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XVII. On the Geometrical Forms of Turbinated and Discoid Shells. 

 By the Rev. H. Moseley, M.A., of St. Johns College, Cambridge, Professor of 

 Natural Philosophy and Astronomy in Kings College. Communicated by 

 Thomas Bell, Esq. F.R.S. 



Received June 14, — ^Read June 21, 1838. 



1 HE surface of any turbinated or discoid shell may be imagined to be generated by 

 the revolution about a fixed axis (the axis of the shell) of the perimeter of a geome- 

 trical figure, which, remaining always geometrically similar to itself, increases conti- 

 nually its dimensions. 



In discoid shells the generating figure retains its position upon the axis as it thus 

 revolves, as in the Nautilus Pompilius (Plate IX. fig. 3.), and the Argonaut. In 

 turbinated shells, including the great families of Trochi, Turbines*, Murices and 

 Strombi, it slides continually along the axis of its revolution (fig. 4.). In some great 

 classes of shells, as the Ammonites, the Nautilus scrobiculatus, the Nautilus spirula, 

 the Helix cornea, the Trochus perspectivus, the Nerita, the generating figure increases 

 its distance from the axis at the same time that it increases its dimensions and re- 

 volves. 



Among the generating figures of conchoidal surfaces are to be found various known 

 geometrical forms. The generating figure of the Conus Virgo is a triangle, that of 

 the Trochus telescopicus and of the Trochus Archimedis, a trapezoid. The species of 

 the genus Turbo have for their generating figure a curve, of double curvature, of a 

 circular or elliptic form, to whose perimeter the axis of revolution is a tangent. The 

 Nautilus Pompilius is generated by the revolution about its shorter diameter of a plane 

 curve, approaching very nearly to a semi-ellipse (fig. 3.) ; and the Cyprsea by the re- 

 volution of a similar curve about its longer diameter. 



There is a mechanical uniformity observable in the description of shells of the same 

 species, which at once suggests the probability that the generating figure of each in- 

 creases, and that the spiral chamber of each expands itself, according to some simple 

 geometrical law common to all. To the determination of this law, if any such exist, 

 the operculum lends itself, in certain classes of shells, with remarkable facility. Conti- 

 nually enlarged by the animal, as the construction of its shell advances, so as to fill up 

 its mouth, the operculum measures the progressive widening of the spiral chamber, by 

 the progressive stages of its growth. 



Of these progressive stages of the growth of the operculum, distinct traces remain 



* The beautiful shell Turbo scalaris (Ventletrap) may be taken as an easy illustration of the properties to be 

 described in this paper. 



