196 Of th SOLIDS 
taken on the fuppofition that x is conftant and a variable, 
viz. 4a5aX«3. Therefore the {pace generated by Cc = 
3 
eed Be 
3 3 
x3a, 
Ir this expreffion be multiplied by x, we have the element of 
the fhell = a aint ak. 
In order to have the folidity of the fhell ACB c, the above 
expreflion muft be integrated relatively to x, that is, fuppofing 
only x variable, and it is then oh at x3 a +C. But C=0, 
becaufe the fluent vanifhes when x vanifhes, therefore the por- 
tion of the fhell ACc = : x3 as a, and when «=a, the whole 
fhell = 4.2 a 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 fhellk 
— = 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 rf - a, 
{uppofing a variable, that is = va 4. 
HENCE 
