On the Oscillations and the Stability of Rotating Gaseous Masses. III. The Distorted Polytropes.

The theory of the oscillations of rotating gaseous masses, developed in an earlier paper of this series, is here applied to determine the effect of a small rotation ( on the fundamental modes of oscillation of a polytrope. The basis for this application is provided by the theory of rotationally distorted polytropes; this theory is reviewed and amplified further to include a discussion of the superpotential. The various tensors, in terms of which the characteristic frequencies of oscillation are expressed, are evaluated for distorted polytropes, appropriately, to the first order in . The final results on the effect of rotation on the characteristic frequencies are presented in the form of tables.