35 ° 
Mr. Ivory on the Attractions 
A= {(a — if + (b—yy + (c—zY j£ 
A'= {(a+x)’+ (i— y)'+ (c — z)-}± 
then, 
h=ffdy.dz.{±--L]: (2) 
this double fluent is to be extended to all the points, or inde- 
finitely small spaces dy . dz , that compose the principal section 
of the solid made by the plane of y and z. 
In like manner, if B and C be integrated ; the first with 
respect to the variable y, and the second with respect to the 
variable z ; two new expressions of these attractions will be 
obtained, exactly similar to the expression for A, that has just 
been investigated. 
3. The general equation of a surface of the second order 
bounding a finite solid, is* 
if the three quantities k, k', k" be supposed to be all equal, then 
the solid will be a sphere ; if two of them, as k' and k " be equal, 
it will be a solid of revolution ; and if all the three be unequal, 
it will be an ellipsoid, or a spheroid, having all its three prin- 
cipal sections ellipses. In what follows, we shall always sup- 
pose that k is the least of the three quantities k, k‘, k ", or the 
least of the semi-axes of the solid. 
The general equation of the ellipsoid, will be satisfied by 
putting x — k cos. (p, y = k' sin. <p cos. and % = k" sin. <p 
sin.t|/; where <p and tj/ denote two indeterminate angles. In 
order to substitute these values of x, y, and 2 in the formula 
{2), we must begin with taking the fluxion of y, on the sup- 
* Mecan. Celeste, Tom. II. p. 7. 
