one vast unformed mafs of matter. It will not seem strange that where the fun itself is fcarcely visible, the gravity toward it fhould be infenfible; and that we should here find no effects of any gravitation toward the fixed ftars.

17. As action and reaction are always equal and in oppofite directions, fo that the earth, for example, gravitates toward every mountain as well as every mountain toward the earth, and gravitates toward every projectile while it is moving in the air, as well as the projectile gravitates towards it; and without this law nothing would be steady or conftant in nature: hence it follows, that the fun gravitates toward all the bodies in the fyftem, and that the primary planets gravitate toward their fatellites. The primary planets alfo gravitate toward one another; fome minute irregularities in their motions, especially in thofe of Jupiter and Saturn, the two greatest planets, when they are in conjunction and come nearest to each other, are evidences of this. The motions of the fatellites of Jupiter and Saturn are also faid to be fubject to irregularities that proceed from their mutual actions. From fo many indications we may at length conclude, that all the bodies in the folar fyftem gravitate toward each other; and tho' we cannot confider gravitation as effential to matter, we must allow that we have as much evidence, from the phænomena, for its univerfality, as for that of any other affection of bodies whatsoever.

CHAP.

1.

H

CHA P. IV.

Of the general gravitation of matter.

Itherto we have confidered only the accelerating force of gravity at different distances, to which the velocity generated by it, in a given time, is always proportional. It remains to fhew that the motion produced by this power, at equal distances from a given centre, is always proportional to the quantity of matter in the heavy body; that the gravity of bodies arifes from the mutual gravitation of their parts; and to afcertain the law of the gravitation of the particles of bodies. It is allowed as to terrestrial bodies, and was confirmed from many accurate experiments by Sir Ifaac Newton, that bodies of the fame bulk and figure, tho' of very different kinds, fufpended by lines of the fame length, performed their vibrations, when moving as pendulums, exactly in the fame time; from which it follows, that the force of their gravity is exactly proportional to their quantity of matter: nor would there be any difference in the times of their vibrations tho' their figure and bulk were different, the distances between their centres of fufpenfion and of ofcillation being equal, if it was not for the refiftance of the air. It has been already fhewed, that the moon would fall toward the earth with the fame velocity as any other heavy body, if he was at the fame diftance from its centre; and it is plain that the forces of bodies moved with equal velocities are as their quantities of matter: fo that the weight of the moon would be to the weight of any heavy body at the fame diftance from the centre of the earth, in the fame proportion as the matter of the moon is to

the matter of that heavy body. The primary planets are acted on variously in their different diftances, but according to the law which fhews that if they were at equal diftances they would defcend with equal velocities toward the fun, fo that their motion would be proportional to their quantity of matter. In the fame manner it appears, that if the fatellites of Jupiter and Saturn were at equal distances from the centres of their respective primary planets, they would defcend towards them with equal velocities. The earth and moon, at equal distances from the fun, are acted upon by equal accelerating forces, and would defcend with equal velocities toward it. Jupiter and his fatellites would defcend with the fame velocity toward the fun, if their projectile motions were deftroyed. The fame is to be faid of Saturn and his fatellites. A very fmall inequality in the accelerating forces that act upon the primary planet and its fatellites would produce very great irregularities in their motion. In all thefe cafes, equal velocities being generated in equal times, the motions of the bodies, and confequently the gravities that produce these motions, must be proportional to the quantities of matter in the bodies; from which it follows, that all equal portions of matter, at equal diftances from the centre of gravitation, are equally heavy; without regard to figure, bulk, or the texture of their parts: and that the gravitation of bodies arifes from the gravitation of the particies of which they are compofed.

2. Because action is always equal to reaction, if you still fuppofe the planets at equal distances from the fun, and therefore gravitating toward the fun with forces proportional to their quantities of matter, the fun will gravitate towards each of the planets with forces in the fame proportion. In general,

the fame body gravitates towards any other bodies, at equal diftances from them, with forces proportional to their quantities of matter; because it gravitates toward them with the fame forces with which they gravitate towards it, which are as their quantities of matter. The power, therefore, that is extended from the centre of the fun and of each of the planets, to all distances around them, is, at equal diftances from their centres, proportional to their quantities of matter: and, in general, it appears that the weight or gravity of a body is the greater, in proportion as its quantity of matter is greater, as the quantity of matter in the body to which it gravitates is greater, and as the fquare of the distance from it is lefs. By compounding these three proportions together, the weight, and motion, of bodies, arifing from their gravitation, may always be determined.

3. Gravity being found, by fo many experiments and observations, to affect all the matter of bodies equally, we have hence more reafon still to conclude its univerfality; fince it appears to be a power that acts not only at the furfaces of bodies, and on such bodies as are removed at a distance from them, but to penetrate into their fubftance, and into that of all other bodies, even to their centres; to affect their internal parts with the fame force as the external, to be obftructed in its action by no intervening body or obftacle; and to admit of no kind of variation in the fame matter, but from its different distances only from that to which it gravitates.

4. The action of gravity on bodies arifes from its action on their parts, and is the aggregate of these actions; so that the gravitation of bodies muft arife from the gravity of all their particles towards each

other.

other. The weight of a body toward the earth arifes from the gravity of the parts of the body: the gravity of a mountain toward the earth arifes from the gravitation of all the parts of the mountain towards

it. The gravitation of the northern hemisphere toward the fouthern arifes from the gravitation of all its parts towards it; and if we fuppose the earth divided into two unequal fegments, the gravitation of the greater toward the leffer arifes from the gravitation of all the parts of the greater toward the leffer. In the fame manner, the gravity of the whole earth, one particle being excepted, toward that particle, muft arise from the quantity of gravitation of all the other particles of the earth toward that particle. Every particle, therefore, of the earth gravitates toward every other particle of it; and, for the fame reason, every particle of matter in the folar fyftem gravitates toward every other particle in it.

5. We now proceed to an important part of this doctrine, to determine the law according to which the particles of bodies gravitate towards each other; after having difcovered the law which is obferved by bodies composed of thofe particles. To a fuperficial enquirer, at first fight, the former might poffibly appear to be neceffarily the fame with the latter: but it is easily fhewn, that the law which is obferved in the attractions of the minute particles of matter is often very different from that which is obferved by fpheres compofed of fuch particles. If, for example, the gravitation of the particles decrease in the fame proportion as the cubes of their distances increafe, or in any higher proportion, the spheres compofed of fuch particles will not gravitate towards each other with forces that decrease in the fame proportion as the cubes of the diftances of their centres increase, or in that higher proportion; for fpheres