176 Proceedings of the Royal Society of Edinburgh. [Sess. 
value of p, the quantities V(*1 2 ~P 2 )/ r are calculated and summed together 
in successive groups of seven, in accordance with Weddles Rule. For each 
case the range is from the value of rj corresponding to r equal to unity to 
the value of rj immediately above p. This leaves a final element to 
evaluate with zero as its limiting co-ordinate. The valuation is effected 
in much the same manner as in the case of the rays. Thus with 
Vi 2 = ^ r i ~ a \ K = a + P 2 \ 
where rj x relate to the upper limit, and r 0 , rj 0 or p to the lower limit, 
we easily find 
2 Jrj x 2 
By appropriately summing together these several integrations in each 
case, we obtain the values of the integral as tabulated in the seventh 
column of Table B (Appendix). It is obviously unnecessary to go beyond 
the vertex of each ray. 
The whole time T of propagation of the disturbance to each point is 
obtained as the sum of the corresponding numbers in columns 7 and 8, 
and is entered in column 9. 
Thus the time of transit is found to every calculated point on each ray. 
The next step is to obtain by interpolation the points on the rays which 
correspond to successive chosen equal intervals of time. 
The times chosen for the Primary waves were eight in all, from 200 
to 900 seconds inclusive at intervals of 100 seconds; and for the Secondary 
waves seven, from 400 seconds to 1600 seconds inclusive at intervals of 
200 seconds. 
Inspection of the simultaneous march of the values of T, 0, and y, or of 
the graphs giving T in terms of d or of y, shows that the relation is 
approximately linear, with slight sinuosities. It was therefore deemed 
sufficiently accurate to calculate the 0 and y in any case for the time 100?i 
(n an integer) by simple interpolation between the sets of numbers corre- 
sponding to the times lying nearest to 100?^ on each side of jt. When 
these interpolated values of 0 and y are found, the values of x and of r 
follow in accordance with the formulae 
x — y cotan 0 , r — y cosec 0. 
These interpolated values are arranged in Table C (Appendix), tabulated 
in columns under the appropriate times, and in rows according to the 
associated seismic rays. The corresponding isochronous points along the 
