Cephalopod theoretical morphology involves mathematical characterization of planispiral shell geometry. Such analysis has been instrumental in facilitating research on fossil cephalpood adaptation and evolution, particularly in matters relating to the hydrostatic properties of the living animals. However, this approach is handicapped by its strict applicability only to shells with circular whorl cross sections. The research described in this proposal will remove this shortcoming by developing equations for generating curve area and other key geometric parameters of compressed and depressed shells. In addition, this work will correct inconsistencies in the methods used by paleontologists to evaluate stability and orientation of fossil cephalopods. The new procedures will then be used to evaluate the effects of variation in shell geometry on buoyancy, orientation, and hydrostatic stability over a much wider range of shell form than could be achieved in the past. The objective is to determine how shell compression and depression influence hydrostatic properties of the shell. The results of this work will substantially improve knowledge of fossil cephalopod life habits and paleoecology, and will make possible much needed work in hydrodynamics, locomotion, and other areas of cephalopod adaptation and evolution.
