Of GREATEST ATTRACTION. 213 
4 1.2114, or as 1218 to 1211.43 fo that the attraction of 
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 Sace, pub- 
lihed 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 hall: have the 
fame attraction with the {phere at the point of contac. If r+ 
be the radius of the fphere, the attraction at any point. of 
its furface, is a iad and, if « be the altitude of the cylinder, ' 
and the radius of its bafe 7, then its attraction on a particle at 
the extremity of its axis is 27 (a+7—Na*-+7°). Since thefe 
attractions are fuppofed equal, 27 (w+r—Na*+r)= all 
3 
and otr—Ne 7 — 2? whence 27" — ening Sr Ite ua 
po RO ONS : 9 3 
Dd2 ind s to ‘Due 
‘' # Notice de la vie de G. L. Le Sace de Genéve, par P, PREVOST, p. 391- 
