AND DIAGRAMS OF FORCES. 179 



this pressure in the directions of the co-ordinate axes, we find the three com- 

 ponents of stress on dydz, which we may call p^dydz, p^dydz, and p m dydz, 

 each equal to p multiplied by the area of the projection of the corresponding 

 element of the diagram of stress on the three co-ordinate planes. Now, the 

 projection on the plane yz, is 



dr) 



Hence we find for the component of stress in the direction of x 



Pxx ~ P \dydz dzdy)' 

 which we may write for brevity at present 



Pzx=pJ(n, ; y, z). 



Similarly, 



P*y=P J (t "> y> ), Px*=pJ(, -n; y, z). 



In the same way, we may find the components of stress on the areas 

 dzdx and dxdy 



; z > x )> P W 



Now, consider the equilibrium of the parallelepiped dxdydz, with respect 

 to the moment of the tangential stresses about its axes. 



The moments of the forces tending to turn this elementary parallelepiped 

 about the axis of x are 



dzdxp^ . dy dxdyp zy . dz. 



To ensure equilibrium as respects rotation about the axis of x, we must have 



P*-fir 



Similarly, for the moments about the axes of y and 2, we obtain the equa- 



tions 



Pzx=p x * and 

 Now, let us assume for the present 



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