This study describes numerical estimates of P-T conditions based on chemical reactions among metamorphic minerals. Firstly, the availability of the P-T curve of the chemical reactions among minerals for geothermobarometry is discussed by assessing the slope of the curve. Steeply sloping and shallowly sloping P-T curves are suitable for use as geothermometers and geobarometers, respectively. Secondly, the uncertainty in the metamorphic conditions inferred from the intersection of two P-T curves

more »

... nd the difference in their dP/dT is discussed. If the difference in the slopes is significant, the uncertainties in the estimated pressure and temperature are low. In addition, uncertainty increases with decreasing difference in the slope of the curves. Furthermore, the intersection of two curves with similar slopes may yield an unrealistic estimate of metamorphic conditions, even if the two curves pass through the probable P-T field estimated by other methods. This result arises from improper thermodynamic modelling of the chemical reaction, an error in the P-T curve, or the use of a nonequilibrium composition and/or a nonequilibrium assemblage. Thirdly, the systematic least squares calculation is presented and the reliability of the estimated P-T conditions is assessed from the statistical point of view. The result of the weight-free least squares analysis is plotted near the intersection of the steepest and shallowest P-T curves and is located at a considerable distance from the weight-free average of the intersections of the curves. The weighted least squares show that the calculated P-T conditions can be used to plot near the curves with the highest and second-highest weights and plot near the weighted average of the intersections of the P-T curves.