838 THE EQUIANGULAR SPIRAL [ch. 



or suppose that it merely became so reduced in relative size as to 

 form no impediment to the continued growth of the ventral one; 

 the latter would continue to grow in the direction of its natural 

 curvature, and would end by forming a complete and coiled 

 logarithmic spiral. It would be precisely analogous to the spiral 

 shell of Nautilus, and, in regard to its ventral position, concave 

 towards the dorsal side, it would even deserve to be called directly 

 homologous with it. Suppose, on the other hand, that the ventral 

 valve were to be greatly reduced, and even to disappear, the dorsal 

 valve would then pursue its unopposed growth; and, were it to be 

 markedly curved, it would come to form a logarithmic spiral, concave 

 towards the ventral side, as is the case in the shell of Spirula*. 

 Were the dorsal valve to be destitute of any marked curvature (or 

 in other words, to have but a low spiral angle), it would form a 

 simple plate, as in the shells of Sepia or Loligo. Indeed, in the 

 shells of these latter, and especially in that of Sepia, we seem to 

 recognise a manifest resemblance to the dorsal plate of the Pteropod 

 shell, as we have it (e.g.) in Cleodora or Hyalaea ; the Httle " 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 ^nargin 

 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 Ammonites. 

 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 



* Cf. Owen, "These shells [Nautilus and Ammonites] are revolutely spiral or 

 coiled over the back of the animal, not involute like Spirula^': Palaeontology, 

 1861, p. 97; cf. Memoir cm the Pearly Nautilus, 4832; also P.Z.S. 1878, p. 95.5. 



