FINITE FOCAL DEPTH REVEALED BY SEISMOMETERS. 
4‘J 
A number of novel consequences with regard to reflexion follow if we admit such a 
great depth of focus, so that before showing how a time curve can be deduced from the 
Pulkovo observed angles e, we may within advantage consider what is to be expected 
in a uniform earth, as thereby we shall be in a better position to deal with what may 
be inferred from the observed data. 
We shall select for discussion a uniform earth R = 6370 km., depth of focus = 0-2 R, 
with Yj/Va having the theoretical ratio \/3, while V x is taken as 10 km./sec. These 
numbers are taken partly for convenience of calculation and partly to get as near as 
possible to the actual case. 
The times for P and S may be computed for different epicentral distances from the 
trigonometrical formula for the paths traversed. The results for epicentral distances 
from 0 degree up to 180 degrees are shown in fig. 1. We may note that the point of 
inflexion on the time curve is very ill-defined, and might easily escape detection by 
direct observations of the time. 
The direct measurement of the angle of emergence is, however, fairly precise, and 
from such measurements we can, in fact, calculate the time curve more accurately than 
we can determine it by direct observations of the time. 
We may further note that the time increases but slowly for the first 1000 km., and 
since the angle of impingence for this region is not far short of 90 degrees, the true P 
might escape observation by horizontal seismographs, since the ground motion is almost 
entirely vertical. 
Passing to waves reflected at the surface, we consider first waves which maintain their 
longitudinal character throughout. We may call them PR . . . PR„ waves. The 
simplest way of computing is to choose the point at which the first reflexion takes place 
and then calculate the epicentral distance to the final point of emergence (the station). 
The results are shown in figs. 2 and 3, where, in order to lead up to the large depth 
of focus, we have first shown the effect for depth 0-01 R (about 64 km.). We find that 
for this depth we cannot get a reflexion at all until A is about 23 degrees, and that for 
A > 23 degrees there are two PR w'aves, the reflexion taking place at two different 
points, and they occur at different times. For depth as small as 0 • 01 R we see that we 
can proceed to PR re , where n is moderately large. 
When we pass to a focal depth 0 • 2 R we find that the smallest epicentral distance for 
which we can get PR is 103 degrees, and beyond this we have two PR’s. But when we 
try to calculate the PR 2 we find that the least epicentral distance is over 180 degrees, and 
so we stop. The corresponding times for PR X are calculated and shown in fig. 1, and 
we note that the earlier arrival refers to the PR X which is reflected at the smaller 
distance from the epicentre. Figs. 2 and 3 are equally applicable to S waves in which 
the vibration is at right angles to the diametral plane through focus and station. The 
times for the SR waves are shown in fig. 1. 
We consider next waves which undergo change from longitudinal to transversal, or 
vice versa, on reflexion. PS or SP, which for a very shallow focus would arrive together 
