Professor Mac Cullagh's Lectures on the Attraction of Ellipsoids. 381 



Peoposition II. 



To calculate the attraction of an ellipsoid on a point placed at the extremity of 

 an axis* 



Let the semi-axes ol' the eUipsoid be a, b, c, where a > b > c, and let the 

 point on which it is required to find the attraction be C, the extremity of the 

 least axis. 



Suppose the ellipsoid to 

 be divided by a series of 

 cones of revolution which 

 have a common vertex C 

 and a common axis CC, C 

 being the vertex of the ellip- 

 soid opposite to C ; it will 

 be sufficient to find an ex- 

 pression for the attraction c 

 of the part of the ellipsoid 

 contained between two con- 

 secutive conical surfaces, 

 whose semi-angles are 6 and 

 6 + do respectively. Sup- 

 pose now the part of the 

 ellipsoid between two con- 

 secutive cones to be di- 

 vided into elementary py- 



FiG. 2. 



ramids with a common vertex C. Let CP be one of these elementary pyra- 

 mids, whose solid angle is w; let PQ be drawn perpendicular to CC; from 

 the centre O draw a radius vector OR parallel to CP, and from the extremity 

 R let fall a perpendicular RS on the axis CC. 



Now the attraction of the elementary pj'ramid CP on the material point //, 

 placed at its vertex = /jfpw. CP ; and the component of this attraction in the 

 direction of the axis is 



Proceedings of the Eoyal Irish Academy, toI. iii. p. 367. 



3d 2 



