164-166] Stresses in Electrostatic Field 147 



On substituting the values of the stress-components, we have 



. . 



dx dy 



On putting 



3F 3F 3F 



~' '' -" 



we find at once that 



= 



a; a?^ 



9.Z 9F 



_ 

 + ~ 



shewing that equation (88) is satisfied. 



165. Thus, to recapitulate, we have found that a system of stresses con- 

 sisting of 



pz 



(i) a tension 5 per unit area in the direction of the lines of force, 



O7T 

 D2 



(ii) a pressure per unit area perpendicular to the lines of force, 



is one which can be transmitted by the medium, in that it does not tend to 

 set up motions in the ether, and is one which will explain the observed 

 forces in the electrostatic field. Moreover it is the only system of stresses 

 capable of doing this, in which the stress at a point depends only on the 

 electric intensity at that point. 



Examples of Stress. 



166. Assuming this system of stresses to exist, it is of value to try to 

 picture the actual stresses in the field in a few simple cases. 



Consider first the field surrounding a point charge. The tubes of force 

 are cones. Let us consider the equilibrium of the ether enclosed by a 

 frustum of one of these cones which is bounded by two ends p, q. If 

 o) p , cog are the areas of these ends, we find that there are tensions of 



102 



