of GREATEST ATTRACTION. 195 
at ics alg j 
Hence +, or the radius of curvature at B= 24. The 
2% 3 
curve, therefore, at B falls wholly without the circle BKA, de- 
{cribed on the diameter AB, as its radius of curvature is 
greater. This is alfo evident from the conftruction. 
Vv 
To find the force with which the folid above defined attracts 
the particle A in the direction AB. 
Ler 4 (Fig. 2.) be a point indefinitely near to B, and ie the curve 
Acb be deferibed fimilar to ACB. Through C draw Cc D per- 
pendicular te AB, and fuppofe the figure thus conftructed to re- 
volve about AB ; then each of the curves ACB, Acé 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 ‘hell, 
the attraction of which is the variation of the attraction of the 
folid ACB, when it changes into Ac d. 
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 Cc, 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 ACc. 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. . 
Bur the circular ring generated by Cc, is =x (DG — Dc’) 
= 27rDCxCGce. Now 2DCXCe is the variation of y’, or 
DC’, while DC pafles into De, and the curve BCA into the 
2 
curve bc A; that is 2 DCX Cc is the fluxion of y*, or of a? x 7x, 
Vou. VI.—P. II. Bb taken 
