Rarehyphen;earth ions in ethylsulfate crystals give rise to sharphyphen;line optical absorption spectra. The purpose of this paper is to give a part of the theory of the Zeeman effect for these lines. Special cases considered especially are when the magnetic field is parallel or perpendicular to thecaxis, when the light polarization is parallel or perpendicular to both thecaxis and the magnetic field, and when the crystal is rotated about thecaxis while the light polarization and magnetichyphen;field directions are held constant. The dependence of the frequency and intensity of the lines on the crystal orientation gives a measure of certain properties of the internal crystal fields which have not been observable before.
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