XI] OF VARIOUS UNIVALVES 813 



The generating figure may be taken as any section of' the shell, 

 whether parallel, normal, or otherwise incHned to the axis. It is very 

 commonly assumed to be identical with the mouth of the shell; in 

 which case it is sometimes a plane curve of simple form ; in other and 

 more numerous cases, it becomes compHcated in form and its boun- 

 daries do not he in one plane: but in such cases as these we may 

 replace it by its "trace," on a plane at some 

 definite angle to the direction of growth, for 

 instance by its form as it appears in a section 

 through the axis of the helicoid shell. The 

 generating curve is of very various shapes. 

 It is circular in Scalaria or Cyclostoma, and 

 in Spirula ; it may be considered as a segment 

 of a circle in Natica or in Planorbis. It is 

 triangular in Conus or Thatcheria, and 

 rhomboidal in Solarium or Potamides. It 

 is very commonly more or less elliptical : the 

 long axis of the ellipse being parallel to the 

 axis of the shell in Oliva and Cypraea; all 

 but perpendicular to it in many Trochi ; and 

 oblique to it in many well-marked cases,^such 

 as Stomatella, Lamellaria, Sigaretus halio- 

 toides (Fig. 396) and Haliotis. In Nautilus 

 pomjpilius it is approximately a semi-ellipse, Fig. 395. Section of a spiral 

 and in A^. umbilicatus rather more than a ^^^^^^> Triton corrugatus 



Lam. jrom Woodward. 



semi-ellipse, the lo'ng axis lying in both cases 



perpendicular to the axis of the shell*. Its form is seldom open to 



easy mathematical expression, save when it is an actual circle or 



spiral. Paul Serret (Th. nouv. . .des lignes a double courbure, 1860, p. 101) called 

 it ""helice cylindroconique'" ; Haton de la Goupilliere calls it a '' conhelice.'" It has 

 also been studied by {int. at.) Tissot, Nouv. ann. de mathem. 1852; G. Pirondini, 

 Mathesis, xix, pp. 153-8, 1899; etc. 



* In Nautilus, the "hood" has somewhat dififerent dimensions in the two 

 sexes, and these differences are impressed upon the shell, that is to say upon its 

 "generating curve." The latter constitutes a somewhat broader ellipse in the 

 male than in the female. But this difference is not to be detected in the young; 

 in other words, the form of the generating cu'rve perceptibly alters with advancing 

 age. Somewhat similar differences in the shells of Ammonites were long ago 

 suspected, by d'Orbigny, to be due to sexual differences. (Cf. Willey, Natural 

 Science, vi, p. 411, 1895; Zoological Results, 1902, p. 742.) 



