Mr. Ivory on the Attractions 
37 ° 
but the two cases of solids of revolution, that of the oblate 
and oblong spheroids, are deserving of particular attention. 
In the oblate spheroid, the two greater semi-axes k ' and k” 
are equal to one another ; and, therefore, it corresponds to 
the supposition of e 2 = e' 2 . In this case the formulas ( 7 ) will 
become 
these expressions may be all integrated by the ordinary me' 
thods, and thus we get 
The formulas express the attractions of an oblate 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 surface, we have 
only to compute h, the semi-axis of revolution of the spheroid, 
whose surface passes through the attracted point, and to sub- 
stitute it for k in the last formulas, in order to have the ex- 
pressions of the attractions sought : and it is to be remarked, 
that the equation for finding h, which in the general case of the 
