G R A V I T A r I O N. 



for the_ heiglit whitli the rrtoon fliould M through in one with the direaion of its motion. Ttir force of gnthr to- 



_ 1 J ? r- . ^ . . .. ng the Irconc! part 



differing only ^'iedth part from that derived from aftu::! of its cllipfe. In this part, the gravity towards the fun in- 

 obfcrvation, to wliich La Phice thinks it pn*ferablc, con- creafes it? velocity in the hme manner' as it hi-forc d-crc afcd 



fidcring the exacliiL-fs of tlie ek-nunts from which it is it ; and the planet will arrive at its perihelion with its 



computed. It would be fufficient to dii-iinifli a little the primitive velocity, and recommences a new revolution fimi- 



jiiafs of the moon to obtjin, by this theory of gravity, lar to the firlt. ' Now th- cnrvatnre of tlie ellipfe at the 



the lame parallax that is given by obiVrvation : but all the aphelion and perihelion being the fame, the radii of cnrva- 



phenomena of the tides concur in giving this fatcllite a tiire are the fame, and, confequentlv, the centrifugal forces 



mafs more confiderablc, and very nearly fuch as has been of thcfe two points are as the Iqiiares of the velocities. The 



ufed in the above computation. But however that may feftors defcribt-d in the fam" time being equal, the aphelion 



be, the fmall difference between the two parallaxes is and perihelion velocities are reciprocally as the corrcfpond- 



within tli; limits of the errors of obfervation, and of the ing diilances of the planet from the fun ; the fquares of 



elements employed in the calculation. It is then certain thefe vehjcities are therefore reciprocally as the fquares of 



that the force v.hich retains the moon in its orbit, is the thefe diilances ; but at the perihelion and aphelion ditlances, 



terreftrial gravity dimiiiifhed in proportion to the fquare the centrifugal forces in tlie ofculalory circumferences are 



of the diftance. evidently e<|ual to the gravity of the planet towards the fun. 



Having thus fiiewnhowthe nature of the forceuliich retains which is therefore in tlie inverfe proportion to the fquares ot 



the moon in its orbit is i.ivelligated, it next remains to inquire thefe dillances. Thus the theoiems of Huygens on the cer- 



if the. fame force of gravity pervades the rell of the iblar trifugal force were fufficient to den;onllrate the tendrtlcv cf 



fyilem. The fame great mathematician, above quoted, ob- the planets towards the fun : for it is highly probable that 



ferves, that " o: all the phenomena of the fohir iyllem, the this law, v\-hich extends from one planet to another, and 



elliptic motion of the planets, and of ti:e comets, feemsthe which is verified in the fame planet, at its aphelion and peri- 



nioll proper to conduct us to the general law of the helion, extends alfo to every part of the planetary crbit, and 



forces by which they are animated. at the fame time to every dillance from the fun But tu 



Obfervation has Ihevvn, that the areas defcribed by the ra- eftablilh it in an inconteltible maimer, it was requifite to de- 



dii vedores of the planets and comets about the fcMi are pro- termine the general expredion of tlie force which, directed 



portional to the times. Now we fee, in the article Centk.m, towards the focus of an ellipfe, would oblige the projeftile to 



Forces, thai, for this to take place, the force which deflefts dcfcribe that curve. And it was Newton who den-.onftrated 



the path of thefe bodes from a right line mull conllantly that this force was reciprocally as the fquare of the radius 



be direfted towards the origin of their radii veftores. The veftor. It was eifential alfo to demondrate rigoroully that 



tendency of the planets and comets to the fun is theretore a the force of gravity towards the fun only varies in one planet 



neceffary confequence of the proportionality of thefe areas from the fame force in another, according to their different 



to the times in which they are defcribed. To determine dillances from it. 



the law of this tendency, let us fuppofe that the planets This great geometri( ian fliewed, that this followed necef. 

 tnove in circular orbits, which fuppolition does not greatly farily from the law of the fquares of the periodic limes being 

 differ from the truth. The fquares ot their real velocities reciprocally as the cubes of the dillances ; fuppofmg therefore 

 will then be proportional to the fquares of the radii of thefe all the planets at rell at the fame dillance from the fun, and 

 orbits, divided by the fquares of the times of their revolu- abandoned to their gravity towards its centre, they woijld 

 tions. But, by the law of Kepler, the fquares of thefe detcend from tlie fame height in equal times : this refult 

 times are to each other as the cubes of their radii; th.e fhould alfo extend to the comets, notwithftanding the greater 

 fquares of the velocities are therefore as thefe radii. It has axes of their orbits are unknown ; for we have leen in the fe- 

 been ihewn, that the central forces of bodies, moving in cir- coiid book, that the magnitude of the areas defcribed by ' 

 cular orbits, are as the fquares of the velocities, divided by their radii veClores, fuppoles the law of the fquares of the 

 the radii of the circumferences defcribed; the tendency, periodic times proportional to the cubes of thuraxes. 

 therefore, of the planets to the fun, is reciprocally as the A general analylis, which embraces every polTble rcfiilt • 

 fquares of the radii of their orbits, fuppofed circular. This from a given law, ihews us that not only an elhpfe, but any 

 hypothefis, it is true, is not rigoroufly Cvacl ; but the con- other conic feClion, may be defcribed by virtue of the force 

 ftant relation of the fquares of the times to the cubes of which retains the planets in their orbits ; a comet may there- • 

 the ereat.u- axes of tlieir orbits being independent of their fin-e move in an hyperbola, but then it would be only once- 

 excentricilies, it is natural to think it would lubfill alfo in vilible, and after its apparition would rvceJe' from the limits- - 

 the cafe of the orbits being circular. Thus, the law of of the folar fyllem, to approach other fnirs, which it would 

 gravity towards the fun, varying reciprocally as the fquare again abandon, thusvlliting the diffpsent fyllems that arc 

 of the dillance, is clearly indicated by this relation : analogy fcattered in the immenlity of the heavens. It is probable, 

 would lead us to fuppofe that this law, whic'i extends from conlidering the infinite variety of nature, that fuch bodies 

 one planet to another, fhould lublill cq\rally for the fame exill. Their apparition lliould be a very rare occurrence ; 

 planet at its different dillances from the fun ; and its elliptic the comets, we ufuallv obfervp, arc thofe which, hanng 

 motion confirms this beyond a doubt. To comprehend this, clofed orbits, return, at the end of intervals more or lefs con- 

 let us attend to this motion, beginning at the departure from liderable, into the regions of fpace that are in the vicinity of 

 its perihelion. Its velocity is then at its maximum, and its the fun The fatellites tend alfo perpetually to the fun. If 

 tendency to recede from the fun furpaffing its gravity to- the moon was not fubjert toitsaftion, intlead of defcribing' 

 wards it, its radius veftor augments, and forms an obtufe angle ;ui orbit &Lnoft circular round the earth, it would foon abau- 



deo.. 



