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II. The Problem of Finite Focal Depth revealed by Seismometers. 
By George W. Walker, A.R.C.Se., M.A., F.R.S., formerly Fellotv of 
Trinity College, Cambridge. 
Received March 25,—Read May 12, 1921. 
The results discussed in this paper were obtained about five years ago. Except for a 
brief reference in ‘ B.A. Reports,’ 1917 (“ Seismology ”) they have not been published. 
There were two reasons for this delay : (1) additional data were desired in a matter of 
somewhat critical importance in the measured properties of the earth ; (2) my official 
duties left little spare time for the pursuit of a purely scientific branch of seismology 
which required a good deal of tentative numerical computation. 
At the present date it appears that one must abandon all hope that additional results 
Avhich were expected from Russian observatories can be obtained. Moreover, it appears 
very doubtful if relevant data from any of the Allied countries can be expected for some 
years to come. Accordingly, publication of the results so far obtained now seems 
desirable, and may serve to show how urgent is the need for the equipment of a few 
seismological observatories capable of obtaining the data that are wanted. 
A brief introduction to the problem is necessary, although it covers ground which is 
fairly familiar to those interested in seismometry. 
If we have complete data giving the brachistochronic time for a seismic ray (say the 
P wave) to travel from a given point on the earth’s surface to any other point on the 
surface, it is possible to calculate the way in which the speed of propagation of the ray 
varies with the depth. Two methods are open : (1) we may use the differential equation 
for the path of the ray, or (2) we may use the integral equation obtained from this. 
Both methods correctly carried out must give the same result, and it is merely a question 
of convenience which one adopts. By using a comparatively rough graphical method 
based on (1), Wiechert and Zoppritz showed, about 14 years ago, from their accumulated 
data that the speed for the P wave increases from 7-17 km./sec. at the surface to 12-7 
km./sec. at a depth of 1500 km., while from 1500 km. to over 3000 km. depth the speed 
increases but slightly. No data are available for investigating greater depths. 
More recently Knott Roy. Soc. Proc.,’ 1918-1919) applied the second method to 
the same data as was used by Zoppritz, and his results do not differ materially from those 
of the earlier and rougher method, 
A very important supposition has to be made, however, before either of these methods 
can be applied. That is, that the true focus is either at the surface or so near the surface 
that a small correction can be made for it. If, however, the focus is at a considerable 
VOL. COXXII, -A o95, H [Published August 5, 1921, 
