Rotational distortion of polytropes by analytic approximation,III

Paper II of this series was less rigorous than desirable, particularly in the fitting of internal and external potentials. A method is developed in this paper properly to fit the external and internal potentials on the distorted configuration boundary. Displacement of the fiting radius from the radius of a nonrotating configuration in general changes the distorted boundary location by an insignificant amount.A comparison of this theory with the numerical integrations of James (1964) shows excellent agreement to at least an angular velocity equalling 70% of critical rotation. The comparison is for polytropic indices of 1.0, 1.5, 2.0 and 3.0.