A substance is considered to diffuse into a finite cylinder through its entire surface from a finite amount of well‐mixed gas which is at concentration equilibrium with the surface. Equations are derived for the time dependence of the amount of substance in the cylinder and its concentration at a point. The results are developed mainly in terms of isotopic self‐diffusion (as in the diffusion‐controlled exchange of isotopic oxygen with an oxide), but may also be applied to the diffusion of an inert substance or to a heat conduction situation.