Of GREATEST ATTRACTION, ^09 



when a maximum is about - of the attraction of a fphere 



5 



of equal folidity. 



XIII. 



Of all the cylinders given in mafs, or quantity of matter, to 

 find that which mall attrad a particle, at the extremity of its 

 axis, with the greater!: force. 



Let DF (Fig. 6.) be a cylinder of which the axis is AB, if AG 

 be drawn, the attraction of the cylinder on the particle A is 

 2 * X (AB -f BC — AG) *, and we have therefore to find when 

 AB -f- BC — AC is a maximum, fuppofing AB . BC 2 to be equal 

 to a given folid. 



Let AB = x, BC zzy, then AG == V** +/, and the quanti- 



ty that is to be a maximum is x-^-y — */x 2 -\~y*> We have 

 therefore x -\- y ~r )' j — 0) an( j ^ x _j_^ fa'-f-yHss 



x x + y y, or (1 -f ? \ (x*+y*) T zzx+y-l° 

 x' X 



But fince irx/r^, 2 x yy -\-y* x z± o, or 2 x y zz — y x, 



and l - _ Z.. 



x 2x 



Therefore 



^Princip. Lib. I. Prop. 91. Alfo Simpson's Fluxions, vol. II. § 379. In 

 the former, the conftant multiplier 2 tt is omitted, as it is in fome other of the 

 theorems relating to the attraction of bodies. This requires to be particularly 

 attended to, when thefe propofitions are to be employed for comparing the at- 

 traction of folids of different fpecies. 



