1918-19.] The Propagation of Earthquake Waves. 173 
10“' V = 12*99. Subtract 12*99 from all the higher values of the rf quantities, 
extract the square root, multiply by the corresponding r, and take the 
reciprocal. Group these numbers in successive sets of seven, sum each set 
according to Weddle’s Rule, and multiply by the value of p. The result 
is the radian measure of the angle between the initial and final radii of 
the set. 
The angle between the final radius of the last set and the radius 
which is asymptotic to the infinite branch is calculated according to the 
formula (13). 
The angular co-ordinates, whether referred to the position of r=l or 
to the position of the asymptote, in the present case of r= *725, are obtained 
obviously by simple addition of the successive inclinations. The following 
table gives the various values of the radii vectores r, the angles contained 
(Ad) etween successive radii vectores, the angular co-ordinates O', referred 
to the radius through the vertex, or 0 referred to the radius through the 
epicentre. Evidently 0-\-0'=a. 
r. 
a e. 
0. 
e'. 
0 
in Degrees. 
0' 
in Degrees. 
1 
0 
0*645 
o 
0 
' 
36 
56 
0*97 
•0149 
0-015 
*630 
0 
51 
36 
5 
•94 
•0180 
033 
•612 
1 
53 
35 
3 
*91 
•0220 
*055 
•590 
3 
9 
33 
47 
•88 
•0269 
•082 
•563 
4 
42 
32 
14 
•85 
*0334 
115 
*530 
6 
36 
30 
20 
•82 
*0427 
•158 
•487 
9 
3 
27 
5,3 
•79 
*0565 
•214 
•431 
12 
17 
24 
39 
•76 
•0867 
•301 
•344 
17 
15 
19 
41 
•73 
•2065 
•508 
*137 
29 
5 
7 
51 
725 
*1369 
•645 
•ooo 
36 
56 
0 
These co-ordinates r and O', or r and 0, give a series of points on the 
one half of the ray, either the portion from the vertex to the surface or 
from the surface at the epicentre to the vertex. The other half is exactly 
similar, but drawn in the other direction, being a mirror reflection of the 
former half in the axis along the radius vector through the vertex. 
In this way seventeen complete seismic rays have been worked out, ten 
for the Primary waves and seven for the Secondary. The results are 
embodied in Table B in the Appendix, and the forms of the paths or rays 
for the Primary waves are shown in fig. 6. The Primary rays are 
numbered successively from I to X. The Secondary rays are numbered 
II, III, V, and VII to X, each Secondary ray corresponding as regards 
depth of vertex with the Primary ray of the same number. 
