292 Mr G. H. Bryan, Application of the Energy Test, &c. [Oct. 29, 
Therefore f diminishes continually as the ratio of h to a@ is 
diminished and by taking the ratio h : a small enough, / may 
be always made so small that the tube is not strained beyond 
the limits of elasticity. 
Taking the thickness of the tube to be the one-hundredth 
part of its diameter, and employing the values of HL, o given by 
Lupton, I find the values of P in c. G. s. atmospheres are for 
GSS S anata renee ee "88 
BRASS eiuiccNeasce nate ere ae DOS 
Gast. irom ¥en cee 2:90 
Steel s247 eco. Ros ote ocak 4-73 
approximately. 
When the tube collapses through instability it does not 
necessarily follow that it will burst. In the case of “collapse into 
four segments” here considered the tube begins by becoming 
elliptical and gets more or less flattened, but unless the bending 
moment should become too great at any point the tube will not 
break but will probably pass into a form somewhat resembling 
eS 
the one here represented, the support afforded by the contact 
of opposite sides preventing further collapse. Moreover it is 
important to notice that on this hypothesis ¢f the pressure be 
removed, the tube will return to the circular form, which it would 
not do if the material gave way at any point. 
We may also find the effect of the pressure on the vibrations 
of the cylinder. If the frequency is p/27, then Lord Rayleigh’s 
formula will be replaced by 
pet (Wiel) eiBaae P ) 
ae em Ga (n? — 1) p/’ 
p being the mass per unit area of surface of the tube. 
The vibrations will all be lowered in pitch, owing to the 
variations of the potential energy being diminished. The above 
formula does not however take into account the sound-waves pro- 
duced in the medium by which the pressure is transmitted to the 
surface of the vibrating cylinder. 
