52 Mr. Gr. Cook on the Collapse of 



provided that the ratio does not exceed *025^ The formula 

 given by them for solid drawn weldless steel tubes is 



p = 50,200,000 (£) , (1) 



and it is notable that the numerical term is some 30 per cent, 

 less than the theoretical value *. 



It is well known that a short tube has a much greater 

 strength to resist collapse than a long one of the same thick- 

 ness and diameter ; it is also known that as the length 

 increases, its influence upon the strength rapidly diminishes. 

 Carman and Stewart have inferred from their experiments 

 that when the length exceeds six diameters, which has been 

 termed the critical length, the collapsing pressure is not 

 affected by a further increase in the length, and that it 

 differs, therefore, from that of an infinite tube by a negligible 

 amount. In the light of the experiments here described, the 

 above value for the critical length appears to be an under- 

 estimate, and there can be little doubt that not only the 

 diameter, but also the thickness of the tube, is a factor w r hich 

 must enter into any expression for its value. It is, indeed, 

 possible that the theoretical value suggested by Southwell f, 

 namely 



= k VT> 



may be true, though there is at present no means of ascer- 

 taining the value of the constant k by mathematical 

 analysis. 



In view of the vagueness which exists in regard to the 

 value of the critical length, an accurate prediction of the 

 strength for any shorter length is hardly to be looked for. 

 It is, indeed, a fact that there is no experimental information 

 available which would indicate the manner in which the 

 collapsing pressure of such tubes is related to the three 

 variables, thickness, diameter, and length. Southwell % has 

 investigated the problem mathematically, and has arrived at 

 an expression for the collapsing pressure which is exceed- 

 ingly interesting as affording an explanation of the hitherto 

 unexplained phenomenon of the variable number of lobes 



* In regard to the theories which have been put forward to account 

 for the discrepancy, papers by S. E. Slocura (Engineering-, Jan. 8, 1909) 

 and R. V. Southwell (Phil. Mag-. Sept. 1913) should be consulted. 



f Phil. Trans. (A) vol. ccxiii". (1913), pp. 187-244. 



% Phil. Trans. (A) vol. ccxiii. (1913), pp. 187-244 ; and Phil. Mag. 

 May, 1913. 



