It has been found possible to generalize Ising's (4) treatment of the linear chain with nearest-neighbour interaction, and his main result, that such interaction cannot lead to cooperative effects, has been shown to hold for very many, if not all, types of lattice in three dimensions. Reasons are given for presuming a similar result for the second nearest-neighbour model. It is found, however, that even a small interaction of the long-range type can lead to cooperative effects at high temperatures, provided that the nearest-neighbour interaction is sufficiently strong. It is therefore claimed that explicit account must be taken of both types of interaction in any acceptable theory, and a possible method of estimating their relative importance is indicated.