Seismic Radiations. 
33 
1909-10.] 
Thus the original rectilinear simple harmonic motion, whose com- 
ponents are 
= - B b sin 6= - Wj cos (o - , 
rj 0 = + B be sin 0 , 
is, in general, changed at the surface into an elliptic motion. The normal 
displacement is accelerated in phase by the angle ~—p, and the tangential 
displacement by the angle —p, where tan_p = 4ec/(c 2 — l) 2 . 
The principal axes of the ellipse so described by any point of the 
surface are in the ratio 
(c 2 — 1 ) sin p _ 2 ec _ 2 f m — nc 2 
2 cos p c 2 - 1 c 2 - 1 V m + n 
Gathering up the results, we see that when the angle of incidence is not 
greater than cotan -1 ( there are two reflected waves of different 
type sent back into the medium, and the associated displacement of each 
point of the surface is a rectilinear sinusoidal motion. In the distortional 
wave the displacement is at right angles to the direction of propagation of 
the wave. Consequently, the displacement in the original incident wave 
makes with the surface an angle equal to the angle of incidence. Hence, 
with original amplitude unity, the £ and rj displacements are measured by 
the sine and the cosine respectively of the angle of incidence. With the 
same numerical data as before, we readily calculate the values of the 
component displacements. These are given in the following table, along 
with the corresponding angles of emergence : — 
Angle of 
Incidence. 
Incident Displacements. 
Surface Displacements. 
Angle of 
Emergence 
tan -1 - . 
V 
ex 
s p-. 
o' 
Vo- 
(normal). 
V 
(tangential). 
o 
0 
0 
1 
0 
2 
O 
0 
0 
10 
0-174 
0-985 
0-396 
1-952 
10-5 
0-203 
20 
0-342 
0-94 
0-756 
1-821 
22-6 
0-415 
30 
0-5 
0-866 
1 
L-732 
30 
0-577 
35 
0-572 
0-819 
0-658 
2-987 
12-5 
0-221 
35 16' 
0-577 
0-816 
0 
3-462 
0 
0 
The angle of emergence is in this case to be compared with the angle 
of incidence, not with its complement. The comparison shows that except 
in the neighbourhood of the critical angle 35° 16' — or more generally 
VOL. xxx. 3 
