The equation of state of a simple classical liquid

Although it still lacks formal mathematical justification the Percus-Yevick equation derived in 1958 has proved a remarkably successful tool for calculations of distribution functions and equations of state at high densities, provided that one is prepared to accept some `smoothing'. In this paper it is shown that various idealized models of the imperfect gas, such as `lattice' and Gaussian models, provide further supporting evidence. Slight modifications are suggested that should speed up calculations without significant loss of accuracy. The probable forms of theories of freezing and boiling, starting from the imperfect gas or liquid phase, can now be foreseen.