18 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
would Still be expecting too much of human fallibility to suppose 
that data of sufficient accuracy could ever be obtained. 
There is, however, a method which is dependent, not upon time 
data, but upon observations of intensity, which seems to offer the 
means of computing the desired quantity. It is well known that 
the intensity or energy per unit area of wave front diminishes as 
the wave moves outwards from the centrum. Like all radiant 
energy, it must be subject to the law of variation inversely as the 
square of the distance. If the elasticity of the medium were perfect 
and its density uniform the law would be rigorous. As a matter of 
fact, it is not so ; but, on the other hand, we are assured that the 
elasticity cannot be very imperfect, since if it were so the propaga¬ 
tion of impulses to veiy great distances would be impossible, and 
the waves would soon be extinguished in work done upon the me¬ 
dium itself Nor is there reason to suppose that the variations* of 
density are extreme. Thus, while the law of inverse squares may 
be in some measure impaired, it may still be assumed as an approxi¬ 
mate expression of the reality. 
If, then, we were able to form a just estimate of the rate of varia¬ 
tion of the intensity along lines radiating from the epicentrum, we 
should have the means of computing the depth of the focus. Thus, 
if O be the focus and E the epicentrum and P any point at a dis¬ 
tance from the epicentrum, the intensity at P would be inversely 
proportional to the square of O P. Calling E P = a;, O P = r, and 
O E = g, and designating by a the intensity at unit distance and 
by y the intensity at any other distance x, we have the equation: 
a a 
y 
This equation corresponds to a curve whose figure is approxi- 
