The following is a simple geometrical demonstration of the well-known theorem that, if matter be distributed over a sphere with a surface-density (i.e., mass per unit of surface) inversely as the cube of the distance from either of two points which are the inversions of each other with respect to the sphere, it will act upon all external masses as if it were collected at the interior point:—and upon all internal masses as if a definite multiple of its mass were concentrated at the exterior point.