Electrical Resistance of Gases. 205 



the expression of the resistance r in a conductor of length 1 

 and section a, traversed by the current i, 



ki 



where k is a constant dependent on the chemical and physical 

 nature of the conductor, as well as on the temperature. The 

 constant k is evidently the resistance in a conductor of sec- 

 tion 1 and length 1, passed through by the current 1 ; - is the 



intensity of the current on the unit of section ; r, or, in other 

 terms, what we have hitherto named the galvanic resistance, 

 is nothing else but the resistance per unit of intensity of 

 the current. In order to distinguish this resistance from the 

 others, in the following we call it the principal resistance. 



(b) Electromotive force, like all other motive forces, is 

 measured by the acceleration which it can impart, in the unit 

 of time, to the unit of mass. Taking this for granted, which 

 we are warranted in doing under all the circumstances, Ohm's 

 law can be without difficulty deduced from ordinary mecha- 

 nical principles. We will nevertheless previously show that 

 the electromotive force is independent of the intensity of the 

 current. 



Electromotive force acts with equal intensity upon every 

 point of the electromotive surface of contact ; consequently 

 the total value of this force increases proportionally to the 

 extent of that surface. Besides, it is evident that the force 

 not only acts upon the aether molecules which are at the con- 

 tact surface itself, but also extends to those situated at a very 

 little distance from that surface. Now let us designate by E 

 the quantity of motion which the electromotive force can com- 

 municate to the mass of aether on each unit of surface in the 

 unit of time. Let us, in the first place, imagine a current 

 sufficiently powerful for the unit of mass to pass, in the unit 

 of time, through each unit of the surface of contact] then each 

 unit of mass will have received the acceleration E. If the 

 extent of the surface of contact be called n, wE will in this 

 case constitute the total value of the electromotive force. Let 

 us suppose, secondly, the surface of contact passed through, 

 in unit of time, by a mass of aether p times as great as before, 

 and which can then be expressed by pn. The aether possessing 

 the same density in a feeble as in an intense current, the velo- 

 city will in this case be p times as great. Each particle of the 

 mass of sether therefore undergoes the action of the electro- 

 motive force during a space of time constituting - of the time 



