184 Proceedings of the Royal Society of Edinburgh. [Bess. 
Secondary wave another calls the Primary, while others doubt if either 
is distinguishable ? On the other hand, the Large Surface waves go right 
round the earth; and in many seismograms certain disturbances which 
have travelled round the greater arc (27 t — 2a) can be identified as corre- 
sponding in time of start with disturbances which have travelled round 
the shorter arc 2a. The surface layers of the earth are therefore able to 
transmit disturbances to distances exceeding the earth’s circumference, 
whereas the Primary and Secondary waves transmitted through the 
earth seem to be unrecognisable at points distant more than 110° from 
the epicentre. 
In 1906, in a paper published in the Quarterly Journal of the Geological 
Society (vol. Ixii), Mr R. D. Oldham put forward the view that the elastic 
properties of the earth underwent a marked change at a certain depth 
below the surface. This view was based upon the seismological evidence 
then available; and he concluded that there was a central nucleus of 
radius about four-tenths of the earth’s radius across which the Secondary 
waves were transmitted with much smaller velocity than through the 
parts of the earth outside the nucleus. Certain difficulties in accepting 
this conclusion were pointed out by Wiechert and Zoppritz ; * but although 
some details of Oldham’s speculation may be criticised, there is no doubt 
that the data now to hand support his main contention that the nucleus 
of radius 0 4 differs physically from the surrounding sheik 
In the calculations given above I have worked from the tables for P 
and S given by Turner in the British Association Reports ; but these are 
admittedly hypothetical for arcual distances greater than 110°. As may 
be seen from Tables IV and V, the rays which correspond to this arcual 
distance reach a depth 3400 km. from the earth’s centre, that is, almost 
exactly half-way down. Long before this depth is reached, however, the 
velocities of propagation of both the Primary and Secondary waves have 
ceased to increase with the depth. The remarkably steady increase in 
both velocities down to these critical depths shows that the moduli k + 4^/3 
and n increase with the depth more rapidly than the density. Then 
apparently at a depth equal to 0*30 of the earth’s radius the ratio njp 
becomes steady or passes slowly through a maximum, whereas the ratio 
( k+4>n/S)/p is still on the increase, and continues increasing till the depth 
036 is reached. Thereafter it becomes steady or passes slowly through 
a maximum. 
There is therefore a change in the manner in which (Aj + 4%/3) and n 
* See their first paper on “ Erdbebenwellen,” Gottingen Nachrichten , mathem.-phys. 
Klasse , 1907, p. 516. 
