MR. R. V. SOUTHWELL OX THE GENERAL THEORY OF ELASTIC STABILITY. '231 



less accurate results when k has a finite value, it does not seem necessary to employ 

 iiur more rigorous method, with the very laborious calculations which it entails. We 

 shall therefore rely upon the approximate theory for the treatment of the tubular 

 'strut problem in its gcnrr.il f'>rm. Slight modifications in method will be introduced, 

 as suggested alx>ve (pp. 224-225), and only the more important steps will be given 

 here. 



Solution by (tie TJteot-y of Thin Shells : General Case. 



We consider tin- stability of an element of the tube, originally bounded by the 



planes 



6, 9+ S6, and z, z + Sz, 

 as shown Ixslow 



The other dimension of the element is the full thickness of the tube, denoted in 

 this paper by 2t. The radius of the middle surface is a. 

 The initial stress system is 



P, = const. = - - = [PJ (say). 



In the distorted position this system produces a radial force on the element, of 

 amount 



. - 



where B is the radius of curvature of a section of the distorted element by an axial 

 plane (see fig. 5). 



It also produces a tangential force, in the direction of 6 increasing, of amount 



where -^ (see fig. 5) = - (l + ) Sz. 



a 06 



