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the geniu,> of Newton ; and diongh Ilooke churned a lliarf 

 of the glory of this difcovery, it was without the fiuallcll 

 foundation ; as liis conjeftures were far Ihort of the proofs 

 which were required in the fuUime dcmonftrations by which 

 the former cftabhfhed this law of the iiniverle. 



Such was the progrefs of the fyftem of univerfal gravi- 

 tation, when this extraordinary man firfl appeared ; who, ac- 

 cording to Pemberton (View of fir Ifaac Newton's Pliilo- 

 fophy, 17^5, 4to.), firll began, about the year i66fi, to fuf- 

 petl the exigence of this principle, and to attempt to apply 

 it to the celcdial motions. Having retired into the country 

 to avoid the plague, which about tliis time prevailed in Lon- 

 don and its vicinity, his meditations turned upon tlie nature 

 of gravity ; and one of his firlt reileftions appears to have 

 been, that this pou-er, which, by its continual action, occa- 

 fions the fall of bodies towards the furface of the fcarth, to 

 whatever height they are taken, might poflibly extend much 

 farther than was commonly, imagined ; as for inftance, to the 

 diftance of the moon, or Hill higher. And if fo, he began 

 to confider, that it might be this force which retained the 

 moon in her orbit, by counterbalancing the centrifugal force 

 which arifes from her revolution round the earth. It alfo 

 occurred to him, at the fame time, that though this power 

 appears to fuffer no diminution at any heights to which we 

 can afcend, thefe bting comparatively extremely fmall, yet 

 it was highly probable, that, at very great diftances from 

 the earth, it might be coniiderably weakened. 



In following therefore tliis conjefture, he was farther led 

 to conceive, that if the attraftion of the earth was the caufe 

 of retaining the moon in htr orbit, the planets, in like man- 

 ner, muft be retained in their orbits by the attractive force 

 of the fun ; and as the fquares of the times of the revolu- 

 tions of the planets had been found by Kepltr to be propor- 

 tional to the cubes of their mean dlltances from, the fun, it 

 followed that the diminution of their centrifugal forces, and 

 of courfe that of gravity, would be reciprocally as the fquares 

 of their diilances from that body. Hence, from the experi- 

 ments which had been already made on the defcent of heavy 

 bodies at fmall elevations, he determined tiie height from 

 which the moon, if left freely to hcrfelf, would defcend to- 

 wards the earth in a ihort interval of time : this is v>ell 

 known to be the verfed line of the arc that Ihe defcribes in 

 that time ; and which, by means of the lunar parallax, may 

 be determined in parts of the earth's radius; fo that to com- 

 pare the diminution of gravity with the obfervations, no- 

 thing more was neceflary than to know the magnitude of this 

 line. 



But Newton having at that time only an incorreft mca- 

 fure of the terreflrial meridian, obtained a refult coniiderably 

 different from that which he expected ; whence, imagining 

 that fonie unknown forces might be connefted with the 

 gravity of the moon, he abandoned his firll ideas. Some 

 years afterwards, hov.ever, his attention was again called to 

 the fubjeCt by a letter of Dr. Hooke ; and as Picaid, about 

 this time, had meafurcd a degree of the earth in France with 

 great exactnefs, he employed this meafure in his calculations 

 inftead of the one he had liefore made ufe of, and found, by 

 that means, that the moon is retained in her orbit by the lole 

 power of gravity, fnppofed to be reciprocally proportional to 

 the fquares of the dillanccs. 



According to this law, he alfo found that the line defcri- 

 bed by bodies in their delcent is an ellipie, of which the 

 centre of the earth occupies one of the foci ; and confider- 

 ing, afterwards, that the orbits of the planets are, in like 

 manner, elliples, having the centre of the fun in one oi their 

 foci, he had the faiisfaction to perceive, that the folution 

 Hrhich he had undertaken, only from curiofity, was apphcable 



ATT 



to fume of the mofl fublime objects of nature. Thefe dif- 

 coveries gave birth to his celebrated work entitled, " Philo- 

 fophia: Naturalis Principia Mathematica," which appeared 

 in 1767 ; and is juftly confidered a.i one of the grcateft mo- 

 numents that has ever been erefted by human genius to t!ic 

 honour of fcicnce. 



In gcneralifing thefe reftarches, this profound geometer 

 afterwards (hewed, that a projeftile may defcribe any conic 

 fedtion whatever, by virtue of a force directed towards its 

 focus, and acting in proportion to the reciprocal fquares of 

 the diilances. He alio developed the various propeitiej of 

 motion in thefe kinds of curveSv.and determined the uccclTary 

 conditions, fo that the feftion fhould be a circle, an eliipfe, 

 a parabola, or an hyperbola, which depend only upon the 

 velocity and primitive pofitiou of the body ; afligning, in' 

 each cafe, the conic feftion which the body would defcribe. 

 He alfo applied thefe refearches to the motion of the fatel- 

 lites and comets, (hewing that the former move round their- 

 primaries, and the latter round the fun, according to the 

 fame law ; and he pointed out the means of determining, by 

 obfervation, the elements of thefe elllpfes. 



In conlidering that the fatellites move round the planets 

 in nearly the fame manner as if thefe planets were quicfccnt, 

 Newton perceived that they muit all equally gravitate to- 

 wards the fun. The equality of acfion and re-adtion, did 

 not allow him to doubt that the fun gravitates towards the 

 planets, as well as thefe towards their fatellites ; and that the 

 earth is attrafted by all the bodies that are attradted towards 

 her. He afterwards extended, by analogy, this property to 

 all the parts of which bodies are compoftd, and eftablifhed 

 it as a principle, that every molecnle of matter attra£ts every 

 other body in proportion to its mafs, and reciprocally as 

 the fquare of the diltance from the body attrafted. 



Having arrived at this principle, Newton foon faw that 

 all the great phenomena of the fyltem of the world might 

 be calily derived from it. In conlidering the force of gra- 

 vity at the fiirface of the ccleltial bodies as the rifultanle of 

 the attractions of all their molecules, he arrived at thefe re- 

 markable conclulions: that the attractive force of a body, 

 or fpherical ftratum, on a point placed without it, 

 is the fame as if the whole of its mafs was united 

 in the centre ; and that a point placed within the body, or 

 more generally in any ftratum terminated by two fimilar el- 

 liptical furfaces, limilarly (ituated, is equally attradttd on all 

 parts. He alfo proved that the rotatioa of the earth upon 

 its axis muft occaiion a flattening of it about its poles, 

 which was afterwards verified by an adlual meafuremtnt; and 

 he determined the law of the variation of the degrees, in 

 different latitudes, upon the fuppofition that the matter of 

 the earth was homogeneous. He likewife faw, that the actions 

 of the fun and moon upon the terreftrial fpheroid, mull pro- 

 duce a movement of rotation of its axis, as well as occafion 

 a rctrocefiion of the equinoxes, and the various ofcillations 

 of the waters of the ocean which are called tlie tides. In 

 (lioi t, he alfo afhired himfelf, that the inequalities of the mo- 

 tion ot the moon aiife from the combined actions of the fun 

 and earth upon this fatellite. 



But, with the exception of what concerns the elliptical 

 motions ot the planets and comets, and the attrattions of 

 fpherical bodies, thefe difcoveries were not wholly coiriplet- 

 ed by Newton. His theory of the figures of tlie planets is 

 limited by the fuppofition of their homogeneity ; and his fo- 

 lution of the problem of the preccfiion of the equinoxes, al- 

 though extremely ingenious, and nearly agreeing with the 

 refults obtained from obfervations, is defedlive in feveral 

 relpedts ; as among the great number of perturbations of 

 the celcftial motions, feveral fmall ones, and particularly 



that 



