179 
1918-19.] The Propagation of Earthquake Waves. 
at once suggested filling in the region between with the Rays IV, V, and 
VI. The table for the Primary Rays III to VII then becomes : — 
Ray. 
r. Sr. 
2a. 28 a. 
25a 
Sr ' 
0. 8<p. 
50 
Jr ' 
III 
IV 
V 
VI 
VII 
' 815 .nxr 
. 77 -045 
•745 '° 25 
•735 ' 01 ° 
•725 010 
47 5B 6 59 
" 9 44 
57 40 ^ pr 9 
65 32 8 19 
73 57 8 iy 
1-55 
3-85 
7-87 
8*32 
30 18 ° ’ 
26 39 £ 6 y 
24 38 0 20 
24 18 ° 
24 3 U 15 
0-811 
•808 
•330 
•250 
On account of the inequality in the successive values of r, it is con- 
venient to supply the two columns headed 2 Sa/Sr and S<f>/8r so as to 
compare the relative rates of change. The numbers in column 6 show 
that the ratio 2 Sa/Sr increases rapidly with the transition from Ray IV 
to Ray VII. 
Another feature of the peculiarity under discussion is the slight change 
in the emergence angles of the Rays IV to VII, although the change in 
the corresponding arcual distances is large. Thus in fig. 6 the four rays 
mentioned form at the start a very close bundle ; but they ultimately 
separate out and reach the surface at wide intervals apart. This rapid 
dispersion of the rays is obviously associated with the advent of the 
change in the sign of the curvature, a change whose significance in 
accordance with equation (7) may be expressed in these words: — 
The speed of propagation through the surface layers increases with 
the depth below the surface down to a certain depth, below which the 
speed of propagation begins to diminish as the depth increases. 
It does not, however, appear that this condition continues or develops 
to any marked extent, for the sinuous form of still deeper rays seems to 
become less evident. As will be seen later, other causes begin to operate. 
In lack of any definite information to the contrary, the energy radiated 
from an earthquake origin may be assumed to be, on the average, equally 
distributed in all directions. Contiguous cones of rays whose initial angles 
of direction differ by a definite chosen amount will emerge along circles 
on the surface enclosing between them a zone over which a definite 
amount of energy will be spread. It needs no calculation to conclude 
that the rapid dispersion of the rays whose arcual distances are in the 
neighbourhood of 65° implies a marked decrease of energy associated with 
unit surface at that distance. It may be of interest, nevertheless, to 
determine for the true law of velocity variation now obtained the 
energy distribution over the surface of the globe, the method being the 
