354 
Mr. Ivory on the Attractions 
shall have h! h" sin. op cos. <p . d<p . dip for its base, and its length 
equal to e/z cos. o? ; then, it is a consequence of what has been 
shown above, that A and A' will likewise express the distances 
of the point, having a' , b', c' for its co-ordinates from the ex- 
tremities of this last prism. Therefore, if we put 
A'= hV'JJ sin. op cos. op . dop . dip | — — •T j : 
then will A' ( when the double fluent is taken between the 
same limits as in the case of A) be equal to the attractive force 
which the ellipsoid of homogeneous matter, whose semi-axes 
are h, h', h", exerts on the point, whose co-ordinates are k cos. 
m, k' sin. m cos. n, k" sin. m sin. ?z, or a! , b', c', in the direction 
parallel to the axis h. For, in the formula for A, as the 
fluxion under the sign of double integration, denotes the at- 
tractive force of an indefinitely small prism of the matter of 
the ellipsoid, whose semi-axes are k, k', k" upon the point whose 
co-ordinates are a, b, c, in the direction parallel to k and h ; so, 
for the like reasons, in the formula for A 1 , the fluxion under 
the same sign, will denote the attractive force of an indefinitely 
small prism of the matter of the ellipsoid, whose semi-axes 
are h, h', /z", upon the point whose co-ordinates are a', b', c' : 
and therefore the two fluents, when extended to all the prisms 
that compose the ellipsoids, will denote the attractions of the 
whole masses upon the respective points, in the direction men- 
tioned. Thus the attractions A and A' depend upon the same 
fluent, and they are manifestly in the same proportion as k' k" 
is to h' h" . 
And if we denote by B' and C' the attractive forces which 
the ellipsoid of homogeneous matter, whose semi-axes are 
h, h' , h" exerts on the point whose co-ordinates are a', b', c in 
