Gases by the Motion of Negatively charged Ions. 207 



The new negative ions travel with the same velocity as the 

 original N ions, so that all the negative ions will be found 

 together during the motion. The number of negative ions 

 produced by N ions travelling through a distance dx will be 

 aNdx ; where a is a constant depending on X, /?, and t. 

 Then 



dN=aNdx. 

 Hence 



N = N 6 a * (1) 



Let n l negative ions be distributed uniformly between two 

 plates at a distance I apart, and let the force X be applied to 

 them. 



The number of ions C that arrive at the positive plate is 



C=Vn e**dx=^(e« l -l), 

 Jo a 



and the ratio of this number to the original number is 



Hence if C denotes the number of negative ions produced by 

 the primary and secondary rays the total current in the gas is 



C=^( e *<-1) (2) 



C , the current when no ions are being produced by collisions, 

 is represented in each curve by the {y) ordinate at the point 

 where the tangent to the curve is practically parallel to the 

 axis of X. p 



Hence the ratio ~ is a function of I ; and by making simple 



^o 



calculations it can be shown that equation (2) completely 



explains the relative shapes of the three curves in each 



diagram. The value of <x can be found by substituting the 



experimentally determined ratio, p , and distance between 

 the plates Z in equation (2). ° 



The small values of a are determined, most accurately, 

 from the curves corresponding to 1=2 ; but in the following 

 tables some of the values have been obtained from two curves, 

 and the agreement between these numbers shows that the 

 effect of separating the plates is completely explained by the 

 theory. The tables give the values of a for different forces 

 X : the determinations made from curves corresponding to 

 distances between the plates of 2, 1, and '5 centimetre are 

 given in the second, third, and fourth columns respectively. 

 A separate table is given for each pressure. 



