Mn Ivory on the Attractions 
nation of the attractive force A, it is evident, will apply equally 
to the attractions denoted by B and C : and, therefore, the 
attractions of an ellipsoid, acting perpendicularly to the planes 
of the principal sections, upon a point situated within the sur- 
face, are as follows, viz. 
the several fluents to be extended to the whole of the surfaces 
of the principal sections, to which the attractions are perpen- 
dicular. 
When the attracted point is without the ellipsoid, it be- 
comes necessary, in the first place, to determine the semi-axes 
of another ellipsoid whose surface shall pass through the at- 
tracted point, and which shall have the same excentricities 
and its principal sections in the same planes, as the given 
ellipsoid : these semi-axes have been denoted by h, hi, ti'> and 
the formulas for computing them have already been given.* 
We must next determine the co-ordinates of the point in the 
surface of the given ellipsoid, that corresponds to the attracted 
point in the surface of the other ellipsoid : and, according to 
the definition that has been given of them, these co-ordinates. 
It It! 
denoted by a' , c' are thus found ; a' — a y—\ b' = b y. ; 
c' = c x pr-'f These things being determined, the attractions of 
the ellipsoid whose semi-axes are h, h', h", upon the point whose 
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t Page 355- 
* Pages 35i and 352. 
