223 
1907-8.] Professor C. G. Knott on Seismic Radiations. 
The position of the straight part and the angle which it subtends at 
the centre are obtained by consideration of the angle with which the outer 
curved part of the ray meets the spherical surface of radius 0*9. This 
angle might be called the angle of immergence into the nucleus of con- 
stant speed of propagation. For the rays which penetrate this nucleus we 
use the formulae already given between the limits x = 1 and x = 0*9 ; and 
then for the straight parts we use the simple formula for constant velocity. 
The important data are given in sufficient detail in the following table, 
which differs from the former table only because of the necessity of dis- 
criminating between the curved and straight parts of the rays when these 
exist. The immergence angle has the meaning already defined, and 
quantities which have to do with the curved and straight parts are marked 
with suffixes 1 and 2 respectively. 
Case II. v = 2445 J 1-06 — a? 2 through the outer shell of 
one-tenth the radius. 
Parameter 
<p. 
Arc. 
Transit time. 
Minimum 
radius 
x v 
Emergence 
angle 
e°. 
Inimer- 
gence 
angle 
i. 
Energy dis- 
tribution 
over surface 
defined 
by arc. 
20!°. 
20 2 °. 
2T r 
2T 2 . 
4 
1-7 
0-4 
0-999 
11-5 
8-03 
3 
6 
2-0 
•977 
42-4 
4596 
2 
17-9 
3-9 
•922 
60-7 
76-10 
1-8 
21-6 
4-5 
•9 
63-8 
80T0 
1*7 
14*2 
38*5 
3-5 
5'1 
•85 
65*4 
19-2 
82-65 
1*5 
10-5 
67-1 
3 
8-6 
•75 
68-4 
33-6 
86-49 
1 
6-7 
111*4 
2-5 
12-9 
•5 
75-8 
68-6 
94 
0-5 
2'6 
146-2 
2-4 
15-3 
•25 
83-0 
73-9 
98-5 
0 
2'3 
15-6 
90 
90 
100 
The whole arc in each case is 2d x + 20 2 , and the time of transit 2T X + 2T 9 . 
Drawing the time-graphs for these two cases and picking out the values 
for every 30° of arc, we get the following abridged table, in which Milne’s 
corrected values are added for the sake of comparison : — 
Transit Times. 
Arc. 
Case I. 
Case II. 
Milne. 
30° 
7*5 
5-7 
5-2 
60° 
11-9 
9-5 
9-8 
90° 
14-5 
13 
13T 
120° 
16-4 
15-6 
15-3 
150° 
17-6 
176 
17 
180° 
18 
17-9 
18 
