4 Prof. E. Edlund's Researches on the Passage 



gases give proof when traversed by the current can be ex- 

 plained with the greatest facility, namely: — that the amount 

 of heat generated is proportional to the intensity of the cur- 

 rent, not to the square of that intensity; that the resistance in 

 a column of gas is independent of the cross section of the 

 column ; that the difference between the electroscopic tensions 

 of two points situated at a distance from one another is pro- 

 portional to the resistance between the same points, not to 

 that resistance multiplied by the intensity of the current, &c. 

 Every thing, consequently, leads to the conclusion that the 

 electric resistance of gases is independent of the intensity of 

 the current, but of course only on the supposition that the 

 current does not sensibly modify the composition, temperature, 

 or density of the gas. 



Let i be the current-intensity in a closed circuit composed 

 exclusively of solid and liquid parts, E the electromotive force 

 of the electromotor, and n the quantity of surface of the latter, 

 L the total length of the circuit, and r its resistance at unit 

 intensity of the current; we shall have for the determination 

 of that intensity the differential equation * 



t di -^ 



Li- T = n&—nri. 

 at 



If we integrate this equation, we shall get, for the case in 

 which the current has been closed a sufficient time for its in- 

 tensity to have become constant, 



that is to say, the known law of Ohm. 



When, on the contrary, the circuit contains in addition a 

 gaseous conductor whose resistance is R, the differential equa- 

 tion becomes 



L =?iE— nR— nri, 

 dt ' 



of which the integral is 



. . B-R 



Therefore the resistance R of the gas has its place in the 

 numerator and not in the denominator as, without closer exami- 

 nation, one would be inclined to place it, according to the 

 usual formula of Ohm. It is seen, then, as a consequence of 

 what has been said above, that E must be greater than R in 

 order that it may be possible for a current to arise. 



* Pogg. Ann. cxMii. p. 421 ; Phil. Mag. [4] xlvi. p. 206. 



