Water clusters of 4000-6000 molecules were produced by condensation of vapor in supersonic flow and cooled by evaporation until they froze at about 200 K. Rates of nucleation up to 10(30) m(-3) s(-1) were determined by electron diffraction measurements at microsecond intervals. Although nucleation rates were 20 orders of magnitude higher than in previous investigations of the freezing of water, this enormous disparity was accounted for naturally by the classical theory of nucleation. The free energy sigma(sl) of the solid-liquid interface implied by the results increases with temperature as T-n, with n approximately 0.3-0.4, the same range of values as found for mercury in the only well-established trend known to the present investigators. The interfacial free energy of 21.6 mJ/m(2) derived for clusters of water is virtually the same as that obtained for small water droplets by several workers but is substantially lower than the value inferred from the interfacial tension in the bulk system at 0 degrees C. This difference is a consequence of the different forms of ice encountered in the different experiments. Bulk water freezes to the thermodynamically stable hexagonal ice (Ih), whereas highly supercooled-water freezes to the kinetically favored cubic ice (Ic), a reaction product offering a lower free energy barrier. Anomalously, the ratio of sigma(sl) to the heat of fusion per unit area derived for supercooled water is only about two-thirds that suggested originally for water by Turnbull but since found to apply quite well to other nonmetallic substances. Two variants of the classical theory of homogeneous nucleation are compared, and some deficiencies of the theory are discussed.