GRAVITATION. 



(lowed with an attraftive force proportional to their mafTea, 

 and varying inverlely as the fquare of the dillance. By 

 the fame principle, the fatellites attraft the planets and the 

 fii:i according to the fame law. This attraftive property, 

 tticn, is common to all the celeftial bodies : it docs not dif- 

 tinb the elliptic motion round the fun, when we canfider only 

 their mutual attion ; for the relative motion of the bodies of 

 a lyftem are not changed by giving them a common ve- 

 locity : by impreffing, therefore, in a contrary direftlon to 

 the ftm and to the planet, the motion of the firil of thefe 

 two bodies, and the aiftion wliich it experiences on the part 

 of the fecond, the fun may be confiJered as immoveable, 

 but the planet wdl be folicited towards it with a force vary- 

 ing reciprocally as the fquare of the diftance, and propor- 

 tional to the fum of the mafles ; its motion round the fun 

 vvill therefore be elliptic. And we fee by the fame reafon- 

 i:ig, that it would be fo if the planet and fun were carried 

 through fpace with a motion common to each of them. It 

 is equally evident that the elliptic motion of a fatellite is not 

 dillurbed by the motion of tranflation of its planet, nor 

 would it be by the attion of the fun, if it was always ex- 

 actly the fame on the iatellite and the planet. 



Neverthelefs, the aclion of the planet on tlie fun influ- 

 ences the length of its revolution, which is diminiflied as the 

 niafs of the planet is more confideratle ; fo that the relation 

 of the fquare of its periodic time, to the cube of the major 

 axis of its orbit, depends on its mafs. But fince this relation 

 is nearly the fame for a'l the planets, their mafles muft evi- 

 dently be very fmall compared with that of the fun, wliich is 

 equally free for the fatellites with refpecl to their principal 

 planets. 



This we may readily fuppofe from their fmallnefs. 

 The attraftlve property of the heavenly bodies not only 

 belongs to tlicm in a mafs, but to each of their particles. 

 If the fun only afted on the centre of the earth without at- 

 tradling particularly every one of its particles, ofciliations 

 would arife in the ocean, infinitely more confiderable and 

 very different from thofe which we obferve. The gravity 

 of the earth to the fun, therefore, is the refult of the gra- 

 vity of all its particles, which confequently attraft the fun 

 in proportion to their refpeftive mafles ; befides, each body 

 on the earth tends towards its centre proportionally to its 

 mafs, it re afts therefore on it, and attrafts it in the fame 

 ratio. If that was not the cafe, and if any part of the 

 earth, however fmall, attrafted another part without being 

 attracted by it, the centre of gravity would move in fpace, 

 in virtue of the force of gravity, which is impoflible. 



The celeftial phenomena, compared with the laws of mo- 

 tion, condiift us therefore to this great principle of nature, 

 namely, that all the particles of matter attratt each other in 

 proportion to their mafles, and iuverfely as the fquares of 

 their diftance. 



Already we may perceive in this univerfal gravitation, the 

 caufe of the perturbations to which the heaveiily bodies are 

 fubjed ; for the planets and comets being uibjedt to the ac- 

 tion of euch other, they muft deviate a little from the laws 

 of the elliptic motion, which they woidd otherwifc exadly 

 follow, if they or.ly obey.-d the adion of the fun. The fa- 

 tellites alfo, deranged in their motions round ,heir i)I:ii.ets by 

 their mutual aftion, and that of the fun, deviate a little from 

 thefe laws. 



We perceive then that the particles of the heavenly bodies, 

 united by their attraction, fliould form a iijals nc'ai !y fp.he- 

 rical ; and that the relult of their aftion ,at the furface of the 

 body fhould produce all the phenomena of gravitation. 



We fee moreover that the motion of rotation of tlie 

 Cekaial bodies fltould flightly alt(;r their fpheric;d figiu-e, 



and flatten them at the poles ; and then the rtfulling force 

 of all their mutual adtions not pafl'mg through their centres 

 of gravity, fhould produce in their axcj of rotation fimilar 

 motions to thofe difcovcred by obfcrvation. Finally, we 

 may perceive why the particles of the ocean, une<;naUy 

 afted on by the fun and moon, fliould have ofciliations 

 llmilar to tiie ebbing and flowing of the tides. But thefe 

 dift'erent effedts of the principle of gravitation muft be par- 

 ticularly developed, to give it all the certainty of which 

 phylical truth is fufceptible. 



It is in the univerfal application of this theory to all the- 

 known celeftial phenomena, that the modern fcirnce of 

 phyfical aftronomy confifts, a fcience which owes its origin 

 to Newton, and which has been cultivated bv everv eminent 

 mathematician, from tlie time of that great pTiiloibpher to 

 the prefent day. It is to La Place that the merit muft be 

 given of having completed this theory, by (hewing that there 

 remains not a fingle phenomenon that it is not capable of 

 explaining: he jullly obferves, tliat there is no queftion here 

 ot vague cnufes, which cannot be fubmitted to analyfis, and 

 which the imagination modifies at pleafurc, to accommodate 

 them to the phenomena. The law of univerfal gravitation 

 has this ineftinrable advantage, that it may be reduced to 

 calculation, and by a comparifon of its refults with obferva- 

 ticn, it prefents the moft certain method of verifvirg its 

 exiftence; and fo far are we from having to far that new 

 obiervations w dl difprove this thv ory, we may be afTured 

 before hand that they will oidy confirm it more and n.ore, 

 and that its confequenccs are equally certain as if ihov had 

 aCtuaUy been obferved. 



The aftronomical phenomena produced bv the mutual 

 gravitation of the heavenly bodies, will be fonnd in the 

 difl^ rent parts of tiiis work. As each fubjec\ will be par- 

 ticidarly treated under its appropriate ar.icle, fee Figure 

 of the Eauth ; Pricejfton nf the EtiUINO.XES ; NtTATtOM 

 of the Earth's a.vis ; Pehtuhbatio.n of the Plantls, Mmh, 

 and Satellites iTlDZS, LlBRATlox of the Moon, SiC. 



But as the inveftigation of laws by which particles of 

 matter gravitate to fpheres and other fohds cannot witlj 

 propriety be referred to any other article, and as it forms 

 fo very eflcntial a part of phyfical aftronomy, we fliall enter 

 on the lubjeft very fully. The more fimple and cafy invcfti- 

 gations of aftronomy fuppofe the aftion to be confined to 

 fimple gravitating points ; now as no fuch points exift in 

 nature, it becomes requifite to confidcr the effeA which an 

 aflemblage of thefe points will produce when ammged in 

 d-ilferent forms. Newton, who firft entered upon thefe fpe- 

 culations, inveftigatcd almoft all the cafes which feem appli- 

 cable to phyfical aftronomy, but profeflor PI ivf.iir has Litely 

 extended thefe refearches, and lias prefented a paper on the 

 fubi'.'A to the Philoiophical Society of Ldinburgh, wttich 

 would reflcrt honour on the firll mathematicians of Europe. 

 A few of the leading propofitions of tins excellent monioir, 

 will follow the inveftigation of the law of gravitation to a 

 fphere. 



Of the gravitation of particles of matter to fplurcs, and 

 other matiiematical figures. 



I . ^ piirticle of nuiller placed ivhhia a fphere of unform Jrif 

 Jiiy, remains in equtlibrio. 



Let A LBM,n//)m, (P/.i/eXV. yf^rcno«if,/f. IJ4.'> bfe 

 two fpherical iiufaces, of which C is the common centre, and 

 let the fpace between tliem be filled wiih gravitating rrwttcr, 

 uniformly denfe. Let p be a particle j liced any where witliin 

 this fpherical fhell, to every particle of whicli it gravitates w ith 

 a force iuverfely as the fquare of its diftance from it. T!>ij 

 particle will have no tendency to move in any direction, becaufe 



its 



