262 Mr. A. E. H. Love on the Oscillations of a Rotating 



The frequency equation, as found from (19) and (20), gives 

 either 



or 



We now introduce the quantity e defined by the equation 



6o^ = 47r7pe (30) 



The condition of steady motion is 



/(3 + 2e/2)=(3+/')tan-/; . . . (31) 

 and we find 



T'2 = 16ao^e7r7p (32) 



Also by (18) and (32), 



Ko=4ao% 

 or 



Coy^(«o'G + H) = 2e (33) 



This, with the identity (22), gives G and H in terms of F, 

 viz., 



(l+/2),o^G=^^.3p^^{/2-3e(l+/^)}-.(l+n.o^^ 



'o'^=f(^^) { -/^ + 26(3 + 2/2) K(1+/WF; 

 where 



F=r" *fc 



J. W + t/(<-«^ + t)5' 

 SO that 



7-^_ 1 rl5 + 25/2 + 8/^ ,^ tan-'/ -] 



^o^-4^L (1+r)^ ^^"^T^J' 



or 



'o-'-/X3+/^)(l+/^)2 2 {S-^Df ' ^""^^ 

 Also by using (18) and these reductions we find 



(34) 



TTjp r 2 



{ao-boy- 2 L3+/2 rC^+D 



(3 + 8/2+/0]. (36) 



