Abstract: "The need often arises for determining the critical chemical concentration of uranium solution in the conical bottom of a plant reactor or storage vessel, or the dimension if the concentration is known. This report describes the mathematical analysis of Poisson's equation for a spherical sector, which approximates a right circular cone. The ratio of the critical dimension of an equivalent sphere to the height of the sector for various sector angles is derived from a comparison of first eigenvalues. No description of further relations between composition and dimensions is discussed in the report."