429 



and velocities at the initial instant of time T = 0, are readily found to 



be (most conveniently vdth the aid of Laplace transforms), 

 q / Cut) \ >* 



(4) 



^=1 



MO, 



V 



a>MA ^^'^'Ct->)ols; 



3 11 Ci^*"*') r*^ 



(5) 



(nl) (nl), . . 



where ^ ^j^ is the ik minor of the shell frequency determinant, Z^ (A J 



A^^^(>) = 



^^f_^c':'W 



A 



(h<) 







A 



(*^<) 





A 



(hD 



■ix 





(6) 



(nl). 



and the quantities ± ^ » , /^ = 1> 2, 3 are the six roots (assayed non- 

 degenerate in Equations (4 and 5)) of the secular equation 



^^'^\a)-o. 



(7) 



Thus the ^ ^"^^ are the ratios of the shell frequencies for the nl mode to 

 the fundcimental frequency v^. From Equation (4), it is seen that a given 



