ON SEISMOLOGICAL INVESTIGATIONS. 65 
station ; ¢ is the effect of the displacement (8) on P or §, as the case may 
be, at the distance of the receiving station ; and c is a constant depending 
on the position of Pulkovo, or other station from which the epicentre is 
determined. 
(6) If the velocity of transmission varies with the azimuth, then, if the 
velocity in azimuth A is not the same as in azimuth A + 180°, there will 
be a first-order harmonic which will be mixed up with that just written, 
due to the error in position of epicentre ; and it may be difficult to separate 
the two. If, however, the velocity is the same for A and A + 180°, then 
we may look for a second-order harmonic to represent the variation. It 
will be seen from what follows that there are no trustworthy indications 
of such terms from the material now discussed. The material is insufficient 
to pronounce definitely against the existence of such terms, especially 
with small coefficients ; but it is apparently sufficient to discredit any 
large term of the kind. For instance, Milne suggested a velocity N. 
and §. sensibly less, in the case of the large waves, from the velocity 
Ki. and W. (Eighteenth Report, § v). No such difference can be detected 
in the velocities for P and 8. 
We will first give in some detail the results for a single earthquake, 
that of 1915, January 11, adopted epicentre 6° N., 117° E. The residuals 
for P, when corrected for distance from epicentre as in Section IV., and 
arranged in azimuth measured from the N. point round the epicentre in 
the direction N., K., 8., W., are as shown in Table VIII. 
We see at a glance the better distribution of the Milne pendulums ; 
most of the modern pendulums are in Europe and appear in the same 
azimuth-class 300°—330°. Were it not for the Milne instruments we 
should have very scanty material for an azimuth discussion; and yet 
this is one of the most favourable cases. The inferiority of the Milne 
instrument suggests giving a smaller weight to its records, but it will be 
seen that we should gain very little thereby. Taking the simple means 
as in the last column and filling in vacant terms by simple interpolation 
(in brackets), we can make a very rough harmonic analysis, obtaining 
—1-6 + 7-5 cos (A—330°) + 2-7 cos 2 (A — 70°). 
Treating the 8 observations in the same way, we get Table IX. 
The material for discussion in azimuth is even more scanty and un- 
certain than before ; but, analysing it for what it is worth, we get 
—1-2 + 8-0 cos (A — 332°) + 4-7 cos 2 (A — 177°). 
__ Now, considering the nature of the material and of the process used, 
It is somewhat remarkable that the results from P and § should accord 
so well in indicating a correction to the epicentre. The direction is in 
azimuth 331° say, and as the azimuth of Pulkovo is 330°, it is pretty 
clear that the estimated A for Pulkovo is in error, owing doubtless to 
the errors of the tables. The amount of displacement is not so easy to 
assess. In the above simple process we have treated all stations, at 
whatever distance from the epicentre, alike. A displacement of the 
epicentre of 1° will, however, alter the times of arrival of P by 16 s. near 
the epicentre, by 5} s. at 90°, and by less still at greater distances. Never- 
a on calculating the alterations for the actual distances, the mean 
14. F 
