Electrical Resistance of Gases. 211 



propagation of the electricity, and this counterpressure being, 

 in gases, independent of the intensity of the current, it is self- 

 evident that the resistance of a column of gas must be inde- 

 pendent of its section. 



The difference of electroscopic tension between two points 

 in the conductor situated at a certain distance from each other 

 is, according to the foregoing, proportional to the resistance 

 between the same points. In solid and liquid conductors, 

 therefore, the difference of tension will be proportional to ri, 

 if r denotes the principal resistance between the points, and i 

 the intensity of the current. For gases, on the contrary, the 

 same difference will be proportional to M, in which k has the 

 signification which has just been mentioned, and I denotes the 

 distance between those points. The difference of electroscopic 

 tension between two points in a column of gas must, then, as 

 has already been proved by experiment, be independent of the 

 intensity of the current ; and it can be predicted that it will 

 also be independent of the 

 ever, has not yet been confirmed by experiment. 



If r designates the principal resistance in the part of a closed 

 circuit composed of solid and liquid conductors, E the resist- 

 ance of a column of gas introduced into the circuit, E the 

 electromotive force, i the intensity of the current, and L the 

 total length of the conductor, the differential equation of 

 motion of the sether will be 



L — = nE—jiR—nri. 



dt 



From this equation we get, for the case in which the cur- 

 rent has had time to become constant, 



. E-E 



The resistance E of the gas has therefore in reality its place 

 in the numerator, although, according to the ordinary formula 

 of Ohm, it ought to be in the denominator. Of course E must 

 be greater than E for a current to be possible. 



If, when gas is introduced into the circuit, i and ij denote 

 two different current-intensities answering to the resistances 

 r and r x of the solid and liquid conductors introduced into the 

 circuit, and if M and M x are the resistances necessary in order 

 to produce the same current-intensities when the gas is ex- 

 cluded from the circuit, we get 



,_ E-E _E 



l ~ r ~M 



