469 



theorem to the attraction of a similar ellipsoid on a point situa- 

 ted on its surface. 



The peculiarity of Mr. M'Cullagh's method consisted in 

 the manner in which he discussed this latter problem. 



The three following propositions contain the complete so- 

 lution of the question : — 



Prop. I. Theorem. — If P be any point on the surface of 

 an ellipsoid, and PCi be drawn perpendicular to any axis OC 

 (where O is the centre and C the extremity of the axis); the 

 component of the attraction of the given ellipsoid on the point 

 P, estimated in the direction OC is equal to the attraction of 

 another ellipsoid similar and similarly placed upon a point 

 situated at its vertex Ci. 



Prop. II. Prob. — To calculate the attraction of an ellip- 

 soid on a point placed at the extremity of an axis. 



Prop. III. Prob. — To find geometrical representations 

 of the attraction of an ellipsoid upon a point situated at the 

 extremity of any axis. 



Having completely discussed the question of the attrac- 

 tion of an ellipsoid, Mr. M'Cullagh found the attraction of 

 any body on a distant point by means of the following expres- 

 sions. 



Let O and N denote the centre of gravity and the at- 

 tracted point ; and let the ellipsoid of gyration be described, 

 having O for its centre. 



Let a tangent plane to this ellipsoid be drawn perpendicu- 

 lar to ON, cutting it in the point S, and touching the ellip- 

 soid in the point T. 



Let M denote the mass of the attracting body, and y' the 

 distance ON, then — 



The attracting force lies in the plane of OST, and if R and 

 P denote the components of attraction in and perpendicular to 

 the direction of the line joining the centre of gravity of the 

 attracting body with the attracted point. 



