Professor Mac Cullagh's Lectures on the Attraction of Ellipsoids. 383 



abccos'B sin OdO 



l7r/x/pj= 



\/{a- cos^e + c- sia^ 6) \/{b^ cos^e + c^ sin'^e) ' 



Let cos 6 — u, and this expression becomes 



. ^ (■' abcu^du 



'''''' Jo /! c' + m' (a' - OK|c' +"'(*'- c')!' ^ -^ 



la the same way it may be shown that the attraction of the ellipsoid on a 

 point fjL placed at the extremity of the mean axis, is 



4 



'ft 



abc ir du 



V\b'->ru'{c■'-b^)\^/\b■ + u'{a^-b'')\' 

 and on a point at the extremity of the greater axis, 

 . J. [' abcu^du 



It will be seen in a subsequent proposition, that these three expressions are 

 not independent of each other, the values of the three attractions in question 

 being connected by an equation. 



Peoposition III. 



To give geometrical representations of the attraction of an ellipsoid on points 

 placed at the extremities of its least and mean axes* 



On the greater axis 

 OAo of the focal ellipse 

 assume a point Ki such 

 that 



OK. =^ OAo; 



from the point Kj draw a 



tangent K.Qi to the focal Fig. 3. 



ellipse, and let T = tangent K, Qi - arc Ao Qi, then the attraction of the 



ellipsoid on the particle /x placed at the extremity C of the least axis is 



i-Kixfpabc- ,2) 



(a'-c') (6^-cO ■ 



* Proceedings of the Royal Irish Academy, vol. iii. p. 367- 



