Equations of motion for post-mortem sinking of cephalopod shells

  • John A. ChamberlainJr.
  • J. Scott Weaver


We have modified our equations of motion for sinking Nautilusshells to a more general form suitable for application to fossil cephalopods. The new equations incorporate the effects of hydrodynamic stability and loss of buoyancy due either to the unrestricted entry of water into the shell during sinking, or to entry by diffusion across the wall of the siphuncular tube. With our new equations it is possible to calculate sinking velocity and pressure across the shell wall as a function of depth for shells of any size and shape. Our system provides a means of analyzing several aspects of the post-mortem history of cephalopod shells including vertical preservation. In the latter case, our equations enable us to find water depth from the geometry of a vertically preserved shell. We calculate the maximum water depth of the Hauptmuschelkalk beds (Triassic, south-central Germany) to have been about 3 m. Our method is unique in providing a way of obtaining numerical values for maximum water depth of ancient sediments and sedimentary environments. These equations also offer the possibility of examining the paleoecology and paleobiology of the living animals, especially with respect to swimming ability and vertical migration.

Key words

cephalopods post-mortem sinking equations 


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  1. Chamberlain, J. A., Jr., 1976, Flow patterns and drag coefficients of cephalopod shells: Palaeontology, v. 19, p. 539–563.Google Scholar
  2. Chamberlain, J. A., Jr. 1978, Permeability of the siphuncular tube ofNautilus: its ecologic and paleoecologic implications: Neues Jahrb. Geol. Paläont. Mh. p. 129–142.Google Scholar
  3. Chamberlain, J. A., Jr., and Weaver, J. S., 1974, Sinking kinematics of nekroplanktonic cephalopod shells: Geol. Soc. Amer. Abstr. Program Annu. Meet., v. 6, p. 685–686.Google Scholar
  4. Chamberlain, J. A., Jr., and Weaver, J. S., in preparation, Paleoenvironmental significance of vertically preserved cephalopod shells.Google Scholar
  5. Collins, D. H., and Minton, P., 1967, Siphuncular tube ofNautilus: Nature, v. 216, p. 916–917.Google Scholar
  6. Geisler, R., 1938, Zur Stratigraphie des Hauptmuschelkalks in der Unbegung von Würzburg mit besonderer Berücksichtigung der Ceratiten: Jahrb. Preuss. Geol. Landenstalt, v. 59, p. 197–248.Google Scholar
  7. Kennedy, W. J., and Cobban, W. A., 1976, Aspects of ammonite biology, biogeography, and biostratigraphy. Paleont. Assoc., Spec. Papers Palaeont., no. 17, 94 pp.Google Scholar
  8. Mutvei, H., and Reyment, R., 1973. Buoyancy control and siphuncle function in ammonoids: Palaeontology, v. 16, p. 623–636.Google Scholar
  9. Raup, D. M., 1967, Geometric analysis of shell coiling: coiling in ammonoids: Jour. Paleont., v. 41, p. 43–65.Google Scholar
  10. Raup, D. M., 1973, Depth inferences from vertically imbedded cephalopods: Lethaia, v. 6, p. 217–226.Google Scholar
  11. Raup, D. M., and Chamberlain, J. A., Jr., 1967, Equations for volume and center of gravity in ammonoid shells: Jour. Paleont., v. 41, p. 566–574.Google Scholar
  12. Reyment, R., 1958, Some factors in the distribution of fossil cephalopods: Stockh. Contrib. Geol., v. 1, p. 97–184.Google Scholar
  13. Reyment, R., 1968. Orthoconic nautiloids as indicators of shoreline surface currents: Jour. Sed. Petrol., v. 38, p. 1398–1389.Google Scholar
  14. Reyment, R. A., 1970, Vertically inbedded cephalpod shells. Some factors in the distribution of fossil cephalopods, 2, Palaeogeo. Palaeoclim. Palaeoecol., v. 7, p. 103–111.Google Scholar
  15. Reyment, R., 1973. Factors in the distribution of fossil cephalopods, 3. Experiments with exact shell models of certain shell types: Bull. Geol. Inst. Univ. Upps., N. S. 4, part 2, p. 7–41.Google Scholar
  16. Saunders, W. B., and Wehman, D. A., 1977, Shell strength ofNautilus as a depth limiting factor: Paleobiology, v. 3, p. 83–89.Google Scholar
  17. Seilacher, A., 1971, Preservational history of ceratite shells: Palaeontology, v. 14, p. 16–21.Google Scholar
  18. Stenzel, H. B., 1964, LivingNautilus: in Treatise on Invertebrate Paleontology, R. C. Moore, Ed., Part K, Mollusca 4, Univ. Kansas Press, Lawrence, p. K59-K93.Google Scholar
  19. Teichert, C., 1970. DriftedNautilus shells in the Bay of Bengal: Jour. Paleont., v. 44, p. 1129–1130.Google Scholar
  20. Trueman, A. E., 1941, The ammonite body-chamber, with special reference to the buoyancy and mode of life of the living ammonite: Quart. Jour. Geol. Soc. London, v. 96, p. 339–383.Google Scholar
  21. Vossmerbäumer, H., 1972, Cephalopoden in Muschelkalk Mainfrankens. Ein biostratinomischer Beitrag, Geol. Bl. Nordost., v. 22, p. 8–22.Google Scholar
  22. Weaver, J. S., and Chamberlain, J. A., Jr., 1976. Equations of motion for postmortem sinking of cephalopod shells and the sinking ofNautilus: Paleobiology, v. 2, p. 8–18.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • John A. ChamberlainJr.
    • 1
  • J. Scott Weaver
    • 2
  1. 1.Department of GeologyBrooklyn College of the City University of New YorkBrooklynUSA
  2. 2.Department of Geological SciencesColumbia UniversityNew YorkUSA

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