On the Superpotential and Supermatrix of a Heterogeneous Ellipsoid.

The potential, superpotential, potential-energy tensor, and supermatrix are calculated for a heterogeneous ellipsoid in which the equidensity surfaces are similar and similarly situated ellipsoids, i.e, in which the ellipsoid is "homoeoidally striated." In analogy with Newton's theorem, that the potential inside a homoeoid is constant, it is proved that the superpotentials of all orders are constant inside a homoeoid. The theory is used to show that the point of bifurcation for a sequence of homoeoidally striated spheroids is reached when the eccentricity e has the value 0 81267 . . . , the eccentricity at which bifuraction occurs for the Maclaurin sequence for incompressible fluids.