Of GREATEST ATTRACTION. 219 



This formula vanifhes whether r be fuppofed infinitely 

 great or infinitely fmall, and, therefore, there muft be fome 

 magnitude of r in which its value will be the greater! pof- 

 fible. 



If r is very fmall in refped of 1, Vi -f- r 6 — 1 -J } and 



r 6 



fo n-\- /i + r 6 — i4-/* 3 4-— , or limply ~ 1-f-r 3 . But 



L(i + r 3 ), if r is very fmall in refpecl: of 1, is r 3 ; and there- 

 fore the ultimate value of the formula, when r is infinitely 



fmall, is — X r 3 = 2 r, which is alfo infinitely fmall. 

 r 



Again, let r be infinitely great , then W rf + 1 55 r 3 , and fo 



2 2 X 3 



the formula is — L . 2 r 3 , or — ^ L . 2 r. But the logarithm 



of an infinitely great quantity r, is an infinite of an order in- 

 comparably lefs than ;•, as is known from the nature of 

 logarithms, (Greg. Fontanel Difquifitiones Phyf. Math. 



de Infinito Logarithmico, Theor. 4.) ; fo that — L 2 r is lefs 



r 



a. r f\ 



than a -, or than -. But - is infinitely fmall, r 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 



Vol. VI.— P. II. Ee bv 



