﻿Ionization by Collision. 409 



those given by Townsend. On p. 30 of his book Tovvnsend 

 points out that the value o£ N leads to an estimate of the 

 radius of a molecule of the gas concerned and finds tbat the 

 radii calculated by this method are somewhat smaller than 

 those deduced by the ordinary methods of the dynamical 

 theory of gases, based on obser\ations of viscosity, &c. The 

 increase in the value of M due to the revised calculations 

 leads to a nearer approximation between the values of the 

 radius calculated by the t*o methods, but the correction is 

 not sufficiently large to abolish the difference. It has been 

 pointed out in § 3 that the error introduced by assumption (2) 

 tends to make the values of N , and therefore of the radius 

 of the molecule, too small. 



11. It will now be of interest to consider the other of the 

 two alternative hypotheses mentioned in § 3, concerning 

 the nature of the negative ion, and to discover in what way 

 the theory will be altered by adopting it. 



It is now supposed that the electron, which represents the 

 negative ion immediately after its formation, can collect 

 round it neutral molecules at subsequent collisions, and thus 

 lose its power of ionizing by collision, except when the 

 electric field is very much greater than that considered in 

 the experiments under discusssion. The simplest hypothesis 

 which can be made in this direction, and that which seems 

 on general grounds most likely to be true, is that, when an 

 electron collides with a neutral molecule after travelling 

 freely under the field a distance less than b and fails to 

 ionize it, it adheres to that neutral molecule and forms what 

 we shall call a " complex ion." Accordingly, on this hypo- 

 thesis, an electron after it has once made a collision at which 

 it fails to ionize the molecule with which it collides can 

 never again ionize on collision in the conditions considered 

 here. However it retains its charge and contributes to 

 the current i in the same way as if it had remained a free 

 electron. 



12. Let f(x) be still the number of free electrons entering 

 from the positive side a layer of gas distant x from the 

 positive electrode in one second ; let g (x) be the corre- 

 sponding number of complex ions for the same layer. AVe 

 shall now have 



ih=/Q)+<i(l) (19) 



g' (x) is the number of complex ions formed per second in 

 the layer x. On our theory it must also be the number ot 

 the free electrons which in that layer collide for the first 

 time with a neutral molecule; having previously travelled 



