Short Tubes by External Pressure. 55 



U-tube indicator, whereby any leakage could immediately 

 be detected. 



In carrying out a test, all the air was first displaced from 

 the vessel, and then the pressure raised very slowly until 

 collapse occurred. This was indicated by a sharp ring, 

 accompanied by a sudden fall in the pressure. Although at 

 this moment a condition of instability probably obtained over 

 the whole circumference of the tube, an inspection showed 

 that in most cases collapse had occurred in only one place. 

 Occasionally, however, two adjacent areas collapsed simul- 

 taneously. The deformation thus produced evidently affected 

 the whole tube, for when the pressure was raised a second 

 time, collapse occurred in another part at a lower pressure. 



The complete results are tabulated below, and curves have 

 been plotted to show : 



(1) The relation of collapsing pressure to - for different 



lengths (PI. I. fig. : 



d 



(2) The relation of collapsing pressure to length for dif- 

 ferent values of -7 (figs. 3 to 7). 



In the last two columns of the table a slight modification has 

 been made in the collapsing pressure, owing to small un- 

 avoidable differences in the ratio 7, and these modified values 



a 



have been used in plotting the curves shown in figs. 3 to 7. 



The present work was limited in scope by the expense of 

 the apparatus involved, and is insufficient to enable a general 

 law of collapse to be determined ; it fixes with accuracy, 

 however, the strengths of certain definite sizes of tubes, 

 which are given in the table, and in the curves shown in 

 figs. 2 to 7. In figs. 3 to 7 are also plotted : 



(1) Curves showing the collapsing pressure as deduced 

 from equation (2), taking Carman's value of the critical 

 length, viz. six times the diameter ; 



(2) Curves obtained from the same equation but assuming 

 the critical length to be much greater, and inversely pro- 

 portional to the square root of the thickness, as suggested 

 by Southwell's equation 



L = Ic 



v? » 



It will be seen that the latter method of calculation gives 

 results much more consistent with the experimental values 



