12 R. F. GWVTIIEK, Spccificaticn of the elevunts of stress. 



(t6), 

 or 



00, a*', ?^, , ^^ 



.r = --5 + -^-_— ' (17), 



d.2 d„r cy 



where just as \\ e have connected 0,,B.,,H, with effective 

 normal stresses, we must now treat "^J^,, ■*1'.,, "^P",; as having 

 the character of effective shearing stresses, so that for the 

 rotational equilibrium of the element we must have 



Similarly for the linear equilibrium of the element, 

 making use of this relation, we shall have 



CF 'vU ?r rB, 



OX cy rz ' rx 



?[/ ?Q ?S (O. 

 c'.v cy cz ' cy 



cx cv cz ' cz 



Returning now to the elastic specification of stress, 

 the elements P, O, A', ^", T, U are given in terms of 

 Oj, 9,, 0,, ^^, ^K, and ^l'„ while the right-hand side of (19) 

 is given in terms of B,, O2, H onl)'. 



It is, however, necessary to consider f, >/, C,. In the 

 usual theory, the values to be given to these quantities 

 are not discussed, but if we follow the course indicated by 

 Green in his analj-sis of the elastic relations, and find the 

 expressions for stresses as following from terms from the 

 work done, which work must be an invariantal expression 



