Electricity through Gases by Charged Io?is. 259 



If N 2 is the maximum value of n 2 , then -^=- measures the time 



that is taken before recombination diminishes the number of 

 the ions to any very appreciable extent. In this time the 

 positive ions would move a distance 8 given by the equation 



where X t is the value of X at the plate. 



&x 2 x,<?=^ 



thus 



1 



Let X x =7X0 where 7 = /3 2 - 2/ < J , 

 ^ yWX*e 



(XI 



r^_7 2 x 



±qe 2 



Thus if 7 is tolerably large, the positive ions will traverse 

 a space much greater than A, before recombining. 



The greatest current that can pass between the plates is 

 when all the ions are used in carrying the current; if I is the 

 distance between the plates, then Iq positive and negative 

 ions are produced in unit time ; thus if I is the maximum 

 current which can pass between the plates 



hence we can write 



I = lqe; 



\ t 

 7~2l' 



The equations 



dX 



,^=47r(tt 1 -n 2 )^ 



^(k 1 7i l X)=q-an 1 n 2 , 



J x {k 2 n 2 X) = — (q — ocn^), 

 (k 1 n 1 + k 2 n 2 )Xe = c } 



