31.3
ASTRONOMY.
servations on the comets of 1331, 1607, and 1682; and havingcalculated the positions and dimensions of their orbits, found themso nearly the same, that he concluded they belonged to the samecomet ;.he, therefore, ventured to predict its return in 1738 or1759:the prediction, was verified, aim the period determined to beabout 75j years. Its next return is expected to be about A. D. 1S34.'Thus also the comet of 1680 appears to be the same asthat seen 44vears B. C. alsoin a 31, and in 1106 , having a period of 075 veers.’(1 94.) As the elliptic orbit of a comet is so very eccentric, that por-tion of it wherein it becomes visible tons, may pass for a parabola.By considering, therefore, that portion as [tart of a parabola nearits vertex, the calculation of their motions becomes much easier;and upon that hypothesis Dr. Halley has constructed and calcu-lated a table, by which, whenever a new comet shall appear, itmaybe determined whether it be any of those which have yet ap-peared, and consequently its period, and the axis of its orbit, bedetermined, and its return foretold.
(193.) The orbits of near 100 comets have been calculated, andthe position of their orbits determined; hence, when a cometshall appear and describe the same or nearly the same path wemay be assured it is the comet before observed. Sir Isaac New-ton remarks, that as the great eccentricity of the orbits of cometsrenders them very liable to be disturbed by the attraction of theplanets and other comets, it is probably to prevent loo great dis-turbances from these-, that while all the planets revolve nearly inthe same plane, the comets are disposed in very different ones, anddisposed all over the heavens ; that when in their greatest distancefrom the Sun, and moving slowast, they might be removed asfar as possible out of the reach of each others action. The sameend is likewise answered in those comets, which by movingslowest in the aphelion descend nearest to him by placing theiraphelion at the greatest height from tin; Sun.
Sect. XV. Op the Bodies or the Sun* and Pi.anets, the
Quantity or Matter they contain, and their Den-sities.
(196.) The primary planets and comets being retained in theirorbits by a power directed towards the Sun , and the secondariesbeing also retained by a similar power directed to the centre ofthe primaries, the same pow er is diffused through their whole sub-stance, and inherent in every particle. This is proved by shew ingthat each of the heavenly bodies attracts the rest, and otherbodies, with such different degrees of force, as that the force oftlie same attracting body is exerted on others, exactly in propor-tion to the quantity of matter contained in the body attracted.The first proof of this is from the experiments made on bodies onour Earth . Pendulums vibrate by the same power which makesheavy bodies fall to the ground; but if the ball of any pendulumof tlie same length with another were more or less attracted iniroportion to the quantity of solid matter it contains, that pendu-mn must then vibrate faster or slower than the other. Now thevibration of pendulums continue for a long time, and the numberof vibrations they make may be easily determined w ithout suspi-cion of error; and Newton assures us, that he examined severalsubstances, as gold, silver, lead, glass, sand, common salt, wood,water, and wheat; in all which he found not the least deviationfrom the theory, though he made the experiment in such a man-ner, that in bodies of the same weight, a difference in the quantityof their matter less than the thousandth part of the whole wouldhave discovered itself. It appears, therefore, that all bodies aremade to descend to the surface of our globe by the power of gra-vity with the same degree of swiftness. This descent to thesurface at the equator has been determined at feet in the
first second from the beginning of their fail. Ifany teircstrial bodycould be conveyed as high up as the Moon , it would descend withthe verysame degree of velocity with w hich the Moon is attractedtowards the Earth ; and therefore the pow er of the Earth upon tlieMoon bears the same proportion it would have upon those bodiesat the same distance as the quantity of matter in the Moon bearsto the quantity in those bodies. Thus the assertion is proved jntlie Earth , and its power on every body it attracts is, at the samedistance from the Earth , proportional to the quantity of solid matterin the body acted upon. As to the Sun, the power of his actionupon the same primary planet is reciprocally in the duplicate pro-portion of its distance; and that his power decreases throughoutin the same proportion, is testified by the motion of the planetstraversing the whole planetary region. This proves that if anyVC!-. I — SO 20.
planet was removed from the Sun to any distance whatever, thedegree of its acceleration towards the Sun would yet be recipro-cally in the duplicate proportion of their distance. But the de-gree of acceleration given to the planets by the Sun is reciprocallyin the duplicate proportion of their respective distances ; all u liirli",compared together, puts it out of doubt, that the power of theSun upon any planet removed into the place of any other, w ouldgive it the same velocity- of descent as it gives that other : andconsequently that the Sun’s action upon ditierent planets at thesame distance would be proportionable to the quantity of matterin each. The Sun attracts the primary planets and their respec-tive secondaries, when at the same distance, in such a maimer asto communicate to both the same .degree of velocity ; and there-fore the force wherewith the Sun acts on the secondary planet bearsthe same proportion to the force wherewith it attracts the pri-mary, as tlie quantity' of matter in the secondary planet bears tothe quantity of matter in the primary. This property therefore kfound in the Sun with regard to both kinds of planets; so that hepossesses the same quality found in the Earth , viz. that of acting onbodies with a degree of force proportional to tlie quantity of matterthey contain. This point being granted, it is hardly to be sup-posed that the power of attraction with which the other planets areendowed, should be different from that of the Earth , if we con-sider the similitude of these bodies; and hence it follows, thatthis attraction extends itself to every particle of matter in the at-tracted body, and that no portion of matter is exempted from theinfluence of these bodies to which this attractive power has beenproved to belong. In a word, the attractive power both of the Sunand planets appears to be the same in all: for it acts in each in thesame proportion to the distance, and in the same manner acts alikeupon every particle of matter. This power, therefore, in the Sun and planets, is not of a ditierent nature from tlie power of graVits-in the Earth : and this enables us to prove, that the attractingpower lodged in the Sun and planets belongs likewise to every partof them ; and that their respective powers upon the same bodv areproportional to the quantity of matter of which they are com-posed; for instance, that the force with which tlie Earth attractsthe Moon , is to the force with which the Sun would attract it ; tthe same distance, as the quantity of solid matter in the Earth isto that in the Sun . 1 he rule that action is equal to re-acf'onholds good in the attractive powers as well as in any other. Themost remarkable force of this kind with which wo are acquainted,next to that of gravity, is the attraction the loadstone has foriron. Now if a loadstone and piece of iron w ere both made toswim on water, both of them would move towards each other, andthus the attraction would lu> shewn to be mutual; and whenthey meet, they will mutually stop each other; which shews thattheir velocities are reciprocally proportional to tlie quantities ofsolid matter in each ; and that by the stone’s attracting the iron,it receives as much motion it-eif in the strict philosophic sense ofthe word, as it communicates to the iron : for it is proved from ex-periments on the percuss'n n of bodies, that if two meet with velo-cities reciprocally proportional to their respective bodies, tb.evwill be stopped by the concourse, unless thev meet with sumoother velocity, or their elasticity put them into fresh molten.
(197.) I rom the times in which tlie satellites perform their revolu-tions, compared with their distances from their respective primaries,tlie proportion between the power with which one primary altra< ishis satellites, and tire force with which any other attract- his, willbe known; and the proportion of the power with which any pla-net attracts a body at its surface, is found by comparing the dis-tanceot the secondary planet from tlie centre of the primary tothe distance of the primary planet’s surface from tiie same; "andfrom hence is deduced the [iroportion between the power of gra-vity upon the surface of one planet to the gravity upou the surfaceof another. By the like method of comparing tlie periodical timeof a primary planet about the Sun, w ith the revolution of a satelliteabout its primary, may be found the proportion of gravity, or ofthe weight of anybody, on the surface of the Sun, to the'gravitvor tlie weight of' the same body upon the surface of the planetwhich carries about the satellite. By computations of this kind,astronomers have found the relative densities of the Sun ; il l suchplanets as have satellites, together with their quantities of u.alter.,and the space through which a heavy body would fall in onesecond to their surfaces. The result of these calculations withmany other particulars will be found in the following tables.
4L (193.) TABLE