The Aeiher as an Elastic Solid. 153 



where A is determined by the equation 



and a longitudinal refracted wave, 



7\ 7\ 



e y = JE - /(* + Aiz + my) ; e z = E - f(t 

 where AI is determined by 



Substituting these values for the displacement in the boundary- 

 conditions which have been already formulated, we obtain the 

 equations which determine the intensities of the reflected and 

 refracted waves ; in particular, it appears that the amplitude of 

 the reflected transverse wave is given by the equation 



A- E _ ljj>i m? (pi - p 2 ) 2 

 A + B Ip 2 I pz (\p z + A!/?I) 



Now if the elastic constants of the media are such that the 

 velocities of propagation of the longitudinal waves are of the 

 same order of magnitude as those of the transverse waves, the 

 direction-cosines of the longitudinal reflected and refracted rays 

 will in general have real values, and these rays will carry away 

 some of the energy which is brought to the interface by the 

 incident wavev-G^een avoided this difficulty by adopting Fresnel's 

 suggestion that the resistance of the aether to compression may V\ 

 be very large in comparison with the resistance to distortion, \\ 

 as is actually the case with such substances as jelly and 

 caoutchouc : in this case the longitudinal waves are degraded in 

 much the same way as the transverse refracted ray is degraded 

 when there is total reflexion, and so do not carry away energy. 

 Making this supposition, so that k\ and & 2 are very large, the 

 quantities A and A : have the values m </ - 1, and we have 



A- B li pi m ( PI - p 2 f 



A + B I 2 



