"[P]icture... a circular piece of a plate which has an approximately spherical curvature at its center point O. Pass a plane XY tangent to the surface at O and let OZ be normal to it at O. Then if a be applied about OX it will not only make the curvature of the plate greater in the plane ZOY but at the same time it will make its curvature less in the plane ZOX to an equal amount as is evident by experiment on a shell of any elastic material, and as is proven in Gauss' theorem of the curvature of thin shells. Since the force applied to produce the given bending moment must produce both these equal changes of curvature simultaneously by producing elongations and compressions in twice as much material as in a plane plate of equal cross section, each of them is only half as great as would be produced in a plane plate in a single direction by this same moment. Hence it. appears that the deformations produced by an applied moment are not more than half as great in a spherical dish shaped plate as in a plane plate..."