480 
ON CYLINDRICAL AND SPHERICAL THIN ELASTIC SHELLS. 
were to take place in the neighbourhood of the edge, it would be possible for Gj to 
vanish there, and also to satisfy the other boundary conditions. 
There seems no reason to doubt that the argument which has been employed in the 
case of a cylindrical shell, would apply equally to the case of a spherical shell, and 
probably also to a shell of any shajDe; in which case, the portions of the displace¬ 
ments upon which extension principally depends, would be small compared with the 
portions upon which bending principally depends, except at points whose distances 
from a free edge are comparable with the thickness. At the same time it would 
be very desirable to obtain the solution of some problem relating to the vibrations 
of a shell whose edges are free, in which no supposition is made as to the relative 
magnitudes of the extensional and flexural terms. 
