168 Proceedings of the Royal Society of Edinburgh. [Sess. 
is expressed, since dp/^(p 2 — rj^) is necessarily a ratio. Dividing each of 
the calculated integrals by 
we find 
log e r| 1 -^= - 1 / 90 = - 0 * 2012 , 
7T 
from which r may be immediately determined. 
Thus for any chosen value of rj, that is, of p, we can calculate the 
corresponding value of r. Knowing r and we find the corresponding 
value of v = rjri, after we have expressed rj in radians. Since p = dT/dQ, the 
factor required is the reciprocal of the factor required to reduce degrees 
to radians, that is, I 8 O/ 7 r. This gives v in earth-radii per second. To 
reduce to kilometres per second, it is necessary to multiply r by the 
number of kilometres in the radius of the earth, namely, 6378. 
The main results are tabulated in the following Tables IV and V and 
graphically shown in fig. 5. In these tables, R=6378r, and the velocity 
is expressed in kilometres per second. 
Table IV. — Primary Wave. 
In Degrees. 
In Radians. 
Integral 
(11). 
Log b to 
r 
Base 10. 
I 
Radial 
Distance, 
R. 
kilom. 
Velocity 
= R/V 
kilom. 
sec. 
1 
2a. 
17 . 
l 
2a. 
V- 
0 
15-5 
0 
888 
0 
6378 
7-18 
5-0 
15 
•047 
860 
0-411 
0-00198 
6349 
7-38 
8-3 
14-5 
•072 
831 
1-093 
•00487 
6307 
7-59 
110 
14 
•096 
802 
1-807 
•00872 
6252 
7-80 
13-4 
13-5 
T17 
774 
2-641 
•01274 
6194 
8-00 
154 
13 
T34 
745 
3-483 
•01640 
6142 
8-24 
17-4 
12-5 
T52 
716 
4*386 
•02116 
6075 
8-48 
19-4 
12 
T69 
688 
5-347 
•02580 
6010 
874 
21 4 
11-5 
T87 
659 
6-402 
•03089 
5940 
9-01 
23 4 
11 
•204 
630 
7 523 
•03630 
5867 
9-31 
25-2 
10-5 
•220 
602 
8-815 
•04253 
5783 
9-61 
27-4 
10 
•239 
573 
10-047 
•04848 
5705 
9-96 
30-0 
9-5 
•262 
544 
11-528 
•05563 
5612 
10-32 
330 
9 
•288 
516 
1332 
•06428 
5501 
10-66 
36-4 
8-5 
•318 
487 
1517 
•07322 
5389 
11 07 
39-8 
8 
•347 
458 
17-30 
•08347 
5263 
11-49 
43-0 
7-5 
•375 
430 
19-86 
•09584 
5115 
11-90 
46-4 
7 
•405 
401 
22-50 
•10856 
4968 
12-39 
53-0 
6-5 
•463 
372 
25-70 
T2401 
4794 
12-89 
71-0 
6'4 
•620 
367 
27-03 
•13041 
4724 
12-87 
74-0 
6-2 
•646 
355 
30 73 
T4827 
4534 
12-77 
77-0 
6 
•672 
344 
3332 
‘16079 
4405 
12-85 
95*0 
5-5 
•829 
315 
41-01 
•19790 
4044 
12-84 
1010 
5 
•881 
287 
49-60 
•23936 
3676 
12*81 
122-0 
4*5 
1-065 
258 
60-18 
•29041 
3268 
12-67 
143 0 
4 
1-248 
227 
74-67 
•34416 
2888 
1273 
