The flow of a thin film of viscous fluid on a spinning disc with a circular arc edge is considered. An approximate film thickness relation is derived which agrees well with experiment. A linearized free-surface instability theory is developed to predict the number of atomization sites at the disc edge. It is concluded that the experimentally determined mean number of atomization sites is within 10% of the theoretical prediction and that 90% of the data will be within a calculable band about the theoretical line, provided the fluid viscosity is below about one stoke. The agreement between theory and experiment is unaffected by surface waves on the disc surface away from the edge or by the type of atomization at the disc edge (ligament or direct-drop). The effect of increasing either the fluid viscosity, surface tension or film thickness is to reduce the number of atomization sites while increasing the angular velocity increases the number. (Author).