January i i, 1894] 



NATURE 



:6l 



existence of an elastic medium for its transmission at a finite, 

 though very great, speed ; such a medium renders an excellent 

 account of all its relations, if we assume it to possess inertia 

 and to be endowed with some elastic quality of resistance to 

 disturbance roughly analogous to what we can observe and 

 study in ordinary elastic solids of the relatively incomptessible 

 kind, such as indiarubber and jellies. Lord Kelvin has been 

 the promoter and developer of a view by which the elastic 

 forces between parts of such a medium may be to some extent 

 got rid of as ultimate elements, and be explained by the inertia 

 of a spinning motion of a dynamically permanent kind, which 

 is distributed throughout its volume. If we imagine very 

 minute rapidly-spinning fly-wheels or gyrostats spread through 

 the medium, they will retain their motion for ever, in the 

 absence of friction on their axles, and they will thus form a 

 concrete dynamical illustration of a type of elasticity which 

 arises so'ely from inertia ; and this illustration will be of great 

 use in realising some of the peculiarities of a related type, 

 which I believe can be thoroughly established as the actuaUype 

 of elasticity transmitting all radiations, whether luminous and 

 thermal or electrical — for they are all one and the same — through 

 the ultimate medium of fluid character of which the vortices 

 constitute matter. 



It has always been the great puzzle of theories of radiation 

 how the medium which conveys it by transverse vibrations, such 

 as we know directly only in media of the elastic-solid type, 

 could yet be so yielding as to admit of the motion of the heavenly 

 bodies through it absolutely without resistance. According to 

 the view of the constitution of the aether which is developed in 

 this paper, not only are these ditilerent properties absolutely 

 consistent with each other, but it is, in fact, their absolute and 

 rigorous coexistence which endows the medium with the qualities 

 necessary for the explanation of a further very wide class of 

 phenomena. The remark which is the key to this matter has 

 been already thrown out by Lord Kelvin, in connection with 

 Sir George Stokes's suggested explanation of the astronomical 

 aberration of light. The motion of the ultimate homogeneous 

 frictionless fluid medium, conditioned by the motion of the 

 vortices existing in it, is, outside these vortices, of an absolutely 

 irrotational character. Now, suppose the medium is endowed 

 with elasticity of a purely rotational type, so that its elastic 

 quality can be called into play only by absolute rotational dis- 

 placement of the elements of the medium ; just as motion of 

 translation of a spinning gyrostat calls into play no reaction, 

 while any alteration of the absolute position of its axis in space 

 is resisted by an opposing couple. As regards the motion of 

 the medium involved in the movements of its vortices, this 

 rotational elasticity remains completely latent, as if it did not 

 exist ; and we can at once set down the whole theory of the 

 vortical hydrodynamical constitution of matter as a part of the 

 manifestations of an ultimate medium of this kind. 



The explanation of the laws of physical optics advanced by 

 Fresnel, and verified by comparison with the phenomena which 

 was possible in several very exact ways, chiefly by himself and 

 Brewster, was, about the year 1835, engaging the attention of 

 several of the chief mathematicians of that time — Augustin 

 Cauchy in France, Franz Neumann in Germany, George Green 

 in England, and James MacCullagh in Ireland. The prevalent 

 mode of attacking the problem was through the analogy with 

 the propagation of elastic waves in solid bodies ; and the com- 

 parison of Fresnel's laws of propagation in crystalline media with 

 the results of the mathematical theory of the elasticity of 

 crystalline bodies gave abundance of crucial tests for the 

 verification, modification, or disproof of the principles assumed 

 in these investigations. 



The greatest achievement of MacCullagh is that contained in 

 his memoir of 1839, entitled an " Essay towards a Dynamical 

 Theory of Crystalline Reflexion and Refraction." He is in 

 quest of a dynamical foundation for the whole scheme of op- 

 tical laws, which had been notably extended and confirmed by 

 himself already. He recognises, I think for the first time in 

 a capital physical problem, that what is required is the dis- 

 covery of the potential-energy function of Lagrange on which 

 the action of the medium depends, and that the explanation 

 of the form of that function is another question which can be 

 treated separately. His memoir is subsequent to, but appar- 

 ently quite independent of, that of Green, in which Green 

 restricted the medium to a constitution like an elastic solid, 

 laid down the general laws of such constitution for the first 

 time, and made a magnificent failure of his attempt to explain 



NO. 126.3, VOL. 49] 



I optical phenomena on that basis. If this thing was to be done, 

 I the power, simplicity, and logical rigour of Green's analysis 

 might have been expected to do it ; and nothing further has 

 come of the matter until the recent new departure of Lord 

 Kelvin in his speculation as to a labile elastic-solid a;ther. To 

 j return to MacCullagh, he is easily able to hit off a simple form 

 j of the potential-energy function, which— on the basis of 

 Lagrange's general dynamics, or more compactly on the basis 

 of the law of Least Action — absolutely sweeps the whole field 

 of optical theory so far as all phenomena are concerned in 

 which absorption of the light does not play a prominent part. 

 He is confident, as any one who follows him in detail must be, 

 that he is on the right track. He tries hard to obtain a dyna- 

 mical basis for his energy-function, that is, to imagine some 

 material medium that shall serve as a model for it, and illus- 

 trate its possibility and its mode of action ; he records his 

 failure in this respect, but at the same time he protests against 

 the limited view which would tie down the unknown and in 

 several ways mysterious and paradoxical properties of the lumin- 

 iferous medium to be the same as those of an ordinary elastic 

 solid. 



The form of MacCullagh's energy-function was derived by him 

 very easily from the consideration of the fact that it is required 

 of It that it shall produce, in crystalline media, plane-polarised 

 waves propagated by di>placements in the plane of the wave 

 front. Though he seems to put his reasoning as demonstrative 

 on this point, it has been pointed out by Sir George Stokes, and 

 is indeed obvious at once from Green's results, that other forms 

 of the energy-function beside MacCullagh's would satisfy this 

 condition. But the important point as regards MacCullagh's 

 function is that it makes the energy in the medium depend 

 solely on the absolute rotational displacements of its elements 

 from their equilibrium orientations, not at all on its distortion 

 or compression, which are the quantities on which the elasticity 

 of a solid would depend according to Green. 



Starting from this conception of rotational elasticity, it can 

 be shown that, if we neglect for the moment optical dispersion, 

 every crystalline optical medium has three principal elastic axes, 

 and its wave-surface is precisely that of Fresnel, while the laws 

 of reflexion and refraction agree precisely with experiment. 

 Further, it follows from the observed fact of transparency in 

 combination with dispersion, that the dispersion of a wave of 

 permanent type is properly accounted for by the addition to 

 the equations, therefore to the energy-function, of subsidiary 

 terms involving spacial differentiations of higher order. To 

 preserve the medium hydrodynamically a perfect fluid, these 

 terms also must satisfy the condition that the elasticity of the 

 medium is thoroughly independent of compression and distortion 

 of its elements, and wholly dependent on absolute rotation. 

 It can be shown, I believe, that this restriction limits the terms 

 to two kinds, one of which retains Fresnel's wave-surface un- 

 altered, while the other modifies it in a definite manner stated 

 without proof by MacCullagh ; but the first terms depend on 

 an interaction between the dispersive property and the wave 

 motion itself, while the second terms involve the square of the 

 dispersive quality. It seems clear that the second type involves 

 only phenomena of a higher order of small quantities than we 

 are here considering ; thus an account of dispersion remains 

 which retains Fresnel's wave-surface unaltered for each homo- 

 geneous constituent of the light, while it includes the dispersion 

 of the optic axes in crystals both as regards their magnitudes and 

 directions — -results quite unapproached by any other theory ever 

 entertained. 



In this analysis of dispersions, all terms have been omitted 

 which possess a unilateral character, such as would be indicated 

 in actuality by rotatory polarisation and other like phenomena. 

 The laws of crystalline material structures seem to prohibit the 

 occurrence of such asymmetry as these terms would indicate, 

 except to the very small extent evidenced by the hemihedral 

 faces of quartz crystals. The influence of this asymmetric 

 arrangement of the molecules on the optical medium must be 

 very much smaller still, for the rotatory terms are in all media 

 exceedingly minute compared with the ordinary dispersional 

 terms. The form of these rotatory terms in the energy function 

 is at once definitely assigned by our condition of perfect fluidity 

 of the medium, both for crystals and for rotational liquids such 

 as turpentine, and this form is the one usually accepted, on 

 MacCullagh's suggestion, as yielding a correct account of the 

 phenomena. 



When dispersional terms are included in the energy function, 



