XI] OF VARIOUS UNIVALVES 815 



The spiral angle (a) 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, causing 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 hkewise 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 a, 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 a is the ratio which subsists between 

 the breadths of successive whorls. The following table gives a few 



* What is sometimes called, as by Leslie, the angle of deflection is the complement 

 of what we have called the spiral angle (a), or obliquity of the spiral. When the 

 angle of deflection is 6° 17' 41", or the spiral angle 83'' 42' 19", the radiants, or 

 breadths of successive whorls, are doubled at each entire circuit. 



