THE EQUILIBRIUM OF ELASTIC SOLIDS. 



3. Two tangential actions on each face. 



37 



Let the six faces of the small parallelepiped be denoted by x lt y l} z 1} 2 , y t , 

 and z,, then the forces acting on. #, are : 



1. A normal pressure p t acting in the direction of x on the area dydz. 



2. A tangential force q 3 acting in the direction of y on the same area. 



3. A tangential force qj acting in the direction of z on the same area, 

 and so on for the other five faces, thus : 



Forces which act in the direction of the axes of 



x y z 



Takmg the moments of these forces round the axes of the particle, we find 



and then equating the forces in the directions of the three axes, and dividing 

 by dx, dy, dz, we find the equations of pressures, 



+ + + 

 dx dy dz 



p, + q i + q 1+ 

 dy dz dx ^ 



dp t dq dq, 

 ~ 



_ 

 - 



Equations of Pressures. 



,(3). 



