We discuss the hydrodynamic equations which describe the shear dynamics of
a liquid composed of anisotropic molecules, both in its normal and its supe
rcooled phases. We use these equations to analyze 90 degrees depolarized li
ght scattering experiments performed in the supercooled phase of a glass fo
rming liquid, metatoluidine, and show that the information extracted from t
his analysis is consistent with independent shear viscosity measurements pe
rformed on that liquid in the same temperature range.