586 EQUILIBRIUM OF ROTATING MASSES OF LIQUID. [CHAP. XII 

 If in the second factor of (12) we put a = b, and write 



we find 

 whence 



cot- 1 = 



s _n du 



u&amp;gt;] 14 

 13+3 3 



(v)*. 



It may readily be verified that this has only one finite root, viz. = 7171, 

 which makes e = *8127. 



As n 2 /27rp diminishes from the above limit, the ratio of one 

 equatorial axis of Jacobi s ellipsoid to the polar axis increases, 

 whilst that of the other diminishes, the asymptotic form being 

 an infinitely long circular cylinder (a = oo , b = c). 



Thomson and Tait, Art. 778 . The / of these writers is equal to our f ~ 1 . 



