1886.] Equilibrium for a Rotating Mass of Fluid. 327 



Approximate Solutions of the Problem — continued. 

 1 1 



A p 3 p 2 ff \p & p 3 ) ' ' 



+ (> + | 2 -|a)]... 



4 2 < i+ ^4^(f 4*4^4444 •• 



The equation (i) for determining the axes is 



3 



Hence equating (m) and (w) and dividing by —q we have 



2 



which is the equation (23) in the text. 

 The equation (c) for a* may be written 



<u 2 _ A 



[ (1 + Q2) ||, T _j|V]. 



=(i-|^)(j-a)-^[| S Q^|j-|a] 



j^= 2 {§(i + Q.4-4- 2 [l + 8^-^-H} 



VOL. XLI. 



