﻿Theory of Ionization hy Collision. 850 



assumptions, none of which nre required by the theory. We 

 have no knowledge as to the exact effect of a collision on the 

 velocity of an ion when the velocities are very large, and 

 the probability of guessing the correct assumptions is A r ery 

 small indeed. Under these conditions one selects that ex- 

 pression for the velocities which gives the simplest formula 

 for the curve. As it happens, a very simple formula, agreeing 

 accurately with the larger values of a, can be obtained. In 

 one respect it is unfortunate perhaps that the formula which 

 I gave does agree with the curves so accurately, as it has led 

 some people to think that it is an integral part of the basis 

 of the theory. As a matter of fact, several such expressions 

 for a may be found which do not differ from the observed 

 numbers by quantities greater than the experimental errors, 

 and it is therefore impossible to decide from the experiments 

 which are the most correct. 



The maximum value of a is of the same order as obtained 

 from many of the formulae, so that possibly the values of N 

 that have been found are correct within 10 per cent. 



The subsequent deductions that can be made from the 

 numbers given for N, as to the sizes of molecules, involve 

 further uncertainties. Thus it is assumed, for instance, that 

 the velocity of agitation of the ions may be neglected. It 

 may be shown experimentally that as the force increases the 

 velocity of agitation of the ions increases abnormally, and 

 the sum of the paths traversed by an ion in going one centi- 

 metre in the direction of the force may be appreciably greater 

 than one centimetre. On this account the values obtained 

 for the diameters of the molecules are probably not as correct 

 as the determination of the maximum values of N. 



Mr. Campbell states that his estimates of the diameters of 

 molecules are nearer those obtained by the theory of viscosity, 

 than the estimates which I gave. It should be remembered, 

 however, that the val ne obtained for the diameter of a molecule 

 depends on the specification of a collision, and a collision as 

 defined by this theory is not the same as a collision as defined 

 in the ordinary theory of viscosity. The diameter of the 

 molecules obtained by the different methods are not necessarily 

 the same. Mr. Campbell's statements appear therefore to be 

 incorrect as regards any matter that is of importance in 

 connexion with the theory of ionization by collision. With 

 regard to other matters, such as the diameters of molecules, 

 his conclusions must be very uncertain. They depend on the 

 validity of his assumptions as to the effects of various kinds 

 of collisions on the velocity of the ions, and there is no 

 evidence to show that his hypotheses arc correct. 



Yours truly. 



John S. Town sen p. 



