54 EXPKRIMKNTS WIIH IONIZED AIR. 



1-4. EU'drolytic mechanism. — If, instead of Z7= 1 cm/sec foi- the field i>f 1 

 volt per c-eiitiiii., the absorptiou velocity found in tlie preceding chajjter as 3 A; = 

 .'J cm. (approximately) were taken, the number /*„ would be of about the same ov- 

 der. In such a case however, from the implied absence of an electric field, a 

 si)ecial mechanism of electrolysis is in (piestion. The following is the point of view 

 taken : 



Let k (replacing 3 k) be the ion velocity of the phosphoric "dust " particle, 

 normallv to a charged wall. A, figure 7. The prism of charged air, figure 7, which 

 reaches ^i will, fur any appreciable length in the direction of k, be at an average 

 potential zero, and its successive layers will on the average shoAV no charge, 

 although saturated with the ionized agency stated. Considei'ed non-statistically, 

 however, the individual sections at molecular distances apart must convey im- 

 mensely different chaiges successively, the distribution of charge or of potential on 

 successive sections following a law something like Maxwell's, for instance, in the 

 kinetic theory of gases. To deal \vith the problem in this broad foini woidd make 

 it needlessly cumbersome, without conducing to the present purposes. It seems 

 possible to obviate the question of distribution somewhat as follows : 



Suppose the distribution of potential in the direction X; is enormously variable, 

 as compared with the potential of ^J, in such a ^vay as to give preference neither to 

 positive nor to negative values. A will lose charge if its potential is instanta- 

 neously greater than that of the section which meets it; it will receive charge in the 

 o})posite case. A at potential zero, therefore, neither receives nor loses charge, since 

 the number of sections reaching A carry e(pial and opposed charges in like distribu- 

 tion. If tiie charge on .1 is positive, tiicrc must be fewer layers which impart 

 charge to A, and more layers which witlidraw it than in the pi'eceding case, since 

 the average charge on the layers is still zero. Thus ^1 will be discharged in the 

 lapse of time and this more rapitUy as its potential giadient, V/x, is higher. Pre- 

 cisely th<' leverse will happen if A is negatively charged. Hence to avoid the law 

 of distribution specified, I sup}iose that the charge per square ceutim. on ^1 is rela- 

 tively so small, that if it is increased ii times, there will be n times more layers to 

 discharge it under like conditions than in the initial case. In other words, I 

 regard the charge on A small enough to correspond to a linear element of the law 

 of distribution of charges along the length of the prism, k. The rate of discharge 

 of A is then taken pi-oportional to V/x. 



If 11 is the total number of ions per cubic ceutim., and t proportional to the 

 average charge (positive or negative) carried by each, Akiie is the total (piantity of 

 free electricity of both kinds promiscuously carried to A per second. Thus kne is 

 the equivalent of conductivity. The rate of discharge of A is thus —di^/dt = 

 ( V /x^fAkiU'. where the constant of proportionality is contained in e. Tiie [mtential 

 of the charged plate of area, A, the other beim: earthed, is therefore V-= V^t -■""•"/(^^ 

 in the lapse of time after charging to the initial potential, F,,, I iMin-- the capacity 

 of the comlen.ser. 



The conveyance of charge into the ionize<l region would be similarly explained, 

 viitually in the way of Clausius. Through any interface in the ionized region two 



