Of 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 f{pace, or to the area of the f{pherical figure which the 
plane figure fubtends at that diftance, 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 {quares 
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 attraGtion decreafes, 
continually approaches as the diftances increafe, and with 
which it may be faid to coincide when the diftances are infi- 
nitely great. 
Tuis propofition, which we ufually take for granted, with- 
out any other proof, I believe, then, fome indiftin& perception 
of what is required by the law of continuity, may be ri- 
goroufly demonftrated from the principle juft eftablithed. 
Let B (Fig. 14.) be a body of any figure whatfoever, A a 
particle fituated at a diftance from B vaftly greater than any 
of the dimenfions of B, fo that B may fubtend a very {mall 
angle at A; from C, a point in the interior of the bedy, 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. 
Tue directions in which A and A’ gravitate to B, as they 
muft tend to fome point within B, muft either coincide with 
AG, or make a very {mall angle with it, which will be always 
the lefs, the greater the diftance. 
Vou. VI.—P. II. Gg Ler 
