%o6 Of the SOLIDS 



XII. 



The preceding theorems relate to the folids, which, of all 

 folids whatfoever of a given content, have the greater!; 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 flraight 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. 



It is known, if t be the femicircumference of the circle of 

 which the radius is 1, that is, if % zz 3. 14 159, &c that the at- 

 traction of the cone ABC, on the particle A, in the direction 



(AD a \ 

 AD XWJ' (S impson ' s Fluxions, vol. ii. 



Art. 377.) 



Let AD zz x, AB zz z, the folid content of the cone zzm*, 

 and its attraction z=, A. 



Then A zz 2 k (x — __\, and «r x (z — x 1 ) zz 3 m>. 



The quantity x , is to be a maximum, and therefore, 



•6 



o, or z 2 *— 2 x z + x 1 . - zz o. 

 z" x 



Again, 



