Structures have been determined for axially symmetric rotating gas masses, in the polytropic and white-dwarf cases. To solve the structure problem near the center of mass, the density and gravitational potential were expanded in power series in the radial variable. The coefficients in these expansions were themselves expanded in terms of Legendre polynomials in the cosine of the co-latitude. Analytic continuation, and finally a step-by-step integration, gave the structure elsewhere. The truncation error was about 0 002 in the worst case considered. Physical parameters for the rotating configurations were obtained for values of n < 3, and for a range of white-dwarf configurations. The existence of forms of bifurcation of the axially symmetric series of equilibrium forms was also investigated. The white-dwarf series proved to lack such points of bifurcation, but they were found on the polytropic series for n < 0.808. The truncation error in this critical value of n is estimated at about 0.0004.