We have measured the paramagnetic susceptibilities of sperm whale azide metmyoglobin and of carp azide, thiocyanate, and nitrite methemoglobin in the quaternary oxy (R) and deoxy (T) structures between about 300 and 90 K, using a new sensitive superconducting magnetometer. We have also measured the pressure dependence of the high- and low-spin optical absorption bands of azide metmyoglobin and of carp azide methemoglobin in the R and T structures between 1 and 2000-4000 atmospheres. At low temperatures all the derivatives show normal Curie behavior, but above 200-250 K this is reversed, so that a thermal spin equilibrium is set up and the paramagnetic susceptibilities rise steeply with rising temperature. At all temperatures the effective magnetic moments in the T structure are higher than in the R structure. The magnetic data for azide methemoglobin have been subjected to detailed analysis. Below 250 K the magnetic moment in the R structure is 1.98 microB, characteristic of pure low spin, but that in the T structure is 2.80 microB, suggestive of a random mixture of high- and low-spin centers which have become frozen in by the immobility of the surrounding protein. Comparison of the thermal spin equilibria above 250 K shows that in the T structure the equilibrium is biased toward higher spin by the equivalent of about 1 kcal/mol relative to the R structure. Hydrostatic pressure reduces the optical density of the high-spin band at 630 nm and increases that of the low-spin bands at 541 and 573 nm. We have calibrated the optical density of the band at 630 nm against the measured paramagnetic susceptibilities of sperm whale azide metmyoglobin and carp azide methemoglobin in the R and T structures and have used this calibration to determine the dependence of the spin equilibria on hydrostatic pressure; this has allowed us to calculate the volume contraction associated with the transition from the fully high to the fully low-spin state. This amounts to -6.7 and -13.3 mL/mol heme for carp azide methemoglobins in the R and T structures, respectively, and to -12.5 mL/mol heme for azide metmyoglobin. These volume contractions are larger than those of about -4 mL/mol Fe found in synthetic iron chelates. Apparently stereochemical changes of the globin surrounding the heme also contribute to the volume changes; these must be larger in the T than in the R structure. The significance of these observations for the mechanism of heme-heme interaction is discussed.