AND DEFORMATION OF A THIN ELASTIC SHELL, 

 and, if p. = at the edge, or the shell be hemispherical, this is 



-*)'' . ( 75 ) 



In the case of the symmetrical vibrations s = and the expressions found involve 

 indeterminates. In any other case the above expressions show that it will not be 

 possible for the motion to be purely tangential, since, for this, A = 0, and we should 

 have to make dT ft /dfi. = 0, T,, = for some value of p..* 



19. In the case of the symmetrical vibrations we have to put M, f, w independent 

 of < in (54), (55), (56) ; this gives 



=s 



j n -' A l " * I 



* 



- 



du 



j 



From which 



2e 



where /8, a have the same meaning as before. 

 Hence, 



I 



ao-j = A I 



The boundary-equations (72) become 



(76) 



(77) 



(78) 



.... (79) 



* Using only the differential equations, MATHIEC supposed that there c mid be onaymmetrical 

 tangential vibrations. 



