Elastic Waves, with Seisnulojical Applications. 05 



Thus we find 



- 7 A t + X= 7 'AS 



( c 2_ 1)Ai+ 2cY=^(c 2 + l)A' L . . (4) 



These give 



2 y A 1 +(c 2 -l)X = O j 



c + 1 1 — r 



Y=^A,+^i±^A' 



lc p 2c 



(5) 



For numerical calculations these expressions are simple 

 enough to be used as they stand. 



This is one of the cases I worked out in my paper of 

 February 1888. 



The vanishing of everything except the reflected distor- 

 tional wave when the cotangent of the angle of reflexion 

 of the condensational-rarefactional part is zero, is clearly 

 brought out both in the Table on page 73, and in the 

 curve (fig. 6). 



The condition is that 7 = in equations (4). 



Hence also 



X = and X = AY, 



so that A' also vanishes if y' has a value differing from zero. 

 This gives 



B = - B l5 



and 



Y = 2B= -^1a i5 



Ic 



but the energy associated with the wave A 1 is proportional to 

 the product pyA x 2 , and therefore vanishes with y. Thus at 

 the critical angle of incidence at which the reflected conden- 

 sational-rarefactional wave runs along- the interface, the 

 refracted condensational wave also vanishes, whatever its 

 angle of refraction may be. The whole energy is found in 

 the reflected distortional wave. 



