it generates the fame velocity in the fame time in all bodies. whatsoever at the fame diftance, it follows that their weight or motion arifing from it, must be proportional to their quantities of matter. In general, to estimate the weight or motion of any sphere that is attracted by another whofe parts are equally denfe at equal diftances from its centre, we are to measure it by compounding three proportions, that of the matter in the heavy bodies that gravitate, that of the matter in the attracting spheres to which they gravitate, and the reciprocal proportion of the fquares of the refpective dittances betwixt the centres of the spheres that tend towards each other; and this is the law which we found from the phæ nomena to take place in the fyftem. See art. 2. of this chapter.

14. Thus Sir Ifaac Newton difcovered and fully described, from undifputed obfervations and unexceptionable calculations, this fimple principle of the gravitation of the particles of matter towards each other; which being extended over the system to all distances, and diffufed from the centre of every globe, is the chain that keeps the parts of each together, and preferves them in their regular motions about their proper centres. The fame gravity, which is fo well known to us on the earth, affects them all; the whole mass of the system is, in this refpect, of a piece; and this one principle, fo regularly diffused over the whole, fhews one general inAluence and conduct, flowing from one caufe equally active and potent every where. Several obfervations have been made of late that greatly confirm his doctrine, and particularly ferve to fhew that the gravitation towards bodies arifes from the gravitation towards their particles. Of this kind are the meafures of a degree on the meridian made lately, with

great

great accuracy, by the French mathematicians; and the declination of the plumb-line from the true vertical, in confequence of the attraction of a great mountain in the neighbourhood.

CHAP. V.

Of the quantity of matter, and denfity, of the fun and

TH

planets.

HUS far our author afcends by way of analyfis, tracing the caufes from their effects, and from the coincidence, or perfect fimilarity, of many effects, fhewing the cause to be more general. But in order to defcend by the fynthefis, and to determine the effects from the cause now known, it was not fufficient to establish the general gravitation of the particles of matter; it was requifite to determine, as far as poffible, the quantities of the powers which act in the fyftem. We have seen that there is a gravity extending from each body in the system on all fides, at equal distances from their centres proportional to their quantities of matter. We know, from experience, the force of this power at the surface of our own earth, and have feen how to estimate its efficacy at any other distance. In order to be able to eftimate all the powers in the fyftem directed to their different bodies, it is neceffary to determine the proportion of their quantities. of matter to that of our earth. If this is once obtained, all the powers that operate in the fyftem being known, it will require no more but a skilful application of geometry and mechanics to determine the motions and phænomena of the celestial bodies, which all flow from them.

2. To measure the matter in the fun and planets was an arduous problem, and, at first fight, seemed above the reach of human art. But the principles of this philofophy afforded a natural and easy folution of it in the most important cafes, and Sir Ifaac Newton has determined the proportions of the matter that is in the Sun, Jupiter, Saturn, and the Moon, to that in our Earth; that is, he has fhewed how many earths might form a Sun, a Jupiter, or a Saturn. To understand how he was able to difcover this, we are to recollect that the matter in each of thefe is in the fame proportion as the force of gravity toward them, at equal diftances from their centres. We know the force of gravity towards our earth from the defcent of heavy bodies, and alfo by calculating how much the moon falls below the tangent of her orbit in any given time. We have no experience of any rectilineal descent of heavy bodies toward the Sun, Jupiter, or Saturn; but as the primary planets revolve about the fun, and their fatellites revolve about Jupiter and Saturn, by computing from their motions how much a primary planet falls below its tangent in a given time, and how much any of Jupiter's and Saturn's fatellites fall below their tangents in the fame time, we are able to determine the proportion which the gravity of a primary planet to the fun, and of a fatellite towards its primary, bears to the gravity of the moon towards the earth, in their respective distances: then from the general law of the variation of gravity, the forces that would act upon them at equal diftances from the Sun, Jupiter, Saturn, and the Earth are computed; which give the proportion of the matter contained in these different bodies.

3. That the quantity of matter in Jupiter is greater than the quantity of matter contained in the earth, we may eafily learn from the motion of his fatellites; all of which revolve about his centre in lefs time than the moon revolves about the earth, and are all, excepting the firft, at a greater diftance from his centre than the moon is from the earth. The fecond fatellite is farther diftant from Jupiter than the moon is from the earth in the proportion of 3 to 2 nearly; and moves in an orbit greater in the fame proportion. But this fatellite finishes its revolution in 3 days, 13 hours, which is less than a feventh part of the moon's periodic time about the earth; confequently its motion must be much more fwift than that of the moon. A fatellite nearer Jupiter would move ftill more swiftly than this fatellite: fo that if a fatellite revolved about Jupiter at a distance from his centre equal to the distance of the moon from the earth, it would move much more swiftly than the moon moves about the earth, and therefore would be acted on by a much greater centripetal force; for it requires always a greater force to bend into the fame orbit a body that moves with a greater velocity. But the quantities of matter in the central bodies are proportional to their attractive powers at equal distances, and therefore the matter in Jupiter must very much exceed the matter in the earth. In like manner, we may eafily obferve that Mercury revolves about the fun in very little more than thrice the time in which the moon revolves about the earth, and yet moves in an orbit about 140 times greater, being so many times farther diftant from the centre of his motion; from which it is easy to see that if a fatellite revolved about the earth as far diftant from it as Mercury is from the fun, this fatellite would move vaftly flower than Mercury: whence

X

Book III. whence it follows that the attractive power of the fun must be vastly fuperior to that of the earth, and therefore that the fun muft contain vastly more matter than the earth. The matter in Saturn is alfo found to be greater than that in the earth. From our author's calculations, founded on these principles, it follows that the quantities of matter in the Sun, Jupiter, Saturn and the Earth are to each other as the numbers 1, 1887, JOZTI 189282•

4. The quantities of matter in these bodies being thus determined, and their bulk being known from aftronomical obfervations, it is eafy to compute what matter each of them contains in the fame bulk; which gives the proportion of their denfities. Thus our author finds the denfities of the Sun, Jupiter, Saturn and the Earth, to be as the numbers 100, 942, 67 and 400.

From which it appears that the earth is more denfe than Jupiter, and Jupiter more denfe than Saturn; that is, thofe planets which are nearer the fun are found to be more denfe, by which they are enabled to bear the greater heat of the fun. This is, the refult of our moft fubtile enquiries into nature, that all things are in the best fituations, and difpofed by perfect wisdom. If our earth was carried down into the orb of Mercury, our ocean would boil and foon be diffipated into vapour, and the dry land would become uninhabitable. If the earth was carried to the orb of Saturn, the ocean would freeze at fo great a distance from the fun, and the cold would foon put a period to the life of plants and animals. A much less variation of the earth's distance from. the fun than this would depopulate the torrid zone if the earth came nearer the fun, and the temperate zones, if it was carried from the fun. A lefs heat

at

1