MODERN CLASSIFICATION. 229 



Mr. Naumann to call it a ' concho-spiral.' Taking, however, the former curve as an 

 approximation to the form produced, vi^e knovp that this depends for its shape entirely on 

 the angle at which it is bent ; and this depends on the law of the growth of the shell. 

 Now, since this law is the same for all the parts of the shell, it follows that the curve 

 described by every point in the same plane is the same, only representing earlier or later 

 portions of one and the same curve. If, therefore, in an Ammonite which is coiled on 

 one plane it is necessary to go back an exact revolution of 360° to reach the part of the 

 curve corresponding to the inner edge of the whorl, it is plain that this will be just in 

 contact with the outside of the preceding whorl, which is an exact revolution behind. 

 If we must go back further the inner edge of the last whorl will lie within the outer edge 

 of the preceding, or the shell will be more or less involute ; if, on the contrary, we have 

 to go back less, it will be uncoiled. The shape, then, of any shell coiled in one plane 

 depends on the magnitude of two angles, viz. the angle of the spiral and the angle of 

 retardation of the inner edge." 



Mfthly. — The absence or presence of the AjJtijchus is the fifth character in the 

 anatomy of the shell which requires our consideration. In several extensive groups the 

 Aptychus is supposed to be absent, as in Phylloceras, Lytoceras, Arcestes, TracUyceras ; at 

 all events it has not yet been found in these. It is present as a horny undivided 

 body in Arietites, Aeyoceras, and Amaltheus. It is divided or bivalved and calcareous in 

 Harpoceras, Oppelia, and Haploceras. It is thin, bivalved, and granulated externally in 

 Stephanoceras, Perisphinctes, and Cosmoceras. It is thick, smooth, and pmictated exter- 

 nally in Simoceras and Aspidoceras, and greatly resembles the large flat grinding teeth 

 of certain genera of fishes from the Carboniferous Limestone ; these thick calcareous 

 Aptychi consist of two layers, an inner and outer. The inner alone exhibits lines of growth 

 concentric with the angle of each plaJte, which is situated on that side of its broad end 

 which is applied to its fellow of the opposite side. The outer layer is composed of many 

 laminae, which in some forms have a porous structure and a punctated and polished 

 surface; there is a remarkable contrast between the thick porous Aptychi of the 

 Kimmeridgian Clay, and Upper Jurassic rocks of Germany, and the thin shelly Aptychi 

 of the Ammonites from the Inferior Oolite, or the horny Anapfychi of the Lias 

 formation. When found undisturbed they occupy the lateral wall about the middle 

 of the body-chamber, having their base in general turned towards the mouth, as 

 seen in figs. 97 and 99. The Solenhofen Lithographic Limestones contain several 

 species of Ammonites with the body-chamber, mouth border and lateral processes of 

 the shell all complete, and in these specimens the relative position of the Aptychi agrees 

 with what I have stated. 



Having described in detail the five characters upon which palaeontologists have based 

 the diagnosis of genera, I now proceed to give the classification proposed by Dr. W. 

 Waagen, as it exhibits, in an analytical form, the results of modern investigations on 

 the different groups of the Ammonitidae. 



