214 Of the SOLIDS 



The altitude of the cylinder is therefore - of the radius, 



or - of the diameter of the fphere, which is Le Sage's Theo- 

 3 



rem. 



This cylinder is alfo known to be equal in folidity to the 

 fphere ; but its attraction is not greater than that of the latter, 

 becaufe the proportion of its altitude to the diameter of its 

 bafe is not that which gives the greateft attraction. Its alti- 

 tude is to the diameter of its bafe, as ? r to 2 r, or 4 to 6 : in 



3 



order to have the greateft effect, it muft be as 4 to 5 nearly, 



(§ 30- 



Notwithstanding, therefore, that the form of the one of 



thefe cylinders is confiderably different from that of the other, 

 their attractions are very nearly equal 5 the one of them being 

 the fame with that of the fphere, and the other greater than it 

 by about the 183d part. On each fide of the form which gives 

 the maximum of attraction, there may be great variations of 

 figure, without much change in the attracting force. A fimi- 

 lar property belongs to all quantities near their greateft or leaft 

 Hate, but feems to hold efpecially in what regards the attrac- 

 tion of bodies. 



XIV. 



In confidering the attraction of the Mountain Shehallien, 

 in fuch a manner as to make a due allowance for the heteroge- 

 neity of the mafs, it became necefTary to determine the attrac- 

 tion of a half cylinder, or of any fector of a cylinder, on a 

 point fituated in its axis, in a given direction, at right angles 



to 



