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XIV. Problems connected with the Tides of a Viscous Spheroid. 
By G. H. Darwin, M.A., Fellow of Trinity College, Cambridge. 
Communicated by J. W. L. Glaisher, M.A., F.P.S. 
Received November 14,—Read December 19, 1878. 
Contents. 
Page 
I. Secular distortion of tbe spheroid, and certain tides of the second order . 539 
II. Distribution of heat generated by internal friction, and secular cooling. 554 
III. The effects of inertia in the forced oscillations of viscous, fluid, and elastic spheroids.. 566 
IY. Discussion of the applicability of the results to the history of the earth . 587 
In the following paper several problems are considered, which were alluded to in my 
two previous papers on this subject.* 
The paper is divided into sections which deal with the problems referred to in the 
table of contents. It was found advantageous to throw the several investigations 
together, because their separation would have entailed a good deal of repetition, 
and one system of notation now serves throughout. 
It has, of course, been impossible to render the mathematical parts entirely inde¬ 
pendent of the previous papers, to which I shall accordingly have occasion to make a 
good many references. 
As the whole inquiry is directed by considerations of applicability to the earth, I 
shall retain the convenient phraseology afforded by speaking of the tidally distorted 
spheroid as the earth, and of the disturbing body as the moon. 
It is probable that but few readers will care to go through the somewhat complex 
arguments and analysis by which the conclusions are supported, and therefore in the 
fourth part a summary of results is given, together with some discussion of their 
physical applicability to the case of the earth. 
I. Secular distortion of the spheroid, and certain tides of the second order. 
In considering the tides of a viscous spheroid, it was supposed that the tidal protu¬ 
berances might be considered as the excess and deficiency of matter above and below 
* “ On the Bodily Tides of Viscous and Semi-elastic Spheroids, and on the Ocean Tides upon a Yielding 
Nucleus,” Phil. Trans., 1879, Part I., and— 
“ On the Precession of a Viscous Spheroid, and on the remote History of the Earth,” immediately pre¬ 
ceding the present paper. They will be referred to hereafter as “ Tides ” and “ Precession ” respectively. 
