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TABLE 1. Instructions for replicating the whorl section and septa used to digitally construct each 3D model. Each of these components are translated, rotated, and scaled down (with respect to the center of the aperture as a datum) to build a shell from the aperture toward the apex. These instructions are necessary for the array generation tool in Blender 2.76 (computer graphics software; Blender Online Community, 2017).

    Translation (mm) Rotation Scale
Nautilida - Nautilus pompilius x 0.0000 -1.600 0.995
y -0.3600 0.000 0.995
z -1.5300 0.000 0.995
Ellesmerocerida - Plectronoceras x 0.0000 0.410 0.991
y 0.0000 0.000 0.991
z 0.9350 0.000 0.991
Adoral poriton of Orthocerid,
Endocerid (Circular),
Endocerid (Depressed)
x 0.0000 0.000 0.996
y 0.0000 0.000 0.996
z 3.0000 0.000 0.996
Adapical poriton of Orthocerid,
Endocerid (Circular),
Endocerid (Depressed)
x 0.0000 0.000 0.986
y 0.0000 0.000 0.986
z 8.0000 0.000 0.986
Oncocerida - Oonoceras x -0.0550 0.000 0.995
y 0.0000 -0.031 0.995
z 0.4400 0.000 0.995
Oncocerida - Euryrizocerina x 0.0358 0.000 0.996
y 0.0000 -0.490 0.996
z 0.4550 0.000 0.996
Discosorida - Phragmoceras
(Early)
x -0.5500 0.000 0.993
y 0.0000 1.000 0.993
z 1.0400 0.000 0.993
Discosorida - Phragmoceras
(Middle)
x -0.5200 0.000 0.993
y 0.0000 1.060 0.993
z 1.1000 0.000 0.993
Discosorida - Phragmoceras
(Late)
x -0.4600 0.000 0.995
y 0.0000 1.100 0.995
z 1.4500 0.000 0.995

 

TABLE 2. Centers of buoyancy, total centers of gravity (y component ignored due to model symmetry), masses and volumes of each component of unique density; sh = shell; sb = soft body; cg = cameral gas; cl = cameral liquid; dep = cameral or endosiphuncular deposits; ct = camerae total; wd = water displaced, separation between centers of buoyancy and gravity (BG), and stability index (St) for each hydrostatic experiment. Experiment (Exp.) numbers correspond to figured hydrostatic models: 2.4 – Nautilus pompilius with soft body flush at aperture; 2.5 – Nautilus pompilius with extended soft body; 2.6 – Nautilus pompilius CT-scanned model; 3.1 – the ellesmerocerid Plectronoceras with a minimum estimate of body chamber ratio (40% body chamber length to total length); 3.2 – the ellesmerocerid Plectronoceras with the body chamber ratio (35% body chamber length to total length) required for near neutral buoyancy; 4.1 – orthocerid model with adapically distributed gas; 4.2 – orthocerid model with adorally distributed gas; 4.3 – evenly distributed Φgas within each camera; 5.1 – orthocerid, larger body chamber, adapical gas; 5.2 – orthocerid, larger body chamber, adoral gas; 5.3 – orthocerid, larger body chamber evenly distributed Φgas; 6.1 – evenly distributed cameral deposits among all camerae; 6.2 – adapical cameral deposits; 6.3 – ventrally displaced cameral deposits; 7.1 – endocerid, central siphuncle; 7.2 – Endoceras; 8.1 – oncocerid, Oonoceras; 8.2 – oncocerid, Euryrizocerina; 9.1 – Phragmoceras, adapical cameral gas; 9.2 – Phragmoceras, adoral cameral gas; 9.3 – Phragmoceras, cameral gas evenly distributed.

  Center of Buoyancy Center of Gravity                  
Exp x (mm) z (mm) x (mm) z (mm) Vsh (cm3) msh (g) Vsb (cm3) msb (g) Vcg (cm3) mcg (g) Vcl (cm3) mcl (g) Vdep (cm3)
2.4 -38.794 -22.716 -35.923 -27.601 53.802 140.961 505.602 538.466 96.851 0.117 33.674 34.516 NA
2.5 -30.715 -13.577 -27.331 -17.378 53.802 140.961 695.690 740.910 109.053 0.131 21.471 22.008 NA
2.6 -32.391 -13.926 -29.408 -17.862 69.881 183.088 778.307 828.897 132.897 0.160 0.000 0.000 NA
3.1 -4.306 25.116 -2.717 21.140 4.093 10.725 22.327 23.778 5.470 0.007 0.000 0.000 NA
3.2 -4.306 25.116 -2.617 20.498 4.260 11.162 20.775 22.125 6.855 0.008 0.000 0.000 NA
4.1 -0.001 176.815 -0.001 137.841 62.483 163.705 277.763 295.817 108.352 0.130 54.086 55.438 NA
4.2 -0.001 176.815 -0.001 159.402 62.483 163.705 277.763 295.817 108.051 0.130 54.293 55.651 NA
4.3 -0.001 176.815 -0.001 147.522 62.483 163.705 277.763 295.817 108.357 0.130 54.278 55.635 NA
5.1 -0.001 176.815 -0.001 138.644 60.015 157.240 328.454 349.804 106.383 0.128 7.938 8.136 NA
5.2 -0.001 176.815 -0.001 141.841 60.015 157.240 328.454 349.804 106.271 0.128 7.941 8.139 NA
5.3 -0.001 176.815 -0.001 140.054 60.015 157.240 328.454 349.804 106.055 0.128 7.928 8.126 NA
6.1 -0.001 176.815 -0.052 147.899 62.483 163.705 277.763 295.817 162.473 0.196 0.000 0.000 21.298
6.2 -0.001 176.815 -0.001 165.130 62.483 163.705 277.763 295.817 162.473 0.196 0.000 0.000 21.258
6.3 -0.001 176.815 -0.840 147.948 62.552 163.887 277.756 295.810 162.410 0.196 0.000 0.000 21.285
7.1 -0.001 176.815 -0.001 149.511 61.683 161.610 278.727 296.844 162.410 0.196 0.000 0.000 21.692
7.2 -0.001 176.816 0.348 150.683 82.767 216.851 346.129 368.627 154.905 0.161 0.000 0.000 8.098
8.1 -7.484 19.929 -6.454 18.152 2.130 5.581 9.182 9.779 3.666 0.004 3.204 3.284 NA
8.2 -9.234 23.448 -7.123 21.424 2.356 6.173 14.448 15.387 4.241 0.005 2.403 2.463 NA
9.1 9.911 50.859 5.023 47.644 15.963 41.824 71.255 75.887 27.096 0.033 10.151 10.405 NA
9.2 9.911 50.859 8.451 46.676 15.963 41.824 71.255 75.887 27.673 0.033 9.892 10.139 NA
9.3 9.911 50.859 6.572 47.500 15.963 41.824 71.255 75.887 27.337 0.033 10.076 10.328 NA

TABLE 2 (continued).

  Center of Buoyancy Center of Gravity                  
Exp x (mm) z (mm) x (mm) z (mm) mdep (g) Vct (cm3) Vwd (cm3) mwd (g) mtotal (g) ɸgas (%) ɸdep (%) B͞͞͞͞G (mm) St
2.4 -38.794 -22.716 -35.923 -27.601 NA 139.438 698.842 716.313 714.059 74.3 NA 5.666 0.064
2.5 -30.715 -13.577 -27.331 -17.378 NA 139.438 882.227 904.283 904.010 83.6 NA 5.090 0.053
2.6 -32.391 -13.926 -29.408 -17.862 NA 132.897 986.400 1011.060 1011.060 100.8 NA 4.938 0.050
3.1 -4.306 25.116 -2.717 21.140 NA 5.470 31.891 32.688 34.503 133 NA 4.282 0.135
3.2 -4.306 25.116 -2.617 20.498 NA 6.855 31.891 32.688 33.287 108 NA 4.917 0.155
4.1 -0.001 176.815 -0.001 137.841 NA 162.473 502.718 515.286 515.091 66.6 NA 38.974 0.490
4.2 -0.001 176.815 -0.001 159.402 NA 162.473 502.718 515.286 515.303 66.6 NA 17.414 0.219
4.3 -0.001 176.815 -0.001 147.522 NA 162.473 502.718 515.286 515.287 66.6 NA 29.293 0.368
5.1 -0.001 176.815 -0.001 138.644 NA 114.249 502.718 515.286 515.307 93.1 NA 38.172 0.480
5.2 -0.001 176.815 -0.001 141.841 NA 114.249 502.718 515.286 515.310 93.1 NA 34.975 0.440
5.3 -0.001 176.815 -0.001 140.054 NA 114.249 502.718 515.286 515.297 93.1 NA 36.762 0.462
6.1 -0.001 176.815 -0.052 147.899 55.800 162.473 502.718 515.286 515.322 100 13.1 28.917 0.364
6.2 -0.001 176.815 -0.001 165.130 55.695 162.473 502.718 515.286 515.217 100 13.1 11.685 0.147
6.3 -0.001 176.815 -0.840 147.948 55.767 162.410 502.718 515.286 515.464 100 13.1 28.880 0.363
7.1 -0.001 176.815 -0.001 149.511 56.833 162.410 502.718 515.286 515.288 100 86.9 27.305 0.343
7.2 -0.001 176.816 0.348 150.683 21.218 154.905 591.900 606.697 606.695 100 27.2 26.135 0.311
8.1 -7.484 19.929 -6.454 18.152 NA 6.873 18.185 18.640 18.648 53.5 NA 2.054 0.078
8.2 -9.234 23.448 -7.123 21.424 NA 6.650 23.454 24.041 24.029 63.7 NA 2.925 0.102
9.1 9.911 50.859 5.023 47.644 NA 37.688 124.906 128.029 128.148 73.4 NA 5.850 0.117
9.2 9.911 50.859 8.451 46.676 NA 37.688 124.906 128.029 127.883 73.4 NA 4.431 0.089
9.3 9.911 50.859 6.572 47.500 NA 37.688 124.906 128.029 128.071 73.4 NA 4.736 0.095

 

 

TABLE 3. Comparison of hydrostatic computations using different density estimates for the soft (ρsb) body and shell (ρsh) for the CT-scanned Nautilus pompilius model. Averaged ρ refers to the densities used in all other hydrostatic experiments in this study. Φgas = percent of phragmocone occupied by cameral gas at neutral buoyancy. St = stability index. The percent change from the averaged density values are denoted by %Δ.

  ρsb (g/cm3) ρsh (g/cm3) Φgas (%) St %ΔΦgas %ΔSt
High ρ (g/cm3) 1.068 2.94 118.9 0.057 18.0 15.7
Low ρ (g/cm3) 1.060 2.53 93.3 0.046 -7.4 -7.7
Averaged ρ (g/cm3) 1.065 2.62 100.8 0.050    

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