Form and function of orthoconic cephalopod shells with concave septa

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Abstract
Models of “ideal” orthoconic shells having simple concave septa with minimal weight and maximal strength and analysis of 72 species of fossil orthocones and cyrtocones yield important insights into the physical principles underlying cephalopod shell design. The ideal septum is a spherical cap weighing only 77% of a hemispherical septum of equal strength. The septa of most longicones approximate this ideal shape while those of brevicones are less curved, probably owing to buoyancy problems. Increase in septal strength leads to weight increase unless the shell becomes more logiconic or septal spacing increases or both. However, increased spacing requires more cameral liquid for septum formation, thus reducing buoyancy. In ideal longicones, septal spacing resembles the cone radius for thick, strong septa but declines to half of the cone radius for thin, weak septa. In ideal intermediates and brevicones, spacings are respectively reduced by factors of about 2 and 4, with similar additional dependence on septal thickness. Most real septa resemble these ideal models. The relative length of the body chamber to the phragmocone varies greatly between about 0.2 and 1.5, depending mainly on the wall thickness and to a lesser degree on the septal thickness, apical angle and body density. Removal of cameral liquid in the adult must be compensated for by additional growth to retain neutral buoyancy. The conditions for neutral equilibrium calculated for longicones with different “counterweights” indicate that: (1) cameral liquid only is least feasible; (2) half-and-half calcium carbonate and liquid results in one-third length and one-quarter volume reduction of the body chamber; (3) with calcium carbonate only, body chamber reduction is minimal. Real ‘counterweights’ appear to be intermediate between (2) and (3), providing the animal with horizontal stability, which is missing in (3). Most uncalcified siphuncles reduce the body chamber only slightly although they improve horizontal stability. If the wall attains full thickness only at the apical end of body chamber, the liquid-only ‘counterweight’ becomes feasible.