Wang's generalization of Bethe's theory of snperlattices is applied to the cases of quadratic and simple cubic lattice. Only neighbour interaction is taken into consideration. All the calculations are carried out to the second approximation.The variation of the critical temperature with composition is calculated. The degree of order, the energy and the specific heat are calculated for the special case of equal numbers of A and B atoms at various temperatures. It is found that the results differ very little from those obtained by Bethe in the second approximation. In the case of the simple cubic lattice the discontinuity of the specific heat is found to be only slightly larger than that obtained by Bethe.