GRAVITATION. 



don it ; and if this fatellite, and tViofe of Jupiter, were not tellite, but it may be fupplied from the following confider- 

 folicited towards the fun, according to the fame law as the ations : 



planets, perceptible inequalities would refult in their motions The force of gravity extends to the fummits of the high- 

 which have not Ix-en recognized by obfcrvation. eft mountains, and the fmall diminution whicli it there expe- ' 



The planets, comets, and fatellites are therefore fubjeft riences, leaves no doubt but that this force would be per- ! 

 to the fame law of gravity towards the fun. At the fame time ceplible at much greater altitudes. Is it not natural to ex- 

 that the fatellites move round their planet, the whole fytlem tend this to the moon, and to fuppofe that the force which 

 of the planet and its fatellites is carried by a common motion, retains it in its orbit, is its gravity tovvards the earth, in the 

 and retained by the fame force, round tlie fun. Thus the fame manner as the folar gravity retains the planets in their 

 relative motion of the planet and its fatellites is nearly tlie orbits round the fun ? for, in faft, thefe two forces feem to 

 fame as if the planet was at rell, and not adted upon by be of the fame nature ; they both of tliem penetrate the moft 

 any external force. intimate parts of matter, animating them with the fame ve- 



We are thus condufted, without the aid of hypothefis, loclties ; for we have feen that the folar gravity folicits 

 by aneceffary confequence of the laws of the celeliial nio- equally all bodies placed at equal diftances from the fun, 

 tions, toconhderthe fun as the centre of a force, which, ex- and that the terreftrial gravity alfo caufes all bodies to fall 

 tending infinitely into fpace, diminiflios as the fquare of the through the fame height in equal times, 

 diftance increales, and which attraits all bodies that are A heavy body, projeded with force horizontally from <( 

 witliin the fphere of its attivity^ Every one of the laws of great heiglit, falls on tlie earth at a confiderable diftance, de- 

 Kepler difcovers a property of this attraftive force. The icribing a curve, whicli is apparently parabolic ; it will fall 

 law of the proportionality of the areas to the times (hews ftill further, if the force is greater, and fuppofmg it about 

 us, that it is conftantly direfted towards the centre of the fun. fevea thouland metres in a fecond, it would not fall to 

 The eUiptic orbits of the planets fhew that this force dimi- the earth, but would circulate round it like a fatelhte, fct- 

 nidics as the diftance increafes ; finally, the law of the pro- ting ahde the refiftance of the air : for it has been fuily 

 portionality of the fquarcs of the periodic times to the fliewn above, that, to form a moon of this projedlile, it mult 

 cubes of the diftances demonftrates, that tlie gravity of all be taken to the height of that body, and theie receive tha 

 the planets towards the fun is the fame at equal diftances. fame motion of projedlion ; and the identity of the moon's 

 This gravity may be called the folar attratlion when it is tendency to the earth, has been already demonftratcd, by 

 confidered as relative to the centre of the fun, towards (hewing that to obtain this tendency, it is lufficient to dimi- 

 vvhich it is direfted ; for without knowing the caufe, we niih the terreftrial gravity according to the general law of 

 may by one of thofe fuppofitions, common among geome- the variation ot the attradtivv force of the celeftial bodies : 

 tricians, imagine an attradlive power refidinginthe centre of and we have feen, that the law of the diminution of gravity, 

 ,the fun. which in planets, accompanied by feveral fatellites, is proved 



The errors to which obfervations are liable, and the finall by a comparifon of their periodic limes, with their diltances, 

 alterations in the elliptic motions of the planets, leave a little is demonftrated for tlie moon, by comparing its motion with 

 imcertainty in the relults deduced from the laws of motion ; that of projeftiies, at the furface of the earth, 

 ^.d it may be doubted if the folar attradlion diminifhes cxaft- The obfervations of the pendulum made at the fummits of 

 ly in the mVevre ratio of the fquare of the diftance. But a mountains, had already indicated this diminution of the tcr- 

 very fmall variation in thi.? law would produce a very per- reftrial gravity ; but they were infufficient to difcover the 

 ceptible difference in the motions of tlie planetary orbits, law, becaufe of the fmall height of the moft elevated moun- 

 The perihelion of the terreftrial orbit would have an annual tains, compared with the radius of the earth : it was requi- 

 motion of i ^ 5' if we only increafed by one ten thoufandth fite to find a body very remote from us, as the moon, to ren- 

 part the power of the diftance to which the folar orbit is re- der the law perceptible, and to convince us, that the force 

 ciprocally proportional; this motion is only 11 '.6 accord- of gravity on the earth is only a particular cafe of a lavr 

 jngto obfervation, and of this we (hall hereafter fee the that pervades the whole univerfe. 



caufe. The law of the fquaije of the diftance "is then, at Every phenomenon throws new light on, and confirms the 

 lea(t, extremely near, and its extreme fimplicity fhould in- laws of nature. Thus the comparifon of experiments on 

 duce us to adopt it, as long as obfervations do not compel gravity with the lunar motion fhews us, that the origin of 

 us to abandon it. At the lame time we muft not mcafure the diftances of the fun and planets, in the calculation of 

 the iimplicity of the laws of nature by our facility of con- their attraftive forces, (hould be placed in their centres of 

 ception, but when thofe which appear to us the moft fim- gravity ; for it is evident, that this takes place on the earth, 

 pie accord perfectly with obfervations of the phenomena, whoie attraftive force is of the fame nature as that of the 

 we are juftified in fuppofing tlicm rigoroufly exaft. fun and planets. 



The gravity of the fatellites towards the centre of their The fun, and thofe planets which are accompanied by fa- 

 planet, is the neceflary confequence of the proportionality tellites, being thus proved to be endowed with an attradHve 

 of the areas defcribed by their radu veftores to the times, force, varying inverlely as the fquare of the diftance, a ftrong 

 and the law of the diminution of this force, according to analogy leads us to attribute the lame property to the other 

 the fquare of the diftance, is indicated by the ellipticity of planets. The Iphencal figure common to all thefe bodies, 

 their orbits. But this ellipticity is hardly to be perceived in indicates that their particles are united roimd tlieir centres of 

 the orbits of the fatellites of Jupiter, Saturn, and Uranus, gravity by a force which, at equal dillances, equally folicits 

 which renders the law of the diminution of the force difficult them towards theie points ; but the followmg confiderations 

 to afcertain by the motion of any one fingle fatellite ; but leave no doulil upon this fubjeft. 



the conftant ratio of the fquares of the times of the ir revo- We have feen, that if the planets and comets were placed 

 lutions to the cubes of their diftances, indicates it beyond a at the fame diftance from the fun, their gravity towards it 

 doubt, by demonftrating, that from one fatelhte to another, would be in proportion to their malfes : now, it is a general 

 the gravity towards the planet is reciprocally as the fquare law in nature, that aftion and re-aftion are equal and con- 

 oi the diftance from its centre. trary ; all thefe bodies, therefore, re-aft on the fun, and at- 



This proof is wanting for the earth, it having but one fa- tract in proportion to their mafl'es : they are tlierefore en-' 



dowcii 



