195 
1918-19.] The Propagation of Earthquake Waves. 
As the final sections of this paper were being written, my attention 
was drawn by Dr Harold Jeffreys to his three papers on the “ Viscosity of 
the Earth,” published in vols. lxxv, lxxvi, Ixxvii of the Monthly Notices 
of the Royal Astronomical Society (1915 to 1917). His main object in 
these papers is to make the lunar secular acceleration due to tidal friction 
compatible witli the existence of the Eulerian nutation ; and in the third 
paper, in which he introduces a law of viscosity suggested by Sir Joseph 
Larmor, he refers to its bearing on the transmission of earthquake waves. 
Maxwell in his second great paper on the dynamical theory of gases (Phil. 
Trans., 1866) gives a simple mathematical description of the phenomena of 
viscosity. He considers the strain S and the stress F to be connected by 
the formula F = ES, E being a constant elastic modulus. In a solid body 
free from viscosity 
dt ~ dt ' 
If there is viscosity, F will tend to disappear at a rate depending on the 
value of F. If this rate is assumed to be proportional to F, then 
JF_ JS_F 
dt ~ atf T; 
Tj being the constant known as the “ time of relaxation.” Hence 
es=f+A 
is the expression for Maxwell’s law of viscosity, and corresponds to the law 
of “ elastico-viscosity ” used by Sir G. H. Darwin in his work on tidal 
friction. Under this law the material yields indefinitely under action of 
a stress, and when the stress is removed it acquires permanent set. 
Larmor’s suggestion is to make the friction proportional to the rate of 
straining, so that the equation connecting F and S becomes 
ES = F — ft— or F’f.S •; T./fV •• F 
dt V 2 dt J 
where T 2 is another constant. 
Under a constant stress the strain approaches its final value F/E 
asymptotically. On removal of the stress the strain falls off asymptoti- 
cally to zero. There is no permanent set. Dr Jeffreys distinguishes this 
kind by the name “ firmo-viscosity.” He shows that, in regard to the 
lunar secular acceleration and the Eulerian nutation, compatibility is 
secured when T 2 is equal to 371 seconds as an average for the whole earth. 
He also shows that, with T 2 equal to 1 second, distortional waves of 20 
seconds period would not penetrate to more than about 100 km. To 
