The equations derived in part I of this series for a one-dimensional dislocation model are applied in this paper to the case of a monolayer on the surface of a crystalline substrate, particularly when the natural lattice spacing of the monolayer differs from that of the substrate. Justification is given for this extension of the equations to the two-dimensional case. It is shown that the theory predicts a certain critical amount of misfit (9% difference in lattice spacing in a simple case) below which the monolayer in its lowest energy state is deformed into exact fit with the substrate, and above which it is only slightly deformed in the mean, having many dislocations between it and the substrate. The energy of adsorption as a function of misfit is also calculated, becoming almost constant above the critical limit. Up to a larger critical misfit (about 14% in the same simple case) the monolayer can be deposited metastably in exact fit on the substrate, at sufficiently low temperature. Since the dislocated layer is mobile on the surface, completely oriented overgrowth of one crystal on another can only be expected if the first monolayer can be formed over the complete surface under subcritical conditions. This is in general agreement with observation.