NATURE 



317 



THURSDAY, FEBRUARY 5, 18S0 



A 



CLERK-MAXWELL'S SCIEXTIFIC WORK 

 T the instance of Sir W. Thomson, Mr. Lockyer, 



and others I proceed to give an account of Clerk- 

 Maxwell's work, necessarily brief, but I hope sufficient to 

 let even the non-mathematical reader see how very great 

 were his contributions to modern science. I have the less 

 hesitation in undertaking this work that I have been 

 intimately acquainted with him since we were schoolboys 

 together. 



If the title of mathematician be restricted (as it too 

 commonly is) to those who possess peculiarly ready 

 mastery over symbols, whether they try to understand the 

 significance of each step or no, Clerk- Maxwell was riot, 

 and certainly never attempted to be, in the foremost rank 

 of mathematicians. He was slow in "writing out," and 

 avoided as far as he could the intricacies of analysis. 

 He preferred always to have before him a geometrical 

 or physical representation of the problem in which he 

 was engaged, and to take all his steps with the aid of 

 this : afterwards, when necessary, translating them into 

 symbols. In the comparative paucity of symbols in many 

 of his great papers, and in the way in which, when wanted, 

 they seem to grow full-blown from pages of ordinary text, 

 his writings resemble much those of Sir William Thomson, 

 which in early life he had with great wisdom chosen as a 

 model. 



There can be no doubt that in this habit, of constructing 

 a mental representation of every problem, lay one of the 

 chief secrets of his wonderful success as an investigator. 

 To this were added an extraordinary power of penetration, 

 and an altogether unusual amount of patient determination. 

 The clearness of his mental vision was quite on a par with 

 that of Faraday ; and in this (the true) sense of the word 

 he was a mathematician of the highest order. 



But the rapidity of his thinking, which he could not 

 control, was such as to destroy, except for the very 

 highest class of students, the value of his lectures. His 

 books and his written addresses (always gone over twice 

 in MS.) are models of clear and precise exposition ; but 

 his extempore lectures exhibited in a manner most aggra- 

 vating to the listener the extraordinary fertility of°his 

 imagination. 



His original work was commenced at a very early age. 

 His first printed paper, " On the Description of Oval 

 Curves, and those having a Plurality of Foci" was 

 communicated for him by Prof. Forbes to the Royal 

 Society of Edinburgh, and inserted in the " Proceedings" 

 for 1846, before he reached his fifteenth year. He had 

 then been taught only a book or two of Euclid, and the 

 merest elements of Algebra. Closely connected with this 

 are three unprinted papers, of which I have copies (taken 

 in the same year), on "Descartes' Ovals," " The Meloid 

 and Apioid," and " Trifocal Curves." All of these 

 which are drawn up in strict geometrical form and divided 

 into consecutive propositions, are devoted to the proper- 

 ties of plane curves whose equations are of the form 

 mr + n> J + pr» +....= constant, 



r, r", r", &c, being the distances of a point on the curve 

 Voi. xxi. — No. 536 



from given fixed points, and m, n, p, &c, mere numbers. 

 Maxwell gives a perfectly general method of tracing all 

 such curves by means of a flexible and inextensible cord. 

 When there are but two terms, if m and n have the same 

 sign we have the ordinary Descartes' Ovals, if their 

 signs be different \vc have what Maxwell called the 

 Meloid and the Apioid. In each case a simple geo- 

 metrical method is given for drawing a tangent at any 

 point, and some of the other properties of the curves are 

 elegantly treated. 



Clerk-Maxwell spent the years 1847-50 at the University 

 of Edinburgh, without keeping the regular course for a 

 degree. He was allowed to work during this period, 

 without assistance or supervision, in the Laboratories of 

 Natural Philosophy and of Chemistry : and he thus experi- 

 mentally taught himself much which other men have to 

 learn with great difficulty from lectures or books. His 

 reading was very extensive. The records of the Uni- 

 versity Library show that he carried home for study 

 during these years, such books as Fourier's T/u'orie de la 

 ChaLur, Monge's Gc'ometrie Descriptive, Newton's Optics, 

 Willis' Principles of Mechanism, Cauchy's Calcnl Dif- 

 fereulicl, Taylor's Scientific Memoirs, and others of a 

 very high order. These were read through, not merely 

 consulted. Unfortunately no list is kept of the books 

 consulted in the Library. One result of this period of 

 steady work consists in two elaborate papers, printed in 

 the Transactions of the Royal Society of Edinburgh. 

 The first (dated 1849) "On the Theory of Rolling 

 Curves," is a purely mathematical treatise, supplied with 

 an immense collection of very elegant particular examples. 

 The second (1850) is "On the Equilibrium of Elastic 

 Solids" Considering the age of the writer at the time 

 this is one of the most remarkable of his investigations! 

 Maxwell reproduces in it, by means of a special set of 

 assumptions, the equations already given by Stokes. He 

 applies them to a number of very interesting cases, such 

 as the toraion of a cylinder, the formation of the large 

 miiror of a reflecting telescope by means of a partial 

 vacuum at the back of a glass plate, and the theory of 

 Orsted's apparatus for the compression of water. But he 

 also applies his equations to the calculation of the strains 

 produced in a transparent plate by applying couples to 

 cylinders which pass through it at right angles, and the 

 study (by polarised light) of the doubly-refracting struc- 

 ture thus produced. He expresses himself as un.ihle to 

 explain the permanence of this structure when on:e pro- 

 duced in isinglass, gutta percha, and other bodies. He 

 recurred to the subject twenty years later, and in 1873 

 communicated to the Royal Society his wry b autiful 

 discovery of the temporary double refraction produced by 

 shearing in viscous liquids. 



During his undergraduateship in Cambridge he deve- 

 loped the germs of his future great work on " Electricity 

 and Magnetism" (1873) in 'he form of a piper "On 

 Faraday's Lines of Force," which was ultimately printed 

 in 1S56 in the "Trans, of the Cam. Phil. Soc." He 

 showed me the MS. of the greater part of it in 1X53. It 

 is a paper of great interest in itselr, but extremely im- 

 portant as indicating the first steps to such a >piendid 

 result. His idea of a fluid, incompressible .ind without 

 mass, but subject to a species of friction in space, was 

 confessedly adopted from the analogy pointed out by 



