t 9 6 Of the SOLIDS 



taken on the fuppofition that x is conftant and a variable, 



viz. ? a 3 a xx*. Therefore the fpace generated by Cc = 

 3 



±la* x 3 a. 

 3 



If this expreffion be multiplied by x, we have the element of 



the fhell = ~ a 3 x T a x. 

 3 



In order to have the folidity of the fhell ACB b c, the above 

 expreffion mufl be integrated relatively to x, that is, fuppofing 



only x variable, and it is then ^ X~ a 3 x 3 a-\- C. But Crro, 

 J 5 3 



becaufe the fluent vanifhes when x vanifhes, therefore the por- 



4 



5 



4. - — * 



tion of the fhell AC c = - x 3 a 3 a, and when xzza, the whole 



fhell = ££ a 1 a. 



5 



Now, if the whole quantity of matter in the fhell were unit- 

 ed at B, its attractive force exerted on A, would be the fame 

 with that of the fhell ', therefore the whole force of the fhell 



zz — a. The fame is true for every other indefinitely thin 



fhell into which the folid may be fuppofed to be divided ; and 



therefore the whole attraction of the folid is equal to f 4-5 a, 



fuppofing a variable, that is zr 45 a. 



Hence 



