180 Proceedings of the Royal Society of Edinburgh. [Sess. 
same as that used in my earlier paper ( Proc . Roy. Soc. Edin., vol. xxviii, 
pp. 228-9). 
Let the figure represent a diametral section o£ the earth through the 
epicentre E, and let EP be a seismic ray emerging at the arcual distance 
EP. If E p is the tangent to the ray at E, the straight line Ep represents 
the course of the ray if the speed of propagation of the seismic disturbance 
had been the same at all depths. The cone traced out by all lines Ep 
which make the same angle with the radius OE cuts the sphere in a small 
circle of which p may be taken as the representative point. The arc EPp 
will then represent that part of the spherical surface whose ratio to the 
E 
whole sphere gives the proportion of energy which falls on the surface 
represented by the arc EP. 
Now the area of the spherical surface represented by the arc EPp is 
proportional to 1+ cos 20, where 0 is the angle OEp. This divided by % 
the value when 0 = 0, represents the fraction of energy which, radiating 
outwards from E, is finally distributed over the surface defined by the arc 
EP. Also the area of this surface in relation to the area of the whole 
spherical surface is |(1 — cos 2a). 
These various connected ratios are laid down in the table on p. 181, 
where 2a is the arcual distance of the ray from epicentre to point of 
emergence, and 0 the angle between the radius and the initial direction 
of the ray. The so-called emergence angle is equal to 90° — 0. 
Each number in column E ( = -|(1 -}- cos 20)) gives the fraction of the 
original energy which emerges over the spherical cap whose arcual radius 
measured from the epicentre has the value 2 a ; and the area of the 
spherical cap is given in the column A ( = ^(1 — cos 2«)). The differences, 
<5E, give the energies associated with the successive zones as we pass from 
