Seismic Radiations. 
29 
1909-10.] 
Also, by formulae (2), 
or 
3(c 2 + 1) = y 2 + 1 
pk'(c 2 + 1 ) = pn(y 2 + 1) , 
2000 (c 2 + 1) = 200,000(y 2 + 1) , 
c' 2 = 100y 2 + 99 . 
1 
which is negligible in comparison 
Thus R is of the order 
p c 20,000 
with 2. Hence we may write 
v 2 r 
Thus, so far as the movements of the surface are concerned, the pro- 
blem is not materially altered when we neglect the air altogether. It is 
sufficient for our present purpose to work out the simple problem of the 
reflexion of elastic disturbances at the plane boundary of an elastic solid. 
The surface conditions then reduce to the second and third given above, 
namely, the vanishing of the surface stresses. Equations (3) become 
- 2yB 1 + (y 2 - 1)(A + A,) = 0 
(y 2 -l)B 1 -2c(A-A 1 ) = 0 
(3 a) 
Hence 
A + A 1 _ 4yc 
A - Ai (y 2 
A + A 1 = 
if 
8yC 
4y c + (y 2 - l) 2 
A - 2 (r~ ~ 1 ) 2 A 
i 4yc + (y 2 -l) 2 
B = My 2 - 1 ) A. 
1 4yc + (y 2 -l) 2 
Substituting in (4) we find 
,_ 2c(y 2 -l)(y 2 +l ) A ^ 6(W) 
* 4cy + (y 2 -l) 2 
4ey(y 2 + l) 
' 4cy + (y 2 -l) 2 
(5) 
Now the £ and rj displacements in the original incident ray 
A exp{ib(cx + y + a)t)} are, for x = 0, 
£ 0 = cAib(? b{y+Mt) ) 
7] 0 = A ] * 
— = 2(y 2 — 1) 7 ' 2 + j 
^ ; 4cy+(y 2 -l) 2 
v_ = 
Vo 
4cy 
y 2 +l 
4cy + (y 2 - 1)S 
Hence 
