Forces derivable from a Potential of the Second Degree. 51 





For the increments in the semi-axes we have 



T 



..... (45) . 



It is easy to prove 66/6 positive, and Sc/c negative, for all values of 

 rj and bja ; thus, of the axes perpendicular to the axis of rotation, the 

 longer lengthens and the shorter shortens. The axis 2a of rotation 

 is always reduced. 



When the flat ellipsoid is spheroidal ( c/c) is greater or less than 

 ( <5a/a), according as rj is greater or less than '25. 



Very Elongated Ellipsoid. 

 10. Treating o/c and 6/c as both very small, we find 



xx . 4l-i 2 3 



Q> C 



{ 2 a 2 + 3 6 2 + i?(a 2 - 3 6 2 ) } i/ 



