FINITE FOCAL DEPTH REVEALED BY SEISMOMETERS. 
53 
From the formulae, p. 3, we have 
V ~ = {J(l - sin e)Y 
so that we can at once calculate V 9 -r— as a function of A from the numbers in fig. 6, 
dA 
The results are shown graphically in fig. 7. Graphical integration of the curve now 
gives us 
I = f IK 1 — sin e)} h dA 
as a function of A, whence 
I 
T = A + — , where A is a constant, 
' 2 
gives T as a function of A. 
Table II. gives the value of the integral I for different epicentral distances. Since 
Zoppritz’s time curve meets with general acceptance for the purpose of determining 
epicentres, we first seek to see how far we can fit our new time curve with Zoppritz’s. 
Taking first Zoppritz’s value for V 2 , viz., 4-01 km./sec., we find that the two curves fit 
over the range 6000 km. to 12,000 km. with a discrepancy + 11 seconds, but the discrepancy 
rises to 100 seconds at 3000 km. Taking a larger V 2 one can fit the curves together over 
various ranges. For example, taking V 2 = 5-63 km./sec. we get the values shown in 
Table II., where over the range 3500 km. to 8000 km. the discrepancy ranges through 
only ± 5 secs., an error we might quite well admit. But large differences must arise 
towards the epicentre, for on the present view A must be a substantial number repre¬ 
senting thn time from focus to epicentre. No special significance is to be attached to 
the above calculation beyond showing that in the middle range of distances we need 
not make any large departure from Zoppritz’s time curve. 
VOL. OCXXII.-A 
I 
