8 R. F. Gnn'VTHKK, Specifidxtion of the elements of stress. 



and that we have specifications which differ in form for 

 P and P\ Q and Q\ R and A". 

 Thus 



F= pe, - «|.'-{e, + e,) + ,-,(e, + e.,)l, 



with two analogous expressions for Q and R . . (7}, 

 and 



with two analogous expressions for Q' and A' . . (8). 



4. If we propose to draw the full conclusions conse- 

 quent from the fulfilment of Hooke's law, we proceed to 

 postulate the identity of the expressions for P and P', Q 

 and Q', R and R'. But the assumption that the differences 

 between the values of P and /'', Q and Q\ R and R' are 

 small compared with P, Q and A" respectively is more 

 in accordance with the object of attaining a description of 

 physical phenomena. It is not proposed, it appears to be 

 unreasonable, to require that the ratio of the differences of 

 these stresses to the stresses themselves should be so 

 minute as to be comparable with that of the second powers 

 of the elements of strain to the first. The difference 

 corresponds much more closely with a variation in the 

 multipliers which we have spoken of as " elastic constants." 

 Accordingly, the elastic theory is here considered as a 

 rough approximation to a natural theory. 



Before a closer approximation is taken into considera- 

 tion, it is desirable to review the assumptions which have 

 already been made. 



Briefly, we have treated 



^ (pBi) 

 vx 



as identical with 



p— ' , etc {a) 



