Cotton-Mouton dichroism has been observed through the absorption bands of a few rare earth ions when a magnetic field is applied perpendicular to the common orientation of the light path and unique crystal axis. The data thus obtained allow the perpendicular g factors of excited states to be determined experimentally. We shall report on such an experiment in a Nd3+Na+−CaWO4 crystal and provide a phenomenological theory pointing out optimal experimental conditions for future work in the field.