224 Proceedings of the Boya.l Society of Edinburgh. [Sess. 
The values for Case II. agree very well with Milne’s corrected values. 
That is to say — 
The observed facts of seismic radiation can be co-ordinated 
on the assumption that throughout all but a comparatively thin 
crust of the earth the elastic waves of highest speed are trans- 
mitted with a speed of 12*23 kilometres per second, and that 
within this crust, of thickness equal to one-tenth the radius, 
the speed diminishes from value 12*23 kilometres per second 
at the inner surface to 6 kilometres per second at the outer 
surface. 
If this wave of highest speed be a compressible wave with longitudinal 
vibrations, the cosine of the angle of emergence of the ray will give the 
ratio of the magnitude of the horizontal motion to the whole amplitude. Now, 
most of the observations have been obtained with instruments recording 
horizontal motion only, and comparatively few with instruments recording 
vertical motion. But at great arcual distances from the epicentre the angle 
of emergence increases towards 90°, with corresponding diminution in the 
value of the cosine, and the horizontal component of the displacement will 
be very small, ultimately vanishing at the antipodal point. At such great 
distances there will consequently be a tendency for the preliminary tremors, 
assumed to be mainly compressional, to be retarded in their arrival. As a 
matter of fact, it is extremely difficult at times to determine the exact 
moment at which the tremors begin on records which have been obtained 
at stations further distant than 100° from the epicentre. 
According to the theory here developed, we may obtain the times for 
the second phase of the preliminary tremors by increasing the times for 
the first phase in the ratio of 31*3 to 18, assuming for the purpose Benndorf’s 
corrected values. The results are as follows : — 
Times of Transit of Second Preliminary Tremors. 
Arc. 
Case I. 
Case II. 
Benndorff. 
30° 
13 
9-9 
11-9 
60 
20-7, 
16-5 
17*5 
90 
25-2 
22*6 
23-8 
120 
28-5 
271 
27-5 
150 
30-6 
30*6 
30-5 
180 
31-3 
311 
31*3 
The agreement here is not quite so good as in the case of the first phase. 
It could be improved by slightly increasing the depth of the shell through 
