The cross-sections are studied for the magnetic scattering of slow neutrons by metallic electrons whose energy states are described by band theory. It is found that both electron spin and current contribute to the scattering. With the aid of certain simplifying assumptions numerical results are obtained for two cases, the free-electron model of a simple metal like sodium, and the collective-electron model of a ferromagnet with particular reference to specific experimental data on iron. Scattering takes place over wide angles and is very weak, although total cross-sections may be of the order of millibarns. Unfortunately, therefore, this technique cannot at present give much information about the electrons. The predictions of the collective-electron model of a ferromagnet are of importance for comparison with experiment and the predictions of the other models. It is here contrasted in detail with the spin-wave predictions.