Of GREATEST ATTRACTION. 219 
Tuts formula vanifhes whether 7 be fuppofed infinitely 
great or infinitely fmall, and, therefore, there muft be fome 
magnitude of r in which its value will be the greateft pof- 
fible. 
Ir r is very {mall in refpe@ of 1,Vi1+7° = 1 +o and 
~6 
fo re--va r* = rtn4+5, or fmply = 1+7?. But 
L (1+73), ifr is very {mall in refpedt of 1, is 735. and there- 
fore the ultimate value of the formula, when + is infinitely 
fmall, is 2. x r? = 21, which is alfo infinitely fmall. 
’ id 
AGAIN, let 7 be infinitely great; then V7* +1 = 73}; and fo 
the formula is = L.2r3, or? ~ 3.27. But the logarithm 
of an infinitely great quantity 7, is an infinite of ‘an order in- 
comparably lefs than r, as is known from the nature of 
logarithms, (Grec. Fontanz Difquifitiones Phyf Math. 
de Infinito Logarithmico, Theor. 4.)3 fo that 2 Lar is lefs 
6 
vr? or than : 
than =. But Cis infinitely fmall, 7 being infinite- 
ly great, and therefore, when the radius of the cylinder be- 
comes infinitely great, its folid content remaining the fame, 
its attraction is lefs even than an infinitefimal of the firft or-’ 
der. 
THE determination of the maximum, by the ordinary me- 
thod, leads to an exponential equation of confiderable difficulty, 
if an accurate folution is required. -It is, however, eafily found 
Vou. VI.—P. II. Fe by 
