  We consider the post-Newtonian approximation for the Dedekind ellipsoids in
the case of axisymmetry. The approach taken by Chandrasekhar & Elbert (1974,
1978) excludes the possibility of finding a uniformly rotating (deformed)
spheroid in the axially symmetric limit, though the solution exists at the
point of axisymmetry. We consider an extension to their work that permits the
possibility of such a limit.
