The potential-energy tensors for subsystems. III. Mass distributions with ellipsoidal and confocal strata

The potential-energy tensors for subsystems, defined in a previous approach, are evaluated in the special case of mass distributions where the surfaces of equal density are confocal ellipsoids. To this aim, demonstration, is provided for a number of theorems, including a generalization of a corollary to Maclaurin's theorem, to the tensor potential. A simple application is made in connection with one-component mass distributions m(alpha) approaching alpha - a crude halo approximation for galaxies-and the isolines within Ellipsoidland (i.e., the whole set of ellipsoids defined by alpha1 greater than or = alpha2 greater than or = alpha3), related to a number of physical parameters (normalized to define reference values) are shown.