The hyper-netted chain approximation proposed in I is reformulated. The formulae in this approximation are rederived for the free energy, chemical potential and pair distribution function. The pair distribution function in our approximation is shown to satisfy a new integral equation, which is compared with the Yvon, Born and Green one. Variational principle for our approximation is given. Errata for I and II are given as appendix.
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Tohru Morita (1960) studied this question.