Nautiloid shell calculations

Since the view of the middle whorl of the Cimomia shell from Kingsley Wood was tangential the breadth of 63 mm measured near the umbilicus is about five chambers and a quarter whorl beyond the smaller septum seen to have edges in the median plane of symmetry 21 and 45 mm from the axis of coiling. The whorl expansion rate W = 45/21 in 360° when converted to a natural logarithm and multiplied by 0.25, and then used as an exponent of e = 2.17 etc. will predict the subsequent increase in breadth and therefore the likely true breadth of the hidden small septum (i.e. it is 63/1.21 – 52 mm). By the same calculation, but going backwards for half a whorl, the radius 45 mm is reduced to 31 mm. The shell diameter is then 45+31 = 76 mm where the breath is 52 mm and the median height 45-21 = 24 mm. One can, however, see that the next whorl expands less and this can be measured as W = 97/63 more reliably than on the partly missing venter (r= 68 mm or more). Using the lower rate the breadth corresponding to a diameter of 76 mm becomes 56 mm or about 74%. Using these revised measurements the shell looks a more normal shape, but still develops a depressed and slowly expanding outer whorl with a more semicircular cross-section. The following museum specimens of Cimomia imperialis are of that variety, if clearly mature with more closely spaced final septa, with relatively pyrite-free calcite rim cements for probably Highgate material. The mature shell of 82.3 mm diameter and 57 mm breadth is labelled Highgate IPM B2155g in the Paris Nat. Hist. Mus. The only specimen, which I saw in Saffron Walden Museum, is almost certainly the one from G.S. Gibson (1818-1883) listed as “Nautilus centralis from Eocene Higate”. It showed a breadth of 59 mm at 65.5 mm. Oxford University Museum specimen 595/2 had no locality but was an old donation with measurement 63 mm at 80 mm. Other specimens from the pyrite-filled variety of Highgate septaria and Essex division E sites on the M11 and M25 are considerably larger, and become more not less compressed on the outer whorl.