at Jupiter's distance is adapted to the greater rarity of his fubftance: the confequences might be as fatal in Jupiter, if he was carried into the orb of the earth, as it would be to us to be carried into the orb of Mercury. The ftill greater rarity of Saturn is fitted to his more remote orb; fo that tho' he is the laft of the planets, and receives 90 times lefs light and heat from the fun than we do, he may neverthelefs be in the best fituation that could poffibly be affigned him in the fyftem; and there the fituation of Jupiter, and of all the lower planets, may appear as terrible as that of Mercury does to us. Saturn terminates the planetary revolutions; and, as if the heat of the fun was too weak in the higher orbs, we find no bodies revolving higher, but fuch as defcend in fome part of their orbit nearer to this great centre of light and heat. Upon the whole we have reafon to conclude, that they are all difpofed in fuch order, and in fuch fituations, from which any confiderable variation would produce fatal effects. The hypothefis of Des Cartes led him to place the more denfe planets at a greater diftance from the fun; but a philofophy founded on the obfervation of nature correfponds better with the final caufes of things, and proves, on every occafion, the wisdom of the author.

5. As aftronomers have found no fatellites revolving about Mercury, Venus, or Mars, we are deprived of the like opportunities of comparing their attractive powers and proportional quantities of matter. But it is highly probable, from what we have faid of the Earth, Jupiter and Saturn, that the denfities of the other planets correfpond to their diftances from the fun, and are greater in the nearer planets. Our author has alfo computed the proportion of the attractive powers of the Sun, Jupiter, Saturn, and X 2

the

the Earth, at their refpective furfaces, and finds them to be in proportion as thefe numbers, 10000, 943, 529, 435, refpectively. From which it appears, that the force of gravity towards these very unequal bodies approaches furprisingly to an equality at their furfaces; fo that tho' Jupiter be feveral hundred times greater than the earth, the force of gravity at his furface is very little more than double what it is at the furface of the earth; and the force of gravity at the furface of Saturn is but about greater than that of terreftrial bodies.

6. The most confiderable powers that act in the fyftem being thus determined; before we proceed to confider their effects, it is neceffary, firft, to enquire whether they act in a void, or if there is any medium that refifts the motions produced by them. We find that the air makes a confiderable refiftance to the motion of projectiles near the earth; which, if it extended unto the planetary regions, would also very confiderably affect their motions. But experiments fhew that the denfity of the air is proportional to the force that compreffes it, and that the weight of the fuperincumbent atmosphere is the force which compreffes the air in every altitude; fo that the higher any portion of air is, having a lefs weight of air above it to comprefs it, it must have lefs denfity in the fame proportion: and from this it follows, that if we abstract from the diminution of gravity, and the altitudes from the furface of the earth be taken in arithmetical progreffion, the densities of the air at these altitudes will decrease in geometrical progreffion *. Since, therefore, it appears from several experiments, made in France and England, that the

See Dr. Halley in Phil. Tranf. No 181. and Schol. Prop. 22. Lib. II. Princip.

I

denfi-

denfity of the air decreases in fuch a manner, that at the height of feven perpendicular miles it is about

of the denfity it has at the level of the fea, at 14 miles it must be of it, at 21 miles, at 28 miles, at 35 miles, at 42 miles, at the height of 49 miles part of it, and at the height of a femidiameter of the earth altogether infenfible. It appears from the laws of motion, and from many accurate experiments, that the refiftance of fluids, arifing from the inertia of their matter, is proportional to their denfity; and therefore the refiftance of the air, tho' sensible at the furface of the earth, would be 16384 times lefs at the height of 49 miles, and could not be fenfible in the greatest number of ages at the height of a femidiameter of the earth: it must be ftill lefs at the diftance of the moon, which therefore, meeting with no refiftance, continues to revolve for ever in her orbit, without any impediment or diminution of motion. As for a more fubtile medium than the air, no experiments nor obfervations fhew that there is any here, or in the celestial spaces, from which any fenfible refiftance can arife.

36

BOOK

X 3

BOOK IV.

The effects of the general power of gravity des duced fynthetically.

CHAP. I.

Of the centre of the folar fyftem.

IR Ifaac Newton having eftablished the general principle of the gravitation of the particles of matter, and having determined the chief powers that act in the fyftem, viz. thofe which tend to the Sun, Jupiter, Saturn, and the Earth; and having found that the celeftial motions are performed in free fpaces, where the refiftance is infenfible; he has now prepared the way for proceeding fynthetically in his account of the fyftem of the world, and enquiring into the various effects that arife from a power fo evidently established. Any general principle afcertained in nature is a great acquifition to philofophy, efpecially when the variations of this power, with its direction and force, are clearly determined; and the fertility of this principle will appear from the various phænomena refolved by it fynthetically, of which we are now to treat. Sir Ifaac Newton begins with enquiring into the centre of the fyftem. The Pythagoreans afcribed this place to the centre of the fun, the followers of AriStotle and Ptolemy to the earth. But Sir Ifaac, having found that thefe gravitate towards each other and towards all the other bodies in the fyftem, neither

of

of them, nor indeed any body in the system, can be fuppofed to be void of all motion.

2. It is the centre of gravity of the whole fyftem that is the only point which can be fuppofed quiefcent in it; the fame point about which all the matter of the fyftem would foon be accumulated, if the. progreffive motions of the bodies in it were deftroyed, and their gravity was permitted to bring them together. The mutual actions of bodies on each other never affect the state of this centre; their attracting or repelling each other produces no effect upon it; and it muft either be quiefcent, or proceed uniformly in a right line. All feem agreed that the centre of the system is at reft, and no reafon or obfervation argues for our afcribing any motion to it. The centre of gravity of the fyftem is, therefore, the only immoveable point, while all the bodies in the fyftem move round it with various motions.

3. As we have our knowledge of gravity, and the laws of nature, from what paffes on the furface of the earth, we cannot illuftrate the motions of the bodies of the folar fyftem, arifing from their mutual gravity, better than by fome images we find of them on the earth, after having fhewn fo fully the fimilarity of the powers that act on the parts of the earth and on the celeftial bodies. We know that when, by any power or machine, a body is projected in the air, the power reacts on the earth with an equal force, and that if the power was fufficient to project a mountain or a much larger part of the earth, it would act on the remainder of the earth with an equal force, in an oppofite direction; fo that while the projected part began to move in its curve, the remainder of the earth would begin at the fame time to move in an oppofite direction, with