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 



C 



Fig. I- 



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 Axis* 



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 C (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 C ; 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 9 and + dd respectively. Suppose now the part of 

 the ellipsoid between two consecutive cones to be divided into 



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

 2A 



