194 Of the SOLIDS 



The folid of greater! 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 

 fphere can do, however great its radius. 



4. To find the radius of curvature at B, the other extremity of 



4 2 

 the axis, fince y* zz a* x T — x 2 , if we divide by a — x, we have 



L — a * x3 x . But at B, when a — x, or the abfcifia 



a — x a — x 



reckoned from B vanifhes, is the diameter of the circle 



it — x • 



having the fame curvature with ACB in B. But when 

 a — * — o, or a zz x, both the numerator and denominator of 



4. 2 



the fraction vanifh, fo that its ultimate value does 



a-< — x 



not appear. To remove this difficulty, let a — xzzz, or 



4 2_ 



xzza — z, then we have / = a 3 (a — z) 3 — (a — z)\ But 

 when z is extremely fmall, its powers, higher than the firft, 



may be rejected; and therefore (a — z) 3 =«Mi J 3 = 



a* (1 ~ &c.) Therefore the equation to the curve becomes 



in this cafe, / = a 3 * X ^ ( 1— — } — «*+ 2azzza — -az— 



* 1 4 



a -j- 2az zz~ az. 



3 



Hence 



