832 THE EQUIANGULAR SPIRAL [ch. 



growth, no successional increments, no "gnomons," no self- 

 similarity in the figm:e. In short it has nothing to do with a 

 logarithmic or equiangular spiral, but is a mere twist, or tapering 

 helix, and it points now one way, now another. The cases in 

 which the heUcoid spires point towards, or point away from, the 

 middle line are ascribed, in zoological classification, to particular 

 "families" of Brachiopods, the former condition defining (or 

 helping to define) the Atrypidae and the latter the Spiriferidae 



Fig. 407. Spiral arms of 

 Spirifer. 



Fig. 408. Inwardly directed 

 spiral arms of Atrypa. 



and Athyridae. It is obvious that the incipient curvature of the 

 arms, and consequently the form and direction of the spirals, will 

 be influenced by the surrounding pressures, and these in turn by 

 the general shape of the shell. We shall expect, accordingly, to 

 find the long outwardly directed spirals associated with shells which 

 are transversely elongated, as Spirifer is; while the more rounded 

 Atrypa will tend to the opposite condition. In a few cases, as in 

 Cyrtina or Reticularia* where the shell is comparatively narrow but 

 long, and where the uncoiled basal support of the arms is long also, 

 the coils into which the latter grow are turned backwards, in the 

 direction where there is most room for them. And in the few cases 

 where the shell is very considerably flattened, the spirals (if they 

 find room to grow at all) will be constrained to do so in a discoid 

 or nearly discoid fashion, and this is actually the case in such 

 flattened forms as Koninckina or Thecidium. 



The shells of Pteropods 



While mathematically speaking we are entitled to look upon 

 the bivalve shell of the Lamellibranch as consisting of two distinct 

 elements, each comparable to the entire shell of the univalve, we 



