A number of statistical mechanical formulas, important to the theory of nucleation, have been used, recently and in the past, in both molecular and phenomenological theories of nucleation without a full description (and possibly without a full understanding) of their fundamental meanings. These formulas have involved the numbers of physical clusters, the reversible work of formation of such clusters, and the distinct roles of translational and internal cluster degrees of freedom. In this paper we perform careful molecular level analyses of some of these formulas in an effort to establish their fundamental bases.