Manchester Memoirs, Vol Iviii. (19 14), No. 5- 7 



Also, whatever values S, T, and U may have, we can 

 always write 



cydz 



T— 2 



-'- ~~ i — K ' 

 (IXOZ 



i^.^ (3). 



And we thereTore shall always have formally 



cy vz- 



e-^e.+ii'+'^'-o, 





^-.e..S + S-o W- 



2. The elements of the stress consequent on Hooke's 

 Law in a homogeneous isotropic elastic solid become, on 

 the substitution for the components of the displacement 

 given in (2), 



^ \r!x- ay^ ^jZ J ^x^ 



with two analogous expressions for Q and R', 



.S' = //;^-(0.,+ e,) 



(^\ivz^ - 



with two analogous expressions for T' and U . . (5)- 



3. In order to make a connection between these two 

 specifications of stress I shall assume 



^3==Mo^ + e,) (6). 



This connection is sufficient, and is not redundant. 

 The consequence is that 



S'^S, T'=T, U" = U, 



