PREFACE

Introduction

The following paper treats of the effects of frictional tides in a planet on the orbit of its satellite. It is the sequel to three previous papers on a similar subject.

The investigation has proved to be one of unexpected complexity, and this must be my apology for the great length of the present paper. This was in part due to the fact that it was found impossible to consider adequately the changes in the orbit of the satellite, without a reconsideration of the parallel changes in the planet. Thus some of the ground covered in the previous paper on “Precession” had to be retraversed; but as the methods here employed are quite different from those used before, this repetition has not been without some advantage.

It will probably conduce to the intelligibility of what follows, if an explanatory outline of the contents of the paper is placed before the reader. Such an outline must of course contain references to future procedure, and cannot therefore be made entirely intelligible, yet it appears to me that some sort of preliminary notions of the nature of the subject will be advantageous, because it is sometimes difficult for a reader to retain the thread of the argument amidst the mass of details of a long investigation, which is leading him in some unknown direction.

Part VIII. contains a general review of the subject in its application to the evolution of the planets of the solar system.

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.