46 
MR. GEORGE W. WALKER ON THE PROBLEM OF 
and unknown depth both methods fail, as is obvious from the consideration that, since 
all the rays we can observe must have passed out from the focus, we have no data for 
the comparatively large range of distance AB on the surface for which brachistochronic 
rays would not penetrate as deep as does the observed seismic ray. In fact, another 
unknown element enters into the connexion between the observed time curve and the 
variation of speed with depth. 
A finite depth of focus implies a minimum angle of emergence at some point on the 
earth’s surface and a point of inflexion on the time curve, and vice versa. Now, in 
considering Zoppritz’s accepted time curve for P, we recognize that up to A — 1000 km. 
the curve is probably hypothetical, but from 1000 km. to 13,000 km. there is no indication 
of a point of inflexion. It is not until we come to consider Galitzin’s direct measure¬ 
ments of the angle of emergence that we are confronted with a most marked minimum 
angle of emergence near A = 4000 km., implying a point of inflexion on the time curve 
and a very considerable depth of focus. As Galitzin’s observations form the whole 
basis of this paper, they are reproduced here (although published elsewhere), as the 
reader may desire to have them convenient for direct reference. 
Table I. 
Epicentra] 
distance. 
A in kilometres. 
For P. 
e from time 
curve. 
e computed. 
e observed at 
Pulkovo. 
0 
O. 
0 
O 
22 
O 
500 
11 
23 
— 
1,000 
21 
27 
— 
1,500 
30 
32 
— 
2,000 
37 
37 
— 
2,500 
44 
42 
48 
3,000 
49 
47 
44 
3,500 
53 
52 
43 
4,000 
57 
54 
42 
4,500 
60 
58 
43 
5,000 
63 
60 
44 
5,500 
65 
62 
46 
6,000 
65 
62 
48 
6,500 
65 
63 
51 
7,000 
65 
63 
54 
7,500 
66 
63 
58 
8,000 
66 
64 
62 
8,500 
67 
64 
65 
9,000 
67 
65 
67 
9,500 
68 
66 
68 
10,000 
69 
67 
70 
10,500 
70 
67 
71 
11,000 
70 
68 
72 
11,500 
71 
69 
72 
12,000 
72 
70 
73 
12,500 
73 
71 
73 
13,000 
74 
72 
74 
