466 M. G. Kirchhoff on a Deduction of Ohm's Laws, 



tential of the free electricity as those given by Ohm's expres- 

 sion of the electric force, i. e. the density of the electricity. 



In fact, if we denote the normal of the element by dw, that 

 having the direction of R by N, then 



R ~^N' 



hence the quantity of positive or negative electricity flowing 

 through dw in a unit of time, is 



The same expression is obtained for this quantity by Ohm's 

 method, if u be used to denote the electroscopic force*. 

 But we may conclude from this expression, without entering 

 into the signification of u, that when the condition of the 

 system has become stationary, u must satisfy the differential 

 equation 



d 2 u d 2 u d 2 u _ 



doc* dy 2 dz 2 



and for each point of the free surfaces of the conductor, the 

 limitary condition 



du 



rfN =0; 



and further, that the equation 



, du l du x _ 



applies in the case of every point of the surfaces of contact of 

 two bodies. 



To these conditions, both as regards Ohm's proposition 

 and those we have enumerated, must be added, that in the 

 case of every point of the same surface of contact, u—u x — the 

 tension of the two bodies. Thus the same equations are 

 obtained for the magnitude u by both propositions. As regards 

 the currents which are determined by the differential quotients 

 of these magnitudes, we consequently obtain the same results 

 from whichever we start. But different results are obtained in 

 regard to the distribution of the free electricity in the circuit. 

 According to Ohm, the value of u at every part of the system 

 directly gives the density of the electricity, which is not the 

 case in the view we have developed, from which, on the 

 contrary, it follows that even in the closed circuit free elec- 



* Poggendorff's Annaloi, vol. lxxv. p. 191. We have used the word 

 tension here to denote Ohm's electroscopic force. 



