MI: i: v SIHTHNVKM. ox TIII: CKNKK.VL THEORY OF ELASTIC STABILITY. 



The extension of this line-element in the third configuration is 



(39) 



and its inclination to lines issuing from the point (in its final position) in the null..!. 

 tangential, and axial directions is given by the direction cosines 



where 



mill 



1, m\, ' 





l+c, 



(40) 



- 



We find also that the other directions of principal stress in the final configuration 

 are initially inclined to radial, tangential, and axial lines through (r, 6, z) at angles 

 whose direction cosines are 



and 



-m,, 1, n a , 



W], Wa, Ij 



and that in the third configuration they have corresponding inclinations to radial, 

 tangential, and axial lines through (r, 6, z) in its final position which are given by 



and 

 where 



and 



_r/ ' 1 

 '< i > " a> * > 



, = 



?l , = 



r d( 



(41) 



The extensions of the corresponding line-elements in the final configuration are 

 respectively 



r r 



(42) 



