2 
MR, DARWIN ON THE BODILY TIDES OF VISCOUS AND SEMI-ELASTIC 
cipally interesting as showing how far Sir W. Thomson’s results are modified by the 
supposition that the elasticity breaks down under continued stress. 
In this paper, then, I follow out these hypotheses, and it will be seen that the 
results are fully as hostile to the idea of any great mobility of the ulterior of the 
earth as is that of Sir W. Thomson. 
The only terrestrial evidence of the existence of a bodily tide in the earth would be 
that the ocean tides would be less in height than is indicated by theory. The subject 
of this paper is therefore intimately connected with the theory of the ocean tides. 
In the first part the equilibrium tide-theory is applied to estimate the reduction 
and alteration of phase of ocean tides as due to bodily tides, but that theory is 
acknowledged on all hands to be quite fallacious in its explanation of tides of short 
period. 
In the second part of this paper, therefore, I have considered the dynamical theory 
of tides in an equatorial canal running round a tidaily-distorted nucleus, and the 
results are almost the same as those given by the equilibrium theory. 
The first two sections of the paper are occupied with the adaptation of Sir W. 
Thomson’s work* to the present hypotheses ; as, of course, it was impossible to repro¬ 
duce the whole of his argument, I fear that the investigation will only be intelligible 
to those who are either already acquainted with that work, or who are willing to 
accept my quotations therefrom as established. 
As some readers may like to know the results of this inquiry without going into 
the mathematics by which they are established, I have given in Part III. a summary 
of the whole, and have as far as possible relegated to that part of the paper the 
comments and conclusions to be drawn. I have tried, however, to give so much 
explanation in the body of the paper as will make it clear whither the argument is 
tending. 
The case of pure viscosity is considered first, because the analysis is somewhat 
simpler, and because the results will afterwards admit of an easy extension to the case 
of elastico-viscosity. 
I. 
THE BODILY TIDES OF VISCOUS AND ELASTICO-VISCOUS SPHEROIDS. 
1. Analogy betiveen the flow of a viscous body and the strain of an elastic one. 
The general equations of flow of a viscous fluid, 'when the effects of inertia are 
neglected, are 
* His paper will be found in Phil. Trans., 1863, p. 573, and §§ 733-737 and 834-846 of Thomson and 
Tait’s ‘Natural Philosophy,’ edit, of 1867. 
