The present paper continues an earlier investigation of the application of Meyer's theory of a gas mixture of two components to a solid solution AB inhabiting a lattice of the type AB by considering the A. atoms inhabiting the two different sublattices as forming two different components. It is proved that the different irreducible cluster integrals are linear functions (and hence the free energy of the solid solution) of coordination numbers of the type ∑λabλa′b′λ……, where a, a′,…, b,b′… are different sites on the two sublattices (say a and β sublattices) and λab is a neighbour matrix defined by λab=1 when a, b are nearest neighbours =0 if otherwise,the product in (1) is irreducible with respect to the suffices (i. e. not divisible into parts with one or no suffice in common) and the summation is taken over all positions of a, a′,…,b b′,…, (a, a′, a",… as well as b, b′… being always different). Galling such coordination numbers as z1,z2,…and writing the free energy F of the solid solution as f0+z1f1, z2f2+…,(2) we point out that these Fi may be calculated from the free energies of the same solution, but now with the sites falling into groups each of which contains a small number of sites and does not contain sites which are neighbours of sites belonging to a different group. Since F of these solid solutions may be found easily (without approximations), we succeed in getting the required free energy F. Of course, this is an approximate method of calculating F, since we can not find the various Fi at one stroke.It is finally pointed out that such a method allows extension to lattices of different structure, to components more than two, to include interactions between next nearest neighbours, etc.