ON THE ACTION OF MAGNETISM ON LIGHT. 367 



still we can say that it is a consequence of forces which the elements of 

 the ponderable matter exert on the elements of the sether. As therefore 

 such forces are present they must exert a direct influence on the motion 

 of the elements of the tether at the boundary of the glass, though in the 

 interior of the glass they have only an indirect influence in altering the 

 elasticity of the fether. The relations of the direct action of these forces 

 at the surface and in the interior are similar to those which hold with 

 capillary forces, which also are only of influence at the surfaces of fluids, 

 and are not felt in the interior.' This quotation has been given at length, 

 as it puts the case precisely. The reply is that it is only a confession of 

 total ignorance as to the distribution of the energy throughout the mass 

 of the media which would permit us to prop up the boundary conditions 

 by extraneous forces in this manner. In the theory of capillarity the 

 surface-tractions are derived from the distribution of energy throughout 

 the mass of the liquid ; and if they could not be deduced rationally from 

 some possible volume distribution of energy, it would have to be held 

 that they were erroneous. So here, if KirchhofF's extraneous surface- 

 tractions cannot be deduced from some energy -function of the complex 

 medium (aether and matter) which is the seat of the undulations, there is 

 absolutely no basis left for them. It will not sufBce to say that at the 

 bou ndary there is interaction between the aether and the matter, and a 

 gradual transition in density caused by the equilibration of such, action : 

 if the depth of this layer of transition is a small fraction of the wave- 

 length, the introduction of the energy-function appropriate to it would have 

 but a small influence on the variation of the total energy, and so would 

 not sensibly affect the results. In so far as the introduction of the pressure 

 arising mathematically from the condition of incompressibiiity will not 

 make an elastic theory work, that theory has simply not been sustained ; 

 in various theories above mentioned the introduction of the pressure is 

 eSicacious, and they are in so far verified and in a position to be further 

 tested by application to more complicated phenomena. 



Although it would seem that Kirchhoff's method cannot be main- 

 tained, yet, as he remarks, his formal equations come out the same as those 

 of the rotational theory represented by MacCullagh's equations ; so that 

 his detailed development of the problem of crystalline reflexion will be 

 in agreement with MacCullagh's, and holds good so far as it goes. 



27. In the theory of Neumann, which contains one of the first 

 attempts at a rational dynamical treatment of reflexion and refraction, 

 he starts with equations for the strain of an elastic crystalline medium, 

 of the imperfect type, however, which the then cnri-ent elastic 

 theory of Navier and Poisson supplied. By assumption of special rela- 

 tions between the constant coefficients of these equations, he obtained a 

 form which led approximately to Fresnel's laws of double refraction.' 

 He then applied this form to the problem of crystalline reflexion,^ but 

 found, I suppose, that the six conditions which he recognised as necessary 

 to ensure continuity of displacement and stress at the interface could not 

 all be satisfied. To satisfy them in a case of an ordinary compressible 

 medium would require the introduction of a wave of longitudinal dis- 

 placement in each medium, set up in the act of refraction ; Neumann's 



' F. E. Neumann, Pogg. Ann., sxv. 



^ F. E. Neumann, Ahliandlungen der Berliner AlMdemic, 1835. This memoir pro- 

 ceeds throughout on the method of raj'S, without explicit consideration of the 

 elasticit)' of the medium. 



