G R xVV I T A T I O N. 



fulcrcd as the mark and meaiure of a change of force, and 

 his audience is referred to experience for tlie nature of this 

 force. He had before exhibited to the fociety a very pretty 

 experiment contrived to (liew the nature of this force. A 

 ball, fufpcnded by a long thread from the ceiling, was made 

 to fwing round another ball, laid on a table immediately 

 below the point of fufpcnfion. When th» impulfe given to 

 the pemlulum was nicely adjufted to its deviation from the 

 perpendicular, it defcribed a perfect circle round the ball on 

 the table ; but when the impulfe was very great, or very 

 fmall, it defcribed an ellipfe, having the other ball in its 

 centre. 



Hooke fhewed that this was the operation of a dcflcfting 

 force proportioned to the dillance from the other ball. 

 He added, that although this illuftrated the planetary motions 

 in fome degree, yet it was not fuitable to their cafe : for 

 the planets defcribe ellipfes, iiaving the fun not in their centre 

 but in tiieir focus. Therefore they are not retained by a 

 force proportional to the dillance from the Inn. 

 • The exalted genius of Newton can fufTer no diminution 

 by the enumeration of the above opinions, for though the 

 idea of fuch a principle as gravitation was not fuggelled firil 

 by Nev>ton, yet fo verv obfcure were the notions of even 

 the molt enlightened pliilofophcrs on th.is fubjcct, that it 

 had never been fuccelsfu'ly applied to the explanation of a 

 lingle aflronomical phenomenon. 



So intimately connected is this great difcovery with the 

 hiftory of the human mind, that every known circumftance 

 relating to it has been recorded with the greateft care. Dr. 

 Pemberton relates that Newton, in the year 1666, having 

 retired from Cambridge to the country on account of the 

 plague, was there led to meditate on the probable caufc of 

 the planetary motions, and upon the nature of that central 

 force that retained them in their orbits. It then occurred 

 to him that pofllbly the fame force, or fome modilication of 

 the fame force which caufed with us a heavy body to defcend 

 with a certain velocity to the earth, might like wife retain 

 the moon in her orbit by caufing a conftant defledtioii from a 

 reftihnear path. Before, however, this conjecture could be 

 put to the tell of calculation, it was neceffary that Newton 

 ihould have formed fome conditional hypotheiis relative to 

 the modiHcalion of the force with refpcft to the diftance. 

 That any agency emanating from a central point (hould de- 

 creafe as the fquare of the diftance from that point increafes, 

 is an hypotheiis fo natural, that we cannot be fnrprized that 

 Newton fliould have feledled it ; but whether or not he had 

 previoufiy tried any other, or whether he had even at this 

 time deduced it from the nature of the planetary orbits, does 

 not now appear. The calculation which it was neceffary to 

 inllitutc, we (hall give with great minutenefs in its proper 

 place; it is therefore only neceffary to remark at prefent, 

 that it requires that the proportion between the radius of 

 the earth and the lunar orbit fhould be exaftly known. Wl-.en 

 Newton firff attempted to verify this hypothefis, thefe re- 

 quifite data had not been exaftly determined, and a flight 

 difcordance between the refult of the calculation and the 

 fappofed fact, induced him for a time to abandon his hy- 

 potheiis. This circumftance has, with great propriety, 

 been recorded as a ftriking inftance of the cool and difpaf- 

 fionate frame of mind wiiich this great philofopher prefcrv- 

 ed, at a moment when he had flattered himfelf with the 

 hope of having difcovered one of the moft important fecrcts 

 of nature. 



Some few years afterwards he was again tempted to re- 

 new thefe calculations, as in this interval a degree of tlie 

 meridian had been meafured in France by Picard. This 

 fccond atte.npt fuceeeded. It is related, that towards the 



end of the calculation he became fo much agitated, as to 

 be obliged to requeil a friend to afTifl him in finifhing it ; 

 and certainly a moment of greater importance in philolophy 

 will never be recorded in the annals of fcience. 



The computation which was made by Newton to deter- 

 mine the identity of the force of terreilrial gravity, wiih 

 that which retains the moon in her orbit, is iHll a fubjfiJt 

 of great intereft to aftronomers, as they now reverfe (he 

 procefs; and taking the theory of gravitation as 'admitted, 

 thev deduce from the fame computation the diftance of the 

 moon from the earth. We fliall give it in the words of 

 La Place. 



The force which at every inftant dcflecls the moon from the 

 tangent of h r orbit, caufes it to defcribe, in one focond, a 

 fpace equal to the vcrfed fine of the arc which it defcribes in 

 that time; iince this fine is the quantity that the moon at the 

 end of a fecond deviates from the dire&ion it had at the be- 

 ginning. Thi.i quantity may be determined by the diftance 

 of t\\^ earth, inferred from the lunar parallax in parts of tlie 

 terreilrial radius; but to obtain a refult independent of the 

 inequalities ol the moon, we muft take for the mean paral- 

 lax that part of it which is independent of thefe inequalities. 

 This part is, according to obfcrvation, 50' S-\ -9' relatively 

 to the radius drawn from the centre of gravity of the 

 earth, to the parallel, of which the iquire of the fine of 

 the latitude is equal to -J. We felecl this parallel becaufe 

 the attraftion of the earth, on the points Ci.rrefponding to 

 its furface, is at the diftance of the moon, very nearly equal 

 to the mafs of the earth divided by the fquare of the dif- 

 tance from its centre of gravity. The radius drawn from 

 a point of this parallel to the centre of gravity of the earth 

 is 6369374 metres, from whence it may be computed the 

 force which folicits the moon towards the earth caufes it 

 to fall o'ooioi727 in one fecond of time. Tt will be fhewn 

 hereafter, that the action of the fun dlminiflies the lunar 

 gravity -j-f-s'l^ part. The precedmg height mull therefore 

 be augmented j-!^th part, to render it independent of the 

 aftion of the fun; it then becomes o"".coi020i I. But in 

 its relative motion round the earth, the moon is fcjicited 

 by a force equal to the maffes of the earth and moon 

 divided, by the fquare of their mutual diftance; therefore 

 to obtain the height which the moon would fall through 

 in one fecond, by the action of the earth alone, the prece- 

 ding fpace muft be diminithed in the ratio of the mafs of 

 the earth to the fun, and of the maffes of tlie earth and 

 moon: but by the phenomena of the tides, it appears that 

 the mafs of the moon is equal to , J-y of that of the earth, 

 multiplying therefore this fpace by; ^;^, we have 6 ' .00100300 

 for the height which the moon falls through in one fecond 

 by the aftion of the earth. 



Let us now compare this height with that which refults 

 from obfervations made on the pendulum. Under the 

 parallel above-mentioned the length of the pendulum vi- 

 brating feconds is equal to 3 '.65706: but on this parallel 

 the attradlion of the earth is lefs than the force of gravity 

 by J of the centrifugal force due to the motion or rotation 

 of the earth at the equator; and tins force is .45lhpartof 

 that of gravity; the preceding fpace mufl therefore be 

 augmented 3 1 ,d part, to get the fpace due to the adion of 

 terreflrial gravity alone, which on this parallel is equal to 

 the mafs divided by the fquare of the terreftrial radius: we 

 fhall therefore have 3 '.66553 for this fpace. At the dif- 

 tance of the moon it fliould be diminlfhed in the ratio of 

 tlie fquare of the radius of the terreftrial fphercid to the 

 fquare of the diflance of the moon : for this purpofe it is 

 fuflicient to multijily it by tlie fquare of the tangent of the 

 lunar parallax, or 56' 55". 2, tliis will give o"'.coioo483 

 7 for 



