196 Proceedings of the Royal Society of Edinburgh. [Sess. 
penetrate without appreciable decay to 3000 km. would therefore require 
a much smaller value of T 2 , say one-fiftieth of a second. Consequently, to 
satisfy the observed phenomena of earthquake waves and also the other 
conditions studied by Dr Jeffreys, we must assume that T 2 is very small 
down to a depth of half the earth’s radius, that about this depth it begins 
to become greater, and that at greater depth it becomes so great as to give 
the average value just mentioned for the whole earth. This high viscosity 
at the central parts of the earth is to be explained as due presumably to 
the increased temperature and pressure; but it is not easy to find an 
explanation in terms of any ordinary theory of the constitution of matter. 
There is no doubt, however, that the main facts can be co-ordinated in 
terms of this hypothesis. 
The view presented in this paper is that the rigidity of the earth’s 
material breaks down under the influence of the increasing temperature, 
but that the non-rigid central core retains a measurable compressibility. 
I have purposely refrained from speaking of this central core as being 
liquid, since that word connotes properties which may not be possessed by 
the material at the earth’s core. It may, under isotropic stress, remain 
practically solid as a whole and yet be unable to transmit distortional 
waves. Such a supposition may not necessarily be incompatible with the 
other conditions required for the solution of the problems discussed by 
Dr Jeffreys. 
The main conclusions of the present paper may be summarised as 
follows : — 
1. For the first time, by a rigorous mathematical method, the forms of 
the seismic rays and of the isochronous surfaces have been deduced 
directly from the data of observation. 
2. The seismic rays, both of the condensational and distortional waves, 
are on the whole concave outwards, indicating that the speeds of propaga- 
tion increase with depth below the earth’s surface until a depth equal to 
about three-tenths of the earth’s radius is reached. 
3. At this depth the speeds of propagation tend to or reach a constant- 
value and then fall off slightly for greater depths, certain seismic rays 
showing a convexity outwards. 
4. The data of observation are insufficient to enable us to trace waves 
which reach a depth lower than six-tenths of the earth’s radius. 
5. The evidence is that at or near this depth the distortional wave is 
killed out, so that over arcual distances from the epicentre greater than 
120° there is no characteristic appearance of the Secondary wave in the 
seismograms. 
