Integral equations for classical fluids

With the help of a Padé technique, it is shown that, given the two requirements that the equation for the hard spheres r.d.f. should involve only convolution integrals (as in the PY and HNC equations) and that it should obey the internal consistency criterion imposed by the equality of the pressures calculated using the virial or the Ornstein-Zernike theorem, an integral equation can be derived without resorting to any postulate regarding its functional form. This equation leads to an equation of state which is satisfactory except in the vicinity of the Alder transition where it under-estimates the pressure by nearly 4 per cent. A detailed examination of the fourth virial coefficient reveals some possible reasons for the validity of the integral equation derived in the present paper.