560 



THE LOGARITHMIC SPIRAL 



[CH. 



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 d. 



A variation with advancing age of 6 is common, but (as Blake 

 points out) it is often not to be distinguished or disentangled from 

 an alteration of a. Whether alone, or combined with a change in 

 a, 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, 



Fig. 286. Trochus niloticus, L. 



Dolium and some Cones, is much the commoner of the two. 

 And such tendency to decrease may lead to 6 becoming a negative 

 angle; in which case we have a depressed gpire, 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 mathematically by the simple statement that the angle 

 9 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 



