[ ] 
IX. On the Tidal Friction of a Planet attended by several Satellites , a,nd on the 
Evolution of the Solar System. 
By G. H. Darwin, F.R.S. 
Received December 27, 1880,—Read January 20, 1881. 
[Plates 61-63.] 
Table of Contents. 
Introduction . 
I. The Theory of the Tidal Friction of a Planet attended by several Satellites. 
§ 1. Statement and limitation of the problem... 
§ 2. Formation and transformation of tlie differential equations.. 
§ 3. Sketch of method for solution of tlie equations by series .... 
§ 4. Graphical solution in the case where there are not more than three satellites 
§ 5. The graphical method in the case of two satellites .. 
II. A Discussion of the Effects of Tidal Friction with reference to the Evolution 
of the Solar System. 
§ 6. General consideration of the problem presented by the solar system. 
§ 7. Numerical data and deductions therefrom ... 
§ 8. On the part played by tidal friction in the evolution of planetary masses .... 
§ 9. General discussion and summary. 
Page 
491 
492 
493 
499 
500 
502 
512 
516 
525 
530 
Introduction. 
In previous papers on the subject of tidal friction* I have confined my attention 
principally to the case of a planet attended by a single satellite. But in order to make 
the investigation applicable to the history of the earth and moon it was necessary to 
take notice of the perturbation of the sun. In consequence of the largeness of the sun’s 
mass it was not there requisite to make a complete investigation of the theory of a 
planet attended by a pair of satellites. 
In the first part of this paper the theory of the tidal friction of a central body 
attended by any number of satellites is considered. 
In the second part I discuss the degree of importance to be attached to tidal friction 
as an element in the evolution of the solar system and of the several planetary sub¬ 
systems. 
* Phil. Trans, Parts I. and II., 1879, and Part II. 1880; Proc. Roy. Soc., No. 197, 1879, and No. 202, 
1880. 
3 S 
MLCCCLXXXI. 
