160 The Aether as an Elastic Solid. 



therefore, in the contractile aether, the conditions that the 

 tangential components of e and of n curl e shall be continuous 

 across an interface are satisfied by the distortional part of the 

 disturbance taken alone. The condition that the component 

 of e normal to the interface is to be continuous is not satisfied 

 by the distortional part of the disturbance taken alone, but is 

 satisfied when the distortional and congressional parts are taken 

 together. 



The energy carried away by the longitudinal waves is 

 infinitesimal, as might be expected, since no work is required in 

 order to generate an irrotational displacement. Hence, with 

 this aether, the behaviour of the transverse waves at an 

 interface may be specified without considering the irrotational 

 part of the disturbance at all, by the conditions that the 

 conservation of energy is to hold and that the tangential 

 components of e and of n curl e are to be continuous. But if 

 we identify these transverse waves with light, assuming that 

 the displacement e is at right angles to the plane of polarization 

 of the light, and assuming moreover that the rigidity n is the 

 same in all media* (the differences between media depending on 

 differences in the inertia p), we have exactly the assumptions 

 of Fresnel's theory of light : whence it follows that transverse 

 waves in the labile aether must obey in reflexion the sine-law 

 and tangent-law of Fresnel. 



The great advantage of the labile aether is that it overcomes 

 the difficulty about securing continuity of the normal com- 

 ponent of displacement at an interface between two media : 

 the light-waves taken alone do not satisfy this condition of 

 continuity ; but the total disturbance consisting of light- waves 

 and irrotational disturbance taken together does satisfy it ; 

 and this is ensured without allowing the irrotational disturbance 

 to carry off any of the energy. f 



* This condition is in any case necessary for stability, as was shown by 

 R. T. Glazebrook : cf. Thomson, Phil. Mag. xxvi, p. 500. 



f The labile-aether theory of light may be compared with the electro-magnetic 

 theory, by interpreting the displacement e as the electric force, and pe as the 

 electric displacement. 



