PHILOSOPHICAL TRANSACTIONS. 
I. On the Bodily Tides of Viscous and Semi-elastic Spheroids, and on the Ocean 
Tides upon a Yielding Nucleus. 
By G. H. Darwin, M.A., Fellow of Trinity College, Cambridge. 
Communicated by J. W. L. Glaisher, M.A., F.R.S. 
Received May 14,—Read May 23, 1878. 
. In a well-known investigation Sir William Thomson Las discussed the problem of 
the bodily tides of a homogeneous elastic sphere, and has drawn therefrom very 
important conclusions as to the great rigidity of the earth. * 
Now it appears improbable that the earth should be perfectly elastic; for the con¬ 
tortions of geological strata show that the matter constituting the earth is somewhat 
plastic, at least near the surface. We know also that even the most refractory metals 
can be made to flow under the action of sufficiently great forces. 
Although Sir W. Thomson’s investigation has gone far to overthrow the old idea of 
a semi-fluid interior to the earth, yet geologists are so strongly impressed by the fact 
that enormous masses of rock are being, and have been, poured out of volcanic vents in 
the earth’s surface, that the belief is not yet extinct that we live on a thin shell over 
a sea of molten lava. Under these circumstances it appears to be of interest to inves¬ 
tigate the consequences which would arise from the supposition that the matter 
constituting the earth is of a viscous or imperfectly elastic nature ; for if the interior 
is constituted in this way, then the solid crust, unless very thick, cannot possess 
rigidity enough to repress the tidal surgings, and these hypotheses must give results 
fairly conformable to the reality. The hypothesis of imperfect elasticity will be prin- 
* Sir William states that M. Lame liad treated the subject at an earlier date, but in an entirely 
different manner. I am not aware, however, that M. Lame had fully discussed the subject in its physical 
aspect. 
MDCCCLXXIX. B 
