226 Proceedings of the Royal Society of Edinburgh. [Sess. 
second phase do not seem to find an immediate explanation along the lines 
of this theory. But may these not he explained as due to the intermingling 
of the quicker distortional vibrations with compressional vibrations of 
longer wave-length which, because of their longer period, have travelled 
slower than the compressional waves of shorter wave-length ? True, the 
mathematical theory of elasticity does not recognise any relation between 
speed of propagation and length of wave ; but this theory is only a first 
approximation to reality, and proves nothing, either one way or the other, 
as to what may occur in seismic vibrations. The fact that the first phase, 
when well developed, always begins with comparatively rapid oscillations, 
seems indeed to establish the truth that the shorter waves of a seismic dis- 
turbance do travel faster than the longer waves. If we take four seconds 
to be the shortest period, we find that the disturbance travelling with a 
speed of 12 23 kilometres per second will have a wave-length of nearly 49 
kilometres. 
It may be of some interest to compare the elastic constants of the 
material of the nucleus of the earth on the assumption that we are dealing 
with compressional and distortional waves. The ratio of the speeds of the 
two types is 31 '3 to 16, or T74 to unity. The ratio of the wave-moduli 
will be as the square of this, or almost exactly 3 to 1. Hence in the notation 
of Thomson and Tait we have 
k + 4?i/3 1= 3 n 
where k is the incompressibility and n the rigidity. This gives 
3 k = on 
a noteworthy result, showing that the inner parts of the earth almost 
accurately fulfil the conditions of isotropy possessed by the ideal elastic 
solid of Navier and Poisson. This conclusion seems to me to be an addi- 
tional argument in favour of the view now being presented. 
Here in the heart of the earth is a material at a high temperature and 
under great pressure, brought into a physical state suggesting homogeneity, 
though not necessarily implying it. As shown long ago by Tait, this globe 
is held together mainly by gravitational attraction. The cohesion between 
the molecules is, however, the force which is involved in the propagation of 
the elastic disturbances which radiate from a seismic centre. The view of 
the French elasticians was that true homogeneity required a definite relation 
between incompressibility and rigidity. This definite relation is not realised 
in the case of materials tested by ordinary combinations of stress and strain. 
This fact, however, was not admitted by de St Venant as disproving the 
