The dielectric constant ερ that appears in the effective force between two ions in solution is expressed in terms of molecular direct correlation functions for quite general mixtures of nonpolarizable molecules, some of which may bear electric charges. For general mixtures there is flexibility in the definition of ερ, the most apt definition depending on the intended application. For nonconducting mixtures one particular definition of ερ corresponds to the dielectric constant seen by an externally applied electric field. In this case the present calculation of ερ, which begins with Adelman’s formulation in term of an effective direct correlation function, agrees with the most general results for the dielectric constant of mixtures which have been reported on the basis of quite different theories. Particular attention is given to the linear coefficient in the equation ερ = ε0+ε(1)ρ+⋅⋅⋅, where ε0 is the solvent dielectric constant and ρ is the total concentration of solutes. The theory of ε(1) is given in terms of molecular direct correlation functions and in terms of second moments of site–site correlation functions hαβ(r), all for quite general solutes. Finally, a cluster expansion for the contribution of nonpairwise components in the McMillan–Mayer (i.e., solvent averaged) Hamiltonian for an ionic solution is shown to lead to the same expression for ε(1) in terms of direct correlation functions, as was obtained from Adelman’s prescription, and quite directly to a cluster expansion for ε(1) in terms of short range contributions to the solvent–solvent and ion–solvent molecular pair correlation functions hab(1 2).