504 Prof. D. N. Mallik: Theory of Electric 



the number of collisions and recombinations per second. 

 Thus [art. 229, 'Conduction of Electricity through Gases' 

 (2nd edition)] let 



A, = mean free path. 



X = electric field, 



e = charge on an ion. 



Then, the mean kinetic energy of an ion = X\e. 



Now, if XXe > a limiting value P, ionization takes place. 

 Let f(X\e) = fraction of collisions that result in ionization, 

 i. e. /(#) = 0, when x<¥. 



Also, let v = average velocity of translation of corpuscles, 

 N = no. of negative ions per c.c. ; 



then — - =no. of collisions per second, 



and no. of ions produced— — /(X<?\). 



Nv . . 



Let 7.—— = no. of ions that disappear through recom- 

 bination. 



Nv 

 Then -j- [ f(lLe\) — 7] = the resultant no. of ions produced, 



i 



neglecting those due to positive ions. 

 Therefore the equation of continuity is 



BN dNw NM r , /Y . -. rK . 



sr'+^r^x-f/^" 73 ' • • • ( 5 ) 



where u = average velocity of translation due to electric field 

 = v nearly. 



Now in order that there should be steady rotation of the 

 discharge as a ivliole we must have 



^=0, ^=0 and .:f(Xe\)-y=0. 

 ^t ' Bar j \ 1 t 



But this is also the condition that the result of collision 

 should be annulled by recombination. We conclude, there- 

 fore, that throughout the stage that this condition holds 

 n and N will continue to remain equal, if they are so, as we 

 have argued (art. 6) that they should be, at the beginning. 



The quantity 7 would obviously depend on the nature of 

 the gas. The same is true of the function /'. 7 may also 

 depend on the conditions of the experiment — for example, 

 whether the discharge is intermittent or continuous. Tt may 

 also depend on the pressure. 



We shall presently see that we have some information on 



