The coverage THETA, of the square-root 3 x square-root 3R30-degrees Ag/Si(111) interface has been measured by micro-Auger electron spectroscopy. With a dose of 5 monolayer (ML), we find THETA almost-equal-to 1 ML for deposition temperature T(d) greater-than-or-equal-to 700 K and THETA almost-equal-to 2/3 ML for T(d) less-than-or-equal-to 620 K. Much smaller changes (almost-equal-to 0.05 ML) were observed during annealing. These effects are explained by a simple kinetic model in which approximately 2 Ag atoms are readily incorporated into the structure, but a third atom must overcome an activation energy E(r) to become embedded, with a gain in energy E(e). We find E(r) = 1.90, E(e) = 0.60, and E(a) = 2.45, all +/- 0.05 eV, where E(a) is the adatom adsorption energy. Possible structural and microstructural models and the interpretation of the energy E(r) are discussed.