Page:Mécanique céleste Vol 2.djvu/13

 CONTENTS OF THE SECOND VOLUME.

THIRD BOOK.

ON THE FIGURES OF THE HEAVENLY BODIES.

CHAPTER 1. ON THE ATTRACTIONS OJ" HOMOGENEOUS SPHEROIDS, TERMINATED BY SURFACES OP THE SECOND ORDER 1

General method of transforming a triple differential into another, relative to three different variable quantities [1348'—1356'"]* Application of this method to the attraction of spheroids [1356""— 1361] . § 1

Formulas of the attractions of a homogeneous spheroid, terminated by a surface of the second order [1368, 1369] §2

On the attraction of a homogeneous ellipsoid, when the attracted point is placed within, or upon its surface. Reduction of this attraction to quadratures [1377, 1379], which, when the spheroid is of revolution, change into finite expressions [1385]. A point placed within an elliptical stratum, whose internal and external surfaces are similar, and similarly placed, is equally attracted in every direction [1369^] § 3

On the attraction of an elliptical spheroid upon an external point. Remarkable equation of partial differentials, which holds good relatively to this attraction [1398]. If we describe through the attracted point, a second ellipsoid, which has the same centre, the same position of the axes, and the same excentricities as the first, the attractions of the two ellipsoids will be in the ratio of their masses [1412""] §4,5,6

Reduction of the attractions of an ellipsoid, upon an external point, to quadratures [1421, 1426], which change into finite expressions [14::18], when the spheroid is of revolution. ... § 7

CHAPTER II. ON THE DEVELOPMENT OF THE ATTRACTION OF ANY SPHEROID IN A SERIES. . . . 63

Various transformations of the equation of partial differentials, of the attractions of spheroids [1429—1435] §8

Development of these attractions, in a series, arranged according to the powers of the distance of the attracted points from the centre of the spheroid [1436, 1444] § 9

Application to spheroids, differing but liltlo from a sphere; singular equation, which obtains between their attractions at the surface [1458] §10