26 ON POTENTIAL. 



the two ends which form part of the conductors. If cr and a-' are the 

 densities on the corresponding elements d and */S', their sum is 

 This sum must be zero, which gives, 



Thus two corresponding elements contain quantities of electricity 

 which are equal and of opposite signs. 



If the two surfaces opposite each other are parallel planes, all the 

 lines of force are perpendicular to the planes ; the corresponding 

 elements are equal, and we have 



cr = cr'. 



This is also the case if the two conductors, though not plane, 

 are infinitely near, for then the surface elements ^S and d$' may be 

 considered equal. 



f 



38. UNIFORM FIELD. When the lines of force are straight and 

 parallel, the equipotential surfaces are parallel planes. The flow of 

 force being constant in a cylindrical tube, it will be seen that the 

 value of the force is constant. The field is then said to be uniform. 



Conversely, if the force in an electrical field is constant in 

 magnitude and direction, the equipotential surfaces are necessarily 

 parallel planes. 



39. ELECTRIFIED SURFACE SEPARATING Two DIELECTRICS. 

 Let us suppose that an electrified surface S (Fig. 8), not belonging 

 to a conductor, separates two different dielectrics. 



Consider an elementary surface ^S, on which the density 

 is cr. Draw through the contour of this element a straight tube 

 terminated by two equal bases, and parallel to dS, and of such a 

 height that the lateral surface is infinitely small as compared with 

 that of the bases. The flow of force relative to the sides of this 

 cylinder may be neglected as compared with the flow which traverses 



