Manchcsfcr Memoirs, Vol. Iviii. (1914), No. 5. il 



7. Elcmoital couples. 



If the motion of an element of the material under 

 consideration is regarded in its widest aspect, and with- 

 out any limitation from habit or from casual experience, 

 the further possibility must be included of an elemental 

 couple in the stress and of an elemental change of angular 

 momentum in the material. 



In the accepted theory it is assumed that either no 

 such elemental couple exists, or that if it does exist it 

 contributes no term to the work done on the element. 

 It is now proposed to include the consideration of such a 

 couple, and to examine more closely the reasons for its 

 admission or inclusion. 



It will therefore be taken that the stresses are, follow- 

 ing an accepted notation, 



p,u=s+i, p,„ - s - ^, 



A.= <^+4, A.- ^-4 . . . . (13), 



so that the elemental couple is measured by 



2^, 2//, 2;' (14), 



and the linear force on the element has the components 



cP dU ?)T d'C d,j 



dx oy dz dy gz' 



vU ?0 dS oE o'C 



vx oy c'z vz ?.t' 



dT ?'S dR dr, dl 



_— +:r- +.- +^ -r- . . . . (15). 

 cx cy rx dx Oy ^ ~" 



In accordance, I shall write the components of the 

 displacement as 



U = U, + — 3 _ -^-, 

 (y cz 



(<z ox 



