﻿838 Messrs. E. W. B. Gill and F. B. Pidduck on 



used, it will be useful to indicate the usual way of estimating 

 the efficacy of the ions in producing new ions by collision 

 with the uncharged molecules of a gas. 



If n ions are set free at the surface of one of two parallel 

 plates, and an electric force of X volts per cm. is applied, 

 the number of ions reaching the other plate exceeds n owing 

 to the formation of fresh ions by collisions in the space 

 between the plates. If on the average each negative ion 

 creates a new ions of each sort per centimetre, and each posi- 

 tive ion /3, the number n reaching the other plate is given by 





(a-(3)d 



where d is the distance between the plates. 



It is perhaps unnecessary to state that the distance d 

 between the plates must be long compared with the mean 

 free path of the ions. 



This formula gives at once a method for estimating a and /Q 

 experimentally ; for if the plates are put at three different 

 distances d u d 2 , d s with corresponding potential-differences 

 Xrf l5 ~Xd 2 , Xd 3 , and n l9 n 2 , n 3 are the numbers of ions 

 arriving at the positive plate [?? being in each case the 

 same], then a and /3 may be determined from the observed 

 ratios n 2 ln l and n 3 /n 2 . 



If more distances be taken, the fact that any three readings 

 give the same values of a and /3 affords a test of the truth of 

 the theory. 



The values a. and ft having been found, there are, however, 

 other methods of testing the theory. 



Evidently a and /3 depend both upon the electric force X 

 and upon the pressure p ; and it may be proved that a/p and 

 /3/p must be functions of X/jp. It is usual to draw curves 

 with X/p as abscissa, and a/p, /3/p as ordinates, and it is 

 found that the points in one figure all lie on one curve, 

 showing that the functional relation is satisfied. 



The most effective test, however, is obtained by calculating 

 the distance between the plates for which sparking is to be 

 expected for the given electric force, for if the plates are at 

 a distance a apart given by a— /3e^ a ~^ a — 0, the formula 

 shows that the number of ions reaching the electrodes is 

 infinitely great compared with the number originally 

 generated, so that a spark will pass. It may be further 

 shown that this sparking potential aX. is a function of pa 

 only, and it is usual to plot Xci against pa. 



