220° Of the SOLIDS 
by trial, that, when the function Su (r3-+NE+47*) is a 
Therefore, becaufe a = 1 = 25 
maximum, r is nearly = : 2, 
Nir 
S 
LoS) 
25 
; 6 ; 
r is nearly to a as F to 30 or as 216 to 1253 and this of con- 
fequence, is, nearly, the ratio of the radius of the bafe, to the 
altitude of the half-cylinder, when its attraction, eftimated ac- 
cording to the ll she of the problem, is the greateft pof- 
fible. 
XVII. 
To determine the oblate fpheroid of a: piven folidity which: 
fhall attract a particle at its pole with the greateft force.. 
Let there be an oblate {pheroid generated by the revolution. 
of the ellipfis ADBE (Pl. 7. Fig. 10.), about the conjugate 
axis AB, and let F be the focus; then if AF be drawn, and’ 
the arch CG defcribed from the centre A, the force with. 
which the fpheroid draws a particle at A, in the direction AC,, 
5 At AC .CD* 
GE: 
Let this force =F, AC =a, CD=4, the angle CAF=9; 
Arak 
a? tan 93 
(CF—CG *).. (Macraurin’s Fluxions, § 650).. 
then CF = a4 tang, and F = (tang—9) a4= 
42h tang—o 
a. tang? — 
Now if m? be the folidity of the fpheroid, fince that folidity 
is two-thirds of the cylinder, having CD for the radius of its 
bafe, 
* Tue multiplier 27, omitted by Macxuauriy, is reftored as above, 
4 X11I. 
™ 
