‘194 Of th SOLIDS 
“Tue folid of greateft attraction, then, at the extremity of its 
‘axis, where the attracted particle is placed, is exceedingly flat, 
approaching more nearly to a plane than the fuperficies of any 
{phere can do, however great its radius. 
4. To find the radius of curvature at B, the other extremity of 
hit) 52 
the axis, fince y° = a* x* — x’, if we divide by a — x, we have 
2 a 2 
J = 4 ** —*, But at B, when a—x, or the abfcifla 
a= & a—wx 
2 
reckoned from B vanithes, cee is the diameter of the circle 
having the fame curvature with ACB in B. But when 
a—x=0, or 4=x, both the numerator and denominator of 
2 
a 
Tl ee 
vanifh, fo that its ultimate value does 
a—«x 
he) 
the fraction 
not appear. To remove this difficulty, let a—x=2z, or 
4 a 
x—=a—z, then we have y’= a? (@a—z)?—(a—z). But 
when x is extremely fmall, its powers, higher than the firft, 
may be rejected; and therefore (a—z)* = a3 G —*)* = 
2 . 
a? (1—2*, &c.) Therefore the equation to the curve becomes 
34 
nests ele 2% &s 2 
in this cafe, y*= 43 X a3 (— = )-a+ Amer Aarmag atte 
a+ naz se az. 
HENCE 
