NATURE 



341 



THURSDAY, SEPTEMBER 14, 191 1. 



LORD KELVIN'S PAPERS. 

 Mathematical and Physical Papers by the Rt. Hon. 

 Sir William Thomson, Baron Kelvin, O.M., P.C., 

 G.C.V.O., 6-c. Arranged and revised with brief 

 annotations by Sir Joseph Larmor, Sec. R.S., M.P. 

 Vol. iv., "Hydrodynamics and General Dynamics." 

 Pp. xvi + 563. Vol. v., "Thermodynamics, Cosmi- 

 cal and Geological Physics, Molecular and Crystal- 

 line Theory Electrodynamics." Pp. xv + 602. 

 (Cambridge University Press, 1910-11.) Price 

 l&s. each. 



THE publication of volumes iv. and v. of Lord 

 Kelvin's "Mathematical and Physical Papers," 

 bringing as it does the collection of these memoirs 

 nearly to an end, is important both to the student 

 of mathematical physics and to the scientific his- 

 torian. It gives the former access to papers of 

 great value scattered through the Transactions and 

 Proceedings of learned societies, or imbedded in the 

 more easily obtainable but also more unexpected 

 pages of the journals of pure and technical science. 

 The latter will seize the opportunity to compare the 

 utterances of the master during the last decade or 

 two of the nineteenth century and the first seven 

 years of the twentieth, with the last developments 

 of the related theories of electrical action and the 

 ultimate constitution of matter. To those who have 

 come to these developments from the point of view 

 of the Maxwellian electromagnetic theory of light, 

 and find in atomic facts and hypotheses a supplement 

 and to some extent a basis for the undulatory propa- 

 gation of electric and magnetic action in a non- 

 conducting and uniform medium, some of these utter- 

 ances will occasion much thought, if they are not, 

 indeed, a source of a good deal of perplexity. 



Consider, for example, the Appendix A of the 

 " Baltimore Lectures," and its continuation in volume 

 iv. of the " Papers." One statement is enough to 

 cite : " Stress in ether, being thus freed from the 

 impossible task of transmitting both electrostatic and 

 magnetic force, is (we may well imagine) quite com- 

 petent to perform the simple duty of transmitting 

 magnetic force alone." (The italics are in the 

 original.) The Maxwellian electrician has the notion 

 ingrained in his mind that, when magnetic force is 

 propagated in the medium, electric force is propa- 

 gated also as a necessary concomitant, and vice versa, 

 and therefore supposes that whatever machinery is 

 effective for the one must be equally concerned with 

 the other. Moreover, as Lord Kelvin states in a note 

 to the first article of this appendix, the " so-called 

 ' electromagnetic theory of light ' " is to be grafted 

 on to the elastic solid theory of the aether. It is, how- 

 ever, to be remembered that Maxwell came to his 

 theory by way of Faraday's experimental researches 

 and Lord Kelvin's mathematical interpretations, and 

 it may be that these utterances, dark as they may 

 appear to some of us, will in time to come throw light 

 on some of the still unsettled questions of electricity. 

 NO. 2185, VOL. 87] 



The student of these papers has a difficult task; but it 

 is one which, if it be not thrown up in despair, will 

 stimulate his power of independent criticism of phy- 

 sical doctrine. 



The arrangement of the papers is both chrono- 

 logical and according to subjects. Hence volume 

 iv., which is mainly devoted to hydrodynamics, goes 

 back to the vortex-motion papers of 1867 and 1869. 

 The first of these contains the famous suggestion 

 that the vortex-rings of Helmholtz are the only true 

 atoms. Their non-creatibility in a perfect fluid does 

 not seem to be regarded as a difficulty, but rather 

 as a recommendation — a creative power above nature 

 brings them into existence, and once they are in 

 existence, their indestructibility by natural agency is 

 assured. 



It is rather remarkable that Helmholtz's great 

 paper of 1858, on the integration of the hydrodynamic 

 equations of vortex motion, should not have attracted 

 the active attention of physical mathematicians in 

 this country at an earlier date than 1867. In that 

 year Tait published his translation of the memoir, 

 and made experiments on vortex-rings rendered 

 visible by smoke in his class-room. It was seeing 

 and, so to speak, handling these rings that sug- 

 gested Kelvin's conception of the vortex-atom 

 constitution of matter, and, with Tait's account of 

 Helmholtz's investigations, led to the paper on vortex- 

 motion in the Edinburgh Transactions for 1869, which 

 will ever rank as one of the great classical memoirs 

 of hydrodynamics. In this Kelvin's point of view 

 and method are curiously different from those of 

 Helmholtz. The results of the latter are derived in 

 the most approved classical manner from the equa- 

 tions of motion of a perfect fluid, unsimplified by the 

 hypothesis of a velocity-potential. It is straight- 

 forward mathematical discussion ; but the march is 

 that of a clear-eyed intellectual giant, and the stages 

 reached are duly chronicled and described in language 

 which shows how completely the author understood 

 the physical meaning of his mathematical results. 



Kelvin, on the other hand, starts from the physical 

 conceptions of linear and angular momentum, and 

 from these ideas, and the impulses required to pro- 

 duce the momenta, the whole subject is developed. 

 The physical meaning of the expressions £= 



^(dwjdy-dvjdz) namely that, multiplied by the 



moment of inertia about diameters parallel to the 

 axes of coordinates, they are the component an- 

 gular momentum of an infinitesimal sphere of the 

 fluid with its centre at the point x, y, z, had been given 

 bv Stokes in 1845, and thus the existence of a velocity 

 potential the criterion for which is the vanishing 

 of $, <], C, had been shown to affirm the non-existence 

 of angular momentum in the fluid to which the cri- 

 terion applied. This physical interpretation is referred 

 to and used by Kelvin, and in a sense is the keynote 

 of his discussion of the subject. 



Perhaps the most important of all the results in 

 the memoir is the theorem of Thomson regarding 

 "circulation "—that is, the line integral, along a 

 specified curve or line of the fluid, of the compo- 



