A cell model is developed for an assembly of identical ions on an adsorption plane. The hexagonal lattice model for the distribution of such ions, currently used to describe the “discreteness-of-charge” effect, is treated as the limiting form of the cell model at low temperatures, high interaction energies or high adsorbed ion densities. Using a Maclaurin series to expand the change in the potential energy of an ion on displacement from a cell centre, the free area per ion, mean energy of displacement and other relevant quantities are calculated for the cell model. The interionic potential energy depends on the structure of the adsorption region and calculations are done for both metallic and dielectric media in contact with aqueous electrolyte solutions of various ionic strengths. The parameters of the adsorption region refer specifically to mercury, silver halide and air/water interfaces. The extent of deviation of the cell model from the limiting lattice form is examined and the latter is shown to be an inadequate representation of the short-range order on the adsorption plane for areas per ion greater than 70Å2.