482 report— 1878. 



On the Sun-7ieat received at the several Latitudes of the Earth, taking Ac- 

 count of the Absorption of Heat by the Atmosphere, with Conclusions as 

 to the absolute Radiation of Earth Seat into Space, and the Minimum 

 Duration of Geological Time. By Professor S. Haughton. 



7. Researches made at Dunsinh on the Annual Parallax of Stars. 

 By Professor R. S. Ball. 



8. On the Precession of a Viscous Spheroid. By Gr. H. Darwin, M.A., 

 Fellow of Trinity College, Cambridge. 



I have teen engaged for some time past in the investigation of the precession of 

 a viscous spheroid, with the intention of seeing whether it would throw any light 

 on the history of the earth in the remote past. As some very curious results have 

 appeared in the course of the work, I propose to give an account of part of them to 

 the British Association. 



The subject is, however, so complex and long, that no attempt will be made 

 even to sketch the analytical methods employed. 



In a paper of mine, read before the Royal Society in May last, a theory was 

 given of the bodily tides of viscous and imperfectly elastic spheroids; and this 

 paper formed the foundation of the present investigation. 



For convenience of diction, I shall speak of the tidally disturbed body as the 

 earth, and of the disturbing bodies as the moon and sun ; moreover, in all the 

 numerical applications, the necessary data were taken from these three bodies. 



An analytical investigation proved that — 



The action of the sun and moon on the tides in the earth is such, that the obli- 

 quity to the ecliptic and the lengths of the day and month all become variable ; 

 the alteration in the length of the year remains, however, quite imperceptible. 



The effect of the internal friction called viscosity is, that the bodily tides in the 

 earth lag, and are less in height, than they would be if the earth were formed of a 

 perfect fluid. 



A general explanation was then given as to how the lagging of the tides pro- 

 duces the effects above referred to.* 



And it appeared therefrom that when the viscosity is such that the bodily tides 

 do not lag by very much, there is an increase of the obliquity to the ecliptic, a 

 retardation of the earth's rotation, and a retardation of the moon's mean motion. 



In this general explanation it was assumed that the lagging tides were exactly 

 the same as though the earth were perfectly fluid or elastic, and as though the 

 tide-raising moon were more advanced in her orbit than the true moon, whilst the 

 moon which attracts the tidal protuberances was the true moon. That is to say, it 

 was assumed that the tides raised were exactly the same as though the earth were 

 perfect fluid, save that the time of high tide is late, and that the tides are reduced 

 in height. 



Now, although this serves in a general way to explain the phenomena which 

 result from the supposition of the earth's viscosity, yet it is by no means an 

 accurate representation of the state of the case. 



In fact, the internal friction sifts out the whole tide-wave into its harmonic 

 constituents) and allows the different constituents to be very differently affected as 

 regards height and phase. 



Thus the lagging tide-wave is not exactly such as the general explanation sup- 

 posed, and the nearer does the spheroid approach to absolute rigidity the greater 

 does the discrepancy become. 



The general explanation is a very fair representation for moderate viscosities ; 



* See 'Nature,' September 26, 1878. 



