184 
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 the two angles, viz., the 
angle of the spiral and the angle of retardation of the inner 
edge.” . 
Fifthly.—The presence or absence of the Aptychus 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 Phylloceras, Lytoceras, Arcestes, 
Trachyceras ; at all events it has not yet been found in some 
of these. It is present as a horny undivided body in Arie- 
tites, Aegoceras, 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 punctated externally 
in Simoceras and Aspidoceras, and greatly resembles the large 
flat grinding teeth of certain genera of fishes from the Car- 
boniferous 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 plate, 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 lamine, which in some forms has a porous structure 
with 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 Anaptychi of the Lias formation. When found undis- 
turbed they occupy the lateral wall about the middle of the 
dwelling-chamber, having their base in general turned towards 
the mouth, as seen in figs. 1 and 38. The Solenhofen Litho- 
graphic Limestones contain several species of Ammonites, with 
