1878.] 



the Precession of a Viscous Spheroid, Sfc. 



193 



of the coefficient of viscosity which is used in this solution is as 

 follows : — If a slab of the materials of the earth an inch thick have 

 one face held fixed, and if the other face be subjected to a tangential 

 stress of 13^ tons to the square inch for 24 hours, then the two faces 

 have been displaced relatively to one another through one-tenth of an 

 inch. Such a material would in ordinary parlance be called a solid, 

 and in the tidal problem this must be regarded as a moderately small 

 viscosity, whence I conclude that the earth may have been habitable, 

 and yet have undergone these changes. 



Amongst the conclusions of interest to geologists is the following : 

 namely, that the amount of heat generated in the interior of the earth 

 by internal friction, during these 56 million years, would be sufficient, if 

 applied all at once, to heat the whole earth's mass 1,755° F., supposing 

 the earth to have the specific heat of iron. If then it is permissible 

 to suppose that any considerable part of these changes has taken 

 place during geological history, the estimate of the age of the earth, 

 which is founded on the assumption that the earth is simply a cooling 

 sphere, would have to undergo modification. 



A second solution of the differential equations is next given, adapted 

 to the hypothesis that the earth stiffened as it cooled ; but no definite 

 law of stiffening is assumed. This solution follows a line closely 

 similar to that of the last up to the point where the day has fallen to 

 6 hrs. 50 mins. The obliquity is, however, found to decrease slightly 

 more than in the previous solution. 



At this point it was found necessary to abandon the approximation 

 by which the three semi-diurnal and the three diurnal tides are classi- 

 fied together. The problem then becomes much more complex, and a 

 new method of solution is required. 



It is found that in the retrospect the obliquity will only continue to 

 diminish a little beyond the point already reached ; for when the 

 month has become equal to twice the day there is no longer a tendency 

 to diminution, and for smaller values of the month the tendency is re- 

 versed. This shows that for values of the month less than twice the 

 day, the position of zero obliquity of the earth's axis is dynamically 

 stable. The whole diminution of obliquity, from the initial state back 

 to the critical point of relationship between the month and day, is 

 found to be 10°. 



After considering the various discrepancies between the ideal pro- 

 blem solved and the real case of the earth, I conclude that while a 

 large part of the obliquity may be probably referred to these causes, 

 yet that there probably remains an outstanding part which is not so 

 explicable. 



The obliquity to the ecliptic is now set on one side, and from a 

 consideration of the equation of conservation of moment of momentum, 

 the initial state is determined, towards which the solution has been 



