Fig. 284. A, Lamellaria perspicua; B, Sigaretus haliotoides.
(After Woodward.)
The general appearance of the entire shell is determined (apart from the form of its generating curve) by the magnitude of three angles; and these in turn are determined, as has been sufficiently explained, by the ratios of certain velocities of growth. These angles are (1) the constant angle of the logarithmic spiral (α); (2) in turbinate shells, the enveloping angle of the cone, or (taking half that angle) the angle (θ) which a tangent to the whorls makes with the axis of the shell; and (3) an angle called the “angle of retardation” (β), which expresses the retardation in growth of {556} the inner as compared with the outer part of each whorl, and therefore measures the extent to which one whorl overlaps, or the extent to which it is separated from, another.
The spiral angle (α) is very small in a limpet, where it is usually taken as = 0°; but it is evidently of a significant amount, though obscured by the shortness of the tubular shell. In Dentalium it is still small, but sufficient to give the appearance of a regular curve; it amounts here probably to about 30° to 40°. In Haliotis it is from about 70° to 75°; in Nautilus about 80°; and it lies between 80° and 85°, or even more, in the majority of Gastropods.
The case of Fissurella is curious. Here we have, apparently, a conical shell with no trace of spiral curvature, or (in other words) with a spiral angle which approximates to 0°; but in the minute embryonic shell (as in that of the limpet) a spiral convolution is distinctly to be seen. It would seem, then, that what we have to do with here is an unusually large growth-factor in the generating curve, which causes the shell to dilate into a cone of very wide angle, the apical portion of which has become lost or absorbed, and the remaining part of which is too short to show clearly its intrinsic curvature. In the closely allied Emarginula, there is likewise a well-marked spiral in the embryo, which however is still manifested in the curvature of the adult, nearly conical, shell. In both cases we have to do with a very wide-angled cone, and with a high retardation-factor for its inner, or posterior, border. The series is continued, from the apparently simple cone to the complete spiral, through such forms as Calyptraea.
The angle α, as we have seen, is not always, nor rigorously, a constant angle. In some Ammonites it may increase with age, the whorls becoming closer and closer; in others it may decrease rapidly, and even fall to zero, the coiled shell then straightening out, as in Lituites and similar forms. It diminishes somewhat, also, in many Orthocerata, which are slightly curved in youth, but straight in age. It tends to increase notably in some common land-shells, the Pupae and Bulimi; and it decreases in Succinea.
Directly related to the angle α is the ratio which subsists between the breadths of successive whorls. The following table gives a few illustrations of this ratio in particular cases, in addition to those which we have already studied. {557}
| Pointed Turbinates | Obtuse Turbinates and Discoids | |||
|---|---|---|---|---|
| Telescopium fuscum | 1·14 | Conus virgo | 1·25 | |
| Acus subulatus | 1·16 | Conus litteratus | 1·40 | |
| *Turritella terebellata | 1·18 | Conus betulina | 1·43 | |
| *Turritella imbricata | 1·20 | *Helix nemoralis | 1·50 | |
| Cerithium palustre | 1·22 | *Solarium perspectivum | 1·50 | |
| Turritella duplicata | 1·23 | Solarium trochleare | 1·62 | |
| Melanopsis terebralis | 1·23 | Solarium magnificum | 1·75 | |
| Cerithium nodulosum | 1·24 | *Natica aperta | 2·00 | |
| *Turritella carinata | 1·25 | Euomphalus pentangulatus | 2·00 | |
| Acus crenulatus | 1·25 | Planorbis corneas | 2·00 | |
| Terebra maculata (Fig. [285]) | 1·25 | Solaropsis pellis-serpentis | 2·00 | |
| *Cerithium lignitarum | 1·26 | Dolium zonatum | 2·10 | |
| Acus dimidiatus | 1·28 | *Natica glaucina | 3·00 | |
| Cerithium sulcatum | 1·32 | Nautilus pompilius | 3·00 | |
| Fusus longissimus | 1·34 | Haliotis excavatus | 4·20 | |
| *Pleurotomaria conoidea | 1·34 | Haliotis parvus | 6·00 | |
| Trochus niloticus (Fig. [286]) | 1·41 | Delphinula atrata | 6·00 | |
| Mitra episcopalis | 1·43 | Haliotis rugoso-plicata | 9·30 | |
| Fusus antiquus | 1·50 | Haliotis viridis | 10·00 | |
| Scalaria pretiosa | 1·56 | |||
| Fusus colosseus | 1·71 | |||
| Phasianella bulloides | 1·80 | |||
| Helicostyla polychroa | 2·00 | |||
| Those marked * from Naumann; the rest from Macalister[526]. | ||||
In the case of turbinate shells, we require to take into account the angle θ, in order to determine the spiral angle α from the ratio of the breadths of consecutive whorls; for the short table given on p. [534] is only applicable to discoid shells, in which the angle θ is an angle of 90°. Our formula, as mentioned on p. [518] now becomes
R = ε2π sin θ cot α .
For this formula I have worked out the following table. {558}