206 Of the SOLIDS a 
XII. 
Tue preceding theorems relate to the folids, which, of all 
folids whatfoever of a given content, have the greateft attrac- 
tion in a given direction. It may be interefting alfo to know, 
among bodies of a given kind, and a given folid content, for 
example, among cones, cylinders, or parallelepipeds, given in 
magnitude, which has the greateft attractive power, in the di- 
rection of a certain ftraight line. We fhall begin with the 
cone. 
Let ABC (Fig. 5.) be a cone of which the axis is AD, re- 
quired to find the angle BAC, when the force which the cone 
exerts, in the direction AD, on the particle A at its vertex, is 
greater than that which any other cone of the fame folid con- 
tent, can exert in the direction of its axis, on a particle at its 
vertex. 
Ir is known, if x be the femicircumference of the circle of 
which the radius is 1, that is, if = 3.14159, &c. that the at- 
traction of the cone ABC, on the particle A, in the direction 
AD’ 
AD? asec 2 « 3% (ap RABE) (Stmpson’s Fluxions, vol. ii. 
Art. 377-) 
Ler AD=x, AB=g, the folid content of the cone = m?, 
and its attraction = A. 
THen A=27 (x —=), and a x (z*—«") = 3m’. 
. x e . 
THE quantity ee to be a maximum, and therefore, 
* yh F 
fee Sp, or 2 =—2xne2+xn. = 0. 
zx ¥ 
AGAIN, 
ee 
