The theory of recombination of gaseous ions

The bearing of the recent results of Marshall on the theory of recombination of gaseous ions is discussed. It is shown, by solution of the Brownian movement equation for two ions of opposite sign, in a gas, that the average relative displacement in a time π is little influenced by the attractive forces, except for distances of the order of magnitude of 10^?5 cm. or less, at ordinary temperatures. This conclusion, that in general the motion of the ions relative to each other is largely one of random diffusion, is in good agreement with the interpretation forced by Marshall's study of the variation of the coefficient of recombination α with time and concentration of ions. This also indicates that the theoretical approach of Langevin to the solution of the recombination problem is untenable, while that of Thomson is justified. The theory, of Thomson is discussed and, is compared with observation. It appears to fit qualitatively as accurately as the facts are known.It is then shown how the success of any theoretical treatment is limited due to our ignorance of the nature of the mass of the ion, a condition which, however, enables us to understand the very small range of variation of α among the different gases.