^3^ 



hiaterial element qcIt ai'e qXcIt, q Ydr, and qZcIt, and the components 

 of llie joint exlernal tensions which act on the surface elements do 

 of the surface that bounds the system: pxdo, p^dc, and pzda, the 

 total work of the external forces, the displacements being §, ^, C, will 

 amount to 



ÖA= i ^ (X^ f Y^i + Zl>) dx + fcp, § + pyii -f p, ?) do . (4) 



Now when the temperature is constant 



(5) 



holdb generally as condition of equilibrium. 

 Hence we derive from (3), (4), and (:») : 



= Cq (X§ + Yn + Zi) dx + J (p,§ + pyn -^ p,5) da 



öi|5 di|' di{? 



' O.Br oyy oz~ 



öi(' d^' öi|? 



oyz ozx oxy ^ 



(6) 



Making use of the relations (2) we get from this after partial 

 integration : 



ƒ[ 



II -^ cos (.v..) -f -^ ro5 (A^y) 4- -^ cos (.Vc) + 



OXx OXy OXz ] 



4- 7 J -^ C06- {Nx) + -^ COS (xV^) 4 V^ COS {Nz) + 



+ ? l^cos {Nx) + --^ cos {Ny) -f -— cos (iV^) 

 [OZx ozy ^ dz~ ' 



p da — 



J' 



dip 





().t- 



dy 





dU 



Ölf? 



'y= 



Öa' 



+ 



dx 

 dz 



dz 



,J'i!l)+'tl) + 



Ö.C 



1 



di/ 



it == ro(X5+ Fij 4z?v/T+r(/>,,i + py,i + jt>,?)c?(j 



(7> 



The quantities 5, i/, and ^ for the different points of the system 

 being quite independent of each other, we obtain from i^7) the relations: 



