of the Ions formed in Gaseous Media. 9 



In the course of recent experiments made by the writer to 

 ascertain the ionic mobilities in a series of gases and vapours 

 it was found that the mobility {k) varied inversely as the pressure 

 {p) over a wide range of pressures ; however, there was observed 

 a tendency of the product ph to increase at low pressures in the 

 case of air, nitrous oxide and carbon dioxide, and a tendency for 

 it to diminish in the case of vapours, e.g. ethyl chloride, when the 

 pressures approached the vapour pressure at the temperature under 

 consideration. Such deviations from the law pk = constant could 

 be ascribed to variations in the size of the cluster constituting the 

 ion ; however, they follow readily from the expression (a) of the 

 mobility if we take into account the deviations from the law of 

 Maxwell which states that the coefficient of viscosity of a gas or 

 vapour is independent of its density. In the case of gases it is 

 known that t) tends to diminish as the pressure is reduced beyond 

 a certain value*; such a diminution would, according to the theory 

 here given, tend to increase the value pk. In the case of vapours 

 it has been established that ?; increases rapidly as the saturated 

 state is approached ; in fact, as a result of Warburg and von Babo's 

 experiments on the viscosity of carbon dioxide at high pressures, 

 Meyerf came to the conclusion that the experimental values above 

 certain pressures could be explained only by supposing carbon 

 dioxide to behave as a liquid, the density of which is practically 

 independent of pressure ; an increase in the value of 17 would, 

 according to expression (a), diminish the product pk, a result in 

 accordance wdth experimental observation. 



In conclusion, it is of interest to note that, on the supposition 

 given above as to the nature of the ion, a satisfactory agreement 

 can be obtained between the calculated and observed values of the 

 coefficients of diffusion of the gaseous ions. The values of these 

 coefficients have been determined by Townsend;]: for four gases. 

 Instead of using the ascertained expression (/3) which is really 

 involved implicitly in the expression (a) of the mobility, a slightly 

 different procedure is advisable. 



If D denote the coefficient of diffusion of the ion through the 

 gas, and d that of a molecule through the gas, we then have from 

 the preceding theory 



d I [ '^PiPi 



The nature of the agreement between the calculated and 

 observed values is shown in the following table : 



* Vide Jeans, Dynamical Theory of Gases, p. 253. 

 t Kinetic Theory of Gases, Eng. trans. Art. 90. 

 + Phil. Trans. A. 193, p. 129, 1900. 



