372 Mr. Ivory on the Attractions , &c. 
which differ from the formulas for the oblate spheroid only 
in the sign of e 1 , as, it is manifest, ought to be the case. By 
integrating, we get 
3^M 
• { 2 • hyp- log- (rr i)~r} 
These formulas express the attractions of an oblong spheroid 
upon a point within the surface or in it ; acting parallel to a, 
b, c, the co-ordinates of that point, of which a is parallel to the 
axis of revolution. 
When the attracted point is without the spheroid, we must 
first compute h, the semi-axis of revolution of the spheroid, 
whose surface passes through the attracted point ; and for this 
purpose we have the following expression, viz. 
2 h* = a 2 -f b* + r 2 + e + V (a* -f 6 3 + c 2 + e 2 )* - 4 a* 77 
observing that a is the ordinate parallel to h : then the attrac- 
tions required will be found merely by substituting h for k in 
the formulas for the case when the attracted point is within 
the spheroid. 
