Seismic Radiations. 
27 
1909 - 10 .] 
The components of stress have the values 
P = (m + ri) v 2 0 - 2 rfa . S = n~ 
Q = (m + n)v 2 <f>-2n d J, T = 
R -(m + nW U = »( 2 ^ + ^-g 
II. 
The components of stress on the plane whose direction-cosines are 
\juiv are 
F = PA + U/x + Tv \ 
G = UA.+ Q/x+ Sv l . . . . III. 
H = TA + S/x + Rv J 
The waves of the 0 - type are condensational - rarefactional waves 
travelling with a speed equal to *J(m + n)/p. The waves of the i/r-type 
are purely distortional waves travelling with speed Jn/p, the vibrations 
being in the plane XY. The f displacement belongs also to a purely 
distortional wave with vibrations perpendicular to the plane of 
incidence XY. 
Here I confine my attention entirely to the case of an elastic solid like 
rock, with its plane surface in contact with air, or, with what is practically 
the same thing, vacuum. The distortional wave f is simply reflected at the 
surface as a distortional wave and sent back into the solid medium. It 
is quite otherwise, however, with the distortional wave represented by \fr. 
Except under specially critical conditions, the ^-type of incident wave will 
produce two reflected waves, one of the x/^-type and the other of the 0-type. 
Similarly, an incident radiation of the 0-type will in general produce a 
reflected wave of type 0 and another of type \fr. The refracted ray will 
in each case pass through the air as a condensational wave. 
I shall consider each in turn, taking the incident condensational wave 
first, as involving the simpler analysis. 
1. Condensational Wave Incident. 
The solution is of the form 
ib{cx+y+<x>t) _|_ ^^ib(-cx+y+(ot) \ 
0= B L . (1) 
0 ' _ gib(c'x+y+u>t) J 
The quantities c, y, d are the cotangents of the angles of incidence, 
reflexion, and refraction of the various rays; 6 and co are connected re- 
