Tendency towards sphericity symmetry of pebbles: The rate change of volume with surface

The primary effect of rocks and stones tending to erode towards sphericity symmetry can be identified with the rate change of volume with surface. Marble pebbles of various shapes and sizes are recorded and modeled mathematically as ellipsoids. The rate change of volume with surface d V /d A is computed for flat-shaped pebbles where the thickness dimension is assumed to be unity. Invoked is the hypothesis that the change of shape and size of pebbles can be characterized by a master curve derived from d A /d L , the 2D version of d V /d A . The sphericity symmetry is assumed to be concerned with the preference of roundness to slenderness regardless of the surface roughness, smoothness and the mineralogical composition. The erosiveness and abrasiveness of the surface and time effects can interact with sphericity, which is an issue beyond the scope of this work.