ON SEISMOLOGICAL INVESTIGATIONS. 13 
™~ [The following note was received after the rest of the Report had been 
sent to press. ] 
Focal Depth and the Time Curve. By Dr. G. W. Water, F.R.S. 
Assuming that P, the first impulse on a seismogram, corresponds to a 
longitudinal wave from the focus of an earthquake, the slope of the time 
curve for P asa function of the epicentral distance Ais connected with the 
apparent angle of emergence é by the well-known relation 
GE tle { 1—sin é \ 4 
INTEL Oe ey ee 
V, being the speed of transversal waves at the surface. 
é has been directly measured by Galitzin at Pulkovo for A from 2,500 
kms. to 13,000 kms., and the results differ markedly from the values of 2 
calculated from Zoppritz’s time curve for P. Galitzin finds a clear 
minimum of 42° for é at A =4,000 kms., whereas no minimum is indicated 
in the calculated values of é@ (cf. ‘ Modern Seismology,’ p. 54). 
Further observations are required before we can regard Galitzin’s 
results as characteristic of the whole earth, but I think it will be difficult 
to explain these results as peculiar to Pulkovo. 
It is important to see how far we can reconcile these conflicting results. 
By graphical integration of the observed values of @, we get the time 
curve,and using Zoppritz’s value of V, I find that the two curves can be 
fitted from 6,000 kms. to 12,000 kms. with a time discrepancy of +11 
seconds. The discrepancy would, however, reach 100s. at 3,000 kms. 
Using a larger value of V, we can fit the curves from 3,500 kms. to 8,000 
kms., with a discrepancy of only +5 sec., but the discrepancy mounts up 
beyond those limits of distance. It is not yet possible to decide what com- 
promise is most reasonable. We may note, however, that considerable 
discrepancy may be allowed for distances < 3,000 kms., as soon as we 
admit finite depth of focus. 
Kovesligethy has shown the connection that exists between a minimum 
angle of emergence and focal depth, and the obvious inference from 
Galitzin’s results is that the focal depth is about 1,300 kms., or even a little 
more. 
This a very startling result, being 10 times the greatest estimate of 
depth hitherto given. Yet there appears no escape from the conclusion if 
we accept Galitzin’s results, and it 1s remarkable that this depth is about 
the same as the depth of Wiechert’s layer of discontinuity. 
If such a depth of focus is correct, the whole question of reflexions has 
to be re-examined. As a qualitative guide to this, I have considered a 
uniform earth with focal depth 0-2 of the earth’s radius taking V,/V.=W 38. 
Some remarkable results follow, which I can indicate but briefly. 
(1) Surface reflexion of waves either entirely longitudinal or entirely 
transversal over their whole path cannot occur till A =103°, and beyond 
this there are two paths for a once-reflected wave. There are no paths for 
a twice- or multiply-reflected wave. I suggest the possible association of 
this with the ambiguous character of § at 90°, noted by Professor Turner. 
(2) PS and SP waves are no longer coincident in point of time. PS 
does not occur until A=149°, and beyond this there are two possible 
