1909-10.] 
Seismic Radiations. 
37 
a very beautiful theorem regarding the curvature of the rays of propaga- 
tion as they cross the surfaces of equal velocity. They build up the final 
solution by supposing the earth to consist of a central core of constant 
velocity surrounded by two spherical shells, within each of which the rays 
have constant curvature. The facts of observation are then found to be 
satisfied on the assumption that the speed of propagation of each type of 
earthquake tremor is nearly constant throughout the interior of the earth 
to within 1500 kilometres of the surface, falling off according to a definite 
law from this depth upwards. In other words, and more explicitly, the 
elastic waves of highest speed are transmitted through a core of radius equal 
to three-quarters of the earth’s radius with a speed of 12*9 kilometres per 
second, and through the remaining layer of thickness equal to one quarter 
of the same radius with a speed which falls off from this value at the inner 
surface to 7T7 kilometres per second at the outer surface. The correspond- 
ing quantities for the second type of tremors are 6*75 and 4 kilometres per 
second, but the radius of the core of constant velocity is somewhat greater. 
In a recent publication Wiechert has slightly modified these conclusions. 
My own results are broadly similar to these, although differing in numerical 
details. Compare the second paragraph on page 23, and the general dis- 
cussion in the first paper. Wiechert and Zoeppritz also discuss, in an 
interesting fashion, the commingling of disturbances which have reached a 
given locality by one continuous path, or by two paths with one reflexion, 
or by three successive paths with two reflexions, and so on. There is no 
doubt that such reflexions will take place. In most cases, however, the 
loss of energy during reflexion within the heterogeneous crust of the earth 
will tend to make the later coming disturbances which have experienced 
such reflexions comparatively feeble. Their presence seems to have been 
recognised in certain seismograms analysed by Wiechert and Zoeppritz. 
{Issued separately December 23 , 1909 .) 
