he significant known hydrated borate mineral assemblages (principally of the western United States) in the system Na2OCaOz.sbnd;MgOB2O3H2O are expressible in three ternary composition diagrams. Phase rule interpretation of the diagrams is consistent with observation, if the activity of H2O is generally considered to be determined by the geologic environment. The absence of conflicting tie-lines on a diagram indicates that the several mineral assemblages of the diagram were formed under relatively narrow ranges of temperature and pressure. The known structural as well as empirical formulas for the minerals are listed, and the more recent (since 1960) crystal structure findings are discussed briefly. Schematic Gibbs free energy-composition diagrams based on known solubility-temperature relations in the systems Na2B4O7-H2O and Na2B4O7-NaCl-H2O, are highly useful in the interpretation and prediction of the stability relations in these systems; in particular these diagrams indicate clearly that tincalconite, although geologically important, is everywhere a metastable phase. Crystal-chemical considerations indicate that the same thermodynamic and kinetic behavior observed in the Na2B4O7-H2O system will hold in the Ca2B6O11-H2O system. This conclusion is confirmed by the petrologic evidence. The chemical relations among the mineral assemblages of a ternary diagram are expressed by a schematic "activity-activity" diagram. These activity-activity diagrams permit the tracing-out of the paragenetic sequences as a function of changing cation and H2O activities. ?? 1967.