The Aether as an, Elastic Solid. 151 



elastic constants already introduced; by substituting this value 

 of <f> in the general variational equation 



III' \w &t + 1* ** + TF*-| ****** = - 



* (where p denotes the density), the equation of motion may be 

 deduced. 



But this method does more than merely furnish the equation 

 of motion 



or, 



/ 4 \ 



pe = - ( k + - n ) grad div e - n curl curl e ; 

 \ / 



pe = -lk + -n\ grad div e + nV z e, 



which had already been obtained by Cauchy ; for it also yields 

 the boundary-conditions which must be satisfied at the interface 

 between two elastic media in contact ; these are, as might be 

 guessed by physical intuition, that the three components of the 

 displacement* and the three components of stress across the 

 interface are to be equal in the two media. If the axis of x 

 be taken normal to the interface, the latter three quantities 

 are 



, 2 \ de x fie z 3e x \ fde v de y 



--TI dive+ 27i , w (-Ji + ), and n (^ + - 



3 ) dx \to fa J \ty dx 



The correct boundary-conditions being thus obtained, it was 

 a simple matter to discuss the reflexion and refraction of an 

 incident wave by the procedure of Fresnel and Cauchy. The 

 result found by Green was that if the vibration of the aethereal 

 molecules is executed at right angles to the plane of incidence, 

 the intensity of the reflected light obeys Fresnel's sine-law, pro- 

 vided the rigidity n is assumed to be the same for all media, 

 but the inertia p to vary from one medium to another. Since 

 the sine-law is known to be true for light polarized in the plane 

 of incidence, Green's conclusion confirmed the hypotheses of 



* These first three conditions are of course not dynamical but geometrical. 



