Statistics of a Two-dimensional Lattice Gas. I

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Abstract
In continuation of former work on a simple model in which two molecules may not occupy neighbouring sites on a plane square lattice, various portions of the virial series are derived. The series is split up, not into individual cluster-sums, but into contributions from various types of groups of sites, in the manner introduced by Rushbrooke and Scoins in 1953. It is concluded that the main contributions to the virial series come from single sites, neighbouring pairs and `open' rings of sites, and that contributions from other types of domains of sites are small in comparison, some vanishing identically.