392 
MR. GEORGE W. WALKER ON 
without considering the other circumstances that may lead to differences in the 
relative magnitude of P and S and their reflexions. 
We may best illustrate the possibilities by taking the theoretical case 8500 km., 
which corresponds closely to fig. 5. The theoretical angle of impingence is 67°, and 
we find that the PS or SP wave divides the arc so that the longitudinal waves 
correspond to 2000 km. angle e — 37° and the transversal to 6500 km. angle e = 64°, 
while PS arrives 40 seconds after S. 
Taking unit amplitude in each case, we have the following relative values for 
H and Y :— 
H. 
Y. 
p. 
-0-86 
- 1-82 
PS. 
+ 1-9 
-0-94 
s. 
- 1-8 
+ 0-82 
SP. 
- 1-4 
- 1-06 
The signs are important. The absolute sign of V is determined by the actual 
record and may be + or — for either P or S. PS and SP theoretically arrive 
together and interfere, but it is likely that they may not coincide in time exactly 
in practice. However that may be, we see that large relative changes may be 
expected. 
If V is of the same sign for P and S we might have a small V in the Wechsel- 
wellen and a large H, while if V is of opposite signs for P and S, the reverse holds. 
Theoretically, we have the means of separating the two constituents of this 
phenomenon by means of the vertical component record if the angles of impingence 
are known. 
Thus if A and B are the proportions of PS and SP present at the station, we have 
K x A + K 2 B = H, K 3 A - K 4 B = Y, 
where H and V are observed at the station, and K X ...K 4 are known numerical 
factors depending only on the angles of impingence and independent of any other 
circumstance. 
We may have a wave twice reflected, viz., PPS. In the present case it would 
divide the arc into two of 1500 km., corresponding to longitudinal waves e = 30°, 
and one of 5500 km., corresponding to transversal waves e = 63°. It should arrive 
28 seconds after PS. 
We might carry the argument to multiple reflexions until the arc corresponding 
to transversal waves is that for which e reaches the critical value 56°. Beyond this 
the argument must cease. Turning to the case fig. 5, we recognise disturbances 
following after S, but find it difficult to regard these as Wechselwellen because the 
