Mr. Ivory on the Attractions 
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relation which has been shewn to take place between the at- 
tractions of the two solids upon corresponding points in one 
another’s surfaces, the case, when the attracted point is placed 
without an ellipsoid, is made to depend upon the case, when 
the attracted point is within the surface. 
4, Let us now consider the formula (2) for the attractive 
force parallel to the axis k, 
A =j]' d y.dz{±-±] 
on the supposition that the attracted point is within the ellip- 
soid. If a — 0 (that is, if the attracted point be in the plane 
of y and z) then — — = 0, for all values of x, y, and % : 
and, in this case, the whole attractive force A is evanescent, 
as it ought to be. For all other values of a, the expression 
” — in the circumstances supposed, is plainly a finite po- 
sitive quantity : and, therefore, supposing b and c to be con- 
stant, and a to increase, we must infer that the attractive force 
A will receive finite increments, so long as the point deter- 
mined by the co-ordinates a, b, c, is within the ellipsoid. If 
this point be in the surface, then the variable ordinates x,y, z, 
when they belong to points indefinitely near to the attracted 
point, will approach indefinitely to an equality with a, b, c\ 
and the corresponding values of ~ and, consequently, 
the fluxions of the force A, will become infinitely great ; on 
which account the continuity of the function A is broken off. 
From what has now been observed, it follows, that we may 
substitute for the force A, its expansion in a series of the 
powers of a, provided we are careful not to extend the con- 
clusions obtained by reasoning from the nature of such series. 
