In extension and confirmation of the work of Bigg, observations on the freezing of large numbers of drops of distilled water, ranging from 10 $\mu $ to 1 cm in diameter and suspended at the interface of two immiscible liquids in order to avoid the nucleating effects of solid surfaces, have established proportionality between the logarithm of the droplet volume and its freezing temperature for a constant rate of cooling. Such a relationship appears to characterize the heterogeneous nucleation of water droplets containing small foreign nuclei, and it is interpreted in terms of the droplets being infected with atmospheric aerosols whose ice-nucleating ability is known to increase roughly logarithmically with decreasing temperature. A technique has been developed for purifying water so that drops of up to 1 mm diameter may be supercooled to temperatures at which freezing occurs spontaneously without the aid of foreign nuclei. The empirical relationship between droplet volume and nucleation temperature, which differs from that representing heterogeneous nucleation, shows good agreement with theory. Photographs taken of freezing droplets upwards of 50 $\mu $ in diameter reveal that, in some cases, solidification was accompanied by rupture of the ice surface and the liberation of a number of small ice splinters. This suggests a secondary mechanism of ice crystal formation in natural clouds.