Abstract
For a self-gravitating free from external pressure fluid body, consisting of two homogeneous Co nfo cal ellipsoids of different density rotating with common angular velocity, we demonstrate the existence of equilibrium figures. No senes is possible, however, since the rotating body attains, for given values of its relative density, a unique degree of flattening. In addition, the analysis shows that there is a lower limit to the relative density (in which case the density of the interior ellipsoid is only slightly larger than twice the density of the exterior one) and a semi-qualitative explanation on the subject is offered. The fluids are assumed ideal and incompressible. Key words: HYDRODYNAMICS
