Standard radio-frequency nuclear resonance spectroscopy techniques have been applied to study the fine structure of the proton magnetic resonance absorption line in single crystals of CoCl₂.6H₂O. Cobaltous Chloride is a paramagnetic crystal at high temperatures and becomes antiferromagnetic at about 2.29°K. The position and number of lines strongly depend on temperature and on the direction of the externally applied magnetic field. Fewer lines than the theoretical number of twenty-four were always observed. At room temperature the proton resonance at 12 Mc/sec. in a field of 2.82 K gauss consists of a single line about six gauss wide. A splitting of this line into a maximum of six components has been observed at liquid helium temperature. The maximum overall separation at 4.2°K is about 110 gauss. For each direction of the externally applied magnetic field the separation between the lines increases with decreasing temperature. The transition temperature is measured and effects due to short-range order above the transition are observed. Theoretical formulae for the positions of the component lines are developed by considering the two-proton spin system within a water molecule of hydration immersed in the homogeneous external field [formula omitted] H and the inhomogeneous time- averaged field of the cobalt ions. Measurements in the antiferromagnetic state have been partially completed. / Science, Faculty of / Physics and Astronomy, Department of / Graduate