DETERMINATION OF EPICENTRE AND FOCUS 67 
between B and A, and C and A, w, the velocity of propagation 
of the disturbance, and y the unknown time from epicentre to 
A. We may then by trial construct the circles of radii pro- 
portional to v7, y+), y +g with centres at A, B, C which inter- 
sect in a point, and we then get the position of the epicentre 
and also the time y from A to X. The above equations are 
approximate and do not take account of the depth of focus. 
But as we shall show in a little if the distances are within from 
200 to 400 km., the error introduced in the times is less than 
half a second even for a focus 40 km. deep, and the observed 
times are not accurate to this extent. The time y is then 
the time from A to the focus or to the epicentre, to less 
than half a second, but we must be careful to observe that the 
time from focus to epicentre is not zero. For the formule 
become inaccurate beyond the range given. 
Having obtained the epicentre we may now set out the 
curves giving P and S as a function of the distance J, and if 
we accept the time of occurrence at the focus given by deduct- 
ing the time y from the time at A, we complete our time curve 
giving the interval of time from focus to station as a function 
of the arc from epicentre to station. We may not, however, 
exterpolate the curve to points quite close to the epicentre, 
until we know the depth of the focus. 
The curves we have obtained are still time curves depend- 
ing on the depth of focus. There is a range of several hundred 
kilometres within which the influence of depth is extremely 
small, but for shorter distances the influence of depth is con- 
siderable and again for greater distances the error may amount 
to a few seconds. 
The curve cannot be freed from the effect of depth and 
so prepared for theoretical investigation unless we know the 
depth of focus or have observations sufficiently near the epi- 
centre to determine it. Zoppritz (l.c.) proposed the following 
method of correcting the time curves when the depth & has been 
obtained. Assuming that the path (fig. 13) is symmetrical we 
may prolong the path SF backwards to meet the earth’s surface 
at O, and the angle EOF = eis equal to the angle of emergence 
at the station. Thus OE=EF cot e=4 cot e and the time to 
5 * 
