Abstract
A study is made of the ` Gaussian ' model of an imperfect gas used by Ford, which assumes the Mayer function exp(-/kT) - 1 to be a Gaussian function of the interatomic distance and is, at any fixed temperature, practically equivalent to an elastic sphere model though it could not give the temperature variation of the virial coefficients. The problem is shown to be closely related to one of `restricted random-walk ' type, which can be solved almost completely, the combinatorial problems being similar to those of circuit theory. It is concluded that the virial series is analytic for all positive V and that the high-order virial coefficients probably alternate in sign, though this limiting behaviour may well be approached very slowly, because of various ` small number effects ' that influence the early terms. The model is not directly comparable with that of rigid spheres, because it can be compressed to zero volume.
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