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pared with that of the Sun, which is equally free for the satellites with respect to their principal planets. This we may readily suppose from the smallness of their volumes.

The attractive property of the heavenly bodies does not only belong to them in a mass, but belongs to each of their particles. If the Sun only acted on the centre of the Earth, without attracting particularly every one of its particles, there would arise in the ocean oscillations infinitely more considerable, and very different from those which we observe. The gravity of the Earth therefore to the Sun is the result of the gravity of all its particles, which consequently attract the Sun in proportion to their respective masses; besides each body on the earth, tends towards its centre proportionally to its mass, it reacts therefore, on it, and attracts it in the same ratio. If that was not the case, and if any part of the Earth, however small, attracted another part without being attracted by it, the centre of gravity would move in space in

virtue of the force of gravity, which is impossible.

The celestial phenomena compared with the laws of motion, conduct us therefore, to this great principle of nature, namely, that all the particles of matter attract each other in proportion to their masses, and inversely as the squares of their distance.

Already we may perceive in this universal gravitation the cause of the perturbations to which the heavenly bodies are subject; for the planets and comets being subject to the action of each other, they must deviate a little from the laws of the elliptic motion, which they would otherwise exactly follow, if they only obeyed the action of the Sun. The satellites also deranged in their motions round their planets by their mutual action and that of the Sun, deviate a little from these laws.

We perceive, then, that the particles of the heavenly bodies, united by their attraction, should form a mass nearly spherical; and that the result of their action at the surface of the body, should produce

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all the phenomena of gravitation. We see, moreover, that the motion of rotation of the celestial bodies should slightly alter their spherical figure, and flatten them at the poles; and then the resulting force of all their mutual actions not passing through their centres of gravity, should produce in their axes of rotation similar motions to those discovered by observation. Finally, we may perceive why the particles of the ocean, unequally acted on by the Sun and Moon, should have oscillations similar to the ebbing and flowing of the tides. But these different effects of the principle of gravitation, must be particularly developed to give it all the certainty of which physical truth is susceptible.

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CHAP. II.

Of the Masses of the Planets, and of Gravity at their Surface.

appears on the first view of the subject impossible to determine the respective masses of the Sun and planets, and to measure the height from which bodies fall in a given time, from the action of gravity at their surface. But the connection of truths with each other conducts us to results which appeared inaccessible, when the principle on which they depend was unknown. Thus the measure of the intensity of gravity at the surface of the planets is rendered practicable by the discovery of universal gravitation. Let us return to the theorems on centrifugal force given in the preceding book. The result derived from them is, that the gravity of a satellite towards its planet is to the gravity of the Earth towards the Sun, as the mean radius of the orbit of the satellite

divided by the square of the time of its sidereal revolution, is to the mean distance of the Earth from the Sun, divided by the square of a sidereal year. To reduce these gravities to the same distance from the bodies which produce them, they must be multiplied respectively by the squares of the radii of the orbits which they describe. And as at equal distances the masses are proportional to their attractions, the mass of the Earth is to that of the Sun, as the cube of the mean radius of the orbit of the satellite, divided by the square of the time of its sidereal revolution, is to the cube of the mean distance of the Earth from the Sun, divided by the square of the sidereal year. Let this result be applied to Jupiter. For this purpose we shall observe that the mean radius of the orbit of the fourth satellite subtends at the mean distance of Jupiter from the Sun an angle of *1530/86, seen at the mean distance of

* 8′ 15′′ 9.

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