ON THE ACTION OF MAGNETISM ON LIGHT. 361 



supposed devoid of consistence to compression, but it is the result of 

 the neglected surface-terms on the energy-function. The correlation 

 between an electric theory and a mechanical theory which follows from 

 this comparison has already been alluded to by Willard Gibbs.' It will 

 be found below that there is a similar correlation between two mechanical 

 theories. 



The vector (i', »;, 4) of FitzGerald's equations is, as lie points out, exactly 

 the displacement in MacCullagh's - gMast'-mechanical theory of optical 

 phenomena ; and his analysis is for non-rotational media very much a 

 translation of MacCullagh's work into electric terminology. The method 

 followed in MacCullagh's extremely powerful investigation, which was 

 independent of and nearly contemporary with those of Green,^ and, I 

 think, of at least equal importance, was to discover some form of the 

 energy-function of the optical medium which shall lead by pure dynamical 

 analysis in Lagrange's manner, without further hypothesis, to the various 

 optical laws of Fresnel. In this he was completely successful, though 

 Stokes ■* gives reason to doubt whether he has obtained the most general 

 solution of his problem. His optical work has, howevei', to a great extent 

 failed to receive due recognition from various causes ; in particular th.e 

 objection has been emphasised by Stokes (loc. cit.), and generally ac- 

 cepted, that the vector (I, ?y, 4f) which represents the light-disturbance in 

 his analysis could not possibly be the displacement in a medium which 

 transmits vibrations by elasticity in the manner of an ordinary elastic 

 solid. ' Indeed MacCuUagh himself expressly disclaimed to have given 

 a mechanical theory of double refraction. (It would seem, however, that 

 he rather felt the want of a mechanical theory, from which to deduce the 

 form of the function Q or V, than doubted the correctness of that form 

 itself.) His methods have been characterised as a sort of mathematical 

 induction, and led him to the discovery of the mathematical laws of 

 certain highly important optical phenomena. The discovery of such 

 laws can hardly fail to be a great assistance towards the future establish- 

 ment of a complete dynamical theoiy.' ^ 



Since the date of these remarks the mechanical theory sought for 

 has, I think, been supplied by Lord Kelvin's notion ^ of a medium domi- 

 nated by some form of molecular angular momentum such as may be 

 typified by spinning gyrostats imbedded in it. The gyrostatic part of 

 the energy of strain of such a medium can be a quadratic function of its 

 elementary twists or rotations, precisely after MacCullagh's form. The 

 conjugate tangential tractions on the faces of a rectangular element of 

 volume, instead of being equal and of the same sign as in the elasticity 

 of solid bodies, are equal and of ojiposite sign,^ just as Stokes pointed 



' J. Willard Gibbs, ' A Comparison . . . ,' P?dl. Mag., 1889. 



" James MacCuUagh, 'An Essay towards a Dynamical Theory of Crystalline 

 Reflexion and Refraction,' Trans. R.I.A., December, 1839. 



^ George Green, ' On the Laws of the Reflexion and Refraction of Light at 

 the Common Surface of two Non-crystaUised Media,' Camhridgc Phil. Trans., 

 December, 1837, with Supplement, May, 1839 ; George Green, ' On the Propagation 

 of Light in Crystallised Jledia,' Cambridge Pldl. Trans., May, 1S39. 



•• Sir G. G. Stokes, 'Report on Double Refraction,' Brit. Assoc, 1862, p. 227. 



* Sir G. G. Stokes, loc. cit., p. 279. 



« Lord Kelvin, Comptes Rendus, Sept., 1889; Collected Papers, vol. iii. 1890, 

 p. 467. 



' Cy. J. Larmor, ' On the Equations of Propagation of Disturbances in gyro- 

 statically-loaded Media,' Proc. Lond. Math. Sue, sxiii. 1891. The medium considered 



