452 OHM ON THE GALVANIC CIRCUIT. 



S = ,j£; (*) 



and in this equation positive values for S show that the current 

 takes place opposed to the direction of the abscissae ; negative, 

 that it occurs in the direction of the abscissae. 



13. In the two preceding paragraphs we have constantly had 

 in view a homogeneous prismatic body, and have inquired into 

 the diffusion of the electricity in such a body, on the supposi- 

 tion that throughout the whole extent of each section, perpen- 

 dicular to its length or axis, the same electroscopic force exists 

 at any time whatsoever. We will now take into consideration 

 the case where two prismatic bodies A and B, of the same 

 kind, but formed of different substances, are adjacent, and touch 

 each other in a common surface. If we establish for both A 

 and B the same origin of abscissae, and designate the elec- 

 troscopic force of A by u, that of B by u', then both u and u' are 

 determined by the equation (a) in paragraph 1 1, if x only retain 

 the value each time corresponding to the pecuUar substance of 

 each body : but u represents a function of t and <r, which holds 

 only so long as the abscissa x corresponds to points in the body 

 A ; M on the other hand denotes a function of t and s, which 

 holds only when the abscissa x corresponds to the body B. But 

 there are still some other conditions at this common surface, 

 which we will now explain. If we denote for this purpose the 

 separate values of u and u, which they first assume at the 

 common surface, by enclosing the general ones between crotchets, 

 we find according to the law advanced in § 10 the following 

 equation between these separate values : 



[u] - («') = a, 



where a represents a constant magnitude otherwise dependent 

 on the nature of the two bodies. Besides this condition, which 

 relates to the electroscopic force, there is still a second, which 

 has reference to the electric current. It consists in this, that 

 the electric current in the common surface must in the first 

 place possess equal magnitude and like direction in both bodies, 

 or, if we retain the common factor w, 



(du\ , /du'\ 

 ^j = ""^ \jxy 



where x represents the actual power of conduction of the 



