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.

The last paragraph contains a discussion of the evidence adduced in this part of the paper, and a short recapitulation of the observed facts in the solar system which bear on the subject. This is probably the only portion which will have any interest for others than mathematicians.

THE THEORY OF THE TIDAL FRICTION OF A PLANET ATTENDED BY ANY NUMBER OF SATELLITES

Statement and limitation of the problem

Suppose there be a planet attended by any number of satellites, all moving in circular orbits, the planes of which coincide with the equator of the planet; and suppose that all the satellites raise tides in the planet.