Wave Propagation through Fluid Contained in a Cylindrical, Elastic Shell*

satisfies it. This indicates that in the limit, as the wall thickness of the hollow tube approaches zero, the only possible mode of torsional wave propagation is the zeroth mode, as would be expected. For completeness, Fig. 1 shows the values of the characteristic numbers k'a plotted agsinst the ratio of the tube inner radii to tube outer radii for the cases calculated. This shows that torsional wave phase velocities increase with decreasing wall thickness of tubes for all modes except he primary, and also increase with the higher modes of motion. The values presented in Tables I through IV were calculated by use of various tables of Bessel functions which are readily available, but particular use was made of the Bureau of Standards n and the Royal Society '• tables for larger values of the arguments than are commonly tabulated. The tabular values presented are calculated to the nearest 0.001 units, to which they are believed accurate.