12 R. F. GwvTHER, Specification of tJie elements 0/ stress, 



I select the case of cylindrical polars, in which does not 

 enter. 



The expressions for the elements of stress (10) then 

 become 



dz' r \dr dz . 



dr ^ dzA dr - J dz' 



dr \ dr J dr 



Tr' 

 rp. d ( d<d., , „ ^ \ dfi ^ 



., c d / d^, ,,, .. d^.,\ d\ 



These conditions are required by Statics, and they^ 

 cover the whole of the statical requirements. 



If the stresses and strains follow Hooke's Law, we 

 obtain the following independent conditions : 



(d'Q I dR 2 dT\ (d' I ^\r„ ^ J 



dS S dU 



Tr-r=^ ^'4). 



These are the necessary and sufficient conditions for 

 the elastic relations. 



If we proceed to find the statical stress which is 

 consistent with Hooke's Law, we combine the two sets of 

 conditions. We maj- write 



