4i8 ANTIENT METAPHYSICS. BookV. 



to be applied to the Motion of the Planets. And here Sir Ifaac ap- 

 pears to have had recourfe again to the Motion of the Projedile, 

 which he fuppofed to be a compounded Motion according to the 

 general belief at this day ; and, therefore, he fuppofed that there 



was 



compofed both of the Velocity and the Mafs. The Velocity, therefore, of all the par- 

 ticles of the Body is the fame as in one. This, I think, is well illuftrated by 

 Montucla, in his hiftory of Mathematics, Vol. II. p. 263. printed at Paris in 1758, 

 where he fuppofes the greater Body divided into equal parts, and let fall altogether, 

 but not united, they will certainly all come to the ground at the fame time. Now, 

 let us fuppofe that they all cohere, fo as to form but one Body, it cannot be concei- 

 ved that they (hould for that come to the ground fooner. 



And, as every particle of the falling Body is moved towards the Centre, fo every 

 particle of the Central Body is moved towards the falling Body; for it appears to be 

 an eftablifiied Law of Nature, that the tendency of ait Bodies towards one another 

 is mutual. But it is likewife a Law of Nature, that the tendency of Bodies to- 

 ward one another is in proportion to their Mafles ; that is to fay, the greater Body 

 in the Centre tends towards the lefler falling Body, as well as the falling Body 

 tends towards it, but with much lefs Velocity. And this explains what the New- 

 tonians fay, that, as the Stone gravitates towards the Earth, fo the Earth gravitates 

 towards the Stone, but- is moved with infinitely lefs Velocity; or, to exprefs it ac- 

 cording to their conceptions of Gravitation, the Earth attrafls the Stone by the Ac- 

 tive Force of all its particles upon the Stone, while the Stone likewife attradls tha 

 Earth, by the operation of all its particles upon the Earth ; the confequence of 

 which is, that the power exerted by the Stone being infinitely lefs than that of the 

 Earth, and the Mafs of the Earth infinitely greater than that of the Sto.ne, the Ve- 

 locity of the Motion of the Earth towards the Stone will be infinitely lefs than the 

 Velocity of the Stone towards the Earth. 



It is to be obferved, that when the DoiSrine of Falling Bodies is applied to the 

 Planets, we are to lay afide entirely the Refiftance of our Atmofphere; which can 

 have no place in the Celeftial Regions, ubl corpora llberrime moventur, as Sir Ifaac 

 expreffes it. 



Galileo went fo far in the difcovery of Gravitation, as to refute the Peripatetics 

 by fhowing that the Velocity of a falling Body did not depend upon the Weight of 

 the Mafs, but upon the Time. But even this he proved no otherwife but by expe- 

 riments ; whereas it may be proved dire£lly and dcmonftratively, from the conflar.t 

 a£lioa of Gravitation, which is thus to be conceived. The Body, in the fiift inftant 

 of its Motion, is moved with a certan Force. In the fecond inftant, the fame Force 

 continues; and there is (ijpperadded another Force as great: The confequence of 

 which neceffarily is, that the Came Body being moved with a double Force, muff. 



