  We show how the complex-shift method introduced by Appell in gravity to the
case of a point mass (and applied among others in electrodynamics by Newman,
Carter, Lynden-Bell, and Kaiser to determine remarkable properties of the
electromagnetic field of rotating charged configurations), can be extended to
obtain new and explicit density-potential pairs for self-gravitating systems
departing significantly from spherical symmetry. The rotational properties of
two axysimmetric baroclinic gaseous configurations derived with the proposed
method are illustrated.
