400 Prof. C. Barus on the Transmission of the 



11. If instead of U=l cm./sec. for the field of 1 volt per 

 centim., the absorption velocity found in my preceding paper 

 as 3& = *9 cm. approximately, were taken, the number n 

 would be of about the same order. In such a case, however, 

 from the implied absence of an electric field, a special 

 mechanism of electrolysis is in question. The following is 

 the point of view taken : — 



Let k (replacing 3k) be the ion velocity of the phosphoric 

 dust particle, normally to a charged wall, A. The prism of 

 charged air (fig. 3) which reaches A will, for any appreciable 

 length in the direction of k, be at an average potential zero, 

 and its successive layers will on the average show no charge, 

 although saturated with the ionized agency stated. Con- 

 sidered non-statistically, however, the individual sections at 

 molecular distances apart must convey immensely different 

 charges 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 with the 

 problem in this broad form would make it needlessly cumber- 

 some, 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 k 

 is enormously variable, as compared with the potential of A, 

 in such a way as to give preference neither to positive nor 

 to negative values. A will lose charge if its potential is 

 instantaneously greater than that of the section which meets 

 it ; it will receive charge in the opposite case. A at potential 

 zero neither receives nor loses charge, since the number of 

 sections reaching A carry equal and opposed charges in like 

 distribution. If the charge on A is positive, there must be 

 fewer layers which impart charge to A, and more layers 

 which withdraw it, than in the preceding case, since the 

 average charge on the layers is still zero. Hence A will be 

 discharged in the lapse of time, and this more rapidly as the 

 potential gradient is higher. Precisely the reverse will 

 happen if A is negatively charged. Hence to avoid the law 

 of distribution specified, I suppose that the charge per square 

 centim. on A is relatively so small, that if it is increased n 

 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 r of distribution of charges along the length 

 of the prism k. The rate of discharge of A is then taken 

 proportional to Y/x. 



If n is the total number of ions per cubic centim., and e 



