James Clerk Maxwell and Modern Physics — Inside the Classic

“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,

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.