This paper continues the development of the molecular theory of vapor-phase nucleation presented in the preceding papers of this series and focuses on the rate of nucleation. The rate theory is developed within the definition of the modified liquid drop model of paper m, which although macroscopic in nature, is consistent with the molecular level definition of clusters found in papers I and II. In addition to providing the framework for a fully molecular rate theory, the present work provides insight into the mechanism of vapor phase nucleation. The key mechanistic result involves the natural occurrence of a non-ad hoc means of distinguishing density fluctuations that serve as embryos for the formation of Liquid drops from those that do not serve in this capacity. In particular, two paths of cluster evolution are found, one leading toward drop formation through a valley on the free energy surface, the other leading toward the decay of clusters back to the supersaturated vapor. The rate of nucleation is taken as the limiting flux through the valley. The calculations for argon agree well with classical theory with respect to the prediction of the dependence of the rate on supersaturation, but differ in the prediction of the temperature dependence. At lower temperatures, the predicted rate is greater than that of classical theory, while at higher temperatures, the reverse is true. This phenomenon has also been observed by other authors using different theories.