Electricity through Gases by Charged Ions. 255 



tbe ratio of the charge to the mass for the particles con- 

 stituting the cathode rays and those of W. Wien * for the 

 ions carrying the positive charge indicate that the ratio of 

 the velocity of the negative ion to that of the positive one 

 under the same potential gradient would be very large. 

 This fact is, I think, sufficient to account for most of the 

 differences between the appearances at the positive and nega- 

 tive electrodes in a vacuum-tube. Schuster (Proc. Roy. Soc. 

 vol. xlvii. p. 526, 1890), from observations on the rates at which 

 positively and negatively electrified bodies lost their charges 

 in a vacuum-tube, came to the conclusion that the negative 

 ions diffused more rapidly than the positive ; other pheno- 

 mena connected with the discharge led me later (Phil. Mag. 

 vol. xl. p. 511, 1895) independently to the same result. 



We shall now proceed to find equations satisfied by the 

 electric intensity in a gas containing charged ions. To simplify 

 the analysis we shall suppose that the electric force is every- 

 where parallel to the axis of x, and that if X is the value of 

 the electric intensity at a point, the velocity of the positive ion 

 at that point is &iX, and that of the negative ion in the 

 opposite direction & 2 X; we shall suppose that at this point the 

 number of positive ions per unit volume is %, the number of 

 negative ions n 2 ; let q be the number of positive or negative 

 ions produced at this point in unit volume in unit time : the 

 number of collisions per unit time between the positive and 

 negative ions is proportional to n x ii 2 . We shall suppose that 

 in a certain fraction of these collisions recombination between 

 the positive and negative ions takes place, so that a number 

 un\n 2 of positive and negative ions disappear in unit time 

 from unit volume in consequence of the recombination of the 

 ions. If e is the charge carried by each ion, the volume 

 density of the electrification is (n x — n 2 ) e, hence we have 



_ =A7r(n 1 -^n 2 )e ! , (1) 



if i is the current through unit area of the gas, and if we 

 neglect any diffusion except that caused by the electric field, 



^n^X + Ji 2 n 2 eK. = i, (2) 



and if things have settled into a steady state, i is constant 

 throughout the gas; from these equations we have 



1 f l , k 2 afX | .... 



" ie= /tT+I 2 lx + i^j' • • • ( 3 ) 



* W. Wien, Verhandl. der phys. GeseUsch. zu Berlin, vol. xvi. p. 165. 



T2 



