A series of laboratory and aircraft measurements have indicated that supercooled liquid water exists to temperatures as low as -70 ¿C. These measurements also show that classical nucleation theory, using standard values for the thermodynamic properties of supercooled water, underestimates the nucleation rate of ice in liquid water at large supercoolings. New theoretical estimates for this homogeneous nucleation rate are presented, based on a new analytic equation of state for liquid water. The new equation of state, which is accurate over a pressure range of 3000 atmospheres and a temperature range of 1200 K, is used to infer the latent heat of melting, liquid water density, and ice-water surface energy of supercooled water. Predictions of the nucleation rate and the homogeneous freezing temperature made by this equation of state are in agreement with observations at temperatures as cold as -70 ¿C and at pressures as high as 2000 atmospheres. These results indicate that it is not necessary to invoke a phase transition at -45 ¿C to explain aircraft and laboratory observations of homogeneous ice nucleation in supercooled water clouds. ¿ 1997 American Geophysical Union