An effective interaction between atoms adsorbed on a substrate is calculated. The interaction arises from the exchange of phonons in the substrate and makes a density-dependent contribution to the ground-state energy per particle of the adsorbed system. Our results are applied to the submonolayer helium film adsorbed on argon-plated copper studied by Stewart and Dash. It is shown that, for this system the interaction is attractive and contributes to the ground-state energy per particle an amount of the order of - 1 °K, which is a significant fraction of the observed binding energy. The role of the effective interaction in bringing about the enhancement of the binding energy and the formation of dense clusters observed by Stewart and Sash is discussed.