The principal result of the work reported in this paper is a first-order differential equation for the neutron spectrum in an energy region where the effects of chemical binding are significant but not dominant. Solutions of the differential equation provide accurate results for the spectrum in the cases of moderation by hydrogen, as well as by the heavier moderators, such as beryllium and graphite. In the derivation of the results, no restrictions are made concerning the nature of the motions of the moderator atoms. Interference effects in the neutron scattering are, however, neglected. The integral properties of the scattering kernel, which are found to influence the spectrum significantly, are calculated by means of the short-collision-time approximation, first introduced by Wick to compute the effects of chemical binding on slow neutron-scattering cross sections. Finally, for heavy moderators the representation of the energy-transfer properties of the moderator in terms of a first-order differential operator are combined with the P1 approximation to give a useful description of the spatially dependent spectrum.