194 



Mr. G. H. Darwin on Problems connected [Dec. 19, 



running back. It is found that the initial condition is one in which 

 moon and earth rotate, as though fixed together, in 5 hrs. 40 mins. ; and 

 that this condition is one of dynamical instability, so that the moon 

 must either have fallen into the earth, or have receded from it, and 

 have then gone through the changes which were traced backwards. 



From this and other considerations it is concluded that, if the moon 

 and earth, were ever molten viscous masses, then it is highly probable 

 that they once formed parts of a common mass. 



The rest of the paper is occupied with a number of miscellaneous 

 propositions, and with a discussion of the physical significance of the 

 results obtained. 



I will here only mention that the case of the Martian satellites 

 appears to me a very striking corroboration of the applicability of 

 these views to the solar system, whilst the Uranian system of satellites 

 is, at first sight, unfavourable. 



A whole series of problems, some of them of great difficulty, still 

 await solution ; and not until they are solved will it be possible either 

 decisively to accept or reject the modified form of the nebular hypo- 

 thesis, to which my results obviously point. 



(Postscript.) Added November 8th, 1878. 



A subsequent investigation has shown that, although the amount of 

 heat which might be generated by internal friction in the earth might 

 be very great, yet its distribution would be such that it could scarcely 

 sensibly affect Sir W. Thomson's investigation of the secular cooling 

 of the earth. 



III. " Problems connected with the Tides of a Viscous Sphe- 

 roid." By G. H. Darwin, M.A., Trinity College, Cambridge. 

 Communicated by J. W. L. Glaisher, F.R.S. Received 

 November 14, 1878. 



(Abstract.) 



In this paper certain problems are treated, which were alluded to 

 in two previous papers on the Tides and Precession of a viscous 

 spheroid,* For brevity the spheroid is spoken of as the earth, and 

 the disturbing body as the moon. 



I. Secular Distortion of the Spheroid, and certain Tides of the second 



order. 



The distortion arises from the nnequal distribution of the tidal 

 frictional couple over the surface of the spheroid. 



* Read before the Royal Society on May 23 and December 19 respectively. 



