﻿74 Mr. R. V. Southwell on the 



does not appear to have been determined), equation (12) will 

 give, as the collapsing pressure of these tubes, 



.- 74,000 , ir . 



^mz 



t + %mt 6 



Dr. Lilly * has given the formula 



»-**£» i"? 



* + 1000* 8 



as very closely representing the results of this series of 

 experiments. Thus (13), which could be written down 

 without reference to any experiments besides that required 

 to find the yield-point and Young's modulus, gives values 

 which closely agree with those actually obtained from 

 hydraulic tests, and which (as may be shown by drawing a line 

 to represent (13) in fig. 3 of Dr. Lilly's paper) err almost 

 invariably on the side of safety. 



It remains to discuss the bearing of Mr. Cook's results 

 upon the problem of spacing u collapse rings/' At a first 

 glance equation (1) may appear paradoxical : for if, as 

 has sometimes been assumed, collapse rings ought to be 

 spaced at distances equal to some multiple of the critical 

 length, the thinnest tubes will receive practically no re- 

 inforcement, whilst the thickest must be fitted with rings at 

 quite short intervals. This manifestly unsound result is due 

 to the inaccuracy of the assumption noticed above ; for the 

 function of collapse rings is to strengthen a tube against 

 collapse by instability, and the ratio in which the resistance 

 is required to be increased (which, on the theory adopted by 

 Mr. Cook t, will be equal to the ratio of the critical length 

 to the distance between collapse rings) is obviously greater 

 in the case of the thinnest tubes. 



At the same time, considerations of safety suggest that 

 collapse rings ought not to be placed too close together ; 

 for a point may be reached at which failure, if it occurs 

 at all, will involve rupture of the tube-wall close to the 

 rings t, — an occurrence which has far more serious con- 

 sequences than the simple flattening of long tubes at collapse. 



* Log. cit. p. 145. 



t Namely, that the collapsing pressure is inversely as the length, for 

 tubes below the critical length. 



I In the author's experience the walls of quite short tubes, which fail 

 at high pressures, were almost invariably sheared through at collapse. 



