Of GREATEST ATTRACTION. 209 
when a maximum is about) oF of the attraction of a {phere 
of equal folidity. 
¢\ EE 
OF all the cylinders given in mafs, or quantity of matter, to 
find. that which {hall attraét a particle, at the extremity of its 
axis, with the greateft force. 
Let DF (Fig. 6.) be a cylinder of which the axis is AB, if AC 
be drawn, the attraction of the cylinder on the particle A is 
2X (AB + BC — AC) *, and we have therefore to find when 
AB + BC — AC is a maximum, fuppofing AB. BC’ to be a 
to a given folid. 
Let AB=«, BC =y, then AC = Vx’ +’, and the quanti- 
ty that is to be a maximum is x + y—Nwv+y. We have 
therefore. .x he ttheon wetyy = o, and (x +4) +y)F= 
Ne ty +y/ 
wx Y J, OF (+2) Wty)? sepyZ. 
id x 
But fince xy? = m3, 2xyy-+y*x = 0, or 2uy=—ya, 
and 2. je) Sir 
Lv 2a 
THEREFORE 
* Princip. Lib. I. Prop. 91. Alfo Simpson’s Fluxions, vol. II. § 379. In 
the former, the conftant multiplier 2 7 is omitted, as it is in fome other of the 
theorems relating to the attraction of bodies. This requires to be particularly 
attended to, when thefe propofitions are to be employed for comparing the at- 
traction of folids of different fpecies, 
