578 Proceedings of Royal Society of Edinburgh. [sess. 
larger waves are propagated round the crust, and not through the 
interior of the earth; hut this supposition seems to lead to the 
somewhat incredible conclusion that the speed of these waves 
increases with the (arcual) distance traversed. (See B.A. Report , 
1898, p. 220.) This question of the nature of the large waves, 
however, cannot be regarded as finally settled. What is needed 
is a more complete discussion of many typical records. 
In an isotropic solid there are two types of waves — the conden- 
sational-rarefactional and the purely distortional. In the latter, 
the speed of propagation is determined by the rigidity or resistance 
to change of form ; in the former, the compressibility comes into 
play also as a determining factor. The condensational wave travels 
more quickly than the distortional. Hence it is natural to regard 
the preliminary tremors as corresponding to the condensational 
type of wave. Now, it is quite conceivable that an increase of 
pressure may influence the resistance to compression to a marked 
degree, and yet have a comparatively slight effect on the resistance 
to distortion. That is to say, the speed of propagation of the 
condensational type of wave may be, through its determining 
elastic constant, affected by change of pressure to a distinctly more 
appreciable extent than either the density or the rigidity. 
If n is the rigidity and k the resistance to compression (the reci- 
procal of the compressibility), the squares of the speeds of the two 
types of wave are respectively 
& + , n 
— and — 
P P 
when p is the density. Now, if we suppose k to have at the 
surface the value fw, and if we assume n to increase with depth 
at the same rate as p (namely, *28 per cent, per mile descent) and 
k + ^n to increase at 1*2 per cent., we find that k must increase by 
about 2 ’2 per cent, per mile descent. 
I am not aware of any experimental attempts to measure com- 
pressibility of solids at high pressure and temperatures such as 
exist in the interior of the earth. All we can say is that the 
relation indicated above, namely, decrease of compressibility with 
increase of pressure and density, is quite consistent with modern 
views of the constitution of matter. 
