5. As all bodies gravitate towards the earth, so does the earth gravitate towards all bodies ; as w ell as all bodies towards particular parts of the earth, as bills, &c. which has been proved by the attraction a hill has upon a plumb line, insensibly drawing it aside. Hence the gravitating force of entire bodies consists of those of all their parts; for, by adding or taking away any part of the matter of a body, its gravity is increased or decreased, in the proportion of the quantity of such por tions to the whole mass. Hence, also, the gravitating powers of bodies at the saute distance from the centre are proportional to the quantities of matter in the bodies.
General or universal gravity, is that by which all the planets tend towards one another ; and, indeed, by which all bodies or'particles of matter in the universe tend towards one another.
The existence of the same principles of gravitation in the superior regions of the heavens as on the earth is one of the great discoveries of Newton, who made the proof of it as easy as that on the earth. This was at first only a conjecture in his mind ; he observed, that all bodies near the earth, and in its atmosphere, had the property of tending directly towards it ; he soon conjectured, that it probably ex tended much higher than to any distance to which we could reach to make experi ments ; and so on, from one distance to another. till he at length saw no reason why it might not extend to the moon, by means of which she might be retained in her orbit, as a stone in a sling is retained by the hand ; and if so, he next inferred, iyhy might not a similar principle exist in e other great bodies in the universe, the sun, and all the other planets, both pri mary and secondary, which might all be retained in their orbits, and perform their revolutions by means of the same univer sal principle of gravitation.
He soon realized and verified these by mathematical proofs. Kepler had found out, by contemplating the motions of the planets about the sun, that the area de scribed by a line connecting the sun and planet, as this revolved in its orbit, was always proportional to the time of its de scription, or that it described equal areas in equal times, in whatever part of its or bit the planet might be, moving always as much the quicker as its distance from the sun was less. And it is also found, that the satellites, or secondary planets, re spect the same law in revolving about their primaries. But it was soon proved,
by Newton, that all bodies moving in any curve line described on a plane, and which, by radii drawn to any certain point, describes areas about the point propor tional to the times, are impelled or acted on by some power tending towards that point. Consequently, the power by which all these planets revolve, and are retained in their orbits, is directed to the centre about which they move, viz. the primary planets to the sun, and the satellites to their several primaries.
Again, Newton demonstrates, that if several bodies revolve with an equal 111D tion in several circles about the same cen tre, and that if the squares of their perio dical times be in the same proportion as the cubes of th eir distances from the com mon centre, then the centripetal forces of the revolving bodies, by which they tend to their central body, will be in the reciprocal or inverse ratio of the squares of the distances. But it had been agreed on by the astronomers, and particularly Kepler, that both these cases obtain in all the planets ; and therefore he inferred, that the centripetal forces of all the pla nets were reciprocally proportional to squares of the distances from the centres of their orbits.
Upon the whole, it appears that the planets are retained in their orbits by some power which is continually acting upon them : that this power is directed towards the centre of their orbits : that the intensity or efficacy of this power in creases upon an approach towards the centre, and diminishes on receding from the same, and that in the reciprocal du plicate ratio of the distances; and that by comparing this centripetal force with the force of gravity on the earth, they are found to be perfectly alike, as may easily be shown in various instances. For ex ample, in the case of the moon, the near est of all the planets, the rectilinear spaces described in any given time, by a body urged by any power, reckoning from the beginning of its descent, are porportion ate to those powers. Consequently, the centripetal force of the moon, revolving in its orbit, will be to the force of gravity on the surface of the earth as the space which the moon would describe in falling, during any small time, by her centripetal force towards the earth, if sh e had no mo tion at all, to the space a body near the earth would describe in falling by its gra vity towards the same.