Self-consistent approximations for molecular distribution functions

The molecular distribution functions of a classical fluid are related to the pressure both by the virial equation of the canonical ensemble and by the equation for the compressibility of the grand canonical ensemble. In general, the two values of the pressure do not agree if approximations to the functions are used. It is shown that a direct correlation function can be devised which removes this discrepancy, and that its removal leads to a significant improvement in the equation of state for hard spheres over those of the Percus-Yevick and hyper-netted chain approximations. Two other inconsistencies are discussed more briefly but are not used constructively.