Elastic Waves, ivith Seismologicai Applications. 71 



elastic substances of equal rigidities but different densities, 

 results are obtained in fair accordance with observation. The 

 media being incompressible, no wave of condensation can be 

 propagated through them. Distortional waves only can exist. 

 Thus an incident distortional wave falling on the bounding sur- 

 face will, in general, be broken up into two waves — one reflected 

 into the first medium, and the other refracted into the second 

 medium. But although distortional waves alone exist in the 

 media, the correct solution of the problem in elastic solids 

 requires us to take account of something existing at the 

 bounding surface of the nature of a condensational wave. 

 We must bear in mind, indeed, what the physical meaning 

 of incompressibility is. It is not that the condensational wave 

 vanishes, but that it is transmitted with infinite velocity. By 

 taking this surface disturbance into account — this pressural 

 wave as Thomson [Kelvin] has called it — we are able par- 

 tially to explain certain phenomena of reflexion and refraction 

 of polarized light in terms of the theory of elastic solids. 



Now in this special problem we begin with a distortional 

 wave incident on the bounding surface ; and, although the 

 media are taken as incompressible, we must not neglect the 

 effect of the pressural wave. Hence, if our methods of attack 

 are to be the same in all cases, we must admit the possibility 

 of true waves of compression being started in media of finite 

 compressibility, when upon their boundary a single distortional 

 wave impinges. In other words, an incident distortional wave 

 may be broken up into four parts : — a reflected distortional, 

 a refracted distortional, a reflected condensational, and a 

 refracted condensational. In like manner, an incident con- 

 densational wave will in general give rise to reflected and 

 refracted distortional waves as well as to reflected and refraated 

 condensational waves. 



The various angles of reflexion and refraction are easily 

 calculated in terms of the angles of incidence, it being- noted 

 that the surface trace is common to all the waves. In other 

 words, each wave velocity is, so to speak, the component in its 

 direction of the velocity of propagation of the surface trace. 



Thus, let a condensational wave be incident at an angle 9 to 

 the normal to the bounding surface ; let m, n, p, and mf } n/ 

 p', be the wave moduli and densities of the two media, in the 

 first of which the incident wave is given. Then if 6' be the 

 ancrle of refraction of the condensational wave, and (p <p' the 

 angles of reflexion and refraction of the distortional waves, 

 the above condition gives these equations : — 



— cosec 2 6 = - cosec J <p = —r cosec* a = — cosec* <p . 

 P P P P 



