Page:Mécanique céleste Vol 1.djvu/22

xvi Application of the preceding principles to the motion of a homogeneous fluid mass, which has a uniform rotatory motion, about one of the axes of the co-ordinates [321] § 34

Determination of the very small oscillations of a homogeneous fluid mass, covering a spheroid, which has a rotatory motion, [324] § 35

Application to the motion of the sea, supposing it to be disturbed from the state of equilibrium, by the action of very small forces, [337] § 36

On the atmosphere of the earth, considered at first in a state of equilibrium, [348]. Its oscillations in a state of motion, noticing only the regular causes which agitate it. The variations which these motions produce in the height of the barometer, [363' v] § 37

SECOND BOOK.

ON THE LAW OP UNIVERSAL GRAVITATION, AND THE MOTIONS OF THE CENTRES OF GRAVITY OF THE HEAVENLY BODIES.

CHAPTER I. THE LAW OF UNIVERSAL GRAVITY DEDUCED FROM OBSERVATION 239

The areas described by the radii vectores of the planets in their motions about the sun, being proportional to the time, the force which acts upon the planets, is directed towards the centre of the sun, [367] ; and reciprocally, if the force be directed towards the sun, the areas described about it, by the planets, will be proportional to the time ^1

The orbits of the planets and comets being conic sections, the force which acts on them, is in the inverse ratio of the square of the distances of the centres of these planets from that of the sun, [SSC]. Reciprocally, if the force follows this ratio, the described curve will be a conic section, [380'^] § 2

The squares of the times of the revolutions of the planets, being proportional to the cubes of the great axes of their orbits ; or, in other words, the areas described in the same time, in different orbits, being proportional to the square roots of their parameters, the force which acts upon the planets and comets, must be the same for all the bodies placed at equal distances from the sun, [385] § 3

The motions of the satellites about their planets exhibiting nearly the same phenomena, as the motions of the planets about the sun ; the satellites must be attracted towards their planets, and towards the sun, by forces reciprocally proportional to the square of the distances, [388] § 4

Investigation of the lunar parallax, from experiments on gravity, supposing gravitation to be in the inverse ratio of the square of the distances, [391]. The result obtained in this manner, being found perfectly conformable to observations, the attractive force of the earth must be of the same nature as that of the heavenly bodies § 5

General reflections on what precedes : they lead us to this general principle, namely, that all the particles of matter attract each other in the direct ratio of the masses^ and in the inverse ratio of the squares of the distances, [391'*', &c] § 6