313] ATTRACTION OF ELLIPSOIDS. 581 



fao ^T^ 



and x = a&cj ^- ........................ (6). 



The potential energy of the mass is given by 



..................... (7), 



where the integrations extend over the volume. Substituting 

 from (4) we find 



V= iro 



(8). 



This expression is negative because the zero of reckoning 

 corresponds to a state of infinite diffusion of the mass. If we 

 adopt as zero of potential energy that of the mass when collected 

 into a sphere of radius a, = (abc) 3 , we must prefix to the right- 

 hand of (8) the term 



........................... (9). 



If the ellipsoid be of revolution, the integrals reduce. If it 

 be of the planetary form we may put 



2c ..................... (10), 



and obtain* = &, = (? + 1) footr 1 ?- ? 2 , 



......... (12), 



provided the zero of V correspond to the spherical form. 

 For an ovary ellipsoid we put 



a = 6 = (g2 &quot; 1 ^c ..................... (13), 



* Most simply by writing c 2 + X = (a 2 - c 2 ) tt 2 . 



