Remarks on the hypernetted chain approximation in the case of simple fluids

In the theory of simple fluids it is a common feature of approximate theories that the energy, the virial and the compressibility theorem give not the same equation of state as it should be. It is shown that in general two conditions must be satisfied in order to remove the inconsistency. Furthermore it is noted that Morita's and Hiroïke's expression for the Helmholtz free energy should be corrected in the case of hard sphere repulsive forces. This turns out to have consequences for the H.N.C. approximation. Lastly, the variational formulation of theory is discussed in view of consistency.