﻿450 Sir J. J. Thomson on Ionization 



where T is the kinetic energy of the first particle, and 

 ... 1 



d*W+{ M i M s 

 + e 2 E 



4 / MxMs V 



-VMx+mJ 



where d is the length of the perpendicular from the second 

 particle on the direction of projection of the first. 



In the case of an encounter between a cathode ray and a 

 corpuscle, M 1 = M 2 and e = E, and the equation becomes 



Q=Tsin 2 0, sin 2 6>= ^— . 



e 



In this case 6 is the .ingle through which the cathode ray 

 is deflected. Thus 



Q=--±_ or *=(£_ l)« . . (1) 



Thus if the corpuscle requires an amount of energy W to 

 escape from the atom, then, in order that the atom should be 

 ionized by the cathode particle, d must not be greater than 

 the value given by (1) when W is written for Q. 



If n is the number of corpuscles in the atoms in unit- 

 volume of the gas, the number of collisions for which d is 

 not greater than the value given by equation (1) made per 

 cm. by a corpuscle moving through the gas is nwd 2 or 



T 



nire^x ^ 



(*-0 



r T2 ' 



this is a maximum when T = 2W. 



When, as in the case of ft rays or cathode particles in a 

 vacuum-tube, T is large compared with W, the preceding- 

 expression reduces to 



??.7T<? 4 



WT ' 



so that the number of ions produced per cm. by a cathode 

 particle on this theory varies as 1/T. 



Mr. Glasson (Phil. Mag. Oct. 1911) has shown that the 

 number of ions made per centimetre by a cathode ray varies 

 approximately inversely as the kinetic energy of the moving 

 particle, so that his results are in accordance with this theory, 

 in which it is to be remarked we have neglected the secon- 

 dary ionization produced by the corpuscles expelled with 



