398 Prof. C. Barus on the Transmission of the 



or normally to an absorbing surface. Thus k is the number 

 lost under these conditions per square centim. per second 

 when R = l. Let k! n 2 be the number decaying per cubic 

 centim. per second. Then the accumulation in the air-plate 

 Alfa; will be per second, — (dn/dx)Akdx — ankdx; the decay 

 in the element will be per second k'n 2 Adx ; and when the 

 flow is stationary dnjdt = ; whence — (dnjdx) = an/ A + k'n 2 /k. 

 If n Q be the value of n at # = 0, the position of the phos- 

 phorus plate, P, this equation admits of integration in finite 

 form leading to n/)i ={a/A)/(a/A-j-n k , /k)(e a ^ A —7i k / lk). If 

 k' = 0, the decay within the element is ignored and the 

 equation takes the simple form n = ne a ^ A , which is specially 

 interesting as n is independent of the absorption velocity also, 

 depending for a given n and x merely on the circumferential 

 area, ax, and the base area A of the cylinder of air-space 

 betu een the plates. 



Thus far no reference has been made to the electric field. 

 "With the velocity k, moreover, it would not be practicable to 

 approach the question of electric conduction at once, for the 

 other variables n and e remain undetermined. If n were 

 found by Aitken's method of nuclear condensation, e would 

 then be deducible by inferences presently to be indicated ; 

 but thus far I have not done this. 



9. Suppose, however, in order to estimate in how far the 

 present argument is tenable, that the number n = nJe ax l A just 

 found is a correct value : the question is put whether this 

 value is in reasonable numerical accord with the usual theory 

 of electrolytic conduction. In other words, let the condenser 

 be charged, remembering that the additional contribution of 

 ions from this cause is insignificant. Let Y be the potential- 

 difference at the time t. Then, if C is the effective capacity 

 of the condenser, U the relative velocity of the ions to each 

 other, e the charge of each, 



- (dY/dt) = ATJYne/Cx = ATSYn ejOxe ax l A 

 when the above value of ?i is inserted. 



Now in the data of Table III. the leakage of the condenser 

 was computed as V = V 10~ C ", which when substituted in the 

 last equation gives on reduction c , = (ATJn e/ClnlO){l/x€ aj:A ), 

 remembering that c' refers to minutes. 



This equation may now be tested with the corrected values 

 (corrected for loss of potency of the ionizer in the lapse of 

 time) of c in Table III. as related to x the distance apart of 

 the plates. These computations are made in the following 

 table by choosing the constant K=AUw e/ClnlO so that the 

 first observations (c' = '200 and x = l'7) coincide. There is 

 no smoothing. 



