Page:Mécanique céleste Vol 4.djvu/201

 CONTENTS OF THE FOURTH VOLUME.

PARTICULAR THEORIES OF THE MOTIONS OF THE HEAVENLY BODIES.

EIGHTH BOOK.

THEORY OF THE SATELLITES OF JUPITER, SATURN, AND URANUS.

Object of this theory [6019] 1

CHAPTER I. EQUATIONS OF THE MOTIONS OF THE SATELLITES OF JUPITER 1

The reciprocal action of the satellites, the sun's attraction, and the oblateness of the spheroid of Jupiter, arc noticed [6020—6077] § 1, 2

CHAPTER II. ON THE INEQAULITIES OF THE MOTIONS OF JUPITER'S SATELLITES, WHICH ARE INDEPENDENT OF THE EXCENTRICITIES AND INCLINATIONS OF THEIR ORBITS 17

Development of the equations of the motions of these satellites. Analytical expressions of the perturbations of their radii vectores and of their longitudes. The sun*s action produces an inequality analogous to the variation in the lunar theory [6078–6125] § 3

Investigation of the terms of these expressions which can acquire considerable values by the divisors introduced by integration; these divisors being very small, in consequence of the nearly commensurable ratios of the mean motions of the three inner satellites. Necessity of retaining, in these small divisors, the terms depending on the product of the constant part of the disturbing force by the variation of the radius vector, this product having a sensible influence upon their values [6125′–6171] § 4

Effect of terms of this kind on the times of the eclipses of the three inner satellites. All the inequalities produced by such terms depend upon the same angle, having a common period of 437$days$,650. This result is conformable to observation [6173–6193] §5

CHAPTER III. ON THE INEallALmES OF THE MOTIONS OP THE SATELLITES DEPENDING ON THB BXCBfTRICITIES OF THE ORBITS « 38

Expression of the different equations of the centre of the satellites, and of the motions of their [6194–6244″] § 6