Stages of Ionization by Collision. 969 



But — ^ = y= *, where N is the number of molecules per 



cubic centimetre in the gas at atmospheric pressure II and 

 at the temperature o£ the room, and k is the factor by which 

 the energy of agitation of an electron exceeds that of a 



molecule of the gas, k being a function of - . Hence (1) 

 becomes P 



V 2 0)- 7 |f +y.«.n=0, .... (2) 



where _ N>Z 



The number of negative ions produced by collisions in a 

 period of time r is given by an integral of the form 



A 1 If f n dx . dy a dz, 



where A involves w x and r. 



Hence the ratio, /*, of the number of ions produced by 

 collision inside the limits x='2 cm. and x = = — '2 cm. to the 

 total number produced is 



("••2 f*2 Z"* 00 



dx I c/~ I n dy 

 . 'o J-oo _ 



— A*" 



I (£# 1 ^ I n dy 



Jo JO J -oo 



Since the emission of ions is confined to the central 

 portion of electrode 2, it becomes apparent that for the larger 



Z 



values of 7- the ions do not extend to the boundary (which 



is represented byco). Hence at the boundary w = and 

 ^ = 0. Equation (2) on integration with regard to y becomes 



boundary limits 



where 7= f 71 dy, the limits of integration being the values of 

 y at opposite points on the boundary. Hence L J =0. 

 Also since the ions for the larger values of y- move in a 



* Proc. Roy. Soc. A. vol. lxxxi. (190S). 



