570 



THE LOGARITHMIC SPIRAL 



[CH. 



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 Pterojjods. 



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 

 have no biological grounds for such a statement ; for the shell 

 arises from a single embryonic origin, and afterwards becomes split 

 into portions which constitute the two separate valves. We can 

 perhaps throw some indirect light upon this phenomenon, and 

 upon several other phenomena connected with shell-growth, by 

 a consideration of the simple conical or tubular shells of the 

 Pteropods. The shells of the latter are in few cases suitable for 

 simple mathematical investigation, but nevertheless they are of 

 very considerable interest in connection with our general problem. 

 The morphology of the Pteropods is by no 

 means well understood, and in speaking of 

 them I will assume that there are still 

 grounds for believing (in spite of Boas' 

 and Pelseneer's arguments) that they are 

 directly related to, or may at least be 

 directly compared with, the Cephalopoda*. 

 The simplest shells among the Pteropods 

 have the form of a tube, more or less 

 cylindrical (Cuvierina), more often conical 

 (Creseis, Clio) ; and this tubular shell (as 

 we have already had occasion to remark, 

 on p. 258), frequently tends, when it is 

 very small and delicate, to assume the 

 Fig. 295. Pteropod shells: character of an unduloid. (In such a case 



(1) Cuvierina columnella; it is more than hkelv that the tiny shell, 



(2) Cleodora chierchiac; ^^ ^^^^ ^^^-^^^ ^f it which Constitutes the 



(3) C. pygmaea. (After . ' 



Boas.) unduloid, has not grown by successive 



* We need not assume a close relationship, nor indeed any more than such a 

 one as permits us to compare the shell of a Nautilus with that of a Gastropod. 



