382 
MR. GEORGE AY. AVALKER ON 
We have not introduced dispersion, but if this exists (as most probably it does) it 
will give rise to a “ trail ” with all classes of disturbance, not confined to the special 
range we have just considered, in a manner analogous to a pressure disturbance 
travelling over deep water (see Lamb, ‘ Hydrodynamics ’). 
The angle of impingence may be calculated from the time curve by means of the 
formula due to Wiechert, 
cos e = Y 0 dT/dA, 
where dT/dA is the slope of the time curve at epicentral distance A and V 0 is the 
surface value of the speed of the corresponding wave whether longitudinal or 
transversal. The results are given in Table III. along with the computed value of e 
for longitudinal waves and the value as directly observed at Pulkovo by measurement 
of the horizontal and vertical disturbance. 
We now consider the magnitude of the first impulse P. Fig. 2 shows that for a 
given value of the incident longitudinal disturbance the horizontal motion of the 
ground exceeds the vertical until the angle of impingence is about 47°, where the 
two become equal. For greater values of e the vertical motion exceeds the horizontal. 
Further, H attains its maximum for e = 27° and thereafter diminishes, which V 
continues to increase right up to 90°. 
Thus quite apart from the falling off of amplitude with distance on account of 
spherical divergence, we should expect H to diminish in importance as we pass to 
great distances, while V, being relatively small for small distances, becomes equal to 
H for A about 2800 km., and for greater distances V exceeds H, the ratio being 
about 2 at 7000 km. and still greater as the distance increases. 
This is in general agreement with observation both at Pulkovo and Eskdalemuir, 
where it has been observed that at about 2500 km. V is about the same magnitude 
as H, while at 8000 km. or more V is much greater than H. 
Actual numbers were published by Galitzin (‘ Lectures on Seismometry ’) and 
are included in Table III., wherein c observed is given by tan e = Y/H, Y and H 
being directly observed. 
The agreement of theory and experiment is good at about 3000 km. and again at 
8500 km., and beyond, but a discordant feature is shown in the intermediate range. 
c as calculated continues to increase, but e as actually observed falls to a minimum 
at 4000 km. substantially less than the calculated value. 
Now the general effect of the crust might be expected to make e greater than the 
value calculated from the time curves. It is extremely difficult to account for the 
discrepancy actually observed. In view of the exhaustive tests applied by Galitzin 
to his instruments, I do not think the discrepancy can be attributed to instrumental 
error. Many more observations have since been made at Pulkovo, and the results 
will be awaited with interest. We shall also require observations at other stations 
before we can decide whether the effect is peculiar to Pulkovo or characteristic of 
