ON SEISMOLOGICAL INVESTIGATIONS. 13 
found, but greater in amount. As has been remarked above, the existence 
of a hill and valley in the curve, which compromise has obliterated, is 
quite a fair possibility. 
The question, however, whether the observations can be fitted to so 
considerable a hill and valley can only be answered after laborious 
re-reduction ; such examination as has been made is not unpromising. 
but is embarrassed by the uncertainties of clock error already referred 
to. A glance at the records, for instance, of 1913, January 27, will show 
the doubtful nature of the records near the epicentre. 
The explanation above suggested brings with it a number of questions. 
Firstly, why should PR; be specially prominent, compared, say, with 
PR, or PR,? The answer is that PR; happens to fall in a place where 
it can be mistaken for S, while the others do not. But the suggestion 
of a sensible focal depth necessitates the re-investigation of other 
reflected waves, especially of PR,. We notice two important points. 
Firstly, the wave which starts along EC reaches the surface as PR, 
at A=8°-6+17°-1=25°-7; and it might at first sight appear that 
we cannot have any PR, for a value of A less than this, for the arcs 
2A and 2B are both greater than 2C, as already remarked. But a wave 
starting along Ea reaches the surface after one reflection at 
Ayes aA A ee 
and from Table VII. we see that the sum of these quantities diminishes 
at first, though it ultimately increases. The minimum valve is given 
by the condition 
d¢=3dA, 
which leads to 
(3?—1) sin *¢=tan? C 
whence Oo Aa 
Within A = 24°, then, no PR, can be received. 
Now, the evidence is distinctly in favour of the existence of some 
inferior limit for A of this kind. Within A = 24° the records are few 
and discordant, and the lowest value of S — P, hitherto found for 
which PR, has been recorded is 204 seconds, corresponding to A = 18°, 
or a focal depth of, say, 45 miles. A more extended investigation of 
this point must, however, be deferred. 
The second point is that at the point C (where A=25°-7) PR, arrives 
not by means of two equal ares of 13°, but by unequal arcs of 8°-6 and 
17°-1. Hence the tabular computation of Table VI. becomes unsuitable. 
Using the adopted tables we should get for A=26° by equal ares of 
13°, 4 (S+P)—PR,=99 seconds, by ares of 8°-7 and 17°-3 4 (S+P)) 
=105 seconds. Hence the large negative values of O—C, at the head 
of Table IIT., should be still further increased ; and, moreover, when we 
deduce from them corrections to P the dividing factor is 1-5 instead of 
2-0, and the corrections apply to larger values of A, all of which changes 
emphasise the positive corrections to P for small values of A. As above 
remarked, however, EC does not give the minimum PR,, which is for 
A=24°, by arcs of 6° and of 18°, 4 (S+P)—PR,=107 seconds, the 
computation by equal ares giving 98 seconds. 
1918. © 
