On Central Ovaloids

An ovaloid is a closed convex surface, and may be defined, according to Minkowski!, as a closed point-set which has in common with an arbitrary straight line in space a finite strip of the line, or a single point, or no point at all, and does not lie completely in a plane. For the purposes of this paper, we shall assume that the principal radii of curvature at any point of the ovaloid exist and are both finite.