12 REPORTS ON THE STATE OF SCIENCE.—!918. 
fact, there can be no PR; when A is much less than 94° (for the actual 
limit see below), which accords with the facts of the quake of 1913, 
March 14, from which the above figures were deduced in the 21st Report, 
if we exclude a doubtful Pulkovo observation. This limiting value for 
A gives us in fact the are 17°-1, and consequently the depth of focus. 
Tf KC be a straight line we find EK = 0-011 of the radius; say 44 miles 
or 70 km. These figures apply only to this particular earthquake, and 
will also require modification if the path cC is curved; but they give 
the order of quantity suggested. 
As we pass to greater values of A the wave must start along Ea or EB. 
If it starts along Ka, the total length of path will be less than 5*5aA, and 
cannot be so small as 50 aA. If it starts along EB the length will exceed 
5.5bB or 5°5aA. 
Thus A=110° may be reached in two ways: either by (let us say for 
illustration) 5 reflections or 6. The times of transmission would be (using 
column ‘ New’ of Table VI.) :— 
5 x time for 22° = 5 x 304s. = 1520 seconds, 
6 x time for 18:3° = 6 x 266 = 1596 seconds, 
and since we observe the earliest disturbance we fix attention on Ea and 
neglect EB. 
Assuming the paths of the waves to be straight lines as in the figure, 
let cC subtend an angle 2C at the centre; and let aA, inclined to cC at 
an angle ¢, subtend an angle 2A at the centre. Then 
cos A=cos C cos ¢=cos 8°'55 cos d 
arc Ka=A—d¢. 
Tn Table VII. are given, for various values of 4¢, first the arcs 2A 
and A—¢, then the whole arcs 10A+(A—¢); then the estimated 
times for Y from the figures quoted above from the 21st Report. From 
these we subtract the time for the arc A—¢, which we can estimate only 
approximately by taking it as 
are in degrees x 14-9s. 
The remainder, divided by 5, gives the time for the are 2A, below 
which is subjoined the present tabular value and the necessary correction, 
followed by the correction deduced from PR, in Table VI. 
TABLE VII. 
° ° o ° ° 
= 0-0 3:0 5-9 6:0 7-0 
2A . : = 17-1 18:0 19-8 20°8 22-0 
A—9 : = 8-6 6:0 49 4-4 4:0 
Whole are = 94:0 96:0 103-9 108-4 114-0 
8. Ss. 5. s. 8. 
Whole time = 1410 1430 1485 1512 1548 
Time of (A—o) = 128 89 73 66 60 
Time of 2A F = 256 268 282 289 298 
Tables é = 246 257 279 291 305 
Correction = +10 +11, +3 a —7 
Table VI. = + 6 + 5 +3 +41 —1 
The last two lines are not very different, and we notice that the cor- 
rections now suggested are generally similar in form to those formerly 
