AND DEFORMATION OP A THIX ELASTIC SHELL. 541 



Eliminating P,, P 2 , we get 



a* <r/9 + l C 



Ml C \ / . <r* < + 1 C 



or 



sin 



From (95), A (n* - D) (p.* - D) = AD 2 - D (B + AD + C 2 ) + BD = - DC 2 ; 

 substituting and re-arranging, we find 



- A 



7 % + ' +CD! - - 



this equation gives the frequency. 



22. In the case of the symmetrical vibrations, * = 0, and we have 



and P 2 = 0, Q 1 = 0, but Q 2 is finite. Thus, the equation just written involves some 

 induterminates. 



We take the solutions 



u = Pj cos p.]Z, 



r = Q 2 sin /ijZ. 



The conditions m = 0, <r l + tro-., = reduce to 



( I + ^ J /tjpj sin /i t c = 0, Q^fig cos fi 2 c = ; 



hence, either 



Q., = 0, and sin /i, c = 0, 



or 



P, = 0, and cos fa c = 0. 



