On the Attraction of Ellipsoids. 



353 



Observing that any two of these parallel planes cut the two 

 surfaces in similar ellipses, such that the semi-axis of one is 

 equal to the parallel ordinate of the other, it is easy to see that 



Fig. 1. 



the reasoning employed by Mac Laurin may be used to esta- 

 blish the truth of the theorem stated above. 



PROPOSITION II. 



To calculate the Attraction of an Ellipsoid on a Point placed at 

 the extremity of an A.XIS* 



Let the semi-axes of the ellipsoid be a, b, c, where a > b > c, 

 and let the point on which it is required to find the attraction 

 be (Fig. 1), the extremity of the least axis. 



Suppose the ellipsoid to be divided by a series of cones of revo- 

 lution which have a common vertex C and a common axis CO', C' 

 being the vertex of the ellipsoid opposite to ; it will be sufficient 

 to find an expression for the attraction of the part of the ellipsoid 

 contained between two consecutive conical surfaces, whose semi- 

 angles are and -f dO respectively. Suppose now the part of 

 the ellipsoid between two consecutive cones to be divided into 



* Proceedings of the Royal Irish Academy, YOL. in. p. 367. 

 2A 



