The mean-free-path phenomena of gases can be explained in a general way by a very elementary form of the kinetic theory, but to develop a satisfactory mathematical treatment of them, yielding accurate numerical results, is less easy. The difficulty varies to some extent with the nature of the molecular model chosen as basis. It is curious that the adoption of one particular model, viz., a centre of force varying inversely as the fifth power of the distance, removes nearly all the analytical complications in the theory. The first accurate treatment of viscosity, conduction, and diffusion, due to Maxwell, was made possible by this fact, and it is remarkable that Maxwell’s theory requires no knowledge of the velocity-distribution function corresponding to the non-uniform state of the gas. If the molecules are of any other type, the function must be determined, a task wherein lies the main difficulty of the investigation. It is, however, of more than mathematical interest to widen the basis of the theory, since Maxwell’s molecular model does not satisfactorily represent the molecules of actual gases.