199, 200] DIELECTRICS AND MAGNETIZABLE BODIES. 385 



exert forces on each other, whose combined action may for either 

 part be represented by a single resultant force applied to dS. Let 

 the force acting through the area dS on the portion of the body 1 

 be denoted by F n dS,F n is not in general normal 

 to dS, but has a tangential component. This 

 tends to cause the two portions 1 and 2 to slide 

 over each other, or to be sheared. The normal 

 component of F nt if directed toward the body 

 2, tends to make the two portions of the body FlG - 79 - 



approach each other, and is called a traction or tension, as in 

 the case of a stretched rope. If the force F n on 1 is directed 

 toward 1, the force is called a pressure, as in the case of 

 liquid pressure. A traction will be considered positive, that is 

 the force acting on a portion of the body has a positive com- 

 ponent along the normal drawn outward from that portion. We 

 shall denote the components of F n by X n , Y n , Z n , the suffix n 

 denoting the direction of the normal to the element of surface to 

 which they are applied. If we consider three sides of an infinite- 

 simal cube at any point, we may specify the stress at that point by 

 giving the components of the stresses on each side, those on the 

 side perpendicular to the X-axis being X x , Y x , Z Xy those on the 

 side perpendicular to the F-axis being X y) Y y) Z y) 

 and those on the face perpendicular to the ^-axis 

 being X z , Y z , Z z . If we consider the equili- 

 brium of an infinitesimal tetrahedron formed by 

 cutting off one corner of this cube by a plane 

 whose normal is n (Fig. 80), the areas of its 

 four faces being dS x , dS y , dS z , dS n , (the suffixes 

 denoting their normals) and its volume being FlG> 80 ' 



dr y we have for the equations of equilibrium, resolving along the 

 three axes, 



Hdr + X x dS x + X y dS y + X z dS z - X n dS n = 0, 



(i) Rdr + Y x d8 x + Y y dS y + Y z dS z - Y n dS n = 0, 



Zdr + Z x dS x + Z y dS y + Z z dS z - Z n dS n = 0. 



Now the faces dS x , dS y , dS z are the projections of the face dS n on 

 the coordinate planes, and accordingly 



dS x = dS n cos (nx), 



dS y dS n cos (ny), 



dS z = dS n cos (nz). 



w. E. 25 



