Abstract
A description is given of an elementary method of justifying the perturbation theory that provides the structure of a slowly rotating, self-gravitating mass in terms of the structure of a corresponding non-rotating configuration (Clairaut Theory). The main point of the method is the adoption of the viewpoint that the density, rather than the angular velocity, be prescribed as a function of position, since this leads to a completely elementary existence theory of rotating, self-gravitating masses. The method is carried out for the case of constant angular velocity, verifying the asymptotic nature of both the classical Clairaut Theory and more general theories (including Chandrasekhar's theory of distorted polytropes) that are in use in astrophysics.
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