The structure of the liquid-vapor interface

A formal derivation is presented for the equilibrium relation between the singlet density in a fluid and the direct correlation function and for the equivalent relation involving the pair number density. It is shown that this relation is equivalent to the macroscopic condition for hydrostatic equilibrium when the singlet density varies sufficiently slowly to permit the introduction of local thermodynamics. Some aspects of the usage of this in the determination of the singlet density in the liquid-vapor transition region are discussed.