A model of an atom in a magnetic solid is used to investigate theoretically features expected in the cross-section for the magnetic scattering of neutrons by the atom. The atom is assumed to have two nondegenerate magnetic states, envisaged as two states in a crystal-field energy level scheme very well separated in energy from all higher states, and the subject of a Weiss molecular field. It is argued that the thermodynamic quantities which determine the weights attached to elastic and inelastic scattering events, the magnetic moment and isothermal susceptibility, respectively, obey a sum rule, and this is exploited to give the temperature dependence of the weights given, say, the separation in energy of the crystal-field levels and the critical temperature below which there is a spontaneous magnetic moment. A small value of the ratio of the energy separation and critical temperature leads to properties significantly different from those of an ion in a Weiss molecular field and not subjected to a crystal-field potential, for which the magnetic moment as a function of temperature is obtained from a Brillouin function. For this special limit of the parameters analytic expressions are provided for the moment and susceptibility.