FINITE FOCAL DEPTH REVEALED BY SEISMOMETERS. 
55 
A — 2J X + J 2 and A = 2zl 2 + A 1} and there is a check on this by means of the 
measured e for the two waves. Further, if I, and I 2 are known integrals for A, A 1 
and d 2 and TV and T 2 , the observed time intervals between P and the two PR waves, 
we have 
Tj = 2A -f- (2l x —p I 2 I)/V 2 
and 
T 2 = 2A + (2L + P - I)/V 2 , 
which theoretically suffice to determine A and V 2 . 
20000, 
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Ep/central Distance of e , Refl ex/on 
kms. 
Fig. 8. 
It is manifestly a matter of great importance in seismology to settle whether the large 
depth of focus suggested by the Pulkovo observations can be maintained. 
If confirmation is obtained by the research suggested above, the problem of deducing 
the focal depth and the velocity at any depth must be attacked anew. The two things 
are related, and it looks as if the process of analysis would be largely tentative. In any 
case, it is clear that the speed at any depth cannot be uniquely determined until the 
focal depth is fixed. But one might hazard a guess that a large depth of focus would 
probably lead to a smaller variation of speed with depth than has been deduced by 
Zoppritz. 
An investigation on S waves might proceed on similar lines, although the relation 
between the angle of impingence and the apparent angle of emergence is more complex 
than for P waves ; c/. ‘ Phil. Trans.,’ lx. ante, p. 378. 
The equations are 
cos e = V 2 , 
2 dA ’ 
tan e 
V 2 sin e' tan 2e 
Y 1 sin e 
where cos e' — ^ cos e . 
Vo 
