830 THE EQUIANGULAR SPIRAL [ch. 



Among the Lamellibranclis it is largest in such forms as Isocardia 

 and Diceras, and in the very curious genus Caprinella; in all of 

 these last-named genera its magnitude leads to the production of 

 a spiral shell of several whorls, precisely as in the univalves. The 

 angle is usually equal, but of opposite sign, in the two valves of 

 the LamelHbranch, and usually of opposite sign but unequal in 

 the two valves of the Brachiopod. It is very unequal in many 

 Ostreidae, and especially in such forms as Gryphaea, or in Caprinella, 

 which is a kind of exaggerated Gryphaea; in the cretaceous genus 

 Requienia, the two valves of the shell closely resemble a turbinate 

 gastropod with its flat calcified operculum. Occasionally it is of the 

 same sign in both valves (that is to say, both valves curve the same 

 way) as we see sometimes in Anomia, and better in Productus or 

 Strophonema. 



It will be observed, and it may not be difficult to explain, that 

 the more the bivalve shell curves in the one direction the more it 

 curves in the other; each valve tends, to be spheroidal, or ellipsoidal, 

 rather than cylindroidal. The cyhndroidal form occurs, excep- 

 tionally, in Solen. But Pecten, Gryphaea, Terebratula are all cases 

 of bivalve shells where one valve is flat and the other curved from 

 side to side ; and the flat valve tends to remain flat in the longitudinal 

 direction also, while the curved valve grows into its logarithmic 

 spiral. 



In the genus Gryphaea, an oyster-hke bivalve from the Jurassic, 

 the creature lay on its side with' its left valve downward, as oysters 

 and scallops also do; and this valve adhered to the ground while 

 the animal was young. The upper valve stays flat, and looks Uke 

 a mere operculum; but the lower or deep valve grows into a more 

 or less pronounced spiral. So is it also in the neighbouring genus 

 Pecten, where P. Jacobaeus has its under-valve much deeper and 

 more curved than, say, P. opercularis ', but Gryphaea incurva is 

 more spirally curved than any of these, and G. arcuata has a spiral 

 angle very near to that of Nautilus itself. In both the spiral is a 

 typical equiangular one, built up of a succession of gnomonic incre- 

 ments, which in turn depend on a constant ratio between the 

 expansion of a generating figure and its rotation about a centre 

 of simihtude. Rate of growth is at the root of the whole matter. 

 Now Gryphaea, Hke some Ammonites of which we spoke before, is 



