﻿The Collapse of Tabes by External Pressure. 67 



Writing « for S, a l for « , a 2 for a 1? etc., we Lave 



r a +?i+l a, 1 / n a /3-l\ 1 



bg^ i a+*) = (ft+i)! s (-1)- \ , x -4r(n 2 ) . ,. 



Or 



„ r *o+?i+l / ?i ft /3-l\ 1 



ioo-+ i (i+.'0 = (/ i + i)! 2 (-i) ao — T n s ) =h — 5, . (6) 



which proves the correctness of the assumed result (4). 



University of Pennsylvania, 

 Philadelphia, Pa., U.S.A. 



IX. On the Collapse of Tabes by External Pressure. — III. 

 By E. V. Southwell, M. A., Fellow of Trinity College, 

 Cambridge*. 



IN an interesting paper recently communicated to this 

 magazine f, Mr. Cook has dealt with the resistance 

 offered to external pressure by short steel tubes — that is to 

 say, by tubes such that an appreciable part of their strength 

 was due to the sealing plugs which in the experiments were 

 employed to preserve their cylindrical form at the ends. 

 The subject is one which possesses practical as well as 

 theoretical interest, since his results, and those of other 

 workers on the same lines, are foundations upon which we 

 may endeavour to base scientific rules for the spacing of 

 " collapse rings " in boiler-flues. 



I propose in the present paper to consider the bearing of 

 these results in regard to design. It appears to me that a 

 discussion of the problem from this standpoint is becoming 

 urgently necessary, since the large amount of scientific interest 

 aroused by it in recent years ~% has resulted in a steadily 

 increasing number of formula?, based either upon analytical 

 investigations or upon isolated series of experiments, and 

 tending, by reason of their variety, merely to bewilder 

 anyone who has not made an extensive study of the subject. 



In the first place, however, I desire to remove a slight 

 difficulty which may be encountered if Mr. Cook's paper is 



* Communicated by the Author. 



t July, 1914. 



X A full discussion of the problem, with a bibliography complete up to 

 the date of publication, was giyen in the Report to the British Associa- 

 tion Committee on Complex Stress Distribution (Birmingham, 1913). 



F2 



