A generalization of lattice-cell theories of liquids is proposed by introduction of a structure of cells of different size. The number of molecules contained in cells with a radius r is determined by a function fc(r) describing essentially the collision probability of two particles. A relation between fc(r) and the radial distribution function g(r) is given. Any regular (lattice-like) arrangement of the molecules is not supposed. The estimation of thermodynamic quantities is shown both in a semiclassical approximation and in a quantum-statistical version. Particularly we studied the equation of state of simple liquids (neon, methane). Correlations are found between the shape of the distribution fc(r) and the course of the equation of state. The theory gives the usual cell theory behaviour and additionally some interesting new features.
