460 Mr. A. Mallock. Instability of India-rubber [Apr. L'.'>. 



Since P is also equal to F* -r- strained area of base of cylinder, 



^H- / T,, 



,, * J 



I/O * 



4ir p 



and by equating this to the former expression, we have for j> in 

 terms of *, 



_ v/*0-i) + 2 



* ' 2 



So that, when K = 3, p = ^/3 + l. 



From this it will be found that the critical value of the radius is 



1-815 TO, 



and that then the length of the tube is T58 1 nearly. 



In the case of the sphere the maximum pressure will also be 

 attained when ic = 3, but, since by symmetry p now = *, we shall 

 have for the critical value of the radius r v/3, or 1'73 v nearly. 



Some experiments were made with india-rubber pipes and balloons 

 to see how nearly their behaviour conformed to the theory just 

 given. 



Fig. 2 (p. 461) shows the apparatus employed. 



The india-rubber to be experimented on was placed in a Is 

 closed vessel, B, full of water. Two pipes C and D passed through 

 the stopper of B ; of these C communicated with the interior of 

 the expeiimental tube or sphere A, and D immediately with the 

 contents of B. A pressure gauge was connected with C. 



When -tubes were being experimented on, the ends were closed 

 with hardwood discs, covered with paraffin, through the upper one of 

 which C entered. Fixed into the centre of the lower disc was a long 

 straight wire, E, which passed freely through C, and the position of 

 whose upper end, E', could be read on the scale S. 



Water could be introduced into A by means of the pipe H con- 

 nected with C. 



When every part of the apparatus was filled with water, and the 

 pressure gauge showed that the internal and external pressures on 

 the india-rubber were equal, more water was admitted through C. 

 The volume of water thus introduced was measured by the amount 

 expelled through D. The pressure gauge showed the internal pressure 

 in A, and the descent of E' gave the elongation of the tube. 



The analysis of the results thus obtained is given by the curves in 

 Diagram I. 



The experiments on spheres were made in the same way, except 

 that the wire E was not used. 



