Of GREATEST ATTRACTION, 213 



7 : 1.2114, or as 1218 to 1211.4; fo that the attraction of 

 7189 



the cylinder, even when its form is moft advantageous, does 

 not exceed that of a fphere, of the fame folid content, by more 

 than a hundred and eighty -third part. 



6. In a note on one of the letters of G. L. Le Sage, pub- 

 lifhed by M. Prevost of Geneva *, the following theo- 

 rem is given concerning the attraction of a cylinder and a 

 fphere : If a cylinder be circumfcribed about a fphere, the 

 particle placed in the extremity of the axis of the cylin- 

 der, or at the point of contact of the fphere, and the bafe 

 of the cylinder, is attracted equally by the fphere, and by that 

 portion of the cylinder which has for its altitude two-thirds of 

 the diameter of the fphere, and of which the folidity is there- 

 fore juft equal to that of the fphere. 



We may inveftigate this theorem, by feeking the altitude of 

 fuch a part of the circumfcribing cylinder as mail have the 

 fame attraction with the fphere at the point of contact. If r 

 be the radius of the fphere, the attraction at any point of 



its furface, is - — ', and if x be the altitude of the cylinder, 



and the radius of its bafe r, then its attraction on a particle at 



the extremity of its axis is 2 v {x -f r — M x 2 -f- r 2 ). Since thefe 



attractions are fuppofed equal, 2 *■ {x -f- r — VV -J- r 2 ) zz ^* r } 



3 



and x-\- r — VV -4- r 2 zz t — , whence — zz , and x zz ££.■ 



3 3 9 3 



D d 2 The 



* Notice de la vie de G. L. Le Sage de Geneve, par P. Prevost, p. 391. 



