206 MR. R V. SOUTHWELL OX THE OKNKHAL THEORY OF ELASTIC STABILITY. 

 The equations of equilibrium, to be satisfied by the stress components (44), are* 



1 ZrO . far . ri'-ee 



<> r $6 



czr 1 cQz czz zr _ 

 ?r r 20 ?2 r ' ' 



where 



and 



Moreover, since 



9 = 0+-!, 

 r + u 



z = 



(45) 



and 



St/ 



i a 



the equations (45) may be expressed in differentials with respect to >-, z The 

 erms which do not involve ', t ,', ' vanish in virtue of the equilibrium conditions 

 the second configuration, and only terms of the first order in these quantities 

 need Ije retained. 



In general, , , <> :t may all be functions of ,-, but in this paper we shall only 



onsider problems in which , and ?z have constant values. Moreover, in all problems 



of practical importance we may neglect terms of order j'... in comparison with 



\^ 



* LOVK, />. fit., 59 (i). 



