The usual theory of diffusion-controlled ionic reactions in electrolytic solutions as developed by Smoluchowski and Debye is outlined and discussed. The electrostatic potential in the neighbourhood of a stationary ion is determined by use of Poisson's equation. This leads to a non-linear integro-differential equation on the elimination of the concentrations of the species of ions present. Approximate solutions of the resulting equation are obtained in two particular cases.
The attempt to extend the theory to include movement of the central ion is found to result in a self-contradiction, which may be removed
by the description of the problem in terms of joint probability functions. An approximate solution of Poisson's equation is found for the electrostatic potential around a moving ion in the new formulation of the problem, and the corresponding rate of reaction has been calculated.
In the course of the thesis I have indicated which parts are original and given the appropriate references for the parts which are not.