4 



Mr. G. H. Darwin. 



[Dec. 18,. 



what less ; and the moon moving in a circular orbit, the plane of 

 which is nearly coincident with the earth's equator. 



This initial configuration suggests that the moon was produced by 

 the rupture, in consequence of rapid rotation or other causes, of a 

 primeval planet, whose mass was made up of the present earth and 

 moon. The coincidence is noted in the paper, that the shortest period 

 of revolution of a fluid mass of the same mean density as the earth, 

 which is consistent with an ellipsoidal form of equilibrium, is 2 hours 

 24 minutes ; and that if the moon were to revolve about the earth 

 with this periodic time, the surfaces of the two bodies would be 

 almost in contact with one another. 



Tidal friction is a vera causa, and the only postulates of this theory 

 of the evolution of our system are lapse, of time, and the non-existence 

 of sufficient diffused matter to materially affect the motions of the 

 moon and earth through space. 



The systems of the other planets of the solar system are reviewed 

 from the point of view of this tidal theory of evolution, and it is found 

 that there are many confirmatory circumstances, and none which 

 appear condemnatory. But as the present investigation only treats 

 of a planet with a single satellite, it necessarily leaves many points 

 untouched. In relation to this theory, the most interesting points are 

 the satellites of Mars, and the inclinations of the orbits of Jupiter's 

 satellites to their proper planes. 



Notes on the Method of Investigation — General Reasoning in Substitution 

 for Analytical Treatment. 



The following are the titles of the several parts into which the paper 

 is divided : — 



I. The theory of the disturbing function. 



II. Secular changes in the inclination of the orbit of a satellite. 



III. The proper planes of the satellite, and of the planet, and their 

 secular changes. 



IV. Integration for changes of the inclination of the orbit, and of 

 the obliquity of the ecliptic. 



Y. Secular changes in the eccentricity of the orbit of a satellite. 



VI. Integration for changes of eccentricity of the orbit. 



VII. Summary and discussion of results. 



VIII. Review of the tidal theory of evolution as applied to the 

 earth, and the other members of the solar system. 



These titles indicate the method of treatment. 



The application of the method of the disturbing function to the 

 present problem has certain peculiarities. The attraction of the tides 

 raised in. the planet by a satellite is the cause of the perturbation of 

 the satellite's motion. Now the state of tidal disturbance of the- 



