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CHAPTER XI THE LOGARITHMIC SPIRAL

35ô¯ in the typical Trochi, such as T. niloticus or T. zizyphinus, and about 25ô¯ or 26ô¯ in Scalaria pretiosa and Phasianella bulloides; it becomes a very acute angle, of 15ô¯, 10ô¯, or even less, in Eulima, Turritella or Cerithium. The costly Conus gloria-maris, one of the {560} great treasures of the conchologist, differs from its congeners in no important particular save in the somewhat 〜produced〝 spire, that is to say in the comparatively low value of the angle ö¡.

A variation with advancing age of ö¡ is common, but (as Blake points out) it is often not to be distinguished or disentangled from an alteration of öÝ. Whether alone, or combined with a change in öÝ, we find it in all those many Gastropods whose whorls cannot all be touched by the same enveloping cone, and whose spire is accordingly described as concave or convex. The former condition, as we have it in Cerithium, and in the cusp-like spire of Cassis,

A cross-section of a conical sea shell showing the internal chambers arranged in a tapering, spiral-like growth pattern.

Dolium and some Cones, is much the commoner of the two. And such tendency to decrease may lead to ö¡ becoming a negative angle; in which case we have a depressed spire, as in the Cypraeae.

When we find a 〜reversed shell,〝 a whelk or a snail for instance whose spire winds to the left instead of to the right, we may describe it mathôÙeôÙmatôÙiôÙcally by the simple statement that the angle ö¡ has changed sign. In the genus Ampullaria, or Apple-snails, inhabiting tropical or sub-tropical rivers, we have a remarkable condition; for in certain 〜species〝 the spiral turns to the right, in others to the left, and in others again we have a flattened {561} 〜discoid〝 shell; and furthermore we have numerous intermediate stages, on either side, shewing right and left-handed spirals of varying degrees of acuteness31. In this case, the angle ö¡ may be said to

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