Fowler (1935) has shown that the Langmuir adsorption isotherm can be deduced from statistical considerations and he (1936) and Peierls (1936) have recently extended the statistical treatment to obtain the form of the isotherm when there is interaction between the adsorbed particles. In the preceding paper J-S. Wang has applied a similar treatment including the effect of interaction between adsorbed particles to the case of diatomic molecules which dissociate on adsorption. For the purpose of obtaining the form of the isotherm the statistical method is of course the correct method to use, but, to obtain from the interpretation of experimental results a full understanding of the various processes occurring at the surface, expressions are required for the rates of these individual processes. The aim of the present paper is to deduce such expressions (4, 5, 8, 9, 11, 12) from kinetical considerations when the effects of interaction between adsorbed particles are included. It is important to check that the expressions obtained lead to an isotherm of the same form as that deduced statistically. The first part of the problem is to obtain the answer to the following and similar questions. If the average probability that a site on the surface is occupied is θ and if a given site is occupied, what is the probability that neighbouring sites are occupied? The answers to these questions are of course given in the complete statistical treatment by Peierls, but they are obtained by considering the partition functions for the whole system including the gas phase, such considerations giving the complete solution of the equilibrium problem. Here we need the result when we consider the surface only, the equilibrium between adsorbed and free atoms being obtained separately by considering the mechanisms of condensation and evaporation. It therefore seems desirable for the sake of clearness to select and repeat in its slightly modified form that part of Peierls’ argument which is relevant.