175 
1918-19.] The Propagation of Earthquake Waves. 
For convenience of showing graphically the forms of these rays, the 
positions have been calculated also in Cartesian co-ordinates, the origin 
being at the earth’s centre and the cc-axis being drawn through the epi- 
centre. In the figure the £C-axis is drawn vertically downwards and the 
y - axis horizontally to the left. Only a little more than a quadrant of a 
diametral plane of the earth is shown. 
In Table B the first column contains the name and number of the ray, 
the value of the parameter p, and the initial value <p 0 between the direction 
of the ray and the epicentral radius. 
The second, third, and fourth columns give the polar . co-ordinates, the 
angle being expressed both in radians and in degrees. 
The fifth and sixth columns contain the co-ordinates, x = r cosd, 
y=r sin 0, used in plotting the representative curves in fig. 6. In this 
figure the rays for the Primary waves only are drawn in. A simple 
comparison of the corresponding co-ordinates in the two types of wave 
shows that the Secondary rays differ very slightly from the corre- 
sponding Primary rays. To have drawn them in also would have 
unnecessarily confused the figure. 
To complete the representation it is useful to indicate the form of the 
wave-front as well as of each ray. The wave-front is obviously an iso- 
chronic surface or surface of equal times of transmission from the source of 
the disturbance. It cuts the diametral plane in a curve whose equation is 
given by equation (3) above, namely, 
when T is put equal to a constant. This curve will cut the rays 
orthogonally. 
As a first step towards construction of the wave-front in various 
positions we calculate from the data now to hand the times of passage of 
the disturbance through the points already determined on each seismic 
ray. The expression for the time consists of two parts, T = T 1 + T 2 , where 
* t J and 
The latter is found at once by multiplying the 6 (in radians) of any 
point on a chosen ray by the value of jp which belongs to that ray. The 
values obtained in this way are tabulated in the eighth column of Table B. 
The value of T must be calculated by quadratures from the quantities 
r and r) 2 = (r/v) 2 tabulated in Table VI. 
The method is clear. For each ray, and therefore for the appropriate 
