362 REPORT — 1893. 



out they would be on MacCullagh's theory. Conseqnently a framework 

 free of elasticity of its own, and carrying a system of such gyrostatic cells, 

 would be a mechanical representation of an aether which corresponds 

 with MacCullagh's expression for the energy-function, and so would 

 afford an explanation of optical phenomena on the lines of his analysis. 

 The axes of the gyrostats will, in crystalline media, be concentrated in 

 certain directions ; but in any one direction as many must point back- 

 wards as forwards. Any very slight violation of the latter condition 

 will introduce into the medium directed rotational property with 

 respect to the resultant axes of angular momentum ; such we may 

 imagine to be the effect of an imposed magnetic field. Non-directed 

 rotational property will be a structural effect, due to mode of aggrega- 

 tion. If the light-disturbance is represented by the displacement of the 

 medium, it will be in the plane of polarisation ; while if it is represented 

 by the rotation, it will be at right angles to that plane. According to 

 this theory of light, the density of the tether will be the same in all 

 media ; but in different media the distribution of angular momentum 

 will vaiy. 



22. The bodily equations of MacCuUagh, when formulated in con- 

 nexion with the boundary conditions appropriate to the theory of the 

 elasticity of solids, which it is, I think, fair to say that their author never 

 intended, and with which, in fact, Stokes pointed out that his whole 

 scheme is inconsistent, have been shown ' by various writers to lead to 

 a wholly untenable account of reflexion. 



The investigation of MacCuUagh himself, based purely on dynamical 

 analysis, leads him to the boundary conditions which alone are consistent 

 with his scheme, much in the manner of FitzGerald's correlative electro- 

 dynamic theory sketched above. These conditions are quite different 

 from the ones appropriate for an elastic solid medium. 



The energy of MacCullagh's medium depends only on rotation, and 

 not sensibly on compression. The compressional term can in general be 

 absent only because either (i) there is no resistance offered to pi'essure, so 

 that no work is done by it, or (ii) the medium is incompressible so that 

 pressure can do no work. The tangential tractions on either side of an 

 interface are expressed in terms of rotation, not of distortion as in the 

 elastic solid theory. 



The surface conditions are, however, theoretically too numerous, as 

 MacCuUagh knew but did not suffer from in the problem of crystalline 

 reflexion, and as FitzGerald found irremediably in the magneto-optic 

 problem. The way to remove this difliculty is to recognise, according 

 to which of the above views we adopt, either (i) a local play of com- 

 pression close to the intei'face which is not propagated away from it, 

 which involves no sensible energy, but which renders it unnecessary to 

 suppose the displacement normal to the interface to be continuous, or 

 (ii) a play of pressure which is propagated from the interface with 

 infinite velocity (i.e., attains instantly an equilibrium distribution 



in this paper is dominated by simple rotators imbedded in its structure, and the 

 forcive is proportional to angular velocity. Lord Kelvin's new rotational medium is 

 dominated by complex gyrostatic cells, containing arrangements of Foucault gyro- 

 stats, of which only the outer cases are firmly imbedded in the medium ; and the 

 forcive is projDortional to the angular displacement. 



' cy. Lord Hayleigh, ' On the Reflexion of Light from Transparent Matter,' Phil. 

 Mag., 1871. 



