"In his great treatise on the Mathematical Theory of Elasticity Love, following the original investigations of Gauss, demonstrates... that when a piece of a thin elastic shell or plate that has a spherical curvature of 1/R is deformed by a small bending without stretching, then in the case of initial spherical curvature one principal curvature of the deformed surface will exceed the initial curvature 1/R by the same amount as the other will be less than l/R. That this is the fact in this case seems evident without following the abstruse analysis of Love... because if x and y be lines drawn tangent to two rectangular normal sections at P, and the spherical surface be bent slightly about x so as to alter the curvature of the section in the normal plane at right angles to x by alternately increasing and decreasing it, it is evident from symmetry that the curvatures of the section in the normal plane at right angles to y will undergo at the same time alterations of curvature which are equal and opposite to those in the first normal plane, altho this equality does not in general hold true in shells that are not spherical in shape. Nevertheless, the same statement evidently holds true for surfaces of revolution about the normal at P as an axis."