Of GREATEST ATTRACTION. 195 



Hence 2L, or the radius of curvature at B ~ -a. The 

 22 3 



curve, therefore, at B falls wholly without the circle BKx\, de- 

 fcribed on the diameter AB, as its radius of curvature is 

 greater. This is alfo evident from the conftru&ion. 



V. 



To find the force with which the folid above defined attracts 

 the particle A in the direction AB. 



Let b (Fig. 2.) be a point indefinitely near to B, and let the curve 

 Ac b be defcribed fimilar to ACB. Through C draw CcD per- 

 pendicular to AB, and fuppofe the figure thus conftructed to re- 

 volve about AB ', then each of the curves ACB, Acb will gene- 

 rate a folid of greateft attraction ; and the excefs of the one of 

 thefe folids above the other, will be an indefinitely thin fhell, 

 the attraction of which is the variation of the attraction of the 

 folid ACB, when it changes into Acb. 



Again, by the line DC, when it revolves along with the reft 

 of the figure about AB, a circle will be defcribed ; and by the 

 part C c, a circular ring, on which, if we fuppofe a folid of in- 

 definitely fmall altitude to be conftituted, it will make the ele- 

 ment of the folid fhell AC c. Now the attraction exerted by 

 this circular ring upon A, will be the fame as if all the matter 

 of it were united in the point C, and the fame, therefore, as if it 

 were all united in B. 



But the circular ring generated by C c, is = r (DC — D c 2 ) 

 — 2* DC X C c. Now 2 DC X C c is the variation of /, or 

 DC 1 , while DC pafies into D c, and the curve BCA into the 



curve be A; that is 2 DC X C c is the fluxion of/ 2 , or of a T x T — x% 

 Vol. VI.— P. II, Bb taken 



