of Recombination of the Ions of Gases. 431 



lOOr I . 



A vqa 



When the maximum number N is reached 

 di 



Wi-> 



~rr=0 } and q = aW. 



Therefore 



, 1 1 + r 



<= ,-r-^loo- 



2aN ° e l-r' 



Now if T be the time taken for the number of ions to fall 

 to half their number when the rajs have ceased 



l = aN T T ; 



therefore 



, T i 1+r 



or 



r= 



2t 

 <?T +1 



The following table gives the values of r deduced for 

 different values of t from the above equation : — 



L 



T 



•125 -123 



•25 -245 



•5 -462 



1 -736 



2 -878 

 4 -998 



For example, in the case of air close to the Crookes' tube, 

 T = *3 sec. Therefore, in '15 sec. the number of ions is 

 nearly one-half of their final value. After an interval of one 

 second the number of ions has practically reached the maxi- 

 mum value. For air distant about a metre from the source 

 of radiation the value of T is much larger, and several seconds 

 will elapse before the number approximates to the final 

 value. 



