576 THE LOGARITHMIC SPIRAL [ch. 



the little "rostrum" of Sepia is but the apex of the primitive cone, 

 and the rounded anterior extremity has grown according to a law 

 precisely such as that which has produced the curved margin of 

 the dorsal valve in the Pteropod. - The ventral portion of the 

 original cone is nearly, but not wholly, wanting. It is represented 

 by the so-called posterior wall of the "siphuncular space." In 

 many decapod cuttle-fishes also (e.g. Todarodes, Illex, etc.) we 

 still see at the posterior end of the " pen," a vestige of the primitive 

 cone, whose dorsal margin only has continued to grow ; and the 

 same phenomenon, on an exaggerated scale, is represented in the 

 Belemnites. 



It is not at all impossible that we may explain on the same 

 lines the development of the curious "operculum" of the Ammon- 

 ites. This consists of a single horny plate {Anaptychus), or of 

 a thicker, more calcified plate divided into two symmetrical 

 halves {Aptychi), often found inside the terminal chamber of the 

 Ammonite, and occasionally to be seen lying in situ, as an 

 operculum which partially closes the mouth of the shell; this 

 structure is known to exist even in connection with the early 

 embryonic shell. In form the Anaptychus, or the pair of con- 

 joined Aptychi, shew an upper and a lower border, the latter 

 strongly convex, the former sometimes slightly concave, sometimes 

 slightly convex, and usually shewing a median projection or 

 slightly developed rostrum. From this "rostral" border the 

 curves of growth start, and course round parallel to, finally 

 constituting, the convex border. It is this convex border which 

 fits into the free margin of the mouth of the Ammonite's shell, 

 while the other is applied to and overlaps the preceding whorl of 

 the spire. Now this relationship is precisely what we should 

 expect, were we to imagine as our starting-point a shell similar 

 to that of Hyalaea, in which however the dorsal part of the spht 

 cone had become separate from the ventral half, had remained 

 11 at, and had grown comparatively slowly, while at the same time 

 it kept slipping forward over the growing and coifing spire into 

 which the ventral half of the original shell develops*. In short, 

 I think there is reason to believe, or at least to suspect, that we 



* The case of Terebratula or of Gryphaea would be closely analogous, if the 

 smaller valve were less closely connected and co-articulated with the larger. 



