Qf GREATEST ATTRACTION. 235 



XXI. 



From the general propofition, that the attraction of any 

 plane figure, whatever its boundary may be, in a line perpen- 

 dicular to the plane, is at any diftance proportional to the 

 angular fpace, or to the area of the fpherical figure which the 

 plane figure fubtends at that diflance, we can eafily deduce a 

 demonftration of this other propofition, that whatever be the 

 figure of any body, its attraction will decreafe in a ratio that 

 approaches continually nearer to the inverfe ratio of the fquares 

 of the diftances, as the diftances themfelves are greater. In 

 other words, the inverfe ratio of the fquares of the diftances, is 

 the limit to which the law by which the attraction decreafes, 

 continually approaches as the diftances increafe, and with 

 which it may be faid to coincide when the diftances are infi- 

 nitely great. 



This propofition, which we ufually take for granted, with- 

 out any other proof, I believe, then, fome indiftinct perception 

 of what is required by the law of continuity, may be ri- 

 gorouily demonftrated from the principle juft eftabliflied. 



Let B (Fig. 14.) be a body of any figure whatfoever, A a 

 particle fituated at a diflance from B vaftly greater than any 

 of the dimenfions of B, fo that B may fubtend a very fmall 

 angle at A ; from C, a point in the interior of the body, fup- 

 pofe its centre of gravity, let a ftraight line be drawn to A, and 

 let A' be another point, more remote from B than A is, Where 

 a particle of matter is alfo placed. 



The directions in which A and A' gravitate to B, as they 

 muft tend to fome point within B, mult either coincide with 

 AC, or make a very fmall angle with it, which will be always 

 the lefs, the greater the diftance. 



Vol. VI— P. II. Gg Let 



