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XIII. On the Precession of a Viscous Spheroid, and on the remote History of the Earth. 
By G. H. Darwin, M.A., Fellow of Trinity College, Cambridge. 
Communicated by J. W. L. Glaishee, M.A., F.R.S. 
Received July 22,—Read December 19, 1878. 
[Plate 36.] 
The following paper contains the investigation of the mass-motion of viscous and 
imperfectly elastic spheroids, as modified by a relative motion of their parts, produced 
in them by the attraction of external disturbing bodies ; it must be regarded as 
the continuation of my previous paper,'”' where the theory of the bodily tides of such 
spheroids was given. 
The problem is one of theoretical dynamics, but the subject is so large and complex, 
that I thought it best, in the first instance, to guide the direction of the speculation 
by considerations of applicability to the case of the earth, as disturbed by the sun 
and moon. 
In order to avoid an incessant use of the conditional mood, I speak simply of the 
earth, sun, and moon ; the first being taken as the type of the rotating body, and the 
two latter as types of the disturbing or tide-raising bodies. This course will be justi¬ 
fied, if these ideas should lead (as I believe they will) to important conclusions with 
respect to the history of the evolution of the-solar system. This plan was the more 
necessary, because it seemed to me impossible to attain a full comprehension of the 
physical meaning of the long and complex formulas which occur, without having 
recourse to numerical values; moreover, the differential equations to be integrated were 
so complex, that a laborious treatment, partly by analysis and partly by numerical 
quadratures, was the only method that I was able to devise. Accordingly, the earth, 
sun, and moon form the system from which the requisite numerical data are taken. 
It will of course be understood that I do not conceive the earth to be really a 
homogeneous viscous or elastico-viscous spheroid, but it does seem probable that the 
earth still possesses some plasticity, and if at one time it was a molten mass (which is 
highly probable), then it seems certain that some changes in the configuration of the 
three bodies must have taken place, closely analogous to those hereafter determined. 
And even if the earth has always been quite rigid, the greater part of the same effects 
would result from oceanic tidal friction, although probably they would have taken 
place with less rapidity. 
* “On tlie Bodily Tides of Viscons and Semi-elastic Spheroids,” &c., Phil. Trans, 1879, Part I. 
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