THE commencement of the fifth year at the Academy was, for many of us boys, a time of cheerfulness and hope. The long period of mere drill and task-work was supposed to be over. We had learned the 800 irregular Greek Verbs, either by our own efforts, or by hearing others say them, and had acquired some moderate skill in Latin verse composition. On entering the rector's class-room, our less mechanical faculties were at once called into play. We found our lessons less burdensome when we had not merely to repeat them, but were continually learning something also in school. And the repetition of Virgil and Horace was a very different thing from the repetition of the rules of gender and quantity. Some foretaste of this more genial method had been afforded us in the previous year, when we had been encouraged to turn some bits of Virgil into English verse. But the change was, notwithstanding, considerable, and it was accompanied with another advance, which for Maxwell was at least equally important, for it was now that we began the serious study of geometry.
In October 1844 Mr. Clerk Maxwell and his sister, Mrs. Wedderbum, were both far from well, and James was received in Edinburgh by his aunt, Miss Cay. He writes to his father, October 14, 1844:—
I like P——[82] better than B——.[83] 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 history of Greece.... I was at Uncle John’s,[84] and he showed me his new electrotype, with which he made a copper impression of the beetle. He can plate silver with it as well as copper, and he gave me a white medium square thing with which it may be done. At night I have generally made vases.
This letter is sealed with the scarabaeus referred to as “the beetle.”
In the next letter we have a trace of his hesitation not being yet conquered:—
P—— says that a person † of education never puts in † hums and haws; he goes † on with his † sentence without senseless interjections.
N.B.—Every † means a dead pause.[85]
While thus privately retorting on his censor, he took a singular means for curing his own defect. He made a plan of the large window in the rector’s room, and wrote the words of the lesson in the spaces of the frame-work. He conned his task in that setting, and, when saying it, looked steadily at the actual window, where, as he averred, the arrangement of the panes then helped to recall the order of the words. The only fear was that by changing his place in the class he might be obliged to stand sideways to the window.
Our mathematical teacher, Mr. Gloag, was a man who combined a real gift for teaching with certain humorous peculiarities of tone and manner. He was sometimes impatient, but had a kind heart, and we liked him all the better because we mimicked him.[86] Old academicians still delight in talking of him. He never allowed us to miss a step in any proof, and made us do many “deductions,” which we puzzled out entirely without help. It must have been the companionship of Maxwell that made those hours so delightful to me. We always walked home together, and the talk was incessant, chiefly on Maxwell’s side. Some new train of ideas would generally begin just when we reached my mother’s door. He would stand there holding the door handle, half in, half out, while,
till voices from within complained of the cold draught, and warned us that we must part.
From some mathematical principle he would start off to a joke of Martinus Scriblerus, or to a quotation from Dryden, interspersing puns and other outrages on language of the wildest kind, “humming and hawing” in spite of P——; or in a quieter mood he would tell the story of Southey’s Thalaba, or explain some new invention, which I often failed to understand. Our common ground in those days was simple geometry, and never, certainly, was emulation more at one with friendship. But whatever outward rivalry there might be, his companions felt no doubt as to his vast superiority from the first. He seemed 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, as we have already seen, the first lessons of geometry branched out at once into inquiries which soon became fruitful.
“Meantime, the rural ditties were not mute.” Besides a serio-comic impromptu on the grievance of a holiday task, and other effusions concerning incidents of our school life, there was a romantic ballad written about Christmas 1844 or 5, and in July 1845 the prize for English verse was gained by the poem on the death of the Douglas, to which he refers in one of his letters to Miss Cay.[87]
But a prize of more consequence was the mathematical medal, of which he writes to his aunt in a tone of undisguised though generous triumph. The following letters were written in June and July 1845:—
To Miss Cay.
June 1845.
I have drawn a picture of Diana,[88] and made an octohedron on a new principle, and found out a great many things in geometry. If you make two circles equal, and make three steps with the compasses (of any size), and cut them out in card, and also three equal strips, with holes at each end, and joint them with thread to the upper side of one circle and the lower side of the other; then if you put a pin through the centre of one and turn the other, the one will turn, and if you draw the same thing on both in the same position,— if you turn them ever so,—they will always be in the same position.
July 1845.
The subjects for prizes are as follows:—English Verses—The gude Schyr James Dowglas; Latin Hexameters and Pentameters—The Isles of Greece; Latin Sapphics—The Rhine. I have been getting information in many books for Douglas, but I found it so difficult not to Marmionise, that is, to speak in imitation of Marmion,—that I am making it in eight syllable lines. I have got Barbour’s Bruce, Buke 20, which is a help in a different language, which is all fair; my motto is:—
“Men. may. weill. wyte. thouch. nane. them. tell. How. angry. for. sorrow. and. how. fell. Is. to. tyne. sic. a. lord. as. he. To. them. that. war. of. hys. mengye.”[89]
Pa and I went to your house on Saturday and watered the plants. I have got the lend of the whole of Horne’s.
The Vampyre, Compylt into Meeter, by Jas Clerk Maxwell.
Introduction to the Knowledge of the Scriptures, and Prideaux’s Connection of the Old and New Testaments, and Townshend’s Harmony, which are of great use.[90]
July 1845.
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[91] on Thursday. I had done them[92] all, and got home at ½ past 2; but Campbell stayed till 4. I was rather tired with writing exercises from 9 till ½ past 2.[93]
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.
His aunt, Miss Cay, to whom these letters are addressed, had begun again to take more charge of him than in the preceding years. Mrs. Wedderburn's health was very uncertain. Cousin Jemima was grown-up and immersed in her own pursuits, and the companionship of his cousin, George Wedderburn, a young man about Edinburgh, and a humourist of a different order, was not in every way the most suitable for the growing boy. The Diary shows that he was continually at his aunt’s house, No. 6 Great Stuart Street, and she is associated with some of my earliest recollections of him. She sought to bring him out amongst her friends, to soften his singularities, and to make him more like other youths of his age. And he would help her with patterns, arrangement of colours, etc., as well as with her flowers. One of his earliest applications of geometry was to set right the perspective of a view of the interior of Roslin Chapel on which she was engaged.
Mr. Clerk Maxwell was a frequent visitor at the Academy at this time. His broad, benevolent face and paternal air, as of a gentler Dandie Dinmont, beaming with kindness for the companions of his son, is vividly remembered by those who were our schoolfellows in 1844-5.
The summer vacation of 1845 was spent almost wholly at Glenlair. James passed a day now and then at Upper Corsock with the Fletcher boys,[94] and sometimes accompanied his father when he went out shooting; but he must have had abundance of time for reading and for following his own devices. The country gentlemen were particularly absorbed that year in political excitement, and Mr. Clerk Maxwell was often called away. The only event worth mentioning was a “jaunt,” evidently suggested by Miss Cay, to Newcastle, Durham, and Carlisle, which gave Maxwell his first direct impression of English Cathedral Architecture.
The taste thus formed was strengthened by a visit to Melrose in the following summer.
Saw the House of Abbotsford and antiquities in it, and go to Melrose. Got there about 2, and settle to remain all night. Spend the day and also the evening about the Abbey. Jane Cay and James drawing.—Diary, 1846, Sept. 10.
On returning to Edinburgh for the winter, Mr. Clerk Maxwell seems to have been roused by the expectation which his son’s first school distinction had awakened amongst his kindred and acquaintance. He became more assiduous than ever in his attendance at meetings of the Edinburgh Society of Arts and Royal Society, and took James with him repeatedly to both. And so it happened that early in his fifteenth year the boy dipped his feet in the current of scientific inquiry, where he was to prove himself so strong a swimmer. In our walks round Arthur’s Seat, etc., he had always something new to tell. For example, in February 1846, he called my attention to the glacier-markings on the rocks, and discoursed volubly on this subject, which was then quite recent, and known to comparatively few.
A prominent member of the Society of Arts at this time was Mr. D. R. Hay, the decorative painter, whose attempt to reduce beauty in form and colour to mathematical principles[95] had attracted considerable attention amongst scientific men. Such ideas had a natural fascination for Clerk Maxwell, and he often discoursed on “egg-and-dart,” “Greek pattern,” “ogive,” and what not, and on the forms of Etruscan urns.
One of the problems in this department of applied science was how to draw a perfect oval; and Maxwell, who had by this time begun the (purely geometrical) study of Conic sections, became eager to find a true practical solution of this. How completely his father entered into his pursuit may best be shown by the following extracts from Mr. Clerk Maxwell's Diary:—
1846,
February.
W. 25.—Called on ... Mr. D. E. Hay at his house, Jordan Lane, and saw his diagrams and showed James’s Ovals—Mr. Hay’s are drawn with a loop on 3 pins, consequently formed of portions of ellipses.
Th. 26.—Call on Prof. Forbes at the College, and see about Jas. Ovals and 3-foci figures and plurality of foci. New to Prof. Forbes, and settle to give him the theory in writing to consider.[96]
March.
M. 2.—Wrote account of James’s ovals for Prof. Forbes. Evening.—Royal Society with James, and gave the above to Mr. Forbes.
W. 4.—Went to the College at 12 and saw Prof. Forbes, about Jas. ovals. Prof. Forbes much pleased with them, investigating in books to see what has been done or known in this subject. To write to me when he has fully considered the matter.
Sa. 7.—Recd. note from Prof. Forbes:—
Edinburgh, 6th March 1846.
My dear Sir—I have looked over your son’s paper carefully, and I think it very ingenious,—certainly very remarkable for his years; and, I believe, substantially new. On the latter point I have referred it to my friend, Professor Kelland, for his opinion.—I remain, dear Sir, yours sincerely,
James D. Forbes.
W. 11.—Recd. note from Professor Forbes:—
3 Park Place, 11th March 1846.
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.
J. Clerk Maxwell, Esq.
Th. 12.—Called for Prof. Forbes at the College and conversed about the ovals.
M. 16.—Went with James to Royal Society.
T. 17.—Jas. at Prof. Forbes’s House, 3 Park Place, to Tea, and to discourse on the ovals. Came home at 10. A successful visit.
T. 24.—Cut out pasteboard trainers for Curves for James.
W. 25.—Call at Adie’s,[97] to see about Report on D. E. Hay’s paper on ovals.
Th. 26.—Recd. D. E. Hay’s paper and machine for drawing ovals, etc.
M. 30.—Called on Prof. Forbes at College and saw Mr. Adie about report on Mr. Hay’s paper. Jas. ovals to be at next meeting of R.S.
M. 6.—Royal Society with Jas. Professor Forbes gave acct. of James’s ovals. Met with very great attention and approbation generally.
The result of the attempt thus eagerly pursued, as communicated by Professor Forbes that evening, is embodied in the Proceedings of the Edinburgh Royal Society, vol. II. pp. 89-93.
Monday, 6th April 1846.
Sir Thomas M. Brisbane, Bart., President, in the Chair.
The following communications were read:—
1. 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.
Mr. Clerk Maxwell ingeniously suggests the extension of the common theory of the foci of conic sections to curves of a higher degree of complication, in the following manner:—
1. As in the ellipse and hyperbola, any point in the curve has the sum or difference of two lines drawn from two points or foci = a constant quantity, so the author infers that curves to a certain degree analogous may be described and determined by the condition that the simple distance from one focus, plus a multiple distance from the other, may be = a constant quantity; or more generally, m times the one distance + n times the other = constant.
2. The author devised a simple mechanical means, by the wrapping of a thread round pins, for producing these curves. See Figs. 1 and 2 (Plate 11). He then thought of extending the principle to other curves, whose property should be, that the sum of the simple or multiple distances of any point of the curve from three of more points or foci, should be = a constant quantity; and this, too, he has effected mechanically, by a very simple arrangement of a string of given length passing round three or more fixed pins, and constraining a tracing point, upper P. See Pig. 3. Further, the author regards curves of the first kind as constituting a particular class of curves of the second kind, two or more foci coinciding in one, a focus in which two strings meet being considered a double focus; when three strings meet a treble focus, etc.
Professor Forbes observed that the equation to curves of the first class are easily found, having the form— StartRoot EndRoot x squared plus y squared equals a plus b StartRoot left parenthesis x minus c right parenthesis squared plus y squared EndRoot comma which is that of the curve known under the name of the First Oval of Descartes. Mr. Maxwell had already observed that, when one of the foci was at an infinite distance (or the thread moved parallel to itself, and was confined, in respect of length, by the edge of a board), a curve resembling an ellipse was traced; from which property Professor Forbes was led first to infer the identity of the oval with the Cartesian oval, which is well known to have this property. But the simplest analogy of all is that derived from the method of description, r and r prime being the radients to any point of the curve from the two foci. m r plus n r Superscript prime Baseline equals constant comma which, in fact, at once expresses on the undulatory theory of light the optical character of the surface in question, namely, that light diverging from one focus upper F without the medium, shall be directly convergent at another point f within it; and in this case the ratio StartFraction n Over m EndFraction expresses the index of refraction of the medium.
If we denote, by the power of either focus, the number of strings leading to it by Mr. Maxwell’s construction, and if one of the foci be removed to an infinite distance,—if the powers of the two foci be equal, the curve is a parabola; if the power of the nearer focus be greater than the other, the curve is an ellipse; if the power of the infinitely distant focus be the greater, the curve is a hyperbola. The first case evidently corresponds to the reflection of parallel rays to a focus, the velocity being unchanged after reflection; the second, to the refraction of parallel rays to a focus in a dense medium (in which light moves slower); the third case, to refraction into a rarer medium.
Fig. 1. Two Foci. Ratios 1:2.
Fig. 2. Two Foci Ratios 2:3.
Fig. 3. Three Foci. Ratios of Equality.
The Ovals of Descartes were described in his Geometry, where he has also given a mechanical method of describing one of them, but only in a particular case, and the method is less simple than Mr. Maxwell's. The demonstration of the optical properties was given by Newton in the Principia, Book I. Prop. 97, by the law of the sines, and by Huygens in 1690, on the Theory of Undulations, in his Traité de la Lumière. It probably has not been suspected that so easy and elegant a method exists of describing these curves by the use of a thread and pins whenever the powers of the foci are commensurable. For instance, the curve, Fig. 2, drawn with powers 3 and 2 respectively, give the proper form for a refracting surface of glass, whose index of refraction is 1·50, in order that rays diverging from f may be refracted to upper F.
As to the higher classes of curves, with three or more focal points, we cannot at present invest them with equally clear and curious physical properties, but the method of drawing a curve by so simple a contrivance, which shall satisfy the condition, m r plus n r Superscript prime Baseline plus p r Superscript double prime Baseline plus etc period period comma equals constant comma is in itself not a little interesting; and if we regard, with Mr. Maxwell, the ovals above described, as the limiting case of the others by the coalescence of two or more foci, we have a further generalisation of the same kind as that so highly commended by Montucla, by which Descartes elucidated the conic sections as particular cases of his oval curves.
This was the beginning of the lifelong friendship between Clerk Maxwell and James D. Forbes. “I loved James Forbes” was his own emphatic statement to me in 1869. Maxwell's gratitude to all from whom he had received any help or stimulus was imperishable.
The curve-drawing, and the problems connected with it, were by no means the only original investigations of this year. Mr. John Scott, of Scott Brothers, Greenock, remembers being in the attic of 31 Heriot Row, and seeing some preparations of jelly with which James was experimenting there. Mr. Scott left Edinburgh in the summer of 1846. What was the exact object of these experiments and others on gutta percha at this time is matter of conjecture. There is little doubt that they prepared the way for the investigation concerning the compression of elastic solids. But it seems probable that they were immediately suggested by Forbes’s Theory of Glaciers, which had recently called attention to the whole question of the difference between solid, liquid, and “viscous” bodies, and the different effects of gravitation and pressure as applied to them.[98] Another set of phenomena with which his mind was soon afterwards engaged, viz. those of the refraction and polarisation of light, were partly studied through similar means.
The work of his cousin, who was now a rising artist, still interested him. An entry in the father’s Diary, December 5, 1845, has reference to this:—
Walk with Jas. and Jemima to Botanical Garden to inspect palm-trees—for her sketching for a picture.
Either in this or the following year I remember his raising the question, Whether it was not possible to determine mathematically the curve of the waves on a particular shore, so as to represent them with perfect truth in a picture.
After contributing to the Proceedings of the Edinburgh Royal Society, it might perhaps have been expected that Clerk Maxwell, although scarcely 15, would at least have been taken from the Academy and sent to the classes of Mathematics and Natural Philosophy at the University. Instead of this, he simply completed his course at school. His inventions may perhaps have interfered a little with his regular studies:—for he missed the Mathematical medal in 1846—but he was one of the few of the class which he had joined in 1841 who continued at the Academy until 1847. And when he left, although still younger than his competitors by about a twelvemonth, he was not only first in mathematics and English, but came very near to being first in Latin. He had not yet “specialised” or “bifurcated,” although the bent of his genius was manifest. Nor have I ever heard him wish that it had been otherwise. On the contrary, he has repeatedly said to me in later years that to make out the meaning of an author with no help excepting grammar and dictionary (which was our case) is one of the best means for training the mind. Some of his school exercises in Latin prose and verse are still extant, and, like everything which he did, are stamped with his peculiar character.[99]
The first Greek play we read (the Alcestis of Euripides) made an impression on him to which he reverted in a conversation many years afterwards.[100] At the same time he had a quick eye for the absurdities of pedantry. One of the teachers was apt to annoy our youthful taste by a literal exactness in translating the Greek particles, which would have pleased some more recent scholars. Maxwell expressed our feelings on this subject in a few lines, of which I can only recall the beginning:—
The frigid climax in “decidedly” is a good instance of his roguish irony.
In September 1846 I made my first visit to Glenlair. It was a time of perpetual gladness, but the particulars are hardly worth recording. James used to sleep long and soundly, and seemed to be the whole day at play, eagerly showing me his treasures and accompanying each exhibition with lively talk, sprinkled with innumerable puns.[101] After such a breakfast as became that land of milk and honey, there was a long interval, while Mr. Maxwell was attending to home business and deliberating what the “expedite” should be. Miss Cay meanwhile was writing letters, or finishing some drawing of Lincluden or New Abbey (where they had lately been), and James would flit to and fro between the little den, where his books and various apparatus lived, and the drawing-room,[102] where his father sat in the arm-chair, with Tobs on knee. Ever and anon we boys would escape out of doors and have a run in the field or the garden, or a bout with the d——1. So the morning would pass till an early luncheon, after which Tobin must do his various tricks; then, if the men were busy, James would himself harness Meg, the Galloway pony, for the drive of the afternoon. After dinner and Toby’s second performance, and another turn at the deil, there would be something more to see—Cousin Jemima’s drawings, recent diagrams or other inventions of his own, the magic discs, etc. etc., the charm of the whole consisting in the flow of talk, incessant, but by no means unbroken,
of which neither of us ever tired. On Sunday there was the drive to Corsock Church (where the absolute gravity of his countenance was itself a study),[103] and the walk home by the river, past the Kirk pool, renowned for bathing, with conversations of a more earnest kind, and a stroll on the estate in the afternoon; or, if we stayed at home, he would show his favourite books and talk about them, till the evening closed with a chapter and a prayer, which the old man read to the assembled household.
During the winter of 1846-47, James was unusually delicate. He was often absent from school, and seems not to have attended the meetings of the Societies. But of these his father was sure to give him a faithful report. He was certainly more than ever interested in science. The two subjects which most engaged his attention were magnetism and the polarisation of light. He was fond of showing “Newtons rings”—the chromatic effect produced by pressing lenses together—and of watching the changing hues on soap bubbles.
In the spring of 1847 (somewhere in April) his uncle, Mr. John Cay, whose scientific tastes have been mentioned more than once above, took James and myself (with whom he chose to share all such delights) to see Mr. Nicol, a friend of Sir David Brewster, and the inventor of the polarising prism.[104] Even before this James had been absorbed in “polarised light,” working with Iceland spar, and twisting his head about to see “Haidinger’s Brushes” in the blue sky with his naked eye. But this visit added a new and important stimulus to his interest in these phenomena, and the speculations to which they give rise.[105]
Shortly afterwards (May 25th) he went with his father to the cutler's to choose magnets suitable for experimenting.
And a little earlier in the same year (March 17), he was taken to hear a lecture[106] on another subject, which was also connected with his subsequent labours, and must have impressed him not a little at the time. This was the discovery by Adams and Leverrier simultaneously, through a striking combination of hypothesis and calculation, of the planet Neptune, which then first “swam into” human “ken.”
The magnetic experiments were continued that autumn at Glenlair, as appears from two entries in the Diary:—
Sept. 3.—Walk round by smiddy; gave steel to be made into bars for magnets for James.
Sept. 7.—James and Robert (Campbell) most of the time at the smiddy, and got the magnet bars.
My brother perfectly remembers the magnetising of these bars of steel.
Lastly, in 184?—unless my memory deceives me—James had commenced the study of chemistry, and had taken extra lessons in German.
There was an odd episode in our school life. To keep our education “abreast of the requirements of the day,” etc., it was thought desirable that we should have lessons in “Physical Science.” So one of the classical masters gave them out of a text-book. The sixth and seventh classes were taught together; and 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.
Maxwell and Tait were by this time acknowledged as the two best mathematicians of the school, and it was already prophesied that Tait, who was about fifteen, would some day be a Senior Wrangler. The two youths had many interchanges of ideas, and Professor Tait remembers that Maxwell had by this time proved, by purely geometrical methods, that the central tangential section of a “tore,” or anchorring, is a pair of intersecting equal and similar curves, probably circles.
This is referred to in the following extract from Professor Tait’s admirable summary:—
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 scholarship, mathematics, and English verse composition. From this time forward I became very intimate with him, and we discussed together, with school-boy 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.[107] 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.[108]
On the whole, he looked back to his school-days with strong affection; and his only revenge on those who had misunderstood him was that he understood them. To many of us, as we advance in life, the remembrance of our early companions, except those to whom we were specially drawn, becomes dim and shadowy. But Maxwell, by some vivid touch, has often recalled to me the image of one and another of our schoolfellows, whose existence I had all but forgotten.
The following letters to his father still belong to his schoolboy life:—