﻿Collapse of 'lubes by External Pressure. 75 



The best procedure would seem to be to arrange the spacing 

 of collapse rings in such a way that the resistance of thin 

 tubes is brought up to the value given by (11): they will thus 

 be enabled to withstand any pressure which is insufficient to 

 cause elastic breakdown, and a greater pressure than this is 

 in any case inadvisable. 



If we take the collapsing pressure for a tube of critical 

 length as given by the equation 



t = 2Ej (15) 



(which, as compared with (8), errs slightly on the side of 

 safety) , and employ Mr. Cook's equation (1) for the critical 

 length, the collapsing pressure for a tube in which the 

 collapse rings are spaced at distances s will be given by 

 the equation 



.-.I < 16 > 



3-46 



s 



Then if the resistance is brought up to the value given by 

 (11) we have 



or s i „ E A T 



s =K ?jiV?- ( 17 > 



so that when collapse rings are to be employed we may use 

 (11) to determine the value of t/d, and fix the rings at 

 intervals given by (17). 



Now the strengthening effects of collapse rings will be 

 nil if s>L: hence, by (1) and (17), their employment is 

 advantageous only when the dimensions given by (12) are 

 such that 



vVi) 



d < V E 



(18) 



It may be remarked that this result will hold whatever be 

 the value of k in (2), provided only that the latter equation 

 is correct in form. Mr. Cook's experiments suggest that it 

 is. Taking for example the figures given by Prof. Stewart, 

 we find from (18) that collapse rings are of no advantage 

 on a tube of which the diameter is loss than 28 times the 

 thickness. 



