Page:Mécanique céleste Vol 3.djvu/25

 CONTENTS OF THE THIRD VOLUME.

PARTICULAR THEORIES OF THE MOTIONS OF THE HEAVENLY BODIES.

SIXTH BOOK.

THEORY OF THE PLANETARY MOTIONS.

Object of this theory 1

CHAPTER I. FOKMULAS FOR THE INEaUALITIES OF THE MOTIONS OF THE PLANETS, WHICH OEfE.VD ON THE SUUARES AND HIGHER POWERS OF THE EXCENTRICITIES AND INCLINATIONS OF THE ORBITS 4

ON THE INEaUALITIES UlltCII DEPEND UPON THE SUUARES AND PRODUCTS OF THE EXCENTRICITIES AND INCLINATIONS 4

Form of the terms whioli produce them [3703,3704]. Influence of the ratio of the mean motions upon tlicse terms, by reason of the small divisors, which are introduced by the integrations [3712]. Preparations of the differential equations for the different cases of these inequalities which occur in the solar system §1,2

Considerations, by which we may distinguish the most important of these inequalities [3732-3735] §3

Development of the terms, which result in the expressions of the radius vector, cf the longitude, ami of the latitude of the disturbed planet [3730— 3800] §-l,5,

ON THE INEQUALITIES DEPENDING ON THE CUBES AND PRODUC'PS OF THREE UI5IENSI0NS OF THE EXCENTRICITIES AND INCLINATIONS OF THE OKIilTS, AND ON THEIR HIGHER POWERS 45 Form of the terms whicii produce them [3807 — 3807'] § 7

Examination of the cases where they become sensible. They depend on the circumstance, that the ratios of the mean motions are nearly commensurable. Application of these principles to the theory of Jupiter and Saturn, in terms of the third degree [3828, &c.] §8

Inequalities depending on terms of the fifth degree [385(7]. They are sensible in the theory of Jupiter and Saturn. Calculation of them for these planets [38G0, iSlc] §9