Apparatus and technique are described for the accurate gasometric macrodetermination of the oxygen-hemoglobin equilibrium in dilute solutions containing around 0.15 gm. Hb/100 ml., equivalent to blood diluted 100:1. At the bottom of the equilibrium curve, i.e., in the range 0-2% Hb02, the method is accurate to ± 0.05% HbO2. Over the main part of the curve the mean accuracy is ± 0.5% Hb02. From such data, together with indirect kinetic information as to the character of the extreme top of the equilibrium curve, it has been possible, in the case of dilute sheep Hb solutions, to compute all four constants in Adair's general intermediate compound equation for the equilibrium between oxygen and hemoglobin. Comparison of the results at pH 7.1 and 9.1 suggests that the first two oxygen molecules combine independently at both pH's. Interaction sets in at the third and more markedly at the fourth stage, but there are detailed differences in the degrees of interaction at these last two stages at the two pH's. It is hoped that these equilibrium data in dilute sheep Hb solution will be of service in interpreting kinetic experiments on the rates of the reactions of oxygen and hemoglobin, which so far can only be carried out in dilute solutions of the latter.