ON THE ACTION OF MAGNETISM ON LIGHT. 363 



tliroughout the medium), and which therefore necessitates the modifi- 

 cation of the equations of propagation as FitzGerald's equations are 

 modified {supra, § 11), \ in that analysis being clearly a hydrostatic 

 pressure when (^, ?;, 4) represents linear displacement of the medium. 



Any actual refracting system is of finite extent, so that the equi- 

 librium state contemplated by (ii) is easily established throughout it : 

 it is only for the simplification of analysis that it is customary to take the 

 interface to be an unlimited plane. 



The discussion of crystalline reflexion which is given by MacCullagh 

 takes no account of this pressure X, but makes an argument in favour of 

 his theory out of the remarkable fact that although there are too many 

 surface conditions compared with the number of variables, yet in no case 

 is the introduction of such a pressure required by the analysis or the 

 optical phenomena, provided the densities of both media are assumed to 

 be the same ; while FitzGerald's further application to magneto-optic 

 reflexion simply leaves the continuity normal to the interface unsatisfied, 

 and so far tacitly adopts the first of the above alternatives, that the 

 medium, considered as a mechanical one, offers no resistance to com- 

 pression — a hypothesis which turns out to be untenable. 



23. If these considerations are sound, we have the following con- 

 clusions. 



The phenomena of light are explained on MacCullagh's mathe- 

 matical equations by a theory of pure rotational elasticity, without any 

 accompaniment of the character of the elasticity due to change of volume 

 or change of shape of an ordinary solid body, for linear vibrations the 

 direction of the displacement of the medium is in the plane of polarisation 

 of the light, while the axis of its rotation is at right angles to that 

 plane. There is, however, no occasion to take the medium devoid of 

 resistance to compression: it may transmit longitudinal waves with finite 

 velocity, and still no such wave will be produced by the refraction of a 

 transverse wave. 



The electric theory of light is formally the same as MacCullagh's 

 theory, magnetic force corresponding to velocity, provided his medium is 

 taken to be incompressible. 



The labile aether theory of Lord Kelvin is one that contemplates 

 elastic quality depending on compression and distortion, ?'.e.,the ordinary 

 elasticity of solid bodies, bat the resistance of the medium to laminar 

 compression is taken to be infinitesimal. 



The difference between MacCullagh's theory and the electric theory 

 does not, as has been just remarked, aff'ect the problem of pi'opagation in 

 crystalline media, nor does it enter into the question of reflexion at an 

 interface between either isotropic or crystalline media, the boundary 

 conditions being all satisfied without any condensational disturbance ; it 

 is not necessary to introduce either (i) interfacial compression or (ii) 

 hydrostatic pressure, according to the two cases above, to preserve the 

 continuity at the interface. But we have already seen that the diS"erence 

 between these hypotheses makes itself felt in the pi'oblem of magneto- 

 optic reflexion. 



The labile aether theory stands, according to the remark of Willard 

 Gibbs, already quoted, in a relation of precise duality to the electric 

 theory, and therefore also to the other limiting interpretation of 

 MacCullagh's theory, which postulates absence of volume elasticity ; the 

 linear displacement in the labile aether corresponds to the rotation in the 



