72 Prof. C. G. Knott on Reflexion and Refraction of 



Now, as n is less than m, there will always be a reflected 

 distortional wave, except of course at normal incidence when 

 = 0°, or at a grazing incidence when 0=90°. There will be 

 refracted waves at all except the limiting incidences if m/p is 

 greater than m'/p' . If m/p should be intermediate in value 

 to m'/p' and n'/p' there will always be a refracted distor- 

 tional wave, but for angles of incidence higher than a certain 

 critical value a refracted condensational wave is impossible. 

 Further, if m/p should be less than n'/p', then, for each refracted 

 wave, there is a special critical angle of incidence at and above 

 which the wave vanishes. When the critical value corre- 

 sponding to the refracted distortional wave is reached, there 

 will be total reflexion, and the whole energy of the incident 

 wave will be divided between the two reflected waves. 



If the incident wave is a distortional wave, there must 

 always be a critical angle of incidence for and above which the 

 reflected condensational wave vanishes. The existence of 

 such critical angles for the refracted waves will depend upon 

 the relative values of the quantities n/p, m'/p', n'/p', — the con- 

 dition for the possibility of total reflexion being that n/p is less 

 than n'/p'. 



If one of the media is a fluid, there can, of course, be no 

 distortional wave in it. It is this somewhat simple case I 

 propose to discuss in detail. I shall not here enter into the 

 purely mathematical method "* by which the energies of the 

 various possible waves have been determined. It is sufficient 

 to say that it is the usual mode of treatment of plane waves, 

 an harmonic form being assumed and the constants determined 

 so as to satisfy the equations of motion and the boundary 

 conditions. 



We shall take then, as the one medium, water; and, as the 

 other, rock of density 3, rigidity 1*5 X 10 u and Poisson ratio 

 •25. The density of the water is taken as unity and the 

 value of the bulk-modulus, which in this case is also the 

 wave-modulus, 2"2x 10 10 . The quantities are given in C.G.S. 

 units. The manner in which, for different angles of incidence 

 in the rock, the energy of the incident wave is distributed 

 amongst the reflected and refracted waves is shown in the 

 following tables. The first refers to the case of the incident 

 wave being condensational ; the second to the case of the 

 incident wave being distortional. The quantities A A x A' 

 represent the energies of the incident, reflected, and refracted 

 condensational waves ; B B : B' the energies of the similar set 



* [The mathematical investigation and formulae are given below, 

 Part in.] 



