parts of a body which is not perceptible to us. - -“We make no assumption with respect to the nature of the small -parts--whether they are all of one magnitude. We do not even assume -them to have extension and figure. Each of them must be measured by its -mass, and any two of them must, like visible bodies, have the power -of acting on one another when they come near enough to do so. The -properties of the body or medium are determined by the configuration of -its parts.” - -These small particles are called molecules, and a molecule in its -physical aspect was defined by Maxwell in the following terms:-- - - “A molecule of a substance is a small body, such that if, on - the one hand, a number of similar molecules were assembled - together, they would form a mass of that substance; while on - the other hand, if any portion of this molecule were removed, - it would no longer be able, along with an assemblage of other - molecules similarly treated, to make up a mass of the original - substance.” - -We are to look upon a gas as an assemblage of molecules flying about -in all directions. The path of any molecule is a straight line, except -during the time when it is under the action of a neighbouring molecule; -this time is usually small compared with that during which it is free. - -The simplest theory we could formulate would be that the molecules -behaved like elastic spheres, and that the action between any two was -a collision following the laws which we know apply to the collision of -elastic bodies. If the average distance between two molecules be great -compared with their dimensions, the time during which any molecule -is in collision will be small compared with the interval between the -collisions, and this is in accordance with the fundamental assumption -just mentioned. It is not, however, necessary to suppose an encounter -between two molecules to be a collision. One molecule may act on -another with a force, which depends on the distance between them, of -such a character that the force is insensible except when the molecules -are extremely close together. - -It is not difficult to see how the pressure exerted by a gas on the -sides of a vessel which contains it may be accounted for on this -assumption. Each molecule as it strikes the side has its momentum -reversed--the molecules are here assumed to be perfectly elastic. - -Thus each molecule of the gas is continually gaining momentum from -the sides of the vessel, while it gives up to the vessel the momentum -which it possessed before the impact. The rate at which this change of -momentum proceeds across a given area measures the force exerted on -that area; the pressure of the gas is the rate of change of momentum -per unit of area of the surface. - -Again, it can be shown that this pressure is proportional to the -product of the mass of each molecule, the number of molecules in a unit -of volume, and the square of the velocity of the molecules. - -Let us consider in the first instance the case of a jet of sand or -water of unit cross section which is playing against a surface. Suppose -for the present that all the molecules which strike the surface have -the same velocity. - -Then the number of molecules which strike the surface per second, will -be proportional to this velocity. If the particles are moving quickly -they can reach the surface in one second from a greater distance than -is possible if they be moving slowly. Again, the number reaching the -surface will be proportional to the number of molecules per unit of -volume. Hence, if we call _v_ the velocity of each particle, and N -the number of particles per unit of volume, the number which strike -the surface in one second will be N _v_; if _m_ be the mass of each -molecule, the mass which strikes the surface per second is N _m_ _v_; -the velocity of each particle of this mass is _v_, therefore the -momentum destroyed per second by the impact is N _m_ _v_ × _v_, or N -_m_ _v_², and this measures the pressure. - -Hence in this case if _p_ be the pressure - - _p_ = N _m_ _v_². - -In the above we assume that _all_ the molecules in the jet are moving -with velocity _v_ perpendicular to the surface. In the case of a crowd -of molecules flying about in a closed space this is clearly not true. -The molecules may strike the surface in any direction; they will not -all be moving normal to the surface. To simplify the case, consider a -cubical box filled with gas. The box has three pairs of equal faces at -right angles. We may suppose one-third of the particles to be moving at -right angles to each face, and in this case the number per unit volume -which we have to consider is not N, but ⅓ N. Hence the formula becomes -_p_ = ⅓ N _m_ _v_². - -Moreover, if _ρ_ be the density of the gas--that is, the mass of -unit volume--then N_m_ is equal to _ρ_, for _m_ is the mass of each -particle, and there are N particles in a unit of volume. - -Hence, finally, _p_ = ⅓ _ρ_ _v_². - -Or, again, if V be the volume of unit mass of the gas, then _ρ_ V is -unity, or ρ is equal to 1/V. - -Hence _p_V = ⅓_v_². - -Formulæ equivalent to these appear first to have been obtained by -Herapath about the year 1816 (Thomson’s “Annals of Philosophy,” 1816). -The results only, however, were stated in that year. A paper which -attempted to establish them was presented to the Royal Society in 1820. -It gave rise to very considerable correspondence, and was withdrawn -by the author before being read. It is printed in full in Thomson’s -“Annals of Philosophy” for 1821, vol. i., pp. 273, 340, 401. The -arguments of the author are no doubt open to criticism, and are in many -points far from sound. Still, by considering the problem of the impact -of a large number of hard bodies, he arrived at a formula connecting -the pressure and volume of a given mass of gas equivalent to that just -given. These results are contained in Propositions viii. and ix. of -Herapath’s paper. - -In his next step, however, Herapath, as we know now, was wrong. One -of his fundamental assumptions is that the temperature of a gas is -measured by the momentum of each of its particles. Hence, assuming -this, we have T = _m_ _v_, if T represents the temperature: and - - _p_ = ⅓ N _m_ _v_² = ⅓ (N/_m_) (_m_ _v_)². - -Or, again-- - - _p_ = ⅓ N·T·_v_ = ⅓·(N/_m_)·T². - -These results are practically given in Proposition viii., Corr. (1) -and (2), and Proposition ix.[49] The temperature as thus defined by -Herapath is an absolute temperature, and he calculates the absolute -zero of temperature at which the gas would have no volume from the -above results. The actual calculation is of course wrong, for, as -we know now by experiment, the pressure is proportional to the -temperature, and not to its square, as Herapath supposed. It will be -seen, however, that Herapath’s formula gives Boyle’s law; for if the -temperature is constant, the formula is equivalent to - - _p_ V = a constant. - -Herapath somewhat extended his work in his “Mathematical Physics” -published in 1847, and applied his principles to explain diffusion, the -relation between specific heat and atomic weight, and other properties -of bodies. He still, however, retained his erroneous supposition -that temperature is to be measured by the momentum of the individual -particles. - -The next step in the theory was made by Waterston. His paper was read -to the Royal Society on March 5th, 1846. It was most unfortunately -committed to the Archives of the Society, and was only disinterred by -Lord Rayleigh in 1892 and printed in the Transactions for that year. - -In the account just given of the theory, it has been supposed that all -the particles move with the same velocity. This is clearly not the -case in a gas. If at starting all the particles had the same velocity, -the collisions would change this state of affairs. Some particles will -be moving quickly, some slowly. We may, however, still apply the -theory by splitting up the particles into groups, and, supposing that -each group has a constant velocity, the particles in this group will -contribute to the pressure an amount--_p_₁--equal to ⅓ N₁ _m_ _v_₁², -where _v_₁ is the velocity of the group and N₁ the number of particles -having that velocity. The whole pressure will be found by adding that -due to the various groups, and will be given as before by _p_ = ⅓ N _m_ -_v_², where _v_ is not now the actual velocity of the particles, but a -mean velocity given by the equation - - N _v_² = N₁ _v_₁² + N₂ _v_₂² + ....., - -which will produce the same pressure as arises from the actual impacts. -This quantity v² is known as the _mean square_ of the molecular -velocity, and is so used by Waterston. - -In a paper in the _Philosophical Magazine_ for 1858 Waterston gives an -account of his own paper of 1846 in the following terms:--“Mr. Herapath -unfortunately assumed heat or temperature to be represented by the -simple ratio of the velocity instead of the square of the velocity, -being in this apparently led astray by the definition of motion -generally received, and thus was baffled in his attempts to reconcile -his theory with observation. If we make this change in Mr. Herapath’s -definition of heat or temperature--viz., that it is proportional -to the vis-viva or square velocity of the moving particle, not to -the momentum or simple ratio of the velocity--we can without much -difficulty deduce not only the primary laws of elastic fluids, but also -the other physical properties of gases enumerated above in the third -objection to Newton’s hypothesis. [The paper from which the quotation -is taken is on ‘The Theory of Sound.’] In the Archives of the Royal -Society for 1845–46 there is a paper on ‘The Physics of Media that -consist of perfectly “Elastic Molecules in a State of Motion,”’ which -contains the synthetical reasoning on which the demonstration of these -matters rests.... This theory does not take account of the size of the -molecules. It assumes that no time is lost at the impact, and that if -the impacts produce rotatory motion, the vis viva thus invested bears -a constant ratio to the rectilineal vis viva, so as not to require -separate consideration. It does, also, not take account of the probable -internal motion of composite molecules; yet the results so closely -accord with observation in every part of the subject as to leave no -doubt that Mr. Herapath’s idea of the physical constitution of gases -approximates closely to the truth.” - -In his introduction to Waterston’s paper (Phil. Trans., 1892) Lord -Rayleigh writes:--“Impressed with the above passage, and with the -general ingenuity and soundness of Waterston’s views, I took the first -opportunity of consulting the Archives, and saw at once that the memoir -justified the large claims made for it, and that it marks an immense -advance in the direction of the now generally received theory.” - -In the first section of the paper Waterston’s great advance consisted -in the statement that the mean square of the kinetic energy of each -molecule measures the temperature. - -According to this we are thus to put in the pressure equation--½ _m_ -_v_² = T, the temperature, and we have at once--_p_ V = ⅔ N · T. - -Now this equation expresses, as we know, the laws of Boyle and Gay -Lussac. - -The second section discusses the properties of media, consisting of -two or more gases, and arrives at the result that “in mixed media -the mean square molecular velocity is inversely proportional to the -specific weights of the molecules.” This was the great law rediscovered -by Maxwell fifteen years later. With modern notation it may be put -thus:--If _m_₁, _m_₂ be the masses of each molecule of two different -sets of molecules mixed together, then, when a steady state has been -reached, since the temperature is the same throughout, _m_₁ _v_₁² is -equal to _m_₂ _v_₂². The average kinetic energy of each molecule is the -same. - -From this Avogadros’ law follows at once--for if _p_₁, _p_₂ be the -pressures, N₁, N₂ the numbers of molecules per unit volume-- - - _p_₁ = ⅓ N₁ _m_₁ _v_₁², - _p_₂ = ⅓ N₂ _m_₂ _v_₂². - -Hence, if _p_₁, is equal to _p_₂, since _m_₁ _v_₁² is equal to _m_₂ -_v_₂², we must have N₁ equal to N₂, or the number of molecules in equal -volumes of two gases at the same pressure and temperature is the same. -The proof of this proposition given by Waterston is not satisfactory. -On this point, however, we shall have more to say. The third section of -the paper deals with adiabatic expansion, and in it there is an error -in calculation which prevented correct results from being attained. - -At the meeting of the British Association at Ipswich, in 1851, a paper -by J. J. Waterston of Bombay, on “The General Theory of Gases,” was -read. The following is an extract from the Proceedings:-- - -The author “conceives that the atoms of a gas, being perfectly elastic, -are in continual motion in all directions, being constrained within -a limited space by their collisions with each other, and with the -particles of surrounding bodies. - -“The vis viva of these motions in a given portion of a gas constitutes -the quantity of heat contained in it. - -“He shows that the result of this state of motion must be to give the -gas an elasticity proportional to the mean square of the velocity of -the molecular motions, and to the total mass of the atoms contained in -unity of bulk” (unit of volume)--that is to say, to the density of the -medium. - -“The elasticity in a given gas is the measure of temperature. -Equilibrium of pressure and heat between two gases takes place when the -number of atoms in unit of volume is equal and the vis viva of each -atom equal. Temperature, therefore, in all gases is proportional to the -mass of one atom multiplied by the mean square of the velocity of the -molecular motions, being measured from an absolute zero 491° below the -zero of Fahrenheit’s thermometer.” - -It appears, therefore, from these extracts that the discovery of the -laws that temperature is measured by the mean kinetic energy of a -single molecule, and that in a mixture of gases the mean kinetic energy -of each molecule is the same for each gas, is due to Waterston. They -were contained in his paper of 1846, and published by him in 1851. Both -these papers, however, appear to have been unnoticed by all subsequent -writers until 1892. - -Meanwhile, in 1848, Joule’s attention was called by his experiments -to the question, and he saw that Herapath’s result gave a means of -calculating the mean velocity of the molecules of a gas. For according -to the result given above, _p_ = ⅓ _ρ v_²; thus _v_² = 3 _p/ρ_, and _p_ -and _ρ_ being known, we find _v_². Thus for hydrogen at freezing-point -and atmospheric pressure Joule obtains for _v_ the value 6,055 feet per -second, or, roughly, six times the velocity of sound in air. - -Clausius was the next writer of importance on the subject. His first -paper is in “Poggendorff’s Annalen,” vol. c., 1857, “On the Kind -of Motion we call Heat.” It gives an exposition of the theory, and -establishes the fact that the kinetic energy of the translatory motion -of a molecule does not represent the whole of the heat it contains. If -we look upon a molecule as a small solid we must consider the energy it -possesses in consequence of its rotation about its centre of gravity, -as well as the energy due to the motion of translation of the whole. - -Clausius’ second paper appeared in 1859. In it he considers the average -length of the path of a molecule during the interval between two -collisions. He determines this path in terms of the average distance -between the molecules and the distance between the centres of two -molecules at the time when a collision is taking place. - -These two papers appear to have attracted Maxwell’s attention to the -matter, and his first paper, entitled “Illustrations of the Dynamical -Theory of Gases,” was read to the British Association at Aberdeen and -Oxford in 1859 and 1860, and appeared in the _Philosophical Magazine_, -January and July, 1860. - -In the introduction to this paper Maxwell points out, while there was -then no means of measuring the quantities which occurred in Clausius’ -expression for the mean free path, “the phenomena of the internal -friction of gases, the conduction of heat through a gas, and the -diffusion of one gas through another, seem to indicate the possibility -of determining accurately the mean length of path which a particle -describes between two collisions. In order, therefore, to lay the -foundation of such investigations on strict mechanical principles,” he -continues, “I shall demonstrate the laws of motion of an indefinite -number of small, hard and perfectly elastic spheres acting on one -another only during impact.” - -Maxwell then proceeds to consider in the first case the impact of two -spheres. - -But a gas consists of an indefinite number of molecules. Now it is -impossible to deal with each molecule individually, to trace its -history and follow its path. In order, therefore, to avoid this -difficulty Maxwell introduced the statistical method of dealing with -such problems, and this introduction is the first great step in -molecular theory with which his name is connected. - -He was led to this method by his investigation into the theory of -Saturn’s rings, which had been completed in 1856, and in which he -had shown that the conditions of stability required the supposition -that the rings are composed of an indefinite number of free particles -revolving round the planet, with velocities depending on their -distances from the centre. These particles may either be arranged in -separate rings, or their motion may be such that they are continually -coming into collision with each other. - -As an example of the statistical method, let us consider a crowd -of people moving along a street. Taken as a whole the crowd moves -steadily forwards. Any individual in the crowd, however, is jostled -backwards and forwards and from side to side; if a line were drawn -across the street we should find people crossing it in both directions. -In a considerable interval more people would cross it, going in the -direction in which the crowd is moving, than in the other, and the -velocity of the crowd might be estimated by counting the number which -crossed the line in a given interval. This velocity so found would -differ greatly from the velocity of any individual, which might have -any value within limits, and which is continually changing. If we knew -the velocity of each individual and the number of individuals we could -calculate the average velocity, and this would agree with the value -found by counting the resultant number of people who cross the line in -a given interval. - -Again, the people in the crowd will naturally fall into groups -according to their velocities. At any moment there will be a certain -number of people whose velocities are all practically equal, or, to be -more accurate, do not differ among themselves by more than some small -quantity. The number of people at any moment in each of these groups -will be very different. The number in any group, which has a velocity -not differing greatly from the mean velocity of the whole, will be -large; comparatively few will have either a very large or a very small -velocity. - -Again, at any moment, individuals are changing from one group to -another; a man is brought to a stop by some obstruction, and his -velocity is considerably altered--he passes from one group to a -different one; but while this is so, if the mean velocity remains -constant, and the size of the crowd be very great, the number of people -at any moment in a given group remains unchanged. People pass from that -group into others, but during any interval the same number pass back -again into that group. - -It is clear that if this condition is satisfied the distribution is -a steady one, and the crowd will continue to move on with the same -uniform mean velocity. - -Now, Maxwell applies these considerations to a crowd of perfectly -elastic spheres, moving anyhow in a closed space, acting upon each -other only when in contact. He shows that they may be divided into -groups according to their velocities, and that, when the steady state -is reached, the number in each group will remain the same, although the -individuals change. Moreover, it is shown that, if A and B represent -any two groups, the state will only be steady when the numbers which -pass from the group A to the group B are equal to the numbers which -pass back from the group B to the group A. This condition, combined -with the fact that the total kinetic energy of the motion remains -unchanged, enables him to calculate the number of particles in any -group in terms of the whole number of particles, the mean velocity, and -the actual velocity of the group. - -From this an accurate expression can be found for the pressure of the -gas, and it is proved that the value found by others, on the assumption -that all the particles were moving with a common velocity, is correct. -Previous to this paper of Maxwell’s it had been realised that the -velocities could not be uniform throughout. There had been no attempt -to determine the distribution of velocity, or to submit the problem to -calculation, making allowance for the variations in velocity. - -Maxwell’s mathematical methods are, in their generality and elegance, -far in advance of anything previously attempted in the subject. - -So far it has been assumed that the particles in the vessel are all -alike. Maxwell next takes the case of a mixture of two kinds of -particles, and inquires what relation must exist between the average -velocities of these different particles, in order that the state may be -steady. - -Now, it can be shown that when two elastic spheres impinge the effect -of the impact is always such as to reduce the difference between their -kinetic energies. - -Hence, after a very large number of impacts the kinetic energies of the -two balls must be the same; the steady state, then, will be reached -when each ball has the same kinetic energy. - -Thus if _m_₁, _m_₂ be the masses of the particles in the two sets -respectively, _v_₁, _v_₂ their mean velocities we must have finally-- - - ½ _m_₁ _v_₁² = ½ _m_₂ _v_₂² - -This is the second of the two great laws enunciated by Waterston in -1845 and 1851, but which, as we have seen, had remained unknown until -1859, when it was again given by Maxwell. - -Now, when gases are mixed their temperatures become equal. Hence we -conclude, in Maxwell’s words, “that the physical condition which -determines that the temperature of two gases shall be the same, is that -the mean kinetic energy of agitation of the individual molecules of the -two gases are equal.” - -Thus, as the result of Maxwell’s more exact researches on the motion of -a system of spherical particles, we find that we again can obtain the -equations-- - - T = ½ _mv_² - _p_ = ⅓ N _mv_² = ⅔ NT = ⅔ _ρ_ T/_m_ - -From these results we obtain as before the laws of Boyle, Charles and -Avrogadro. - -Again if _σ_ be the specific heat of the gas at constant volume, the -quantity of heat required to raise a single molecule of mass _m_ one -degree will be _σ_ _m_. - -Thus, when a molecule is heated, the kinetic energy must increase by -this amount. But the increase of temperature, which in this case is 1°, -is measured by the increase of kinetic energy of the single molecule. -Hence the amount of heat required to raise the temperature of a single -molecule of all gases 1° is the same. Thus the quantity _σ_ _m_ is the -same for all gases; or, in other words, the specific heat of a gas is -inversely proportional to the mass of its individual molecules. The -density of a gas--since the number of molecules per unit volume at -a given pressure and temperature is the same for all gases--is also -proportional to the mass of each individual molecule. Thus the specific -heats of all gases are inversely proportional to their densities. -This is the law discovered experimentally by Dulong and Petit to be -approximately true for a large number of substances. - - * * * * * - -In the next part of the paper Maxwell proceeded to determine the -average number of collisions in a given time, and hence, knowing the -velocities, to determine, in terms of the size of the particles and -their numbers, the mean free path of a particle; the result so found -differed somewhat from that already obtained by Clausius. - -Having done this he showed how, by means of experiments on the -viscosity of gases, the length of the mean free path could be -determined. - -An illustration due to Professor Balfour Stewart will perhaps make this -clear. Let us suppose we have two trains running with uniform speed in -opposite directions on parallel lines, and, further, that the engines -continue to work at the same rate, developing just sufficient energy to -overcome the resistance of the line, etc., and to maintain the speed -constant. Now suppose passengers commence to jump across from one train -to the other. Each man carries with him his own momentum, which is in -the opposite direction to that of the train into which he jumps; the -result is that the momentum of each train is reduced by the process; -the velocities of the two decrease; it appears as though a frictional -force were acting between the two. Maxwell suggests that a similar -process will account for the apparent viscosity of gases. - -Consider two streams of gas, moving in opposite directions one over -the other; it is found that in each case the layers of gas near the -separating surface move more slowly than those in the interior of -the streams; there is apparently a frictional force between the two -streams along this surface, tending to reduce their relative velocity. -Maxwell’s explanation of this is that at the common surface particles -from the one stream enter the other, and carry with them their own -momentum; thus near this surface the momentum of each stream is -reduced, just as the momentum of the trains is reduced by the people -jumping across. Internal friction or viscosity is due to the diffusion -of momentum across this common surface. The effect does not penetrate -far into the gas, for the particles soon acquire the velocity of the -stream to which they have come. - -Now, the rate at which the momentum is diffused will measure the -frictional force, and will depend on the mean free path of the -particles. If this is considerable, so that on the average a particle -can penetrate a considerable distance into the second gas before a -collision takes place and its motion is changed, the viscosity will be -considerable; if, on the other hand, the mean free path is small, the -reverse will be true. Thus it is possible to obtain a relation between -the mean free path and the coefficient of viscosity, and from this, if -the coefficient of viscosity be known, a value for the mean free path -can be found. - -Maxwell, in the paper under discussion, was the first to do this, -and, using a value found by Professor Stokes for the coefficient of -viscosity, obtained as the length of the mean free path of molecules -of air 1/447000 of an inch, while the number of collisions per second -experienced by each molecule is found to be about 8,077,200,000. - -Moreover, it appeared from his theory that the coefficient of viscosity -should be independent of the number of molecules of gas present, so -that it is not altered by varying the density. This result Maxwell -characterises as startling, and he instituted an elaborate series of -experiments a few years later with a view of testing it. The reason -for this result will appear if we remember that, when the density is -decreased, the mean free path is increased; relatively, then, to the -total number of molecules present, the number which cross the surface -in a given time is increased. And it appears from Maxwell’s result that -this relative increase is such that the total number crossing remains -unchanged. Hence the momentum conveyed across each unit area per second -remains the same, in spite of the decrease in density. - -Another consequence of the same investigation is that the coefficient -of viscosity is proportional to the mean velocity of the molecules. -Since the absolute temperature is proportional to the square of the -velocity, it follows that the coefficient of viscosity is proportional -to the square root of the absolute temperature. - -The second part of the paper deals with the process of diffusion of two -or more kinds of moving particles among one another. - -If two different gases are placed in two vessels separated by a porous -diaphragm such as a piece of unglazed earthenware, or connected by -means of a narrow tube, Graham had shewn that, after sufficient time -has elapsed, the two are mixed together. The same process takes place -when two gases of different density are placed together in the same -vessel. At first the denser gas may be at the bottom, the less dense -above, but after a time the two are found to be uniformly distributed -throughout. - -Maxwell attempted to calculate from his theory the rate at which -the diffusion takes place in these cases. The conditions of most of -Graham’s experiments were too complicated to admit of direct comparison -with the theory, from which it appeared that there is a relation -between the mean free path and the rate of diffusion. One experiment, -however, was found, the conditions of which could be made the subject -of calculation, and from it Maxwell obtained as the value of the mean -free path in air 1/389000 of an inch. - -The number was close enough to that found from the viscosity to afford -some confirmation of his theory. - -However, a few years later Clausius criticised the details of this -part of the paper, and Maxwell, in his memoir of 1866, admits the -calculation to have been erroneous. The main principles remained -unaffected, the molecules pass from one gas to the other, and this -constitutes diffusion. - -Now, suppose we have two sets of particles in contact of such a nature -that the mean kinetic energy of the one set is different from that of -the other; the temperatures of the two will then be different. These -two sets will diffuse into each other, and the diffusing particles will -carry with them their kinetic energy, which will gradually pass from -those which have the greater energy to those which have the less, until -the average kinetic energy is equalised throughout. But the kinetic -energy of translation is the heat of the particles. This diffusion of -kinetic energy is a diffusion of heat by conduction, and we have here -the mechanical theory of the conduction of heat in a gas. - -Maxwell obtained an expression, which, however, he afterwards modified, -for the conductivity of a gas in terms of the mean free path. It -followed from this that the conductivity of air was only about 1/7000 -of that of copper. - -Thus the diffusion of gases, the viscosity of gases, and the conduction -of heat in gases, are all connected with the diffusion of the particles -carrying with them their momenta and their energy; while values of the -mean free path can be obtained from observations on any one of these -properties. - -In the third part of his paper Maxwell considers the consequences -of supposing the particles not to be spherical. In this case the -impacts would tend to set up a motion of rotation in the particles. -The direction of the force acting on any particle at impact would not -necessarily pass through its centre; thus by impact the velocity of its -centre would be changed, and in addition the particles would be made to -spin. Some part, therefore, of the energy of the particles will appear -in the form of the translational energy of their centres, while the -rest will take the form of rotational energy of each particle about its -centre. - -It follows from Maxwell’s work that for each particle the average value -of these two portions of energy would be equal. The total energy will -be half translational and half rotational. - -This theorem, in a more general form which was afterwards given to -it, has led to much discussion, and will be again considered later. -For the present we will assume it to be true. Clausius had already -called attention to the fact that some of the energy must be rotational -unless the molecules be smooth spheres, and had given some reasons -for supposing that the ratio of the whole energy to the energy of -translation is in a steady state a constant. Maxwell shows that for -rigid bodies this constant is 2. Let us denote it for the present by -the symbol β. Thus, if the translational energy of a molecule is ½ _m_ -_v_², its whole energy is ½ β _m_ _v_². - -The temperature is still measured by the translational energy, or ½ _m_ -_v_²; the heat depends on the whole energy. Hence if H represent the -amount of heat--measured as energy--contained by a single molecule, -and T its temperature, we have-- - - H = βT - -From this it can be shewn[50] that if γ represent the ratio of the -specific heat of a gas at constant pressure to the specific heat at -constant volume, then-- - - β = ⅔ 1/(γ-1) - -For air and some other gases the value of γ has been shown to be 1·408. -From this it follows that β = 1·634. Now, Maxwell’s theory required -that for smooth hard particles, approximately spherical in shape, β -should be 2, and hence he concludes “we have shown that a system of -such particles could not possibly satisfy the known relation between -the two specific heats of all gases.” - -Since this statement was made many more experiments on the value of γ -have been undertaken; it is not equal to 1·408 for _all_ gases. Hence -the value of β is different for various gases. - -It is of some importance to notice that the value of β just found for -air is very approximately 1·66 or 5/3. - -For mercury vapour the value of γ has been shown by Kundt to be 1·33 -or 1⅓, and hence β is equal to 1. Thus all the energy of a particle of -mercury vapour is translational, and its behaviour in this respect is -consistent with the assumption that a particle of mercury vapour is a -smooth sphere. - -The two results of this theory which seemed to lend themselves most -readily to experimental verification were (1) that the viscosity of -a gas is independent of its density, and (2) that it is proportional -to the square root of the absolute temperature. The next piece -of work connected with the theory was an attempt to test these -consequences, and a description of the experiments was published in the -“Philosophical Transactions” for 1865, in a paper on the “Viscosity -or Internal Friction of Air and other Gases,” and forms the Bakerian -lecture for that year. - -The first result was completely proved. It is shewn that the value of -the coefficient[51] of viscosity “is the same for air at 0·5 inch and -at 30 inches pressure, provided that the temperature remains the same.” - -It was clear also that the viscosity depended on the temperature, -and the results of the experiments seemed to show that it was nearly -proportional to the absolute temperature. Thus for two temperatures, -185° Fah. and 51° Fah., the ratio of the two coefficients found was -1·2624; the ratio of the two temperatures, each measured from absolute -zero, is 1·2605. - -This result, then, does not agree with the hypothesis that a gas -consists of spherical molecules acting only on each other by a kind of -impact, for, if this were so, the coefficient would, as we have seen, -depend on the square root of the absolute temperature. But Maxwell’s -result, connecting viscosity with the first power of the absolute -temperature, has not been confirmed by other investigators. According -to it we should have as the relation between μ, the coefficient of -viscosity at t° and μ₀, that at zero the equation-- - - μ = μ₀ (1 + .00365 t). - -The most recent results of Professor Holman (_Philosophical Magazine_, -Vol. xxi., p. 212) give-- - - μ = μ₀ (1 + .00275 t - .00000034 t²). - -And results similar to this are given by O. E. Meyer, Puluj, and -Obermeyer. Maxwell’s coefficient ·00365 is too large, but ·00182, the -coefficient obtained by supposing the viscosity proportional to the -square root of the temperature, would be too small. - -It still remains true, therefore, that the laws of the viscosity of -gases cannot be explained by the hypothesis of the impact of hard -spheres; but some deductions drawn by Maxwell in his next paper from -his supposed law of proportionality to the first power of the absolute -temperature require modification. - -It was clear from his experiments just described that the simple -hypothesis of the impact of elastic bodies would not account for all -the phenomena observed. Accordingly, in 1866, Maxwell took up the -problem in a more general form in his paper on the “Dynamical Theory of -Gases,” Phil. Trans., 1866. - -In it he considered the molecules of the gas not as elastic spheres -of definite radius, but as small bodies, or groups of smaller -molecules, repelling one another with a force whose direction always -passes very nearly through the centre of gravity of the molecules, -and whose magnitude is represented very nearly by some function of -the distance of the centres of gravity. “I have made,” he continues, -“this modification of the theory in consequence of the results of my -experiments on the viscosity of air at different temperatures, and I -have deduced from these experiments that the repulsion is inversely as -the fifth power of the distance.” - -Since more recent observation has shown that the numerical results of -Maxwell’s work connecting viscosity and temperature are erroneous, this -last deduction does not hold; the inverse fifth power law of force -will not give the correct relation between viscosity and temperature. -Maxwell himself at a later date, “On the Stresses in Rarefied Gases,” -Phil. Trans., 1879, realised this; but even in this last paper he -adhered to the fifth power law because it leads to an important -simplification in the equations to be dealt with. - -The paper of 1866 is chiefly important because it contains for the -first time the application of general dynamical methods to molecular -problems. The law of the distribution of velocities among the molecules -is again investigated, and a result practically identical with that -found for the elastic spheres is arrived at. In obtaining this -conclusion, however, it is assumed that the distribution of velocities -is uniform in all directions about any point, whatever actions may be -taking place in the gas. If, for example, the temperature is different -at different points, then, for a given velocity, all directions are not -equally probable. Maxwell’s expression, therefore, for the number of -molecules which at any moment have a given velocity only applies to the -permanent state in which the distribution of temperature is uniform. -When dealing, for example, with the conduction of heat, a modification -of the expression is necessary. This was pointed out by Boltzmann.[52] - -In the paper of 1866, Maxwell applies his generalised results to the -final distribution of two gases under the action of gravity, the -equilibrium of temperature between two gases, and the distribution of -temperature in a vertical column. These results are, as he states, -independent of the law of force between the molecules. The dynamical -causes of diffusion viscosity and conduction of heat are dealt with, -and these involve the law of force. - -It follows also from the investigation that, on the hypotheses assumed -as its basis, if two kinds of gases be mixed, the difference between -the average kinetic energies of translation of the gases of each kind -diminishes rapidly in consequence of the action between the two. The -average kinetic energy of translation, therefore, tends to become the -same for each kind of gas, and as before, it is this average energy of -translation which measures the temperature. - -A molecule in the theory is a portion of a gas which moves about as a -single body. It may be a mere point, a centre of force having inertia, -capable of doing work while losing velocity. There may be also in each -molecule systems of several such centres of force bound together by -their mutual actions. Again, a molecule may be a small solid body of -determinate form; but in this case we must, as Maxwell points out, -introduce a new set of forces binding together the parts of each -molecule: we must have a molecular theory of the second order. In any -case, the most general supposition made is that a molecule consists of -a series of parts which stick together, but are capable of relative -motion among each other. - -In this case the kinetic energy of the molecule consists of the energy -of its centre of gravity, together with the energy of its component -parts, relative to its centre of gravity.[53] - -Now Clausius had, as we have seen, given reasons for believing that the -ratio of the whole energy of a molecule to the energy of translation of -its centre of gravity tends to become constant. We have already used β -to denote this constant. Thus, while the temperature is measured by the -average kinetic energy of translation of the centre of gravity of each -molecule, the heat contained in a molecule is its whole energy, and is -β times this quantity. Thus the conclusions as to specific heat, etc., -already given on page 130, apply in this case, and in particular we -have the result that if γ be the ratio of the specific heat at constant -pressure to that at constant volume, then-- - - β = ⅔ 1/(γ-1) - -Maxwell’s theorem of the distribution of kinetic energy among a system -of molecules applied, as he gave it in 1866, to the kinetic energy of -translation of the centre of gravity of each molecule. Two years later -Dr. Boltzmann, in the paper we have already referred to, extended -it (under certain limitations) to the parts of which a molecule is -composed. According to Maxwell the average kinetic energy of the centre -of gravity of each molecule tends to become the same. According to -Boltzmann the average kinetic energy of each part of the molecule tends -to become the same. - -Maxwell, in the last paper he wrote on the subject (“On Boltzmann’s -Theorem on the Average Distribution of Energy in a System of -Material Points,” Camb. Phil. Trans., XII.), took up this problem. -Watson had given a proof of it in 1876 differing from Boltzmann’s, -but still limited by the stipulation that the time, during which a -particle is encountering other particles, is very small compared with -the time during which there is no sensible action between it and -other particles, and also that the time during which a particle is -simultaneously within the distance of more than one other particle may -be neglected. - -Maxwell claims that his proof is free from any such limitation. The -material points may act on each other at all distances, and according -to any law which is consistent with the conservation of energy; they -may also be acted on by forces external to the system, provided these -are consistent with that law. - -The only assumption which is necessary for the direct proof is that -the system, if left to itself in its actual state of motion, will -sooner or later pass through every phase which is consistent with the -conservation of energy. - -In this paper Maxwell finds in a very general manner an expression for -the number of molecules which at any time have a given velocity, and -this, when simplified by the assumptions of the former papers, reduces -to the form already found. He also shows that the average kinetic -energy corresponding to any one of the variables which define his -system is the same for every one of the variables of his system. - -Thus, according to this theorem, if each molecule be a single small -solid body, six variables will be required to determine the position -of each, three variables will give us the position of the centre of -gravity of the molecule, while three others will determine the position -of the body relative to its centre of gravity. If the six variables -be properly chosen, the kinetic energy can be expressed as a sum of -six squares, one square corresponding to each variable. According to -the theorem the part of the kinetic energy depending on each square is -the same. Thus, the whole energy is six times as great as that which -arises from any one of the variables. The kinetic energy of translation -is three times as great as that arising from each variable, for it -involves the three variables which determine the position of the centre -of gravity. Hence, if we denote by K the kinetic energy due to one -variable, the whole energy is 6 K, and the translational energy is 3 K; -thus, for this case-- - - β = 6K/3K = 2 - -Or, again, if we suppose that the molecule is such that _m_ variables -are required to determine its position relatively to its centre of -gravity, since 3 are needed to fix the centre of gravity, the total -number of variables defining the position of the molecule is _m_ + 3, -and it is said to have _m_ + 3 degrees of freedom. Hence, in this case, -its total energy is (_m_ + 3) K and its energy of translation is 3 K, -thus we find-- - - β = (_m_ + 3)/3 - - Hence γ = 1 + 2/(_m_ + 3) = 1 + 2/_n_ - -if _n_ be the number of degrees of freedom of the molecule. - -Thus, if this Boltzmann-Maxwell theorem be true, the specific heat of a -gas will depend solely on the number of degrees of freedom of each of -its molecules. For hard rigid bodies we should have _n_ equal to 6, and -hence γ = 1·333. Now the fact that this is not the value of γ for any -of the known gases is a fundamental difficulty in the way of accepting -the complete theory. - -Boltzmann has called attention to the fact that if _n_ be equal to -five, then γ has the value 1·40. And this agrees fairly with the value -found by experiment for air, oxygen, nitrogen, and various other gases. -We will, however, return to this point shortly. - -There is, perhaps, no result in the domain of physical science in -recent years which has been more discussed than the two fundamental -theorems of the molecular theory which we owe to Maxwell and to -Boltzmann. - -The two results in question are (1) the expression for the number of -molecules which at any moment will have a given velocity, and (2) the -proposition that the kinetic energy is ultimately equally divided -among all the variables which determine the system. - -With regard to (1) Maxwell showed that his error law was one possible -condition of permanence. If at any moment the velocities are -distributed according to the error law, that distribution will be a -permanent one. He did not prove that such a distribution is the only -one which can satisfy all the conditions of the problem. - -The proof that this law is a necessary, as well as a sufficient, -condition of permanence was first given by Boltzmann, for a single -monatomic gas in 1872, for a mixture of such gases in 1886, and for a -polyatomic gas in 1887. Other proofs have been given since by Watson -and Burbury. It would be quite beyond the limits of this book to go -into the question of the completeness or sufficiency of the proofs. The -discussion of the question is still in progress. - -The British Association Report for 1894 contains an important -contribution to the question, in the shape of a report by Mr. G. H. -Bryan, and the discussion he started at Oxford by reading this report -has been continued in the pages of _Nature_ and elsewhere since that -time. - -Mr. Bryan shows in the first place what may be the nature of the -systems of molecules to which the results will apply, and discusses -various points of difficulty in the proof. - -The theorem in question, from which the result (1) follows as a simple -deduction, has been thus stated by Dr. Larmor.[54] - -“There exists a positive function belonging to a group of molecules -which, as they settle themselves into a steady state--on the average -derived from a great number of configurations--maintains a steady -downward trend. The Maxwell-Boltzmann steady state is the one in which -this function has finally attained its minimum value, and is thus a -unique steady state, it still being borne in mind that this is only a -proposition of averages derived from a great number of instances in -which nothing is conserved in encounters, except the energy, and that -exceptional circumstances may exist, comparatively very few in number, -in which the trend is, at any rate, temporarily the other way.” - -This theorem, when applied to cases of motion, such as that of a gas at -constant temperature enclosed in a rigid envelope impermeable to heat, -appears to be proved. For such a case, therefore, the Maxwell-Boltzmann -law is the only one possible. - -But whether this be so or not, the law first introduced by Maxwell is -one of those possible, and the advance in molecular science due to its -introduction is enormous. - -We come now to the second result, the equal partition of the energy -among all the degrees of freedom of each molecule. Lord Kelvin -has pointed out a flaw in Maxwell’s proof, but Boltzmann showed -(_Philosophical Magazine_, March, 1893) how this flaw can easily -be corrected, and it may be said that in all cases in which the -Boltzmann-Maxwell law of the distribution of velocities holds, -Maxwell’s law of the equal partition of energy holds also. - -Three cases are considered by Mr. Bryan, in which the law of -distribution fails for rigid molecules: the first is when the molecules -have all, in addition to their velocities of agitation, a common -velocity of translation in a fixed direction; the second is when the -gas has a motion of uniform rotation about a fixed axis; while the -third is when each molecule has an axis of symmetry. In this last case -the forces acting during a collision necessarily pass through the -axis of symmetry, the angular velocity, therefore, of any molecule -about this axis remains constant, the number of molecules having a -given angular velocity will remain the same throughout the motion, -and the part of the kinetic energy which depends on this component of -the motion will remain fixed, and will not come into consideration -when dealing with the equal partition of the energy among the various -degrees of freedom. - -Such a molecule has five, and not six, degrees of freedom; three -quantities are needed to determine the position of its centre of -gravity, and two to fix the position of the axis of symmetry. - -In this case, then, as Boltzmann points out, in the expression for the -ratio of the specific heats, we must have _n_ equal to 5, and hence - - γ = 1 + 2/_n_ = 1 + 2/5 = 1·4 - -agreeing fairly with the value found for air and various other -permanent gases. - -For cases, then, in which we consider each atom as a single rigid body, -the Boltzmann-Maxwell theorem appears to give a unique solution, -and the Maxwell law of the distribution of the energy to be in fair -accordance with the results of observation.[55] - -If we can never go further--and it must be admitted that the -difficulties in the way of further advance are enormous--it may, -I think, be claimed for Maxwell that the progress already made is -greatly due to him. Both these laws, for the case of elastic spheres, -are contained in his first paper of 1860; and while it is to the -genius of Boltzmann that we owe their earliest generalisation, and in -particular the proof of the uniqueness of the solution under proper -restrictions, Maxwell’s last paper contributed in no small degree to -the security of the position. Not merely the foundations, but much of -the superstructure of molecular science is his work. - -The difficulties in the way of advance are, as we have said, enormous. -Boltzmann, in one of his papers, has considered the properties of a -complex molecule of a gas, consisting maybe of a number of atoms and -possibly of ether atoms bound with them, and he concludes that such a -molecule will behave in its progressive motion, and in its collisions -with other molecules, nearly like a rigid body. But to quote from Mr. -Bryan: “The case of a polyatomic molecule, whose atoms are capable of -vibrating relative to one another, affords an interesting field for -investigation and speculation. Is the Boltzmann distribution still -unique, or do other permanent distributions exist in which the kinetic -energy is unequally divided?” - -Again, the spectroscope reveals to us vibrations of the ether, which -are connected in some way with the vibrations of the molecules of -gas, whose spectrum we are observing. It seems clear that the law of -equal partition does not apply to these, and yet, if we are to suppose -that the ether vibrations are due to actual vibrations of the atoms -which constitute a molecule, why does it not apply? Where does the -condition come in which leads to failure in the proof? Or, again, -is it, as has been suggested, the fact that the complex spectrum -of a gas represents the terms of a Fourier Series, into which some -elaborate vibration of the atoms is resolved by the ether? or is the -spectrum due simply to electro-magnetic vibrations on the surface of -the molecules--vibrations whose period is determined chiefly by the -size and shape of the molecule, but in which the atoms of which it is -composed take part? There are grave difficulties in the way of either -of these explanations, but we must not let our dread of the task which -remains to be done blind our eyes to the greatness of Maxwell’s work. - -One other important paper, and a number of shorter articles, remain to -be mentioned. - -The Boltzmann-Maxwell law applies only to cases in which the -temperature is uniform throughout. In a paper published in the -Philosophical Transactions for 1879, on “Stresses in Rarefied Gases -Arising from Inequalities of Temperature,” Maxwell deals, among other -matters, with the theory of the radiometer. He shows that the observed -motions will not take place unless gas, in contact with a solid, can -slide along the surface of the solid with a finite velocity between -places where the temperature is different; and in an appendix he proves -that, on certain assumptions regarding the nature of the contact of the -solid and the gas, there will be, even when the pressure is constant, a -flow of gas along the surface from the colder to the hotter parts. - -Among his less important papers bearing on molecular theory must be -mentioned a lecture on “Molecules” to the British Association at its -Bradford meeting; “Scientific Papers of Clerk Maxwell,” vol. ii., p. -361; and another on “The Molecular Constitution of Bodies,” Scientific -Papers, vol. ii., p. 418. - -In this latter, and also in a review in _Nature_ of Van der Waals’ -book on “The Continuity of the Gaseous and Liquid States,”[56] he -explains and discusses Clausius’ virial equation, by means of which the -variations of the permanent gases from Boyle’s law are explained. The -lecture gives a clear account, in Maxwell’s own inimitable style, of -the advances made in the kinetic theory up to the date at which it was -delivered, and puts clearly the difficulties it has to meet. Maxwell -thought that those arising from the known values of the ratio of the -specific heats were the most serious. - -In the articles, “Atomic Constitution of Bodies” and “Diffusion,” in -the ninth edition of the _Encyclopædia Britannica_, we have Maxwell’s -later views on the fundamental assumptions of the molecular theory. - -The text-book on “Heat” contains some further developments of the -theory. In particular he shows how the conclusions of the second law -of thermo-dynamics are connected with the fact that the coarseness of -our faculties will not allow us to grapple with individual molecules. - -The work described in the foregoing chapters would have been sufficient -to secure to Maxwell a distinguished place among those who have -advanced our knowledge; it remains still to describe his greatest work, -his theory of Electricity and Magnetism. - - - - -CHAPTER IX. - -SCIENTIFIC WORK.--ELECTRICAL THEORIES. - - -Clerk Maxwell’s first electrical paper--that on Faraday’s “Lines of -Force”--was read to the Cambridge Philosophical Society on December -10th, 1855, and Part II. on February 11th, 1856. The author was then a -Bachelor of Arts, only twenty-three years in age, and of less than one -year’s standing from the time of taking his degree. - -The opening words of the paper are as follows (Scientific Papers, vol. -i., p. 155):-- - - “The present state of electrical science seems peculiarly - unfavourable to speculation. The laws of the distribution of - electricity on the surface of conductors have been analytically - deduced from experiment; some parts of the mathematical - theory of magnetism are established, while in other parts the - experimental data are wanting; the theory of the conduction of - galvanism, and that of the mutual attraction of conductors, - have been reduced to mathematical formulæ, but have not - fallen into relation with the other parts of the science. No - electrical theory can now be put forth, unless it shows the - connection, not only between electricity at rest and current - electricity, but between the attractions and inductive effects - of electricity in both states. Such a theory must accurately - satisfy those laws, the mathematical form of which is known, - and must afford the means of calculating the effects in the - limiting cases where the known formulæ are inapplicable. - In order, therefore, to appreciate the requirements of the - science, the student must make himself familiar with a - considerable body of most intricate mathematics, the mere - retention of which in the memory materially interferes with - further progress. The first process, therefore, in the - effectual study of the science, must be one of simplification - and reduction of the results of previous investigation to a - form in which the mind can grasp them. The results of this - simplification may take the form of a purely mathematical - formula or of a physical hypothesis. In the first case we - entirely lose sight of the phenomena to be explained; and - though we may trace out the consequences of given laws, we can - never obtain more extended views of the connections of the - subject. If, on the other hand, we adopt a physical hypothesis, - we see the phenomena only through a medium, and are liable - to that blindness to facts and rashness in assumption which - a partial explanation encourages. We must therefore discover - some method of investigation which allows the mind at every - step to lay hold of a clear physical conception, without being - committed to any theory founded on the physical science from - which that conception is borrowed, so that it is neither drawn - aside from the subject in pursuit of analytical subtleties, nor - carried beyond the truth by a favourite hypothesis. - - “In order to obtain physical ideas without adopting a physical - theory we must make ourselves familiar with the existence of - physical analogies. By a physical analogy I mean that partial - similarity between the laws of one science and those of another - which makes each of them illustrate the other. Thus all the - mathematical sciences are founded on relations between physical - laws and laws of numbers, so that the aim of exact science - is to reduce the problems of Nature to the determination of - quantities by operations with members. Passing from the most - universal of all analogies to a very partial one, we find the - same resemblance in mathematical form between two different - phenomena giving rise to a physical theory of light. - - “The changes of direction which light undergoes in passing from - one medium to another are identical with the deviations of the - path of a particle in moving through a narrow space in which - intense forces act. This analogy, which extends only to the - direction, and not to the velocity of motion, was long believed - to be the true explanation of the refraction of light; and we - still find it useful in the solution of certain problems, in - which we employ it without danger as an artificial method. The - other analogy, between light and the vibrations of an elastic - medium, extends much farther, but, though its importance and - fruitfulness cannot be over-estimated, we must recollect that - it is founded only on a resemblance _in form_ between the - laws of light and those of vibrations. By stripping it of its - physical dress and reducing it to a theory of ‘transverse - alternations,’ we might obtain a system of truth strictly - founded on observation, but probably deficient both in the - vividness of its conceptions and the fertility of its method. - I have said thus much on the disputed questions of optics, as - a preparation for the discussion of the almost universally - admitted theory of attraction at a distance. - - “We have all acquired the mathematical conception of these - attractions. We can reason about them and determine their - appropriate forms or formulæ. These formulæ have a distinct - mathematical significance, and their results are found to be - in accordance with natural phenomena. There is no formula - in applied mathematics more consistent with Nature than the - formula of attractions, and no theory better established in - the minds of men than that of the action of bodies on one - another at a distance. The laws of the conduction of heat in - uniform media appear at first sight among the most different in - their physical relations from those relating to attractions. - The quantities which enter into them are _temperature_, _flow - of heat_, _conductivity_. The word _force_ is foreign to the - subject. Yet we find that the mathematical laws of the uniform - motion of heat in homogeneous media are identical in form - with those of attractions varying inversely as the square of - the distance. We have only to substitute _source of heat_ for - _centre of attraction_, _flow of heat_ for _accelerating effect - of attraction_ at any point, and _temperature_ for _potential_, - and the solution of a problem in attractions is transformed - into that of a problem in heat. - - “This analogy between the formulæ of heat and attraction was, I - believe, first pointed out by Professor William Thomson in the - _Cambridge Mathematical Journal_, Vol. III. - - “Now the conduction of heat is supposed to proceed by an - action between contiguous parts of a medium, while the force - of attraction is a relation between distant bodies, and yet, - if we knew nothing more than is expressed in the mathematical - formulæ, there would be nothing to distinguish between the one - set of phenomena and the other. - - “It is true that, if we introduce other considerations and - observe additional facts, the two subjects will assume very - different aspects, but the mathematical resemblance of some - of their laws will remain, and may still be made useful in - exciting appropriate mathematical ideas. - - “It is by the use of analogies of this kind that I have - attempted to bring before the mind, in a convenient and - manageable form, those mathematical ideas which are necessary - to the study of the phenomena of electricity. The methods are - generally those suggested by the processes of reasoning which - are found in the researches of Faraday, and which, though they - have been interpreted mathematically by Professor Thomson and - others, are very generally supposed to be of an indefinite and - unmathematical character, when compared with those employed by - the professed mathematicians. By the method which I adopt, I - hope to render it evident that I am not attempting to establish - any physical theory of a science in which I have hardly made - a single experiment, and that the limit of my design is to - show how, by a strict application of the ideas and methods - of Faraday, the connection of the very different orders of - phenomena which he has discovered may be clearly placed before - the mathematical mind. I shall therefore avoid as much as I can - the introduction of anything which does not serve as a direct - illustration of Faraday’s methods, or of the mathematical - deductions which may be made from them. In treating the simpler - parts of the subject I shall use Faraday’s mathematical methods - as well as his ideas. When the complexity of the subject - requires it, I shall use analytical notation, still confining - myself to the development of ideas originated by the same - philosopher. - - “I have in the first place to explain and illustrate the idea - of ‘lines of force.’ - - “When a body is electrified in any manner, a small body - charged with positive electricity, and placed in any given - position, will experience a force urging it in a certain - direction. If the small body be now negatively electrified, it - will be urged by an equal force in a direction exactly opposite. - - “The same relations hold between a magnetic body and the north - or south poles of a small magnet. If the north pole is urged - in one direction, the south pole is urged in the opposite - direction. - - “In this way we might find a line passing through any point - of space, such that it represents the direction of the - force acting on a positively electrified particle, or on an - elementary north pole, and the reverse direction of the force - on a negatively electrified particle or an elementary south - pole. Since at every point of space such a direction may be - found, if we commence at any point and draw a line so that, - as we go along it, its direction at any point shall always - coincide with that of the resultant force at that point, this - curve will indicate the direction of that force for every point - through which it passes, and might be called on that account a - _line of force_. We might in the same way draw other lines of - force, till we had filled all space with curves indicating by - their direction that of the force at any assigned point. - - “We should thus obtain a geometrical model of the physical - phenomena, which would tell us the _direction_ of the force, - but we should still require some method of indicating the - _intensity_ of the force at any point. If we consider these - curves not as mere lines, but as fine tubes of variable section - carrying an incompressible fluid, then, since the velocity of - the fluid is inversely as the section of the tube, we may make - the velocity vary according to any given law, by regulating the - section of the tube, and in this way we might represent the - intensity of the force as well as its direction by the motion - of the fluid in these tubes. This method of representing the - intensity of a force by the velocity of an imaginary fluid in - a tube is applicable to any conceivable system of forces, but - it is capable of great simplification in the case in which - the forces are such as can be explained by the hypothesis of - attractions varying inversely as the square of the distance, - such as those observed in electrical and magnetic phenomena. - In the case of a perfectly arbitrary system of forces, there - will generally be interstices between the tubes; but in the - case of electric and magnetic forces it is possible to arrange - the tubes so as to leave no interstices. The tubes will then be - mere surfaces, directing the motion of a fluid filling up the - whole space. It has been usual to commence the investigation of - the laws of these forces by at once assuming that the phenomena - are due to attractive or repulsive forces acting between - certain points. We may, however, obtain a different view of the - subject, and one more suited to our more difficult inquiries, - by adopting for the definition of the forces of which we treat, - that they may be represented in magnitude and direction by the - uniform motion of an incompressible fluid. - - “I propose, then, first to describe a method by which the - motion of such a fluid can be clearly conceived; secondly - to trace the consequences of assuming certain conditions of - motion, and to point out the application of the method to some - of the less complicated phenomena of electricity, magnetism, - and galvanism; and lastly, to show how by an extension of these - methods, and the introduction of another idea due to Faraday, - the laws of the attractions and inductive actions of magnets - and currents may be clearly conceived, without making any - assumptions as to the physical nature of electricity, or adding - anything to that which has been already proved by experiment. - - “By referring everything to the purely geometrical idea of the - motion of an imaginary fluid, I hope to attain generality and - precision, and to avoid the dangers arising from a premature - theory professing to explain the cause of the phenomena. - If the results of mere speculation which I have collected - are found to be of any use to experimental philosophers, in - arranging and interpreting their results, they will have served - their purpose, and a mature theory, in which physical facts - will be physically explained, will be formed by those who by - interrogating Nature herself can obtain the only true solution - of the questions which the mathematical theory suggests.” - -The idea was a bold one: for a youth of twenty-three to explain, by -means of the motions of an incompressible fluid, some of the less -complicated phenomena of electricity and magnetism, to show how -the laws of the attractions of magnets and currents may be clearly -conceived without making any assumption as to the physical nature of -electricity, or adding anything to that which has already been proved -by experiment. - -It may be useful to review in a very few words the position of -electrical theory[57] in 1855. - -Coulomb’s experiments had established the fundamental facts of -electrostatic attraction and repulsion, and Coulomb himself, about -1785, had stated a theory based on these experiments which could “only -be attacked by proving his experimental results to be inaccurate.”[58] - -Coulomb supposes the existence of two electric fluids, the theory -developed previously by Franklin, but says-- - - “Je préviens pour mettre la théorie qui va suivre à l’abri de - toute dispute systématique, que dans la supposition de deux - fluides électriques, je n’ai autre intention que de présenter - avec le moins d’éléments possible les résultats du calcul et - de l’expérience, et non d’indiquer les véritables causes de - l’électricité.” - -Cavendish was working in England about the same time as Coulomb, but -he published very little, and the value and importance of his work -was not recognised until the appearance in 1879 of the “Electrical -Researches of Henry Cavendish,” edited by Clerk Maxwell. - -Early in the present century the application of mathematical analysis -to electrical problems was begun by Laplace, who investigated the -distribution of electricity on spheroids, and about 1811 Poisson’s -great work on the distribution of electricity on two spheres placed -at any given distance apart was published. Meanwhile the properties -of the electric current were being investigated. Galvani’s discovery -of the muscular contraction in a frog’s leg, caused by the contact of -dissimilar metals, was made in 1790. Volta invented the voltaic pile in -1800, and Oersted in 1820 discovered that an electric current produced -magnetic force in its neighbourhood. On this Ampère laid the foundation -of his theory of electro-dynamics, in which he showed how to calculate -the forces between circuits carrying currents from an assumed law of -force between each pair of elements of the circuits. His experiments -proved that the consequences which follow from this law are consistent -with all the observed facts. They do not prove that Ampère’s law alone -can explain the facts. - -Maxwell, writing on this subject in the “Electricity an Magnetism,” -vol. ii., p. 162, says-- - - “The experimental investigation by which Ampère established the - laws of the mechanical action between electric currents is one - of the most brilliant achievements in science. - - “The whole, theory and experiment, seems as if it had leaped - full grown and full armed from the brain of the ‘Newton - of Electricity.’ It is perfect in form and unassailable in - accuracy, and it is summed up in a formula from which all the - phenomena may be deduced, and which must always remain the - cardinal formula of electro-dynamics. - - “The method of Ampère, however, though cast into an inductive - form, does not allow us to trace the formation of the ideas - which guided it. We can scarcely believe that Ampère really - discovered the law of action by means of the experiments which - he describes. We are led to suspect, what, indeed, he tells us - himself, that he discovered the law by some process which he - has not shown us, and that when he had afterwards built up a - perfect demonstration, he removed all traces of the scaffolding - by which he had built it.” - -The experimental evidence for Ampère’s theory, so far, at least, as -it was possible to obtain it from experiments on closed circuits, was -rendered unimpeachable by W. Weber about 1846, while in the previous -year Grassman and F. E. Neumann both published laws for the attraction -between two elements of current which differ from that of Ampère, but -lead to the same result for closed circuits. In a paper published in -1846 Weber announced his hypothesis connecting together electrostatic -and electro-dynamic action. In this paper he supposed that the force -between two particles of electricity depends on the motion of the -particles as well as on their distance apart. A somewhat similar -theory was proposed by Gauss and published after his death in his -collected works. It has been shown, however, that Gauss’ theory is -inconsistent with the conservation of energy. Weber’s theory avoids -this inconsistency and leads, for closed circuits, to the same results -as Ampère. It has been proved, however, by Von Helmholtz, that, under -certain circumstances, according to it, a body would behave as though -its mass were negative--it would move in a direction opposite to that -of the force.[59] - -Since 1846 many other theories have been proposed to explain Ampère’s -laws. Meanwhile, in 1821, Faraday observed that under certain -circumstances a wire carrying a current could be kept in continuous -rotation in a magnetic field by the action between the magnets and -the current. In 1824 Arago observed the motion of a magnet caused by -rotating a copper disc in its neighbourhood, while in 1831 Faraday -began his experimental researches into electro-magnetic induction. -About the same period Joseph Henry, of Washington, was making, -independently of Faraday, experiments of fundamental importance on -electro-magnetic induction, but sufficient attention was not called to -his work until comparatively recent years. - -In 1833 Lenz made some important researches, which led him to discover -the connection between the direction of the induced currents and -Ampère’s laws, summed up in his rule that the direction of the induced -current is always such as to oppose by its electro-magnetic action the -motion which induces it. - -In 1845 F. E. Neumann developed from this law the mathematical theory -of electro-magnetic induction, and about the same time W. Weber showed -how it might be deduced from his elementary law of electrical action. - -The great name of Von Helmholtz first appears in connection with this -subject in 1851, but of his writings we shall have more to say at a -later stage. - -Meanwhile, during the same period, various writers, Murphy, Plana, -Charles, Sturm, and Gauss, extended Poisson’s work on electrostatics, -treating the questions which arose as problems in the distribution of -an attracting fluid, attracting or repelling according to Newton’s law, -though here again the greatest advances were made by a self-taught -Nottingham shoemaker, George Green by name, in his paper “On the -Application of Mathematical Analysis to the Theories of Electricity and -Magnetism,” 1828. - -Green’s researches, Lord Kelvin writes, “have led to the elementary -proposition which must constitute the legitimate foundation of every -perfect mathematical structure that is to be made from the materials -furnished by the experimental laws of Coulomb.” - -Green, it may be remarked, was the inventor of the term Potential. -His essay, however, lay neglected from 1828, until Lord Kelvin called -attention to it in 1845. Meanwhile, some of its most important results -had been re-discovered by Gauss and Charles and Thomson himself. - -Until about 1845, the experimental work on which these mathematical -researches in electrostatics were based was that of Coulomb. An -electrified body is supposed to have a charge of some imponderable -fluid “electricity.” Particles of electricity repel each other -according to a certain law, and the fluid distributes itself in -equilibrium over the surface of any charged conductor in accordance -with this law. There are on this theory two opposite kinds of electric -fluid, positive and negative, two charges of the same kind repel, two -charges of opposite kinds attract; the repulsion or attraction is -proportional to the product of the charges, and inversely proportional -to the square of the distance between them. - -The action between two charges is action at a distance taking place -across the space which separates the two. - -Faraday, in 1837, in the eleventh series of his “Experimental -Researches,” published his first paper on “Electrostatic Induction.” -He showed--as indeed Cavendish had proved long previously, though the -result remained unpublished--that the force between two charged bodies -will depend on the insulating medium which surrounds them, not merely -on their shape and position. Induction, as he expresses it, takes place -along curved lines, and is an action of contiguous particles; these -curved lines he calls the “lines of force.” - -Discussing these researches in 1845, Lord Kelvin writes[60]:-- - - “Mr. Faraday’s researches ... were undertaken with a view to - test an idea which he had long possessed that the forces of - attraction and repulsion exercised by free electricity are not - the resultants of actions exercised at a distance, but are - propagated by means of molecular action among the contiguous - particles of the insulating medium surrounding the electrified - bodies, which he therefore calls the dielectric. By this idea - he has been led to some very remarkable views upon induction, - or, in fact, upon electrical action in general. As it is - impossible that the phenomena observed by Faraday can be - incompatible with the results of experiment which constitute - Coulomb’s theory, it is to be expected that the difference - of his ideas from those of Coulomb must arise solely from a - different method of stating and interpreting physically the - same laws; and further, it may, I think, be shown that either - method of viewing this subject, when carried sufficiently - far, may be made the foundation of a mathematical theory - which would lead to the elementary principles of the other as - consequences. This theory would, accordingly, be the expression - of the ultimate law of the phenomena, independently of any - physical hypothesis we might from other circumstances be led - to adopt. That there are necessarily two distinct elementary - ways of viewing the theory of electricity may be seen from the - following considerations....” - -In the pages which follow, Lord Kelvin develops the consequences of an -analogy between the conduction of heat and electrostatic action, which -he had pointed out three years earlier (1842), in his paper on “The -Uniform Motion of Heat in Homogeneous Solid Bodies,” and discusses its -connection with the mathematical theory of electricity. - -The problem of distributing sources of heat in a given homogeneous -conductor of heat, so as to produce a definite steady temperature at -each point on the conductor is shewn to be _mathematically_ identical -with that of distributing electricity in equilibrium, so as to produce -at each point an electrical potential having the same value as the -temperature. - -Thus the fundamental laws of the conduction of heat may be made the -basis of the mathematical theory of electricity, but the physical -idea which they suggest is that of the propagation of some effect by -means of the mutual action of contiguous particles, rather than that -of material particles attracting or repelling at a distance, which -naturally follows from the statement of Coulomb’s law. - -Lord Kelvin continues:-- - - “All the views which Faraday has brought forward and - illustrated, as demonstrated by experiment, lead to this method - of establishing the mathematical theory, and, as far as the - analysis is concerned, it would in most _general_ propositions - be more simple, if possible, than that of Coulomb. Of course - the analysis of _particular_ problems would be identical in the - two methods. It is thus that Faraday arrives at a knowledge of - some of the most important of the mathematical theorems which - from their nature seemed destined never to be perceived except - as mathematical truths.” - -Lord Kelvin’s papers on “The Mathematical Theory of Electricity,” -published from 1848 to 1850, his “Propositions on the Theory of -Attraction” (1842), his “Theory of Electrical Images” (1847), and his -paper on “The Mathematical Theory of Magnetism” (1849), contain a -statement of the most important results achieved in the mathematical -sciences of Electrostatics and Magnetism up to the time of Maxwell’s -first paper. - -The opening sentences of that paper have already been quoted. In the -preface to the “Electricity and Magnetism” Maxwell writes thus:-- - - “Before I began the study of electricity I resolved to read - no mathematics on the subject till I had first read through - ‘Experimental Researches on Electricity.’ I was aware that - there was supposed to be a difference between Faraday’s way of - conceiving phenomena and that of the mathematicians, so that - neither he nor they were satisfied with each other’s language. - I had also the conviction that this discrepancy did not arise - from either party being wrong. I was first convinced of this by - Sir William Thomson, to whose advice and assistance, as well as - to his published papers, I owe most of what I have learned on - the subject. - - “As I proceeded with the study of Faraday, I perceived that his - method of conceiving the phenomena was also a mathematical - one, though not exhibited in the conventional form of - mathematical symbols. I also found that these methods were - capable of being expressed in the ordinary mathematical forms, - and thus compared with those of the professed mathematicians. - - “For instance, Faraday, in his mind’s eye, saw lines of force - traversing all space where the mathematicians saw centres of - force attracting at a distance. Faraday saw a medium where - they saw nothing but distance. Faraday sought the seat of the - phenomena in real actions going on in the medium. They were - satisfied that they had found it in a power of action at a - distance impressed on the electric fluids.” - -Now, Maxwell saw an analogy between electrostatics and the steady -motion of an incompressible fluid like water, and it is this analogy -which he develops in the first part of his paper. The water flows along -definite lines; a surface which consists wholly of such lines of flow -will have the property that no water ever crosses it. In any stream -of water we can imagine a number of such surfaces drawn, dividing it -up into a series of tubes; each of these will be a tube of flow, each -of these tubes remain always filled with water. Hence, the quantity -of water which crosses per second any section of a tube of flow -perpendicular to its length is always the same. Thus, from the form of -the tube, we can obtain information as to the direction and strength of -the flow, for where the tube is wide the flow will be proportionately -small, and _vice versâ_. - -Again, we can draw in the fluid a number of surfaces, over each of -which the pressure is the same; these surfaces will cut the tubes -of flow at right angles. Let us suppose they are drawn so that the -difference of pressure between any two consecutive surfaces is unity, -then the surfaces will be close together at points at which the -pressure changes rapidly; where the variation of pressure is slow, the -distance between two consecutive surfaces will be considerable. - -If, then, in any case of motion, we can draw the pressure surfaces, -and the tubes of flow, we can determine the motion of the fluid -completely. Now, the same mathematical expressions which appear in -the hydro-dynamical theory occur also in the theory of electricity, -the meaning only of the symbols is changed. For velocity of fluid we -have to write electrical force. For difference of fluid pressure we -substitute work done, or difference of electrical potential or pressure. - -The surfaces and tubes, drawn as the solution of any hydro-dynamical -problem, give us also the solution of an electrical problem; the -tubes of flow are Faraday’s tubes of force, or tubes of induction, -the surfaces of constant pressure are surfaces of equal electrical -potential. Induction may take place in curved lines just as the tubes -of flow may be bent and curved; the analogy between the two is a -complete one. - -But, as Maxwell shows, the analogy reaches further still. An electric -current flowing along a wire had been recognised as having many -properties similar to those of a current of liquid in a tube. When a -steady current is passing through any solid conductor, there are formed -in the conductor tubes of electrical flow and surfaces of constant -pressure. These tubes and surfaces are the same as those formed by the -flow of liquid through a solid whose boundary surface is the same -as that of the conductor, provided the flow of liquid is properly -proportioned to the flow of electricity. - -These analogies refer to steady currents in which, therefore, the flow -at any point of the conductor does not depend on the time. In Part -II. of his paper Maxwell deals with Faraday’s electro-tonic state. -Faraday had found that when _changes_ are produced in the magnetic -phenomena surrounding a conductor, an electric current is set up in -the conductor, which continues so long as the magnetic changes are in -progress, but which ceases when the magnetic state becomes steady. - - “Considerations of this kind led Professor Faraday to connect - with his discovery of the induction of electric currents the - conception of a state into which all bodies are thrown by the - presence of magnets and currents. This state does not manifest - itself by any known phenomena as long as it is undisturbed, - but any change in this state is indicated by a current or - tendency towards a current. To this state he gave the name of - the ‘Electro-tonic State,’ and although he afterwards succeeded - in explaining the phenomena which suggested it by means of less - hypothetical conceptions, he has on several occasions hinted at - the probability that some phenomena might be discovered which - would render the electro-tonic state an object of legitimate - induction. These speculations, into which Faraday had been - led by the study of laws which he has well established, and - which he abandoned only for want of experimental data for the - direct proof of the unknown state, have not, I think, been - made the subject of mathematical investigation. Perhaps it - may be thought that the quantitative determinations of the - various phenomena are not sufficiently rigorous to be made - the basis of a mathematical theory. Faraday, however, has not - contented himself with simply stating the numerical results - of his experiments and leaving the law to be discovered by - calculation. Where he has perceived a law he has at once stated - it, in terms as unambiguous as those of pure mathematics, - and if the mathematician, receiving this as a physical - truth, deduces from it other laws capable of being tested by - experiment, he has merely assisted the physicist in arranging - his own ideas, which is confessedly a necessary step in - scientific induction. - - “In the following investigation, therefore, the laws - established by Faraday will be assumed as true, and it will - be shown that by following out his speculations other and - more general laws can be deduced from them. If it should, - then, appear that these laws, originally devised to include - one set of phenomena, may be generalised so as to extend to - phenomena of a different class, these mathematical connections - may suggest to physicists the means of establishing physical - connections, and thus mere speculation may be turned to account - in experimental science.” - -Maxwell shows how to obtain a mathematical expression for Faraday’s -electro-tonic state. In his “Electricity and Magnetism,” this -electro-tonic state receives a new name. It is known as the Vector -Potential,[61] and the paper under consideration contains, though -in an incomplete form, his first statement of those equations of the -electric field which are so indissolubly bound up with Maxwell’s name. - -The great advance in theory made in the paper is the distinct -recognition of certain mathematical functions as representing Faraday’s -electrotonic-state, and their use in solving electro-magnetic problems. - -The paper contains no new physical theory of electricity, but in a -few years one appeared. In his later writings Maxwell adopted a more -general view of the electro-magnetic field than that contained in his -early papers on “Physical Lines of Force.” It must, therefore, not be -supposed that the somewhat gross conception of cog-wheels and pulleys, -which we are about to describe, were anything more to their author than -a model, which enabled him to realise how the changes, which occur when -a current of electricity passes through a wire, might be represented by -the motion of actual material particles. - -The problem before him was to devise a physical theory of electricity, -which would explain the forces exerted on electrified bodies by means -of action between the contiguous parts of the medium in the space -surrounding these bodies, rather than by direct action across the -distance which separates them. A similar question, still unanswered, -had arisen in the case of gravitation. Astronomers have determined the -forces between attracting bodies; they do not know how those forces -arise. - -Maxwell’s fondness for models has already been alluded to; it had led -him to construct his top to illustrate the dynamics of a rigid body -rotating about a fixed point, and his model of Saturn’s rings (now in -the Cavendish Laboratory) to illustrate the motion of the satellites -in the rings. He had explained many of the gaseous laws by means of -the impact of molecules, and now his fertile ingenuity was to imagine -a mechanical model of the state of the electro-magnetic field near a -system of conductors carrying currents. - -Faraday, as we have seen, looked upon electrostatic and magnetic -induction as taking place along curved lines of force. He pictures -these lines as ropes of molecules starting from a charged conductor, or -a magnet, as the case may be, and acting on other bodies near. These -ropes of molecules tend to shorten, and at the same time to swell -outwards laterally. Thus the charged conductor tends to draw other -bodies to itself, there is a tension along the lines of force, while -at the same time each tube of molecules pushes its neighbours aside; a -pressure at right angles to the lines of force is combined with this -tension. Assuming for a moment this pressure and tension to exist, can -we devise a mechanism to account for it? Maxwell himself has likened -the lines of force to the fibres of a muscle. As the fibres contract, -causing the limb to which they are attached to move, they swell -outwards, and the muscle thickens. - -Again, from another point of view, we might consider a line of force -as consisting of a string of small cells of some flexible material -each filled with fluid. If we then suppose this series of cells caused -to rotate rapidly about the direction of the line of force, the cells -will expand laterally and contract longitudinally; there will again be -tension along the lines of force and pressure at right angles to them. -It was this last idea, as we shall see shortly, of which Maxwell made -use-- - - “I propose now” [he writes (“On Physical Lines of Force,” - _Phil. Mag._, vol. xxi.)] “to examine magnetic phenomena from - a mechanical point of view, and to determine what tensions in, - or motions of, a medium are capable of producing the mechanical - phenomena observed. If by the same hypothesis we can connect - the phenomena of magnetic attraction with electro-magnetic - phenomena, and with those of induced currents, we shall have - found a theory which, if not true, can only be proved to be - erroneous by experiments, which will greatly enlarge our - knowledge of this part of physics.” - -Lord Kelvin had in 1847 given a mechanical representation of electric, -magnetic and galvanic forces by means of the displacements of an -elastic solid in a state of strain. The angular displacement at each -point of the solid was taken as proportional to the magnetic force, and -from this the relation between the various other electric quantities -and the motion of the solid was developed. But Lord Kelvin did not -attempt to explain the origin of the observed forces by the effects due -to these strains, but merely made use of the mathematical analogy to -assist the imagination in the study of both. - -Maxwell considered magnetic action as existing in the form of pressure -or tension, or more generally, of some stress in some medium. The -existence of a medium capable of exerting force on material bodies and -of withstanding considerable stress, both pressure and tension, is -thus a fundamental hypothesis with him; this medium is to be capable -of motion, and electro-magnetic forces arise from its motion and its -stresses. - -Now, Maxwell’s fundamental supposition is that, in a magnetic field, -there is a rotation of the molecules continually in progress about the -lines of magnetic force. Consider now the case of a uniform magnetic -field, whose direction is perpendicular to the paper; we are to look -upon the lines of force as parallel strings of molecules, the axes of -these strings being perpendicular to the paper. Each string is supposed -to be rotating in the same direction about its axis, and the angular -velocity of rotation is a measure of the magnetic force. In consequence -of this rotation there will be differences of pressure in different -directions in the medium; the pressure along the axes of the strings -will be less than it would be if the medium were at rest, that in the -directions at right angles to the axes will be greater, the medium will -behave as though it were under tension along the axes of the molecules -under pressure at right angles to them. Moreover, it can be shown that -the pressure and the tension are both proportional to the square of the -angular velocity--the square, that is, of the magnetic force--and this -result is in accordance with the consequences of experiment. - -More elaborate calculation shows that this statement is true generally. -If we draw the lines of force in any magnetic field, and then suppose -the molecules of the medium set in rotation about these lines of force -as axes, with velocities which at each point are proportional to the -magnetic force, the distribution of pressure throughout is that which -we know actually to exist in the magnetic field. - -According to this hypothesis, then, a permanent bar magnet has the -power of setting the medium round it into continuous molecular rotation -about the lines of force as axes. The molecules which are set in -rotation we may consider as spherical, or nearly spherical, cells -filled with a fluid, or an elastic solid substance, and surrounded by a -kind of membrane, or sack, holding the contents together. - -So far the model does not give any account of electrical actions which -go on in the magnetic field. - -The energy is wholly rotational, and the forces wholly magnetic. - -Consider, however, any two contiguous strings of molecules. Let them -cut the paper as shown in the two circles in Fig. 1:-- - -[Illustration: Fig. 1. - -Fig. 2.] - -Then these cells are both rotating in the same direction, hence at C, -where they touch, their points of contact will be moving in opposite -directions, as shown by the arrow heads, and it is difficult to imagine -how such motion can continue; it would require the surfaces of the -cells to be perfectly smooth, and if this were so they would lose the -power of transmitting action from one cell to the next. - -The cells A and B may be compared to two cog-wheels placed close -together, which we wish to turn in the same direction. If the cogs can -interlock, as in Fig. 2, this is impossible: consecutive wheels in the -train must move in opposite directions. - -[Illustration: Fig. 3.] - -But in many machines the desired end is attained by inserting between -the two wheels A and B a third idle wheel C, as shewn in Fig. 3. This -may be very small, its only function is to transmit the motion of A to -B in such a way that A and B may both turn in the same direction. It is -not necessary that there should be cogs on the wheels; if the surfaces -be perfectly rough, so that no slipping can take place, the same result -follows without the cogs. - -Guided by this analogy Maxwell extended his model by supposing each -cell coated with a number of small particles which roll on its surface. -These particles play the part of the idle wheels in the machine, and by -their rolling merely enable the adjacent parts of two cells to move in -opposite directions. - -Consider now a number of such cells and their idle wheels lying in a -plane, that of the paper, and suppose each cell is rotating with the -same uniform angular velocity about an axis at right angles to that -plane, each idle wheel will be acted on by two equal and opposite -forces at the ends of the diameter in which it is touched by the -adjacent cells; it will therefore be set in rotation, but there will be -no force tending to drive it onwards; it does not matter whether the -axis on which it rotates is free to move or fixed, in either case the -idle wheel simply rotates. But suppose now the adjacent cells are not -rotating at the same rate. In addition to its rotation the idle wheel -will be urged onward with a velocity which depends on the difference -between the rotations, and, if it can move freely, it will move on from -between the two cells. Imagine now that the interstices between the -cells are fitted with a string of idle wheels. So long as the adjacent -cells move with different velocity there will be a continual stream of -rolling particles or idle wheels between them. Maxwell in the paper -considered these rolling particles to be particles of electricity. -Their motion constitutes an electric current. In a uniform magnetic -field there is no electric current; if the strength of the field -varies, the idle wheels are set in motion and there may be a current. - -These particles are very small compared with the magnetic vortices. -The mass of all the particles is inappreciable compared with the mass -of the vortices, and a great many vortices with their surrounding -particles are contained in a molecule of the medium; the particles -roll on the vortices without touching each other, so that so long as -they remain within the same molecule there is no loss of energy by -resistance. When, however, there is a current or general transference -of particles in one direction they must pass from one molecule to -another, and in doing so may experience resistance and generate heat. - -Maxwell states that the conception of a particle, having its motion -connected with that of a vortex by perfect rolling contact, may appear -somewhat awkward. “I do not bring it forward,” he writes, “as a mode of -connection existing in Nature, or even as that which I would willingly -assent to as an electrical hypothesis. It is, however, a mode of -connection which is mechanically conceivable and easily investigated, -and it serves to bring out the actual mechanical connections between -the known electro-magnetic phenomena, so that I venture to say that -anyone who understands the provisional and temporary character of this -hypothesis will find himself rather helped than hindered by it in his -search after the true interpretation of the phenomena.” - -The first part of the paper deals with the theory of magnetism; in the -second part the hypothesis is applied to the phenomena of electric -currents, and it is shown how the known laws of steady currents and -of electro-magnetic induction can be deduced from it. In Part III., -published January and February, 1862, the theory of molecular vortices -is applied to statical electricity. - -The distinction between a conductor and an insulator or dielectric -is supposed to be that in the former the particles of electricity -can pass with more or less freedom from molecule to molecule. In the -latter such transference is impossible, the particles can only be -displaced within the molecule with which they are connected; the cells -or vortices of the medium are supposed to be elastic, and to resist by -their elasticity the displacement of the particles within them. When -electrical force acts on the medium this displacement of the particles -within each molecule takes place until the stresses due to the elastic -reaction of the vortices balance the electrical force; the medium -behaves like an elastic body yielding to pressure until the pressure is -balanced by the elastic stress. When the electric force is removed the -cells or vortices recover their form, the electricity returns to its -former position. - -In a medium such as this waves of periodic displacement could be -set up, and would travel with a velocity depending on its electric -properties. The value for this velocity can be obtained from electrical -observations, and Maxwell showed that this velocity, so found, was, -within the limits of experimental error, the same as that of light. -Moreover, the electrical oscillations take place, like those of light, -in the front of the wave. Hence, he concludes, “the elasticity of the -magnetic medium in air is the same as that of the luminiferous medium, -if these two coexistent, coextensive, and equally elastic media are not -rather one medium.” - -The paper thus contains the first germs of the electro-magnetic theory -of light. Moreover, it is shown that the attraction between two small -bodies charged with given quantities of electricity depends on the -medium in which they are placed, while the specific inductive capacity -is found to be proportional to the square of the refractive index. - -The fourth and final part of the paper investigates the propagation of -light in a magnetic field. - -Faraday had shown that the direction of vibration in a wave of -polarised light travelling parallel to the lines of force in a magnetic -field is rotated by its passage through the field. The numerical laws -of this relation had been investigated by Verdet, and Maxwell showed -how his hypothesis of molecular vortices led to laws which agree in the -main with those found by Verdet. - -He points out that the connection between magnetism and electricity -has the same mathematical form as that between certain other pairs -of phenomena, one of which has a _linear_ and the other a _rotatory_ -character; and, further, that an analogy may be worked out assuming -either the linear character for magnetism and the rotatory character -for electricity, or the reverse. He alludes to Prof. Challis’ theory, -according to which magnetism is to consist in currents in a fluid -whose directions correspond with the lines of magnetic force, while -electric currents are supposed to be accompanied by, if not dependent -upon, a rotatory motion of the fluid about the axis of the current; -and to Von Helmholtz’s theory of a somewhat similar character. He then -gives his own reasons--agreeing with those of Sir W. Thomson (Lord -Kelvin)--for supposing that there must be a real rotation going on in -a magnetic field in order to account for the rotation of the plane of -polarisation, and, accepting these reasons as valid, he develops the -consequences of his theory with the results stated above. - -His own verdict on the theory is given in the “Electricity and -Magnetism” (vol. ii., § 831, first edition, p. 416):-- - - “A theory of molecular vortices, which I worked out at - considerable length, was published in the _Phil. Mag._ for - March, April, and May, 1861; Jan. and Feb., 1862. - - “I think we have good evidence for the opinion that some - phenomenon of rotation is going on in the magnetic field, that - this rotation is performed by a great number of very small - portions of matter, each rotating on its own axis, this axis - being parallel to the direction of the magnetic force, and that - the rotations of these different vortices are made to depend on - one another by means of some kind of mechanism connecting them. - - “The attempt which I then made to imagine a working model of - this mechanism must be taken for no more than it really is, - a demonstration that mechanism may be imagined capable of - producing a connection mechanically equivalent to the actual - connection of the parts of the electro-magnetic field. The - problem of determining the mechanism required to establish a - given species of connection between the motions of the parts of - a system always admits of an infinite number of solutions. Of - these, some may be more clumsy or more complex than others, but - all must satisfy the conditions of mechanism in general. - - “The following results of the theory, however, are of higher - value:-- - - “(1) Magnetic force is the effect of the centrifugal force of - the vortices. - - “(2) Electro-magnetic induction of currents is the effect of - the forces called into play when the velocity of the vortices - is changing. - - “(3) Electromotive force arises from the stress on the - connecting mechanism. - - “(4) Electric displacement arises from the elastic yielding of - the connecting mechanism.” - -In studying this part of Maxwell’s work, it must clearly be remembered -that he did not look upon the ether as a series of cog-wheels with -idle wheels between, or anything of the kind. He devised a mechanical -model of such cogs and idle wheels, the properties of which would in -some respects closely resemble those of the ether; from this model he -deduced, among other things, the important fact that electric waves -would travel outwards with the velocity of light. Other such models -have been devised since his time to illustrate the same laws. Prof. -Fitzgerald has actually constructed one of wheels connected together by -elastic bands, which shows clearly the kind of processes which Maxwell -supposed to go on in a dielectric when under electric force. Professor -Lodge, in his book, “Modern Views of Electricity,” has very fully -developed a somewhat different arrangement of cog-wheels to attain the -same result. - -Maxwell’s predictions as to the propagation of electric waves have -in recent days received their full verification in the brilliant -experiments of Hertz and his followers; it remains for us, before -dealing with these, to trace their final development in his hands. - -The papers we have been discussing were perhaps too material to receive -the full attention they deserved; the ether is not a series of cogs, -and electricity is something different from material idle wheels. In -his paper on “The Dynamical Theory of the Electro-magnetic Field,” -_Phil. Trans._, 1864, Maxwell treats the same questions in a more -general manner. On a former occasion he says, “I have attempted to -describe a particular kind of motion and a particular kind of strain -so arranged as to account for the phenomena. In the present paper I -avoid any hypothesis of this kind; and in using such words as electric -momentum and electric elasticity in reference to the known phenomena of -the induction of currents and the polarisation of dielectrics, I wish -merely to direct the mind of the reader to mechanical phenomena, which -will assist him in understanding the electrical ones. All such phrases -in the present paper are to be considered as illustrative and not as -explanatory.” He then continues:-- - - “In speaking of the energy of the field, however, I wish to - be understood literally. All energy is the same as mechanical - energy, whether it exists in the form of motion or in that of - elasticity, or in any other form. - - “The energy in electro-magnetic phenomena is mechanical energy. - The only question is, Where does it reside? - - “On the old theories it resides in the electrified bodies, - conducting circuits, and magnets, in the form of an unknown - quality called potential energy, or the power of producing - certain effects at a distance. On our theory it resides in - the electro-magnetic field, in the space surrounding the - electrified and magnetic bodies, as well as in those bodies - themselves, and is in two different forms, which may be - described without hypothesis as magnetic polarisation and - electric polarisation, or, according to a very probable - hypothesis, as the motion and the strain of one and the same - medium. - - “The conclusions arrived at in the present paper are - independent of this hypothesis, being deduced from experimental - facts of three kinds:-- - - “(1) The induction of electric currents by the increase or - diminution of neighbouring currents according to the changes in - the lines of force passing through the circuit. - - “(2) The distribution of magnetic intensity according to the - variations of a magnetic potential. - - “(3) The induction (or influence) of statical electricity - through dielectrics. - - “We may now proceed to demonstrate from these principles the - existence and laws of the mechanical forces, which act upon - electric currents, magnets, and electrified bodies placed in - the electro-magnetic field.” - -In his introduction to the paper, he discusses in a general way the -various explanations of electric phenomena which had been given, and -points out that-- - - “It appears, therefore, that certain phenomena in electricity - and magnetism lead to the same conclusion as those of optics, - namely, that there is an ætherial medium pervading all bodies, - and modified only in degree by their presence; that the parts - of this medium are capable of being set in motion by electric - currents and magnets; that this motion is communicated from - one part of the medium to another by forces arising from the - connection of those parts; that under the action of these - forces there is a certain yielding depending on the elasticity - of these connections; and that, therefore, energy in two - different forms may exist in the medium, the one form being - the actual energy of motion of its parts, and the other being - the potential energy stored up in the connections in virtue of - their elasticity. - - “Thus, then, we are led to the conception of a complicated - mechanism capable of a vast variety of motion, but at the - same time so connected that the motion of one part depends, - according to definite relations, on the motion of other parts, - these motions being communicated by forces arising from the - relative displacement of the connected parts, in virtue of - their elasticity. Such a mechanism must be subject to the - general laws of dynamics, and we ought to be able to work out - all the consequences of its motion, provided we know the form - of the relation between the motions of the parts.” - -These general laws of dynamics, applicable to the motion of any -connected system, had been developed by Lagrange, and are expressed -in his generalised equations of motion. It is one of Maxwell’s chief -claims to fame that he saw in the electric field a connected system to -which Lagrange’s equations could be applied, and that he was able to -deduce the mechanical and electrical actions which take place by means -of fundamental propositions of dynamics. - -The methods of the paper now under discussion were developed further -in the “Treatise on Electricity and Magnetism,” published in 1873; in -endeavouring to give some slight account of Maxwell’s work, we shall -describe it in the form it ultimately took. - -The task which Maxwell set himself was a double one; he had first to -express in symbols, in as general a form as possible, the fundamental -laws of electro-magnetism as deduced from experiments, chiefly -the experiments of Faraday, and the relations between the various -quantities involved; when this was done he had to show how these laws -could be deduced from the general dynamical laws applicable to any -system of moving bodies. - -There are two classes of phenomena, electric and magnetic, which have -been known from very early times, and which are connected together. -When a piece of sealing-wax is rubbed it is found to attract other -bodies, it is said to exert electric force throughout the space -surrounding it; when two different metals are dipped in slightly -acidulated water and connected by a wire, certain changes take place -in the plates, the water, the wire, and the space round the wire, -electric force is again exerted and a current of electricity is said -to flow in the wire. Again, certain bodies, such as the lodestone, or -pieces of iron and steel which have been treated in a certain manner, -exhibit phenomena of action at a distance: they are said to exert -magnetic force, and it is found that this magnetic force exists in the -neighbourhood of an electric current and is connected with the current. - -Again, when electric force is applied to a body, the effects may be in -part electrical, in part mechanical; the electrical state of the body -is in general changed, while in addition, mechanical forces tending to -move the body are set up. Experiment must teach us how the electrical -state depends on the electric force, and what is the connection -between this electric force and the magnetic forces which may, under -certain circumstances, be observed. Now, in specifying the electric -and magnetic conditions of the system, various other quantities, in -addition to the electric force, will have to be introduced; the first -step is to formulate the necessary quantities, and to determine the -relations between them and the electric force. - -Consider now a wire connecting the two poles of an electric battery--in -its simplest form, a piece of zinc and a piece of copper in a vessel -of dilute acid--electric force is produced at each point of the wire. -Let us suppose this force known; an electric current depending on the -material and the size of the wire flows along it, its value can be -determined at each point of the wire in terms of the electric force -by Ohm’s law. If we take either this current or the electric force -as known, we can determine by known laws the electric and magnetic -conditions elsewhere. If we suppose the wire to be straight and very -long, then, so long as the current is steady and we neglect the small -effect due to the electrostatic charge on the wire, there is no -electric force outside the wire. There is, however, magnetic force, -and it is found that the lines of magnetic force are circles round the -wire. It is found also that the work done in travelling once completely -round the wire against the magnetic force is measured by the current -flowing through the wire, and is obtained in the system of units -usually adopted by multiplying the current by 4π. This last result then -gives us one of the necessary relations, that between the magnetic -force due to a current and the strength of the current. - -Again, consider a steady current flowing in a conductor of any form or -shape, the total flow of current across any section of the conductor -can be measured in various ways, and it is found that at any time this -total flow is the same for each section of the conductor. In this -respect the flow of a current resembles that of an incompressible -fluid through a pipe; where the pipe is narrow the velocity of flow -is greater than it is where the pipe is broad, but the total quantity -crossing each section at any given instant is the same. - -Consider now two conducting bodies, two spheres, or two flat plates -placed near together but insulated. Let each conductor be connected -to one of the poles of the battery by a conducting wire. Then, for a -very short interval after the contact is made, it is found that there -is a current in each wire which rapidly dies away to zero. In the -neighbourhood of the balls there is electric force; the balls are said -to be charged with electricity, and the lines of force are curved lines -running from one ball to the other. It is found that the balls slightly -attract each other, and the space between them is now in a different -condition from what it was before the balls were charged. According -to Maxwell, _Electric Displacement_ has been produced in this space, -and the electric displacement at each point is proportional to the -electric force at that point. - -Thus, (i) when electric force acts on a conductor, it produces a -current, the current being by Ohm’s law proportional to the force: -(ii) when it acts on an insulator it produces electric displacement, -and the displacement is proportional to the force; while (iii) there -is magnetic force in the neighbourhood of the current, and the work -done in carrying a magnetic pole round any complete circuit linked -with the current is proportional to the current. The first two of -these principles give us two sets of equations connecting together the -electric force and the current in a conductor or the displacement in a -dielectric respectively; the third connects the magnetic force and the -current. - -Now let us go back to the variable period when the current is flowing -in the wires; and to make ideas precise, let the two conductors be two -equal large flat plates placed with their faces parallel, and at some -small distance apart. In this case, when the plates are charged, and -the current has ceased, the electric displacement and the force are -confined almost entirely to the space between the plates. During the -variable period the total flow at any instant across each section of -the wire is the same, but in the ordinary sense of the word there is no -flow of electricity across the insulating medium between the plates. -In this space, however, the electric displacement is continuously -changing, rising from zero initially to its final steady value when the -current ceases. It is a fundamental part of Maxwell’s theory that this -variation of electric displacement is equivalent in all respects to a -current. The current at any point in a dielectric is measured by the -rate of change of displacement at that point. - -Moreover, it is also an essential point that if we consider any section -of the dielectric between the two plates, the rate of change of the -total displacement across this section is at each moment equal to the -total flow of current across each section of the conducting wire. - -Currents of electricity, therefore, including displacement -currents, always flow in closed circuits, and obey the laws of an -incompressible fluid in that the total flow across each section of the -circuit--conducting or dielectric--is at any moment the same. - -It should be clearly remembered that this fundamental hypothesis of -Maxwell’s theory is an assumption only to be justified by experiment. -Von Helmholtz, in his paper on “The Equations of Motion of Electricity -for Bodies at Rest,” formed his equations in an entirely different -manner from Maxwell, and arrived at results of a more general -character, which do not require us to suppose that currents flow always -in closed circuits, but permit of the condensation of electricity at -points in the circuit where the conductors end and the non-conducting -part of the circuit begins. We leave for the present the question which -of the two theories, if either, represents the facts. - -We have obtained above three fundamental relations--(i) that between -electric force and electric current in a conductor; (ii) that between -electric force and electric displacement in a dielectric; (iii) that -between magnetic force and the current which gives rise to it. And -we have seen that an electric current--_i.e._ in a dielectric the -variation of the strength of an electric field of force--gives rise -to magnetic force. Now, magnetic force acting on a medium produces -“magnetic displacement,” or magnetic induction, as it is called. In -all media except iron, nickel, cobalt, and a few other substances, the -magnetic induction is proportional to the magnetic force, and the ratio -between the magnetic induction produced by a given force and the force -is found to be very nearly the same for all such media. This ratio is -known as the permeability, and is generally denoted by the symbol μ. - -A relation reciprocal to that given in (iii) above might be -anticipated, and was, in fact, discovered by Faraday. Changes in a -field of magnetic induction give rise to electric force, and hence to -displacement currents in a dielectric or to conduction currents in a -conductor. In considering the relation between these changes and the -electric force, it is simplest at first not to deal with magnetic -matter such as iron, nickel, or cobalt; and then we may say that (iv) -the work which at any instant would be done in carrying a unit quantity -of electricity round a closed circuit in a magnetic field against the -electric forces due to the field is equal to the rate at which the -total magnetic induction which threads the circuit is being decreased. -This law, summing up Faraday’s experiments on electro-magnetic -induction, gives a fourth principle, leading to a fourth series of -equations connecting together the electric and magnetic quantities -involved. - -The equations deduced from the above four principles, together with the -condition implied in the continuity of an electric current, constitute -Maxwell’s equations of the electro-magnetic field. - -If we are dealing only with a dielectric medium, the reciprocal -relation between the third and fourth principle may be made more clear -by the following statement:-- - -(A) The work done at any moment in carrying a unit quantity of -magnetism round a closed circuit in a field in which electric -displacement is varying, is equal to the rate of change of the total -electric displacement through the circuit multiplied by 4 π.[62] - -(B) The work done at any moment in carrying a unit quantity of -electricity round a circuit in a field in which the magnetic induction -is varying, is equal to the rate of change of the total magnetic -induction through the circuit. - -From these two principles, combined with the laws connecting electric -force and displacement, magnetic force and induction, and with the -condition of continuity, Maxwell obtained his equations of the field. - -Faraday’s experiments on electro-magnetic induction afford the proof of -the truth of the fourth principle. It follows from those experiments -that when the number of lines of magnetic induction which are linked -with any closed circuit are made to vary, an induced electromotive -force is brought into play round that circuit. This electromotive force -is, according to Faraday’s results, measured by the rate of decrease -in the number of lines of magnetic induction which thread the circuit. -Maxwell applies this principle to all circuits, whether conducting or -not. - -In obtaining equations to express in symbols the results of the fourth -principle just enunciated, Maxwell introduces a new quantity, to which -he gives the name of the “vector potential.” This quantity appears in -his analysis, and its physical meaning is not at first quite clear. -Professor Poynting has, however, put Maxwell’s principles in a slightly -different form, which enables us to see definitely the meaning of the -vector potential, and to deduce Maxwell’s equations more readily from -the fundamental statements. - -We are dealing with a circuit with which lines of magnetic induction -are linked, while the number of such lines linked with the circuit is -varying. Now, let us suppose the variation to take place in consequence -of the lines of induction moving outwards or inwards, as the case may -be, so as to cut the circuit. Originally there are none linked with -the circuit. As the magnetic field has grown to its present strength -lines of magnetic induction have moved inwards. Each little element of -the circuit has been cut by some, and the total number linked with the -circuit can be found by adding together those cut by each element. Now, -Professor Poynting’s statement of Maxwell’s fourth principle is that -the electrical force in the direction of any element of the circuit is -found by dividing by the length of the element the number of lines of -magnetic induction which are cut in one second by it. - -Moreover, the total number of lines of magnetic induction which have -been cut by an element of unit length is defined as the component -of the vector potential in the direction of the element; hence the -electrical force in any direction is the rate of decrease of the -component of the vector potential in that direction. We have thus a -physical meaning for the vector potential, and shall find that in the -dynamical theory this quantity is of great importance. - -Professor Poynting has modified Maxwell’s third principle in a similar -manner; he looks upon the variation in the electric displacement as -due to the motion of tubes of electric induction,[63] and the magnetic -force along any circuit is equal to the number of tubes of electric -induction cutting or cut by unit length of the circuit per second, -multiplied by 4π. - -From the equations of the field, as found by Maxwell, it is possible -to derive two sets of symmetrical equations. The one set connects the -rate of change of the electric force with quantities depending on the -magnetic force; the other set connects in a similar manner the rate of -change of the magnetic force with quantities depending on the electric -force. Several writers in recent years adopt these equations as the -fundamental relations of the field, establishing them by the argument -that they lead to consequences which are found to be in accordance with -experiment. - -We have endeavoured to give some account of Maxwell’s historical -method, according to which the equations are deduced from the laws of -electric currents and of electro-magnetic induction derived directly -from experiment. - -While the manner in which Maxwell obtained his equations is all his -own, he was not alone in stating and discussing general equations -of the electro-magnetic field. The next steps which we are about to -consider are, however, in a special manner due to him. An electrical -or magnetic system is the seat of energy; this energy is partly -electrical, partly magnetic, and various expressions can be found for -it. In Maxwell’s theory it is a fundamental assumption that energy has -position. “The electric and magnetic energies of any electro-magnetic -system,” says Professor Poynting, “reside, therefore, somewhere in the -field.” It follows from this that they are present wherever electric -and magnetic force can be shown to exist. Maxwell showed that all the -electric energy is accounted for by supposing that in the neighbourhood -of a point at which the electric force is R there is an amount of -energy per unit of volume equal to KR²/8π, K being the inductive -capacity of the medium, while in the neighbourhood of a point at which -the magnetic force is H, the magnetic energy per unit of volume is -μH²/8π, μ being the permeability. He supposes, then, that at each point -of an electro-magnetic system energy is stored according to these -laws. It follows, then, that the electro-magnetic field resembles a -dynamical system in which energy is stored. Can we discover more of -the mechanism by which the actions in the field are maintained? Now -the motion of any point of a connected system depends on that of other -points of the system; there are generally, in any machine, a certain -number of points called driving-points, the motion of which controls -the motion of all other parts of the machine; if the motion of the -driving-points be known, that of any other point can be determined. -Thus in a steam engine the motion of a point on the fly-wheel can be -found if the motion of the piston and the connections between the -piston and the wheel be known. - -In order to determine the force which is acting on any part of the -machine we must find its momentum, and then calculate the rate at -which this momentum is being changed. This rate of change will give us -the force. The method of calculation which it is necessary to employ -was first given by Lagrange, and afterwards developed, with some -modifications, by Hamilton. It is usually referred to as Hamilton’s -principle; when the equations in the original form are used they are -known as Lagrange’s equations. - -Now Maxwell showed how these methods of calculation could be applied -to the electro-magnetic field. The energy of a dynamical system is -partly kinetic, partly potential. Maxwell supposes that the magnetic -energy of the field is kinetic energy, the electric energy potential. -When the kinetic energy of a system is known, the momentum of any -part of the system can be calculated by recognised processes. Thus if -we consider a circuit in an electro-magnetic field we can calculate -the energy of the field, and hence obtain the momentum corresponding -to this circuit. If we deal with a simple case in which the conducting -circuits are fixed in position, and only the current in each circuit is -allowed to vary, the rate of change of momentum corresponding to any -circuit will give the force in that circuit. The momentum in question -is electric momentum, and the force is electric force. Now we have -already seen that the electric force at any point of a conducting -circuit is given by the rate of change of the vector potential in the -direction considered. Hence we are led to identify the vector potential -with the electric momentum of our dynamical system; and, referring to -the original definition of vector potential, we see that the electric -momentum of a circuit is measured by the number of lines of magnetic -induction which are interlinked with it. - -Again, the kinetic energy of a dynamical system can be expressed in -terms of the squares and products of the velocities of its several -parts. It can also be expressed by multiplying the velocity of each -driving-point by the momentum corresponding to that driving-point, and -taking half the sum of the products. Suppose, now, we are dealing with -a system consisting of a number of wire circuits in which currents are -running, and let us suppose that we may represent the current in each -wire as the velocity of a driving-point in our dynamical system. We can -also express in terms of these currents the electric momentum of each -wire circuit; let this be done, and let half the sum of the products of -the corresponding velocities and momenta be formed. - -In maintaining the currents in the wires energy is needed to supply -the heat which is produced in each wire; but in starting the currents -it is found that more energy is needed than is requisite for the -supply of this heat. This excess of energy can be calculated, and when -the calculation is made it is found that the excess is equal to half -the sum of the products of the currents and corresponding momenta. -Moreover, if this sum be expressed in terms of the magnetic force, it -is found to be equal to μ H²/8 π, which is the magnetic energy of the -field. Now, when a dynamical system is set in motion against known -forces, more energy is supplied than is needed to do the work against -the forces; this excess of energy measures the kinetic energy acquired -by the system. - -Hence, Maxwell was justified in taking the magnetic energy of the field -as the kinetic energy of the mechanical system, and if the strengths -of the currents in the wires be taken to represent the velocities of -the driving-points, this energy is measured in terms of the electrical -velocities and momenta in exactly the same way as the energy of a -mechanical system is measured in terms of the velocities and momenta of -its driving-points. - -The mechanical system in which, according to Maxwell, the energy is -stored is the ether. A state of motion or of strain is set up in the -ether of the field. The electric forces which drive the currents, and -also the mechanical forces acting on the conductors carrying the -currents, are due to this state of motion, or it may be of strain, in -the ether. It must not be supposed that the term electric displacement -in Maxwell’s mind meant an actual bodily displacement of the particles -of the ether; it is in some way connected with such a material -displacement. In his view, without motion of the ether particles -there would be no electric action, but he does not identify electric -displacement and the displacement of an ether particle. - -His mechanical theory, however, does account for the electro-magnetic -forces between conductors carrying currents. The energy of the system -depends on the relative positions of the currents which form part of -it. Now, any conservative mechanical system tends to set itself in -such a position that its potential energy is least, its kinetic energy -greatest. The circuits of the system, then, will tend to set themselves -so that the electro-kinetic energy of the system may be as large as -possible; forces will be needed to hold them in any position in which -this condition is not satisfied. - -We have another proof of the correctness of the value found for the -energy of the field in that the forces calculated from this value agree -with those which are determined by direct experiment. - -Again, the forces applied at the various driving-points are transmitted -to other points by the connections of the machine; the connections -are thrown into a state of strain; stress exists throughout their -substance. When we see the piston-rod and the shaft of an engine -connected by the crank and the connecting-rod, we recognise that the -work done on the piston is transmitted thus to the shaft. So, too, in -the electro-magnetic field, the ether forms the connection between the -various circuits in the field; the forces with which those circuits -act on each other are transmitted from one circuit to another by the -stresses set up in the ether. - -To take another instance, consider the electrostatic attraction between -two charged bodies. Let us suppose the bodies charged by connecting -each to the opposite pole of a battery; a current flows from the -battery setting up electric displacement in the space between the -bodies, and throwing the ether into a state of strain. As the strain -increases the current gets less; the reaction resulting from the strain -tends to stop it, until at last this reaction is so great that the -current is stopped. When this is the case the wires to the battery may -be removed, provided this is done without destroying the insulation of -the bodies; the state of strain will remain and shows itself in the -attraction between the balls. - -Looking at the problem in this manner, we are face to face with two -great questions--the one, What is the state of strain in the ether -which will enable it to produce the observed electrostatic attractions -and repulsions between charged bodies? and the other, What is the -mechanical structure of the ether which would give rise to such a state -of strain as will account for the observed forces? Maxwell gives one -answer to the first question; it is not the only answer which could -be given, but it does account for the facts. He failed to answer the -second. He says (“Electricity and Magnetism,” vol. i. p. 132):-- - - “It must be carefully borne in mind that we have made only - one step in the theory of the action of the medium. We have - supposed it to be in a state of stress, but have not in - any way accounted for this stress, or explained how it is - maintained.... I have not been able to make the next step, - namely, to account by mechanical considerations for these - stresses in the dielectric.” - -Faraday had pointed out that the inductive action between two bodies -takes place along the lines of force, which tend to shorten along their -length and to spread outwards in other directions. Maxwell compares -them to the fibres of a muscle, which contracts and at the same time -thickens when exerting force. In the electric field there is, on -Maxwell’s theory, a tension along the lines of electric force and a -pressure at right angles to those lines. Maxwell proved that a tension -K R²/8 π along the lines of force, combined with an equal pressure -in perpendicular directions, would maintain the equilibrium of the -field, and would give rise to the observed attractions or repulsions -between electrified bodies. Other distributions of stress might be -found which would lead to the same result. The one just stated will -always be connected with Maxwell’s name. It will be noticed that the -tension along the lines of force and the pressure at right angles to -them are each numerically equal to the potential energy stored per unit -of volume in the field. The value of each of the three quantities is K -R²/8 π. - -In the same way, in a magnetic field, there is a state of stress, and -on Maxwell’s theory this, too, consists of a tension along the lines -of force and an equal pressure at right angles to them, the values of -the tension and the pressure being each equal to that of the magnetic -energy per unit of volume, or μH²/8π. - -In a case in which both electric and magnetic force exists, these two -states of stress are superposed. The total energy per unit of volume -is KR²/8π + μH²/8π; the total stress is made up of tensions KR²/8π and -μH²/8π along the lines of electric and magnetic force respectively, and -equal pressures at right angles to these lines. - -We see, then, from Maxwell’s theory, that electric force produced at -any given point in space is transmitted from that point by the action -of the ether. The question suggests itself, Does the transmission take -time, and if so, does it proceed with a definite velocity depending on -the nature of the medium through which the change is proceeding? - -According to the molecular-vortex theory, we have seen that waves of -electric force are transmitted with a definite velocity. The more -general theory developed in the “Electricity and Magnetism” leads to -the same result. Electric force produced at any point travels outwards -from that point with a velocity given by 1/√(Kμ). At a distant point -the force is zero, until the disturbance reaches it. If the disturbance -last only for a limited interval, its effects will at any future time -be confined to the space within a spherical shell of constant thickness -depending on the interval; the radii of this shell increase with -uniform speed 1/√(Kμ). - -If the initial disturbance be periodic, periodic waves of electric -force will travel out from the centre, just as waves of sound travel -out from a bell, or waves of light from a candle flame. A wire carrying -an alternating current may be such a source of periodic disturbance, -and from the wire waves travel outwards into space. - -Now, it is known that in a sound wave the displacements of the air -particles take place in the direction in which the wave is travelling; -they lie at right angles to the wave front, and are spoken of as -longitudinal. In light waves, on the other hand, the displacements are, -as Fresnel proved, in the wave front, at right angles, that is, to the -direction of propagation; they are transverse. - -Theory shows that in general both these waves may exist in an elastic -solid body, and that they travel with different velocities. Of which -nature are the waves of electric displacement in a dielectric? It -can be shewn to follow as a necessary consequence of Maxwell’s views -as to the closed character of all electric currents, that waves of -electric displacement are transverse. Electric vibrations, like those -of light, are in the wave front and at right angles to the direction -of propagation; they depend on the rigidity or quasi-rigidity of the -medium through which they travel, not on its resistance to compression. - -Again, an electric current, whether due to variation of displacement -in a dielectric or to conduction in a conductor, is accompanied by -magnetic force. A wave of periodic electric displacement, then, will be -also a wave of periodic magnetic force travelling at the same rate; -and Maxwell shewed that the direction of this magnetic force also -lies in the wave front, and is always at right angles to the electric -displacement. In the ordinary theory of light the wave of linear -displacement is accompanied by a wave of periodic angular twist about -a direction lying in the wave front and perpendicular to the linear -displacement. - -In many respects, then, waves of electric displacement resemble waves -of light, and, indeed, as we proceed we shall find closer connections -still. Hence comes Maxwell’s electro-magnetic theory of light. - -It is only in dielectric media that electric force is propagated by -wave motion. In conductors, although the third and fourth of Maxwell’s -principles given on page 185 still are true, the relation between -the electric force and the electric current differs from that which -holds in a dielectric. Hence the equations satisfied by the force are -different. The laws of its propagation resemble those of the conduction -of heat rather than those of the transmission of light. - -Again, light travels with different velocities in different transparent -media. The velocity of electric waves, as has been stated, is equal to -1/√(μK); but in making this statement it is assumed that the simple -laws which hold where there is no gross matter--or, rather, where -air is the only dielectric with which we are concerned--hold also in -solid or liquid dielectrics. In a solid or a liquid, as in vacuo, the -waves are propagated by the ether. We assume, as a first step towards -a complete theory, that so far as the electric waves are concerned -the sole effect produced by the matter shews itself in a change of -inductive capacity or of permeability. It is not likely that such a -supposition should be the whole truth, and we may, therefore, expect -results deduced from it to be only approximation to the true result. - -Now, electro-magnetic experiments show that, excluding magnetic -substances, the permeability of all bodies is very nearly the same, -and differs very slightly from that of air. The inductive capacity, -however, of different bodies is different, and hence the velocity with -which electro-magnetic waves travel differs in different bodies. - -But the refraction of waves of light depends on the fact that light -travels with different velocities in different media; hence we should -expect to have waves of electric displacement reflected and refracted -when they pass from one dielectric, such as air, to another, such as -glass or gutta-percha; moreover, for light the refractive index of -a medium such as glass is the ratio of the velocity in air to the -velocity in the glass. - -Thus the electrical refractive index of glass is the ratio of the -velocity of electric waves in air to their velocity in glass. - -Now let K₀ be the inductive capacity of air, K₁ that of glass, taking -the permeability of air and glass to be the same, we have the result -that-- - - Electrical refractive index = √(K₁/K₀). - -But the ratio of the inductive capacity of glass to that of air is -known as the specific inductive capacity of glass. - -Hence, the specific inductive capacity of any medium is equal to the -square of the electrical refractive index of that medium. - -Since Maxwell’s time the mathematical laws of the reflexion and -refraction of electric waves have been investigated by various writers, -and it has been shewn that they agree exactly with those enunciated by -Fresnel for light. - -Hitherto we have been discussing the propagation of electric waves -in an isotropic medium, one which has identical properties in all -directions about a point. Let us now consider how these laws are -modified if the dielectric be crystalline in structure. - -Maxwell assumes that the crystalline character of the dielectric can -be sufficiently represented by supposing the inductive capacity to -be different in different directions; experiments have since shewn -that this is true for crystals such as Iceland Spar and Aragonite; -he assumes also, and this, too, is justified by experiment, that the -magnetic permeability does not depend on the direction. It follows -from these assumptions that a crystal will produce double refraction -and polarisation of electric waves which fall upon it, and, further, -that the laws of double refraction will be those given by Fresnel for -light waves in a doubly refracting medium. There will be two waves in -the crystal. The disturbance in each of these will be plane polarised; -their velocity and the position of their plane of polarisation can be -found from the direction in which they are travelling by Fresnel’s -construction exactly. - -Maxwell’s theory, then, would appear to indicate some close connection -between electric waves and those of light. Faraday’s experiments on -the rotation of the plane of polarisation by magnetic force shew one -phenomenon in which the two are connected, and Maxwell endeavoured to -apply his theory to explain this. Here, however, it became necessary -to introduce an additional hypothesis--there must be some connection -between the motion of the ether to which magnetic force is due and that -which constitutes light. It is impossible to give a mechanical account -of the rotation of the plane of polarisation without some assumption as -to the relation between these two kinds of motion. Maxwell, therefore, -supposes the linear displacements of a point in the ether to be those -which give rise to light, while the components of the magnetic force -are connected with these in the same way as the components of a vortex -in a liquid in vortex motion are connected with the displacements of -the liquid. He further assumes the existence of a term of special form -in the expression for the kinetic energy, and from these assumptions he -deduces the laws of the propagation of polarised light in a magnetic -field. These laws agree in the main with the results of Verdet’s -experiments. - - - - -CHAPTER X. - -DEVELOPMENT OF MAXWELL’S THEORY. - - -We have endeavoured in the preceding pages to give some account of -Maxwell’s contributions to electrical theory and the physics of the -ether. We must now consider very briefly what evidence there is to -support these views. At Maxwell’s death such evidence, though strong, -was indirect. His supporters were limited to some few English-speaking -pupils, young and enthusiastic, who were convinced, it may be, in no -small measure, by the affection and reverence with which they regarded -their master. Abroad his views had made very little way. - -In the last words of his book he writes, speaking of various -distinguished workers-- - - “There appears to be in the minds of these eminent men some - prejudice, or _à priori_ objection, against the hypothesis - of a medium in which the phenomena of radiation of light and - heat, and the electric actions at a distance, take place. It - is true that, at one time, those who speculated as to the - causes of physical phenomena were in the habit of accounting - for each kind of action at a distance by means of a special - ætherial fluid, whose function and property it was to produce - these actions. They filled all space three and four times over - with æthers of different kinds, the properties of which were - invented merely to ‘save appearances,’ so that more rational - enquirers were willing rather to accept not only Newton’s - definite law of attraction at a distance, but even the dogma - of Cotes,[64] that action at a distance is one of the primary - properties of matter, and that no explanation can be more - intelligible than this fact. Hence the undulatory theory of - light has met with much opposition, directed not against its - failure to explain the phenomena, but against its assumption of - the existence of a medium in which light is propagated. - - “We have seen that the mathematical expression for - electro-dynamic action led, in the mind of Gauss, to the - conviction that a theory of the propagation of electric - action in time would be found to be the very key-stone of - electro-dynamics. Now we are unable to conceive of propagation - in time, except either as the flight of a material substance - through space, or as the propagation of a condition of motion, - or stress, in a medium already existing in space. - - “In the theory of Neumann, the mathematical conception called - potential, which we are unable to conceive as a material - substance, is supposed to be projected from one particle to - another in a manner which is quite independent of a medium, - and which, as Neumann has himself pointed out, is extremely - different from that of the propagation of light. - - “In the theories of Riemann and Betti it would appear that the - action is supposed to be propagated in a manner somewhat more - similar to that of light. - - “But in all of these theories the question naturally - occurs:--If something is transmitted from one particle to - another at a distance, what is its condition after it has - left one particle and before it has reached the other? If - this something is the potential energy of the two particles, - as in Neumann’s theory, how are we to conceive this energy - as existing in a point of space, coinciding neither with the - one particle nor with the other? In fact, whenever energy is - transmitted from one body to another in time, there must be - a medium or substance in which the energy exists after it - leaves one body and before it reaches the other, for energy, - as Torricelli[65] remarked, ‘is a quintessence of so subtle a - nature that it cannot be contained in any vessel except the - inmost substance of material things.’ Hence all these theories - lead to a conception of a medium in which the propagation takes - place, and if we admit this medium as an hypothesis, I think - it ought to occupy a prominent place in our investigations, - and that we ought to endeavour to construct a mental - representation of all the details of its action, and this has - been my constant aim in this treatise.” - -Let us see, then, what were the experimental grounds in Maxwell’s day -for accepting as true his views on electrical action, and how since -then, by the genius of Heinrich Hertz and the labours of his followers, -those grounds have been rendered so sure that nearly the whole progress -of electrical science during the last twenty years has consisted in -the development of ideas which are to be found in the “Treatise on -Electricity and Magnetism.” - -The purely electrical consequences of Maxwell’s theory were of course -in accord with all known electrical observations. The equations of the -field accounted for the electro-magnetic forces observed in various -experiments, and from them the laws of electro-magnetic induction -could be correctly deduced; but there was nothing very special in -this. Similar equations had been obtained from the theory of action at -a distance by various writers; in fact, Helmholtz’s theory, based on -the most general form of expression for the force between two elements -of current consistent with certain experiments of Ampère’s, was more -general in its character than Maxwell’s. The destructive features of -Maxwell’s theory were: - -(1) The assumption that all currents flow in closed circuits. - -(2) The idea of energy residing throughout the electro-magnetic -field in consequence of the strains and stresses set up in the -electro-magnetic medium by the actions to which it was subject. - -(3) The identification of this electro-magnetic medium with the -luminiferous ether, and the consequent view that light is an -electro-magnetic phenomena. - -(4) The view that electro-magnetic forces arise entirely from strains -and stresses set up in the ether; the electrostatic charge of an -insulated conductor being one of the forms in which the ether strain is -manifested to us. - -(5) A dielectric under the action of electric force is said to -become polarised, and, according to Maxwell (vol. i. p. 133), all -electrification is the residual effect of the polarisation of the -dielectric. - -Now it must, I think, be admitted that in Maxwell’s day there was -direct proof of very few of these propositions. No one has even yet so -measured the displacement currents in a dielectric as to show that the -total flow across every section of a circuit is at any given moment -the same, though there are other experiments of an indirect character -which have now completely justified Maxwell’s hypothesis. Experiments -by Schiller and Von Helmholtz prove it is true that some action in -the dielectric must be taken into consideration in any satisfactory -theory; they therefore upset various theories based on direct action at -a distance, “but they tell us nothing as to whether any special form -of the dielectric theory, such as Maxwell’s or Helmholtz’s, is true or -not.” (J. J. Thomson, “Report on Electrical Theories,” B.A. Report, -1885, p. 149.) - -When Maxwell died there had been little if any experimental evidence -as to the stresses set up in a body by electric force. Fontana, Govi, -and Duter had all observed that changes take place in the volume of -the dielectric of a condenser when it is charged. Quincke had taken -up the work, and the first of his classic papers on this subject was -published in 1880, the year following Maxwell’s death. Maxwell himself -was fond of shewing an experiment in which a charged insulated sphere -was brought near to the surface of paraffin; the stress on the surface -causes a heaping up of the paraffin under the sphere. - -Kerr had shewn in 1875 that many substances become doubly refracting -under electric stress; his complete determination of the laws of this -action was published at a later date. - -As to direct measurements on electric waves, there were none; the value -of the velocity with which, if Maxwell’s theory were true, they must -travel had been determined from electrical observations of quite a -different character. Weber and Kohlrausch had measured the value of K -for air, for which μ is unity, and from their observations it follows -that the value of the wave velocity for electro-magnetic waves is about -31 × 10⁹ centimetres per second. The velocity of light was known, from -the experiments of Fizeau and Foucault, to have about this value, and -it was the near coincidence of these two values which led Maxwell to -write in 1864:-- - -“The agreement of the results seems to show that light and magnetism -are affections of the same substance, and that light is an -electro-magnetic disturbance propagated through the field according to -electro-magnetic laws.” - -By the time the first edition of the “Electricity and Magnetism” -was published, Maxwell and Thomson (Lord Kelvin) had both made -determinations of K, and had shewn that for air at least the resulting -value for the velocity of electro-magnetic waves was very nearly that -of light. - -For other substances at that date the observations were fewer still. -Gibson and Barclay had determined the specific inductive capacity -of paraffin, and found that its square root was 1·405, while its -refractive index for long waves is 1·422. Maxwell himself thought -that if a similar agreement could be shewn to hold for a number of -substances, we should be warranted in concluding that “the square root -of K, though it may not be the complete expression for the index of -refraction, is at least the most important term in it.” - -Between this time and Maxwell’s death enough had been done to more -than justify this statement. It was clear from the observations of -Boltzmann, Silow, Hopkinson, and others that there were many substances -for which the square root of the specific inductive capacity was very -nearly indeed equal to the refractive index, and good reason had been -given why in some cases there should be a considerable difference -between the two. - -Hopkinson found that in the case of glass the differences were very -large, and they have since been found to be considerable for most -solids examined, with the exception of paraffin and sulphur. For -petroleum oil, benzine, toluene, carbon-bisulphide, and some other -liquids the agreement between Maxwell’s theory and experiment is -close. For the fatty oils, such as castor oil, olive oil, sperm oil, -neatsfoot oil, and also for ether, the differences are considerable. - -It seems probable that the reason for this difference lies in the -fact that, in the light waves, we are dealing with the wave velocity -of a disturbance of an extremely short period. Now, we know that the -substances mentioned shew optical dispersion, and we have at present -no completely satisfactory theory from which we can calculate, from -experiments on very short waves, what the velocity for very long -waves will be. In most cases Cauchy’s formula has been used to obtain -the numbers given. The value of K, however, as found by experiment, -corresponds to these infinitely long waves, and to quote Professor -J. J. Thomson’s words, “the marvel is not that there should not be -substances for which the relation K = μ² does not hold, but that there -should be any for which it does.”[66] - -It has been shewn, moreover, both by Professor J. J. Thomson himself -and by Blondlot, that when the value of K is measured under very -rapidly varying electrifications, changing at the rate of about -25,000,000 to the second, the value of the inductive capacity for glass -is reduced from about 6·8 or 7 to about 2·7; the square root of this is -1·6, which does not differ much from its refractive index. The values -of the inductive capacity of paraffin and sulphur, which it will be -remembered agree fairly with Maxwell’s theory, were found to be not -greatly different in the steady and in the rapidly varying field. - -On the other hand, some experiments of Arons and Rubens in rapidly -varying fields lead to values which do not differ greatly from those -given by other methods. The theory, however, of these experiments seems -open to criticism. - -To attempt anything like a complete account of modern verifications -of Maxwell’s views and modern developments of his theory is a task -beyond our limits, but an account of Maxwell written in 1895 would be -incomplete without a reference to the work of Heinrich Hertz. - -Maxwell told us what the properties of electro-magnetic waves in air -must be. Hertz[67] in 1887 enabled us to measure those properties, and -the measurements have verified completely Maxwell’s views. - -The method of producing electrical oscillations in a conductor had -long been known. Thomson and Von Helmholtz had both pointed it out. -Schiller had examined such oscillations in 1874, and had determined the -inductive capacity of glass by their means, using oscillations whose -period varied from ·000056 to ·00012 of a second. - -These oscillations were produced by discharging a condenser through a -coil of wire having self-induction. If the electrical resistance of the -coil be not too great, the charge oscillates backwards and forwards -between the plates of the condenser until its energy is dissipated in -the heat produced in the wire, and in the electro-magnetic radiations -which leave it. - -The period of these oscillations under proper conditions is given by -the formula T = 2π√(CL) where L, the coefficient of self induction, -and _C_ the capacity of the condenser. These quantities can be -calculated, and hence the time of an oscillation is known. From such -an arrangement waves radiate out into space. If we could measure -by any method the length of such a wave we could determine its -velocity by dividing the wave length by the period. But it is clear -that since the velocity is comparable with that of light the wave -length will be enormous, unless the period is very short. Thus, a -wave, travelling with the velocity of light, whose period was ·0001 -second, such as the waves Schiller worked with, would have a length of -·0001 × 30,000,000,000 or 3,000,000 centimetres, and would be quite -unmeasurable. Before measurements on electric waves could be made it -was necessary (1) to produce waves of sufficiently rapid period, (2) to -devise means to detect them. This is what Hertz did. - -The wave length of the electrical oscillations can be reduced by -reducing either the electrical capacity of the system, or the -coefficient of self-induction of the wire. Hertz adopted both these -expedients. His vibrator, in some of his more important experiments, -consisted of two square brass plates 40 cm. in the side. To each of -these is attached a piece of copper wire about 30 cm. in length, and -each wire ends in a small highly-polished brass ball. The plates are -placed so that the wires lie in the same straight line, the brass -balls being separated by a very small air gap. The two plates are then -charged, the one positively the other negatively, until the insulation -resistance of the air gap breaks down and a discharge passes across. -Under these conditions the discharge is oscillatory. It does not -consist of a single spark, but of a series of sparks, which pass -and repass in opposite directions, until the energy of the original -charge is radiated into space or dissipated as heat; the plates are -then recharged and the process repeated. In Hertz’s experiments the -oscillator was charged by being connected to the secondary terminals of -an induction coil. - -In 1883 Professor Fitzgerald had called attention to this method of -producing electric waves in air, and had given two metres as the -minimum wave length which might be attained. In 1870 Herr von Bezold -had actually made observations on the propagation and reflection of -electrical oscillations, but his work, published as a preliminary -communication, had attracted little notice. Hertz was the first to -undertake in 1887 in a systematic manner the investigation of the -electric waves in air which proceed from such an oscillator with a view -to testing various theories of electro-magnetic action. - -It remained, however, necessary to devise an apparatus for detecting -the waves. When the waves are incident on a conductor, electric -surgings are set up in the conductor, and may, under proper conditions, -be observed as tiny sparks. Hertz used as his detector a loop of wire, -the ends of which terminated in two small brass balls. The wire was -bent so that the balls were very close together, and the sparks could -be seen passing across the tiny air gap which separated them. Such -a wire will have a definite period of its own for oscillations of -electricity with which it may be charged, and if the frequency of the -electric waves which fall on it agrees with that of the waves which -it can itself emit, the oscillations which are set up in the wire will -be stronger than under other conditions, the sparks seen will be more -brilliant.[68] Hertz’s resonator was a circle of wire thirty-five -centimetres in radius, the period for such a resonator would, he -calculated, be the same as that of his vibrator. - -There is, however, very considerable difficulty in determining the -period of an electric oscillator from its dimensions, and the value -obtained from calculation for that of Hertz’s radiator is not very -trustworthy. The complete period is, however, comparable with two -one hundredth millionths of a second; in his original papers, Hertz, -through an error, gave a value greater than this. - -With these arrangements Hertz was able to detect the presence of -electrical radiation at considerable distances from the radiator; he -was also able to measure its wave length. In the case of sound waves -the existence of nodes and loops formed under proper conditions is -well known. When waves are directly reflected from a flat surface, -interference takes place between the incident and reflected waves, -stationary vibrations are set up, and nodes and loops--places, that -is, of minimum and of maximum motion respectively--are formed. The -position of these nodes and loops can be determined by the aid of -suitable apparatus, and it can be shewn that the distance between two -consecutive nodes is half the wave length. - -Similarly when electrical vibrations fall on a reflector, a large -flat surface of metal, for example, stationary vibrations due to the -interference between the incident and reflected waves are produced, and -these give rise to electrical nodes and loops. The position of such -nodes and loops can be found by the use of Hertz’s apparatus, or in -other ways, and hence the length of the electrical waves can be found. -The existence of the nodes and loops shews that the electric effects -are propagated by wave motion. The length of the waves is found to be -definite, since the nodes and loops recur at equal intervals apart. - -If it be assumed that the frequency is known, the velocity of wave -propagation can be determined. Hertz found from his experiments that -in air the waves travelled with the velocity of light. It appears, -however, that there were two errors in the calculation which happened -to correct each other, so that neither the value of the frequency given -in Hertz’s paper nor the wave length observed is correct. - -By modifying the apparatus it was possible to measure the wave length -of the waves transmitted along a copper wire, and hence, again -assuming the period of oscillation, to calculate the velocity of wave -propagation along the wire. Hertz made the experiment, and found from -his first observations that the waves were propagated along the wire -with a finite velocity, but that the velocity differed from that in -air. The half-wave length in the wire was only about 2·8 metres; that -in air was about 4·5 metres. - -Now, this experiment afforded a crucial test between the theories of -Maxwell and Von Helmholtz. According to the former, the waves do not -travel in the wire at all; they travel through the air alongside the -wire, and the wave length observed by Hertz ought to have been the same -as in air. According to Von Helmholtz, the two velocities observed -by Hertz should have been different, as, indeed, they were, and the -experiment appeared to prove that Maxwell’s theory was insufficient and -that a more general one, such as that of Von Helmholtz, was necessary. -But other experiments have not led to the same result. Hertz himself, -using more rapid oscillations in some later measurements, found that -the wave length of the electric waves from a given oscillator was the -same whether they were transmitted through free space or conducted -along a wire.[69] Lecher and J. J. Thomson have arrived at the same -result; but the most complete experiments on this point are those of -Sarasin and De la Rive. - -It may be taken, then, as established that Maxwell’s theory is -sufficient, and that the greater generality of Von Helmholtz is -unnecessary. - -In a later paper Hertz showed that electric waves could be reflected -and refracted, polarised and analysed, just like light waves. In his -introduction to his “Collected Papers” he writes (p. 19):-- - - “Casting now a glance backwards, we see that by the experiments - above sketched the propagation in time of a supposed action - at a distance is for the first time proved. This fact forms - the philosophic result of the experiments, and indeed, in a - certain sense, the most important result. The proof includes - a recognition of the fact that the electric forces can - disentangle themselves from material bodies, and can continue - to subsist as conditions or changes in the state of space. The - details of the experiments further prove that the particular - manner in which the electric force is propagated exhibits the - closest analogy[70] with the propagation of light; indeed, that - it corresponds almost completely to it. The hypothesis that - light is an electrical phenomenon is thus made highly probable. - To give a strict proof of this hypothesis would logically - require experiments upon light itself. - - “What we here indicate as having been accomplished by the - experiments is accomplished independently of the correctness - of particular theories. Nevertheless, there is an obvious - connection between the experiments and the theory in connection - with which they were really undertaken. Since the year 1861 - science has been in possession of a theory which Maxwell - constructed upon Faraday’s views, and which we therefore call - the Faraday-Maxwell theory. This theory affirms the possibility - of the class of phenomena here discovered just as positively - as the remaining electrical theories are compelled to deny - it. From the outset Maxwell’s theory excelled all others in - elegance and in the abundance of the relations between the - various phenomena which it included. - - “The probability of this theory, and therefore the number of - its adherents, increased from year to year. But as long as - Maxwell’s theory depended solely upon the probability of its - results, and not on the certainty of its hypotheses, it could - not completely displace the theories which were opposed to it. - - “The fundamental hypotheses of Maxwell’s theory contradicted - the usual views, and did not rest upon the evidence of decisive - experiments. In this connection we can best characterise the - object and the result of our experiments by saying: The object - of these experiments was to test the fundamental hypotheses of - the Faraday-Maxwell theory, and the result of the experiments - is to confirm the fundamental hypotheses of the theory.” - -Since Maxwell’s death volumes have been written on electrical -questions, which have all been inspired by his work. The standpoint -from which electrical theory is regarded has been entirely changed. The -greatest masters of mathematical physics have found, in the development -of Maxwell’s views, a task that called for all their powers, and the -harvest of new truths which has been garnered has proved most rich. But -while this is so, the question is still often asked, What is Maxwell’s -theory? Hertz himself concludes the introduction just referred to with -his most interesting answer to this question. Prof. Boltzmann has made -the theory the subject of an important course of lectures. Poincaré, -in the introduction to his “Lectures on Maxwell’s Theories and the -Electro-magnetic Theory of Light,” expresses the difficulty, which many -feel, in understanding what the theory is. “The first time,” he says, -“that a French reader opens Maxwell’s book a feeling of uneasiness, -often even of distrust, is mingled with his admiration. It is only -after prolonged study, and at the cost of many efforts, that this -feeling is dissipated. Some great minds retain it always.” And again -he writes: “A French _savant_, one of those who have most completely -fathomed Maxwell’s meaning, said to me once, ‘I understand everything -in the book except what is meant by a body charged with electricity.’” - -In considering this question, Poincaré’s own remark--“Maxwell does -not give a mechanical explanation of electricity and magnetism, he is -only concerned to show that such an explanation is possible”--is most -important. - -We cannot find in the “Electricity” an answer to the question--What is -an electric charge? Maxwell did not pretend to know, and the attempt to -give too great definiteness to his views on this point is apt to lead -to a misconception of what those views were. - -On the old theories of action at a distance and of electric and -magnetic fluids attracting according to known laws, it was easy to be -mechanical. It was only necessary to investigate the manner in which -such fluids could distribute themselves so as to be in equilibrium, -and to calculate the forces arising from the distribution. The problem -of assigning such a mechanical structure to the ether as will permit -of its exerting the action which occurs in an electro-magnetic field -is a harder one to solve, and till it is solved the question--What is -an electric charge?--must remain unanswered. Still, in order to grasp -Maxwell’s theory this knowledge is not necessary. - -The properties of ether in dielectrics and in conductors must be quite -different. In a dielectric the ether has the power of storing energy by -some change in its configuration or its structure; in a conductor this -power is absent, owing probably to the action of the matter of which -the conductor is composed. - -When we are said to charge an insulated conductor we really act on the -ether in the neighbourhood of the body so as to store it with energy; -if there be another conductor in the field we cannot store energy in -the ether it contains. As, then, we pass from the outside of this -conductor to its interior there is a sudden change in some mechanical -quantity connected with the ether, and this change shows itself as a -force of attraction between the two conductors. Maxwell called the -change in structure, or in property, which occurs when a dielectric -is thus stored with electrostatic energy, _Electric Displacement_; if -we denote it by D, then the electric force R is equal to 4πD/K, and -hence the energy in a unit of volume is 2πD²/K, where K is a quantity -depending on the insulator. - -Now, D, the electric displacement, is a quantity which has direction -as well as magnitude. Its value, therefore, at any point can be -represented by a straight line in the usual way; inside a conductor it -is zero. The total change in D, which takes place all over the surface -of a conductor as we enter it from the outside measures, according -to Maxwell, the total charge on the conductor. At points at which -the lines representing D enter the conductor the charge is negative; -at points at which they leave it the charge is positive; along the -lines of the displacement there exists throughout the ether a tension -measured by 2πD²/K; at right angles to these lines there is a pressure -of the same amount. - -In addition to the above the components of the displacement D must -satisfy certain relations which can only be expressed in mathematical -form, the physical meaning of which it is difficult to state in -non-mathematical language. - -When these relations are so expressed the problem of finding the value -of the displacement at all points of space becomes determinate, and -the forces acting on the conductors can be obtained. Moreover, the -total change of displacement on entering or leaving a conductor can be -calculated, and this gives the quantity which is known as the total -electrical charge on the conductor. The forces obtained by the above -method are exactly the same as those which would exist if we supposed -each conductor to be charged in the ordinary sense with the quantities -just found, and to attract or repel according to the ordinary laws. - -If, then, we define electric displacement as that change which takes -place in a dielectric when it becomes the seat of electrostatic -energy, and if, further, we suppose that the change, whatever it -be mechanically, satisfies certain well-known laws, and that in -consequence certain pressures and tensions exist in the dielectric, -electrostatic problems can be solved without reference to a charge of -electricity residing on the conductors. - -Something such as this, it appears to me, is Maxwell’s theory of -electricity as applied to electrostatics. It is not necessary, in order -to understand it, to know what change in the ether constitutes electric -displacement, or what is an electric charge, though, of course, such -knowledge would render our views more definite, and would make the -theory a mechanical one. - -When we turn to magnetism and electro-magnetism, Maxwell’s theory -develops itself naturally. Experiment proves that magnetic induction is -connected with the rate of change of electric displacement, according -to the laws already given. If, then, we knew the nature of the change -to which the name “electric displacement” has been given, the nature -of magnetic induction would be known. The difficulties in the way of -any mechanical explanation are, it is true, very great; assuming, -however, that some mechanical conception of “electric displacement” -is possible, Maxwell’s theory gives a consistent account of the other -phenomena of electro-magnetism. - -Again, we have, it is true, an electro-magnetic theory of light, but -we do not know the nature of the change in the ether which affects -our eyes with the sensation of light. Is it the same as electric -displacement, or as magnetic induction, or since, when electric -displacement is varying, magnetic induction always accompanies it, is -the sensation of light due to the combined effect of the two? - -These questions remain unanswered. It may be that light is neither -electric displacement nor magnetic induction, but some quite different -periodic change of structure of the ether, which travels through the -ether at the same rate as these quantities, and obeys many of the same -laws. - -In this respect there is a material difference between the ordinary -theory of light and the electro-magnetic theory. The former is a -mechanical theory; it starts from the assumption that the periodic -change which constitutes light is the ordinary linear displacement of a -medium--the ether--having certain mechanical properties, and from those -properties it deduces the laws of optics with more or less success. - -Lord Kelvin, in his labile ether, has devised a medium which could -exist and which has the necessary mechanical properties. The periodic -linear displacements of the labile ether would obey the laws of -light, and from the fundamental hypotheses of the theory, a mechanical -explanation, reasonably satisfactory in its main features, can be given -of most purely optical phenomena. The relations between light and -electricity, or light and magnetism, are not, however, touched by this -theory; indeed, they cannot be touched without making some assumption -as to what electric displacement is. - -In recent years various suggestions have been made as to the nature -of the change which constitutes electric displacement. One theory, -due to Von Helmholtz, supposes that the electro-kinetic momentum, or -vector potential of Maxwell, is actually the momentum of the moving -ether; according to another, suggested, it would appear originally -in a crude form by Challis, and developed within the last few months -in very satisfactory detail by Larmor, the velocity of the ether is -magnetic force; others have been devised, but we are still waiting for -a second Newton to give us a theory of the ether which shall include -the facts of electricity and magnetism, luminous radiation, and it may -be gravitation.[71] - -Meanwhile we believe that Maxwell has taken the first steps towards -this discovery, and has pointed out the lines along which the future -discoverer must direct his search, and hence we claim for him a -foremost place among the leaders of this century of science. - - - - -FOOTNOTES - - -[1] A full biographical account of the Clerk and Maxwell families is -given in a note by Miss Isabella Clerk in the “Life of James Clerk -Maxwell,” and from this the above brief statement has been taken. - -[2] “Life of J. C. Maxwell,” p. 26. - -[3] “Life of J. C. Maxwell,” p. 27. - -[4] “Life of J. C. Maxwell,” p. 49. - -[5] “Life of J. C. Maxwell,” p. 52. - -[6] “Life of J. C. Maxwell,” p. 56. - -[7] “Life of J. C. Maxwell,” p. 67. - -[8] “Life of J. C. Maxwell,” p. 75. - -[9] Professor Garnett in _Nature_, November 13th, 1879. - -[10] “Life of J. C. Maxwell,” p. 105. - -[11] “Life of J. C. Maxwell,” p. 116. - -[12] “Life of J. C. Maxwell,” pp. 123–129. - -[13] “Life of J. C. Maxwell,” p. 190. - -[14] Dean of Canterbury. - -[15] Master of Trinity. - -[16] “Life of J. C. Maxwell,” p. 174. - -[17] “Life of J. C. Maxwell,” p. 195. - -[18] “Life of J. C. Maxwell,” p. 207. - -[19] “Life of J. C. Maxwell,” p. 208. - -[20] “Life of J. C. Maxwell,” p. 210. - -[21] “Life of J. C. Maxwell,” p. 211. - -[22] “Life of J. C. Maxwell,” p. 216. - -[23] “Life of J. C. Maxwell,” p. 256. - -[24] “Life of J. C. Maxwell,” p. 267. - -[25] “Life of J. C. Maxwell,” p. 269. - -[26] “Life of J. C. Maxwell,” p. 278. - -[27] “Life of J. C. Maxwell,” p. 292. - -[28] “Life of J. C. Maxwell,” p. 303. - -[29] “Life of J. C. Maxwell,” p. 259. - -[30] B.A. Report, Newcastle, 1863. - -[31] “Life of J. C. Maxwell,” p. 340. - -[32] “Life of J. C. Maxwell,” p. 332. - -[33] “Life of J. C. Maxwell,” p. 336. - -[34] The Professors who were consulted were Challis, Willis, Stokes, -Cayley, Adams, and Liveing. - -[35] “Life of J. C. Maxwell,” p. 349. - -[36] “Life of J. C. Maxwell,” p. 381. - -[37] “Life of J. C. Maxwell,” p. 379. - -[38] An account of the laboratory is given in _Nature_, vol. x., p. 139. - -[39] The Chancellor continued to take to the end of his life a warm -interest in the work at the laboratory. In 1887, the Jubilee year, as -Proctor--at the same time I held the office of Demonstrator--it was -my duty to accompany the Chancellor and other officers to Windsor to -present an address from the University to Her Majesty. I was introduced -to the Chancellor at Paddington, and he at once began to question me -closely about the progress of the laboratory, the number of students, -and the work being done there, showing himself fully acquainted with -recent progress. - -[40] In 1894 the list contained, in Part II., sixteen names, and in -Part I., one hundred and three names. - -[41] Under the new regulations Physics was removed from the first part -of the Tripos and formed, with the more advanced parts of Astronomy -and Pure Mathematics, a part by itself, to which only the Wranglers -were admitted. Thus the number of men encouraged to read Physics was -very limited. This pernicious system was altered in the regulations -at present in force, which came into action in 1892. Part I. of the -Mathematical Tripos now contains Heat, Elementary Hydrodynamics -and Sound, and the simpler parts of Electricity and Magnetism, and -candidates for this examination do come to the laboratory, though not -in very large numbers. The more advanced parts both of Mathematics and -Physics are included in Part II. - -[42] “Life of J. C. Maxwell,” p. 383. - -[43] “Statique Expérimentale et Théorique des Liquides soumis aux -seules Forces Moléculaires.” Par J. Plateau, Professeur à l’Université -de Gaud. - -[44] The “Red Lions” are a club formed by Members of the British -Association to meet for relaxation after the graver labours of the day. - -[45] “Leonum arida nutrix.”--_Horace._ - -[46] _v.r._, endless. - -[47] “Life of J. C. Maxwell,” p. 394. - -[48] “Life of J. C. Maxwell,” p. 404. - -[49] In his “Hydrodynamics,” published in 1738, Daniel Bernouilli -had discussed the constitution of a gas, and had proved from general -considerations that the pressure, if it arose from the impact of a -number of moving particles, must be proportional to the square of their -velocity. (_See_ “Pogg. Ann.,” Bd. 107, 1859, p. 490.) - -[50] The proof is as follows:-- - -If σ be the specific heat at constant volume, σ′ at constant pressure, -and consider a unit of mass of gas at pressure p and volume v, let the -volume increase by an amount dv, while the temperature dy. - - Thus σ′dT = σdT + pdv - - But pv = ⅔T/m - - Hence p being constant, - - pdv = ⅔ dT/m - Therefore σ′ = σ + ⅔ 1/m - -Now suppose an amount of heat, dH, is given to a single molecule and -that its temperature is T. Its specific heat is σ, and - - dH = σmdT - But dH = βdT - Therefore β = σm - - Hence 1/m = σ/β - - Thus σ′ = σ(1 + 2/(3β)) - - And σ′/σ = γ - - Therefore γ = 1 + 2/(3β) - - Or β = 2/(3(γ-1)) - - -[51] Owing to an error of calculation the actual value obtained by -Maxwell from these observations for the coefficient of viscosity is too -great. More recent observers have found lower values than those given -by him; the difference is thus explained. - -[52] Studien über das Gleichgewicht der lebendigen Kraft zwischen -bewegten materiellen Punkten Sitz d. k. Akad Wien, Band LVIII., 1868. - -[53] Another supposition which might be made, and which is necessary -in order to explain various actions observed in a compound gas under -electric force, is that the parts of which a molecule is composed are -continually changing. Thus a molecule of steam consists of two parts of -hydrogen, one of oxygen, but a given molecule of oxygen is not always -combined with the same two molecules of hydrogen; the particles are -continually changed. In Maxwell’s paper an hypothesis of this kind is -not dealt with. - -[54] _Nature_, vol. 1., p. 152 (December 13th, 1894). - -[55] See papers by Mr. Capstick, _Phil. Trans._, vols. 185–186. - -[56] _Nature_, vol. x. - -[57] An historical account of the development of the science of -electricity will be found in the article “Electricity” in the -_Encyclopædia Britannica_, ninth edition, by Professor Chrystal. - -[58] Thomson (Lord Kelvin), “Papers on Electrostatics and Magnetism,” -p. 15. - -[59] J. J. Thomson, B.A., Report, 1885, pp. 109, 113, Report on -Electrical Theories. - -[60] Papers on “Electrostatics,” etc., p. 26. - -[61] It is difficult to explain without analysis exactly what is -measured by Maxwell’s Vector Potential. Its rate of change at any -point of space measures the electromotive force at that point, so far -as it is due to variations of the electric current in neighbouring -conductors; the magnetic induction depends on the first differential -coefficients of the components of the electro-tonic state; the -electric current is related to their second differential coefficients -in the same manner as the density of attracting matter is related -to the potential it produces. In language which is now frequently -used in mathematical physics, the electromotive force at a point -due to magnetic induction is proportioned to the rate of change of -the Vector Potential, the magnetic induction depends on the “curl” -of the Vector Potential, while the electric current is measured by -the “concentration” of the Vector Potential. From a knowledge of the -Vector Potential these other quantities can be obtained by processes of -differentiation. - -[62] The 4 π is introduced because of the system of units usually -employed to measure electrical quantities. If we adopted Mr. Oliver -Heaviside’s “rational units,” it would disappear, as it does in (B). - -[63] For an exact statement as to the relation between the directions -of the lines of electric displacement and of the magnetic force, -reference must be made to Professor Poynting’s paper, _Phil. Trans._, -1885, Part II., pp. 280, 281. The ideas are further developed in a -series of articles in the _Electrician_, September, 1895. Reference -should also be made to J. J. Thomson’s “Recent Researches in -Electricity and Magnetism.” - -[64] Preface to Newton’s “Principia,” 2nd edition. - -[65] “Lezioni Accademiche” (Firenze, 1715), p. 25. - -[66] In his sentence μ stands for the refractive index. - -[67] Hertz’s papers have been translated into English by D. E. Jones, -and are published under the title of _Electric Waves_. - -[68] Some of the consequences of this electrical resonance have been -very strikingly shown by Professor Oliver Lodge. _See_ _Nature_, -February 20th, 1890. - -[69] Hertz’s original results were no doubt affected by waves reflected -from the walls and floor of the room in which he worked. An iron -stove also, which was near his apparatus, may have had a disturbing -influence; but for all this, it is to his genius and his brilliant -achievements that the complete establishment of Maxwell’s theory is due. - -[70] The analogy does not consist only in the agreement between the -more or less accurately measured velocities. The approximately equal -velocity is only one element among many others. - -[71] For a very suggestive account of some possible theories, -reference should be made to the presidential address of Professor W. M. -Hicks to Section A of the British Association at Ipswich in 1895. - - - - -INDEX. - - - Aberdeen, Maxwell elected Professor at, 45; - formation of University of, 51 - - Adams, W. G., succeeds Maxwell as Professor at King’s College, - London, 58 - - Adams Prize, The, 48; - gained by Maxwell, 50 - - Ampère, 155, 204 - - Ampère’s Law, 155, 156 - - _Annals of Philosophy_, Thomson’s, 112, 113 - - “Apostles,” club so called, 30, 89 - - Arago, 157 - - Aragonite, 200 - - Atom, article by Maxwell in _Encyclopædia Britannica_, 108 - - Avogadros’ Law, 117, 124 - - - Bakerian Lecture, delivered by Maxwell, 58 - - Berkeley on the Theory of Vision, 38 - - Bernouilli, D., 113 - - Blackburne, Professor, 16 - - Blore, Rev. E. W., 67 - - Boehm, Bust of Maxwell by, 90 - - Boltzmann, Dr., 135, 137, 138, 144, 216 - - Boltzmann-Maxwell Theory, The, 140, 145 - - Boscovitch on Atoms, 108, 109 - - Boyle’s Law, 114, 117, 124 - - Brewster, Sir David, on Colour Sensation, 99 - - British Association, Maxwell and, 42,54; - Lecture before, 80–82; - Lines on President’s address, 83, 84 - - Butler, Dr. H. M., extract from sermon on Maxwell, 32–35 - - Bryan, G. H., 141, 143 - - - Cambridge, Maxwell at, 28–46; - Mathematical Tripos at, 60; - Foundation of Professorship of Experimental Physics at, 66 - - _Cambridge and Dublin Mathematical Journal_, Papers by Maxwell in, 30 - - Campbell, Professor L., 9, 10, 12, 14, 22, 52, 57, 79 - - Cauchy’s Formula, 208 - - Cavendish, Henry, 73, 74; - Works of, edited by Maxwell, 87, 154, 155 - - Cavendish Laboratory, built and presented to University of - Cambridge, 73, 74 - - Cay, Miss Frances, 11 - - Cayley Portrait Fund, lines to Committee, 86 - - Challis, Professor, 49 - - Charles’ Law, 124 - - Chemical Society, Maxwell’s lecture before, 80–82 - - Clausius, on kinetic theory of gases, 119, 129, 130, 137 - - Clerks of Penicuik, The, 9, 10 - - Colour Perception, 94 - - Colour Sensation, Young on, 97, 98; - Sir D. Brewster on, 99 - - Colours, paper by Maxwell, on, 40, 41; - Helmholtz on, 99 - - Conductors and Insulators, Distinction between, 173 - - Cookson, Dr., 61 - - Corsock, Maxwell buried at, 90 - - Cotes, 202 - - Coulomb, 154 - - Curves, investigated by Maxwell, 19 - - - Daniell’s cells, 77 - - Democritus, 108 - - Demonstrator of Physics, W. Garnett appointed, 75 - - Description of Oval Curves, first paper by Maxwell, 19 - - Devonshire, Duke of, Cavendish Laboratory built by, 73, 74; - Letter of Thanks from University of Cambridge, 74 - - Dewar, Miss K. M., her marriage to Maxwell, 51 - - Dickinson, Lowes; Portrait of Maxwell by, 90 - - Diffusion of gases, 128 - - Discs for colour experiments, 99–101 - - Droop, H. R., 57 - - Dynamical Theory of the Electro-magnetic Field, Maxwell on, 57, 177 - - Dynamical Theory of Gases, Maxwell on, 58, 134 - - - Edinburgh Academy, Maxwell’s school-life at, 13–18 - - Edinburgh, Royal Society of, Maxwell at meetings of, 18 - - Edinburgh, University of, Maxwell at, 22 - - Elastic Spheres, 144 - - Electric Displacement, 218, 219, 220 - - Electrical Theories, 94, 154, 155 - - Electricity and Magnetism, Maxwell’s book on, 59, 77, 79, 147, 155, - 156, 176, 180–201; - papers by Lord Kelvin on, 161–2; - Application of Mathematical Analysis to, paper by G. Green, 158 - - Electricity, Modern Views of, by Professor Lodge, 177 - - Electro-kinetic Momentum, 221 - - Electro-magnetic Field, Dynamical Theory of, Maxwell on, 57, 177 - - Electro-magnetic Induction, 157 - - Electro-magnetic Theory of Light, 174 - - Electro-tonic State, 164 - - Electrostatic Induction, Faraday on, 159 - - _Encyclopædia Britannica_, articles by Maxwell in, 80, 108, 146 - - Ether, labile, 220 - - Experimental Physics, foundation of Professorship at Cambridge, 66; - Election of Maxwell, 68 - - - Faraday on electrical science, 157; - on electrostatic induction, 159 - - Faraday’s Lines of Force, paper by Maxwell on, 44, 45, 148–153 - - Fawcett, W. M., architect of Cavendish Laboratory, 73 - - Fitzgerald, Professor, 177, 211 - - Forbes, Professor J. D., 18, 44, 54; - friendship with Maxwell, 19; - paper on Theory of Glaciers, 19; - resigns Professorship at Edinburgh, 54 - - - Galvani, 155 - - Garnett, W., appointed Demonstrator of Physics at Cambridge, 75; - Life of Maxwell by, 94 - - Gases, Molecular theory of, 57, 108; - Waterston on general theory of, 118; - Clausius on, 119; - diffusion of, 128 - - Gauss’ Theory, 156 - - Gay Lussac’s Law, 117 - - General Theory of Gases, Waterston on, 118; - Clausius on, 119 - - Glenlair, home of Maxwell, 11, 23; - laboratory at, 24; - Maxwell’s life at, 58, 59; - “Electricity and Magnetism” written at, 79 - - Gordon, J. E. H., 77, 78 - - Green, G., of Nottingham, paper on electricity and magnetism, 158; - inventor of term “Potential,” 158 - - - Hamilton, Sir W. R., 22 - - Hamilton’s Principle, 190 - - Heat, Text-book on, by Maxwell, 79 - - Helmholtz, 99, 156, 157, 175, 221 - - Henry, J., of Washington, on electro-magnetic induction, 157 - - Herapath on molecules, 112–116 - - Hertz, Heinrich, 204, 209–213 - - Hicks, W. M., 221 - - Hockin, C., 56 - - Holman, Professor, 133 - - - Iceland Spar, 200 - - Insulators and Conductors, Distinction between, 173 - - - Jenkin, Fleeming, 55, 56 - - - Kelland, Professor, 22 - - Kelvin, Lord, 16, 142, 158, 159, 160, 168; - on the Uniform Motion of Heat, 160; - papers on Electricity and Magnetism, 161, 162 - - Kinetic energy, 124, 129, 136, 139, 191 - - King’s College, London, Maxwell elected Professor at, 54 - - Kohlrausch, 206 - - Kundt, 132 - - - Labile Ether, 220 - - Laboratory at Glenlair, 24 - - Lagrange, 179 - - Lagrange’s Equations, 179, 190 - - Laplace, 155 - - Larmor, J., 141, 142 - - Lecher, 214 - - Lenz, 157 - - Litchfield, R. B., 46 - - Light, Electro-magnetic Theory of, 174; - Waves of, 198, 199 - - Lodge, Professor, book on Modern Views of Electricity, 177 - - Lucretius, 108 - - Luminous Radiation, 221 - - - Mathematical Tripos at Cambridge, subjects, 60; - Maxwell an examiner for, 60, 80; - experimental work in, 76 - - Matter and Motion, Maxwell on, 79 - - Maxwell, James Clerk, parentage and birthplace, 10, 11; - childhood and school-days, 12–18; - his mother’s death, 13; - first lessons in geometry, 17; - attends meetings of Royal Society of Edinburgh, 18; - his first published paper, 19; - friendship with Professor Forbes, 19; - his polariscope, 20; - enters the University of Edinburgh, 22; - papers on Rolling Curves and Elastic Solids, 23; - vacations at Glenlair, 23; - laboratory at Glenlair, 24; - undergraduate life at Cambridge, 28–36; - elected scholar of Trinity, 29; - illness at Lowestoft, 29; - his friends at Cambridge, 30; - Tripos and degree, 35–37; - early researches, 38–44; - paper on Colours, 40, 41; - elected Fellow of Trinity, 43; - Lecturer at Trinity, 43; - Professor at Aberdeen, 45; - his father’s death, 45; - gains the Adams Prize, 50; - marriage, 51; - powers as teacher and lecturer, 52, 53; - Professor at King’s College, London, 54; - gains the Rumford Medal, 55; - delivers Bakerian lecture, 58; - resigns Professorship at King’s College, London, 58; - life at Glenlair, 58, 59; - visit to Italy, 59; - Examiner for Mathematical Tripos, 60, 80; - elected Professor of Experimental Physics at Cambridge, 68; - Introductory Lecture, 68–72; - Examiner for Natural Sciences Tripos, 79; - articles in _Encyclopædia Britannica_, 80, 118, 146; - papers in Nature, 80; - lectures before British Association and Chemical Society, 80–82; - humorous poems, 83–87; - delivers Rede Lecture on the Telephone, 89; - last illness and death, 89, 90; - buried at Corsock, 90; - bust and portrait, 90; - religious views, 91, 92 - - Maxwell, John Clerk, 10, 11 - - Meyer, O. E., 133 - - Mill’s Logic, 38 - - Molecular Evolution, Lines on, 85 - - ---- Physics, 94 - - ---- Constitution of Bodies, Maxwell on, 146 - - ---- Theory of Gases, 57, 108 - - Molecules, 109, 110; - Herapath on, 112–116; - lecture by Maxwell on, 146 - - Motion of Saturn’s Rings, subject for Adams Prize, 49 - - Munro, J. C., 40, 56, 68, 82 - - - Natural Sciences Tripos, Maxwell Examiner for, 79 - - _Nature_, papers by Maxwell in, 80 - - Neumann, F. E., 156, 157 - - Newton’s Lunar Theory and Astronomy, 50 - - ---- Principia, 202 - - Nicol, Wm., inventor of the polarising prism, 20 - - Niven, W. D., 27, 46, 51, 52, 60, 78, 87, 88, 93 - - - Obermeyer, 134 - - Ohm’s Law, 77 - - Ophthalmoscope devised by Maxwell, 83 - - Oval Curves, Description of, Maxwell’s first paper, 19 - - - Parkinson, Dr., 49 - - _Philosophical Magazine_, 56, 99, 115, 120, 133, 142 - - _Philosophical Transactions_, 56, 89, 132, 145 - - Physical Lines of Force, Maxwell on, 56, 158 - - Physics, Instruction in, at Cambridge, 61; - Report of Syndicate on, 62–64; - Demonstrator appointed, 75 - - Poincaré, 216 - - Poisson, 44; - on distribution of electricity, 155 - - Polariscope, made by Maxwell, 20 - - “Potential,” term invented by G. Green, 158; - the Vector, 165, 221 - - Poynting, Professor, 187–189 - - Puluj, 134 - - - Quincke, 206 - - - Radiation, Luminous, 221 - - Rarefied Gases, Stresses in, paper by Maxwell, 135, 145 - - Rayleigh, Lord, 67, 77 - - Rede Lecture on the Telephone, delivered by Maxwell, 89 - - Report on Electrical Theories, J. J. Thomson, 204 - - ---- of Syndicate as to instruction in Physics at Cambridge, 62–64 - - Robertson, C. H., 28 - - Rolling Curves, Maxwell on, 23 - - Royal Society, The, Maxwell and, 55; - Transactions of, 89 - - Rumford Medal gained by Maxwell, 55, 106 - - - Sabine, Major-General, Vice-President of Royal Society, 106 - - Smith’s Prizes, 36 - - Standards of Electrical Resistance, Committee on, 55 - - Stewart, Balfour, 56, 125 - - Stresses in Rarefied Gases, Maxwell on, 135, 155 - - - Tait, Professor P. G., 21, 26, 94 - - Tayler, Rev. C. B., 29 - - Telephone, Rede Lecture by Maxwell on, 89 - - Theory of Glaciers, Prof. Forbes on, 19 - - Thomson, J. J., 157, 208; - Report on Electrical Theories, 205 - - Thomson’s _Annals of Philosophy_, 112, 113 - - - Uniform Motion of Heat in Homogeneous Solid Bodies, paper by Lord - Kelvin, 160, 161 - - University Commission, 47, 48, 62 - - Urr, Vale of, 11 - - - Vector Potential, The, 165, 221 - - Viscosity of Gases, Experiments on, 58, 125, 132 - - Volta, Inventor of voltaic pile, 155 - - - Waterston, J. J., on molecular theory of gases, 114, 115; - on general theory of gases, 118 - - Waves of Light, 198, 199 - - Weber, W., 156, 206 - - Wedderburn, Mrs., 14 - - Wheatstone’s Bridge, 77 - - Williams, J., Archdeacon of Cardigan, 16 - - Willis, Professor, 44 - - Wilson, E., lines in memory of, 86, 87 - - - Young, T., on colour sensation, 97, 98 - - -PRINTED BY CASSELL & COMPANY, LIMITED, LA BELLE SAUVAGE, LONDON, E.C. - - - - - * * * * * * - - - - -Transcriber’s note: - -Punctuation, hyphenation, and spelling were made consistent when a -predominant preference was found in the original book; otherwise they -were not changed. - -Simple typographical errors were corrected; unpaired quotation -marks were remedied when the change was obvious, and otherwise left -unpaired. - -Illustrations in this eBook have been positioned between paragraphs -and outside quotations. - -Footnotes, originally at the bottoms of pages, have been collected, -renumbered, and placed just before the Index. - -The Index was not checked for proper alphabetization or correct page -references. - -Some values in the original book are known today to be incorrect, but -have not been changed here. - -Page 133: The last equation on the page, - - μ = μ₀ (1 + .00275 t - .00000034 t²) - -was misprinted as - - μ = μ₀ {1 + .00275 t .00000034 t²}. - -It is shown here with corrections based on its cited source: - - https://archive.org/details/s05philosophicalmag21londuoft/page/212 - -Page 144: “possibly of ether atoms bound with them” was printed that -way, but “ether” may be a misprint for “other”. - -Page 170: “hence at C, where they touch” was printed as “A”, but Figure -1 at that point is labelled “C”. - - - -***END OF THE PROJECT GUTENBERG EBOOK JAMES CLERK MAXWELL AND MODERN -PHYSICS*** - - -******* This file should be named 65359-0.txt or 65359-0.zip ******* - - -This and all associated files of various formats will be found in: -http://www.gutenberg.org/dirs/6/5/3/5/65359 - - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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- height: 4px; - border-width: 4px 0 0 0; /* remove all borders except the top one */ - border-style: solid; - border-color: #000000; - clear: both; } - </style> -</head> -<body> -<h1 class="pgx" title="">The Project Gutenberg eBook, James Clerk Maxwell and Modern Physics, by -Richard Glazebrook</h1> -<p>This eBook is for the use of anyone anywhere in the United States -and most other parts of the world at no cost and with almost no -restrictions whatsoever. You may copy it, give it away or re-use it -under the terms of the Project Gutenberg License included with this -eBook or online at <a -href="https://www.gutenberg.org">www.gutenberg.org</a>. If you are not -located in the United States, you'll have to check the laws of the -country where you are located before using this ebook.</p> -<p>Title: James Clerk Maxwell and Modern Physics</p> -<p>Author: Richard Glazebrook</p> -<p>Release Date: May 16, 2021 [eBook #65359]</p> -<p>Language: English</p> -<p>Character set encoding: UTF-8</p> -<p>***START OF THE PROJECT GUTENBERG EBOOK JAMES CLERK MAXWELL AND MODERN PHYSICS***</p> -<p> </p> -<h4 class="pgx" title="">E-text prepared by Fay Dunn, Charlie Howard,<br /> - and the Online Distributed Proofreading Team<br /> - (https://www.pgdp.net)<br /> - from page images generously made available by<br /> - Internet Archive<br /> - (https://archive.org)</h4> -<p> </p> -<table border="0" style="background-color: #ccccff;margin: 0 auto;" cellpadding="10"> - <tr> - <td valign="top"> - Note: - </td> - <td> - Images of the original pages are available through - Internet Archive. See - https://archive.org/details/jamesclerkmaxwel00glaziala - </td> - </tr> -</table> -<p> </p> -<div class="transnote"> -<p class="center larger">Transcriber’s Note</p> - -<p>Larger versions of most illustrations may be seen by right-clicking them -and selecting an option to view them separately, or by double-tapping and/or -stretching them.</p> -</div> -<p> </p> -<hr class="pgx" /> -<p> </p> -<p> </p> -<p> </p> - -<div class="figcenter" style="max-width: 25em;"> - <img src="images/cover.jpg" alt="cover" /> -</div> - -<div class="narrow center"> -<p class="newpage p4"><i class="u">THE CENTURY SCIENCE SERIES</i></p> - -<p><span class="u"><span class="smcap">Edited by</span> SIR HENRY E. ROSCOE, D.C.L., LL.D., F.R.S.</span></p> -</div> - -<h1 class="p4 wspace">JAMES CLERK MAXWELL<br /> -AND MODERN PHYSICS</h1> - -<hr /> - -<div class="chapter"><div class="bbox" id="ad"> -<p class="center xlarge wspace b1">The Century Science Series.</p> - -<p class="center vspace wspace"><span class="smaller">EDITED BY</span><br /> - -<span class="larger">SIR HENRY E. ROSCOE, D.C.L., F.R.S., M.P.</span></p> - -<hr class="narrow" /> -<p class="bold">John Dalton and the Rise of Modern Chemistry.</p> - -<div class="blockquot"> - -<p>By Sir <span class="smcap">Henry E. Roscoe</span>, F.R.S.</p> -</div> - -<p class="bold">Major Rennell, F.R.S., and the Rise of English Geography.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">Clements R. Markham</span>, C.B., F.R.S., President -of the Royal Geographical Society.</p> -</div> - -<p class="bold">Justus von Liebig: his Life and Work (1803–1873).</p> - -<div class="blockquot"> - -<p>By <span class="smcap">W. A. Shenstone</span>, F.I.C., Lecturer on Chemistry in -Clifton College.</p> -</div> - -<p class="bold">The Herschels and Modern Astronomy.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">Agnes M. Clerke</span>, Author of “A Popular History -of Astronomy during the 19th Century,” &c.</p> -</div> - -<p class="bold">Charles Lyell and Modern Geology.</p> - -<div class="blockquot"> - -<p>By Rev. Professor <span class="smcap">T. G. Bonney</span>, F.R.S.</p> -</div> - -<p class="bold">James Clerk Maxwell and Modern Physics.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">R. T. GLazebrook</span>, F.R.S., Fellow of Trinity College, -Cambridge.</p> -</div> - -<p class="p1 b1 center"><i>In Preparation.</i></p> - -<p class="bold">Michael Faraday: his Life and Work.</p> - -<div class="blockquot"> - -<p>By Professor <span class="smcap">Silvanus P. Thompson</span>, F.R.S.</p> -</div> - -<p class="bold">Humphry Davy.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">T. E. Thorpe</span>, F.R.S., Principal Chemist of the -Government Laboratories.</p> -</div> - -<p class="bold">Pasteur: his Life and Work.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">M. Armand Ruffer</span>, M.D., Director of the British -Institute of Preventive Medicine.</p> -</div> - -<p class="bold">Charles Darwin and the Origin of Species.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">Edward B. Poulton</span>, M.A., F.R.S., Hope Professor -of Zoology in the University of Oxford.</p> -</div> - -<p class="bold">Hermann von Helmholtz.</p> - -<div class="blockquot"> - -<p>By <span class="smcap">A. W. Rücker</span>, F.R.S., Professor of Physics in the -Royal College of Science, London.</p> -</div> - -<p class="p1 center">CASSELL & COMPANY, <span class="smcap">Limited</span>, <i>London</i>; <i>Paris</i> & <i>Melbourne</i>.</p> -</div></div> - -<div id="if_i_001" class="figcenter" style="max-width: 30em;"> - <img src="images/i_001.jpg" width="1284" height="1744" alt="includes signature" /> - <div class="caption"><p class="xlarge">J. Clerk Maxwell</p> - -<p>(<i>From a Photograph of the Picture by G. Lowes Dickinson, Esq., in the Hall of -Trinity College, Cambridge.</i>)</p></div></div> - -<hr /> - -<div class="chapter"><div class="newpage p4 center vspace wspace larger"> - -<p><i class="u">THE CENTURY SCIENCE SERIES</i></p> - -<p class="p4 vspace3"><span class="smcap xxlarge">James Clerk Maxwell</span><br /> - -<span class="larger">AND MODERN PHYSICS</span></p> - -<p class="p4 vspace"><span class="small">BY</span><br /> -<span class="larger">R. T. GLAZEBROOK, F.R.S.</span></p> - -<p class="small"><i>Fellow of Trinity College, Cambridge<br /> -University Lecturer in Mathematics, and Assistant Director of the<br /> -Cavendish Laboratory</i></p> - -<p class="p4"><span class="smcap wspace">CASSELL and COMPANY, Limited</span><br /> -<span class="small wspace"><i>LONDON, PARIS & MELBOURNE</i></span><br /> -<span class="smaller">1896</span></p> - -<p class="small wspace">ALL RIGHTS RESERVED</p> -</div></div> - -<hr /> -<div id="if_i_004" class="figcenter" style="max-width: 9em;"> - <img src="images/i_004.png" width="419" height="431" alt="" /></div> - -<hr /> - -<div class="chapter"> -<p><span class="pagenum" id="Page_v">v</span></p> - -<h2 class="nobreak" id="PREFACE">PREFACE.</h2> -</div> - -<p class="in0"><span class="firstword">The</span> task of giving some account of Maxwell’s work—of -describing the share that he has taken in the -advance of Physical Science during the latter half -of this nineteenth century—has proved no light -labour. The problems which he attacked are of -such magnitude and complexity, that the attempt -to explain them and their importance, satisfactorily, -without the aid of symbols, is almost foredoomed -to failure. However, the attempt has been made, -in the belief that there are many who, though they -cannot follow the mathematical analysis of Maxwell’s -work, have sufficient general knowledge of physical -ideas and principles to make an account of Maxwell -and of the development of the truths that he discovered, -subjects of intelligent interest.</p> - -<p>Maxwell’s life was written in 1882 by two of those -who were most intimately connected with him, Professor -Lewis Campbell and Dr. Garnett. Many of the -biographical details of the earlier part of this book -are taken from their work. My thanks are due to<span class="pagenum" id="Page_vi">vi</span> -them and to their publishers, Messrs. Macmillan, for -permission to use any of the letters which appear -in their biography. I trust that my brief account -may be sufficient to induce many to read Professor -Campbell’s “Life and Letters,” with a view of learning -more of the inner thoughts of one who has -left so strong an imprint on all he undertook, and -was so deeply loved by all who knew him.</p> - -<p class="sigright">R. T. G.</p> - -<p class="p0 smaller"> -<i>Cambridge,<br /> -<span class="in4">December, 1895.</span></i> -</p> - -<hr /> - -<div class="chapter"> -<p><span class="pagenum" id="Page_vii">vii</span></p> - -<h2 class="nobreak" id="CONTENTS">CONTENTS.</h2> -</div> - -<table id="toc" summary="Contents"> -<tr class="small"> - <td class="tdr"><span class="smcap larger">Chapter</span></td> - <td> </td> - <td class="tdr">PAGE</td> -</tr> -<tr> - <td class="tdr top">I.</td> - <td class="tdl"><span class="smcap">Early Life</span></td> - <td class="tdr"><a href="#toclink_9">9</a></td> -</tr> -<tr> - <td class="tdr top">II.</td> - <td class="tdl"><span class="smcap">Undergraduate Life at Cambridge</span></td> - <td class="tdr"><a href="#toclink_28">28</a></td> -</tr> -<tr> - <td class="tdr top">III.</td> - <td class="tdl"><span class="smcap">Early Researches—Professor at Aberdeen</span></td> - <td class="tdr"><a href="#toclink_38">38</a></td> -</tr> -<tr> - <td class="tdr top">IV.</td> - <td class="tdl"><span class="smcap">Professor at King’s College, London—Life at Glenlair</span></td> - <td class="tdr"><a href="#toclink_54">54</a></td> -</tr> -<tr> - <td class="tdr top">V.</td> - <td class="tdl"><span class="smcap">Cambridge—Professor or Physics</span></td> - <td class="tdr"><a href="#toclink_60">60</a></td> -</tr> -<tr> - <td class="tdr top">VI.</td> - <td class="tdl"><span class="smcap">Cambridge—The Cavendish Laboratory</span></td> - <td class="tdr"><a href="#toclink_73">73</a></td> -</tr> -<tr> - <td class="tdr top">VII.</td> - <td class="tdl"><span class="smcap">Scientific Work—Colour Vision</span></td> - <td class="tdr"><a href="#toclink_93">93</a></td> -</tr> -<tr> - <td class="tdr top">VIII.</td> - <td class="tdl"><span class="smcap">Scientific Work—Molecular Theory</span></td> - <td class="tdr"><a href="#toclink_108">108</a></td> -</tr> -<tr> - <td class="tdr top">IX.</td> - <td class="tdl"><span class="smcap">Scientific Work—Electrical Theories</span></td> - <td class="tdr"><a href="#toclink_148">148</a></td> -</tr> -<tr> - <td class="tdr top">X.</td> - <td class="tdl"><span class="smcap">Development of Maxwell’s Theory</span></td> - <td class="tdr"><a href="#toclink_202">202</a></td> -</tr> -</table> - -<hr /> - -<div id="toclink_9" class="chapter"> -<p><span class="pagenum" id="Page_9">9</span></p> - -<h2 class="nobreak b2" id="James_Clerk_Maxwell"><span class="smcap large">James Clerk Maxwell</span><br /> - -<span class="subhead">AND MODERN PHYSICS.</span></h2> -</div> - -<hr class="narrow" /> - -<h2 class="nobreak" id="CHAPTER_I">CHAPTER I.<br /> - -<span class="subhead">EARLY LIFE.</span></h2> - -<p class="in0"><span class="firstword">“One</span> who has enriched the inheritance left by -Newton and has consolidated the work of Faraday—one -who impelled the mind of Cambridge to a -fresh course of real investigation—has clearly earned -his place in human memory.” It was thus that -Professor Lewis Campbell and Mr. Garnett began in -1882 their life of James Clerk Maxwell. The years -which have passed, since that date, have all tended to -strengthen the belief in the greatness of Maxwell’s -work and in the fertility of his genius, which has -inspired the labours of those who, not in Cambridge -only, but throughout the world, have aided in developing -the seeds sown by him. My object in the -following pages will be to give some very brief -account of his life and writings, in a form which may, -I hope, enable many to realise what Physical Science -owes to one who was to me a most kind friend as well -as a revered master.</p> - -<p>The Clerks of Penicuik, from whom Clerk Maxwell -was descended, were a distinguished family. Sir John -Clerk, the great-great-grandfather of Clerk Maxwell,<span class="pagenum" id="Page_10">10</span> -was a Baron of the Exchequer in Scotland from 1707 -to 1755; he was also one of the Commissioners of -the Union, and was in many ways an accomplished -scholar. His second son George married a first cousin, -Dorothea Maxwell, the heiress of Middlebie in Dumfriesshire, -and took the name of Maxwell. By the -death of his elder brother James in 1782 George -Clerk Maxwell succeeded to the baronetcy and the -property of Penicuik. Before this time he had -become involved in mining and manufacturing speculations, -and most of the Middlebie property had been -sold to pay his debts.</p> - -<p>The property of Sir George Clerk Maxwell descended -in 1798 to his two grandsons, Sir George -Clerk and Mr. John Clerk Maxwell. It had been -arranged that the younger of the two was to take -the remains of the Middlebie property and to assume -with it the name of Maxwell. Sir George Clerk was -member for Midlothian, and held office under Sir -Robert Peel. John Clerk Maxwell was the father of -James Clerk Maxwell, the subject of this sketch.<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">1</a></p> - -<p>John Clerk Maxwell lived with his widowed mother -in Edinburgh until her death in 1824. He was a -lawyer, and from time to time did some little -business in the courts. At the same time he maintained -an interest in scientific pursuits, especially -those of a practical nature. Professor Campbell -tells us of an endeavour to devise a bellows which -would give a continuous draught of air. In 1831 he<span class="pagenum" id="Page_11">11</span> -contributed to the <i>Edinburgh Medical and Philosophical -Journal</i> a paper entitled “Outlines of a Plan -for combining Machinery with the Manual Printing -Press.”</p> - -<p>In 1826 John Clerk Maxwell married Miss Frances -Cay, of North Charlton, Northumberland. For the -first few years of their married life their home was in -Edinburgh. The old estate of Middlebie had been -greatly reduced in extent, and there was not a house -on it in which the laird could live. However, soon -after his marriage, John Clerk Maxwell purchased the -adjoining property of Glenlair and built a mansion-house -for himself and his wife. Mr. Maxwell superintended -the building work. The actual working -plans for some further additions made in 1843 were -his handiwork. A garden was laid out and planted, -and a dreary stony waste was converted into a -pleasant home. For some years after he settled at -Glenlair the house in Edinburgh was retained by Mr. -Maxwell, and here, on June 13, 1831, was born his -only son, James Clerk Maxwell. A daughter, born -earlier, died in infancy. Glenlair, however, was his -parents’ home, and nearly all the reminiscences we -have of his childhood are connected with it. The -laird devoted himself to his estates and to the education -of his son, taking, however, from time to time -his full share in such county business as fell to him. -Glenlair in 1830 was very much in the wilds; the journey -from Edinburgh occupied two days. “Carriages -in the modern sense were hardly known to the Vale of -Urr. A sort of double gig with a hood was the best -apology for a travelling coach, and the most active<span class="pagenum" id="Page_12">12</span> -mode of locomotion was in a kind of rough dog-cart -known in the family speech as a hurly.”<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">2</a></p> - -<p>Mrs. Maxwell writes thus<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">3</a>, when the boy was -nearly three years old, to her sister, Miss Jane <span class="locked">Cay:—</span></p> - -<div class="blockquot"> - -<p>“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.”</p> -</div> - -<p>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 <em>particular</em> go of that?”</p> - -<p>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<span class="pagenum" id="Page_13">13</span> -toy known as a magic disc, which afterwards developed -into the zoetrope or wheel of life, and in -which, by means of an ingenious contrivance of -mirrors, the impression of a continuous movement -was produced.</p> - -<p>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.”</p> - -<p>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.</p> - -<p>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<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">4</a>; and the reply they received -<span class="locked">was—</span></p> - -<div class="poetry-container"> -<div class="poetry"> - <div class="stanza"> - <div class="verse indentq">“Div ye ken ’twas a man,</div> - <div class="verse indent0">And he lived in a house,</div> - <div class="verse indent0">In whilk was a mouse.”</div> - </div> -</div> -</div> - -<p class="in0">He returned to Heriot Row that afternoon, says -Professor Campbell, “with his tunic in rags and<span class="pagenum" id="Page_14">14</span> -wanting the skirt, his neat frill rumpled and torn—himself -excessively amused by his experiences and -showing not the slightest sign of irritation.”</p> - -<p>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.</p> - -<p>Much of what we know of Clerk Maxwell’s life -during this period comes from the letters which -passed between him and his father. They tell us of -the close intimacy and affection which existed between -the two, of the boy’s eager desire to please and -amuse his father in the dull solitude of Glenlair, and -his father’s anxiety for his welfare and progress.</p> - -<p>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 <span class="locked">writes<a id="FNanchor_5" href="#Footnote_5" class="fnanchor">5</a>:—</span></p> - -<div class="blockquot"> - -<p>“He came to know Swift and Dryden, and after a while -Hobbes, and Butler’s ‘Hudibras.’ Then, if his father was in -Edinburgh, they walked together, especially on the Saturday -half-holiday, and ‘viewed’ Leith Fort, or the preparations for -the Granton railway, or the stratification of Salisbury Crags—always -learning something new, and winning ideas for imagination -to feed upon. One Saturday, February 12, 1842, he -had a special treat, being taken ‘to see electro-magnetic -machines.’”</p> -</div> - -<p><span class="pagenum" id="Page_15">15</span></p> - -<p class="in0">And again, speaking of his <span class="locked">school-life:—</span></p> - -<div class="blockquot"> - -<p>“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.</p> - -<p>“On the whole he attained a measure of success which -helped to secure for him a certain respect; and, however -strange he sometimes seemed to his companions, he had three -qualities which they could not fail to understand—agile -strength of limb, imperturbable courage, and profound good-nature. -Professor James Muirhead remembers him as ‘a -friendly boy, though never quite amalgamating with the rest.’ -And another old class-fellow, the Rev. W. Macfarlane of -Lenzie, records the following as his impression:—‘Clerk -Maxwell, when he entered the Academy, was somewhat rustic -and somewhat eccentric. Boys called him “Dafty,” and used -to try to make fun of him. On one occasion I remember he -turned with tremendous vigour, with a kind of demonic force, -on his tormentors. I think he was let alone after that, and -gradually won the respect even of the most thoughtless of his -schoolfellows.’”</p> -</div> - -<p>The first reference to mathematical studies occurs, -says Professor Campbell, in a letter to his father -written soon after his thirteenth birthday.<a id="FNanchor_6" href="#Footnote_6" class="fnanchor">6</a></p> - -<div class="blockquot"> - -<p>“After describing the Virginian Minstrels, and betwixt -inquiries after various pets at Glenlair, he remarks, as if it -were an ordinary piece of news, ‘I have made a tetrahedron, -a dodecahedron, and two other hedrons, whose names I don’t -know.’ We had not yet begun geometry, and he had certainly -not at this time learnt the definitions in Euclid; yet he had<span class="pagenum" id="Page_16">16</span> -not merely realised the nature of the five regular solids -sufficiently to construct them out of pasteboard with approximate -accuracy, but had further contrived other symmetrical -polyhedra derived from them, specimens of which -(as improved in 1848) may be still seen at the Cavendish -Laboratory.</p> - -<p>“Who first called his attention to the pyramid, cube, etc., I -do not know. He may have seen an account of them by -chance in a book. But the fact remains that at this early time -his fancy, like that of the old Greek geometers, was arrested -by these types of complete symmetry; and his imagination so -thoroughly mastered them that he proceeded to make them -with his own hand. That he himself attached more importance -to this moment than the letter indicates is proved by the care -with which he has preserved these perishable things, so that -they (or those which replaced them in 1848) are still in -existence after thirty-seven years.”</p> -</div> - -<p>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<span class="pagenum" id="Page_17">17</span> -so much monotonous parsing. In the English Milton -is better than the History of Greece....”</p> - -<p>P—— was the boys’ nickname for the rector; -B—— for Mr. Carmichael, the second master. This<a id="FNanchor_7" href="#Footnote_7" class="fnanchor">7</a> -is the account of Maxwell’s first interview with the -<span class="locked">rector:—</span></p> - -<p><i>Rector</i>: “What part of Galloway do you come -from?”</p> - -<p><i>J. C. M.</i>: “From the Vale of Urr. Ye spell it -o, err, err, or oo, err, err.”</p> - -<p>The study of geometry was begun, and in the -mathematical master, Mr. Gloag, Maxwell found a -teacher with a real gift for his task. It was here -that Maxwell’s vast superiority to many who were -his companions at once showed itself. “He seemed,” -says Professor Campbell, “to be in the heart of the -subject when they were only at the boundary; but the -boyish game of contesting point by point with such -a mind was a most wholesome stimulus, so that the -mere exercise of faculty was a pure joy. With -Maxwell the first lessons of geometry branched out -at once into inquiries which became fruitful.”</p> - -<p>In July, 1845, he <span class="locked">writes:—</span></p> - -<div class="blockquot"> - -<p>“I have got the 11th prize for Scholarship, the 1st for -English, the prize for English verses, and the Mathematical -Medal. I tried for Scripture knowledge, and Hamilton in the -7th has got it. We tried for the Medal on Thursday. I had -done them all, and got home at half-past two; but Campbell -stayed till four. I was rather tired with writing exercises -from nine till half-past two.</p> - -<p>“Campbell and I went ‘once more unto the b(r)each’<span class="pagenum" id="Page_18">18</span> -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 <em>my</em> medal; but there is no rivalry betwixt us, as -B—— Carmichael says.”</p> -</div> - -<p>After a summer spent chiefly at Glenlair, he -returned with his father to Edinburgh for the winter, -and began, at the age of fourteen, to go to the -meetings of the Royal Society of Edinburgh. At -the Society of Arts he met Mr. R. D. Hay, the -decorative painter, who had interested himself in the -attempt to reduce beauty in form and colour to -mathematical principles. Clerk Maxwell was interested -in the question how to draw a perfect oval, -and devised a method of drawing oval curves which -was referred by his father to Professor Forbes for -his criticism and suggestions. After discussing the -matter with Professor Kelland, Professor Forbes -wrote as <span class="locked">follows<a id="FNanchor_8" href="#Footnote_8" class="fnanchor">8</a>:—</span></p> - -<div class="blockquot"> - -<p>“<span class="smcap">My Dear Sir</span>,—I am glad to find to-day, from Professor -Kelland, that his opinion of your son’s paper agrees with mine, -namely, that it is most ingenious, most creditable to him, and, -we believe, a new way of considering higher curves with -reference to foci. Unfortunately, these ovals appear to be -curves of a very high and intractable order, so that possibly -the elegant method of description may not lead to a corresponding -simplicity in investigating their properties. But that -is not the present point. If you wish it, I think that the -simplicity and elegance of the method would entitle it to be -brought before the Royal Society.—Believe me, my dear sir, -yours truly,</p> - -<p class="sigright"> -“<span class="smcap">James D. Forbes</span>.” -</p> -</div> - -<p>In consequence of this, Clerk Maxwell’s first<span class="pagenum" id="Page_19">19</span> -published paper was communicated to the Royal -Society of Edinburgh on April 6th, 1846, when its -author was barely fifteen. Its title is as follows: -“On the Description of Oval Curves and those having -a Plurality of Foci. By Mr. Clerk Maxwell, Junior. -With Remarks by Professor Forbes. Communicated -by Professor Forbes.”</p> - -<p>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.”</p> - -<p>This was the beginning of the lifelong friendship -between Maxwell and Forbes.</p> - -<p>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.</p> - -<p>The curves are of great importance in the -theory of light, for if this constant factor expresses -the refractive index of any medium, then -light diverging from one focus without the medium -and refracted at a surface bounding the medium, and -having the form of one of Maxwell’s ovals, will be -refracted so as to converge to the second focus.</p> - -<p>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.”</p> - -<p>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<span class="pagenum" id="Page_20">20</span> -then first in mathematics and in English, and nearly -first in Latin.</p> - -<p>In 1847 he was working at magnetism and the -polarisation of light. Some time in that year he was -taken by his uncle, Mr. John Cay, to see William -Nicol, the inventor of the polarising prism, who -showed him the colours exhibited by polarised light -after passing through unannealed glass. On his -return, he made a polariscope with a glass reflector. -The framework of the first instrument was of cardboard, -but a superior article was afterwards constructed -of wood. Small lenses mounted on cardboard were -employed when a conical pencil was needed. By -means of this instrument he examined the figures -exhibited by pieces of unannealed glass, which he -prepared himself; and, with a camera lucida and box -of colours, he reproduced these figures on paper, -taking care to sketch no outlines, but to shade each -coloured band imperceptibly into the next. Some of -these coloured drawings he forwarded to Nicol, and -was more than repaid by the receipt shortly afterwards -of a pair of prisms prepared by Nicol himself. -These prisms were always very highly prized by -Maxwell. Once, when at Trinity, the little box -containing them was carried off by his bed-maker -during a vacation, and destined for destruction. The -bed-maker died before term commenced, and it was -only by diligent search among her effects that the -prisms were recovered.<a id="FNanchor_9" href="#Footnote_9" class="fnanchor">9</a> After this they were more -carefully guarded, and they are now, together with -the wooden polariscope, the bits of unannealed glass,<span class="pagenum" id="Page_21">21</span> -and the water-colour drawings, in one of the showcases -at the Cavendish Laboratory.</p> - -<p>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.”</p> - -<p>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 -<span class="locked">taken:—</span></p> - -<div class="blockquot"> - -<p>“When I first made Clerk Maxwell’s acquaintance, about -thirty-five years ago, at the Edinburgh Academy, he was a -year before me, being in the fifth class, while I was in the -fourth.</p> - -<p>“At school he was at first regarded as shy and rather dull. -He made no friendships, and he spent his occasional holidays -in reading old ballads, drawing curious diagrams, and making -rude mechanical models. This absorption in such pursuits, -totally unintelligible to his schoolfellows (who were then quite -innocent of mathematics), of course procured him a not very -complimentary nickname, which I know is still remembered -by many Fellows of this Society. About the middle of his -school career, however, he surprised his companions by -suddenly becoming one of the most brilliant among them, -gaining high, and sometimes the highest, prizes for scholarships, -mathematics, and English verse composition. From -this time forward I became very intimate with him, and we -discussed together, with schoolboy enthusiasm, numerous<span class="pagenum" id="Page_22">22</span> -curious problems, among which I remember particularly the -various plane sections of a ring or tore, and the form of a -cylindrical mirror which should show one his own image -unperverted. I still possess some of the MSS. we exchanged -in 1846 and early in 1847. Those by Maxwell are on ‘The -Conical Pendulum,’ ‘Descartes’ Ovals,’ ‘Meloid and Apioid,’ -and ‘Trifocal Curves.’ All are drawn up in strict geometrical -form and divided into consecutive propositions. The three -latter are connected with his first published paper, communicated -by Forbes to this society and printed in our ‘Proceedings,’ -vol. ii., under the title, ‘On the Description of Oval -Curves and those having a Plurality of Foci’ (1846). At the -time when these papers were written he had received no -instruction in mathematics beyond a few books of Euclid and -the merest elements of algebra.”</p> -</div> - -<p>In November, 1847, Clerk Maxwell entered the -University of Edinburgh, learning mathematics from -Kelland, natural philosophy from J. D. Forbes, and -logic from Sir W. R. Hamilton. At this time, according -to Professor <span class="locked">Campbell<a id="FNanchor_10" href="#Footnote_10" class="fnanchor">10</a>—</span></p> - -<div class="blockquot"> - -<p class="in0">“he still occasioned some concern to the more conventional -amongst his friends by the originality and simplicity of -his ways. His replies in ordinary conversation were indirect -and enigmatical, often uttered with hesitation and in a -monotonous key. While extremely neat in his person, he had -a rooted objection to the vanities of starch and gloves. He -had a pious horror of destroying anything, even a scrap of -writing-paper. He preferred travelling by the third class in -railway journeys, saying he liked a hard seat. When at table -he often seemed abstracted from what was going on, being -absorbed in observing the effects of refracted light in the -finger-glasses, or in trying some experiment with his eyes—seeing -round a corner, making invisible stereoscopes, and the -like. Miss Cay used to call his attention by crying, ‘Jamsie, -you’re in a prop.’ He never tasted wine; and he spoke to<span class="pagenum" id="Page_23">23</span> -gentle and simple in exactly the same tone. On the other -hand, his teachers—Forbes above all—had formed the highest -opinion of his intellectual originality and force; and a few -experienced observers, in watching his devotion to his father, -began to have some inkling of his heroic singleness of heart. -To his college companions, whom he could now select at will, -his quaint humour was an endless delight. His chief associates, -after I went to the University of Glasgow, were my brother, -Robert Campbell (still at the Academy), P. G. Tait, and Allan -Stewart. Tait went to Peterhouse, Cambridge, in 1848, after -one session of the University of Edinburgh; Stewart to the -same college in 1849; Maxwell did not go up until 1850.”</p> -</div> - -<p>During this period he wrote two important papers. -The one, on “Rolling Curves,” was read to the -Royal Society of Edinburgh by Professor Kelland—(“it -was not thought proper for a boy in a round -jacket to mount the rostrum”)—in February, 1849; -the other, on “The Equilibrium of Elastic Solids,” -appeared in the spring of 1850.</p> - -<p>The vacations were spent at Glenlair, and we learn -from letters to Professor Campbell and others how -the time was passed.</p> - -<p>“On Saturday,” he writes<a id="FNanchor_11" href="#Footnote_11" class="fnanchor">11</a>—April 26th, 1848, just -after his arrival home—“the natural philosophers -ran up Arthur’s Seat with the barometer. The -Professor set it down at the top.... He did not -set it straight, and made the hill grow fifty feet; but -we got it down again.”</p> - -<p>In a letter of July in the same year he describes -his <span class="locked">laboratory:—</span></p> - -<div class="blockquot"> - -<p>“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,<span class="pagenum" id="Page_24">24</span> -and two chairs, of which one is safe, and a skylight above -which will slide up and down.</p> - -<p>“On the door (or table) there is a lot of bowls, jugs, -plates, jam pigs, etc., containing water, salt, soda, sulphuric -acid, blue vitriol, plumbago ore; also broken glass, iron, and -copper wire, copper and zinc plate, bees’ wax, sealing wax, -clay, rosin, charcoal, a lens, a Smee’s galvanic apparatus, and -a countless variety of little beetles, spiders, and wood lice, -which fall into the different liquids and poison themselves. I -intend to get up some more galvanism in jam pigs; but I -must first copper the interiors of the pigs, so I am experimenting -on the best methods of electrotyping. So I am making -copper seals with the device of a beetle. First, I thought a -beetle was a good conductor, so I embedded one in wax (not -at all cruel, because I slew him in boiling water, in which he -never kicked), leaving his back out; but he would not do. -Then I took a cast of him in sealing wax, and pressed wax -into the hollow, and blackleaded it with a brush; but neither -would that do. So at last I took my fingers and rubbed it, -which I find the best way to use the blacklead. Then it -coppered famously. I melt out the wax with the lens, that -being the cleanest way of getting a strong heat, so I do most -things with it that need heat. To-day I astonished the -natives as follows. I took a crystal of blue vitriol and put -the lens to it, and so drove off the water, leaving a white -powder. Then I did the same to some washing soda, and -mixed the two white powders together, and made a small -native spit on them, which turned them green by a mutual -exchange, thus:—1. Sulphate of copper and carbonate of soda. -2. Sulphate of soda and carbonate of copper (blue or green).”</p> -</div> - -<p>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.”</p> - -<p>In September he was busy with polarised light. -“We were at Castle Douglas yesterday, and got<span class="pagenum" id="Page_25">25</span> -crystals of saltpetre, which I have been cutting up -into plates to-day in hopes to see rings.”</p> - -<p>In July, 1849, he <span class="locked">writes<a id="FNanchor_12" href="#Footnote_12" class="fnanchor">12</a>:—</span></p> - -<div class="blockquot"> - -<p>“I have set up the machine for showing the rings in -crystals, which I planned during your visit last year. It -answers very well. I also made some experiments on compressed -jellies in illustration of my props. on that subject. -The principal one was this:—The jelly is poured while hot -into the annular space contained between a paper cylinder and -a cork; then, when cold, the cork is twisted round and the -jelly exposed to polarised light, when a transverse cross, <span class="sans smaller">x</span>, -not +, appears, with rings as the inverse square of the radius, -all which is fully verified. Hip! etc. <i>Q.E.D.</i>”</p> -</div> - -<p class="in0">And again on March 22nd, <span class="locked">1850:—</span></p> - -<div class="blockquot"> - -<p>“At Practical Mechanics I have been turning Devils of -sorts. For private studies I have been reading Young’s -‘Lectures,’ Willis’s ‘Principles of Mechanism,’ Moseley’s -‘Engineering and Mechanics,’ Dixon on ‘Heat,’ and Moigno’s -‘Répertoire d’Optique.’ This last is a very complete analysis -of all that has been done in the optical way from Fresnel to -the end of 1849, and there is another volume a-coming which -will complete the work. There is in it, besides common optics, -all about the other things which accompany light, as heat, -chemical action, photographic rays, action on vegetables, etc.</p> - -<p>“My notions are rather few, as I do not <em>entertain</em> them -just now. I have a notion for the torsion of wires and rods, -not to be made till the vacation; of experiments on the action -of compression on glass, jelly, etc., numerically done up; of -papers for the Physico-Mathematical Society (which is to -revive in earnest next session!); on the relations of optical -and mechanical constants, their desirableness, etc.; and suspension -bridges, and catenaries, and elastic curves. Alex. -Campbell, Agnew, and I are appointed to read up the subject -of periodical shooting stars, and to prepare a list of the -phenomena to be observed on the 9th August and 13th<span class="pagenum" id="Page_26">26</span> -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.”</p> -</div> - -<p>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.</p> - -<p>Of this period of his life Tait writes as <span class="locked">follows:—</span></p> - -<div class="blockquot"> - -<p>“The winter of 1847 found us together in the classes of -Forbes and Kelland, where he highly distinguished himself. -With the former he was a particular favourite, being admitted -to the free use of the class apparatus for original experiments. -He lingered here behind most of his former associates, having -spent three years at the University of Edinburgh, working -(without any assistance or supervision) with physical and -chemical apparatus, and devouring all sorts of scientific works -in the library. During this period he wrote two valuable -papers, which are published in our ‘Transactions,’ on ‘The -Theory of Rolling Curves’ and on ‘The Equilibrium of Elastic -Solids.’ Thus he brought to Cambridge, in the autumn of -1850, a mass of knowledge which was really immense for so -young a man, but in a state of disorder appalling to his -methodical private tutor. Though that tutor was William -Hopkins, the pupil to a great extent took his own way, and it -may safely be said that no high wrangler of recent years ever -entered the Senate House more imperfectly trained to produce -‘paying’ work than did Clerk Maxwell. But by sheer strength -of intellect, though with the very minimum of knowledge how -to use it to advantage under the conditions of the examination, -he obtained the position of Second Wrangler, and was -bracketed equal with the Senior Wrangler in the higher ordeal -of the Smith’s Prizes. His name appears in the Cambridge -‘Calendar’ as Maxwell of Trinity, but he was originally -entered at Peterhouse, and kept his first term there, in that<span class="pagenum" id="Page_27">27</span> -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.”</p> -</div> - -<p class="in0">While W. D. Niven, in his preface to Maxwell’s -collected works (p. xii.), <span class="locked">says:—</span></p> - -<div class="blockquot"> - -<p>“It may readily be supposed that his preparatory training -for the Cambridge course was far removed from the ordinary -type. There had indeed for some time been practically no -restraint upon his plan of study, and his mind had been -allowed to follow its natural bent towards science, though not -to an extent so absorbing as to withdraw him from other -pursuits. Though he was not a sportsman—indeed, sport so-called -was always repugnant to him—he was yet exceedingly -fond of a country life. He was a good horseman and a good -swimmer. Whence, however, he derived his chief enjoyment -may be gathered from the account which Mr. Campbell gives -of the zest with which he quoted on one occasion the lines of -Burns which describe the poet finding inspiration while -wandering along the banks of a stream in the free indulgence -of his fancies. Maxwell was not only a lover of poetry, but -himself a poet, as the fine pieces gathered together by Mr. -Campbell abundantly testify. He saw, however, that his true -calling was science, and never regarded these poetical efforts -as other than mere pastime. Devotion to science, already -stimulated by successful endeavour; a tendency to ponder -over philosophical problems; and an attachment to English -literature, particularly to English poetry—these tastes, implanted -in a mind of singular strength and purity, may be said -to have been the endowments with which young Maxwell -began his Cambridge career. Besides this, his scientific -reading, as we may gather from his papers to the Royal -Society of Edinburgh referred to above, was already extensive -and varied. He brought with him, says Professor Tait, a mass -of knowledge which was really immense for so young a man, -but in a state of disorder appalling to his methodical private -tutor.”</p> -</div> - -<hr /> - -<div id="toclink_28" class="chapter"> -<p><span class="pagenum" id="Page_28">28</span></p> - -<h2 class="nobreak" id="CHAPTER_II">CHAPTER II.<br /> - -<span class="subhead">UNDERGRADUATE LIFE AT CAMBRIDGE.</span></h2> -</div> - -<p class="in0"><span class="firstword">Maxwell</span> 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.”</p> - -<p>The change was pressed upon him by many -friends, the grounds of the advice being that, from -the large number of high wranglers recently at -Peterhouse and the smallness of the foundation, the -chances of a Fellowship there for a mathematical -man were less than at Trinity. It was a step he -never regretted; the prospect of a Fellowship had -but little influence on his mind. He found, however, -at the larger college ampler opportunities for self-improvement, -and it was possible for him to select his -friends from among men whom he otherwise would -never have known.</p> - -<p>The record of his undergraduate life is not very -full; his letters to his father have, unfortunately, -been lost, but we have enough in the recollections of -friends still living to picture what it was like. At -first he lodged in King’s Parade with an old Edinburgh -schoolfellow, C. H. Robertson. He attended the<span class="pagenum" id="Page_29">29</span> -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.”</p> - -<p>In his second year he became a pupil of Hopkins, -the great coach; he also attended Stokes’ lectures, -and the friendship which lasted till his death was -thus begun. In April, 1852, he was elected a scholar, -and obtained rooms in College (G, Old Court). In -June, 1852, he came of age. “I trust you will be as -discreet when major as you have been while minor,” -writes his father the day before. The next academic -year, October, 1852, to June, 1853, was a very busy -one; hard grind for the Tripos occupied his time, and -he seems to have been thoroughly overstrained. He -was taken ill while staying near Lowestoft with the -Rev. C. B. Tayler, the uncle of a College friend. His -own account of the illness is given in a letter to -Professor Campbell<a id="FNanchor_13" href="#Footnote_13" class="fnanchor">13</a>, dated July 14th, 1853.</p> - -<div class="blockquot"> - -<p>“You wrote just in time for your letter to reach me as I -reached Cambridge. After examination, I went to visit the -Rev. C. B. Tayler (uncle to a Tayler whom I think you have -seen under the name of <em>Freshman</em>, etc., and author of many -tracts and other didactic works). We had little expedites and -walks, and things parochial and educational, and domesticity. -I intended to return on the 18th June, but on the 17th I felt<span class="pagenum" id="Page_30">30</span> -unwell, and took measures accordingly to be well again—<i>i.e.</i> -went to bed, and made up my mind to recover. But it lasted -more than a fortnight, during which time I was taken care of -beyond expectation (not that I did not expect much before). -When I was perfectly useless and could not sit up without -fainting, Mr. Tayler did everything for me in such a way that -I had no fear of giving trouble. So did Mrs. Tayler; and the -two nephews did all they could. So they kept me in great -happiness all the time, and detained me till I was able to walk -about and got back strength. I returned on the 4th July.</p> - -<p>“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.”</p> -</div> - -<p>During this period he wrote some papers for the -<i>Cambridge and Dublin Mathematical Journal</i> which -will be referred to again later. He was also a member -of a discussion society known as the “Apostles,” and -some of the essays contributed by him are preserved -by Professor Campbell. Mr. Niven, in his preface to -the collected edition of Maxwell’s works, suggests -that the composition of these essays laid the foundation -of that literary finish which is one of the -characteristics of Maxwell’s scientific writings.</p> - -<p>Among his friends at the time were Tait, Charles -Mackenzie of Caius, the missionary bishop of Central -Africa, Henry and Frank Mackenzie of Trinity, -Droop, third Wrangler in 1854; Gedge, Isaac Taylor, -Blakiston, F. W. Farrar,<a id="FNanchor_14" href="#Footnote_14" class="fnanchor">14</a> H. M. Butler,<a id="FNanchor_15" href="#Footnote_15" class="fnanchor">15</a> Hort, V. -Lushington, Cecil Munro, G. W. H. Tayler, and W. N. -Lawson. Some of these who survived him have<span class="pagenum" id="Page_31">31</span> -given to Professor Campbell their recollections of -these undergraduate days, which are full of interest.</p> - -<p>Thus Mr. Lawson <span class="locked">writes<a id="FNanchor_16" href="#Footnote_16" class="fnanchor">16</a>:—</span></p> - -<div class="blockquot"> - -<p>“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.</p> - -<p>“I remember Maxwell coming to me one morning with a -copy of verses beginning, ‘Gin a body meet a body going -through the air,’ in which he had twisted the well-known song -into a description of the laws of impact of solid bodies.</p> - -<p>“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.’</p> - -<p>“These last words, however meant, were, in fact, a description -of his own wonderful power. I remember, one day in -lecture, our lecturer had filled the black-board three times -with the investigation of some hard problem in Geometry of -Three Dimensions, and was not at the end of it, when Maxwell -came up with a question whether it would not come out -geometrically, and showed how, with a figure, and in a few -lines, there was the solution at once.</p> - -<p>“Maxwell was, I daresay you remember, very fond of a -talk upon almost anything. He and I were pupils (at an -enormous distance apart) of Hopkins, and I well recollect how, -when I had been working the night before and all the morning -at Hopkins’s problems, with little or no result, Maxwell would -come in for a gossip, and talk on while I was wishing him far -away, till at last, about half an hour or so before our meeting -at Hopkins’s, he would say, ‘Well, I must go to old Hop.’s -problems’; and, by the time we met there, they were all done.</p> - -<p>“I remember Hopkins telling me, when speaking of -Maxwell, either just before or just after his degree, ‘It is not<span class="pagenum" id="Page_32">32</span> -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.”</p> -</div> - -<p>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 <span class="locked">writes:—</span></p> - -<div class="blockquot"> - -<p>“He (Hopkins) was talking to me this evening about -Maxwell. He says he is unquestionably the most extraordinary -man he has met with in the whole range of his -experience; he says it appears impossible for Maxwell to -think incorrectly on physical subjects; that in his analysis, -however, he is far more deficient. He looks upon him as a -great genius with all its eccentricities, and prophesies that -one day he will shine as a light in physical science—a prophecy -in which all his fellow-students strenuously unite.”</p> -</div> - -<p>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!</p> - -<p>Dr. Butler, a friend of these early days, preached -the University sermon on November 16th, 1879, ten -days after Maxwell’s death, and spoke <span class="locked">thus:—</span></p> - -<div class="blockquot"> - -<p>“It is a solemn thing—even the least thoughtful is touched -by it—when a great intellect passes away into the silence and -we see it no more. Such a loss, such a void, is present, I feel -certain, to many here to-day. It is not often, even in this -great home of thought and knowledge, that so bright a light -is extinguished as that which is now mourned by many illustrious -mourners, here chiefly, but also far beyond this place. I -shall be believed when I say in all simplicity that I wish it had -fallen to some more competent tongue to put into words those -feelings of reverent affection which are, I am persuaded, uppermost -in many hearts on this Sunday. My poor words shall be<span class="pagenum" id="Page_33">33</span> -few, but believe me they come from the heart. You know, -brethren, with what an eager pride we follow the fortunes of -those whom we have loved and reverenced in our undergraduate -days. We may see them but seldom, few letters may -pass between us, but their names are never common names. -They never become to us only what other men are. When -I came up to Trinity twenty-eight years ago, James Clerk -Maxwell was just beginning his second year. His position -among us—I speak in the presence of many who remember -that time—was unique. He was the one acknowledged man -of genius among the undergraduates. We understood even -then that, though barely of age, he was in his own line of -inquiry not a beginner but a master. His name was already -a familiar name to men of science. If he lived, it was certain -that he was one of that small but sacred band to whom it -would be given to enlarge the bounds of human knowledge. -It was a position which might have turned the head of a -smaller man; but the friend of whom we were all so proud, -and who seemed, as it were, to link us thus early with the -great outside world of the pioneers of knowledge, had one of -those rich and lavish natures which no prosperity can impoverish, -and which make faith in goodness easy for others. I -have often thought that those who never knew the grand old -Adam Sedgwick and the then young and ever-youthful Clerk -Maxwell had yet to learn the largeness and fulness of the -moulds in which some choice natures are framed. Of the -scientific greatness of our friend we were most of us unable to -judge; but anyone could see and admire the boy-like glee, the -joyous invention, the wide reading, the eager thirst for truth, -the subtle thought, the perfect temper, the unfailing reverence, -the singular absence of any taint of the breath of worldliness -in any of its thousand forms.</p> - -<p>“Brethren, you may know such men now among your college -friends, though there can be but few in any year, or indeed in -any century, that possess the rare genius of the man whom we -deplore. If it be so, then, if you will accept the counsel of a -stranger, thank God for His gift. Believe me when I tell you -that few such blessings will come to you in later life. There<span class="pagenum" id="Page_34">34</span> -are blessings that come once in a lifetime. One of these is the -reverence with which we look up to greatness and goodness in -a college friend—above us, beyond us, far out of our mental or -moral grasp, but still one of us, near to us, our own. You -know, in part at least, how in this case the promise of youth -was more than fulfilled, and how the man who, but a fortnight -ago, was the ornament of the University, and—shall I be -wrong in saying it?—almost the discoverer of a new world of -knowledge, was even more loved than he was admired, retaining -after twenty years of fame that mirth, that simplicity, that -child-like delight in all that is fresh and wonderful which we -rejoice to think of as some of the surest accompaniment of -true scientific genius.</p> - -<p>“You know, also, that he was a devout as well as thoughtful -Christian. I do not note this in the triumphant spirit of a -controversialist. I will not for a moment assume that there is -any natural opposition between scientific genius and simple -Christian faith. I will not compare him with others who have -had the genius without the faith. Christianity, though she -thankfully welcomes and deeply prizes them, does not need -now, any more than when St. Paul first preached the Cross at -Corinth, the speculations of the subtle or the wisdom of the -wise. If I wished to show men, especially young men, the -living force of the Gospel, I would take them not so much to -a learned and devout Christian man to whom all stores of -knowledge were familiar, but to some country village where -for fifty years there had been devout traditions and devout -practice. There they would see the Gospel lived out; truths, -which other men spoke of, seen and known; a spirit not of -this world, visibly, hourly present; citizenship in heaven daily -assumed and daily realised. Such characters I believe to be -the most convincing preachers to those who ask whether -Revelation is a fable and God an unknowable. Yes, in most -cases—not, I admit, in all—simple faith, even peradventure -more than devout genius, is mighty for removing doubts and -implanting fresh conviction. But having said this, we may -well give thanks to God that our friend was what he was, a -firm Christian believer, and that his powerful mind, after<span class="pagenum" id="Page_35">35</span> -ranging at will through the illimitable spaces of Creation and -almost handling what he called ‘the foundation-stones of the -material universe,’ found its true rest and happiness in the -love and the mercy of Him whom the humblest Christian calls -his Father. Of such a man it may be truly said that he had -his citizenship in heaven, and that he looked for, as a Saviour, -the Lord Jesus Christ, through whom the unnumbered worlds -were made, and in the likeness of whose image our new and -spiritual body will be fashioned.”</p> -</div> - -<p>The Tripos came in January, 1854. “You will -need to get muffetees for the Senate Room. Take -your plaid or rug to wrap round your feet and legs,” -was his father’s advice—advice which will appeal to -many who can remember the Senate House as it felt -on a cold January morning.</p> - -<p>Maxwell had been preparing carefully for this -examination. Thus to his aunt, Miss Cay, in June, -1853, he writes:—“If anyone asks how I am getting -on in mathematics, say that I am busy arranging -everything so as to be able to express all distinctly, -so that examiner may be satisfied now and pupils -edified hereafter. It is pleasant work and very -strengthening, but not nearly finished.”</p> - -<p>Still, the illness of July, 1853, had left some effect. -Professor Baynes states that he said that on entering -the Senate House for the first paper he felt his mind -almost a blank, but by-and-by his mental vision -became preternaturally clear.</p> - -<p>The moderators were Mackenzie of Caius, whose -advice had been mainly instrumental in leading him -to migrate to Trinity, Wm. Walton of Trinity, -Wolstenholme of Christ’s, and Percival Frost of St. -John’s.</p> - -<p><span class="pagenum" id="Page_36">36</span></p> - -<p>When the lists were published, Routh of Peterhouse -was senior, Maxwell second. The examination -for the Smith’s Prizes followed in a few days, and -then Routh and Maxwell were declared equal.</p> - -<p>In a letter to Miss Cay<a id="FNanchor_17" href="#Footnote_17" class="fnanchor">17</a> of January 13th, while -waiting for the three days’ list, he <span class="locked">writes:—</span></p> - -<div class="blockquot"> - -<p>“All my correspondents have been writing to me, which is -kind, and have not been writing questions, which is kinder. -So I answer you now, while I am slacking speed to get up -steam, leaving Lewis and Stewart, etc., till next week, when I -will give an account of the <em>five days</em>. There are a good many -up here at present, and we get on very jolly on the whole; but -some are not well, and some are going to be plucked or -gulphed, as the case may be, and others are reading so hard -that they are invisible. I go to-morrow to breakfast with -shaky men, and after food I am to go and hear the list read -out, and whether they are through, and bring them word. -When the honour list comes out the poll men act as messengers. -Bob Campbell comes in occasionally of an evening now, to -discuss matters and vary sports. During examination I have -had men at night working with gutta-percha, magnets, etc. -It is much better than reading novels or talking after 5½ -hours’ hard writing.”</p> -</div> - -<p>His father, on hearing the news, wrote from -<span class="locked">Edinburgh:—</span></p> - -<div class="blockquot"> - -<p>“I heartily congratulate you on your place in the list. I -suppose it is higher than the speculators would have guessed, -and quite as high as Hopkins reckoned on. I wish you success -in the Smith’s Prizes; be sure to write me the result. I will -see Mrs. Morrieson, and I think I will call on Dr. Gloag to -congratulate him. He has at least three pupils gaining -honours.”</p> -</div> - -<p>His friends in Edinburgh were greatly pleased.<span class="pagenum" id="Page_37">37</span> -“I get congratulations on all hands,” his father writes,<a id="FNanchor_18" href="#Footnote_18" class="fnanchor">18</a> -“including Professor Kelland and Sandy Fraser and -all others competent.... To-night or on Monday -I shall expect to hear of the Smith’s Prizes.” And -again, February 6th, 1854:—“George Wedderburn -came into my room at 2 a.m. yesterday morning, -having seen the Saturday <i>Times</i>, received by the -express train.... As you are equal to the -Senior in the champion trial, you are very little -behind him.”</p> - -<p>Or again, March 5th, <span class="locked">1854:—</span></p> - -<div class="blockquot"> - -<p>“Aunt Jane stirred me up to sit for my picture, as she -said you wished for it and were entitled to ask for it <i xml:lang="la" lang="la">qua</i> -Wrangler. I have had four sittings to Sir John Watson -Gordon, and it is now far advanced; I think it is very like. -It is kitcat size, to be a companion to Dyce’s picture of your -mother and self, which Aunt Jane says she is to leave to you.”</p> -</div> - -<p>And now the long years of preparation were -nearly over. The cunning craftsman was fitted with -his tools; he could set to work to unlock the secrets -of Nature; he was free to employ his genius and his -knowledge on those tasks for which he felt most -fitted.</p> - -<hr /> - -<div id="toclink_38" class="chapter"> -<p><span class="pagenum" id="Page_38">38</span></p> - -<h2 class="nobreak" id="CHAPTER_III">CHAPTER III.<br /> - -<span class="subhead">EARLY RESEARCHES.—PROFESSOR AT ABERDEEN.</span></h2> -</div> - -<p class="in0"><span class="firstword">From</span> 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.</p> - -<p>He continued in Cambridge till the Long Vacation -of 1854, reading Mill’s “Logic.” “I am experiencing -the effects of Mill,” he writes, March 25th, 1854, “but -I take him slowly. I do not think him the last of -his kind. I think more is wanted to bring the connexion -of sensation with science to light, and to show -what it is not.” He also read Berkeley on “The -Theory of Vision” and “greatly admired it.”</p> - -<p>About the same time he devised an ophthalmoscope.<a id="FNanchor_19" href="#Footnote_19" class="fnanchor">19</a></p> - -<div class="blockquot"> - -<p>“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<span class="pagenum" id="Page_39">39</span> -glorious bright patches and networks of blue, yellow, and -green, with blood-vessels great and small.”</p> -</div> - -<p>After the vacation he returned to Cambridge, and -the letters refer to the colour-top. Thus to Miss Cay, -November 24th, 1854, p. <span class="locked">208:—</span></p> - -<div class="blockquot"> - -<p>“I have been very busy of late with various things, and -am just beginning to make papers for the examination at -Cheltenham, which I have to conduct about the 11th of -December. I have also to make papers to polish off my pups. -with. I have been spinning colours a great deal, and have got -most accurate results, proving that ordinary people’s eyes are -all made alike, though some are better than others, and that -other people see two colours instead of three; but all those -who do so agree amongst themselves. I have made a triangle -of colours by which you may make out everything.</p> - -<p>“If you can find out any people in Edinburgh who do not -see colours (I know the Dicksons don’t), pray drop a hint that -I would like to see them. I have put one here up to a dodge -by which he distinguishes colours without fail. I have also -constructed a pair of squinting spectacles, and am beginning -operations on a squinting man.”</p> -</div> - -<p>A paper written for his own use originally some -time in 1854, but communicated as a parting gift to -his friend Farrar, who was about to become a master -at Marlborough, gives us some insight into his view -of life at the age of twenty-three.</p> - -<div class="blockquot"> - -<p>“He that would enjoy life and act with freedom must have -the work of the day continually before his eyes. Not yesterday’s -work, lest he fall into despair; nor to-morrow’s, lest he -become a visionary—not that which ends with the day, which -is a worldly work; nor yet that only which remains to eternity, -for by it he cannot shape his actions.</p> - -<p>“Happy is the man who can recognise in the work of -to-day a connected portion of the work of life and an<span class="pagenum" id="Page_40">40</span> -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.</p> - -<p>“Thus ought Man to be an impersonation of the divine -process of nature, and to show forth the union of the infinite -with the finite, not slighting his temporal existence, remembering -that in it only is individual action possible; nor yet -shutting out from his view that which is eternal, knowing that -Time is a mystery which man cannot endure to contemplate -until eternal Truth enlighten it.”</p> -</div> - -<p>His father was unwell in the Christmas vacation -of that year, and he could not return to Cambridge at -the beginning of the Lent term. “My steps,” he -writes<a id="FNanchor_20" href="#Footnote_20" class="fnanchor">20</a> 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.”</p> - -<p>He was back in Cambridge for the May term, -working at the motion of fluids and at his colour-top. -A paper on “Experiments on Colour as Perceived by -the Eye” was communicated to the Royal Society of -Edinburgh on March 19th, 1855. The experiments -were shown to the Cambridge Philosophical Society -in May following, and the results are thus described -in two letters<a id="FNanchor_21" href="#Footnote_21" class="fnanchor">21</a> to his father, Saturday, May 5th, 1855:</p> - -<div class="blockquot"> - -<p>“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<span class="pagenum" id="Page_41">41</span> -evening, and I have been there preparing their experiments in -the gaslight. There is to be a meeting in my rooms to-night -to discuss Adam Smith’s ‘Theory of Moral Sentiments,’ so I -must clear up my litter presently. I am working away at -electricity again, and have been working my way into the -views of heavy German writers. It takes a long time to -reduce to order all the notions one gets from these men, but -I hope to see my way through the subject and arrive at something -intelligible in the way of a theory....</p> - -<p>“The colour trick came off on Monday, 7th. I had the -proof-sheets of my paper, and was going to read; but I -changed my mind and talked instead, which was more to the -purpose. There were sundry men who thought that blue and -yellow make green, so I had to undeceive them. I have got -Hay’s book of colours out of the Univ. Library, and am -working through the specimens, matching them with the top. -I have a new trick of stretching the string horizontally above -the top, so as to touch the upper part of the axis. The motion -of the axis sets the string a-vibrating in the same time with -the revolutions of the top, and the colours are seen in the haze -produced by the vibration. Thomson has been spinning the -top, and he finds my diagram of colours agrees with his -experiments, but he doubts about browns, what is their -composition. I have got colcothar brown, and can make white -with it, and blue and green; also, by mixing red with a little -blue and green and a great deal of black, I can match colcothar -exactly.</p> - -<p>“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.</p> - -<p><span class="pagenum" id="Page_42">42</span></p> - -<p>“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.”</p> -</div> - -<p>The British Association met at Glasgow in September, -1855, and Maxwell was present, and showed -his colour-top at Professor Ramsay’s house to some of -those interested. Letters<a id="FNanchor_22" href="#Footnote_22" class="fnanchor">22</a> to his father about this -time describe some of the events of the meeting and -his own plans for the term.</p> - -<div class="blockquot"> - -<p>“We had a paper from Brewster on ‘The theory of three -colours in the spectrum,’ in which he treated Whewell with -philosophic pity, commending him to the care of Prof. Wartman -of Geneva, who was considered the greatest authority in -cases of his kind—cases, in fact, of colour-blindness. Whewell -was in the room, but went out and avoided the quarrel; and -Stokes made a few remarks, stating the case not only clearly -but courteously. However, Brewster did not seem to see that -Stokes admitted his experiments to be correct, and the newspapers -represented Stokes as calling in question the accuracy -of the experiments.</p> - -<p>“I am getting my electrical mathematics into shape, and I -see through some parts which were rather hazy before; but I -do not find very much time for it at present, because I am -reading about heat and fluids, so as not to tell lies in my -lectures. I got a note from the Society of Arts about the -platometer, awarding thanks and offering to defray the expenses -to the extent of £10, on the machine being produced in -working order. When I have arranged it in my head, I intend -to write to James Bryson about it.</p> - -<p>“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.</p> - -<p>“... It is difficult to keep up one’s interest in<span class="pagenum" id="Page_43">43</span> -intellectual matters when friends of the intellectual kind are -scarce. However, there are plenty friends not intellectual -who serve to bring out the active and practical habits of mind, -which overly-intellectual people seldom do. Wherefore, if I -am to be up this term, I intend to addict myself rather to the -working men who are getting up classes than to pups., who -are in the main a vexation. Meanwhile, there is the examination -to consider.</p> - -<p>“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.’</p> - -<p>“Macmillan proposes to get up a book of optics with my -assistance, and I feel inclined for the job. There is great -bother in making a mathematical book, especially on a subject -with which you are familiar, for in correcting it you do as you -would to pups.—look if the principle and result is right, and -forget to look out for small errors in the course of the work. -However, I expect the work will be salutary, as involving -hard work, and in the end much abuse from coaches and -students, and certainly no vain fame, except in Macmillan’s -puffs. But, if I have rightly conceived the plan of an -educational book on optics, it will be very different in manner, -though not in matter, from those now used.”</p> -</div> - -<p>The examination referred to was that for a -Fellowship at Trinity, and Maxwell was elected on -October 10th, 1855.</p> - -<p>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.</p> - -<p><span class="pagenum" id="Page_44">44</span></p> - -<p>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.”</p> - -<p>Still, he found time to attend Professor Willis’s -lectures on mechanism and to continue his reading. -“I have been reading,” he writes, “old books on -optics, and find many things in them far better than -what is new. The foreign mathematicians are discovering -for themselves methods which were well -known at Cambridge in 1720, but are now forgotten.”</p> - -<p>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.</p> - -<p>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.</p> - -<p>He decided to be a candidate if his father -approved. “For my own part,” he writes, “I think -the sooner I get into regular work the better, and -that the best way of getting into such work is to -profess one’s readiness by applying for it.” On the<span class="pagenum" id="Page_45">45</span> -20th of February he writes: “However, wisdom is of -many kinds, and I do not know which dwells with -wise counsellors most, whether scientific, practical, -political, or ecclesiastical. I hear there are candidates -of all kinds relying on the predominance of one or -other of these kinds of wisdom in the constitution of -the Government.”</p> - -<p>The second part of the paper on “Faraday’s Lines -of Force” was read during the term. Writing on the -4th of March, he expresses the hope soon to be able -to write out fully the paper. “I have done nothing -in that way this term,” he says, “but am just beginning -to feel the electrical state come on again.”</p> - -<p>His father was working at Edinburgh in support -of his candidature for Aberdeen, and when, in the -middle of March, he returned North, he found everything -well prepared. The two returned to Glenlair -together after a few days in Edinburgh, and Maxwell -was preparing to go back to Cambridge, when, on the -2nd of April, his father died suddenly.</p> - -<p>Writing to Mrs. Blackburn, he says: “My father -died suddenly to-day at twelve o’clock. He had been -giving directions about the garden, and he said he -would sit down and rest a little, as usual. After a -few minutes I asked him to lie down on the sofa, and -he did not seem inclined to do so; and then I got -him some ether, which had helped him before. -Before he could take any he had a slight struggle, -and all was over. He hardly breathed afterwards.”</p> - -<p>Almost immediately after this, Maxwell was -appointed to Aberdeen. His father’s death had -frustrated some at least of the intentions with which<span class="pagenum" id="Page_46">46</span> -he had applied for the post. He knew the old man -would be glad to see him the occupant of a Scotch -chair. He hoped, too, to be able to live with his -father at Glenlair for one half the year; but this was -not to be. No doubt the laboratory and the freedom -of the post, when compared with the routine work -of preparing men for the Tripos, had their inducements; -still, it may be doubted if the choice was -a wise one for him. The work of drilling classes, -composed, for the most part, of raw untrained lads, -in the elements of physics and mechanics was, as -Niven says in his preface to the collected works, not -that for which he was best fitted; while at Cambridge, -had he stayed, he must always have had among his -pupils some of the best mathematicians of the time; -and he might have founded some ten or fifteen years -before he did that Cambridge School of Physicists -which looks back with so much pride to him as their -master.</p> - -<p>Leave-taking at Trinity was a sad task. He -writes<a id="FNanchor_23" href="#Footnote_23" class="fnanchor">23</a> thus, June 4th, to Mr. R. B. <span class="locked">Litchfield:—</span></p> - -<div class="blockquot"> - -<p>“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.</p> - -<p>“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.”</p> -</div> - -<p><span class="pagenum" id="Page_47">47</span></p> - -<p>The summer of 1856 was spent at Glenlair, -where various friends were his guests—Lushington, -MacLennan, the two cousins Cay, and others. He -continued to work at optics, electricity, and magnetism, -and in October was busy with “a solemn address or -manifesto to the Natural Philosophers of the North, -which needed coffee and anchovies and a roaring hot -fire and spread coat-tails to make it natural.” This -was his inaugural lecture.</p> - -<p>In November he was at Aberdeen. Letters<a id="FNanchor_24" href="#Footnote_24" class="fnanchor">24</a> 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.</p> - -<div class="blockquot"> - -<p>“The session went off smoothly enough. I had Sun, all -the beginning of optics, and worked off all the experimental -part up to Fraunhofer’s lines, which were glorious to see with -a water-prism I have set up in the form of a cubical box, five -inch side....</p> - -<p>“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....</p> - -<p>“Last week I brewed chlorophyll (as the chemists word it), -a green liquor, which turns the invisible light red....</p> - -<p>“My last grind was the reduction of equations of colour -which I made last year. The result was eminently satisfactory.”</p> -</div> - -<p>Another letter,<a id="FNanchor_25" href="#Footnote_25" class="fnanchor">25</a> June 5th, 1857, also to Munro, -refers to the work of the University Commission and -the new statutes.</p> - -<p><span class="pagenum" id="Page_48">48</span></p> - -<div class="blockquot"> - -<p>“I have not seen Article 7, but I agree with your dissent -from it entirely. On the vested interest principle, I think the -men who intended to keep their fellowships by celibacy and -ordination, and got them on that footing, should not be -allowed to desert the virgin choir or neglect the priestly -office, but on those principles should be allowed to live out -their days, provided the whole amount of souls cured annually -does not amount to £20 in the King’s Book. But my doctrine -is that the various grades of College officers should be set on -such a basis that, although chance lecturers might be sometimes -chosen from among fresh fellows who are going away -soon, the reliable assistant tutors, and those that have a plain -calling that way, should, after a few years, be elected permanent -officers of the College, and be tutors and deans in their time, -and seniors also, with leave to marry, or, rather, never prohibited -or asked any questions on that head, and with leave to -retire after so many years’ service as seniors. As for the men -of the world, we should have a limited term of existence, and -that independent of marriage or ‘parsonage.’”</p> -</div> - -<p>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.</p> - -<p>For the winter session of 1857–58 he was again -at Aberdeen.</p> - -<p>The Adams Prize had been established in 1848 by -some members of St. John’s College, and connected -by them with the name of Adams “in testimony of -their sense of the honour he had conferred upon his -College and the University by having been the first -among the mathematicians of Europe to determine -from perturbations the unknown place of a disturbing<span class="pagenum" id="Page_49">49</span> -planet exterior to Uranus.” Professor Challis, Dr. -Parkinson, and Sir William Thomson, the examiners, -had selected as the subject for the prize to be awarded -in 1857 the “Motions of Saturn’s Rings.” For this -Maxwell had decided to compete, and his letters at -the end of 1857 tell of the progress of the task. -Thus, writing<a id="FNanchor_26" href="#Footnote_26" class="fnanchor">26</a> to Lewis Campbell from Glenlair on -August 28th, he <span class="locked">says:—</span></p> - -<div class="blockquot"> - -<p>“I have been battering away at Saturn, returning to the -charge every now and then. I have effected several breaches -in the solid ring, and now I am splash into the fluid one, amid -a clash of symbols truly astounding. When I reappear it will -be in the dusky ring, which is something like the state of the -air supposing the siege of Sebastopol conducted from a forest -of guns 100 miles one way, and 30,000 miles the other, and the -shot never to stop, but go spinning away round a circle, radius -170,000 miles.”</p> -</div> - -<p class="in0">And again<a id="FNanchor_27" href="#Footnote_27" class="fnanchor">27</a> to Miss Cay on the 28th of <span class="locked">November:—</span></p> - -<div class="blockquot"> - -<p>“I have been pretty steady at work since I came. The -class is small and not bright, but I am going to give them -plenty to do from the first, and I find it a good plan. I have -a large attendance of my old pupils, who go on with the higher -subjects. This is not part of the College course, so they come -merely from choice, and I have begun with the least amusing -part of what I intend to give them. Many had been reading -in summer, for they did very good papers for me on the old -subjects at the beginning of the month. Most of my spare -time I have been doing Saturn’s rings, which is getting on -now, but lately I have had a great many long letters to write—some -to Glenlair, some to private friends, and some all about -science.... I have had letters from Thomson and Challis -about Saturn—from Hayward, of Durham University, about<span class="pagenum" id="Page_50">50</span> -the brass top, of which he wants one. He says that the earth -has been really found to change its axis regularly in the way -I supposed. Faraday has also been writing about his own -subjects. I have had also to write Forbes a long report on -colours; so that for every note I have got I have had to write -a couple of sheets in reply, and reporting progress takes a deal -of writing and spelling.”</p> -</div> - -<p>He devised a model (now at the Cavendish -Laboratory) to exhibit the motions of the satellites -in a disturbed ring, “for the edification of sensible -image-worshippers.”</p> - -<p>The essay was awarded the prize, and secured for -its author great credit among scientific men.</p> - -<p>In another letter, written during the same session, -he says: “I find my principal work here is teaching -my men to avoid vague expressions, as ‘a certain -force,’ meaning uncertain; <em>may</em> instead of <em>must</em>; -<em>will be</em> instead of <em>is</em>; <em>proportional</em> instead of <em>equal</em>.”</p> - -<p>The death, during the autumn, of his College -friend Pomeroy, from fever in India, was a great blow -to him; his letters at the time show the depth of his -feelings and his beliefs.</p> - -<p>The question of the fusion of the two Colleges at -Aberdeen, King’s College and the Marischal College, -was coming to the fore. “Know all men,” he says, -in a letter to Professor Campbell, “that I am a -Fusionist.”</p> - -<p>In February, 1858, he was still engaged on Saturn’s -rings, while hard at work during the same time with -his classes. He had established a voluntary class for -his students of the previous year, and was reading -with them Newton’s “Lunar Theory and Astronomy.” -This was followed by “Electricity and Magnetism,”<span class="pagenum" id="Page_51">51</span> -Faraday’s book being the backbone of everything, “as -he himself is the nucleus of everything electric -since 1830.”</p> - -<p>In February, 1858, he announced his engagement -to Katherine Mary Dewar, the daughter of the -Principal of Marischal College.</p> - -<div class="blockquot"> - -<p>“Dear Aunt” (he says,<a id="FNanchor_28" href="#Footnote_28" class="fnanchor">28</a> February 18th, 1858), “this comes -to tell you that I am going to have a wife....</p> - -<p>“Don’t be afraid; she is not mathematical, but there are -other things besides that, and she certainly won’t stop mathematics. -The only one that can speak as an eye-witness is -Johnnie, and he only saw her when we were both trying to act -the indifferent. We have been trying it since, but it would -not do, and it was not good for either.”</p> -</div> - -<p>The wedding took place early in June. Professor -Campbell has preserved some of the letters written -by Maxwell to Miss Dewar, and these contain “the -record of feelings which in the years that followed -were transfused in action and embodied in a married -life which can only be spoken of as one of unexampled -devotion.”</p> - -<p>The project for the fusion of the two Colleges, -to which reference has been made, went on, and the -scheme was completed in 1860.</p> - -<p>The two Colleges were united to form the University -of Aberdeen, and the new chair of Natural -Philosophy thus created was filled by the appointment -of David Thomson, Professor of Natural Philosophy -in King’s College, and Maxwell’s senior. Mr. W. D. -Niven, in his preface to Maxwell’s works, when -dealing with this appointment, <span class="locked">writes:—</span></p> - -<p><span class="pagenum" id="Page_52">52</span></p> - -<div class="blockquot"> - -<p>“Professor Thomson, though not comparable to Maxwell -as a physicist, was nevertheless a remarkable man. He was -distinguished by singular force of character and great administrative -faculty, and he had been prominent in bringing -about the fusion of the Colleges. He was also an admirable -lecturer and teacher, and had done much to raise the standard -of scientific education in the north of Scotland. Thus the -choice made by the Commissioners, though almost inevitable, -had the effect of making it appear that Maxwell failed as a -teacher. There seems, however, to be no evidence to support -such an inference. On the contrary, if we may judge from the -number of voluntary students attending his classes in his last -College session, he would seem to have been as popular as a -professor as he was personally estimable.”</p> -</div> - -<p>The question whether Maxwell was a great teacher -has sometimes been discussed. I trust that the -following pages will give an answer to it. He was -not a prominent lecturer. As Professor Campbell -says,<a id="FNanchor_29" href="#Footnote_29" class="fnanchor">29</a> “Between his students’ ignorance and his vast -knowledge it was difficult to find a common measure. -The advice which he once gave to a friend whose -duty it was to preach to a country congregation, -‘Why don’t you give it them thinner?’ must often -have been applicable to himself.... Illustrations -of <i xml:lang="la" lang="la">ignotum per ignotius</i>, or of the abstruse -by some unobserved property of the familiar, -were multiplied with dazzling rapidity. Then the -spirit of indirectness and paradox, though he was -aware of its dangers, would often take possession of -him against his will, and, either from shyness or -momentary excitement, or the despair of making -himself understood, would land him in ‘chaotic<span class="pagenum" id="Page_53">53</span> -statements,’ breaking off with some quirk of ironical -humour.”</p> - -<p>But teaching is not all done by lecturing. His -books and papers are vast storehouses of suggestions -and ideas which the ablest minds of the past twenty -years have been since developing. To talk with him -for an hour was to gain inspiration for a year’s work; -to see his enthusiasm and to win his praise or -commendation were enough to compensate for many -weary struggles over some stubborn piece of apparatus -which would not go right, or some small source of -error which threatened to prove intractable and -declined to submit itself to calculation. The sure -judgment of posterity will confirm the verdict that -Clerk Maxwell was a great teacher, though lecturing -to a crowd of untrained undergraduates was a task -for which others were better fitted than he.</p> - -<hr /> - -<div id="toclink_54" class="chapter"> -<p><span class="pagenum" id="Page_54">54</span></p> - -<h2 class="nobreak" id="CHAPTER_IV">CHAPTER IV.<br /> - -<span class="subhead">PROFESSOR AT KING’S COLLEGE, LONDON.—LIFE -AT GLENLAIR.</span></h2> -</div> - -<p class="in0"><span class="firstword">In</span> 1860 Forbes resigned the chair of Natural -Philosophy at Edinburgh. Maxwell and Tait were -candidates, and Tait was appointed. In the summer -of the same year Maxwell obtained the vacant -Professorship of Natural Philosophy at King’s College, -London. This he held to 1865, and this period of -his life is distinguished by the appearance of some of -his most important papers. The work was arduous; -the College course extended over nine months of the -year; there were as well evening lectures to artisans -as part of his regular duties. His life in London was -useful to him in the opportunities it gave him for -becoming personally acquainted with Faraday and -others. He also renewed his intimacy with various -Cambridge friends.</p> - -<p>He was at the celebrated Oxford meeting of the -British Association in 1860, where he exhibited his -colour-box for mixing the colours of the spectrum. -In 1859, at the meeting at Aberdeen, he had read to -Section A his first paper on the “Dynamical Theory -of Gases,” published in the <i>Philosophical Magazine</i> -for January, 1860. The second part of the paper, -dealing with the conduction of heat and other -phenomena in a gas, was published in July, 1860, -after the Oxford meeting.</p> - -<p>A paper on the “Theory of Compound Colours”<span class="pagenum" id="Page_55">55</span> -was communicated to the Royal Society by Professor -Stokes in January, 1860. It contains the account of -his colour-box in the form finally adopted (most of -the important parts of the apparatus are still at the -Cavendish Laboratory), and a number of observations -by Mrs. Maxwell and himself, which will be more -fully described later.</p> - -<p>In November, 1860, he received for this work the -Rumford medal of the Royal Society.</p> - -<p>The next year, 1861, is of great importance in the -history of electrical science. The British Association -met at Manchester, and a Committee was appointed -on Standards of Electrical Resistance. Maxwell was -not a member. The committee reported at the -Cambridge meeting in 1862, and were reappointed -with extended duties. Maxwell’s name, among -others, was added, and he took a prominent part in -the deliberations of the committee, which, as their -Report<a id="FNanchor_30" href="#Footnote_30" class="fnanchor">30</a> presented in 1863 states, came to the -opinion, “after mature consideration, that the system -of so-called absolute electrical units, based on -purely mechanical measurements, is not only the best -system yet proposed, but is the only one consistent -with our present knowledge both of the relations -existing between the various electrical phenomena and -of the connection between these and the fundamental -measurements of time, space, and mass.”</p> - -<p>Appendix C of this Report, “On the Elementary -Relations between Electrical Measurements,” bears the -names of Clerk Maxwell and Fleeming Jenkin, and is -the foundation of everything that has been done in<span class="pagenum" id="Page_56">56</span> -the way of absolute electrical measurement since that -date; while Appendix D gives an account by the -same two workers of the experiments on the absolute -unit of electrical resistance made in the laboratory of -King’s College by Maxwell, Fleeming Jenkin, and -Balfour Stewart. Further experiments are described -in the report for 1864. The work thus begun was -consummated during the year 1894 by the legalisation -throughout the civilised world of a system of electrical -units based on those described in these reports.</p> - -<p>Meanwhile, Maxwell’s views on electro-magnetic -theory were quietly developing. Papers on “Physical -Lines of Force,” which appeared in the <i>Philosophical -Magazine</i> during 1861 and 1862, contain the germs -of his theory—expressed at that time, it is true, in a -somewhat material form. In the paper published -January, 1862, the now well-known relation between -the ratio of the electric units and the velocity of light -was established, and his correspondence with Fleeming -Jenkin and C. J. Munro about this time relates in -part to the experimental verification of this relation. -His experiments on this matter were published in the -“Philosophical Transactions” for 1868.</p> - -<p>This electrical theory occupied his mind mainly -during 1863 and 1864. In September of the latter -year he writes<a id="FNanchor_31" href="#Footnote_31" class="fnanchor">31</a> from Glenlair to C. Hockin, who had -taken Balfour Stewart’s place during the second series -of experiments on the measurement of resistance.</p> - -<div class="blockquot"> - -<p>“I have been doing several electrical problems. I have got -a theory of ‘electric absorption,’ <i>i.e.</i>, residual charge, etc., and -I very much want determinations of the specific induction,<span class="pagenum" id="Page_57">57</span> -electric resistance, and absorption of good dielectrics, such as -glass, shell-lac, gutta-percha, ebonite, sulphur, etc.</p> - -<p>“I have also cleared the electromagnetic theory of light -from all unwarrantable assumption, so that we may safely -determine the velocity of light by measuring the attraction -between bodies kept at a given difference of potential, the -value of which is known in electromagnetic measure.</p> - -<p>“I hope there will be resistance coils at the British Association.”</p> -</div> - -<p>This work resulted in his greatest electrical paper, -“A Dynamical Theory of the Electromagnetic Field,” -read to the Royal Society December 8th, 1864.</p> - -<p>But the molecular theory of gases was still -prominently before his mind.</p> - -<p>In 1862, writing<a id="FNanchor_32" href="#Footnote_32" class="fnanchor">32</a> to H. R. Droop, he <span class="locked">says:—</span></p> - -<div class="blockquot"> - -<p>“Some time ago, when investigating Bernoulli’s theory -of gases, I was surprised to find that the internal friction of -a gas (if it depends on the collision of particles) should be -independent of the density.</p> - -<p>“Stokes has been examining Graham’s experiments on the -rate of flow of gases through fine tubes, and he finds that the -friction, if independent of density, accounts for Graham’s -results; but, if taken proportional to density, differs from -those results very much. This seems rather a curious result, -and an additional phenomenon, explained by the ‘collision of -particles’ theory of gases. Still one phenomenon goes against -that theory—the relation between specific heat at constant -pressure and at constant volume, which is in air = 1·408, -while it ought to be 1·333.”</p> -</div> - -<p class="in0">And again<a id="FNanchor_33" href="#Footnote_33" class="fnanchor">33</a> in the same year, 21st April, 1862, to -Lewis <span class="locked">Campbell:—</span></p> - -<div class="blockquot"> - -<p>“Herr Clausius of Zürich, one of the heat philosophers, has -been working at the theory of gases being little bodies flying<span class="pagenum" id="Page_58">58</span> -about, and has found some cases in which he and I don’t tally. -So I am working it out again. Several experimental results -have turned up lately rather confirmatory than otherwise of -that theory.</p> - -<p>“I hope you enjoy the absence of pupils. I find the division -of them into smaller classes is a great help to me and to them; -but the total oblivion of them for definite intervals is a -necessary condition for doing them justice at the proper time.”</p> -</div> - -<p>The experiments on the viscosity of gases, which -formed the Bakerian Lecture to the Royal Society -read on February 8th, 1866, were the outcome of this -work. His house in 8, Palace Gardens, Kensington, -contained a large garret running the complete length.</p> - -<p>“To maintain the proper temperature a large fire -was for some days kept up in the room in the midst -of very hot weather. Kettles were kept on the fire and -large quantities of steam allowed to flow into the -room. Mrs. Maxwell acted as stoker, which was very -exhausting work when maintained for several consecutive -hours. After this the room was kept cool for -subsequent experiments by the employment of a -considerable amount of ice.”</p> - -<p>Next year, May, 1866, was read his paper on the -“Dynamical Theory of Gases,” in which errors in his -former papers, which had been pointed out by -Clausius, were corrected.</p> - -<p>Meanwhile he had resigned his London Professorship -at the end of the Session of 1865, and had been -succeeded by Professor W. G. Adams.</p> - -<p>For the next four years he lived chiefly at Glenlair, -working at his theory of electricity, occasionally, as -we shall see, visiting London and Cambridge, and<span class="pagenum" id="Page_59">59</span> -taking an active interest in the affairs of his own -neighbourhood. In 1865 he had a serious illness, -through which he was nursed with great care by Mrs. -Maxwell. His correspondence was considerable, and -absorbed much of his time. Much also was given to -the study of English literature; he was fond of -reading Chaucer, Milton, or Shakespeare aloud to -Mrs. Maxwell.</p> - -<p>He also read much theological and philosophical -literature, and all he read helped only to strengthen -that firm faith in the fundamentals of Christianity in -which he lived and died.</p> - -<p>In 1867 he and Mrs. Maxwell paid a visit to Italy, -which was a source of great pleasure to both.</p> - -<p>His chief scientific work was the preparation of -his “Electricity and Magnetism,” which did not -appear till 1873; the time was in the main one of -quiet thought and preparation for his next great task, -the foundation of the School of Physics in Cambridge.</p> - -<p>In 1868 the principalship of the United College -in the University of St. Andrews was vacant by the -resignation of Forbes, and Maxwell was invited by -several of the professors to stand. He, however, -declined to submit his name to the Crown.</p> - -<hr /> - -<div id="toclink_60" class="chapter"> -<p><span class="pagenum" id="Page_60">60</span></p> - -<h2 class="nobreak" id="CHAPTER_V">CHAPTER V.<br /> - -<span class="subhead">CAMBRIDGE.—PROFESSOR OF PHYSICS.</span></h2> -</div> - -<p class="in0"><span class="firstword">During</span> his retirement at Glenlair from 1865 to 1870 -Maxwell was frequently at Cambridge. He examined -in the Mathematical Tripos in 1866 and 1867, and -again in 1869 and 1870.</p> - -<p>The regulations for the Tripos had been in force -practically unchanged since 1848, and it was felt by -many that the range of subjects included was not -sufficiently extensive, and that changes were urgently -needed if Cambridge were to retain its position as the -centre of mathematical teaching. Natural Philosophy -was mentioned in the Schedule, but Natural Philosophy -included only Dynamics and Astronomy, Hydrostatics -and Physical Optics, with some simple Hydrodynamics -and Sound.</p> - -<p>The subjects of Heat, Electricity and Magnetism, -the Theory of Elastic Solids and Vibrations, Vortex-Motion -in Hydrodynamics, and much else, were -practically new since 1848. Stokes, Thomson, and -Maxwell in England, and Helmholtz in Germany, had -created them.</p> - -<p>Accordingly in June, 1868, a new plan of examinations -was sanctioned by the Senate to come into -force in January, 1873, and these various subjects -were explicitly included.</p> - -<p>Mr. Niven, who was one of those examined by -Maxwell in 1866, writes in the preface to the collected -<span class="locked">works:—</span></p> - -<p><span class="pagenum" id="Page_61">61</span></p> - -<div class="blockquot"> - -<p>“For some years previous to 1866, when Maxwell returned -to Cambridge as Moderator in the Mathematical Tripos, the -studies in the University had lost touch with the great -scientific movements going on outside her walls. It was said -that some of the subjects most in vogue had but little interest -for the present generation, and loud complaints began to be -heard that while such branches of knowledge as Heat, Electricity, -and Magnetism were left out of the Tripos examination, -the candidates were wasting their time and energy upon -mathematical trifles barren of scientific interest and of -practical results. Into the movement for reform Maxwell -entered warmly. By his questions in 1866, and subsequent -years, he infused new life into the examination; he took an -active part in drafting the new scheme introduced in 1873; -but most of all by his writings he exerted a powerful influence -on the younger members of the University, and was largely -instrumental in bringing about the change which has been -now effected.”</p> -</div> - -<p>But the University possessed no means of teaching -these subjects, and a Syndicate or Committee was -appointed, November 25th, 1868, “to consider the -best means of giving instruction to students in -Physics, especially in Heat, Electricity and Magnetism, -and the methods of providing apparatus for -this purpose.”</p> - -<p>Dr. Cookson, Master of St. Peter’s College, took an -active part in the work of the Syndicate. Professor -Stokes, Professor Liveing, Professor Humphry, Dr. -Phear, and Dr. Routh were among the members. -Maxwell himself was in Cambridge that winter, as -Examiner for the Tripos, and his work as Moderator -and Examiner in the two previous years had done -much to show the necessity of alterations and to -indicate the direction which changes should take.</p> - -<p><span class="pagenum" id="Page_62">62</span></p> - -<p>The Syndicate reported February 27th, 1869. They -called attention to the Report of the Royal Commission -of 1850. The Commissioners had “prominently -urged the importance of cultivating a knowledge of -the great branches of Experimental Physics in the -University”; and in page 118 of their Report, after -commending the manner in which the subject of -Physical Optics is studied in the University, and -pointing out that “there is, perhaps, no public institution -where it is better represented or prosecuted with -more zeal and success in the way of original research,” -they had stated that “no reason can be assigned why -other great branches of Natural Science should not -become equally objects of attention, or why Cambridge -should not become a great school of physical and -experimental, as it is already of mathematical and -classical, instruction.”</p> - -<p>And again the Commissioners remark: “In a -University so thoroughly imbued with the mathematical -spirit, physical study might be expected to -assume within its precincts its highest and severest -tone, be studied under more abstract forms, with -more continual reference to mathematical laws, and -therefore with better hope of bringing them one by -one under the domain of mathematical investigation -than elsewhere.”</p> - -<p>After calling attention to these statements the -Report of the Syndicate then <span class="locked">continues:—</span></p> - -<p>“In the scheme of Examination for Honours in -the Mathematical Tripos approved by Grace of the -Senate on the 2nd of June, 1868, Heat, Electricity and -Magnetism, if not introduced for the first time, had a<span class="pagenum" id="Page_63">63</span> -much greater degree of importance assigned to them -than at any previous period, and these subjects will -henceforth demand a corresponding amount of attention -from the candidates for Mathematical Honours. -The Syndicate have limited their attention almost -entirely to the question of providing public instruction -in Heat, Electricity and Magnetism. They recognise -the importance and advantage of tutorial instruction -in these subjects in the several colleges, but they are -also alive to the great impulse given to studies of this -kind, and to the large amount of additional training -which students may receive through the instruction -of a public Professor, and by knowledge gained in a -well-appointed laboratory.”</p> - -<p>“In accordance with these views, and at an early -period in their deliberations, they requested the Professors<a id="FNanchor_34" href="#Footnote_34" class="fnanchor">34</a> -of the University, who are engaged in teaching -Mathematical and Physical Science, to confer together -upon the present means of teaching Experimental -Physics, especially Heat, Electricity and Magnetism, -and to inform them how the increased requirements -of the University in this respect could be met by -them.”</p> - -<p>“The Professors, so consulted, favoured the Syndicate -with a report on the subject, which the Syndicate -now beg leave to lay before the Senate. It points out -how the requirements of the University might be -“partially met,” but the Professors state distinctly -that they “do not think that they are able to meet -the want of an extensive course of lectures on Physics<span class="pagenum" id="Page_64">64</span> -treated as such, and in great measure experimentally. -As Experimental Physics may fairly be considered to -come within the province of one or more of the above-mentioned -Professors, the Syndicate have considered -whether now or at some future time some arrangement -might not be made to secure the effective -teaching of this branch of science, without having -resort to the services of an additional Professor. They -are, however, of opinion that such an arrangement -cannot be made at the present time, and that the -exigencies of the case may be best met by founding a -new professorship which shall terminate with the -tenure of office of the Professor first elected. The -services of a man of the highest attainments in -science, devoting his life to public teaching as such -Professor, and engaged in original research, would be -of incalculable benefit to the University.”</p> - -<p>The Report goes on to point out that a laboratory -would be necessary, and also apparatus. It is -estimated that £5,000 would cover the cost of the -laboratory, and £1,300 the necessary apparatus. Provision -is also made for a demonstrator and a laboratory -assistant, and the Report closes with a recommendation -that a special Syndicate of Finance should be -appointed to consider the means of raising the funds.</p> - -<p>The Professors in their Report to the Syndicate -point out that teaching in Experimental Physics is -needed for the Mathematical Tripos, the Natural -Sciences Tripos, certain Special examinations, and the -first examination for the degree of M.B. It appeared -to them clear that there was work for a new Professor.</p> - -<p>In May, 1869, the Financial Syndicate<span class="pagenum" id="Page_65">65</span> -recommended by the above Report was appointed “to -consider the means of raising the necessary funds for -establishing a professor and demonstrator of Experimental -Physics, and for providing buildings and -apparatus required for that department of science, -and further to consider other wants of the University, -and the sources from which those wants may be -supplied.”</p> - -<p>The Syndicate endeavoured to meet the expenditure -by inquiry from the several Colleges whether -they would be willing to make contributions from -their corporate funds, but without success.</p> - -<p>“The answers of the Colleges indicated such a -want of concurrence in any proposal to raise contributions -from the corporate funds of Colleges by any -kind of direct taxation that the Syndicate felt obliged -to abandon the notion of obtaining the necessary funds -from this source, and accordingly to limit the number -of objects which they should recommend the Senate -to accomplish.”</p> - -<p>External authority was necessary before the -colleges would submit to taxation for University -purposes, and it was left to the Royal Commission of -1877 to carry into effect many of the suggestions made -by the Syndicate. Meanwhile they contented themselves -with recommending means for raising an annual -stipend of £660 for the professor, demonstrator, and -assistant, and a capital sum of £5,000, or thereabouts, -for the expenses of a building.</p> - -<p>The Syndicate’s Report was issued in an amended -form in the May term of 1870, and before any decision -was taken on it the Vice-Chancellor, Dr. Atkinson, on<span class="pagenum" id="Page_66">66</span> -October 13th, 1870, published “the following munificent -offer of his grace the Duke of Devonshire, the -Chancellor of the University,” who had been chairman -of the Commission on Scientific Education.</p> - -<div class="blockquot"> -<p class="sigright"> -<span class="l4">“Holker Hall,</span><br /> -Grange, Lancashire. -</p> - -<p>“<span class="smcap">My dear Mr. Vice-Chancellor</span>,—I have the honour to -address you for the purpose of making an offer to the University, -which, if you see no objection, I shall be much obliged to you -to submit in such manner as you may think fit for the consideration -of the Council and the University.</p> - -<p>“I find in the report dated February 29th, 1869, of the -Physical Science Syndicate, recommending the establishment -of a Professor and Demonstrator of Experimental Physics, that -the buildings and apparatus required for this department of -science are estimated to cost £6,300.</p> - -<p>“I am desirous to assist the University in carrying this -recommendation into effect, and shall accordingly be prepared -to provide the funds required for the building and apparatus -as soon as the University shall have in other respects completed -its arrangements for teaching Experimental Physics, and shall -have approved the plan of the building.</p> - -<p class="sigright"> -“I remain, my dear Mr. Vice-Chancellor,<br /> -<span class="l2">“Yours very faithfully,</span><br /> -“<span class="smcap">Devonshire</span>.” -</p> -</div> - -<p>By his generous action the University was relieved -from all expense connected with the building. A -Grace establishing a Professorship of Experimental -Physics was confirmed by the Senate February 9th, -1871, and March 8th was fixed for the election.</p> - -<p>Meanwhile who was to be Professor? Sir W. -Thomson’s name had been mentioned, but he, it was -known, would not accept the post. Maxwell was then -applied to, and at first he was unwilling to leave -Glenlair. Professor Stokes, the Hon. J. W. Strutt<span class="pagenum" id="Page_67">67</span> -(Lord Rayleigh), Mr. Blore of Trinity, and others -wrote to him. Lord Rayleigh’s letter<a id="FNanchor_35" href="#Footnote_35" class="fnanchor">35</a> is as follows:</p> - -<div class="blockquot"> -<p class="sigright"> -“Cambridge, 14th February, 1871. -</p> - -<p>“When I came here last Friday I found everyone talking -about the new professorship, and hoping that you would come. -Thomson, it seems, has definitely declined.... There is -no one here in the least fit for the post. What is wanted by -most who know anything about it is not so much a lecturer as -a mathematician who has actual experience in experimenting, -and who might direct the energies of the younger Fellows and -bachelors into a proper channel. There must be many who -would be willing to work under a competent man, and who, -while learning themselves, would materially assist him.... -I hope you may be induced to come; if not, I don’t know -who it is to be. Do not trouble to answer me about this, as I -believe others have written to you about it.”</p> -</div> - -<p>On the 15th of February, Maxwell wrote to Mr. -<span class="locked">Blore:—</span></p> - -<div class="blockquot"> - -<p>“I had no intention of applying for the post when I got -your letter, and I have none now, unless I come to see that I -can do some good by it.” The letter continues:—“The -class of Physical Investigations, which might be undertaken -with the help of men of Cambridge education, and which -would be creditable to the University, demand in general a -considerable amount of dull labour, which may or may not be -attractive to the pupils.”</p> -</div> - -<p>However, on the 24th of February, Mr. Blore wrote -to the Electoral <span class="locked">Roll:—</span></p> - -<p>“I am authorised to give notice that Mr. John (<i xml:lang="la" lang="la">sic</i>) -Clerk Maxwell, F.R.S., formerly Professor of Natural -Philosophy at Aberdeen, and at King’s College, -London, is a candidate for the professorship of -Experimental Physics.”</p> - -<p><span class="pagenum" id="Page_68">68</span></p> - -<p>Maxwell was elected without opposition. Writing<a id="FNanchor_36" href="#Footnote_36" class="fnanchor">36</a> -to his wife from Cambridge, 20th March, 1871, he -<span class="locked">says:—</span></p> - -<div class="blockquot"> - -<p>“There are two parties about the professorship. One wants -popular lectures, and the other cares more for experimental -work. I think there should be a gradation—popular lectures -and rough experiments for the masses; real experiments for -real students; and laborious experiments for first-rate men -like Trotter and Stuart and Strutt.”</p> -</div> - -<p class="in0">While in a letter<a id="FNanchor_37" href="#Footnote_37" class="fnanchor">37</a> from Glenlair to C. J. Munro, dated -March 15th, 1871, he writes:—“The Experimental -Physics at Cambridge is not built yet, but we are -going to try. The desideratum is to set a Don and a -Freshman to observe and register (say) the vibrations -of a magnet together, or the Don to turn a watch and -the Freshman to observe and govern him.”</p> - -<p>In October he delivered his Introductory Lecture. -A few quotations will show the spirit in which he -approached his task.</p> - -<div class="blockquot"> - -<p>“In a course of Experimental Physics we may consider -either the Physics or the Experiments as the leading feature. -We may either employ the experiments to illustrate the -phenomena of a particular branch of Physics, or we may -make some physical research in order to exemplify a particular -experimental method. In the order of time, we should begin, -in the Lecture Room, with a course of lectures on some branch -of Physics aided by experiments of illustration, and conclude, -in the Laboratory, with a course of experiments of research.</p> - -<p>“Let me say a few words on these two classes of experiments—Experiments -of Illustration and Experiments of -Research. The aim of an experiment of illustration is to<span class="pagenum" id="Page_69">69</span> -throw light upon some scientific idea so that the student may -be enabled to grasp it. The circumstances of the experiment -are so arranged that the phenomenon which we wish to observe -or to exhibit is brought into prominence, instead of being -obscured and entangled among other phenomena, as it is when -it occurs in the ordinary course of nature. To exhibit illustrative -experiments, to encourage others to make them, and to -cultivate in every way the ideas on which they throw light, -forms an important part of our duty. The simpler the -materials of an illustrative experiment, and the more familiar -they are to the student, the more thoroughly is he likely to -acquire the idea which it is meant to illustrate. The educational -value of such experiments is often inversely proportional -to the complexity of the apparatus. The student who uses -home-made apparatus, which is always going wrong, often -learns more than one who has the use of carefully adjusted -instruments, to which he is apt to trust, and which he dares -not take to pieces.</p> - -<p>“It is very necessary that those who are trying to learn from -books the facts of physical science should be enabled by the -help of a few illustrative experiments to recognise these facts -when they meet with them out of doors. Science appears to -us with a very different aspect after we have found out that it -is not in lecture-rooms only, and by means of the electric light -projected on a screen, that we may witness physical phenomena, -but that we may find illustrations of the highest doctrines of -science in games and gymnastics, in travelling by land and by -water, in storms of the air and of the sea, and wherever there -is matter in motion.</p> - -<p>“If, therefore, we desire, for our own advantage and for the -honour of our University, that the Devonshire Laboratory -should be successful, we must endeavour to maintain it in -living union with the other organs and faculties of our learned -body. We shall therefore first consider the relation in which -we stand to those mathematical studies which have so long -flourished among us, which deal with our own subjects, and -which differ from our experimental studies only in the mode in -which they are presented to the mind.</p> - -<p><span class="pagenum" id="Page_70">70</span></p> - -<p>“There is no more powerful method for introducing knowledge -into the mind than that of presenting it in as many -different ways as we can. When the ideas, after entering -through different gateways, effect a junction in the citadel of -the mind, the position they occupy becomes impregnable. -Opticians tell us that the mental combination of the views of -an object which we obtain from stations no further apart than -our two eyes is sufficient to produce in our minds an impression -of the solidity of the object seen; and we find that this impression -is produced even when we are aware that we are -really looking at two flat pictures placed in a stereoscope. It -is therefore natural to expect that the knowledge of physical -science obtained by the combined use of mathematical analysis -and experimental research will be of a more solid, available, -and enduring kind than that possessed by the mere mathematician -or the mere experimenter.</p> - -<p>“But what will be the effect on the University if men -pursuing that course of reading which has produced so many -distinguished Wranglers turn aside to work experiments? -Will not their attendance at the Laboratory count not merely -as time withdrawn from their more legitimate studies, but as -the introduction of a disturbing element, tainting their mathematical -conceptions with material imagery, and sapping their -faith in the formulæ of the text-books? Besides this, we have -already heard complaints of the undue extension of our studies, -and of the strain put upon our questionists by the weight of -learning which they try to carry with them into the Senate-House. -If we now ask them to get up their subjects not only -by books and writing, but at the same time by observation and -manipulation, will they not break down altogether? The -Physical Laboratory, we are told, may perhaps be useful to -those who are going out in Natural Science, and who do not -take in Mathematics, but to attempt to combine both kinds of -study during the time of residence at the University is more -than one mind can bear.</p> - -<p>“No doubt there is some reason for this feeling. Many of -us have already overcome the initial difficulties of mathematical -training. When we now go on with our study, we feel<span class="pagenum" id="Page_71">71</span> -that it requires exertion and involves fatigue, but we are confident -that if we only work hard our progress will be certain.</p> - -<p>“Some of us, on the other hand, may have had some -experience of the routine of experimental work. As soon as -we can read scales, observe times, focus telescopes, and so on, -this kind of work ceases to require any great mental effort. -We may, perhaps, tire our eyes and weary our backs, but we -do not greatly fatigue our minds.</p> - -<p>“It is not till we attempt to bring the theoretical part of -our training into contact with the practical that we begin to -experience the full effect of what Faraday has called ‘mental -inertia’—not only the difficulty of recognising, among the -concrete objects before us, the abstract relation which we have -learned from books, but the distracting pain of wrenching the -mind away from the symbols to the objects, and from the -objects back to the symbols. This, however, is the price we -have to pay for new ideas.</p> - -<p>“But when we have overcome these difficulties, and -successfully bridged over the gulph between the abstract and -the concrete, it is not a mere piece of knowledge that we have -obtained; we have acquired the rudiment of a permanent -mental endowment. When, by a repetition of efforts of this -kind, we have more fully developed the scientific faculty, the -exercise of this faculty in detecting scientific principles in -nature, and in directing practice by theory, is no longer irksome, -but becomes an unfailing source of enjoyment, to which -we return so often that at last even our careless thoughts -begin to run in a scientific channel.</p> - -<p>“Our principal work, however, in the Laboratory must be -to acquaint ourselves with all kinds of scientific methods, to -compare them and to estimate their value. It will, I think, -be a result worthy of our University, and more likely to be -accomplished here than in any private laboratory, if, by the -free and full discussion of the relative value of different -scientific procedures, we succeed in forming a school of -scientific criticism and in assisting the development of the -doctrine of method.</p> - -<p>“But admitting that a practical acquaintance with the<span class="pagenum" id="Page_72">72</span> -methods of Physical Science is an essential part of a mathematical -and scientific education, we may be asked whether we -are not attributing too much importance to science altogether -as part of a liberal education.</p> - -<p>“Fortunately, there is no question here whether the -University should continue to be a place of liberal education, -or should devote itself to preparing young men for particular -professions. Hence, though some of us may, I hope, see reason -to make the pursuit of science the main business of our lives, -it must be one of our most constant aims to maintain a living -connexion between our work and the other liberal studies of -Cambridge, whether literary, philological, historical, or -philosophical.</p> - -<p>“There is a narrow professional spirit which may grow up -among men of science just as it does among men who practise -any other special business. But surely a University is the -very place where we should be able to overcome this tendency -of men to become, as it were, granulated into small worlds, -which are all the more worldly for their very smallness? We -lose the advantage of having men of varied pursuits collected -into one body if we do not endeavour to imbibe some of the -spirit even of those whose special branch of learning is different -from our own.”</p> -</div> - -<p>Another expression of his views on the position of -Physics at the time will be found in his address to -Section A of the British Association, when President -at the Liverpool meeting of 1870.</p> - -<hr /> - -<div id="toclink_73" class="chapter"> -<p><span class="pagenum" id="Page_73">73</span></p> - -<h2 class="nobreak" id="CHAPTER_VI">CHAPTER VI.<br /> - -<span class="subhead">CAMBRIDGE—THE CAVENDISH LABORATORY.</span></h2> -</div> - -<p class="in0"><span class="firstword">But</span> the laboratory was not yet built. A Syndicate, -of which Maxwell was a member, was appointed to -consider the question of a site, to take professional -advice, and to obtain plans and estimates. Professor -Maxwell and Mr. Trotter visited various laboratories -at home and abroad for the purpose of ascertaining -the best arrangements. Mr. W. M. Fawcett was -appointed architect; the tender of Mr. John Loveday, -of Kebworth, for the building at a cost of £8,450, -exclusive of gas, water, and heating, was accepted in -March, 1872, and the building<a id="FNanchor_38" href="#Footnote_38" class="fnanchor">38</a> was begun during the -summer.</p> - -<p>In the meantime Maxwell began to lecture, finding -a home where he could.</p> - -<div class="blockquot"> - -<p>“Lectures begin 24th,” he writes from Glenlair, October -19th, 1872. “Laboratory rising, I hear, but I have no place -to erect my chair, but move about like the cuckoo, depositing -my notions in the Chemical Lecture-room 1st term; in the -Botanical in Lent, and in Comparative Anatomy in Easter.”</p> -</div> - -<p>It was not till June, 1874, that the building was -complete, and on the 16th the Chancellor formally -presented his gift of the Cavendish Laboratory to the -University. In the correspondence previous to this -time it was spoken of as the Devonshire Laboratory. -The name Cavendish commemorated the work of the -great physicist of a century earlier, whose writings<span class="pagenum" id="Page_74">74</span> -Maxwell was shortly to edit, as well as the generosity -of the Chancellor.</p> - -<p>In their letter of thanks to the Duke of Devonshire -the University <span class="locked">write:—</span></p> - -<p>“<span xml:lang="la" lang="la">Unde vero conventius poterat illis artibus -succurri quam e tua domo quæ in ipsis jam pridem -inclaruerat. Notum est Henricum Cavendish quem -secutus est Coulombius primum ita docuisse, quæ sit -vis electrica ut eam numerorum modulis illustraret; -adhibitis rationibus quas hodie veras esse constat.</span>” -And they suggest the name as suitable for the -building. To this the Chancellor replied, after referring -to the work of Henry Cavendish: “<span xml:lang="la" lang="la">Quod -pono in officinâ ipsâ nuncupandâ nomen ejus commemorare -dignati sitis, id grato animo accepi.</span>”</p> - -<p>The building had cost far more than the original -estimate, but the Chancellor’s generosity was not -limited, and on July 21st, 1874, he wrote to the <span class="locked">Vice-Chancellor:—</span></p> - -<p>“It is my wish to provide all instruments for the -Cavendish Laboratory which Professor Maxwell may -consider to be immediately required, either in his -lectures or otherwise.”</p> - -<p>Maxwell prepared a list, but explained while doing -it that time and thought were necessary to secure the -best form of instruments; and he continues, writing to -the Vice-Chancellor: “I think the Duke fully understood -from what I said to him that to furnish the -Laboratory will be a matter of several years’ duration. -I shall consider myself, however,” he says, “at liberty -to contribute to the Laboratory any instruments -which I have had constructed in former years, and<span class="pagenum" id="Page_75">75</span> -which may be found still useful, and also from time to -time to procure others for special researches.”</p> - -<p>In 1877 in his annual report Professor Maxwell -announced that the Chancellor<a id="FNanchor_39" href="#Footnote_39" class="fnanchor">39</a> had now “completed -his gift to the University by furnishing the Cavendish -Laboratory with apparatus suited to the present state -of science.”</p> - -<p>The stock of apparatus, however, was still small, -although Maxwell in the most generous manner -himself spent large sums in adding to it; for the -Professor was most particular in procuring only -expensive instruments by the best makers, with such -additional improvements as he could himself suggest.</p> - -<p>In March, 1874, a Demonstratorship of Physics -had been established, and Mr. Garnett of St. John’s -College was appointed.</p> - -<p>Work began in the laboratory in October, 1874. -At first the number of students was small. Only -seventeen names appear in the Natural Sciences -Tripos<a id="FNanchor_40" href="#Footnote_40" class="fnanchor">40</a> list for 1874, and few of those did Physics.</p> - -<p>The fear alluded to by the Professor in his introductory -lecture, that men reading for the Mathematical<span class="pagenum" id="Page_76">76</span> -Tripos would not find time for attendance at the -laboratory, was justified. One of the weaknesses of -our Cambridge plan has been the divorce between -Mathematics and experimental work, encouraged -by our system of examinations. Experimental -knowledge is supposed not to be needed for the -Mathematical Tripos; the Mathematics permitted in -the Natural Sciences Tripos are very simple; thus -it came about that few men while reading for the -Mathematical Tripos attended the laboratory, and -this unfortunate result was intensified by the action -of the University in 1877–78, when the regulations -for the Mathematical Tripos were again altered.<a id="FNanchor_41" href="#Footnote_41" class="fnanchor">41</a></p> - -<p>Still there were pupils eager and willing to work, -though they were chiefly men who had already taken -their B.A. degree, and who wished to continue -Physical reading and research, even though it involved -“a considerable amount of dull labour not -altogether attractive.” My own work there began in -1876, and it may be interesting if I recall my reminiscences -of that time.</p> - -<p>The first experiments I can recollect related to the -measurement of electrical resistance. I well remember<span class="pagenum" id="Page_77">77</span> -Maxwell explaining the principle of Wheatstone’s -bridge, and my own wish at the time that I had come -to the laboratory before the Tripos, instead of afterwards. -Lord Rayleigh had, during the examination, -set an easy question which I failed to do for want -of some slight experimental knowledge, and the first -few words of Maxwell’s talk showed me the solution.</p> - -<p>I did not attend his lectures regularly—they were -given, I think, at an hour which I was obliged to -devote to teaching; besides, there was his book, the -“Electricity and Magnetism,” into which I had just -dipped before the Tripos, to work at.</p> - -<p>Chrystal and Saunder were then busy at their -verification of Ohm’s law. They were using a number -of the Thomson form of tray Daniell’s cells, and -Maxwell was anxious for tests of various kinds to -be made on these cells; these I undertook, and -spent some time over various simple measurements -on them. He then set me to work at some of the -properties of a stratified dielectric, consisting, if I -remember rightly, of sheets of paraffin paper and -mica. By this means I became acquainted with -various pieces of apparatus. There were no regular -classes and no set drill of demonstrations arranged -for examination purposes; these came later. In Maxwell’s -time those who wished to work had the use of -the laboratory and assistance and help from him, but -they were left pretty much to themselves to find out -about the apparatus and the best methods of using it.</p> - -<p>Rather later than this Schuster came and did -some of his spectroscope work. J. E. H. Gordon -was busy with the preliminary observations for his<span class="pagenum" id="Page_78">78</span> -determination of Verdet’s constant, and Niven had -various electrical experiments on hand; while Fleming -was at work on the B. A. resistance coils.</p> - -<p>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.</p> - -<p>Eventually I selected as a subject the form of the -wave surface in a biaxial crystal, and set to work in -a room assigned to me. The Professor used to come -in on most days to see how I was getting on. Generally -he brought his dog, which sometimes was shut up in -the next room while he went to college. Dogs were -not allowed in college, and Maxwell had an amusing -way of describing how Toby once wandered into -Trinity, and by some doggish instinct discovered -immediately, to his intense amazement, that he was -in a place where no dogs had been since the college -was. Toby was not always quiet in his master’s -absence, and his presence in the next room was somewhat -disturbing.</p> - -<p>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 <span class="locked">said:—</span></p> - -<p>“Well, Chrystal has been talking to me, and<span class="pagenum" id="Page_79">79</span> -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.”</p> - -<p>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.</p> - -<p>For the next year and a half I was working -regularly at the laboratory and saw him almost daily -during term time.</p> - -<p>Of these last years there really is but little to tell. -His own scientific work went on. The “Electricity -and Magnetism” was written mostly at Glenlair. -About the time of his return to Cambridge, in October, -1872, he writes<a id="FNanchor_42" href="#Footnote_42" class="fnanchor">42</a> to Lewis <span class="locked">Campbell:—</span></p> - -<div class="blockquot"> - -<p>“I am continually engaged in stirring up the Clarendon -Press, but they have been tolerably regular for two months. I -find nine sheets in thirteen weeks is their average. Tait gives -me great help in detecting absurdities. I am getting converted -to quaternions, and have put some in my book.”</p> -</div> - -<p>The book was published in 1873. The Text-book -of Heat was written during the same period, while -“Matter and Motion,” “a small book on a great -subject,” was published in 1876.</p> - -<p>In 1873 and 1874 he was one of the examiners for -the Natural Sciences Tripos, and in 1873 he was the<span class="pagenum" id="Page_80">80</span> -first additional examiner for the Mathematical Tripos, -in accordance with the scheme which he had done so -much to promote in 1868.</p> - -<p>Many of his shorter papers were written about the -same time. The ninth edition of the <i>Encyclopædia -Britannica</i> was being published, and Professor Baynes -had enlisted his aid in the work. The articles -“Atom,” “Attraction,” “Capillary Action,” “Constitution -of Bodies,” “Diffusion,” “Ether,” “Faraday,” and -others are by him.</p> - -<p>He also wrote a number of papers for <i>Nature</i>. -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 <span class="locked">follow:—</span></p> - -<div class="blockquot"> - -<p>“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.</p> - -<p>“Each molecule therefore throughout the universe bears<span class="pagenum" id="Page_81">81</span> -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.</p> - -<p>“No theory of evolution can be formed to account for the -similarity of molecules, for evolution necessarily implies continuous -change, and the molecule is incapable of growth or -decay, of generation or destruction.</p> - -<p>“None of the processes of Nature, since the time when -Nature began, have produced the slightest difference in the -properties of any molecule. We are therefore unable to -ascribe either the existence of the molecules or the identity -of their properties to any of the causes which we call natural.</p> - -<p>“On the other hand, the exact equality of each molecule to -all others of the same kind gives it, as Sir John Herschel has -well said, the essential character of a manufactured article, -and precludes the idea of its being eternal and self-existent.</p> - -<p>“Thus we have been led along a strictly scientific path, -very near to the point at which Science must stop—not that -Science is debarred from studying the internal mechanism of a -molecule which she cannot take to pieces any more than from -investigating an organism which she cannot put together. But -in tracing back the history of matter, Science is arrested when -she assures herself, on the one hand, that the molecule has -been made, and, on the other, that it has not been made by -any of the processes we call natural.</p> - -<p>“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.</p> - -<p>“It is only when we contemplate, not matter in itself, but -the form in which it actually exists, that our mind finds something -on which it can lay hold.</p> - -<p>“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<span class="pagenum" id="Page_82">82</span> -such truths for purposes of deduction, but we have no data for -speculating as to their origin.</p> - -<p>“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 -<em>collocation</em>, to use the expression of Dr. Chalmers, of things -which we have no difficulty in imagining to have been arranged -otherwise.</p> - -<p>“The form and dimensions of the orbits of the planets, for -instance, are not determined by any law of nature, but depend -upon a particular collocation of matter. The same is the case -with respect to the size of the earth, from which the standard -of what is called the metrical system has been derived. But -these astronomical and terrestrial magnitudes are far inferior -in scientific importance to that most fundamental of all -standards which forms the base of the molecular system. -Natural causes, as we know, are at work which tend to modify, -if they do not at length destroy, all the arrangements and -dimensions of the earth and the whole solar system. But -though in the course of ages catastrophes have occurred and -may yet occur in the heavens, though ancient systems may be -dissolved and new systems evolved out of their ruins, the -molecules out of which these systems are built—the foundation -stones of the material universe—remain unbroken and unworn. -They continue this day as they were created—perfect in -number and measure and weight; and from the ineffaceable -characters impressed on them we may learn that those aspirations -after accuracy in measurement, and justice in action, -which we reckon among our noblest attributes as men, are -ours because they are essential constituents of the image of -Him who in the beginning created, not only the heaven and -the earth, but the materials of which heaven and earth consist.”</p> -</div> - -<p>This was criticised in <i>Nature</i> by Mr. C. J. Munro, -and at a later time by Clifford in one of his essays.</p> - -<p>Some correspondence with the Bishop of Gloucester -and Bristol on the authority for the comparison -of molecules to manufactured articles is<span class="pagenum" id="Page_83">83</span> -given by Professor Campbell, and in it Maxwell -points out that the latter part of the article “Atom” -in the <i>Encyclopædia</i> is intended to meet Mr. Munro’s -criticism.</p> - -<p>In 1874 the British Association met at Belfast, -under the presidency of Tyndall. Maxwell was present, -and published afterwards in <i>Blackwood’s Magazine</i> -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.</p> - -<hr class="narrow" /> -<p class="p1 center noafter">BRITISH ASSOCIATION, 1874.</p> - -<p class="center smaller p1 b1 noafter"><i>Notes of the President’s Address.</i></p> - -<div class="poetry-container nobreak"> -<div class="poetry"> - <div class="stanza"> - <div class="verse indent0">In the very beginnings of science, the parsons, who managed things then,</div> - <div class="verse indent0">Being handy with hammer and chisel, made gods in the likeness of men;</div> - <div class="verse indent0">Till commerce arose, and at length some men of exceptional power</div> - <div class="verse indent0">Supplanted both demons and gods by the atoms, which last to this hour.</div> - <div class="verse indent0">Yet they did not abolish the gods, but they sent them well out of the way,</div> - <div class="verse indent0">With the rarest of nectar to drink, and blue fields of nothing to sway.</div> - <div class="verse indent0">From nothing comes nothing, they told us—naught happens by chance, but by fate;</div> - <div class="verse indent0">There is nothing but atoms and void, all else is mere whims out of date!</div> - <div class="verse indent0">Then why should a man curry favour with beings who cannot exist,</div> - <div class="verse indent0">To compass some petty promotion in nebulous kingdoms of mist?</div> - <div class="verse indent0">But not by the rays of the sun, nor the glittering shafts of the day,</div> - <div class="verse indent0">Must the fear of the gods be dispelled, but by words, and their wonderful play.</div><span class="pagenum" id="Page_84">84</span> - <div class="verse indent0">So treading a path all untrod, the poet-philosopher sings</div> - <div class="verse indent0">Of the seeds of the mighty world—the first-beginnings of things;</div> - <div class="verse indent0">How freely he scatters his atoms before the beginning of years;</div> - <div class="verse indent0">How he clothes them with force as a garment, those small incompressible spheres!</div> - <div class="verse indent0">Nor yet does he leave them hard-hearted—he dowers them with love and with hate,</div> - <div class="verse indent0">Like spherical small British Asses in infinitesimal state;</div> - <div class="verse indent0">Till just as that living Plato, whom foreigners nickname Plateau,<a id="FNanchor_43" href="#Footnote_43" class="fnanchor">43</a></div> - <div class="verse indent0">Drops oil in his whisky-and-water (for foreigners sweeten it so);</div> - <div class="verse indent0">Each drop keeps apart from the other, enclosed in a flexible skin,</div> - <div class="verse indent0">Till touched by the gentle emotion evolved by the prick of a pin:</div> - <div class="verse indent0">Thus in atoms a simple collision excites a sensational thrill,</div> - <div class="verse indent0">Evolved through all sorts of emotion, as sense, understanding, and will</div> - <div class="verse indent0">(For by laying their heads all together, the atoms, as councillors do,</div> - <div class="verse indent0">May combine to express an opinion to every one of them new).</div> - <div class="verse indent0">There is nobody here, I should say, has felt true indignation at all,</div> - <div class="verse indent0">Till an indignation meeting is held in the Ulster Hall;</div> - <div class="verse indent0">Then gathers the wave of emotion, then noble feelings arise,</div> - <div class="verse indent0">Till you all pass a resolution which takes every man by surprise.</div> - <div class="verse indent0">Thus the pure elementary atom, the unit of mass and of thought,</div> - <div class="verse indent0">By force of mere juxtaposition to life and sensation is brought;</div> - <div class="verse indent0">So, down through untold generations, transmission of structureless gorms</div> - <div class="verse indent0">Enables our race to inherit the thoughts of beasts, fishes, and worms.</div> - <div class="verse indent0">We honour our fathers and mothers, grandfathers and grandmothers too;</div> - <div class="verse indent0">But how shall we honour the vista of ancestors now in our view?</div> - <div class="verse indent0">First, then, let us honour the atom, so lively, so wise, and so small;</div> - <div class="verse indent0">The atomists next let us praise, Epicurus, Lucretius, and all.</div> - <div class="verse indent0">Let us damn with faint praise Bishop Butler, in whom many atoms combined</div> - <div class="verse indent0">To form that remarkable structure it pleased him to call—his mind.</div> - <div class="verse indent0">Last, praise we the noble body to which, for the time, we belong,</div> - <div class="verse indent0">Ere yet the swift whirl of the atoms has hurried us, ruthless, along,</div> - <div class="verse indent0">The British Association—like Leviathan worshipped by Hobbes,</div> - <div class="verse indent0">The incarnation of wisdom, built up of our witless nobs,</div> - <div class="verse indent0">Which will carry on endless discussions when I, and probably you,</div> - <div class="verse indent0">Have melted in infinite azure—in English, till all is blue.</div> - </div> -</div> -</div> -<p><span class="pagenum" id="Page_85">85</span></p> - -<hr class="narrow" /> -<p class="p1 center noafter">MOLECULAR EVOLUTION.</p> - -<p class="center smaller p1 b1 noafter"><i>Belfast, 1874.</i></p> - -<div class="poetry-container nobreak"> -<div class="poetry"> - <div class="stanza"> - <div class="verse indent0">At quite uncertain times and places,</div> - <div class="verse indent2">The atoms left their heavenly path,</div> - <div class="verse indent0">And by fortuitous embraces</div> - <div class="verse indent2">Engendered all that being hath.</div> - <div class="verse indent0">And though they seem to cling together,</div> - <div class="verse indent2">And form “associations” here,</div> - <div class="verse indent0">Yet, soon or late, they burst their tether,</div> - <div class="verse indent2">And through the depths of space career.</div> - </div> - <div class="stanza"> - <div class="verse indent0">So we who sat, oppressed with science,</div> - <div class="verse indent2">As British Asses, wise and grave,</div> - <div class="verse indent0">Are now transformed to wild Red Lions,<a id="FNanchor_44" href="#Footnote_44" class="fnanchor">44</a></div> - <div class="verse indent2">As round our prey we ramp and rave.</div> - <div class="verse indent0">Thus, by a swift metamorphōsis,</div> - <div class="verse indent2">Wisdom turns wit, and science joke,</div> - <div class="verse indent0">Nonsense is incense to our noses,</div> - <div class="verse indent2">For when Red Lions speak they smoke.</div> - </div> - <div class="stanza"> - <div class="verse indent0">Hail, Nonsense! dry nurse of Red Lions,<a id="FNanchor_45" href="#Footnote_45" class="fnanchor">45</a></div> - <div class="verse indent2">From thee the wise their wisdom learn;</div> - <div class="verse indent0">From thee they cull those truths of science,</div> - <div class="verse indent2">Which into thee again they turn.</div> - <div class="verse indent0">What combinations of ideas</div> - <div class="verse indent2">Nonsense alone can wisely form!</div> - <div class="verse indent0">What sage has half the power that she has,</div> - <div class="verse indent2">To take the towers of Truth by storm?</div> - </div> - <div class="stanza"> - <div class="verse indent0">Yield, then, ye rules of rigid reason!</div> - <div class="verse indent2">Dissolve, thou too, too solid sense!</div> - <div class="verse indent0">Melt into nonsense for a season,</div> - <div class="verse indent2">Then in some nobler form condense.</div> - <div class="verse indent0">Soon, all too soon, the chilly morning</div> - <div class="verse indent2">This flow of soul will crystallise;</div> - <div class="verse indent0">Then those who Nonsense now are scorning</div> - <div class="verse indent2">May learn, too late, where wisdom lies.</div> - </div> -</div> -</div> -<p><span class="pagenum" id="Page_86">86</span></p> - -<hr class="narrow" /> -<p class="p1 center noafter">TO THE COMMITTEE OF THE CAYLEY -PORTRAIT FUND.</p> - -<p class="p1 b1 center smaller noafter">1874.</p> - -<div class="poetry-container nobreak"> -<div class="poetry"> - <div class="stanza"> - <div class="verse indent0">O wretched race of men, to space confined!</div> - <div class="verse indent0">What honour can ye pay to him, whose mind</div> - <div class="verse indent2">To that which lies beyond hath penetrated?</div> - <div class="verse indent0">The symbols he hath formed shall sound his praise,</div> - <div class="verse indent0">And lead him on through unimagined ways</div> - <div class="verse indent2">To conquests new, in worlds not yet created.</div> - </div> - <div class="stanza"> - <div class="verse indent0">First, ye Determinants! in ordered row</div> - <div class="verse indent0">And massive column ranged, before him go,</div> - <div class="verse indent2">To form a phalanx for his safe protection.</div> - <div class="verse indent0">Ye powers of the <em>n<sup>th</sup></em> roots of -1!</div> - <div class="verse indent0">Around his head in ceaseless<a id="FNanchor_46" href="#Footnote_46" class="fnanchor">46</a> cycles run,</div> - <div class="verse indent2">As unembodied spirits of direction.</div> - </div> - <div class="stanza"> - <div class="verse indent0">And you, ye undevelopable scrolls!</div> - <div class="verse indent0">Above the host wave your emblazoned rolls,</div> - <div class="verse indent2">Ruled for the record of his bright inventions.</div> - <div class="verse indent0">Ye cubic surfaces! by threes and nines</div> - <div class="verse indent0">Draw round his camp your seven-and-twenty lines—</div> - <div class="verse indent2">The seal of Solomon in three dimensions.</div> - </div> - <div class="stanza"> - <div class="verse indent0">March on, symbolic host! with step sublime,</div> - <div class="verse indent0">Up to the flaming bounds of Space and Time!</div> - <div class="verse indent2">There pause, until by Dickinson depicted,</div> - <div class="verse indent0">In two dimensions, we the form may trace</div> - <div class="verse indent0">Of him whose soul, too large for vulgar space,</div> - <div class="verse indent2">In <em>n</em> dimensions flourished unrestricted.</div> - </div> -</div> -</div> - -<hr class="narrow" /> - -<p class="p1 center noafter">IN MEMORY OF EDWARD WILSON,</p> - -<p class="p1 b1 center smaller noafter"><i>Who repented of what was in his mind to write after section.</i></p> - -<p class="p1 b1 center noafter"><span class="smcap">Rigid Body</span> (<i class="smaller">sings</i>).</p> - -<div class="poetry-container nobreak"> -<div class="poetry"> - <div class="stanza"> - <div class="verse indent0"><span class="smcap">Gin</span> a body meet a body</div> - <div class="verse indent2">Flyin’ through the air,</div> - <div class="verse indent0">Gin a body hit a body,</div> - <div class="verse indent2">Will it fly? and where?</div><span class="pagenum" id="Page_87">87</span> - <div class="verse indent0">Ilka impact has its measure,</div> - <div class="verse indent2">Ne’er a ane hae I;</div> - <div class="verse indent0">Yet a’ the lads they measure me,</div> - <div class="verse indent2">Or, at least, they try.</div> - </div> - <div class="stanza"> - <div class="verse indent0">Gin a body meet a body</div> - <div class="verse indent2">Altogether free,</div> - <div class="verse indent0">How they travel afterwards</div> - <div class="verse indent2">We do not always see.</div> - <div class="verse indent0">Ilka problem has its method</div> - <div class="verse indent2">By analytics high;</div> - <div class="verse indent0">For me, I ken na ane o’ them,</div> - <div class="verse indent2">But what the waur am I?</div> - </div> -</div> -</div> - -<p>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.</p> - -<p>Niven, in his preface to the collected papers -dealing with this book, writes <span class="locked">thus:—</span></p> - -<div class="blockquot"> - -<p>“This work, published in 1879, has had the effect of -increasing the reputation of Cavendish, disclosing as it does -the unsuspected advances which that acute physicist had -made in the Theory of Electricity, especially in the measurement -of electrical quantities. The work is enriched by a -variety of valuable notes, in which Cavendish’s views and -results are examined by the light of modern theory and -methods. Especially valuable are the methods applied to the -determination of the electrical capacities of conductors and -condensers, a subject in which Cavendish himself showed considerable -skill both of a mathematical and experimental -character.</p> - -<p><span class="pagenum" id="Page_88">88</span></p> - -<p>“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 <span class="locked">them:—</span></p> - -<p>“‘It is somewhat difficult to account for the fact that -though Cavendish had prepared a complete description of his -experiments on the charges of bodies, and had even taken the -trouble to write out a fair copy, and though all this seems to -have been done before 1774, and he continued to make experiments -in electricity till 1781, and lived on till 1810, he kept -his manuscript by him and never published it.</p> - -<p>“‘Cavendish cared more for investigation than for publication. -He would undertake the most laborious researches in -order to clear up a difficulty which no one but himself could -appreciate or was even aware of, and we cannot doubt that the -result of his enquiries, when successful, gave him a certain -degree of satisfaction. But it did not excite in him that -desire to communicate the discovery to others, which in the -case of ordinary men of science generally ensures the publication -of their results. How completely these researches of -Cavendish remained unknown to other men of science is shown -by the external history of electricity.’</p> - -<p>“It will probably be thought a matter of some difficulty -to place oneself in the position of a physicist of a century -ago, and to ascertain the exact bearing of his experiments. -But Maxwell entered upon this undertaking with the utmost -enthusiasm, and succeeded in identifying himself with -Cavendish’s methods. He showed that Cavendish had really -anticipated several of the discoveries in electrical science -which have been made since his time. Cavendish was the -first to form the conception of and to measure Electrostatic -Capacity and Specific Inductive Capacity; he also anticipated -Ohm’s law.”</p> -</div> - -<p>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,<span class="pagenum" id="Page_89">89</span> -but conducted his lectures and experiments at the -laboratory as usual.</p> - -<p>About this time some of those who had been -“Apostles” in 1853–57 revived the habit of meeting -together for discussion. The club, which included -Professors Lightfoot, Hort and Westcott, was christened -the “Eranus,” and three of Maxwell’s contributions -to it have been preserved and are printed by -Professor Campbell.</p> - -<p>After the Cavendish papers were finished, Maxwell -had more time for his own original researches, -and two important papers were published in 1879. -The one on “Stresses in Rarefied Gases arising from -Inequalities of Temperature” was printed in the -Royal Society’s Transactions, and deals with the -Theory of the Radiometer; the other on “Boltzmann’s -Theorem” appears in the Transactions of the Cambridge -Philosophical Society. In the previous year -he had delivered the Rede lecture on “The Telephone.” -He also began to prepare a second edition -of “Electricity and Magnetism.”</p> - -<p>His health gave way during the Easter term of -1879; indeed for two years previously he had been -troubled with dyspeptic symptoms, but had consulted -no one on the subject. He left Cambridge as -usual in June, hoping that he would quickly recover -at Glenlair, but he grew worse instead. In October -he was told by Dr. Sanders of Edinburgh that he had -not a month to live. He returned to Cambridge in -order to be under the care of Dr. Paget, who was able -in some measure to relieve his most severe suffering -but the disease, of which his mother had died at the<span class="pagenum" id="Page_90">90</span> -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.</p> - -<p>A funeral service took place in the chapel at -Trinity College, and afterwards his remains were conveyed -to Scotland and interred in the family burying-place -at Corsock, Kirkcudbright.</p> - -<p>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.</p> - -<p>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.</p> - -<div class="tb">* * * * *</div> - -<p>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 <span class="locked">feelings—</span></p> - -<p><span class="pagenum" id="Page_91">91</span></p> - -<div class="poetry-container"> -<div class="poetry"> - <div class="stanza"> - <div class="verse indent0">Through the creatures Thou hast made</div> - <div class="verse indent2">Show the brightness of Thy glory,</div> - <div class="verse indent0">Be eternal truth displayed</div> - <div class="verse indent2">In their substance transitory,</div> - <div class="verse indent0">Till green earth and ocean hoary,</div> - <div class="verse indent2">Massy rock and tender blade,</div> - <div class="verse indent0">Tell the same unending story,</div> - <div class="verse indent2">“We are Truth in form arrayed.”</div> - </div> - <div class="stanza"> - <div class="verse indent0">Teach me so Thy works to read</div> - <div class="verse indent2">That my faith, new strength accruing,</div> - <div class="verse indent0">May from world to world proceed,</div> - <div class="verse indent2">Wisdom’s fruitful search pursuing,</div> - <div class="verse indent0">Till Thy breath my mind imbuing,</div> - <div class="verse indent2">I proclaim the eternal creed,</div> - <div class="verse indent0">Oft the glorious theme renewing,</div> - <div class="verse indent2">God our Lord is God indeed.</div> - </div> -</div> -</div> - -<p>His views on the relation of Science to Faith are -given in his letter<a id="FNanchor_47" href="#Footnote_47" class="fnanchor">47</a> to Bishop Ellicott already referred -<span class="locked">to—</span></p> - -<div class="blockquot"> - -<p>“But I should be very sorry if an interpretation founded -on a most conjectural scientific hypothesis were to get fastened -to the text in Genesis, even if by so doing it got rid of -the old statement of the commentators which has long ceased -to be intelligible. The rate of change of scientific hypothesis -is naturally much more rapid than that of Biblical interpretations, -so that if an interpretation is founded on such an -hypothesis, it may help to keep the hypothesis above ground -long after it ought to be buried and forgotten.</p> - -<p>“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 (<i>see</i> ‘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.”</p> -</div> - -<p><span class="pagenum" id="Page_92">92</span></p> - -<p class="in0">And again in his letter<a id="FNanchor_48" href="#Footnote_48" class="fnanchor">48</a> to the secretary of the -Victoria Institute giving his reasons for declining -to become a <span class="locked">member—</span></p> - -<div class="blockquot"> - -<p>“I think men of science as well as other men need to learn -from Christ, and I think Christians whose minds are scientific -are bound to study science, that their view of the glory of God -may be as extensive as their being is capable of. But I think -that the results which each man arrives at in his attempts to -harmonise his science with his Christianity ought not to be -regarded as having any significance except to the man himself, -and to him only for a time, and should not receive the stamp -of a society.”</p> -</div> - -<p>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.</p> - -<hr /> - -<div id="toclink_93" class="chapter"> -<p><span class="pagenum" id="Page_93">93</span></p> - -<h2 class="nobreak" id="CHAPTER_VII">CHAPTER VII.<br /> - -<span class="subhead">SCIENTIFIC WORK—COLOUR VISION.</span></h2> -</div> - -<p class="in0"><span class="firstword">Fifteen</span> 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.</p> - -<p>Thus Niven, at the close of his obituary notice -in the Proceedings of the Royal Society, says: “It -is seldom that the faculties of invention and exposition, -the attachment to physical science and capability -of developing it mathematically, have been -found existing in one mind to the same degree. It -would, however, require powers somewhat akin to -Maxwell’s own to describe the more delicate features of -the works resulting from this combination, every one -of which is stamped with the subtle but unmistakable -impress of genius.” And again in the preface to -Maxwell’s works, issued in 1890, he wrote: “Nor -does it appear to the present editor that the time -has yet arrived when the quickening influence of -Maxwell’s mind on modern scientific thought can be -duly estimated.”</p> - -<p>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.<span class="pagenum" id="Page_94">94</span> -While attempting it I wish to express my indebtedness -to others who have already written about Maxwell’s -scientific work, especially to Mr. W. D. Niven, -whose preface to the Maxwell papers has been so often -referred to; to Mr. Garnett, the author of Part II. -of the “Life of Maxwell,” which deals with his contributions -to science; and to Professor Tait, who in -<i>Nature</i> 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.”</p> - -<p>Maxwell’s main contributions to science may be -classified under three heads—“Colour Perception,” -“Molecular Physics,” and “Electrical Theories.” In -addition to these there were other papers of the -highest interest and importance, such as the essay on -“Saturn’s Rings,” the paper on the “Equilibrium of -Elastic Solids,” and various memoirs on pure geometry -and questions of mechanics, which would, if they stood -alone, have secured for their author a distinguished -position as a physicist and mathematician, but which -are not the works by which his name will be mostly -remembered.</p> - -<p>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.</p> - -<p>His first published paper on the subject was a<span class="pagenum" id="Page_95">95</span> -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.</p> - -<p>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.</p> - -<p>He points out first the distinction between the -<em>optical</em> properties and the <em>chromatic</em> properties of a -beam of light. “The optical properties are those -which have reference to its origin and propagation -through media until it falls on the sensitive organ of -vision;” they depend on the periods and amplitudes -of the ether vibrations which compose the beam. -“The chromatic properties are those which have -reference to its power of exciting certain sensations of -colour perceived through the organ of vision.” It is -possible for two beams to be optically very different -and chromatically alike. The converse is not true; -two beams which are optically alike are also chromatically -alike.</p> - -<p>The foundation of the theory of compound colours -was laid by Newton. He first shewed that “by the -mixture of homogeneal light colours may be produced -which are like to the colours of homogeneal -light as to the appearance of colour, but not as to the -immutability of colour and constitution of light.” Two<span class="pagenum" id="Page_96">96</span> -beams which differ optically may yet be alike chromatically; -it is possible by mixing red and yellow to -obtain an orange colour chromatically similar to the -orange of the spectrum, but optically different to that -orange, for the compound orange can be analysed by -a prism into its component red and yellow; the -spectrum orange is incapable of further resolution.</p> - -<p>Newton also solves the following <span class="locked">problem:—</span></p> - -<p><em>In a mixture of primary colours, the quantity -and quality of each being given to know the colour -of the compound</em> (Optics, Book 1, Part 2, Prop. 6), -and his solution is the following:—He arranges the -seven colours of the spectrum round the circumference -of a circle, the length occupied by each colour -being proportional to the musical interval to which, -in Newton’s views, the colour corresponded. At the -centre of gravity of each of these arcs he supposes a -weight placed proportional to the number of rays of -the corresponding colour which enter into the mixture -under consideration. The position of the centre of -gravity of these weights indicates the nature of the -resultant colour. A radius drawn through this centre -of gravity points out the colour of the spectrum which -it most resembles; the distance of the centre of gravity -from the centre gives the fulness of the colour. -The centre itself is white. Newton gives no proof -of this rule; he merely says, “This rule I conceive to -be accurate enough for practice, though not mathematically -accurate.”</p> - -<p>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<span class="pagenum" id="Page_97">97</span> -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.</p> - -<p>Thomas Young appears to have been the next, after -Newton, to work at the theory of colour sensation. He -made observations by spinning coloured discs much -in the same way as that which was afterwards adopted -by Maxwell, and he developed the theory that three -different primary sensations may be excited in the eye -by light, while the colour of any beam depends on -the proportions in which these three sensations are -excited. He supposes the three primary sensations to -correspond to red, green, and violet. A blue ray is -capable of exciting both the green and the violet; a -yellow ray excites the red and the green. Any colour, -according to Young’s theory, may be matched by a -mixture of these three primary colours taken in proper -proportion; the quality of the colour depends on -the proportion of the intensities of the components; -its brightness depends on the sum of these -intensities.</p> - -<p>Maxwell’s experiments were undertaken with the -object of proving or disproving the physical part of -Young’s theory. He does not consider the question -whether there are three distinct sensations corresponding -to the three primary colours; that is a -physiological inquiry, and one to which no completely -satisfactory answer has yet been given. He does show -that by a proper mixture of any three arbitrarily -chosen standard colours it is possible to match any<span class="pagenum" id="Page_98">98</span> -other colour; the words “proper mixture,” however, -need, as will appear shortly, some development.</p> - -<p>We may with advantage compare the problem -with one in acoustics.</p> - -<p>When a compound musical note consisting of -a pure tone and its overtones is sounded, the -trained ear can distinguish the various overtones -and analyse the sound into its simple components. -The same sensation cannot be excited in two different -ways. The eye has no such corresponding power. -A given yellow may be a pure spectral yellow, corresponding -to a pure tone in music, or it may be a -mixture of a number of other pure tones; in either -case it can be matched by a proper combination of -three standard colours—this Maxwell proved. It -may be, as Young supposed, that if the three standard -colours be properly selected they correspond exactly -to three primary sensations of the brain. Maxwell’s -experiments do not afford any light on this point, -which still remains more than doubtful.</p> - -<p>When Maxwell began his work the theory of -colours was exciting considerable interest. Sir David -Brewster had recently developed a new theory of -colour sensation which had formed the basis of some -discussions, and in 1852 von Helmholtz published -his first paper on the subject. According to Brewster, -the three primitive colours were red, yellow and blue, -and he supposed that they corresponded to three -different kinds of objective light. Helmholtz pointed -out that experiments up to that date had been conducted -by mixing pigments, with the exception of those -in which the rotating disc was used, and that it is<span class="pagenum" id="Page_99">99</span> -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.</p> - -<p>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.</p> - -<p>In a later paper (<i>Philosophical Magazine</i>, 1854) -Helmholtz described a method for ascertaining the -various pairs of complementary colours—colours, that -is, which when mixed will give white—which had -been shown by Grassman to exist if Newton’s theory -were true. He also gave a provisional diagram of -the curve formed by the spectrum, which ought to -take the place of the circle in Newton’s diagram; -for this, however, his experiments did not give the -complete data.</p> - -<p>Such was the state of the question when Maxwell -began. His first colour-box was made in 1852. -Others were designed in 1855 and 1856, and the final -paper appeared in 1860. But before that time he -had established important results by means of his -rotatory discs and colour top. In his own description -of this he says: “The coloured paper is cut into the -form of disc, each with a hole in the centre and -divided along a radius so as to admit of several of -them being placed on the same axis, so that part of -each is exposed. By slipping one disc over another -we can expose any given portion of each colour.<span class="pagenum" id="Page_100">100</span> -These discs are placed on a top or teetotum, which -is spun rapidly. The axis of the top passes through -the centre of the discs, and the quantity of each -colour exposed is measured by graduations on the -rim of the top, which is divided into 100 parts. -When the top is spun sufficiently rapidly, the -impressions due to each colour separately follow each -other in quick succession at each point of the retina, -and are blended together; the strength of the impression -due to each colour is, as can be shown -experimentally, the same as when the three kinds of -light in the same relative proportions enter the -eye simultaneously. These relative proportions are -measured by the areas of the various discs which -are exposed. Two sets of discs of different radius -are used; the largest discs are put on first, then the -smaller, so that the centre portion of the top shows -the colour arising from the mixture of those of the -smaller discs; the outer portion, that of the larger -discs.”</p> - -<p>In experimenting, six discs of each size are used, -black, white, red, green, yellow and blue. It is found -by experiment that a match can be arranged between -any five of these. Thus three of the larger discs are -placed on the top—say black, yellow and blue—and -two of the smaller discs, red and green, are placed -above these. Then it is found that it is possible so -to adjust the amount exposed of each disc that the two -parts of the top appear when it is spun to be of the -same tint. In one series of experiments the chromatic -effect of 46·8 parts of black, 29·1 of yellow, and 24·1 -of blue was found to be the same as that of 66·6 of<span class="pagenum" id="Page_101">101</span> -red and 33·4 of green; each set of discs has a dirty -yellow tinge.</p> - -<p>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.</p> - -<p>Thus we have shown that 66·6 parts of red and -33·4 parts of green produce the same chromatic effect -as 29·1 of yellow and 24·1 of blue. Similarly in this -manner a match can be arranged between any four -colours and black, the black being necessary to -complete the circumference of the discs.</p> - -<p>Thus using A, B, C, D to denote the various -colours, <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i> the amounts of each colour taken, -we can get a series of results expressed as follows: -<i>a</i> parts of A together with <i>b</i> parts of B match <i>c</i> parts -of C together with <i>d</i> parts of D; or we may write this -as an equation <span class="locked">thus:—</span></p> - -<p class="center"><i>a</i> A + <i>b</i> B = <i>c</i> C + <i>d</i> D, -</p> - -<p class="in0">where the + stands for “combined with,” and the = -for “matches in tint.”</p> - -<p>We may also write the <span class="locked">above—</span></p> - -<p class="center"><i>d</i> D = <i>a</i> A + <i>b</i> B - <i>c</i> C, -</p> - -<p class="in0">or <i>d</i> parts of D can be matched by a <em>proper</em> combination -of colours A, B, C. The sign - shows that in -order to make the match we have to combine the -colour C with D; the combination then matches -a mixture of A and B.</p> - -<p><span class="pagenum" id="Page_102">102</span></p> - -<p>In this way we can form a number of equations -for all possible colours, and if we like to take any -three colours A, B, C as standards, we obtain a result -which may be written <span class="locked">generally—</span></p> - -<p class="center"><i>x</i> X = <i>a</i> A + <i>b</i> B + <i>c</i> C, -</p> - -<p class="in0">or <i>x</i> parts of X can be matched by <i>a</i> parts of A, -combined with <i>b</i> parts of B and <i>c</i> parts of C. If the -sign of one of the quantities <i>a</i>, <i>b</i>, or <i>c</i> is negative, it -indicates that that colour must be combined with X -to match the other two.</p> - -<p>Now Maxwell was able to show that, if A, B, C -be properly selected, nearly every other colour can -be matched by positive combinations of these -three. These three colours, then, are primary colours, -and nearly every other colour can be matched by a -combination of the three primary colours.</p> - -<p>Experiments, however, with coloured discs, such -as were undertaken by Young, Forbes and Maxwell, -were not capable of giving satisfactory results. The -colours of the discs were not pure spectrum colours, -and varied to some extent with the nature of the -incident light. It was for this reason that Helmholtz -in 1852 experimented with the spectrum, and that -Maxwell about the same time invented his colour -box.</p> - -<p>The principle of the latter was very simple. Suppose -we have a slit S, and some arrangement for -forming a pure spectrum on a screen. Let there -now be a slit R placed in the red part of the spectrum -on the screen. When light falls on the slit S, only -the red rays can reach R, and hence conversely, if the<span class="pagenum" id="Page_103">103</span> -white source be placed at the other end of the apparatus, -so that R is illuminated with white light, only red -rays will reach S. Similarly, if another slit be placed -in the green at G, and this be illuminated by white -light, only the green rays will reach S, while from -a third slit V in the violet, violet light only can -arrive at S. Thus by opening the three slits at V, -G and R simultaneously, and looking through S, the -retina receives the impression of the three different -colours. The amount of light of each colour will -depend on the breadth to which the corresponding -slit is opened, and the relative intensities of the three -different components can be compared by comparing -the breadths of the three slits. Any other colour -which is allowed by some suitable contrivance to -enter the eye simultaneously can now be matched, -provided the red, green and violet are primary -colours.</p> - -<p>By means of experiments with the colour box -Maxwell showed conclusively that a match could be -obtained between any four colours; the experiments -could not be carried out in quite the simple manner -suggested by the above description of the principle of -the box. An account of the method will be found in -Maxwell’s own paper. It consisted in matching a -standard white by various combinations of other -colours.</p> - -<p>The main object of his research, however, was -to examine the chromatic properties of the different -parts of the spectrum, and to determine the form -of the curve which ought to replace the circle in -Newton’s diagram of colour.</p> - -<p><span class="pagenum" id="Page_104">104</span></p> - -<p>Maxwell adopted as his three standard colours: -red, of about wave length 6,302; green, wave length -5,281; and violet, 4,569 tenth metres. On the scale -of Maxwell’s instrument these are represented by the -numbers 24, 44 and 68.</p> - -<p>Let us take three points A, B, C at the corners -of an equilateral triangle to represent on a diagram -these three colours. The position of any other colour -on the diagram will be found by taking weights -proportional to the amounts of the colours A, B, C -required to make the match between A, B, C and the -given colour; these weights are placed at A, B, C -respectively; the position of their centre of gravity -is the point required. Thus the position of white is -given by the <span class="locked">equation—</span></p> - -<p class="center">W = 18·6 (24) + 31·4 (44) + 30·5 (68) -</p> - -<p class="in0">which means that weights proportional to 18·6, 31·4 -and 30·5 are to be placed at A, B, C respectively, -and their centre of gravity is to be found. The point -so found is the position of white. Any other colour -is given by the <span class="locked">equation—</span></p> - -<p class="center">X = <i>a</i> (24) + <i>b</i> (44) + <i>c</i> (68). -</p> - -<p>Again, the position on the diagram for all colours -for which <i>a</i>, <i>b</i>, <i>c</i> are all positive lies within the -triangle A B C. If one of the coefficients, say <i>c</i>, is -negative the same construction applies, but the -weight applied at C must be treated as acting -in the opposite direction to those at A and B. -A mixture of the given colour and C matches a -mixture of A and B. It is clear that the point -corresponding to X will then lie outside the triangle<span class="pagenum" id="Page_105">105</span> -A B C. Maxwell showed that, with his standards, -nearly all colours could be represented by points -inside the triangle. The colours he had selected -as standards were very close to primary colours.</p> - -<p>Again, he proved that any spectrum colour between -red and green, when combined with a very slight -admixture of violet, could be matched, in the case -of either Mrs. Maxwell or himself, by a proper mixture -of the red and green. The positions, therefore, -of the spectrum colours between red and green lie -just outside the triangle A B C, being very close -to the line A B, while for the colours between green -and violet Maxwell obtained a curve lying rather -further outside the side B C. Any spectrum colour -between green and violet, together with a slight -admixture of red, can be matched by a proper mixture -of green and violet.</p> - -<p>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.</p> - -<p>To find the point on the diagram corresponding -to the colour obtained by mixing any two or more -spectrum colours we must, in accordance with Newton’s -rule, place weights at the points corresponding -to the selected colours, and find the centre of gravity -of these weights.</p> - -<p>This, then, was the outcome of Maxwell’s work on<span class="pagenum" id="Page_106">106</span> -colour. It verified the essential part of Newton’s -construction, and obtained for the first time the true -form of the spectrum curve on the diagram.</p> - -<p>The form of this curve will of course depend -on the eye of the individual observer. Thus Maxwell -and Mrs. Maxwell both made observations, and -distinct differences were found in their eyes. It -appears, however, that a large majority of persons -have normal vision, and that matches made by one -such person are accepted by most others as satisfactory. -Some people, however, are colour blind, and -Maxwell examined a few such. In the case of those -whom he examined it appeared as though vision was -dichromatic, the red sensation seemed to be absent; -nearly all colours could be matched by combinations -of green and violet. The colour diagram was reduced -to the straight line B C. Other forms of colour blindness -have since been investigated.</p> - -<p>In awarding to Maxwell the Rumford medal in -1860, Major-General Sabine, vice-president of the -Royal Society, after explaining the theory of colour -vision and the possible method of verifying it, said: -“Professor Maxwell has subjected the theory to this -verification, and thereby raised the composition of -colours to the rank of a branch of mathematical -physics,” and he continues: “The researches for which -the Rumford medal is awarded lead to the remarkable -result that to a very near degree of approximation -all the colours of the spectrum, and therefore -all colours in nature which are only mixtures of these, -can be perfectly imitated by mixtures of three -actually attainable colours, which are the red, green<span class="pagenum" id="Page_107">107</span> -and blue belonging respectively to three particular -parts of the spectrum.”</p> - -<p>It should be noticed in concluding our remarks -on this part of Maxwell’s work that his results are -purely physical. They are not inconsistent with the -physiological part of Young’s theory, viz., that there -are three primary sensations of colour which can be -transmitted to the brain, and that the colour of any -object depends on the relative proportions in which -these sensations are excited, but they do not prove -that theory. Any physiological theory which can be -accepted as true must explain Maxwell’s observations, -and Young’s theory does this; but it is, of course, -possible that other theories may explain them equally -well, and be more in accordance with physiological -observations than Young’s. Maxwell has given us -the physical facts which have to be explained; it is -for the physiologists to do the rest.</p> - -<hr /> - -<div id="toclink_108" class="chapter"> -<p><span class="pagenum" id="Page_108">108</span></p> - -<h2 class="nobreak" id="CHAPTER_VIII">CHAPTER VIII.<br /> - -<span class="subhead">SCIENTIFIC WORK—MOLECULAR THEORY.</span></h2> -</div> - -<p class="in0"><span class="firstword">Maxwell</span> in his article “Atom,” in the ninth edition of -the <i>Encyclopædia Britannica</i>, has given some account -of Modern Molecular Science, and in particular of the -molecular theory of gases. Of this science, Clausius -and Maxwell are the founders, though to their names -it has recently been shown that a third, that of -Waterston, must be added. In the present chapter -it is intended to give an outline of Maxwell’s contributions -to molecular science, and to explain the -advances due to him.</p> - -<p>The doctrine that bodies are composed of small -particles in rapid motion is very ancient. Democritus -was its founder, Lucretius—de Rerum Naturâ—explained -its principles. The atoms do not fill space; -there is void between.</p> - -<div class="poetry-container"> -<div class="poetry"> - <div class="stanza" xml:lang="la" lang="la"> - <div class="verse indentq">“Quapropter locus est intactus inane vacansque,</div> - <div class="verse indent0">Quod si non esset, nullâ ratione moveri</div> - <div class="verse indent0">Res possent; namque officium quod corporis extat</div> - <div class="verse indent0">Officere atque obstare, id in omni tempore adesset</div> - <div class="verse indent0">Omnibus. Haud igitur quicquam procedere posset</div> - <div class="verse indent0">Principium quoniam cedendi nulla daret res.”</div> - </div> -</div> -</div> - -<p>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<span class="pagenum" id="Page_109">109</span> -apart. It has no parts or dimensions: it is a mere -geometrical point without extension in space; it has -not the property of impenetrability, for two atoms -can, it is supposed, exist at the same point.</p> - -<p>In modern molecular science according to -Maxwell, “we begin by assuming that bodies are -made up of parts each of which is capable of motion, -and that these parts act on each other in a manner -consistent with the principle of the conservation of -energy. In making these assumptions we are -justified by the facts that bodies may be divided into -smaller parts, and that all bodies with which we are -acquainted are conservative systems, which would not -be the case unless their parts were also conservative -systems.</p> - -<p>“We may also assume that these small parts are in -motion. This is the most general assumption we can -make, for it includes as a particular case the theory -that the small parts are at rest. The phenomena of -the diffusion of gases and liquids through each other -show that there may be a motion of the small parts of -a body which is not perceptible to us.</p> - -<p>“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.”</p> - -<p>These small particles are called molecules, and a<span class="pagenum" id="Page_110">110</span> -molecule in its physical aspect was defined by -Maxwell in the following <span class="locked">terms:—</span></p> - -<div class="blockquot"> - -<p>“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.”</p> -</div> - -<p>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.</p> - -<p>The simplest theory we could formulate would be -that the molecules behaved like elastic spheres, and -that the action between any two was a collision following -the laws which we know apply to the collision of -elastic bodies. If the average distance between two -molecules be great compared with their dimensions, -the time during which any molecule is in collision -will be small compared with the interval between the -collisions, and this is in accordance with the fundamental -assumption just mentioned. It is not, -however, necessary to suppose an encounter between -two molecules to be a collision. One molecule may -act on another with a force, which depends on the -distance between them, of such a character that the -force is insensible except when the molecules are -extremely close together.</p> - -<p>It is not difficult to see how the pressure exerted<span class="pagenum" id="Page_111">111</span> -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.</p> - -<p>Thus each molecule of the gas is continually -gaining momentum from the sides of the vessel, while -it gives up to the vessel the momentum which it -possessed before the impact. The rate at which this -change of momentum proceeds across a given area -measures the force exerted on that area; the pressure -of the gas is the rate of change of momentum per -unit of area of the surface.</p> - -<p>Again, it can be shown that this pressure is proportional -to the product of the mass of each molecule, -the number of molecules in a unit of volume, and -the square of the velocity of the molecules.</p> - -<p>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.</p> - -<p>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 <i>v</i> 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 <i>v</i>;<span class="pagenum" id="Page_112">112</span> -if <i>m</i> be the mass of each molecule, the mass which -strikes the surface per second is N <i>m</i> <i>v</i>; the velocity -of each particle of this mass is <i>v</i>, therefore the -momentum destroyed per second by the impact is -N <i>m</i> <i>v</i> × <i>v</i>, or N <i>m</i> <i>v</i>², and this measures the pressure.</p> - -<p>Hence in this case if <i>p</i> be the pressure</p> - -<p class="center"><i>p</i> = N <i>m</i> <i>v</i>². -</p> - -<p>In the above we assume that <em>all</em> the molecules in -the jet are moving with velocity <i>v</i> perpendicular to -the surface. In the case of a crowd of molecules -flying about in a closed space this is clearly not true. -The molecules may strike the surface in any direction; -they will not all be moving normal to the surface. -To simplify the case, consider a cubical box filled -with gas. The box has three pairs of equal faces at -right angles. We may suppose one-third of the -particles to be moving at right angles to each face, -and in this case the number per unit volume which -we have to consider is not N, but ⅓ N. Hence the -formula becomes <i>p</i> = ⅓ N <i>m</i> <i>v</i>².</p> - -<p>Moreover, if <i>ρ</i> be the density of the gas—that is, -the mass of unit volume—then N<i>m</i> is equal to <i>ρ</i>, -for <i>m</i> is the mass of each particle, and there are N -particles in a unit of volume.</p> - -<p>Hence, finally, <i>p</i> = ⅓ <i>ρ</i> <i>v</i>².</p> - -<p>Or, again, if V be the volume of unit mass of the -gas, then <i>ρ</i> V is unity, or ρ is equal to 1/V.</p> - -<p>Hence <i>p</i>V = ⅓<i>v</i>².</p> - -<p>Formulæ equivalent to these appear first to have -been obtained by Herapath about the year 1816 -(Thomson’s “Annals of Philosophy,” 1816). The<span class="pagenum" id="Page_113">113</span> -results only, however, were stated in that year. A -paper which attempted to establish them was presented -to the Royal Society in 1820. It gave rise to -very considerable correspondence, and was withdrawn -by the author before being read. It is printed in full -in Thomson’s “Annals of Philosophy” for 1821, vol. i., -pp. 273, 340, 401. The arguments of the author are -no doubt open to criticism, and are in many points -far from sound. Still, by considering the problem of -the impact of a large number of hard bodies, he -arrived at a formula connecting the pressure and -volume of a given mass of gas equivalent to that -just given. These results are contained in Propositions -viii. and ix. of Herapath’s paper.</p> - -<p>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>m</i> <i>v</i>, if T represents the temperature: -and</p> - -<p class="center"><i>p</i> = ⅓ N <i>m</i> <i>v</i>² = ⅓ (N/<i>m</i>) (<i>m</i> <i>v</i>)². -</p> - -<p class="in0">Or, <span class="locked">again—</span></p> - -<p class="center"><i>p</i> = ⅓ N·T·<i>v</i> = ⅓·(N/<i>m</i>)·T². -</p> - -<p class="in0">These results are practically given in Proposition viii., -Corr. (1) and (2), and Proposition ix.<a id="FNanchor_49" href="#Footnote_49" class="fnanchor">49</a> The<span class="pagenum" id="Page_114">114</span> -temperature as thus defined by Herapath is an absolute -temperature, and he calculates the absolute zero of -temperature at which the gas would have no volume -from the above results. The actual calculation is of -course wrong, for, as we know now by experiment, the -pressure is proportional to the temperature, and not -to its square, as Herapath supposed. It will be seen, -however, that Herapath’s formula gives Boyle’s law; -for if the temperature is constant, the formula is -equivalent to</p> - -<p class="center"><i>p</i> V = a constant. -</p> - -<p>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.</p> - -<p>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.</p> - -<p>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,<span class="pagenum" id="Page_115">115</span> -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—<i>p</i>₁—equal -to ⅓ N₁ <i>m</i> <i>v</i>₁², where <i>v</i>₁ is the velocity of the group -and N₁ the number of particles having that velocity. -The whole pressure will be found by adding that due -to the various groups, and will be given as before by -<i>p</i> = ⅓ N <i>m</i> <i>v</i>², where <i>v</i> is not now the actual velocity -of the particles, but a mean velocity given by the -equation</p> - -<p class="center">N <i>v</i>² = N₁ <i>v</i>₁² + N₂ <i>v</i>₂² + ....., -</p> - -<p class="in0">which will produce the same pressure as arises from -the actual impacts. This quantity v² is known as the -<em>mean square</em> of the molecular velocity, and is so used -by Waterston.</p> - -<p>In a paper in the <i>Philosophical Magazine</i> for -1858 Waterston gives an account of his own paper -of 1846 in the following terms:—“Mr. Herapath -unfortunately assumed heat or temperature to be -represented by the simple ratio of the velocity instead -of the square of the velocity, being in this apparently -led astray by the definition of motion generally received, -and thus was baffled in his attempts to -reconcile his theory with observation. If we make -this change in Mr. Herapath’s definition of heat or -temperature—viz., that it is proportional to the vis-viva -or square velocity of the moving particle, not to -the momentum or simple ratio of the velocity—we -can without much difficulty deduce not only the -primary laws of elastic fluids, but also the other<span class="pagenum" id="Page_116">116</span> -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.”</p> - -<p>In his introduction to Waterston’s paper (Phil. -Trans., 1892) Lord Rayleigh writes:—“Impressed -with the above passage, and with the general ingenuity -and soundness of Waterston’s views, I took -the first opportunity of consulting the Archives, and -saw at once that the memoir justified the large claims -made for it, and that it marks an immense advance -in the direction of the now generally received theory.”</p> - -<p>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.</p> - -<p><span class="pagenum" id="Page_117">117</span></p> - -<p>According to this we are thus to put in the pressure -equation—½ <i>m</i> <i>v</i>² = T, the temperature, and we -have at once—<i>p</i> V = ⅔ N · T.</p> - -<p>Now this equation expresses, as we know, the -laws of Boyle and Gay Lussac.</p> - -<p>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 -<i>m</i>₁, <i>m</i>₂ be the masses of each molecule of two different -sets of molecules mixed together, then, when -a steady state has been reached, since the temperature -is the same throughout, <i>m</i>₁ <i>v</i>₁² is equal to <i>m</i>₂ <i>v</i>₂². The -average kinetic energy of each molecule is the same.</p> - -<p>From this Avogadros’ law follows at once—for if -<i>p</i>₁, <i>p</i>₂ be the pressures, N₁, N₂ the numbers of molecules -per unit <span class="locked">volume—</span></p> - -<p class="center"><i>p</i>₁ = ⅓ N₁ <i>m</i>₁ <i>v</i>₁², -<i>p</i>₂ = ⅓ N₂ <i>m</i>₂ <i>v</i>₂². -</p> - -<p>Hence, if <i>p</i>₁, is equal to <i>p</i>₂, since <i>m</i>₁ <i>v</i>₁² is equal to -<i>m</i>₂ <i>v</i>₂², we must have N₁ equal to N₂, or the number -of molecules in equal volumes of two gases at the -same pressure and temperature is the same. The -proof of this proposition given by Waterston is not -satisfactory. On this point, however, we shall have -more to say. The third section of the paper deals with -adiabatic expansion, and in it there is an error in calculation -which prevented correct results from being attained.</p> - -<p><span class="pagenum" id="Page_118">118</span></p> - -<p>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 <span class="locked">Proceedings:—</span></p> - -<p>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.</p> - -<p>“The vis viva of these motions in a given portion -of a gas constitutes the quantity of heat contained -in it.</p> - -<p>“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.</p> - -<p>“The elasticity in a given gas is the measure -of temperature. Equilibrium of pressure and heat -between two gases takes place when the number -of atoms in unit of volume is equal and the vis -viva of each atom equal. Temperature, therefore, -in all gases is proportional to the mass of one atom -multiplied by the mean square of the velocity of the -molecular motions, being measured from an absolute -zero 491° below the zero of Fahrenheit’s thermometer.”</p> - -<p>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<span class="pagenum" id="Page_119">119</span> -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.</p> - -<p>Meanwhile, in 1848, Joule’s attention was called -by his experiments to the question, and he saw that -Herapath’s result gave a means of calculating the -mean velocity of the molecules of a gas. For according -to the result given above, <i>p</i> = ⅓ <i>ρ v</i>²; thus -<i>v</i>² = 3 <i>p/ρ</i>, and <i>p</i> and <i>ρ</i> being known, we find <i>v</i>². Thus -for hydrogen at freezing-point and atmospheric pressure -Joule obtains for <i>v</i> the value 6,055 feet per second, -or, roughly, six times the velocity of sound in air.</p> - -<p>Clausius was the next writer of importance on the -subject. His first paper is in “Poggendorff’s Annalen,” -vol. c., 1857, “On the Kind of Motion we call -Heat.” It gives an exposition of the theory, and -establishes the fact that the kinetic energy of the -translatory motion of a molecule does not represent -the whole of the heat it contains. If we look upon -a molecule as a small solid we must consider the -energy it possesses in consequence of its rotation -about its centre of gravity, as well as the energy due -to the motion of translation of the whole.</p> - -<p>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.</p> - -<p><span class="pagenum" id="Page_120">120</span></p> - -<p>These two papers appear to have attracted Maxwell’s -attention to the matter, and his first paper, -entitled “Illustrations of the Dynamical Theory of -Gases,” was read to the British Association at Aberdeen -and Oxford in 1859 and 1860, and appeared in -the <i>Philosophical Magazine</i>, January and July, 1860.</p> - -<p>In the introduction to this paper Maxwell points -out, while there was then no means of measuring the -quantities which occurred in Clausius’ expression for -the mean free path, “the phenomena of the internal -friction of gases, the conduction of heat through a gas, -and the diffusion of one gas through another, seem to -indicate the possibility of determining accurately the -mean length of path which a particle describes between -two collisions. In order, therefore, to lay the foundation -of such investigations on strict mechanical principles,” -he continues, “I shall demonstrate the laws -of motion of an indefinite number of small, hard and -perfectly elastic spheres acting on one another only -during impact.”</p> - -<p>Maxwell then proceeds to consider in the first case -the impact of two spheres.</p> - -<p>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.</p> - -<p>He was led to this method by his investigation -into the theory of Saturn’s rings, which had been<span class="pagenum" id="Page_121">121</span> -completed in 1856, and in which he had shown that the -conditions of stability required the supposition that -the rings are composed of an indefinite number of free -particles revolving round the planet, with velocities -depending on their distances from the centre. These -particles may either be arranged in separate rings, or -their motion may be such that they are continually -coming into collision with each other.</p> - -<p>As an example of the statistical method, let us -consider a crowd of people moving along a street. -Taken as a whole the crowd moves steadily forwards. -Any individual in the crowd, however, is jostled backwards -and forwards and from side to side; if a line -were drawn across the street we should find people -crossing it in both directions. In a considerable interval -more people would cross it, going in the direction -in which the crowd is moving, than in the other, -and the velocity of the crowd might be estimated -by counting the number which crossed the line in -a given interval. This velocity so found would differ -greatly from the velocity of any individual, which -might have any value within limits, and which is -continually changing. If we knew the velocity of -each individual and the number of individuals we -could calculate the average velocity, and this would -agree with the value found by counting the resultant -number of people who cross the line in a given interval.</p> - -<p>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<span class="pagenum" id="Page_122">122</span> -more accurate, do not differ among themselves by -more than some small quantity. The number of -people at any moment in each of these groups will -be very different. The number in any group, which -has a velocity not differing greatly from the mean -velocity of the whole, will be large; comparatively few -will have either a very large or a very small velocity.</p> - -<p>Again, at any moment, individuals are changing -from one group to another; a man is brought to -a stop by some obstruction, and his velocity is considerably -altered—he passes from one group to a -different one; but while this is so, if the mean velocity -remains constant, and the size of the crowd be very -great, the number of people at any moment in a -given group remains unchanged. People pass from -that group into others, but during any interval the -same number pass back again into that group.</p> - -<p>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.</p> - -<p>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<span class="pagenum" id="Page_123">123</span> -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.</p> - -<p>From this an accurate expression can be found for -the pressure of the gas, and it is proved that the value -found by others, on the assumption that all the -particles were moving with a common velocity, is -correct. Previous to this paper of Maxwell’s it had -been realised that the velocities could not be uniform -throughout. There had been no attempt to determine -the distribution of velocity, or to submit the problem -to calculation, making allowance for the variations in -velocity.</p> - -<p>Maxwell’s mathematical methods are, in their -generality and elegance, far in advance of anything -previously attempted in the subject.</p> - -<p>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.</p> - -<p>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.</p> - -<p>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.</p> - -<p>Thus if <i>m</i>₁, <i>m</i>₂ be the masses of the particles in<span class="pagenum" id="Page_124">124</span> -the two sets respectively, <i>v</i>₁, <i>v</i>₂ their mean velocities -we must have <span class="locked">finally—</span></p> - -<p class="center">½ <i>m</i>₁ <i>v</i>₁² = ½ <i>m</i>₂ <i>v</i>₂² -</p> - -<p>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.</p> - -<p>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.”</p> - -<p>Thus, as the result of Maxwell’s more exact researches -on the motion of a system of spherical -particles, we find that we again can obtain the -<span class="locked">equations—</span></p> - -<p class="center">T = ½ <i>mv</i>² -<i>p</i> = ⅓ N <i>mv</i>² = ⅔ NT = ⅔ <i>ρ</i> T/<i>m</i> -</p> - -<p>From these results we obtain as before the laws of -Boyle, Charles and Avrogadro.</p> - -<p>Again if <i>σ</i> be the specific heat of the gas at -constant volume, the quantity of heat required to -raise a single molecule of mass <i>m</i> one degree will be -<i>σ</i> <i>m</i>.</p> - -<p>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<span class="pagenum" id="Page_125">125</span> -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 <i>σ</i> <i>m</i> is -the same for all gases; or, in other words, the -specific heat of a gas is inversely proportional to the -mass of its individual molecules. The density of a -gas—since the number of molecules per unit volume -at a given pressure and temperature is the same for -all gases—is also proportional to the mass of each individual -molecule. Thus the specific heats of all gases -are inversely proportional to their densities. This -is the law discovered experimentally by Dulong and -Petit to be approximately true for a large number of -substances.</p> - -<div class="tb">* * * * *</div> - -<p>In the next part of the paper Maxwell proceeded -to determine the average number of collisions in a -given time, and hence, knowing the velocities, to -determine, in terms of the size of the particles and -their numbers, the mean free path of a particle; the -result so found differed somewhat from that already -obtained by Clausius.</p> - -<p>Having done this he showed how, by means of -experiments on the viscosity of gases, the length of -the mean free path could be determined.</p> - -<p>An illustration due to Professor Balfour Stewart -will perhaps make this clear. Let us suppose we -have two trains running with uniform speed in -opposite directions on parallel lines, and, further, that -the engines continue to work at the same rate, -developing just sufficient energy to overcome the -resistance of the line, etc., and to maintain the speed<span class="pagenum" id="Page_126">126</span> -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.</p> - -<p>Consider two streams of gas, moving in opposite -directions one over the other; it is found that in -each case the layers of gas near the separating surface -move more slowly than those in the interior of -the streams; there is apparently a frictional force -between the two streams along this surface, tending -to reduce their relative velocity. Maxwell’s explanation -of this is that at the common surface particles -from the one stream enter the other, and carry with -them their own momentum; thus near this surface -the momentum of each stream is reduced, just as the -momentum of the trains is reduced by the people -jumping across. Internal friction or viscosity is due -to the diffusion of momentum across this common -surface. The effect does not penetrate far into the -gas, for the particles soon acquire the velocity of the -stream to which they have come.</p> - -<p>Now, the rate at which the momentum is diffused -will measure the frictional force, and will depend on -the mean free path of the particles. If this is considerable, -so that on the average a particle can penetrate a -considerable distance into the second gas before a<span class="pagenum" id="Page_127">127</span> -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.</p> - -<p>Maxwell, in the paper under discussion, was the -first to do this, and, using a value found by Professor -Stokes for the coefficient of viscosity, obtained as the -length of the mean free path of molecules of air -1/447000 of an inch, while the number of collisions per -second experienced by each molecule is found to be -about 8,077,200,000.</p> - -<p>Moreover, it appeared from his theory that the coefficient -of viscosity should be independent of the -number of molecules of gas present, so that it is not -altered by varying the density. This result Maxwell -characterises as startling, and he instituted an elaborate -series of experiments a few years later with a view of -testing it. The reason for this result will appear if -we remember that, when the density is decreased, the -mean free path is increased; relatively, then, to the -total number of molecules present, the number which -cross the surface in a given time is increased. And it -appears from Maxwell’s result that this relative increase -is such that the total number crossing remains -unchanged. Hence the momentum conveyed across -each unit area per second remains the same, in spite -of the decrease in density.</p> - -<p>Another consequence of the same investigation is -that the coefficient of viscosity is proportional to the<span class="pagenum" id="Page_128">128</span> -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.</p> - -<p>The second part of the paper deals with the -process of diffusion of two or more kinds of moving -particles among one another.</p> - -<p>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.</p> - -<p>Maxwell attempted to calculate from his theory -the rate at which the diffusion takes place in these -cases. The conditions of most of Graham’s experiments -were too complicated to admit of direct comparison -with the theory, from which it appeared that -there is a relation between the mean free path and -the rate of diffusion. One experiment, however, was -found, the conditions of which could be made the -subject of calculation, and from it Maxwell obtained -as the value of the mean free path in air 1/389000 of an -inch.</p> - -<p>The number was close enough to that found from -the viscosity to afford some confirmation of his -theory.</p> - -<p><span class="pagenum" id="Page_129">129</span></p> - -<p>However, a few years later Clausius criticised the -details of this part of the paper, and Maxwell, in his -memoir of 1866, admits the calculation to have been -erroneous. The main principles remained unaffected, -the molecules pass from one gas to the other, and this -constitutes diffusion.</p> - -<p>Now, suppose we have two sets of particles in -contact of such a nature that the mean kinetic -energy of the one set is different from that of the -other; the temperatures of the two will then be different. -These two sets will diffuse into each other, and -the diffusing particles will carry with them their -kinetic energy, which will gradually pass from those -which have the greater energy to those which have -the less, until the average kinetic energy is equalised -throughout. But the kinetic energy of translation is -the heat of the particles. This diffusion of kinetic -energy is a diffusion of heat by conduction, and we -have here the mechanical theory of the conduction -of heat in a gas.</p> - -<p>Maxwell obtained an expression, which, however, -he afterwards modified, for the conductivity of a gas -in terms of the mean free path. It followed from this -that the conductivity of air was only about 1/7000 of -that of copper.</p> - -<p>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.</p> - -<p>In the third part of his paper Maxwell considers<span class="pagenum" id="Page_130">130</span> -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.</p> - -<p>It follows from Maxwell’s work that for each particle -the average value of these two portions of energy -would be equal. The total energy will be half translational -and half rotational.</p> - -<p>This theorem, in a more general form which was -afterwards given to it, has led to much discussion, -and will be again considered later. For the present -we will assume it to be true. Clausius had already -called attention to the fact that some of the energy -must be rotational unless the molecules be smooth -spheres, and had given some reasons for supposing -that the ratio of the whole energy to the energy -of translation is in a steady state a constant. Maxwell -shows that for rigid bodies this constant is 2. -Let us denote it for the present by the symbol β. -Thus, if the translational energy of a molecule is -½ <i>m</i> <i>v</i>², its whole energy is ½ β <i>m</i> <i>v</i>².</p> - -<p>The temperature is still measured by the translational -energy, or ½ <i>m</i> <i>v</i>²; the heat depends on the -whole energy. Hence if H represent the amount of<span class="pagenum" id="Page_131">131</span> -heat—measured as energy—contained by a single -molecule, and T its temperature, we <span class="locked">have—</span></p> - -<p class="center">H = βT -</p> - -<p>From this it can be shewn<a id="FNanchor_50" href="#Footnote_50" class="fnanchor">50</a> that if γ represent the -ratio of the specific heat of a gas at constant pressure -to the specific heat at constant volume, <span class="locked">then—</span></p> - -<p class="center">β = ⅔ 1/(γ-1) -</p> - -<p>For air and some other gases the value of γ has -been shown to be 1·408. From this it follows that<span class="pagenum" id="Page_132">132</span> -β = 1·634. Now, Maxwell’s theory required that for -smooth hard particles, approximately spherical in -shape, β should be 2, and hence he concludes “we -have shown that a system of such particles could not -possibly satisfy the known relation between the two -specific heats of all gases.”</p> - -<p>Since this statement was made many more experiments -on the value of γ have been undertaken; it is -not equal to 1·408 for <i>all</i> gases. Hence the value of -β is different for various gases.</p> - -<p>It is of some importance to notice that the -value of β just found for air is very approximately -1·66 or 5/3.</p> - -<p>For mercury vapour the value of γ has been shown -by Kundt to be 1·33 or 1⅓, and hence β is equal to 1. -Thus all the energy of a particle of mercury vapour is -translational, and its behaviour in this respect is consistent -with the assumption that a particle of mercury -vapour is a smooth sphere.</p> - -<p>The two results of this theory which seemed to -lend themselves most readily to experimental verification -were (1) that the viscosity of a gas is -independent of its density, and (2) that it is proportional -to the square root of the absolute -temperature. The next piece of work connected with -the theory was an attempt to test these consequences, -and a description of the experiments was published -in the “Philosophical Transactions” for 1865, in a -paper on the “Viscosity or Internal Friction of Air -and other Gases,” and forms the Bakerian lecture for -that year.</p> - -<p>The first result was completely proved. It is<span class="pagenum" id="Page_133">133</span> -shewn that the value of the coefficient<a id="FNanchor_51" href="#Footnote_51" class="fnanchor">51</a> of viscosity -“is the same for air at 0·5 inch and at 30 inches -pressure, provided that the temperature remains the -same.”</p> - -<p>It was clear also that the viscosity depended on -the temperature, and the results of the experiments -seemed to show that it was nearly proportional to the -absolute temperature. Thus for two temperatures, -185° Fah. and 51° Fah., the ratio of the two coefficients -found was 1·2624; the ratio of the two -temperatures, each measured from absolute zero, is -1·2605.</p> - -<p>This result, then, does not agree with the hypothesis -that a gas consists of spherical molecules acting only -on each other by a kind of impact, for, if this were so, -the coefficient would, as we have seen, depend on the -square root of the absolute temperature. But Maxwell’s -result, connecting viscosity with the first power -of the absolute temperature, has not been confirmed -by other investigators. According to it we should -have as the relation between μ, the coefficient of -viscosity at t° and μ₀, that at zero the <span class="locked">equation—</span></p> - -<p class="center">μ = μ₀ (1 + .00365 t). -</p> - -<p>The most recent results of Professor Holman -(<i>Philosophical Magazine</i>, Vol. xxi., p. 212) <span class="locked">give—</span></p> - -<p class="center">μ = μ₀ (1 + .00275 t - .00000034 t²). -</p> - -<p class="in0">And results similar to this are given by O. E. Meyer,<span class="pagenum" id="Page_134">134</span> -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.</p> - -<p>It still remains true, therefore, that the laws of the -viscosity of gases cannot be explained by the hypothesis -of the impact of hard spheres; but some deductions -drawn by Maxwell in his next paper from his supposed -law of proportionality to the first power of the -absolute temperature require modification.</p> - -<p>It was clear from his experiments just described -that the simple hypothesis of the impact of elastic -bodies would not account for all the phenomena -observed. Accordingly, in 1866, Maxwell took up -the problem in a more general form in his paper on -the “Dynamical Theory of Gases,” Phil. Trans., 1866.</p> - -<p>In it he considered the molecules of the gas not -as elastic spheres of definite radius, but as small -bodies, or groups of smaller molecules, repelling one -another with a force whose direction always passes -very nearly through the centre of gravity of the -molecules, and whose magnitude is represented very -nearly by some function of the distance of the centres -of gravity. “I have made,” he continues, “this -modification of the theory in consequence of the -results of my experiments on the viscosity of air at -different temperatures, and I have deduced from -these experiments that the repulsion is inversely as -the fifth power of the distance.”</p> - -<p>Since more recent observation has shown that the -numerical results of Maxwell’s work connecting -viscosity and temperature are erroneous, this last<span class="pagenum" id="Page_135">135</span> -deduction does not hold; the inverse fifth power law -of force will not give the correct relation between -viscosity and temperature. Maxwell himself at a -later date, “On the Stresses in Rarefied Gases,” Phil. -Trans., 1879, realised this; but even in this last paper -he adhered to the fifth power law because it leads to -an important simplification in the equations to be -dealt with.</p> - -<p>The paper of 1866 is chiefly important because it -contains for the first time the application of general -dynamical methods to molecular problems. The law -of the distribution of velocities among the molecules -is again investigated, and a result practically identical -with that found for the elastic spheres is arrived at. -In obtaining this conclusion, however, it is assumed -that the distribution of velocities is uniform in all -directions about any point, whatever actions may be -taking place in the gas. If, for example, the temperature -is different at different points, then, for a given -velocity, all directions are not equally probable. -Maxwell’s expression, therefore, for the number of -molecules which at any moment have a given velocity -only applies to the permanent state in which the distribution -of temperature is uniform. When dealing, -for example, with the conduction of heat, a modification -of the expression is necessary. This was -pointed out by Boltzmann.<a id="FNanchor_52" href="#Footnote_52" class="fnanchor">52</a></p> - -<p>In the paper of 1866, Maxwell applies his generalised -results to the final distribution of two gases<span class="pagenum" id="Page_136">136</span> -under the action of gravity, the equilibrium of temperature -between two gases, and the distribution of -temperature in a vertical column. These results are, -as he states, independent of the law of force between -the molecules. The dynamical causes of diffusion -viscosity and conduction of heat are dealt with, and -these involve the law of force.</p> - -<p>It follows also from the investigation that, on the -hypotheses assumed as its basis, if two kinds of gases -be mixed, the difference between the average kinetic -energies of translation of the gases of each kind -diminishes rapidly in consequence of the action -between the two. The average kinetic energy of -translation, therefore, tends to become the same for -each kind of gas, and as before, it is this average -energy of translation which measures the temperature.</p> - -<p>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.</p> - -<p><span class="pagenum" id="Page_137">137</span></p> - -<p>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.<a id="FNanchor_53" href="#Footnote_53" class="fnanchor">53</a></p> - -<p>Now Clausius had, as we have seen, given reasons -for believing that the ratio of the whole energy of a -molecule to the energy of translation of its centre of -gravity tends to become constant. We have already -used β to denote this constant. Thus, while the temperature -is measured by the average kinetic energy -of translation of the centre of gravity of each molecule, -the heat contained in a molecule is its whole -energy, and is β times this quantity. Thus the conclusions -as to specific heat, etc., already given on page -130, apply in this case, and in particular we have the -result that if γ be the ratio of the specific heat at -constant pressure to that at constant volume, <span class="locked">then—</span></p> - -<p class="center">β = ⅔ 1/(γ-1) -</p> - -<p class="in0">Maxwell’s theorem of the distribution of kinetic -energy among a system of molecules applied, as he -gave it in 1866, to the kinetic energy of translation of -the centre of gravity of each molecule. Two years -later Dr. Boltzmann, in the paper we have already<span class="pagenum" id="Page_138">138</span> -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.</p> - -<p>Maxwell, in the last paper he wrote on the subject -(“On Boltzmann’s Theorem on the Average Distribution -of Energy in a System of Material Points,” -Camb. Phil. Trans., XII.), took up this problem. -Watson had given a proof of it in 1876 differing from -Boltzmann’s, but still limited by the stipulation that -the time, during which a particle is encountering other -particles, is very small compared with the time during -which there is no sensible action between it and other -particles, and also that the time during which a -particle is simultaneously within the distance of more -than one other particle may be neglected.</p> - -<p>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.</p> - -<p>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.</p> - -<p>In this paper Maxwell finds in a very general -manner an expression for the number of molecules<span class="pagenum" id="Page_139">139</span> -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.</p> - -<p>Thus, according to this theorem, if each molecule -be a single small solid body, six variables will be required -to determine the position of each, three -variables will give us the position of the centre of -gravity of the molecule, while three others will determine -the position of the body relative to its centre of -gravity. If the six variables be properly chosen, the -kinetic energy can be expressed as a sum of six -squares, one square corresponding to each variable. -According to the theorem the part of the kinetic -energy depending on each square is the same. Thus, -the whole energy is six times as great as that which -arises from any one of the variables. The kinetic -energy of translation is three times as great as that -arising from each variable, for it involves the three -variables which determine the position of the centre -of gravity. Hence, if we denote by K the kinetic -energy due to one variable, the whole energy is 6 K, -and the translational energy is 3 K; thus, for this -<span class="locked">case—</span></p> - -<p class="center">β = 6K/3K = 2 -</p> - -<p class="in0">Or, again, if we suppose that the molecule is such that -<i>m</i> 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<span class="pagenum" id="Page_140">140</span> -of variables defining the position of the molecule is -<i>m</i> + 3, and it is said to have <i>m</i> + 3 degrees of freedom. -Hence, in this case, its total energy is (<i>m</i> + 3) K and -its energy of translation is 3 K, thus we <span class="locked">find—</span></p> - -<p class="center">β = (<i>m</i> + 3)/3</p> - -<p class="center">Hence <span class="in2">γ = 1 + 2/(<i>m</i> + 3) = 1 + 2/<i>n</i></span> -</p> - -<p class="in0">if <i>n</i> be the number of degrees of freedom of the -molecule.</p> - -<p>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 <i>n</i> equal to 6, -and hence γ = 1·333. Now the fact that this is not -the value of γ for any of the known gases is a -fundamental difficulty in the way of accepting the -complete theory.</p> - -<p>Boltzmann has called attention to the fact that if -<i>n</i> be equal to five, then γ has the value 1·40. And this -agrees fairly with the value found by experiment for -air, oxygen, nitrogen, and various other gases. We -will, however, return to this point shortly.</p> - -<p>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.</p> - -<p>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<span class="pagenum" id="Page_141">141</span> -that the kinetic energy is ultimately equally divided -among all the variables which determine the system.</p> - -<p>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.</p> - -<p>The proof that this law is a necessary, as well as a -sufficient, condition of permanence was first given by -Boltzmann, for a single monatomic gas in 1872, for a -mixture of such gases in 1886, and for a polyatomic gas -in 1887. Other proofs have been given since by Watson -and Burbury. It would be quite beyond the limits of -this book to go into the question of the completeness -or sufficiency of the proofs. The discussion of the -question is still in progress.</p> - -<p>The British Association Report for 1894 contains -an important contribution to the question, in the -shape of a report by Mr. G. H. Bryan, and the discussion -he started at Oxford by reading this report -has been continued in the pages of <i>Nature</i> and elsewhere -since that time.</p> - -<p>Mr. Bryan shows in the first place what may be -the nature of the systems of molecules to which the -results will apply, and discusses various points of -difficulty in the proof.</p> - -<p>The theorem in question, from which the result (1) -follows as a simple deduction, has been thus stated by -Dr. Larmor.<a id="FNanchor_54" href="#Footnote_54" class="fnanchor">54</a></p> - -<p><span class="pagenum" id="Page_142">142</span></p> - -<p>“There exists a positive function belonging to a -group of molecules which, as they settle themselves -into a steady state—on the average derived from a -great number of configurations—maintains a steady -downward trend. The Maxwell-Boltzmann steady state -is the one in which this function has finally attained -its minimum value, and is thus a unique steady state, -it still being borne in mind that this is only a proposition -of averages derived from a great number of -instances in which nothing is conserved in encounters, -except the energy, and that exceptional circumstances -may exist, comparatively very few in number, in -which the trend is, at any rate, temporarily the -other way.”</p> - -<p>This theorem, when applied to cases of motion, -such as that of a gas at constant temperature enclosed -in a rigid envelope impermeable to heat, -appears to be proved. For such a case, therefore, -the Maxwell-Boltzmann law is the only one possible.</p> - -<p>But whether this be so or not, the law first introduced -by Maxwell is one of those possible, and the -advance in molecular science due to its introduction -is enormous.</p> - -<p>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 -(<i>Philosophical Magazine</i>, March, 1893) how this flaw -can easily be corrected, and it may be said that in all -cases in which the Boltzmann-Maxwell law of the -distribution of velocities holds, Maxwell’s law of the -equal partition of energy holds also.</p> - -<p><span class="pagenum" id="Page_143">143</span></p> - -<p>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.</p> - -<p>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.</p> - -<p>In this case, then, as Boltzmann points out, in the -expression for the ratio of the specific heats, we must -have <i>n</i> equal to 5, and hence</p> - -<p class="center">γ = 1 + 2/<i>n</i> = 1 + 2/5 = 1·4 -</p> - -<p class="in0">agreeing fairly with the value found for air and -various other permanent gases.</p> - -<p>For cases, then, in which we consider each atom -as a single rigid body, the Boltzmann-Maxwell<span class="pagenum" id="Page_144">144</span> -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.<a id="FNanchor_55" href="#Footnote_55" class="fnanchor">55</a></p> - -<p>If we can never go further—and it must be -admitted that the difficulties in the way of further -advance are enormous—it may, I think, be claimed -for Maxwell that the progress already made is greatly -due to him. Both these laws, for the case of elastic -spheres, are contained in his first paper of 1860; -and while it is to the genius of Boltzmann that we owe -their earliest generalisation, and in particular the -proof of the uniqueness of the solution under proper -restrictions, Maxwell’s last paper contributed in no -small degree to the security of the position. Not -merely the foundations, but much of the superstructure -of molecular science is his work.</p> - -<p>The difficulties in the way of advance are, as we -have said, enormous. Boltzmann, in one of his papers, -has considered the properties of a complex molecule -of a gas, consisting maybe of a number of atoms -and possibly of ether atoms bound with them, and he -concludes that such a molecule will behave in its -progressive motion, and in its collisions with other -molecules, nearly like a rigid body. But to quote -from Mr. Bryan: “The case of a polyatomic molecule, -whose atoms are capable of vibrating relative -to one another, affords an interesting field for investigation -and speculation. Is the Boltzmann distribution -still unique, or do other permanent distributions -exist in which the kinetic energy is unequally -divided?”</p> - -<p><span class="pagenum" id="Page_145">145</span></p> - -<p>Again, the spectroscope reveals to us vibrations -of the ether, which are connected in some way with -the vibrations of the molecules of gas, whose spectrum -we are observing. It seems clear that the law of -equal partition does not apply to these, and yet, -if we are to suppose that the ether vibrations are -due to actual vibrations of the atoms which constitute -a molecule, why does it not apply? Where -does the condition come in which leads to failure in -the proof? Or, again, is it, as has been suggested, the -fact that the complex spectrum of a gas represents -the terms of a Fourier Series, into which some -elaborate vibration of the atoms is resolved by the -ether? or is the spectrum due simply to electro-magnetic -vibrations on the surface of the molecules—vibrations -whose period is determined chiefly by the -size and shape of the molecule, but in which the -atoms of which it is composed take part? There are -grave difficulties in the way of either of these explanations, -but we must not let our dread of the task -which remains to be done blind our eyes to the greatness -of Maxwell’s work.</p> - -<p>One other important paper, and a number of -shorter articles, remain to be mentioned.</p> - -<p>The Boltzmann-Maxwell law applies only to cases -in which the temperature is uniform throughout. In -a paper published in the Philosophical Transactions -for 1879, on “Stresses in Rarefied Gases Arising from -Inequalities of Temperature,” Maxwell deals, among -other matters, with the theory of the radiometer. He -shows that the observed motions will not take place -unless gas, in contact with a solid, can slide along<span class="pagenum" id="Page_146">146</span> -the surface of the solid with a finite velocity between -places where the temperature is different; and in an -appendix he proves that, on certain assumptions regarding -the nature of the contact of the solid and -the gas, there will be, even when the pressure is constant, -a flow of gas along the surface from the colder -to the hotter parts.</p> - -<p>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.</p> - -<p>In this latter, and also in a review in <i>Nature</i> of -Van der Waals’ book on “The Continuity of the -Gaseous and Liquid States,”<a id="FNanchor_56" href="#Footnote_56" class="fnanchor">56</a> he explains and discusses -Clausius’ virial equation, by means of which -the variations of the permanent gases from Boyle’s -law are explained. The lecture gives a clear account, -in Maxwell’s own inimitable style, of the advances -made in the kinetic theory up to the date at which it -was delivered, and puts clearly the difficulties it has -to meet. Maxwell thought that those arising from -the known values of the ratio of the specific heats -were the most serious.</p> - -<p>In the articles, “Atomic Constitution of Bodies” -and “Diffusion,” in the ninth edition of the <i>Encyclopædia -Britannica</i>, we have Maxwell’s later views on -the fundamental assumptions of the molecular theory.</p> - -<p>The text-book on “Heat” contains some further -developments of the theory. In particular he shows<span class="pagenum" id="Page_147">147</span> -how the conclusions of the second law of thermo-dynamics -are connected with the fact that the coarseness -of our faculties will not allow us to grapple with -individual molecules.</p> - -<p>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.</p> - -<hr /> - -<div id="toclink_148" class="chapter"> -<p><span class="pagenum" id="Page_148">148</span></p> - -<h2 class="nobreak" id="CHAPTER_IX">CHAPTER IX.<br /> - -<span class="subhead">SCIENTIFIC WORK.—ELECTRICAL THEORIES.</span></h2> -</div> - -<p class="in0"><span class="firstword">Clerk Maxwell’s</span> first electrical paper—that on -Faraday’s “Lines of Force”—was read to the Cambridge -Philosophical Society on December 10th, 1855, -and Part II. on February 11th, 1856. The author -was then a Bachelor of Arts, only twenty-three years -in age, and of less than one year’s standing from the -time of taking his degree.</p> - -<p>The opening words of the paper are as follows -(Scientific Papers, vol. i., p. <span class="locked">155):—</span></p> - -<div class="blockquot"> - -<p>“The present state of electrical science seems peculiarly -unfavourable to speculation. The laws of the distribution of -electricity on the surface of conductors have been analytically -deduced from experiment; some parts of the mathematical -theory of magnetism are established, while in other parts the -experimental data are wanting; the theory of the conduction -of galvanism, and that of the mutual attraction of conductors, -have been reduced to mathematical formulæ, but have not -fallen into relation with the other parts of the science. No -electrical theory can now be put forth, unless it shows the -connection, not only between electricity at rest and current -electricity, but between the attractions and inductive effects of -electricity in both states. Such a theory must accurately -satisfy those laws, the mathematical form of which is known, -and must afford the means of calculating the effects in the -limiting cases where the known formulæ are inapplicable. In -order, therefore, to appreciate the requirements of the science, -the student must make himself familiar with a considerable -body of most intricate mathematics, the mere retention -of which in the memory materially interferes with further<span class="pagenum" id="Page_149">149</span> -progress. The first process, therefore, in the effectual study -of the science, must be one of simplification and reduction of -the results of previous investigation to a form in which the -mind can grasp them. The results of this simplification may -take the form of a purely mathematical formula or of a physical -hypothesis. In the first case we entirely lose sight of the -phenomena to be explained; and though we may trace out -the consequences of given laws, we can never obtain more -extended views of the connections of the subject. If, on the -other hand, we adopt a physical hypothesis, we see the -phenomena only through a medium, and are liable to that -blindness to facts and rashness in assumption which a partial -explanation encourages. We must therefore discover some -method of investigation which allows the mind at every step -to lay hold of a clear physical conception, without being committed -to any theory founded on the physical science from -which that conception is borrowed, so that it is neither drawn -aside from the subject in pursuit of analytical subtleties, nor -carried beyond the truth by a favourite hypothesis.</p> - -<p>“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.</p> - -<p>“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;<span class="pagenum" id="Page_150">150</span> -and we still find it useful in the solution of certain problems, -in which we employ it without danger as an artificial method. -The other analogy, between light and the vibrations of an -elastic medium, extends much farther, but, though its importance -and fruitfulness cannot be over-estimated, we must -recollect that it is founded only on a resemblance <em>in form</em> -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.</p> - -<p>“We have all acquired the mathematical conception of these -attractions. We can reason about them and determine their -appropriate forms or formulæ. These formulæ have a distinct -mathematical significance, and their results are found to be in -accordance with natural phenomena. There is no formula in -applied mathematics more consistent with Nature than the -formula of attractions, and no theory better established in the -minds of men than that of the action of bodies on one another -at a distance. The laws of the conduction of heat in uniform -media appear at first sight among the most different in their -physical relations from those relating to attractions. The -quantities which enter into them are <em>temperature</em>, <em>flow of heat</em>, -<em>conductivity</em>. The word <em>force</em> 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 <em>source of heat</em> for <em>centre of attraction</em>, -<em>flow of heat</em> for <em>accelerating effect of attraction</em> at any point, -and <em>temperature</em> for <em>potential</em>, and the solution of a problem in -attractions is transformed into that of a problem in heat.</p> - -<p>“This analogy between the formulæ of heat and attraction -was, I believe, first pointed out by Professor William Thomson -in the <cite>Cambridge Mathematical Journal</cite>, Vol. III.</p> - -<p>“Now the conduction of heat is supposed to proceed by an<span class="pagenum" id="Page_151">151</span> -action between contiguous parts of a medium, while the force -of attraction is a relation between distant bodies, and yet, if -we knew nothing more than is expressed in the mathematical -formulæ, there would be nothing to distinguish between the -one set of phenomena and the other.</p> - -<p>“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.</p> - -<p>“It is by the use of analogies of this kind that I have attempted -to bring before the mind, in a convenient and manageable -form, those mathematical ideas which are necessary to the -study of the phenomena of electricity. The methods are generally -those suggested by the processes of reasoning which are -found in the researches of Faraday, and which, though they -have been interpreted mathematically by Professor Thomson -and others, are very generally supposed to be of an indefinite -and unmathematical character, when compared with those -employed by the professed mathematicians. By the method -which I adopt, I hope to render it evident that I am not -attempting to establish any physical theory of a science in -which I have hardly made a single experiment, and that the -limit of my design is to show how, by a strict application of -the ideas and methods of Faraday, the connection of the very -different orders of phenomena which he has discovered may be -clearly placed before the mathematical mind. I shall therefore -avoid as much as I can the introduction of anything which does -not serve as a direct illustration of Faraday’s methods, or of -the mathematical deductions which may be made from them. -In treating the simpler parts of the subject I shall use Faraday’s -mathematical methods as well as his ideas. When the complexity -of the subject requires it, I shall use analytical notation, -still confining myself to the development of ideas originated by -the same philosopher.</p> - -<p>“I have in the first place to explain and illustrate the idea -of ‘lines of force.’</p> - -<p>“When a body is electrified in any manner, a small body<span class="pagenum" id="Page_152">152</span> -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.</p> - -<p>“The same relations hold between a magnetic body and the -north or south poles of a small magnet. If the north pole is -urged in one direction, the south pole is urged in the opposite -direction.</p> - -<p>“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 <em>line of force</em>. 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.</p> - -<p>“We should thus obtain a geometrical model of the physical -phenomena, which would tell us the <em>direction</em> of the force, but -we should still require some method of indicating the <em>intensity</em> -of the force at any point. If we consider these curves not as -mere lines, but as fine tubes of variable section carrying an -incompressible fluid, then, since the velocity of the fluid is -inversely as the section of the tube, we may make the velocity -vary according to any given law, by regulating the section of -the tube, and in this way we might represent the intensity of -the force as well as its direction by the motion of the fluid in -these tubes. This method of representing the intensity of a -force by the velocity of an imaginary fluid in a tube is -applicable to any conceivable system of forces, but it is -capable of great simplification in the case in which the forces -are such as can be explained by the hypothesis of attractions -varying inversely as the square of the distance, such as those<span class="pagenum" id="Page_153">153</span> -observed in electrical and magnetic phenomena. In the case -of a perfectly arbitrary system of forces, there will generally be -interstices between the tubes; but in the case of electric and -magnetic forces it is possible to arrange the tubes so as to -leave no interstices. The tubes will then be mere surfaces, -directing the motion of a fluid filling up the whole space. It -has been usual to commence the investigation of the laws of -these forces by at once assuming that the phenomena are due -to attractive or repulsive forces acting between certain points. -We may, however, obtain a different view of the subject, and -one more suited to our more difficult inquiries, by adopting for -the definition of the forces of which we treat, that they may be -represented in magnitude and direction by the uniform motion -of an incompressible fluid.</p> - -<p>“I propose, then, first to describe a method by which the -motion of such a fluid can be clearly conceived; secondly to -trace the consequences of assuming certain conditions of -motion, and to point out the application of the method to -some of the less complicated phenomena of electricity, -magnetism, and galvanism; and lastly, to show how by an -extension of these methods, and the introduction of another -idea due to Faraday, the laws of the attractions and inductive -actions of magnets and currents may be clearly conceived, -without making any assumptions as to the physical nature of -electricity, or adding anything to that which has been already -proved by experiment.</p> - -<p>“By referring everything to the purely geometrical idea of -the motion of an imaginary fluid, I hope to attain generality -and precision, and to avoid the dangers arising from a premature -theory professing to explain the cause of the -phenomena. If the results of mere speculation which I have -collected are found to be of any use to experimental philosophers, -in arranging and interpreting their results, they will -have served their purpose, and a mature theory, in which -physical facts will be physically explained, will be formed by -those who by interrogating Nature herself can obtain the only -true solution of the questions which the mathematical theory -suggests.”</p> -</div> - -<p><span class="pagenum" id="Page_154">154</span></p> - -<p>The idea was a bold one: for a youth of twenty-three -to explain, by means of the motions of an -incompressible fluid, some of the less complicated -phenomena of electricity and magnetism, to show how -the laws of the attractions of magnets and currents -may be clearly conceived without making any assumption -as to the physical nature of electricity, or -adding anything to that which has already been -proved by experiment.</p> - -<p>It may be useful to review in a very few words -the position of electrical theory<a id="FNanchor_57" href="#Footnote_57" class="fnanchor">57</a> in 1855.</p> - -<p>Coulomb’s experiments had established the fundamental -facts of electrostatic attraction and repulsion, -and Coulomb himself, about 1785, had stated a theory -based on these experiments which could “only be -attacked by proving his experimental results to be -inaccurate.”<a id="FNanchor_58" href="#Footnote_58" class="fnanchor">58</a></p> - -<p>Coulomb supposes the existence of two electric -fluids, the theory developed previously by Franklin, -but <span class="locked">says—</span></p> - -<div class="blockquot"> - -<p>“Je préviens pour mettre la théorie qui va suivre à l’abri -de toute dispute systématique, que dans la supposition de -deux fluides électriques, je n’ai autre intention que de présenter -avec le moins d’éléments possible les résultats du calcul et -de l’expérience, et non d’indiquer les véritables causes de -l’électricité.”</p> -</div> - -<p>Cavendish was working in England about the -same time as Coulomb, but he published very little,<span class="pagenum" id="Page_155">155</span> -and the value and importance of his work was not -recognised until the appearance in 1879 of the -“Electrical Researches of Henry Cavendish,” edited -by Clerk Maxwell.</p> - -<p>Early in the present century the application of -mathematical analysis to electrical problems was -begun by Laplace, who investigated the distribution -of electricity on spheroids, and about 1811 Poisson’s -great work on the distribution of electricity on two -spheres placed at any given distance apart was published. -Meanwhile the properties of the electric -current were being investigated. Galvani’s discovery -of the muscular contraction in a frog’s leg, caused by -the contact of dissimilar metals, was made in 1790. -Volta invented the voltaic pile in 1800, and Oersted in -1820 discovered that an electric current produced -magnetic force in its neighbourhood. On this Ampère -laid the foundation of his theory of electro-dynamics, -in which he showed how to calculate the forces between -circuits carrying currents from an assumed law -of force between each pair of elements of the circuits. -His experiments proved that the consequences which -follow from this law are consistent with all the -observed facts. They do not prove that Ampère’s law -alone can explain the facts.</p> - -<p>Maxwell, writing on this subject in the “Electricity -an Magnetism,” vol. ii., p. 162, <span class="locked">says—</span></p> - -<div class="blockquot"> - -<p>“The experimental investigation by which Ampère established -the laws of the mechanical action between electric -currents is one of the most brilliant achievements in science.</p> - -<p>“The whole, theory and experiment, seems as if it had -leaped full grown and full armed from the brain of the<span class="pagenum" id="Page_156">156</span> -‘Newton of Electricity.’ It is perfect in form and unassailable -in accuracy, and it is summed up in a formula from -which all the phenomena may be deduced, and which must -always remain the cardinal formula of electro-dynamics.</p> - -<p>“The method of Ampère, however, though cast into an -inductive form, does not allow us to trace the formation of the -ideas which guided it. We can scarcely believe that Ampère -really discovered the law of action by means of the experiments -which he describes. We are led to suspect, what, indeed, -he tells us himself, that he discovered the law by some process -which he has not shown us, and that when he had afterwards -built up a perfect demonstration, he removed all traces of the -scaffolding by which he had built it.”</p> -</div> - -<p>The experimental evidence for Ampère’s theory, -so far, at least, as it was possible to obtain it from -experiments on closed circuits, was rendered unimpeachable -by W. Weber about 1846, while in the -previous year Grassman and F. E. Neumann both -published laws for the attraction between two elements -of current which differ from that of Ampère, but lead -to the same result for closed circuits. In a paper -published in 1846 Weber announced his hypothesis -connecting together electrostatic and electro-dynamic -action. In this paper he supposed that the force -between two particles of electricity depends on the -motion of the particles as well as on their distance -apart. A somewhat similar theory was proposed by -Gauss and published after his death in his collected -works. It has been shown, however, that Gauss’ -theory is inconsistent with the conservation of energy. -Weber’s theory avoids this inconsistency and leads, for -closed circuits, to the same results as Ampère. It has -been proved, however, by Von Helmholtz, that, under -certain circumstances, according to it, a body would<span class="pagenum" id="Page_157">157</span> -behave as though its mass were negative—it would -move in a direction opposite to that of the force.<a id="FNanchor_59" href="#Footnote_59" class="fnanchor">59</a></p> - -<p>Since 1846 many other theories have been proposed -to explain Ampère’s laws. Meanwhile, in 1821, -Faraday observed that under certain circumstances a -wire carrying a current could be kept in continuous -rotation in a magnetic field by the action between the -magnets and the current. In 1824 Arago observed -the motion of a magnet caused by rotating a copper -disc in its neighbourhood, while in 1831 Faraday -began his experimental researches into electro-magnetic -induction. About the same period Joseph Henry, of -Washington, was making, independently of Faraday, -experiments of fundamental importance on electro-magnetic -induction, but sufficient attention was not -called to his work until comparatively recent years.</p> - -<p>In 1833 Lenz made some important researches, -which led him to discover the connection between the -direction of the induced currents and Ampère’s laws, -summed up in his rule that the direction of the -induced current is always such as to oppose by its -electro-magnetic action the motion which induces it.</p> - -<p>In 1845 F. E. Neumann developed from this law -the mathematical theory of electro-magnetic induction, -and about the same time W. Weber showed how it -might be deduced from his elementary law of -electrical action.</p> - -<p>The great name of Von Helmholtz first appears in -connection with this subject in 1851, but of his -writings we shall have more to say at a later stage.</p> - -<p><span class="pagenum" id="Page_158">158</span></p> - -<p>Meanwhile, during the same period, various -writers, Murphy, Plana, Charles, Sturm, and Gauss, -extended Poisson’s work on electrostatics, treating the -questions which arose as problems in the distribution -of an attracting fluid, attracting or repelling according -to Newton’s law, though here again the greatest -advances were made by a self-taught Nottingham -shoemaker, George Green by name, in his paper “On -the Application of Mathematical Analysis to the -Theories of Electricity and Magnetism,” 1828.</p> - -<p>Green’s researches, Lord Kelvin writes, “have led to -the elementary proposition which must constitute the -legitimate foundation of every perfect mathematical -structure that is to be made from the materials furnished -by the experimental laws of Coulomb.”</p> - -<p>Green, it may be remarked, was the inventor of -the term Potential. His essay, however, lay neglected -from 1828, until Lord Kelvin called attention to it in -1845. Meanwhile, some of its most important results -had been re-discovered by Gauss and Charles and -Thomson himself.</p> - -<p>Until about 1845, the experimental work on which -these mathematical researches in electrostatics were -based was that of Coulomb. An electrified body is -supposed to have a charge of some imponderable fluid -“electricity.” Particles of electricity repel each other -according to a certain law, and the fluid distributes -itself in equilibrium over the surface of any charged -conductor in accordance with this law. There are on -this theory two opposite kinds of electric fluid, positive -and negative, two charges of the same kind repel, two -charges of opposite kinds attract; the repulsion or<span class="pagenum" id="Page_159">159</span> -attraction is proportional to the product of the charges, -and inversely proportional to the square of the -distance between them.</p> - -<p>The action between two charges is action at a -distance taking place across the space which separates -the two.</p> - -<p>Faraday, in 1837, in the eleventh series of his -“Experimental Researches,” published his first paper -on “Electrostatic Induction.” He showed—as indeed -Cavendish had proved long previously, though the -result remained unpublished—that the force between -two charged bodies will depend on the insulating -medium which surrounds them, not merely on their -shape and position. Induction, as he expresses it, -takes place along curved lines, and is an action of -contiguous particles; these curved lines he calls the -“lines of force.”</p> - -<p>Discussing these researches in 1845, Lord Kelvin -<span class="locked">writes<a id="FNanchor_60" href="#Footnote_60" class="fnanchor">60</a>:—</span></p> - -<div class="blockquot"> - -<p>“Mr. Faraday’s researches ... were undertaken with a -view to test an idea which he had long possessed that the -forces of attraction and repulsion exercised by free electricity -are not the resultants of actions exercised at a distance, but are -propagated by means of molecular action among the contiguous -particles of the insulating medium surrounding the -electrified bodies, which he therefore calls the dielectric. By -this idea he has been led to some very remarkable views upon -induction, or, in fact, upon electrical action in general. As it -is impossible that the phenomena observed by Faraday can be -incompatible with the results of experiment which constitute -Coulomb’s theory, it is to be expected that the difference of -his ideas from those of Coulomb must arise solely from a -different method of stating and interpreting physically the<span class="pagenum" id="Page_160">160</span> -same laws; and further, it may, I think, be shown that either -method of viewing this subject, when carried sufficiently far, -may be made the foundation of a mathematical theory which -would lead to the elementary principles of the other as consequences. -This theory would, accordingly, be the expression of -the ultimate law of the phenomena, independently of any -physical hypothesis we might from other circumstances be led -to adopt. That there are necessarily two distinct elementary -ways of viewing the theory of electricity may be seen from the -following considerations....”</p> -</div> - -<p>In the pages which follow, Lord Kelvin develops -the consequences of an analogy between the conduction -of heat and electrostatic action, which he had -pointed out three years earlier (1842), in his paper on -“The Uniform Motion of Heat in Homogeneous Solid -Bodies,” and discusses its connection with the mathematical -theory of electricity.</p> - -<p>The problem of distributing sources of heat in a -given homogeneous conductor of heat, so as to produce -a definite steady temperature at each point on -the conductor is shewn to be <em>mathematically</em> identical -with that of distributing electricity in equilibrium, so -as to produce at each point an electrical potential -having the same value as the temperature.</p> - -<p>Thus the fundamental laws of the conduction of -heat may be made the basis of the mathematical -theory of electricity, but the physical idea which -they suggest is that of the propagation of some effect -by means of the mutual action of contiguous particles, -rather than that of material particles attracting or -repelling at a distance, which naturally follows from -the statement of Coulomb’s law.</p> - -<p>Lord Kelvin <span class="locked">continues:—</span></p> - -<p><span class="pagenum" id="Page_161">161</span></p> - -<div class="blockquot"> - -<p>“All the views which Faraday has brought forward and -illustrated, as demonstrated by experiment, lead to this method -of establishing the mathematical theory, and, as far as the -analysis is concerned, it would in most <em>general</em> propositions be -more simple, if possible, than that of Coulomb. Of course the -analysis of <em>particular</em> problems would be identical in the two -methods. It is thus that Faraday arrives at a knowledge of -some of the most important of the mathematical theorems -which from their nature seemed destined never to be perceived -except as mathematical truths.”</p> -</div> - -<p>Lord Kelvin’s papers on “The Mathematical -Theory of Electricity,” published from 1848 to 1850, -his “Propositions on the Theory of Attraction” -(1842), his “Theory of Electrical Images” (1847), -and his paper on “The Mathematical Theory of -Magnetism” (1849), contain a statement of the most -important results achieved in the mathematical -sciences of Electrostatics and Magnetism up to the -time of Maxwell’s first paper.</p> - -<p>The opening sentences of that paper have already -been quoted. In the preface to the “Electricity and -Magnetism” Maxwell writes <span class="locked">thus:—</span></p> - -<div class="blockquot"> - -<p>“Before I began the study of electricity I resolved to read -no mathematics on the subject till I had first read through -‘Experimental Researches on Electricity.’ I was aware that -there was supposed to be a difference between Faraday’s way -of conceiving phenomena and that of the mathematicians, so -that neither he nor they were satisfied with each other’s -language. I had also the conviction that this discrepancy did -not arise from either party being wrong. I was first convinced -of this by Sir William Thomson, to whose advice and assistance, -as well as to his published papers, I owe most of what I -have learned on the subject.</p> - -<p>“As I proceeded with the study of Faraday, I perceived -that his method of conceiving the phenomena was also a<span class="pagenum" id="Page_162">162</span> -mathematical one, though not exhibited in the conventional -form of mathematical symbols. I also found that these -methods were capable of being expressed in the ordinary -mathematical forms, and thus compared with those of the professed -mathematicians.</p> - -<p>“For instance, Faraday, in his mind’s eye, saw lines of -force traversing all space where the mathematicians saw -centres of force attracting at a distance. Faraday saw a -medium where they saw nothing but distance. Faraday -sought the seat of the phenomena in real actions going on in -the medium. They were satisfied that they had found it -in a power of action at a distance impressed on the electric -fluids.”</p> -</div> - -<p>Now, Maxwell saw an analogy between electrostatics -and the steady motion of an incompressible -fluid like water, and it is this analogy which he develops -in the first part of his paper. The water flows along -definite lines; a surface which consists wholly of such -lines of flow will have the property that no water ever -crosses it. In any stream of water we can imagine a -number of such surfaces drawn, dividing it up into a -series of tubes; each of these will be a tube of flow, each -of these tubes remain always filled with water. Hence, -the quantity of water which crosses per second any -section of a tube of flow perpendicular to its length is -always the same. Thus, from the form of the tube, -we can obtain information as to the direction and -strength of the flow, for where the tube is wide the -flow will be proportionately small, and <i xml:lang="la" lang="la">vice versâ</i>.</p> - -<p>Again, we can draw in the fluid a number of surfaces, -over each of which the pressure is the same; -these surfaces will cut the tubes of flow at right -angles. Let us suppose they are drawn so that the -difference of pressure between any two consecutive<span class="pagenum" id="Page_163">163</span> -surfaces is unity, then the surfaces will be close -together at points at which the pressure changes -rapidly; where the variation of pressure is slow, the -distance between two consecutive surfaces will be -considerable.</p> - -<p>If, then, in any case of motion, we can draw the -pressure surfaces, and the tubes of flow, we can determine -the motion of the fluid completely. Now, -the same mathematical expressions which appear in -the hydro-dynamical theory occur also in the theory -of electricity, the meaning only of the symbols is -changed. For velocity of fluid we have to write -electrical force. For difference of fluid pressure we -substitute work done, or difference of electrical -potential or pressure.</p> - -<p>The surfaces and tubes, drawn as the solution -of any hydro-dynamical problem, give us also the -solution of an electrical problem; the tubes of flow are -Faraday’s tubes of force, or tubes of induction, the -surfaces of constant pressure are surfaces of equal -electrical potential. Induction may take place in -curved lines just as the tubes of flow may be bent and -curved; the analogy between the two is a complete -one.</p> - -<p>But, as Maxwell shows, the analogy reaches further -still. An electric current flowing along a wire had -been recognised as having many properties similar to -those of a current of liquid in a tube. When a steady -current is passing through any solid conductor, there -are formed in the conductor tubes of electrical flow -and surfaces of constant pressure. These tubes and -surfaces are the same as those formed by the flow of<span class="pagenum" id="Page_164">164</span> -liquid through a solid whose boundary surface is the -same as that of the conductor, provided the flow of -liquid is properly proportioned to the flow of electricity.</p> - -<p>These analogies refer to steady currents in which, -therefore, the flow at any point of the conductor does -not depend on the time. In Part II. of his paper Maxwell -deals with Faraday’s electro-tonic state. Faraday -had found that when <em>changes</em> are produced in the magnetic -phenomena surrounding a conductor, an electric -current is set up in the conductor, which continues so -long as the magnetic changes are in progress, but -which ceases when the magnetic state becomes steady.</p> - -<div class="blockquot"> - -<p>“Considerations of this kind led Professor Faraday to -connect with his discovery of the induction of electric currents -the conception of a state into which all bodies are thrown by -the presence of magnets and currents. This state does not -manifest itself by any known phenomena as long as it is undisturbed, -but any change in this state is indicated by a -current or tendency towards a current. To this state he gave -the name of the ‘Electro-tonic State,’ and although he afterwards -succeeded in explaining the phenomena which suggested -it by means of less hypothetical conceptions, he has on several -occasions hinted at the probability that some phenomena -might be discovered which would render the electro-tonic -state an object of legitimate induction. These speculations, -into which Faraday had been led by the study of laws which -he has well established, and which he abandoned only for -want of experimental data for the direct proof of the unknown -state, have not, I think, been made the subject of mathematical -investigation. Perhaps it may be thought that the quantitative -determinations of the various phenomena are not sufficiently -rigorous to be made the basis of a mathematical theory. -Faraday, however, has not contented himself with simply -stating the numerical results of his experiments and leaving<span class="pagenum" id="Page_165">165</span> -the law to be discovered by calculation. Where he has perceived -a law he has at once stated it, in terms as unambiguous -as those of pure mathematics, and if the mathematician, receiving -this as a physical truth, deduces from it other laws -capable of being tested by experiment, he has merely assisted -the physicist in arranging his own ideas, which is confessedly -a necessary step in scientific induction.</p> - -<p>“In the following investigation, therefore, the laws established -by Faraday will be assumed as true, and it will be -shown that by following out his speculations other and more -general laws can be deduced from them. If it should, then, -appear that these laws, originally devised to include one set of -phenomena, may be generalised so as to extend to phenomena -of a different class, these mathematical connections may -suggest to physicists the means of establishing physical connections, -and thus mere speculation may be turned to account -in experimental science.”</p> -</div> - -<p>Maxwell shows how to obtain a mathematical expression -for Faraday’s electro-tonic state. In his -“Electricity and Magnetism,” this electro-tonic state -receives a new name. It is known as the Vector -Potential,<a id="FNanchor_61" href="#Footnote_61" class="fnanchor">61</a> and the paper under consideration contains,<span class="pagenum" id="Page_166">166</span> -though in an incomplete form, his first statement of -those equations of the electric field which are so indissolubly -bound up with Maxwell’s name.</p> - -<p>The great advance in theory made in the paper is -the distinct recognition of certain mathematical -functions as representing Faraday’s electrotonic-state, -and their use in solving electro-magnetic problems.</p> - -<p>The paper contains no new physical theory of -electricity, but in a few years one appeared. In his -later writings Maxwell adopted a more general view -of the electro-magnetic field than that contained -in his early papers on “Physical Lines of Force.” It -must, therefore, not be supposed that the somewhat -gross conception of cog-wheels and pulleys, which we -are about to describe, were anything more to their -author than a model, which enabled him to realise -how the changes, which occur when a current of -electricity passes through a wire, might be represented -by the motion of actual material particles.</p> - -<p>The problem before him was to devise a physical -theory of electricity, which would explain the forces -exerted on electrified bodies by means of action -between the contiguous parts of the medium in the -space surrounding these bodies, rather than by direct -action across the distance which separates them. A -similar question, still unanswered, had arisen in the -case of gravitation. Astronomers have determined -the forces between attracting bodies; they do not -know how those forces arise.</p> - -<p>Maxwell’s fondness for models has already been -alluded to; it had led him to construct his top to -illustrate the dynamics of a rigid body rotating about<span class="pagenum" id="Page_167">167</span> -a fixed point, and his model of Saturn’s rings (now in -the Cavendish Laboratory) to illustrate the motion of -the satellites in the rings. He had explained many of -the gaseous laws by means of the impact of molecules, -and now his fertile ingenuity was to imagine a -mechanical model of the state of the electro-magnetic -field near a system of conductors carrying currents.</p> - -<p>Faraday, as we have seen, looked upon electrostatic -and magnetic induction as taking place along -curved lines of force. He pictures these lines as -ropes of molecules starting from a charged conductor, -or a magnet, as the case may be, and acting on other -bodies near. These ropes of molecules tend to -shorten, and at the same time to swell outwards -laterally. Thus the charged conductor tends to draw -other bodies to itself, there is a tension along the -lines of force, while at the same time each tube of -molecules pushes its neighbours aside; a pressure at -right angles to the lines of force is combined with -this tension. Assuming for a moment this pressure -and tension to exist, can we devise a mechanism to -account for it? Maxwell himself has likened the -lines of force to the fibres of a muscle. As the fibres -contract, causing the limb to which they are attached -to move, they swell outwards, and the muscle thickens.</p> - -<p>Again, from another point of view, we might consider -a line of force as consisting of a string of small -cells of some flexible material each filled with fluid. -If we then suppose this series of cells caused to -rotate rapidly about the direction of the line of force, -the cells will expand laterally and contract longitudinally; -there will again be tension along the lines<span class="pagenum" id="Page_168">168</span> -of force and pressure at right angles to them. It was -this last idea, as we shall see shortly, of which Maxwell -made <span class="locked">use—</span></p> - -<div class="blockquot"> - -<p>“I propose now” [he writes (“On Physical Lines of Force,” -<cite>Phil. Mag.</cite>, vol. xxi.)] “to examine magnetic phenomena from -a mechanical point of view, and to determine what tensions -in, or motions of, a medium are capable of producing the -mechanical phenomena observed. If by the same hypothesis -we can connect the phenomena of magnetic attraction with -electro-magnetic phenomena, and with those of induced currents, -we shall have found a theory which, if not true, can -only be proved to be erroneous by experiments, which will -greatly enlarge our knowledge of this part of physics.”</p> -</div> - -<p>Lord Kelvin had in 1847 given a mechanical -representation of electric, magnetic and galvanic forces -by means of the displacements of an elastic solid in a -state of strain. The angular displacement at each -point of the solid was taken as proportional to the -magnetic force, and from this the relation between -the various other electric quantities and the motion -of the solid was developed. But Lord Kelvin did not -attempt to explain the origin of the observed forces -by the effects due to these strains, but merely made -use of the mathematical analogy to assist the imagination -in the study of both.</p> - -<p>Maxwell considered magnetic action as existing -in the form of pressure or tension, or more generally, -of some stress in some medium. The existence -of a medium capable of exerting force on material -bodies and of withstanding considerable stress, both -pressure and tension, is thus a fundamental hypothesis -with him; this medium is to be capable of motion,<span class="pagenum" id="Page_169">169</span> -and electro-magnetic forces arise from its motion and -its stresses.</p> - -<p>Now, Maxwell’s fundamental supposition is that, -in a magnetic field, there is a rotation of the molecules -continually in progress about the lines of magnetic -force. Consider now the case of a uniform -magnetic field, whose direction is perpendicular to -the paper; we are to look upon the lines of force -as parallel strings of molecules, the axes of these -strings being perpendicular to the paper. Each -string is supposed to be rotating in the same direction -about its axis, and the angular velocity of rotation -is a measure of the magnetic force. In consequence -of this rotation there will be differences of -pressure in different directions in the medium; the -pressure along the axes of the strings will be less than -it would be if the medium were at rest, that in the -directions at right angles to the axes will be greater, -the medium will behave as though it were under -tension along the axes of the molecules under -pressure at right angles to them. Moreover, it can -be shown that the pressure and the tension are both -proportional to the square of the angular velocity—the -square, that is, of the magnetic force—and -this result is in accordance with the consequences -of experiment.</p> - -<p>More elaborate calculation shows that this statement -is true generally. If we draw the lines of force -in any magnetic field, and then suppose the molecules -of the medium set in rotation about these lines of -force as axes, with velocities which at each point are -proportional to the magnetic force, the distribution of<span class="pagenum" id="Page_170">170</span> -pressure throughout is that which we know actually -to exist in the magnetic field.</p> - -<p>According to this hypothesis, then, a permanent -bar magnet has the power of setting the medium -round it into continuous molecular rotation about the -lines of force as axes. The molecules which are set -in rotation we may consider as spherical, or nearly -spherical, cells filled with a fluid, or an elastic solid -substance, and surrounded by a kind of membrane, or -sack, holding the contents together.</p> - -<p>So far the model does not give any account of -electrical actions which go on in the magnetic field.</p> - -<p>The energy is wholly rotational, and the forces -wholly magnetic.</p> - -<p>Consider, however, any two contiguous strings of -molecules. Let them cut the paper as shown in the -two circles in <span class="locked"><a href="#ip_170">Fig. 1</a>:—</span></p> - -<div id="ip_170" class="figcenter" style="max-width: 28em;"> - <img src="images/i_170.png" width="1343" height="284" alt="" /> - <div class="caption"><p> <span class="floatl in4">Fig. 1.</span> - <span class="floatr l4">Fig. 2.</span></p></div></div> - -<p>Then these cells are both rotating in the same -direction, hence at C, where they touch, their points of -contact will be moving in opposite directions, as shown -by the arrow heads, and it is difficult to imagine how -such motion can continue; it would require the surfaces -of the cells to be perfectly smooth, and if this -were so they would lose the power of transmitting -action from one cell to the next.</p> - -<p>The cells A and B may be compared to two<span class="pagenum" id="Page_171">171</span> -cog-wheels placed close together, which we wish to turn -in the same direction. If the cogs can interlock, as in -<a href="#ip_170">Fig. 2</a>, this is impossible: consecutive wheels in the -train must move in opposite directions.</p> - -<div id="ip_171" class="figcenter" style="max-width: 15em;"> - <img src="images/i_171.png" width="707" height="283" alt="" /> - <div class="caption">Fig. 3.</div></div> - -<p>But in many machines the desired end is attained -by inserting between the two wheels A and B a third -idle wheel C, as shewn in <a href="#ip_171">Fig. 3</a>. This may be very -small, its only function is to transmit the motion of A -to B in such a way that A and B may both turn in the -same direction. It is not necessary that there should -be cogs on the wheels; if the surfaces be perfectly -rough, so that no slipping can take place, the same -result follows without the cogs.</p> - -<p>Guided by this analogy Maxwell extended his -model by supposing each cell coated with a number -of small particles which roll on its surface. These -particles play the part of the idle wheels in the -machine, and by their rolling merely enable the -adjacent parts of two cells to move in opposite -directions.</p> - -<p>Consider now a number of such cells and their idle -wheels lying in a plane, that of the paper, and suppose -each cell is rotating with the same uniform angular -velocity about an axis at right angles to that plane, -each idle wheel will be acted on by two equal and -opposite forces at the ends of the diameter in which<span class="pagenum" id="Page_172">172</span> -it is touched by the adjacent cells; it will therefore -be set in rotation, but there will be no force tending -to drive it onwards; it does not matter whether the -axis on which it rotates is free to move or fixed, in -either case the idle wheel simply rotates. But suppose -now the adjacent cells are not rotating at the same -rate. In addition to its rotation the idle wheel will be -urged onward with a velocity which depends on the -difference between the rotations, and, if it can move -freely, it will move on from between the two cells. -Imagine now that the interstices between the cells -are fitted with a string of idle wheels. So long as the -adjacent cells move with different velocity there will -be a continual stream of rolling particles or idle wheels -between them. Maxwell in the paper considered -these rolling particles to be particles of electricity. -Their motion constitutes an electric current. In a -uniform magnetic field there is no electric current; -if the strength of the field varies, the idle wheels are -set in motion and there may be a current.</p> - -<p>These particles are very small compared with the -magnetic vortices. The mass of all the particles is inappreciable -compared with the mass of the vortices, -and a great many vortices with their surrounding -particles are contained in a molecule of the medium; -the particles roll on the vortices without touching -each other, so that so long as they remain within the -same molecule there is no loss of energy by resistance. -When, however, there is a current or general transference -of particles in one direction they must pass -from one molecule to another, and in doing so may -experience resistance and generate heat.</p> - -<p><span class="pagenum" id="Page_173">173</span></p> - -<p>Maxwell states that the conception of a particle, -having its motion connected with that of a vortex by -perfect rolling contact, may appear somewhat awkward. -“I do not bring it forward,” he writes, “as a mode of -connection existing in Nature, or even as that which -I would willingly assent to as an electrical hypothesis. -It is, however, a mode of connection which is mechanically -conceivable and easily investigated, and it serves -to bring out the actual mechanical connections -between the known electro-magnetic phenomena, so -that I venture to say that anyone who understands -the provisional and temporary character of this -hypothesis will find himself rather helped than -hindered by it in his search after the true interpretation -of the phenomena.”</p> - -<p>The first part of the paper deals with the theory -of magnetism; in the second part the hypothesis is -applied to the phenomena of electric currents, and it -is shown how the known laws of steady currents and -of electro-magnetic induction can be deduced from it. -In Part III., published January and February, 1862, the -theory of molecular vortices is applied to statical -electricity.</p> - -<p>The distinction between a conductor and an -insulator or dielectric is supposed to be that in the -former the particles of electricity can pass with more -or less freedom from molecule to molecule. In the -latter such transference is impossible, the particles can -only be displaced within the molecule with which -they are connected; the cells or vortices of the -medium are supposed to be elastic, and to resist by -their elasticity the displacement of the particles within<span class="pagenum" id="Page_174">174</span> -them. When electrical force acts on the medium this -displacement of the particles within each molecule -takes place until the stresses due to the elastic reaction -of the vortices balance the electrical force; the -medium behaves like an elastic body yielding to -pressure until the pressure is balanced by the elastic -stress. When the electric force is removed the cells -or vortices recover their form, the electricity returns -to its former position.</p> - -<p>In a medium such as this waves of periodic -displacement could be set up, and would travel with -a velocity depending on its electric properties. The -value for this velocity can be obtained from electrical -observations, and Maxwell showed that this velocity, -so found, was, within the limits of experimental error, -the same as that of light. Moreover, the electrical -oscillations take place, like those of light, in the front -of the wave. Hence, he concludes, “the elasticity of -the magnetic medium in air is the same as that of -the luminiferous medium, if these two coexistent, -coextensive, and equally elastic media are not rather -one medium.”</p> - -<p>The paper thus contains the first germs of the -electro-magnetic theory of light. Moreover, it is -shown that the attraction between two small bodies -charged with given quantities of electricity depends -on the medium in which they are placed, while the -specific inductive capacity is found to be proportional -to the square of the refractive index.</p> - -<p>The fourth and final part of the paper investigates -the propagation of light in a magnetic field.</p> - -<p>Faraday had shown that the direction of vibration<span class="pagenum" id="Page_175">175</span> -in a wave of polarised light travelling parallel to the -lines of force in a magnetic field is rotated by its -passage through the field. The numerical laws of -this relation had been investigated by Verdet, and -Maxwell showed how his hypothesis of molecular -vortices led to laws which agree in the main with -those found by Verdet.</p> - -<p>He points out that the connection between -magnetism and electricity has the same mathematical -form as that between certain other pairs of -phenomena, one of which has a <em>linear</em> and the other -a <em>rotatory</em> character; and, further, that an analogy -may be worked out assuming either the linear -character for magnetism and the rotatory character -for electricity, or the reverse. He alludes to Prof. -Challis’ theory, according to which magnetism is to -consist in currents in a fluid whose directions correspond -with the lines of magnetic force, while electric -currents are supposed to be accompanied by, if not -dependent upon, a rotatory motion of the fluid about -the axis of the current; and to Von Helmholtz’s -theory of a somewhat similar character. He then -gives his own reasons—agreeing with those of Sir -W. Thomson (Lord Kelvin)—for supposing that there -must be a real rotation going on in a magnetic field -in order to account for the rotation of the plane of -polarisation, and, accepting these reasons as valid, he -develops the consequences of his theory with the -results stated above.</p> - -<p>His own verdict on the theory is given in the -“Electricity and Magnetism” (vol. ii., § 831, first -edition, <span class="locked">p. 416):—</span></p> - -<p><span class="pagenum" id="Page_176">176</span></p> - -<div class="blockquot"> - -<p>“A theory of molecular vortices, which I worked out at considerable -length, was published in the <i>Phil. Mag.</i> for March, -April, and May, 1861; Jan. and Feb., 1862.</p> - -<p>“I think we have good evidence for the opinion that some -phenomenon of rotation is going on in the magnetic field, that -this rotation is performed by a great number of very small -portions of matter, each rotating on its own axis, this axis -being parallel to the direction of the magnetic force, and that -the rotations of these different vortices are made to depend on one -another by means of some kind of mechanism connecting them.</p> - -<p>“The attempt which I then made to imagine a working -model of this mechanism must be taken for no more than it -really is, a demonstration that mechanism may be imagined -capable of producing a connection mechanically equivalent to -the actual connection of the parts of the electro-magnetic field. -The problem of determining the mechanism required to -establish a given species of connection between the motions of -the parts of a system always admits of an infinite number of -solutions. Of these, some may be more clumsy or more complex -than others, but all must satisfy the conditions of -mechanism in general.</p> - -<p>“The following results of the theory, however, are of -higher <span class="locked">value:—</span></p> - -<p>“(1) Magnetic force is the effect of the centrifugal force of -the vortices.</p> - -<p>“(2) Electro-magnetic induction of currents is the effect of -the forces called into play when the velocity of the vortices is -changing.</p> - -<p>“(3) Electromotive force arises from the stress on the connecting -mechanism.</p> - -<p>“(4) Electric displacement arises from the elastic yielding -of the connecting mechanism.”</p> -</div> - -<p>In studying this part of Maxwell’s work, it must -clearly be remembered that he did not look upon the -ether as a series of cog-wheels with idle wheels between, -or anything of the kind. He devised a mechanical -model of such cogs and idle wheels, the properties<span class="pagenum" id="Page_177">177</span> -of which would in some respects closely resemble -those of the ether; from this model he deduced, -among other things, the important fact that electric -waves would travel outwards with the velocity of -light. Other such models have been devised since -his time to illustrate the same laws. Prof. Fitzgerald -has actually constructed one of wheels connected -together by elastic bands, which shows clearly the kind -of processes which Maxwell supposed to go on in a -dielectric when under electric force. Professor Lodge, -in his book, “Modern Views of Electricity,” has very -fully developed a somewhat different arrangement of -cog-wheels to attain the same result.</p> - -<p>Maxwell’s predictions as to the propagation of -electric waves have in recent days received their full -verification in the brilliant experiments of Hertz and -his followers; it remains for us, before dealing with -these, to trace their final development in his hands.</p> - -<p>The papers we have been discussing were perhaps -too material to receive the full attention they -deserved; the ether is not a series of cogs, and electricity -is something different from material idle -wheels. In his paper on “The Dynamical Theory of the -Electro-magnetic Field,” <i>Phil. Trans.</i>, 1864, Maxwell -treats the same questions in a more general manner. -On a former occasion he says, “I have attempted to -describe a particular kind of motion and a particular -kind of strain so arranged as to account for the -phenomena. In the present paper I avoid any -hypothesis of this kind; and in using such words as -electric momentum and electric elasticity in reference -to the known phenomena of the induction of currents<span class="pagenum" id="Page_178">178</span> -and the polarisation of dielectrics, I wish merely to -direct the mind of the reader to mechanical phenomena, -which will assist him in understanding the -electrical ones. All such phrases in the present -paper are to be considered as illustrative and not as -explanatory.” He then <span class="locked">continues:—</span></p> - -<div class="blockquot"> - -<p>“In speaking of the energy of the field, however, I wish to -be understood literally. All energy is the same as mechanical -energy, whether it exists in the form of motion or in that of -elasticity, or in any other form.</p> - -<p>“The energy in electro-magnetic phenomena is mechanical -energy. The only question is, Where does it reside?</p> - -<p>“On the old theories it resides in the electrified bodies, conducting -circuits, and magnets, in the form of an unknown -quality called potential energy, or the power of producing -certain effects at a distance. On our theory it resides in the -electro-magnetic field, in the space surrounding the electrified -and magnetic bodies, as well as in those bodies themselves, -and is in two different forms, which may be described without -hypothesis as magnetic polarisation and electric polarisation, -or, according to a very probable hypothesis, as the motion and -the strain of one and the same medium.</p> - -<p>“The conclusions arrived at in the present paper are independent -of this hypothesis, being deduced from experimental -facts of three <span class="locked">kinds:—</span></p> - -<p>“(1) The induction of electric currents by the increase or -diminution of neighbouring currents according to the changes -in the lines of force passing through the circuit.</p> - -<p>“(2) The distribution of magnetic intensity according to -the variations of a magnetic potential.</p> - -<p>“(3) The induction (or influence) of statical electricity -through dielectrics.</p> - -<p>“We may now proceed to demonstrate from these principles -the existence and laws of the mechanical forces, which act -upon electric currents, magnets, and electrified bodies placed -in the electro-magnetic field.”</p> -</div> - -<p><span class="pagenum" id="Page_179">179</span></p> - -<p>In his introduction to the paper, he discusses in a -general way the various explanations of electric phenomena -which had been given, and points out <span class="locked">that—</span></p> - -<div class="blockquot"> - -<p>“It appears, therefore, that certain phenomena in electricity -and magnetism lead to the same conclusion as those of optics, -namely, that there is an ætherial medium pervading all bodies, -and modified only in degree by their presence; that the parts -of this medium are capable of being set in motion by electric -currents and magnets; that this motion is communicated from -one part of the medium to another by forces arising from the -connection of those parts; that under the action of these -forces there is a certain yielding depending on the elasticity of -these connections; and that, therefore, energy in two different -forms may exist in the medium, the one form being the actual -energy of motion of its parts, and the other being the potential -energy stored up in the connections in virtue of their elasticity.</p> - -<p>“Thus, then, we are led to the conception of a complicated -mechanism capable of a vast variety of motion, but at the -same time so connected that the motion of one part depends, -according to definite relations, on the motion of other parts, -these motions being communicated by forces arising from the -relative displacement of the connected parts, in virtue of their -elasticity. Such a mechanism must be subject to the general -laws of dynamics, and we ought to be able to work out all the -consequences of its motion, provided we know the form of the -relation between the motions of the parts.”</p> -</div> - -<p>These general laws of dynamics, applicable to the -motion of any connected system, had been developed -by Lagrange, and are expressed in his generalised -equations of motion. It is one of Maxwell’s chief -claims to fame that he saw in the electric field a -connected system to which Lagrange’s equations could -be applied, and that he was able to deduce the -mechanical and electrical actions which take place by -means of fundamental propositions of dynamics.</p> - -<p><span class="pagenum" id="Page_180">180</span></p> - -<p>The methods of the paper now under discussion -were developed further in the “Treatise on Electricity -and Magnetism,” published in 1873; in endeavouring -to give some slight account of Maxwell’s work, we -shall describe it in the form it ultimately took.</p> - -<p>The task which Maxwell set himself was a double -one; he had first to express in symbols, in as general -a form as possible, the fundamental laws of electro-magnetism -as deduced from experiments, chiefly the -experiments of Faraday, and the relations between -the various quantities involved; when this was done -he had to show how these laws could be deduced from -the general dynamical laws applicable to any system -of moving bodies.</p> - -<p>There are two classes of phenomena, electric and -magnetic, which have been known from very early -times, and which are connected together. When a -piece of sealing-wax is rubbed it is found to attract -other bodies, it is said to exert electric force throughout -the space surrounding it; when two different -metals are dipped in slightly acidulated water and -connected by a wire, certain changes take place in the -plates, the water, the wire, and the space round the -wire, electric force is again exerted and a current of -electricity is said to flow in the wire. Again, certain -bodies, such as the lodestone, or pieces of iron and -steel which have been treated in a certain manner, -exhibit phenomena of action at a distance: they are -said to exert magnetic force, and it is found that this -magnetic force exists in the neighbourhood of an -electric current and is connected with the current.</p> - -<p>Again, when electric force is applied to a body, the<span class="pagenum" id="Page_181">181</span> -effects may be in part electrical, in part mechanical; -the electrical state of the body is in general changed, -while in addition, mechanical forces tending to move -the body are set up. Experiment must teach us how -the electrical state depends on the electric force, and -what is the connection between this electric force and -the magnetic forces which may, under certain circumstances, -be observed. Now, in specifying the electric -and magnetic conditions of the system, various other -quantities, in addition to the electric force, will have -to be introduced; the first step is to formulate the -necessary quantities, and to determine the relations -between them and the electric force.</p> - -<p>Consider now a wire connecting the two poles of -an electric battery—in its simplest form, a piece of -zinc and a piece of copper in a vessel of dilute acid—electric -force is produced at each point of the wire. -Let us suppose this force known; an electric current -depending on the material and the size of the wire -flows along it, its value can be determined at each -point of the wire in terms of the electric force by -Ohm’s law. If we take either this current or the -electric force as known, we can determine by known -laws the electric and magnetic conditions elsewhere. -If we suppose the wire to be straight and very long, -then, so long as the current is steady and we neglect -the small effect due to the electrostatic charge on the -wire, there is no electric force outside the wire. There -is, however, magnetic force, and it is found that the -lines of magnetic force are circles round the wire. It -is found also that the work done in travelling once -completely round the wire against the magnetic force<span class="pagenum" id="Page_182">182</span> -is measured by the current flowing through the wire, -and is obtained in the system of units usually adopted -by multiplying the current by 4π. This last result then -gives us one of the necessary relations, that between -the magnetic force due to a current and the strength -of the current.</p> - -<p>Again, consider a steady current flowing in a -conductor of any form or shape, the total flow of -current across any section of the conductor can be -measured in various ways, and it is found that at any -time this total flow is the same for each section of the -conductor. In this respect the flow of a current resembles -that of an incompressible fluid through a -pipe; where the pipe is narrow the velocity of flow -is greater than it is where the pipe is broad, but the -total quantity crossing each section at any given -instant is the same.</p> - -<p>Consider now two conducting bodies, two spheres, -or two flat plates placed near together but insulated. -Let each conductor be connected to one of the poles -of the battery by a conducting wire. Then, for a very -short interval after the contact is made, it is found -that there is a current in each wire which rapidly dies -away to zero. In the neighbourhood of the balls -there is electric force; the balls are said to be charged -with electricity, and the lines of force are curved lines -running from one ball to the other. It is found that -the balls slightly attract each other, and the space -between them is now in a different condition from what -it was before the balls were charged. According to -Maxwell, <em>Electric Displacement</em> has been produced -in this space, and the electric displacement at each<span class="pagenum" id="Page_183">183</span> -point is proportional to the electric force at that -point.</p> - -<p>Thus, (i) when electric force acts on a conductor, it -produces a current, the current being by Ohm’s law -proportional to the force: (ii) when it acts on an -insulator it produces electric displacement, and the -displacement is proportional to the force; while (iii) -there is magnetic force in the neighbourhood of the -current, and the work done in carrying a magnetic -pole round any complete circuit linked with the -current is proportional to the current. The first two -of these principles give us two sets of equations connecting -together the electric force and the current -in a conductor or the displacement in a dielectric -respectively; the third connects the magnetic force -and the current.</p> - -<p>Now let us go back to the variable period when -the current is flowing in the wires; and to make ideas -precise, let the two conductors be two equal large flat -plates placed with their faces parallel, and at some -small distance apart. In this case, when the plates -are charged, and the current has ceased, the electric -displacement and the force are confined almost entirely -to the space between the plates. During the variable -period the total flow at any instant across each section -of the wire is the same, but in the ordinary sense of -the word there is no flow of electricity across the -insulating medium between the plates. In this space, -however, the electric displacement is continuously -changing, rising from zero initially to its final steady -value when the current ceases. It is a fundamental -part of Maxwell’s theory that this variation of electric<span class="pagenum" id="Page_184">184</span> -displacement is equivalent in all respects to a current. -The current at any point in a dielectric is measured -by the rate of change of displacement at that point.</p> - -<p>Moreover, it is also an essential point that if we -consider any section of the dielectric between the two -plates, the rate of change of the total displacement -across this section is at each moment equal to the -total flow of current across each section of the conducting -wire.</p> - -<p>Currents of electricity, therefore, including displacement -currents, always flow in closed circuits, -and obey the laws of an incompressible fluid in -that the total flow across each section of the circuit—conducting -or dielectric—is at any moment the -same.</p> - -<p>It should be clearly remembered that this fundamental -hypothesis of Maxwell’s theory is an assumption -only to be justified by experiment. Von -Helmholtz, in his paper on “The Equations of -Motion of Electricity for Bodies at Rest,” formed -his equations in an entirely different manner from -Maxwell, and arrived at results of a more general -character, which do not require us to suppose that -currents flow always in closed circuits, but permit of -the condensation of electricity at points in the circuit -where the conductors end and the non-conducting -part of the circuit begins. We leave for the present -the question which of the two theories, if either, -represents the facts.</p> - -<p>We have obtained above three fundamental relations—(i) -that between electric force and electric -current in a conductor; (ii) that between electric<span class="pagenum" id="Page_185">185</span> -force and electric displacement in a dielectric; (iii) -that between magnetic force and the current which -gives rise to it. And we have seen that an electric -current—<i>i.e.</i> in a dielectric the variation of the -strength of an electric field of force—gives rise to -magnetic force. Now, magnetic force acting on a -medium produces “magnetic displacement,” or magnetic -induction, as it is called. In all media except -iron, nickel, cobalt, and a few other substances, the -magnetic induction is proportional to the magnetic -force, and the ratio between the magnetic induction -produced by a given force and the force is found to -be very nearly the same for all such media. This -ratio is known as the permeability, and is generally -denoted by the symbol μ.</p> - -<p>A relation reciprocal to that given in (iii) above -might be anticipated, and was, in fact, discovered by -Faraday. Changes in a field of magnetic induction -give rise to electric force, and hence to displacement -currents in a dielectric or to conduction currents in -a conductor. In considering the relation between -these changes and the electric force, it is simplest -at first not to deal with magnetic matter such as -iron, nickel, or cobalt; and then we may say that (iv) -the work which at any instant would be done in -carrying a unit quantity of electricity round a -closed circuit in a magnetic field against the electric -forces due to the field is equal to the rate at which -the total magnetic induction which threads the -circuit is being decreased. This law, summing up -Faraday’s experiments on electro-magnetic induction, -gives a fourth principle, leading to a fourth series<span class="pagenum" id="Page_186">186</span> -of equations connecting together the electric and -magnetic quantities involved.</p> - -<p>The equations deduced from the above four -principles, together with the condition implied in -the continuity of an electric current, constitute -Maxwell’s equations of the electro-magnetic field.</p> - -<p>If we are dealing only with a dielectric medium, -the reciprocal relation between the third and fourth -principle may be made more clear by the following -<span class="locked">statement:—</span></p> - -<p>(A) The work done at any moment in carrying -a unit quantity of magnetism round a closed circuit -in a field in which electric displacement is varying, is -equal to the rate of change of the total electric -displacement through the circuit multiplied by 4 π.<a id="FNanchor_62" href="#Footnote_62" class="fnanchor">62</a></p> - -<p>(B) The work done at any moment in carrying a -unit quantity of electricity round a circuit in a field -in which the magnetic induction is varying, is equal -to the rate of change of the total magnetic induction -through the circuit.</p> - -<p>From these two principles, combined with the -laws connecting electric force and displacement, -magnetic force and induction, and with the condition -of continuity, Maxwell obtained his equations of the -field.</p> - -<p>Faraday’s experiments on electro-magnetic induction -afford the proof of the truth of the fourth -principle. It follows from those experiments that -when the number of lines of magnetic induction<span class="pagenum" id="Page_187">187</span> -which are linked with any closed circuit are made -to vary, an induced electromotive force is brought -into play round that circuit. This electromotive force -is, according to Faraday’s results, measured by the -rate of decrease in the number of lines of magnetic -induction which thread the circuit. Maxwell applies -this principle to all circuits, whether conducting or not.</p> - -<p>In obtaining equations to express in symbols -the results of the fourth principle just enunciated, -Maxwell introduces a new quantity, to which he gives -the name of the “vector potential.” This quantity -appears in his analysis, and its physical meaning is -not at first quite clear. Professor Poynting has, however, -put Maxwell’s principles in a slightly different -form, which enables us to see definitely the meaning of -the vector potential, and to deduce Maxwell’s equations -more readily from the fundamental statements.</p> - -<p>We are dealing with a circuit with which lines -of magnetic induction are linked, while the number -of such lines linked with the circuit is varying. Now, -let us suppose the variation to take place in consequence -of the lines of induction moving outwards -or inwards, as the case may be, so as to cut the circuit. -Originally there are none linked with the circuit. As -the magnetic field has grown to its present strength -lines of magnetic induction have moved inwards. -Each little element of the circuit has been cut by some, -and the total number linked with the circuit can be -found by adding together those cut by each element. -Now, Professor Poynting’s statement of Maxwell’s -fourth principle is that the electrical force in the -direction of any element of the circuit is found by<span class="pagenum" id="Page_188">188</span> -dividing by the length of the element the number of -lines of magnetic induction which are cut in one -second by it.</p> - -<p>Moreover, the total number of lines of magnetic induction -which have been cut by an element of unit -length is defined as the component of the vector -potential in the direction of the element; hence the -electrical force in any direction is the rate of decrease -of the component of the vector potential in that -direction. We have thus a physical meaning for the -vector potential, and shall find that in the dynamical -theory this quantity is of great importance.</p> - -<p>Professor Poynting has modified Maxwell’s third -principle in a similar manner; he looks upon the -variation in the electric displacement as due to the -motion of tubes of electric induction,<a id="FNanchor_63" href="#Footnote_63" class="fnanchor">63</a> and the magnetic -force along any circuit is equal to the number -of tubes of electric induction cutting or cut by unit -length of the circuit per second, multiplied by 4π.</p> - -<p>From the equations of the field, as found by -Maxwell, it is possible to derive two sets of symmetrical -equations. The one set connects the rate of -change of the electric force with quantities depending -on the magnetic force; the other set connects in a -similar manner the rate of change of the magnetic -force with quantities depending on the electric force.<span class="pagenum" id="Page_189">189</span> -Several writers in recent years adopt these equations -as the fundamental relations of the field, establishing -them by the argument that they lead to consequences -which are found to be in accordance with experiment.</p> - -<p>We have endeavoured to give some account of -Maxwell’s historical method, according to which the -equations are deduced from the laws of electric -currents and of electro-magnetic induction derived -directly from experiment.</p> - -<p>While the manner in which Maxwell obtained -his equations is all his own, he was not alone in -stating and discussing general equations of the electro-magnetic -field. The next steps which we are about -to consider are, however, in a special manner due -to him. An electrical or magnetic system is the -seat of energy; this energy is partly electrical, partly -magnetic, and various expressions can be found for -it. In Maxwell’s theory it is a fundamental assumption -that energy has position. “The electric and magnetic -energies of any electro-magnetic system,” says -Professor Poynting, “reside, therefore, somewhere in -the field.” It follows from this that they are present -wherever electric and magnetic force can be shown to -exist. Maxwell showed that all the electric energy is -accounted for by supposing that in the neighbourhood -of a point at which the electric force is R there is -an amount of energy per unit of volume equal to -KR²/8π, K being the inductive capacity of the -medium, while in the neighbourhood of a point at -which the magnetic force is H, the magnetic energy -per unit of volume is μH²/8π, μ being the permeability. -He supposes, then, that at each point of<span class="pagenum" id="Page_190">190</span> -an electro-magnetic system energy is stored according -to these laws. It follows, then, that the electro-magnetic -field resembles a dynamical system in -which energy is stored. Can we discover more of -the mechanism by which the actions in the field -are maintained? Now the motion of any point of a -connected system depends on that of other points of -the system; there are generally, in any machine, a -certain number of points called driving-points, the -motion of which controls the motion of all other -parts of the machine; if the motion of the driving-points -be known, that of any other point can be determined. -Thus in a steam engine the motion of a -point on the fly-wheel can be found if the motion of -the piston and the connections between the piston -and the wheel be known.</p> - -<p>In order to determine the force which is acting on -any part of the machine we must find its momentum, -and then calculate the rate at which this momentum -is being changed. This rate of change will give us -the force. The method of calculation which it is -necessary to employ was first given by Lagrange, and -afterwards developed, with some modifications, by -Hamilton. It is usually referred to as Hamilton’s -principle; when the equations in the original form -are used they are known as Lagrange’s equations.</p> - -<p>Now Maxwell showed how these methods of calculation -could be applied to the electro-magnetic field. -The energy of a dynamical system is partly kinetic, -partly potential. Maxwell supposes that the magnetic -energy of the field is kinetic energy, the electric -energy potential. When the kinetic energy of a<span class="pagenum" id="Page_191">191</span> -system is known, the momentum of any part of the -system can be calculated by recognised processes. -Thus if we consider a circuit in an electro-magnetic -field we can calculate the energy of the field, and -hence obtain the momentum corresponding to this -circuit. If we deal with a simple case in which the -conducting circuits are fixed in position, and only the -current in each circuit is allowed to vary, the rate of -change of momentum corresponding to any circuit -will give the force in that circuit. The momentum -in question is electric momentum, and the force is -electric force. Now we have already seen that the -electric force at any point of a conducting circuit is -given by the rate of change of the vector potential -in the direction considered. Hence we are led to -identify the vector potential with the electric momentum -of our dynamical system; and, referring to -the original definition of vector potential, we see that -the electric momentum of a circuit is measured by the -number of lines of magnetic induction which are -interlinked with it.</p> - -<p>Again, the kinetic energy of a dynamical system -can be expressed in terms of the squares and products -of the velocities of its several parts. It can also be -expressed by multiplying the velocity of each driving-point -by the momentum corresponding to that driving-point, -and taking half the sum of the products. -Suppose, now, we are dealing with a system consisting -of a number of wire circuits in which currents are -running, and let us suppose that we may represent -the current in each wire as the velocity of a driving-point -in our dynamical system. We can also express<span class="pagenum" id="Page_192">192</span> -in terms of these currents the electric momentum of -each wire circuit; let this be done, and let half the -sum of the products of the corresponding velocities -and momenta be formed.</p> - -<p>In maintaining the currents in the wires energy is -needed to supply the heat which is produced in each -wire; but in starting the currents it is found that -more energy is needed than is requisite for the supply -of this heat. This excess of energy can be calculated, -and when the calculation is made it is found that the -excess is equal to half the sum of the products of the -currents and corresponding momenta. Moreover, if -this sum be expressed in terms of the magnetic force, -it is found to be equal to μ H²/8 π, which is the magnetic -energy of the field. Now, when a dynamical -system is set in motion against known forces, more -energy is supplied than is needed to do the work -against the forces; this excess of energy measures the -kinetic energy acquired by the system.</p> - -<p>Hence, Maxwell was justified in taking the magnetic -energy of the field as the kinetic energy of the -mechanical system, and if the strengths of the currents -in the wires be taken to represent the velocities of the -driving-points, this energy is measured in terms of -the electrical velocities and momenta in exactly the -same way as the energy of a mechanical system is -measured in terms of the velocities and momenta of -its driving-points.</p> - -<p>The mechanical system in which, according to -Maxwell, the energy is stored is the ether. A state of -motion or of strain is set up in the ether of the field. -The electric forces which drive the currents, and also<span class="pagenum" id="Page_193">193</span> -the mechanical forces acting on the conductors carrying -the currents, are due to this state of motion, or it -may be of strain, in the ether. It must not be supposed -that the term electric displacement in Maxwell’s -mind meant an actual bodily displacement of the -particles of the ether; it is in some way connected -with such a material displacement. In his view, without -motion of the ether particles there would be no -electric action, but he does not identify electric -displacement and the displacement of an ether -particle.</p> - -<p>His mechanical theory, however, does account for -the electro-magnetic forces between conductors carrying -currents. The energy of the system depends on -the relative positions of the currents which form part -of it. Now, any conservative mechanical system -tends to set itself in such a position that its potential -energy is least, its kinetic energy greatest. The -circuits of the system, then, will tend to set themselves -so that the electro-kinetic energy of the system may -be as large as possible; forces will be needed to hold -them in any position in which this condition is not -satisfied.</p> - -<p>We have another proof of the correctness of the -value found for the energy of the field in that the -forces calculated from this value agree with those -which are determined by direct experiment.</p> - -<p>Again, the forces applied at the various driving-points -are transmitted to other points by the connections -of the machine; the connections are thrown -into a state of strain; stress exists throughout their -substance. When we see the piston-rod and the shaft<span class="pagenum" id="Page_194">194</span> -of an engine connected by the crank and the connecting-rod, -we recognise that the work done on the -piston is transmitted thus to the shaft. So, too, in -the electro-magnetic field, the ether forms the connection -between the various circuits in the field; -the forces with which those circuits act on each other -are transmitted from one circuit to another by the -stresses set up in the ether.</p> - -<p>To take another instance, consider the electrostatic -attraction between two charged bodies. Let us -suppose the bodies charged by connecting each to -the opposite pole of a battery; a current flows from -the battery setting up electric displacement in the -space between the bodies, and throwing the ether into -a state of strain. As the strain increases the current -gets less; the reaction resulting from the strain tends -to stop it, until at last this reaction is so great that -the current is stopped. When this is the case the -wires to the battery may be removed, provided this is -done without destroying the insulation of the bodies; -the state of strain will remain and shows itself in the -attraction between the balls.</p> - -<p>Looking at the problem in this manner, we are -face to face with two great questions—the one, What -is the state of strain in the ether which will enable it -to produce the observed electrostatic attractions and -repulsions between charged bodies? and the other, -What is the mechanical structure of the ether which -would give rise to such a state of strain as will -account for the observed forces? Maxwell gives one -answer to the first question; it is not the only answer -which could be given, but it does account for the<span class="pagenum" id="Page_195">195</span> -facts. He failed to answer the second. He says -(“Electricity and Magnetism,” vol. i. <span class="locked">p. 132):—</span></p> - -<div class="blockquot"> - -<p>“It must be carefully borne in mind that we have made -only one step in the theory of the action of the medium. We -have supposed it to be in a state of stress, but have not in any -way accounted for this stress, or explained how it is maintained.... -I have not been able to make the next step, namely, to -account by mechanical considerations for these stresses in the -dielectric.”</p> -</div> - -<p>Faraday had pointed out that the inductive action -between two bodies takes place along the lines of -force, which tend to shorten along their length and -to spread outwards in other directions. Maxwell -compares them to the fibres of a muscle, which -contracts and at the same time thickens when -exerting force. In the electric field there is, on -Maxwell’s theory, a tension along the lines of electric -force and a pressure at right angles to those lines. -Maxwell proved that a tension K R²/8 π along the -lines of force, combined with an equal pressure in -perpendicular directions, would maintain the equilibrium -of the field, and would give rise to the observed -attractions or repulsions between electrified bodies. -Other distributions of stress might be found which -would lead to the same result. The one just stated -will always be connected with Maxwell’s name. It -will be noticed that the tension along the lines of -force and the pressure at right angles to them are -each numerically equal to the potential energy stored -per unit of volume in the field. The value of each of -the three quantities is K R²/8 π.</p> - -<p>In the same way, in a magnetic field, there is -a state of stress, and on Maxwell’s theory this, too,<span class="pagenum" id="Page_196">196</span> -consists of a tension along the lines of force and an -equal pressure at right angles to them, the values -of the tension and the pressure being each equal -to that of the magnetic energy per unit of volume, -or μH²/8π.</p> - -<p>In a case in which both electric and magnetic -force exists, these two states of stress are superposed. -The total energy per unit of volume is -KR²/8π + μH²/8π; the total stress is made up -of tensions KR²/8π and μH²/8π along the lines -of electric and magnetic force respectively, and equal -pressures at right angles to these lines.</p> - -<p>We see, then, from Maxwell’s theory, that electric -force produced at any given point in space is transmitted -from that point by the action of the ether. -The question suggests itself, Does the transmission -take time, and if so, does it proceed with a definite -velocity depending on the nature of the medium -through which the change is proceeding?</p> - -<p>According to the molecular-vortex theory, we -have seen that waves of electric force are transmitted -with a definite velocity. The more general theory -developed in the “Electricity and Magnetism” leads -to the same result. Electric force produced at any -point travels outwards from that point with a velocity -given by 1/√(Kμ). At a distant point the force is -zero, until the disturbance reaches it. If the disturbance -last only for a limited interval, its effects -will at any future time be confined to the space -within a spherical shell of constant thickness depending -on the interval; the radii of this shell increase -with uniform speed 1/√(Kμ).</p> - -<p><span class="pagenum" id="Page_197">197</span></p> - -<p>If the initial disturbance be periodic, periodic -waves of electric force will travel out from the centre, -just as waves of sound travel out from a bell, or waves -of light from a candle flame. A wire carrying an -alternating current may be such a source of periodic -disturbance, and from the wire waves travel outwards -into space.</p> - -<p>Now, it is known that in a sound wave the displacements -of the air particles take place in the -direction in which the wave is travelling; they lie -at right angles to the wave front, and are spoken of -as longitudinal. In light waves, on the other hand, -the displacements are, as Fresnel proved, in the wave -front, at right angles, that is, to the direction of -propagation; they are transverse.</p> - -<p>Theory shows that in general both these waves -may exist in an elastic solid body, and that they -travel with different velocities. Of which nature are -the waves of electric displacement in a dielectric? -It can be shewn to follow as a necessary consequence -of Maxwell’s views as to the closed character of all -electric currents, that waves of electric displacement -are transverse. Electric vibrations, like those of light, -are in the wave front and at right angles to the direction -of propagation; they depend on the rigidity or quasi-rigidity -of the medium through which they travel, -not on its resistance to compression.</p> - -<p>Again, an electric current, whether due to variation -of displacement in a dielectric or to conduction -in a conductor, is accompanied by magnetic force. -A wave of periodic electric displacement, then, will -be also a wave of periodic magnetic force travelling at<span class="pagenum" id="Page_198">198</span> -the same rate; and Maxwell shewed that the direction -of this magnetic force also lies in the wave front, -and is always at right angles to the electric displacement. -In the ordinary theory of light the wave of -linear displacement is accompanied by a wave of -periodic angular twist about a direction lying in -the wave front and perpendicular to the linear displacement.</p> - -<p>In many respects, then, waves of electric displacement -resemble waves of light, and, indeed, as we -proceed we shall find closer connections still. Hence -comes Maxwell’s electro-magnetic theory of light.</p> - -<p>It is only in dielectric media that electric force is -propagated by wave motion. In conductors, although -the third and fourth of Maxwell’s principles given on -page 185 still are true, the relation between the electric -force and the electric current differs from that which -holds in a dielectric. Hence the equations satisfied -by the force are different. The laws of its propagation -resemble those of the conduction of heat rather than -those of the transmission of light.</p> - -<p>Again, light travels with different velocities in -different transparent media. The velocity of electric -waves, as has been stated, is equal to 1/√(μK); but -in making this statement it is assumed that the -simple laws which hold where there is no gross -matter—or, rather, where air is the only dielectric -with which we are concerned—hold also in solid or liquid -dielectrics. In a solid or a liquid, as in vacuo, -the waves are propagated by the ether. We assume, -as a first step towards a complete theory, that so far -as the electric waves are concerned the sole effect<span class="pagenum" id="Page_199">199</span> -produced by the matter shews itself in a change of -inductive capacity or of permeability. It is not likely -that such a supposition should be the whole truth, -and we may, therefore, expect results deduced from it -to be only approximation to the true result.</p> - -<p>Now, electro-magnetic experiments show that, -excluding magnetic substances, the permeability of -all bodies is very nearly the same, and differs very -slightly from that of air. The inductive capacity, -however, of different bodies is different, and hence -the velocity with which electro-magnetic waves travel -differs in different bodies.</p> - -<p>But the refraction of waves of light depends on -the fact that light travels with different velocities in -different media; hence we should expect to have -waves of electric displacement reflected and refracted -when they pass from one dielectric, such as air, to -another, such as glass or gutta-percha; moreover, -for light the refractive index of a medium such as -glass is the ratio of the velocity in air to the velocity -in the glass.</p> - -<p>Thus the electrical refractive index of glass is the -ratio of the velocity of electric waves in air to their -velocity in glass.</p> - -<p>Now let K₀ be the inductive capacity of air, K₁ that -of glass, taking the permeability of air and glass to be -the same, we have the result <span class="locked">that—</span></p> - -<p class="center">Electrical refractive index = √(K₁/K₀). -</p> - -<p>But the ratio of the inductive capacity of glass to -that of air is known as the specific inductive capacity -of glass.</p> - -<p><span class="pagenum" id="Page_200">200</span></p> - -<p>Hence, the specific inductive capacity of any -medium is equal to the square of the electrical refractive -index of that medium.</p> - -<p>Since Maxwell’s time the mathematical laws of -the reflexion and refraction of electric waves have -been investigated by various writers, and it has been -shewn that they agree exactly with those enunciated -by Fresnel for light.</p> - -<p>Hitherto we have been discussing the propagation -of electric waves in an isotropic medium, one which -has identical properties in all directions about a point. -Let us now consider how these laws are modified if -the dielectric be crystalline in structure.</p> - -<p>Maxwell assumes that the crystalline character -of the dielectric can be sufficiently represented by -supposing the inductive capacity to be different in -different directions; experiments have since shewn -that this is true for crystals such as Iceland -Spar and Aragonite; he assumes also, and this, too, -is justified by experiment, that the magnetic permeability -does not depend on the direction. It -follows from these assumptions that a crystal will -produce double refraction and polarisation of electric -waves which fall upon it, and, further, that the laws -of double refraction will be those given by Fresnel -for light waves in a doubly refracting medium. -There will be two waves in the crystal. The disturbance -in each of these will be plane polarised; -their velocity and the position of their plane of -polarisation can be found from the direction in which -they are travelling by Fresnel’s construction exactly.</p> - -<p>Maxwell’s theory, then, would appear to indicate<span class="pagenum" id="Page_201">201</span> -some close connection between electric waves and -those of light. Faraday’s experiments on the rotation -of the plane of polarisation by magnetic force -shew one phenomenon in which the two are connected, -and Maxwell endeavoured to apply his theory -to explain this. Here, however, it became necessary -to introduce an additional hypothesis—there must be -some connection between the motion of the ether -to which magnetic force is due and that which constitutes -light. It is impossible to give a mechanical -account of the rotation of the plane of polarisation -without some assumption as to the relation between -these two kinds of motion. Maxwell, therefore, -supposes the linear displacements of a point in the -ether to be those which give rise to light, while the -components of the magnetic force are connected with -these in the same way as the components of a vortex -in a liquid in vortex motion are connected with the -displacements of the liquid. He further assumes the -existence of a term of special form in the expression -for the kinetic energy, and from these assumptions he -deduces the laws of the propagation of polarised -light in a magnetic field. These laws agree in the -main with the results of Verdet’s experiments.</p> - -<hr /> - -<div id="toclink_202" class="chapter"> -<p><span class="pagenum" id="Page_202">202</span></p> - -<h2 class="nobreak" id="CHAPTER_X">CHAPTER X.<br /> - -<span class="subhead">DEVELOPMENT OF MAXWELL’S THEORY.</span></h2> -</div> - -<p class="in0"><span class="firstword">We</span> have endeavoured in the preceding pages to give -some account of Maxwell’s contributions to electrical -theory and the physics of the ether. We must now -consider very briefly what evidence there is to support -these views. At Maxwell’s death such evidence, -though strong, was indirect. His supporters were -limited to some few English-speaking pupils, young -and enthusiastic, who were convinced, it may be, in -no small measure, by the affection and reverence with -which they regarded their master. Abroad his views -had made very little way.</p> - -<p>In the last words of his book he writes, speaking -of various distinguished <span class="locked">workers—</span></p> - -<div class="blockquot"> - -<p>“There appears to be in the minds of these eminent men -some prejudice, or <i xml:lang="la" lang="la">à priori</i> objection, against the hypothesis of -a medium in which the phenomena of radiation of light and -heat, and the electric actions at a distance, take place. It is -true that, at one time, those who speculated as to the causes of -physical phenomena were in the habit of accounting for each -kind of action at a distance by means of a special ætherial -fluid, whose function and property it was to produce these -actions. They filled all space three and four times over with -æthers of different kinds, the properties of which were invented -merely to ‘save appearances,’ so that more rational -enquirers were willing rather to accept not only Newton’s -definite law of attraction at a distance, but even the dogma of -Cotes,<a id="FNanchor_64" href="#Footnote_64" class="fnanchor">64</a> that action at a distance is one of the primary properties -of matter, and that no explanation can be more intelligible -than this fact. Hence the undulatory theory of light<span class="pagenum" id="Page_203">203</span> -has met with much opposition, directed not against its failure -to explain the phenomena, but against its assumption of the -existence of a medium in which light is propagated.</p> - -<p>“We have seen that the mathematical expression for -electro-dynamic action led, in the mind of Gauss, to the conviction -that a theory of the propagation of electric action in -time would be found to be the very key-stone of electro-dynamics. -Now we are unable to conceive of propagation in -time, except either as the flight of a material substance through -space, or as the propagation of a condition of motion, or stress, -in a medium already existing in space.</p> - -<p>“In the theory of Neumann, the mathematical conception -called potential, which we are unable to conceive as a material -substance, is supposed to be projected from one particle to -another in a manner which is quite independent of a medium, -and which, as Neumann has himself pointed out, is extremely -different from that of the propagation of light.</p> - -<p>“In the theories of Riemann and Betti it would appear -that the action is supposed to be propagated in a manner -somewhat more similar to that of light.</p> - -<p>“But in all of these theories the question naturally occurs:—If -something is transmitted from one particle to another at a -distance, what is its condition after it has left one particle and -before it has reached the other? If this something is the -potential energy of the two particles, as in Neumann’s theory, -how are we to conceive this energy as existing in a point of -space, coinciding neither with the one particle nor with the -other? In fact, whenever energy is transmitted from one body -to another in time, there must be a medium or substance in -which the energy exists after it leaves one body and before it -reaches the other, for energy, as Torricelli<a id="FNanchor_65" href="#Footnote_65" class="fnanchor">65</a> remarked, ‘is a -quintessence of so subtle a nature that it cannot be contained -in any vessel except the inmost substance of material things.’ -Hence all these theories lead to a conception of a medium in -which the propagation takes place, and if we admit this -medium as an hypothesis, I think it ought to occupy a prominent -place in our investigations, and that we ought to<span class="pagenum" id="Page_204">204</span> -endeavour to construct a mental representation of all the -details of its action, and this has been my constant aim in this -treatise.”</p> -</div> - -<p>Let us see, then, what were the experimental -grounds in Maxwell’s day for accepting as true his -views on electrical action, and how since then, by the -genius of Heinrich Hertz and the labours of his -followers, those grounds have been rendered so sure -that nearly the whole progress of electrical science -during the last twenty years has consisted in the -development of ideas which are to be found in the -“Treatise on Electricity and Magnetism.”</p> - -<p>The purely electrical consequences of Maxwell’s -theory were of course in accord with all known electrical -observations. The equations of the field accounted -for the electro-magnetic forces observed in -various experiments, and from them the laws of electro-magnetic -induction could be correctly deduced; but -there was nothing very special in this. Similar equations -had been obtained from the theory of action at -a distance by various writers; in fact, Helmholtz’s -theory, based on the most general form of expression -for the force between two elements of current consistent -with certain experiments of Ampère’s, was -more general in its character than Maxwell’s. The -destructive features of Maxwell’s theory were:</p> - -<p>(1) The assumption that all currents flow in closed -circuits.</p> - -<p>(2) The idea of energy residing throughout the -electro-magnetic field in consequence of the strains -and stresses set up in the electro-magnetic medium -by the actions to which it was subject.</p> - -<p><span class="pagenum" id="Page_205">205</span></p> - -<p>(3) The identification of this electro-magnetic -medium with the luminiferous ether, and the consequent -view that light is an electro-magnetic -phenomena.</p> - -<p>(4) The view that electro-magnetic forces arise -entirely from strains and stresses set up in the ether; -the electrostatic charge of an insulated conductor -being one of the forms in which the ether strain is -manifested to us.</p> - -<p>(5) A dielectric under the action of electric force -is said to become polarised, and, according to Maxwell -(vol. i. p. 133), all electrification is the residual effect -of the polarisation of the dielectric.</p> - -<p>Now it must, I think, be admitted that in Maxwell’s -day there was direct proof of very few of these -propositions. No one has even yet so measured the -displacement currents in a dielectric as to show that -the total flow across every section of a circuit is at -any given moment the same, though there are other -experiments of an indirect character which have now -completely justified Maxwell’s hypothesis. Experiments -by Schiller and Von Helmholtz prove it is -true that some action in the dielectric must be taken -into consideration in any satisfactory theory; they -therefore upset various theories based on direct action -at a distance, “but they tell us nothing as to whether -any special form of the dielectric theory, such as -Maxwell’s or Helmholtz’s, is true or not.” (J. J. -Thomson, “Report on Electrical Theories,” B.A. Report, -1885, p. 149.)</p> - -<p>When Maxwell died there had been little if any -experimental evidence as to the stresses set up in a<span class="pagenum" id="Page_206">206</span> -body by electric force. Fontana, Govi, and Duter -had all observed that changes take place in the -volume of the dielectric of a condenser when it is -charged. Quincke had taken up the work, and the -first of his classic papers on this subject was published -in 1880, the year following Maxwell’s death. Maxwell -himself was fond of shewing an experiment in which -a charged insulated sphere was brought near to the -surface of paraffin; the stress on the surface causes a -heaping up of the paraffin under the sphere.</p> - -<p>Kerr had shewn in 1875 that many substances -become doubly refracting under electric stress; his -complete determination of the laws of this action was -published at a later date.</p> - -<p>As to direct measurements on electric waves, there -were none; the value of the velocity with which, if -Maxwell’s theory were true, they must travel had -been determined from electrical observations of quite -a different character. Weber and Kohlrausch had -measured the value of K for air, for which μ is unity, -and from their observations it follows that the value -of the wave velocity for electro-magnetic waves is -about 31 × 10⁹ centimetres per second. The velocity -of light was known, from the experiments of Fizeau -and Foucault, to have about this value, and it was the -near coincidence of these two values which led Maxwell -to write in <span class="locked">1864:—</span></p> - -<p>“The agreement of the results seems to show that -light and magnetism are affections of the same -substance, and that light is an electro-magnetic -disturbance propagated through the field according -to electro-magnetic laws.”</p> - -<p><span class="pagenum" id="Page_207">207</span></p> - -<p>By the time the first edition of the “Electricity -and Magnetism” was published, Maxwell and Thomson -(Lord Kelvin) had both made determinations of K, -and had shewn that for air at least the resulting value -for the velocity of electro-magnetic waves was very -nearly that of light.</p> - -<p>For other substances at that date the observations -were fewer still. Gibson and Barclay had determined -the specific inductive capacity of paraffin, and found -that its square root was 1·405, while its refractive index -for long waves is 1·422. Maxwell himself thought -that if a similar agreement could be shewn to hold -for a number of substances, we should be warranted -in concluding that “the square root of K, though it -may not be the complete expression for the index of -refraction, is at least the most important term in it.”</p> - -<p>Between this time and Maxwell’s death enough -had been done to more than justify this statement. -It was clear from the observations of Boltzmann, -Silow, Hopkinson, and others that there were many -substances for which the square root of the specific -inductive capacity was very nearly indeed equal to -the refractive index, and good reason had been given -why in some cases there should be a considerable -difference between the two.</p> - -<p>Hopkinson found that in the case of glass the -differences were very large, and they have since been -found to be considerable for most solids examined, -with the exception of paraffin and sulphur. For -petroleum oil, benzine, toluene, carbon-bisulphide, and -some other liquids the agreement between Maxwell’s -theory and experiment is close. For the fatty oils,<span class="pagenum" id="Page_208">208</span> -such as castor oil, olive oil, sperm oil, neatsfoot oil, -and also for ether, the differences are considerable.</p> - -<p>It seems probable that the reason for this difference -lies in the fact that, in the light waves, we are dealing -with the wave velocity of a disturbance of an extremely -short period. Now, we know that the substances -mentioned shew optical dispersion, and we -have at present no completely satisfactory theory from -which we can calculate, from experiments on very -short waves, what the velocity for very long waves -will be. In most cases Cauchy’s formula has been -used to obtain the numbers given. The value of K, -however, as found by experiment, corresponds to these -infinitely long waves, and to quote Professor J. J. -Thomson’s words, “the marvel is not that there -should not be substances for which the relation K -= μ² does not hold, but that there should be any for -which it does.”<a id="FNanchor_66" href="#Footnote_66" class="fnanchor">66</a></p> - -<p>It has been shewn, moreover, both by Professor J. -J. Thomson himself and by Blondlot, that when the -value of K is measured under very rapidly varying -electrifications, changing at the rate of about 25,000,000 -to the second, the value of the inductive capacity for -glass is reduced from about 6·8 or 7 to about 2·7; the -square root of this is 1·6, which does not differ much -from its refractive index. The values of the inductive -capacity of paraffin and sulphur, which it will be -remembered agree fairly with Maxwell’s theory, were -found to be not greatly different in the steady and -in the rapidly varying field.</p> - -<p>On the other hand, some experiments of Arons<span class="pagenum" id="Page_209">209</span> -and Rubens in rapidly varying fields lead to values -which do not differ greatly from those given by other -methods. The theory, however, of these experiments -seems open to criticism.</p> - -<p>To attempt anything like a complete account of -modern verifications of Maxwell’s views and modern -developments of his theory is a task beyond our -limits, but an account of Maxwell written in 1895 -would be incomplete without a reference to the work -of Heinrich Hertz.</p> - -<p>Maxwell told us what the properties of electro-magnetic -waves in air must be. Hertz<a id="FNanchor_67" href="#Footnote_67" class="fnanchor">67</a> in 1887 enabled -us to measure those properties, and the measurements -have verified completely Maxwell’s views.</p> - -<p>The method of producing electrical oscillations in -a conductor had long been known. Thomson and Von -Helmholtz had both pointed it out. Schiller had -examined such oscillations in 1874, and had determined -the inductive capacity of glass by their means, -using oscillations whose period varied from ·000056 to -·00012 of a second.</p> - -<p>These oscillations were produced by discharging -a condenser through a coil of wire having self-induction. -If the electrical resistance of the coil be -not too great, the charge oscillates backwards and -forwards between the plates of the condenser until its -energy is dissipated in the heat produced in the wire, -and in the electro-magnetic radiations which leave it.</p> - -<p>The period of these oscillations under proper -conditions is given by the formula T = 2π√(CL) where<span class="pagenum" id="Page_210">210</span> -L, the coefficient of self induction, and <i>C</i> the capacity -of the condenser. These quantities can be calculated, -and hence the time of an oscillation is known. From -such an arrangement waves radiate out into space. If -we could measure by any method the length of such a -wave we could determine its velocity by dividing the -wave length by the period. But it is clear that since -the velocity is comparable with that of light the wave -length will be enormous, unless the period is very -short. Thus, a wave, travelling with the velocity of -light, whose period was ·0001 second, such as the -waves Schiller worked with, would have a length of -·0001 × 30,000,000,000 or 3,000,000 centimetres, and -would be quite unmeasurable. Before measurements -on electric waves could be made it was necessary (1) -to produce waves of sufficiently rapid period, (2) to -devise means to detect them. This is what Hertz did.</p> - -<p>The wave length of the electrical oscillations -can be reduced by reducing either the electrical -capacity of the system, or the coefficient of self-induction -of the wire. Hertz adopted both these -expedients. His vibrator, in some of his more important -experiments, consisted of two square brass -plates 40 cm. in the side. To each of these is attached -a piece of copper wire about 30 cm. in length, and each -wire ends in a small highly-polished brass ball. The -plates are placed so that the wires lie in the same -straight line, the brass balls being separated by a very -small air gap. The two plates are then charged, the -one positively the other negatively, until the insulation -resistance of the air gap breaks down and a discharge -passes across. Under these conditions the discharge<span class="pagenum" id="Page_211">211</span> -is oscillatory. It does not consist of a single spark, -but of a series of sparks, which pass and repass in -opposite directions, until the energy of the original -charge is radiated into space or dissipated as heat; -the plates are then recharged and the process repeated. -In Hertz’s experiments the oscillator was charged by -being connected to the secondary terminals of an -induction coil.</p> - -<p>In 1883 Professor Fitzgerald had called attention -to this method of producing electric waves in air, and -had given two metres as the minimum wave length -which might be attained. In 1870 Herr von Bezold -had actually made observations on the propagation -and reflection of electrical oscillations, but his work, -published as a preliminary communication, had attracted -little notice. Hertz was the first to undertake -in 1887 in a systematic manner the investigation of -the electric waves in air which proceed from such an -oscillator with a view to testing various theories of -electro-magnetic action.</p> - -<p>It remained, however, necessary to devise an -apparatus for detecting the waves. When the waves -are incident on a conductor, electric surgings are set -up in the conductor, and may, under proper conditions, -be observed as tiny sparks. Hertz used as his detector -a loop of wire, the ends of which terminated in -two small brass balls. The wire was bent so that the -balls were very close together, and the sparks could -be seen passing across the tiny air gap which separated -them. Such a wire will have a definite period of its -own for oscillations of electricity with which it may -be charged, and if the frequency of the electric waves<span class="pagenum" id="Page_212">212</span> -which fall on it agrees with that of the waves which -it can itself emit, the oscillations which are set up in -the wire will be stronger than under other conditions, -the sparks seen will be more brilliant.<a id="FNanchor_68" href="#Footnote_68" class="fnanchor">68</a> Hertz’s resonator -was a circle of wire thirty-five centimetres in -radius, the period for such a resonator would, he -calculated, be the same as that of his vibrator.</p> - -<p>There is, however, very considerable difficulty in -determining the period of an electric oscillator from its -dimensions, and the value obtained from calculation -for that of Hertz’s radiator is not very trustworthy. -The complete period is, however, comparable with two -one hundredth millionths of a second; in his original -papers, Hertz, through an error, gave a value greater -than this.</p> - -<p>With these arrangements Hertz was able to detect -the presence of electrical radiation at considerable -distances from the radiator; he was also able to -measure its wave length. In the case of sound waves -the existence of nodes and loops formed under proper -conditions is well known. When waves are directly -reflected from a flat surface, interference takes place -between the incident and reflected waves, stationary -vibrations are set up, and nodes and loops—places, that -is, of minimum and of maximum motion respectively—are -formed. The position of these nodes and loops -can be determined by the aid of suitable apparatus, -and it can be shewn that the distance between two -consecutive nodes is half the wave length.</p> - -<p><span class="pagenum" id="Page_213">213</span></p> - -<p>Similarly when electrical vibrations fall on a reflector, -a large flat surface of metal, for example, -stationary vibrations due to the interference between -the incident and reflected waves are produced, and -these give rise to electrical nodes and loops. The -position of such nodes and loops can be found by the -use of Hertz’s apparatus, or in other ways, and hence -the length of the electrical waves can be found. The -existence of the nodes and loops shews that the -electric effects are propagated by wave motion. The -length of the waves is found to be definite, since the -nodes and loops recur at equal intervals apart.</p> - -<p>If it be assumed that the frequency is known, the -velocity of wave propagation can be determined. -Hertz found from his experiments that in air the -waves travelled with the velocity of light. It appears, -however, that there were two errors in the calculation -which happened to correct each other, so that neither -the value of the frequency given in Hertz’s paper -nor the wave length observed is correct.</p> - -<p>By modifying the apparatus it was possible to -measure the wave length of the waves transmitted -along a copper wire, and hence, again assuming the -period of oscillation, to calculate the velocity of wave -propagation along the wire. Hertz made the experiment, -and found from his first observations that the -waves were propagated along the wire with a finite -velocity, but that the velocity differed from that in -air. The half-wave length in the wire was only about -2·8 metres; that in air was about 4·5 metres.</p> - -<p>Now, this experiment afforded a crucial test -between the theories of Maxwell and Von Helmholtz.<span class="pagenum" id="Page_214">214</span> -According to the former, the waves do not travel in -the wire at all; they travel through the air alongside -the wire, and the wave length observed by Hertz -ought to have been the same as in air. According to -Von Helmholtz, the two velocities observed by Hertz -should have been different, as, indeed, they were, and -the experiment appeared to prove that Maxwell’s -theory was insufficient and that a more general one, -such as that of Von Helmholtz, was necessary. But -other experiments have not led to the same result. -Hertz himself, using more rapid oscillations in some -later measurements, found that the wave length of -the electric waves from a given oscillator was the -same whether they were transmitted through free -space or conducted along a wire.<a id="FNanchor_69" href="#Footnote_69" class="fnanchor">69</a> Lecher and J. J. -Thomson have arrived at the same result; but the -most complete experiments on this point are those of -Sarasin and De la Rive.</p> - -<p>It may be taken, then, as established that -Maxwell’s theory is sufficient, and that the greater -generality of Von Helmholtz is unnecessary.</p> - -<p>In a later paper Hertz showed that electric -waves could be reflected and refracted, polarised and -analysed, just like light waves. In his introduction -to his “Collected Papers” he writes (<span class="locked">p. 19):—</span></p> - -<div class="blockquot"> - -<p>“Casting now a glance backwards, we see that by the -experiments above sketched the propagation in time of a<span class="pagenum" id="Page_215">215</span> -supposed action at a distance is for the first time proved. -This fact forms the philosophic result of the experiments, and -indeed, in a certain sense, the most important result. The -proof includes a recognition of the fact that the electric forces -can disentangle themselves from material bodies, and can -continue to subsist as conditions or changes in the state of -space. The details of the experiments further prove that the -particular manner in which the electric force is propagated -exhibits the closest analogy<a id="FNanchor_70" href="#Footnote_70" class="fnanchor">70</a> with the propagation of light; -indeed, that it corresponds almost completely to it. The -hypothesis that light is an electrical phenomenon is thus made -highly probable. To give a strict proof of this hypothesis -would logically require experiments upon light itself.</p> - -<p>“What we here indicate as having been accomplished by -the experiments is accomplished independently of the correctness -of particular theories. Nevertheless, there is an obvious -connection between the experiments and the theory in connection -with which they were really undertaken. Since the year -1861 science has been in possession of a theory which Maxwell -constructed upon Faraday’s views, and which we therefore -call the Faraday-Maxwell theory. This theory affirms the -possibility of the class of phenomena here discovered just as -positively as the remaining electrical theories are compelled -to deny it. From the outset Maxwell’s theory excelled all -others in elegance and in the abundance of the relations -between the various phenomena which it included.</p> - -<p>“The probability of this theory, and therefore the number -of its adherents, increased from year to year. But as long as -Maxwell’s theory depended solely upon the probability of its -results, and not on the certainty of its hypotheses, it could not -completely displace the theories which were opposed to it.</p> - -<p>“The fundamental hypotheses of Maxwell’s theory contradicted -the usual views, and did not rest upon the evidence -of decisive experiments. In this connection we can best -characterise the object and the result of our experiments by<span class="pagenum" id="Page_216">216</span> -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.”</p> -</div> - -<p>Since Maxwell’s death volumes have been written -on electrical questions, which have all been inspired -by his work. The standpoint from which electrical -theory is regarded has been entirely changed. The -greatest masters of mathematical physics have found, -in the development of Maxwell’s views, a task that -called for all their powers, and the harvest of new -truths which has been garnered has proved most rich. -But while this is so, the question is still often asked, -What is Maxwell’s theory? Hertz himself concludes -the introduction just referred to with his most interesting -answer to this question. Prof. Boltzmann -has made the theory the subject of an important -course of lectures. Poincaré, in the introduction to -his “Lectures on Maxwell’s Theories and the Electro-magnetic -Theory of Light,” expresses the difficulty, -which many feel, in understanding what the theory is. -“The first time,” he says, “that a French reader opens -Maxwell’s book a feeling of uneasiness, often even of -distrust, is mingled with his admiration. It is only -after prolonged study, and at the cost of many efforts, -that this feeling is dissipated. Some great minds -retain it always.” And again he writes: “A French -<i xml:lang="fr" lang="fr">savant</i>, 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.’”</p> - -<p>In considering this question, Poincaré’s own<span class="pagenum" id="Page_217">217</span> -remark—“Maxwell does not give a mechanical explanation -of electricity and magnetism, he is only -concerned to show that such an explanation is -possible”—is most important.</p> - -<p>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.</p> - -<p>On the old theories of action at a distance and of -electric and magnetic fluids attracting according to -known laws, it was easy to be mechanical. It was only -necessary to investigate the manner in which such -fluids could distribute themselves so as to be in equilibrium, -and to calculate the forces arising from the -distribution. The problem of assigning such a -mechanical structure to the ether as will permit of -its exerting the action which occurs in an electro-magnetic -field is a harder one to solve, and till it is -solved the question—What is an electric charge?—must -remain unanswered. Still, in order to grasp -Maxwell’s theory this knowledge is not necessary.</p> - -<p>The properties of ether in dielectrics and in conductors -must be quite different. In a dielectric the -ether has the power of storing energy by some change -in its configuration or its structure; in a conductor this -power is absent, owing probably to the action of the -matter of which the conductor is composed.</p> - -<p>When we are said to charge an insulated conductor -we really act on the ether in the neighbourhood of the -body so as to store it with energy; if there be another -conductor in the field we cannot store energy in the<span class="pagenum" id="Page_218">218</span> -ether it contains. As, then, we pass from the outside -of this conductor to its interior there is a sudden -change in some mechanical quantity connected with -the ether, and this change shows itself as a force of -attraction between the two conductors. Maxwell -called the change in structure, or in property, which -occurs when a dielectric is thus stored with electrostatic -energy, <em>Electric Displacement</em>; if we denote -it by D, then the electric force R is equal to 4πD/K, -and hence the energy in a unit of volume is 2πD²/K, -where K is a quantity depending on the insulator.</p> - -<p>Now, D, the electric displacement, is a quantity -which has direction as well as magnitude. Its value, -therefore, at any point can be represented by a straight -line in the usual way; inside a conductor it is zero. -The total change in D, which takes place all over -the surface of a conductor as we enter it from the -outside measures, according to Maxwell, the total -charge on the conductor. At points at which the -lines representing D enter the conductor the charge -is negative; at points at which they leave it the -charge is positive; along the lines of the displacement -there exists throughout the ether a tension measured -by 2πD²/K; at right angles to these lines there is -a pressure of the same amount.</p> - -<p>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.</p> - -<p>When these relations are so expressed the problem -of finding the value of the displacement at all points<span class="pagenum" id="Page_219">219</span> -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.</p> - -<p>If, then, we define electric displacement as that -change which takes place in a dielectric when it -becomes the seat of electrostatic energy, and if, -further, we suppose that the change, whatever it be -mechanically, satisfies certain well-known laws, and -that in consequence certain pressures and tensions -exist in the dielectric, electrostatic problems can be -solved without reference to a charge of electricity -residing on the conductors.</p> - -<p>Something such as this, it appears to me, is Maxwell’s -theory of electricity as applied to electrostatics. -It is not necessary, in order to understand it, to know -what change in the ether constitutes electric displacement, -or what is an electric charge, though, of course, -such knowledge would render our views more definite, -and would make the theory a mechanical one.</p> - -<p>When we turn to magnetism and electro-magnetism, -Maxwell’s theory develops itself naturally. -Experiment proves that magnetic induction is connected -with the rate of change of electric displacement, -according to the laws already given. If, then, -we knew the nature of the change to which the name<span class="pagenum" id="Page_220">220</span> -“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.</p> - -<p>Again, we have, it is true, an electro-magnetic -theory of light, but we do not know the nature of the -change in the ether which affects our eyes with the -sensation of light. Is it the same as electric displacement, -or as magnetic induction, or since, when electric -displacement is varying, magnetic induction always -accompanies it, is the sensation of light due to the -combined effect of the two?</p> - -<p>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.</p> - -<p>In this respect there is a material difference between -the ordinary theory of light and the electro-magnetic -theory. The former is a mechanical theory; -it starts from the assumption that the periodic change -which constitutes light is the ordinary linear displacement -of a medium—the ether—having certain -mechanical properties, and from those properties it -deduces the laws of optics with more or less success.</p> - -<p>Lord Kelvin, in his labile ether, has devised a -medium which could exist and which has the -necessary mechanical properties. The periodic linear<span class="pagenum" id="Page_221">221</span> -displacements of the labile ether would obey the laws -of light, and from the fundamental hypotheses of the -theory, a mechanical explanation, reasonably satisfactory -in its main features, can be given of most -purely optical phenomena. The relations between -light and electricity, or light and magnetism, are not, -however, touched by this theory; indeed, they cannot -be touched without making some assumption as to -what electric displacement is.</p> - -<p>In recent years various suggestions have been -made as to the nature of the change which constitutes -electric displacement. One theory, due to Von Helmholtz, -supposes that the electro-kinetic momentum, or -vector potential of Maxwell, is actually the momentum -of the moving ether; according to another, suggested, -it would appear originally in a crude form -by Challis, and developed within the last few months -in very satisfactory detail by Larmor, the velocity -of the ether is magnetic force; others have been -devised, but we are still waiting for a second Newton -to give us a theory of the ether which shall include -the facts of electricity and magnetism, luminous radiation, -and it may be gravitation.<a id="FNanchor_71" href="#Footnote_71" class="fnanchor">71</a></p> - -<p>Meanwhile we believe that Maxwell has taken the -first steps towards this discovery, and has pointed out -the lines along which the future discoverer must direct -his search, and hence we claim for him a foremost -place among the leaders of this century of science.</p> - -<div class="chapter"><div class="footnotes"> -<h2 class="nobreak" id="FOOTNOTES">FOOTNOTES</h2> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_1" href="#FNanchor_1" class="fnanchor">1</a> 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.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_2" href="#FNanchor_2" class="fnanchor">2</a> “Life of J. C. Maxwell,” p. 26.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_3" href="#FNanchor_3" class="fnanchor">3</a> “Life of J. C. Maxwell,” p. 27.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_4" href="#FNanchor_4" class="fnanchor">4</a> “Life of J. C. Maxwell,” p. 49.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_5" href="#FNanchor_5" class="fnanchor">5</a> “Life of J. C. Maxwell,” p. 52.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_6" href="#FNanchor_6" class="fnanchor">6</a> “Life of J. C. Maxwell,” p. 56.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_7" href="#FNanchor_7" class="fnanchor">7</a> “Life of J. C. Maxwell,” p. 67.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_8" href="#FNanchor_8" class="fnanchor">8</a> “Life of J. C. Maxwell,” p. 75.</p> - -</div> - -<div class="footnote"> - -<p class="fn1"><a id="Footnote_9" href="#FNanchor_9" class="fnanchor">9</a> Professor Garnett in <cite>Nature</cite>, November 13th, 1879.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_10" href="#FNanchor_10" class="fnanchor">10</a> “Life of J. C. Maxwell,” p. 105.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_11" href="#FNanchor_11" class="fnanchor">11</a> “Life of J. C. Maxwell,” p. 116.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_12" href="#FNanchor_12" class="fnanchor">12</a> “Life of J. C. Maxwell,” pp. 123–129.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_13" href="#FNanchor_13" class="fnanchor">13</a> “Life of J. C. Maxwell,” p. 190.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_14" href="#FNanchor_14" class="fnanchor">14</a> Dean of Canterbury.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_15" href="#FNanchor_15" class="fnanchor">15</a> Master of Trinity.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_16" href="#FNanchor_16" class="fnanchor">16</a> “Life of J. C. Maxwell,” p. 174.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_17" href="#FNanchor_17" class="fnanchor">17</a> “Life of J. C. Maxwell,” p. 195.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_18" href="#FNanchor_18" class="fnanchor">18</a> “Life of J. C. Maxwell,” p. 207.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_19" href="#FNanchor_19" class="fnanchor">19</a> “Life of J. C. Maxwell,” p. 208.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_20" href="#FNanchor_20" class="fnanchor">20</a> “Life of J. C. Maxwell,” p. 210.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_21" href="#FNanchor_21" class="fnanchor">21</a> “Life of J. C. Maxwell,” p. 211.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_22" href="#FNanchor_22" class="fnanchor">22</a> “Life of J. C. Maxwell,” p. 216.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_23" href="#FNanchor_23" class="fnanchor">23</a> “Life of J. C. Maxwell,” p. 256.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_24" href="#FNanchor_24" class="fnanchor">24</a> “Life of J. C. Maxwell,” p. 267.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_25" href="#FNanchor_25" class="fnanchor">25</a> “Life of J. C. Maxwell,” p. 269.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_26" href="#FNanchor_26" class="fnanchor">26</a> “Life of J. C. Maxwell,” p. 278.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_27" href="#FNanchor_27" class="fnanchor">27</a> “Life of J. C. Maxwell,” p. 292.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_28" href="#FNanchor_28" class="fnanchor">28</a> “Life of J. C. Maxwell,” p. 303.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_29" href="#FNanchor_29" class="fnanchor">29</a> “Life of J. C. Maxwell,” p. 259.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_30" href="#FNanchor_30" class="fnanchor">30</a> B.A. Report, Newcastle, 1863.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_31" href="#FNanchor_31" class="fnanchor">31</a> “Life of J. C. Maxwell,” p. 340.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_32" href="#FNanchor_32" class="fnanchor">32</a> “Life of J. C. Maxwell,” p. 332.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_33" href="#FNanchor_33" class="fnanchor">33</a> “Life of J. C. Maxwell,” p. 336.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_34" href="#FNanchor_34" class="fnanchor">34</a> The Professors who were consulted were Challis, Willis, Stokes, -Cayley, Adams, and Liveing.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_35" href="#FNanchor_35" class="fnanchor">35</a> “Life of J. C. Maxwell,” p. 349.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_36" href="#FNanchor_36" class="fnanchor">36</a> “Life of J. C. Maxwell,” p. 381.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_37" href="#FNanchor_37" class="fnanchor">37</a> “Life of J. C. Maxwell,” p. 379.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_38" href="#FNanchor_38" class="fnanchor">38</a> An account of the laboratory is given in <cite>Nature</cite>, vol. x., p. 139.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_39" href="#FNanchor_39" class="fnanchor">39</a> The Chancellor continued to take to the end of his life a warm -interest in the work at the laboratory. In 1887, the Jubilee year, as -Proctor—at the same time I held the office of Demonstrator—it was -my duty to accompany the Chancellor and other officers to Windsor -to present an address from the University to Her Majesty. I was -introduced to the Chancellor at Paddington, and he at once began to -question me closely about the progress of the laboratory, the number -of students, and the work being done there, showing himself fully -acquainted with recent progress.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_40" href="#FNanchor_40" class="fnanchor">40</a> In 1894 the list contained, in Part II., sixteen names, and in -Part I., one hundred and three names.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_41" href="#FNanchor_41" class="fnanchor">41</a> Under the new regulations Physics was removed from the first -part of the Tripos and formed, with the more advanced parts of -Astronomy and Pure Mathematics, a part by itself, to which only the -Wranglers were admitted. Thus the number of men encouraged to -read Physics was very limited. This pernicious system was altered -in the regulations at present in force, which came into action in 1892. -Part I. of the Mathematical Tripos now contains Heat, Elementary -Hydrodynamics and Sound, and the simpler parts of Electricity and -Magnetism, and candidates for this examination do come to the -laboratory, though not in very large numbers. The more advanced -parts both of Mathematics and Physics are included in Part II.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_42" href="#FNanchor_42" class="fnanchor">42</a> “Life of J. C. Maxwell,” p. 383.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_43" href="#FNanchor_43" class="fnanchor">43</a> “<span xml:lang="fr" lang="fr">Statique Expérimentale et Théorique des Liquides soumis aux seules -Forces Moléculaires</span>.” Par J. Plateau, <span xml:lang="fr" lang="fr">Professeur à l’Université de Gaud</span>.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_44" href="#FNanchor_44" class="fnanchor">44</a> The “Red Lions” are a club formed by Members of the British Association -to meet for relaxation after the graver labours of the day.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_45" href="#FNanchor_45" class="fnanchor">45</a> “<span xml:lang="la" lang="la">Leonum arida nutrix.</span>”—<cite>Horace.</cite></p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_46" href="#FNanchor_46" class="fnanchor">46</a> <i>v.r.</i>, endless.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_47" href="#FNanchor_47" class="fnanchor">47</a> “Life of J. C. Maxwell,” p. 394.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_48" href="#FNanchor_48" class="fnanchor">48</a> “Life of J. C. Maxwell,” p. 404.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_49" href="#FNanchor_49" class="fnanchor">49</a> In his “Hydrodynamics,” published in 1738, Daniel Bernouilli -had discussed the constitution of a gas, and had proved from general -considerations that the pressure, if it arose from the impact of a -number of moving particles, must be proportional to the square -of their velocity. (<i>See</i> “Pogg. Ann.,” Bd. 107, 1859, p. 490.)</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_50" href="#FNanchor_50" class="fnanchor">50</a> The proof is as <span class="locked">follows:—</span></p> - -<p>If σ be the specific heat at constant volume, σ′ at constant pressure, -and consider a unit of mass of gas at pressure p and volume v, let the -volume increase by an amount dv, while the temperature dy.</p> - -<p class="center">Thus <span class="in2 l4">σ′dT = σdT + pdv</span></p> - -<p class="center">But <span class="in2 l4">pv = ⅔T/m</span></p> - -<p class="in0">Hence p being constant,</p> - -<p class="center">pdv = ⅔ dT/m<br /> -Therefore <span class="in2 l5">σ′ = σ + ⅔ 1/m</span></p> - -<p>Now suppose an amount of heat, dH, is given to a single molecule -and that its temperature is T. Its specific heat is σ, and</p> - -<p class="center">dH = σmdT<br /> -But <span class="in2 l3">dH = βdT</span><br /> -Therefore <span class="in2 l5">β = σm</span></p> - -<p class="center">Hence <span class="in2 l5">1/m = σ/β</span></p> - -<p class="center">Thus <span class="in2 l4">σ′ = σ(1 + 2/(3β))</span></p> - -<p class="center">And <span class="in2 l4">σ′/σ = γ</span></p> - -<p class="center">Therefore <span class="in2 l6">γ = 1 + 2/(3β)</span></p> - -<p class="center">Or <span class="in2 l3">β = 2/(3(γ-1))</span></p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_51" href="#FNanchor_51" class="fnanchor">51</a> 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.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_52" href="#FNanchor_52" class="fnanchor">52</a> <span xml:lang="de" lang="de">Studien über das Gleichgewicht der lebendigen Kraft zwischen -bewegten materiellen Punkten Sitz d. k. Akad Wien, Band LVIII.</span>, -1868.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_53" href="#FNanchor_53" class="fnanchor">53</a> 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.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_54" href="#FNanchor_54" class="fnanchor">54</a> <cite>Nature</cite>, vol. 1., p. 152 (December 13th, 1894).</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_55" href="#FNanchor_55" class="fnanchor">55</a> See papers by Mr. Capstick, <cite>Phil. Trans.</cite>, vols. 185–186.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_56" href="#FNanchor_56" class="fnanchor">56</a> <cite>Nature</cite>, vol. x.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_57" href="#FNanchor_57" class="fnanchor">57</a> An historical account of the development of the science of -electricity will be found in the article “Electricity” in the <cite>Encyclopædia -Britannica</cite>, ninth edition, by Professor Chrystal.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_58" href="#FNanchor_58" class="fnanchor">58</a> Thomson (Lord Kelvin), “Papers on Electrostatics and Magnetism,” -p. 15.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_59" href="#FNanchor_59" class="fnanchor">59</a> J. J. Thomson, B.A., Report, 1885, pp. 109, 113, Report on -Electrical Theories.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_60" href="#FNanchor_60" class="fnanchor">60</a> Papers on “Electrostatics,” etc., p. 26.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_61" href="#FNanchor_61" class="fnanchor">61</a> It is difficult to explain without analysis exactly what is -measured by Maxwell’s Vector Potential. Its rate of change at any -point of space measures the electromotive force at that point, so far -as it is due to variations of the electric current in neighbouring conductors; -the magnetic induction depends on the first differential -coefficients of the components of the electro-tonic state; the electric -current is related to their second differential coefficients in the same -manner as the density of attracting matter is related to the potential -it produces. In language which is now frequently used in mathematical -physics, the electromotive force at a point due to magnetic -induction is proportioned to the rate of change of the Vector Potential, -the magnetic induction depends on the “curl” of the Vector Potential, -while the electric current is measured by the “concentration” of the -Vector Potential. From a knowledge of the Vector Potential these -other quantities can be obtained by processes of differentiation.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_62" href="#FNanchor_62" class="fnanchor">62</a> The 4 π is introduced because of the system of units usually -employed to measure electrical quantities. If we adopted Mr. Oliver -Heaviside’s “rational units,” it would disappear, as it does in (B).</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_63" href="#FNanchor_63" class="fnanchor">63</a> For an exact statement as to the relation between the directions -of the lines of electric displacement and of the magnetic force, reference -must be made to Professor Poynting’s paper, <cite>Phil. Trans.</cite>, 1885, -Part II., pp. 280, 281. The ideas are further developed in a series of -articles in the <cite>Electrician</cite>, September, 1895. Reference should also be -made to J. J. Thomson’s “Recent Researches in Electricity and -Magnetism.”</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_64" href="#FNanchor_64" class="fnanchor">64</a> Preface to Newton’s “Principia,” 2nd edition.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_65" href="#FNanchor_65" class="fnanchor">65</a> “Lezioni Accademiche” (Firenze, 1715), p. 25.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_66" href="#FNanchor_66" class="fnanchor">66</a> In his sentence μ stands for the refractive index.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_67" href="#FNanchor_67" class="fnanchor">67</a> Hertz’s papers have been translated into English by D. E. Jones, -and are published under the title of <i>Electric Waves</i>.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_68" href="#FNanchor_68" class="fnanchor">68</a> Some of the consequences of this electrical resonance have -been very strikingly shown by Professor Oliver Lodge. <i>See</i> <cite>Nature</cite>, -February 20th, 1890.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_69" href="#FNanchor_69" class="fnanchor">69</a> Hertz’s original results were no doubt affected by waves -reflected from the walls and floor of the room in which he worked. -An iron stove also, which was near his apparatus, may have had -a disturbing influence; but for all this, it is to his genius and his -brilliant achievements that the complete establishment of Maxwell’s -theory is due.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_70" href="#FNanchor_70" class="fnanchor">70</a> 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.</p> - -</div> - -<div class="footnote"> - -<p class="fn2"><a id="Footnote_71" href="#FNanchor_71" class="fnanchor">71</a> For a very suggestive account of some possible theories, reference -should be made to the presidential address of Professor W. M. Hicks -to Section A of the British Association at Ipswich in 1895.</p> - -</div> -</div></div> - -<div class="chapter"><div class="index"> -<p><span class="pagenum" id="Page_222">222</span></p> -<h2 class="nobreak" id="INDEX">INDEX.</h2> - -<ul class="index"> -<li class="ifrst">Aberdeen, Maxwell elected Professor at, <a href="#Page_45">45</a>;</li> -<li class="isub1">formation of University of, <a href="#Page_51">51</a></li> - -<li class="indx">Adams, W. G., succeeds Maxwell as Professor at King’s College, London, <a href="#Page_58">58</a></li> - -<li class="indx">Adams Prize, The, <a href="#Page_48">48</a>;</li> -<li class="isub1">gained by Maxwell, <a href="#Page_50">50</a></li> - -<li class="indx">Ampère, <a href="#Page_155">155</a>, <a href="#Page_204">204</a></li> - -<li class="indx">Ampère’s Law, <a href="#Page_155">155</a>, <a href="#Page_156">156</a></li> - -<li class="indx"><i>Annals of Philosophy</i>, Thomson’s, <a href="#Page_112">112</a>, <a href="#Page_113">113</a></li> - -<li class="indx">“Apostles,” club so called, <a href="#Page_30">30</a>, <a href="#Page_89">89</a></li> - -<li class="indx">Arago, <a href="#Page_157">157</a></li> - -<li class="indx">Aragonite, <a href="#Page_200">200</a></li> - -<li class="indx">Atom, article by Maxwell in <i>Encyclopædia Britannica</i>, <a href="#Page_108">108</a></li> - -<li class="indx">Avogadros’ Law, <a href="#Page_117">117</a>, <a href="#Page_124">124</a></li> - -<li class="ifrst">Bakerian Lecture, delivered by Maxwell, <a href="#Page_58">58</a></li> - -<li class="indx">Berkeley on the Theory of Vision, <a href="#Page_38">38</a></li> - -<li class="indx">Bernouilli, D., <a href="#Page_113">113</a></li> - -<li class="indx">Blackburne, Professor, <a href="#Page_16">16</a></li> - -<li class="indx">Blore, Rev. E. W., <a href="#Page_67">67</a></li> - -<li class="indx">Boehm, Bust of Maxwell by, <a href="#Page_90">90</a></li> - -<li class="indx">Boltzmann, Dr., <a href="#Page_135">135</a>, <a href="#Page_137">137</a>, <a href="#Page_138">138</a>, <a href="#Page_144">144</a>, <a href="#Page_216">216</a></li> - -<li class="indx">Boltzmann-Maxwell Theory, The, <a href="#Page_140">140</a>, <a href="#Page_145">145</a></li> - -<li class="indx">Boscovitch on Atoms, <a href="#Page_108">108</a>, <a href="#Page_109">109</a></li> - -<li class="indx">Boyle’s Law, <a href="#Page_114">114</a>, <a href="#Page_117">117</a>, <a href="#Page_124">124</a></li> - -<li class="indx">Brewster, Sir David, on Colour Sensation, <a href="#Page_99">99</a></li> - -<li class="indx">British Association, Maxwell and, <a href="#Page_42">42</a>,54;</li> -<li class="isub1">Lecture before, <a href="#Page_80">80–82</a>;</li> -<li class="isub1">Lines on President’s address, <a href="#Page_83">83</a>, <a href="#Page_84">84</a></li> - -<li class="indx">Butler, Dr. H. M., extract from sermon on Maxwell, <a href="#Page_32">32–35</a></li> - -<li class="indx">Bryan, G. H., <a href="#Page_141">141</a>, <a href="#Page_143">143</a></li> - -<li class="ifrst">Cambridge, Maxwell at, <a href="#Page_28">28–46</a>;</li> -<li class="isub1">Mathematical Tripos at, <a href="#Page_60">60</a>;</li> -<li class="isub1">Foundation of Professorship of Experimental Physics at, <a href="#Page_66">66</a></li> - -<li class="indx"><i>Cambridge and Dublin Mathematical Journal</i>, Papers by Maxwell in, <a href="#Page_30">30</a></li> - -<li class="indx">Campbell, Professor L., <a href="#Page_9">9</a>, <a href="#Page_10">10</a>, <a href="#Page_12">12</a>, <a href="#Page_14">14</a>, <a href="#Page_22">22</a>, <a href="#Page_52">52</a>, <a href="#Page_57">57</a>, <a href="#Page_79">79</a></li> - -<li class="indx">Cauchy’s Formula, <a href="#Page_208">208</a></li> - -<li class="indx">Cavendish, Henry, <a href="#Page_73">73</a>, <a href="#Page_74">74</a>;</li> -<li class="isub1">Works of, edited by Maxwell, <a href="#Page_87">87</a>, <a href="#Page_154">154</a>, <a href="#Page_155">155</a></li> - -<li class="indx">Cavendish Laboratory, built and presented to University of Cambridge, <a href="#Page_73">73</a>, <a href="#Page_74">74</a></li> - -<li class="indx">Cay, Miss Frances, <a href="#Page_11">11</a></li> - -<li class="indx">Cayley Portrait Fund, lines to Committee, <a href="#Page_86">86</a></li> - -<li class="indx">Challis, Professor, <a href="#Page_49">49</a></li> - -<li class="indx">Charles’ Law, <a href="#Page_124">124</a></li> - -<li class="indx">Chemical Society, Maxwell’s lecture before, <a href="#Page_80">80–82</a></li> - -<li class="indx">Clausius, on kinetic theory of gases, <a href="#Page_119">119</a>, <a href="#Page_129">129</a>, <a href="#Page_130">130</a>, <a href="#Page_137">137</a></li> - -<li class="indx">Clerks of Penicuik, The, <a href="#Page_9">9</a>, <a href="#Page_10">10</a></li> - -<li class="indx">Colour Perception, <a href="#Page_94">94</a></li> - -<li class="indx">Colour Sensation, Young on, <a href="#Page_97">97</a>, <a href="#Page_98">98</a>;</li> -<li class="isub1">Sir D. Brewster on, <a href="#Page_99">99</a></li> - -<li class="indx">Colours, paper by Maxwell, on, <a href="#Page_40">40</a>, <a href="#Page_41">41</a>;</li> -<li class="isub1">Helmholtz on, <a href="#Page_99">99</a></li> - -<li class="indx">Conductors and Insulators, Distinction between, <a href="#Page_173">173</a></li> - -<li class="indx">Cookson, Dr., <a href="#Page_61">61</a></li> - -<li class="indx">Corsock, Maxwell buried at, <a href="#Page_90">90</a></li> - -<li class="indx">Cotes, <a href="#Page_202">202</a></li> - -<li class="indx">Coulomb, <a href="#Page_154">154</a></li> - -<li class="indx">Curves, investigated by Maxwell, <a href="#Page_19">19</a></li> - -<li class="ifrst">Daniell’s cells, <a href="#Page_77">77</a></li> - -<li class="indx">Democritus, <a href="#Page_108">108</a></li> - -<li class="indx">Demonstrator of Physics, W. Garnett appointed, <a href="#Page_75">75</a></li> - -<li class="indx">Description of Oval Curves, first paper by Maxwell, <a href="#Page_19">19</a></li> - -<li class="indx">Devonshire, Duke of, Cavendish Laboratory built by, <a href="#Page_73">73</a>, <a href="#Page_74">74</a>;</li> -<li class="isub1">Letter of Thanks from University of Cambridge, <a href="#Page_74">74</a></li> - -<li class="indx">Dewar, Miss K. M., her marriage to Maxwell, <a href="#Page_51">51</a></li> - -<li class="indx">Dickinson, Lowes; Portrait of Maxwell by, <a href="#Page_90">90</a></li> - -<li class="indx">Diffusion of gases, <a href="#Page_128">128</a></li> - -<li class="indx">Discs for colour experiments, <a href="#Page_99">99–101</a></li> - -<li class="indx">Droop, H. R., <a href="#Page_57">57</a></li> - -<li class="indx">Dynamical Theory of the Electro-magnetic Field, Maxwell on, <a href="#Page_57">57</a>, <a href="#Page_177">177</a></li> - -<li class="indx">Dynamical Theory of Gases, Maxwell on, <a href="#Page_58">58</a>, <a href="#Page_134">134</a></li> - -<li class="ifrst">Edinburgh Academy, Maxwell’s school-life at, <a href="#Page_13">13–18</a></li> - -<li class="indx">Edinburgh, Royal Society of, Maxwell at meetings of, <a href="#Page_18">18</a></li> - -<li class="indx">Edinburgh, University of, Maxwell at, <a href="#Page_22">22</a></li> - -<li class="indx">Elastic Spheres, <a href="#Page_144">144</a></li> - -<li class="indx">Electric Displacement, <a href="#Page_218">218</a>, <a href="#Page_219">219</a>, <a href="#Page_220">220</a></li> - -<li class="indx">Electrical Theories, <a href="#Page_94">94</a>, <a href="#Page_154">154</a>, <a href="#Page_155">155</a></li> - -<li class="indx">Electricity and Magnetism, Maxwell’s book on, <a href="#Page_59">59</a>, <a href="#Page_77">77</a>, <a href="#Page_79">79</a>, <a href="#Page_147">147</a>, <a href="#Page_155">155</a>, <a href="#Page_156">156</a>, <a href="#Page_176">176</a>, <a href="#Page_180">180–201</a>;</li> -<li class="isub1">papers by Lord Kelvin on, <a href="#Page_161">161–2</a>;</li> -<li class="isub1">Application of Mathematical Analysis to, paper by G. Green, <a href="#Page_158">158</a></li> - -<li class="indx">Electricity, Modern Views of, by Professor Lodge, <a href="#Page_177">177</a></li> - -<li class="indx">Electro-kinetic Momentum, <a href="#Page_221">221</a></li> - -<li class="indx">Electro-magnetic Field, Dynamical Theory of, Maxwell on, <a href="#Page_57">57</a>, <a href="#Page_177">177</a></li> - -<li class="indx">Electro-magnetic Induction, <a href="#Page_157">157</a></li> - -<li class="indx"><span class="pagenum" id="Page_223">223</span>Electro-magnetic Theory of Light, <a href="#Page_174">174</a></li> - -<li class="indx">Electro-tonic State, <a href="#Page_164">164</a></li> - -<li class="indx">Electrostatic Induction, Faraday on, <a href="#Page_159">159</a></li> - -<li class="indx"><i>Encyclopædia Britannica</i>, articles by Maxwell in, <a href="#Page_80">80</a>, <a href="#Page_108">108</a>, <a href="#Page_146">146</a></li> - -<li class="indx">Ether, labile, <a href="#Page_220">220</a></li> - -<li class="indx">Experimental Physics, foundation of Professorship at Cambridge, <a href="#Page_66">66</a>;</li> -<li class="isub1">Election of Maxwell, <a href="#Page_68">68</a></li> - -<li class="ifrst">Faraday on electrical science, <a href="#Page_157">157</a>;</li> -<li class="isub1">on electrostatic induction, <a href="#Page_159">159</a></li> - -<li class="indx">Faraday’s Lines of Force, paper by Maxwell on, <a href="#Page_44">44</a>, <a href="#Page_45">45</a>, <a href="#Page_148">148–153</a></li> - -<li class="indx">Fawcett, W. M., architect of Cavendish Laboratory, <a href="#Page_73">73</a></li> - -<li class="indx">Fitzgerald, Professor, <a href="#Page_177">177</a>, <a href="#Page_211">211</a></li> - -<li class="indx">Forbes, Professor J. D., <a href="#Page_18">18</a>, <a href="#Page_44">44</a>, <a href="#Page_54">54</a>;</li> -<li class="isub1">friendship with Maxwell, <a href="#Page_19">19</a>;</li> -<li class="isub1">paper on Theory of Glaciers, <a href="#Page_19">19</a>;</li> -<li class="isub1">resigns Professorship at Edinburgh, <a href="#Page_54">54</a></li> - -<li class="ifrst">Galvani, <a href="#Page_155">155</a></li> - -<li class="indx">Garnett, W., appointed Demonstrator of Physics at Cambridge, <a href="#Page_75">75</a>;</li> -<li class="isub1">Life of Maxwell by, <a href="#Page_94">94</a></li> - -<li class="indx">Gases, Molecular theory of, <a href="#Page_57">57</a>, <a href="#Page_108">108</a>;</li> -<li class="isub1">Waterston on general theory of, <a href="#Page_118">118</a>;</li> -<li class="isub1">Clausius on, <a href="#Page_119">119</a>;</li> -<li class="isub1">diffusion of, <a href="#Page_128">128</a></li> - -<li class="indx">Gauss’ Theory, <a href="#Page_156">156</a></li> - -<li class="indx">Gay Lussac’s Law, <a href="#Page_117">117</a></li> - -<li class="indx">General Theory of Gases, Waterston on, <a href="#Page_118">118</a>;</li> -<li class="isub1">Clausius on, <a href="#Page_119">119</a></li> - -<li class="indx">Glenlair, home of Maxwell, <a href="#Page_11">11</a>, <a href="#Page_23">23</a>;</li> -<li class="isub1">laboratory at, <a href="#Page_24">24</a>;</li> -<li class="isub1">Maxwell’s life at, <a href="#Page_58">58</a>, <a href="#Page_59">59</a>;</li> -<li class="isub1">“Electricity and Magnetism” written at, <a href="#Page_79">79</a></li> - -<li class="indx">Gordon, J. E. H., <a href="#Page_77">77</a>, <a href="#Page_78">78</a></li> - -<li class="indx">Green, G., of Nottingham, paper on electricity and magnetism, <a href="#Page_158">158</a>;</li> -<li class="isub1">inventor of term “Potential,” <a href="#Page_158">158</a></li> - -<li class="ifrst">Hamilton, Sir W. R., <a href="#Page_22">22</a></li> - -<li class="indx">Hamilton’s Principle, <a href="#Page_190">190</a></li> - -<li class="indx">Heat, Text-book on, by Maxwell, <a href="#Page_79">79</a></li> - -<li class="indx">Helmholtz, <a href="#Page_99">99</a>, <a href="#Page_156">156</a>, <a href="#Page_157">157</a>, <a href="#Page_175">175</a>, <a href="#Page_221">221</a></li> - -<li class="indx">Henry, J., of Washington, on electro-magnetic induction, <a href="#Page_157">157</a></li> - -<li class="indx">Herapath on molecules, <a href="#Page_112">112–116</a></li> - -<li class="indx">Hertz, Heinrich, <a href="#Page_204">204</a>, <a href="#Page_209">209–213</a></li> - -<li class="indx">Hicks, W. M., <a href="#Page_221">221</a></li> - -<li class="indx">Hockin, C., <a href="#Page_56">56</a></li> - -<li class="indx">Holman, Professor, <a href="#Page_133">133</a></li> - -<li class="ifrst">Iceland Spar, <a href="#Page_200">200</a></li> - -<li class="indx">Insulators and Conductors, Distinction between, <a href="#Page_173">173</a></li> - -<li class="ifrst">Jenkin, Fleeming, <a href="#Page_55">55</a>, <a href="#Page_56">56</a></li> - -<li class="ifrst">Kelland, Professor, <a href="#Page_22">22</a></li> - -<li class="indx">Kelvin, Lord, <a href="#Page_16">16</a>, <a href="#Page_142">142</a>, <a href="#Page_158">158</a>, <a href="#Page_159">159</a>, <a href="#Page_160">160</a>, <a href="#Page_168">168</a>;</li> -<li class="isub1">on the Uniform Motion of Heat, <a href="#Page_160">160</a>;</li> -<li class="isub1">papers on Electricity and Magnetism, <a href="#Page_161">161</a>, <a href="#Page_162">162</a></li> - -<li class="indx">Kinetic energy, <a href="#Page_124">124</a>, <a href="#Page_129">129</a>, <a href="#Page_136">136</a>, <a href="#Page_139">139</a>, <a href="#Page_191">191</a></li> - -<li class="indx">King’s College, London, Maxwell elected Professor at, <a href="#Page_54">54</a></li> - -<li class="indx">Kohlrausch, <a href="#Page_206">206</a></li> - -<li class="indx">Kundt, <a href="#Page_132">132</a></li> - -<li class="ifrst">Labile Ether, <a href="#Page_220">220</a></li> - -<li class="indx">Laboratory at Glenlair, <a href="#Page_24">24</a></li> - -<li class="indx">Lagrange, <a href="#Page_179">179</a></li> - -<li class="indx">Lagrange’s Equations, <a href="#Page_179">179</a>, <a href="#Page_190">190</a></li> - -<li class="indx">Laplace, <a href="#Page_155">155</a></li> - -<li class="indx">Larmor, J., <a href="#Page_141">141</a>, <a href="#Page_142">142</a></li> - -<li class="indx">Lecher, <a href="#Page_214">214</a></li> - -<li class="indx">Lenz, <a href="#Page_157">157</a></li> - -<li class="indx">Litchfield, R. B., <a href="#Page_46">46</a></li> - -<li class="indx">Light, Electro-magnetic Theory of, <a href="#Page_174">174</a>;</li> -<li class="isub1">Waves of, <a href="#Page_198">198</a>, <a href="#Page_199">199</a></li> - -<li class="indx">Lodge, Professor, book on Modern Views of Electricity, <a href="#Page_177">177</a></li> - -<li class="indx">Lucretius, <a href="#Page_108">108</a></li> - -<li class="indx">Luminous Radiation, <a href="#Page_221">221</a></li> - -<li class="ifrst">Mathematical Tripos at Cambridge, subjects, <a href="#Page_60">60</a>;</li> -<li class="isub1">Maxwell an examiner for, <a href="#Page_60">60</a>, <a href="#Page_80">80</a>;</li> -<li class="isub1">experimental work in, <a href="#Page_76">76</a></li> - -<li class="indx">Matter and Motion, Maxwell on, <a href="#Page_79">79</a></li> - -<li class="indx">Maxwell, James Clerk, parentage and birthplace, <a href="#Page_10">10</a>, <a href="#Page_11">11</a>;</li> -<li class="isub1">childhood and school-days, <a href="#Page_12">12–18</a>;</li> -<li class="isub1">his mother’s death, <a href="#Page_13">13</a>;</li> -<li class="isub1">first lessons in geometry, <a href="#Page_17">17</a>;</li> -<li class="isub1">attends meetings of Royal Society of Edinburgh, <a href="#Page_18">18</a>;</li> -<li class="isub1">his first published paper, <a href="#Page_19">19</a>;</li> -<li class="isub1">friendship with Professor Forbes, <a href="#Page_19">19</a>;</li> -<li class="isub1">his polariscope, <a href="#Page_20">20</a>;</li> -<li class="isub1">enters the University of Edinburgh, <a href="#Page_22">22</a>;</li> -<li class="isub1">papers on Rolling Curves and Elastic Solids, <a href="#Page_23">23</a>;</li> -<li class="isub1">vacations at Glenlair, <a href="#Page_23">23</a>;</li> -<li class="isub1">laboratory at Glenlair, <a href="#Page_24">24</a>;</li> -<li class="isub1">undergraduate life at Cambridge, <a href="#Page_28">28–36</a>;</li> -<li class="isub1">elected scholar of Trinity, <a href="#Page_29">29</a>;</li> -<li class="isub1">illness at Lowestoft, <a href="#Page_29">29</a>;</li> -<li class="isub1">his friends at Cambridge, <a href="#Page_30">30</a>;</li> -<li class="isub1">Tripos and degree, <a href="#Page_35">35–37</a>;</li> -<li class="isub1">early researches, <a href="#Page_38">38–44</a>;</li> -<li class="isub1">paper on Colours, <a href="#Page_40">40</a>, <a href="#Page_41">41</a>;</li> -<li class="isub1">elected Fellow of Trinity, <a href="#Page_43">43</a>;</li> -<li class="isub1">Lecturer at Trinity, <a href="#Page_43">43</a>;</li> -<li class="isub1">Professor at Aberdeen, <a href="#Page_45">45</a>;</li> -<li class="isub1">his father’s death, <a href="#Page_45">45</a>;</li> -<li class="isub1">gains the Adams Prize, <a href="#Page_50">50</a>;</li> -<li class="isub1">marriage, <a href="#Page_51">51</a>;</li> -<li class="isub1">powers as teacher and lecturer, <a href="#Page_52">52</a>, <a href="#Page_53">53</a>;</li> -<li class="isub1">Professor at King’s College, London, <a href="#Page_54">54</a>;</li> -<li class="isub1">gains the Rumford Medal, <a href="#Page_55">55</a>;</li> -<li class="isub1">delivers Bakerian lecture, <a href="#Page_58">58</a>;</li> -<li class="isub1">resigns Professorship at King’s College, London, <a href="#Page_58">58</a>;</li> -<li class="isub1">life at Glenlair, <a href="#Page_58">58</a>, <a href="#Page_59">59</a>;</li> -<li class="isub1">visit to Italy, <a href="#Page_59">59</a>;</li> -<li class="isub1">Examiner for Mathematical Tripos, <a href="#Page_60">60</a>, <a href="#Page_80">80</a>;</li> -<li class="isub1">elected Professor of Experimental Physics at Cambridge, <a href="#Page_68">68</a>;</li> -<li class="isub1">Introductory Lecture, <a href="#Page_68">68–72</a>;</li> -<li class="isub1">Examiner for Natural Sciences Tripos, <a href="#Page_79">79</a>;</li> -<li class="isub1"><span class="pagenum" id="Page_224">224</span>articles in <i>Encyclopædia Britannica</i>, <a href="#Page_80">80</a>, <a href="#Page_118">118</a>, <a href="#Page_146">146</a>;</li> -<li class="isub1">papers in Nature, <a href="#Page_80">80</a>;</li> -<li class="isub1">lectures before British Association and Chemical Society, <a href="#Page_80">80–82</a>;</li> -<li class="isub1">humorous poems, <a href="#Page_83">83–87</a>;</li> -<li class="isub1">delivers Rede Lecture on the Telephone, <a href="#Page_89">89</a>;</li> -<li class="isub1">last illness and death, <a href="#Page_89">89</a>, <a href="#Page_90">90</a>;</li> -<li class="isub1">buried at Corsock, <a href="#Page_90">90</a>;</li> -<li class="isub1">bust and portrait, <a href="#Page_90">90</a>;</li> -<li class="isub1">religious views, <a href="#Page_91">91</a>, <a href="#Page_92">92</a></li> - -<li class="indx">Maxwell, John Clerk, <a href="#Page_10">10</a>, <a href="#Page_11">11</a></li> - -<li class="indx">Meyer, O. E., <a href="#Page_133">133</a></li> - -<li class="indx">Mill’s Logic, <a href="#Page_38">38</a></li> - -<li class="indx">Molecular Evolution, Lines on, <a href="#Page_85">85</a></li> - -<li class="indx">—— Physics, <a href="#Page_94">94</a></li> - -<li class="indx">—— Constitution of Bodies, Maxwell on, <a href="#Page_146">146</a></li> - -<li class="indx">—— Theory of Gases, <a href="#Page_57">57</a>, <a href="#Page_108">108</a></li> - -<li class="indx">Molecules, <a href="#Page_109">109</a>, <a href="#Page_110">110</a>;</li> -<li class="isub1">Herapath on, <a href="#Page_112">112–116</a>;</li> -<li class="isub1">lecture by Maxwell on, <a href="#Page_146">146</a></li> - -<li class="indx">Motion of Saturn’s Rings, subject for Adams Prize, <a href="#Page_49">49</a></li> - -<li class="indx">Munro, J. C., <a href="#Page_40">40</a>, <a href="#Page_56">56</a>, <a href="#Page_68">68</a>, <a href="#Page_82">82</a></li> - -<li class="ifrst">Natural Sciences Tripos, Maxwell Examiner for, <a href="#Page_79">79</a></li> - -<li class="indx"><i>Nature</i>, papers by Maxwell in, <a href="#Page_80">80</a></li> - -<li class="indx">Neumann, F. E., <a href="#Page_156">156</a>, <a href="#Page_157">157</a></li> - -<li class="indx">Newton’s Lunar Theory and Astronomy, <a href="#Page_50">50</a></li> - -<li class="indx">—— Principia, <a href="#Page_202">202</a></li> - -<li class="indx">Nicol, Wm., inventor of the polarising prism, <a href="#Page_20">20</a></li> - -<li class="indx">Niven, W. D., <a href="#Page_27">27</a>, <a href="#Page_46">46</a>, <a href="#Page_51">51</a>, <a href="#Page_52">52</a>, <a href="#Page_60">60</a>, <a href="#Page_78">78</a>, <a href="#Page_87">87</a>, <a href="#Page_88">88</a>, <a href="#Page_93">93</a></li> - -<li class="ifrst">Obermeyer, <a href="#Page_134">134</a></li> - -<li class="indx">Ohm’s Law, <a href="#Page_77">77</a></li> - -<li class="indx">Ophthalmoscope devised by Maxwell, <a href="#Page_83">83</a></li> - -<li class="indx">Oval Curves, Description of, Maxwell’s first paper, <a href="#Page_19">19</a></li> - -<li class="ifrst">Parkinson, Dr., <a href="#Page_49">49</a></li> - -<li class="indx"><i>Philosophical Magazine</i>, <a href="#Page_56">56</a>, <a href="#Page_99">99</a>, <a href="#Page_115">115</a>, <a href="#Page_120">120</a>, <a href="#Page_133">133</a>, <a href="#Page_142">142</a></li> - -<li class="indx"><i>Philosophical Transactions</i>, <a href="#Page_56">56</a>, <a href="#Page_89">89</a>, <a href="#Page_132">132</a>, <a href="#Page_145">145</a></li> - -<li class="indx">Physical Lines of Force, Maxwell on, <a href="#Page_56">56</a>, <a href="#Page_158">158</a></li> - -<li class="indx">Physics, Instruction in, at Cambridge, <a href="#Page_61">61</a>;</li> -<li class="isub1">Report of Syndicate on, <a href="#Page_62">62–64</a>;</li> -<li class="isub1">Demonstrator appointed, <a href="#Page_75">75</a></li> - -<li class="indx">Poincaré, <a href="#Page_216">216</a></li> - -<li class="indx">Poisson, <a href="#Page_44">44</a>;</li> -<li class="isub1">on distribution of electricity, <a href="#Page_155">155</a></li> - -<li class="indx">Polariscope, made by Maxwell, <a href="#Page_20">20</a></li> - -<li class="indx">“Potential,” term invented by G. Green, <a href="#Page_158">158</a>;</li> -<li class="isub1">the Vector, <a href="#Page_165">165</a>, <a href="#Page_221">221</a></li> - -<li class="indx">Poynting, Professor, <a href="#Page_187">187–189</a></li> - -<li class="indx">Puluj, <a href="#Page_134">134</a></li> - -<li class="ifrst">Quincke, <a href="#Page_206">206</a></li> - -<li class="ifrst">Radiation, Luminous, <a href="#Page_221">221</a></li> - -<li class="indx">Rarefied Gases, Stresses in, paper by Maxwell, <a href="#Page_135">135</a>, <a href="#Page_145">145</a></li> - -<li class="indx">Rayleigh, Lord, <a href="#Page_67">67</a>, <a href="#Page_77">77</a></li> - -<li class="indx">Rede Lecture on the Telephone, delivered by Maxwell, <a href="#Page_89">89</a></li> - -<li class="indx">Report on Electrical Theories, J. J. Thomson, <a href="#Page_204">204</a></li> - -<li class="indx">—— of Syndicate as to instruction in Physics at Cambridge, <a href="#Page_62">62–64</a></li> - -<li class="indx">Robertson, C. H., <a href="#Page_28">28</a></li> - -<li class="indx">Rolling Curves, Maxwell on, <a href="#Page_23">23</a></li> - -<li class="indx">Royal Society, The, Maxwell and, <a href="#Page_55">55</a>;</li> -<li class="isub1">Transactions of, <a href="#Page_89">89</a></li> - -<li class="indx">Rumford Medal gained by Maxwell, <a href="#Page_55">55</a>, <a href="#Page_106">106</a></li> - -<li class="ifrst">Sabine, Major-General, Vice-President of Royal Society, <a href="#Page_106">106</a></li> - -<li class="indx">Smith’s Prizes, <a href="#Page_36">36</a></li> - -<li class="indx">Standards of Electrical Resistance, Committee on, <a href="#Page_55">55</a></li> - -<li class="indx">Stewart, Balfour, <a href="#Page_56">56</a>, <a href="#Page_125">125</a></li> - -<li class="indx">Stresses in Rarefied Gases, Maxwell on, <a href="#Page_135">135</a>, <a href="#Page_155">155</a></li> - -<li class="ifrst">Tait, Professor P. G., <a href="#Page_21">21</a>, <a href="#Page_26">26</a>, <a href="#Page_94">94</a></li> - -<li class="indx">Tayler, Rev. C. B., <a href="#Page_29">29</a></li> - -<li class="indx">Telephone, Rede Lecture by Maxwell on, <a href="#Page_89">89</a></li> - -<li class="indx">Theory of Glaciers, Prof. Forbes on, <a href="#Page_19">19</a></li> - -<li class="indx">Thomson, J. J., <a href="#Page_157">157</a>, <a href="#Page_208">208</a>;</li> -<li class="isub1">Report on Electrical Theories, <a href="#Page_205">205</a></li> - -<li class="indx">Thomson’s <i>Annals of Philosophy</i>, <a href="#Page_112">112</a>, <a href="#Page_113">113</a></li> - -<li class="ifrst">Uniform Motion of Heat in Homogeneous Solid Bodies, paper by Lord Kelvin, <a href="#Page_160">160</a>, <a href="#Page_161">161</a></li> - -<li class="indx">University Commission, <a href="#Page_47">47</a>, <a href="#Page_48">48</a>, <a href="#Page_62">62</a></li> - -<li class="indx">Urr, Vale of, <a href="#Page_11">11</a></li> - -<li class="ifrst">Vector Potential, The, <a href="#Page_165">165</a>, <a href="#Page_221">221</a></li> - -<li class="indx">Viscosity of Gases, Experiments on, <a href="#Page_58">58</a>, <a href="#Page_125">125</a>, <a href="#Page_132">132</a></li> - -<li class="indx">Volta, Inventor of voltaic pile, <a href="#Page_155">155</a></li> - -<li class="ifrst">Waterston, J. J., on molecular theory of gases, <a href="#Page_114">114</a>, <a href="#Page_115">115</a>;</li> -<li class="isub1">on general theory of gases, <a href="#Page_118">118</a></li> - -<li class="indx">Waves of Light, <a href="#Page_198">198</a>, <a href="#Page_199">199</a></li> - -<li class="indx">Weber, W., <a href="#Page_156">156</a>, <a href="#Page_206">206</a></li> - -<li class="indx">Wedderburn, Mrs., <a href="#Page_14">14</a></li> - -<li class="indx">Wheatstone’s Bridge, <a href="#Page_77">77</a></li> - -<li class="indx">Williams, J., Archdeacon of Cardigan, <a href="#Page_16">16</a></li> - -<li class="indx">Willis, Professor, <a href="#Page_44">44</a></li> - -<li class="indx">Wilson, E., lines in memory of, <a href="#Page_86">86</a>, <a href="#Page_87">87</a></li> - -<li class="ifrst">Young, T., on colour sensation, <a href="#Page_97">97</a>, <a href="#Page_98">98</a></li> -</ul> -</div></div> - -<p class="newpage p2 center smaller"><span class="smcap">Printed by Cassell & Company, Limited, La Belle Sauvage, London, E.C.</span></p> - -<p> </p> -<hr /> -<p> </p> - -<div class="chapter"><div class="transnote"> -<h2 class="nobreak" id="Transcribers_Notes">Transcriber’s Note</h2> - -<p>Punctuation, hyphenation, and spelling were made -consistent when a predominant preference was found -in the original book; otherwise they were not changed.</p> - -<p>Simple typographical errors were corrected; unpaired -quotation marks were remedied when the change was -obvious, and otherwise left unpaired.</p> - -<p>Illustrations in this eBook have been positioned -between paragraphs and outside quotations. In versions -of this eBook that support hyperlinks, the page -references in the List of Illustrations lead to the -corresponding illustrations.</p> - -<p>Footnotes, originally at the bottoms of pages, -have been collected, renumbered, and placed -just before the Index.</p> - -<p>The Index was not checked for proper alphabetization -or correct page references.</p> - -<p>Some values in the original book are known -today to be incorrect, but have not been -changed here.</p> - -<p><a href="#Page_133">Page 133</a>: The last equation on the page,</p> - -<p class="center">μ = μ₀ (1 + .00275 t - .00000034 t²)</p> - -<p class="in0">was misprinted as</p> - -<p class="center">μ = μ₀ {1 + .00275 t .00000034 t²}.</p> - -<p>It is shown here with corrections based on its cited source:</p> - -<p class="center"><a href="https://archive.org/details/s05philosophicalmag21londuoft/page/212">https://archive.org/details/s05philosophicalmag21londuoft/page/212</a></p> - -<p><a href="#Page_144">Page 144</a>: “possibly of ether atoms bound with them” -was printed that way, but “ether” may be a -misprint for “other”.</p> - -<p><a href="#Page_170">Page 170</a>: “hence at C, where they touch” was -printed as “A”, but Figure 1 at that point -is labelled “C”.</p> -</div></div> - -<p> </p> -<p> </p> -<hr class="pgx" /> -<p>***END OF THE PROJECT GUTENBERG EBOOK JAMES CLERK MAXWELL AND MODERN PHYSICS***</p> -<p>******* This file should be named 65359-h.htm or 65359-h.zip *******</p> -<p>This and all associated files of various formats will be found in:<br /> -<a href="http://www.gutenberg.org/dirs/6/5/3/5/65359">http://www.gutenberg.org/6/5/3/5/65359</a></p> -<p> -Updated editions will replace the previous one--the old editions will -be renamed.</p> - -<p>Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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