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

 If in the second factor of (12) we put a = 6, and write 



we find 

 whence 



i- 



W 2 J 1-fW 2 



(iv), 



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

 which makes e='8127. 



As tf/Zirp 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 , 6 = c). 



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



