= ees tS 
183 
the various turns of the shell or the whorls, as they are called, 
in general cover to a greater or less extent the preceding whorl ; 
this is called the amount of involution of the whorls, a feature 
in the diagnosis of the shell which requires consideration when 
taken in connection with the other features I have described, 
as the extent of the involution is found to be generally the 
same in the different species of different groups. Some shells, 
for example, as those of Lytoceras (fig. 27), are only slightly 
involute; and others, like Arietites (fig. 12), have a wide 
umbilicus, with their inner whorls largely exposed; in others, 
as Amaltheus and Harpoceras, the whorls are much covered by 
the preceding whorl; in some species of Phylloceras they are 
entirely enveloped ; and in others the umbilicus is completely 
closed. This character, the amount of whorl involution, appears 
to depend on the angle at which the shell bends round in the 
process of growth, and as it appears to be a very constant 
feature, it is of value in forming a diagnosis of generic charac- 
ters. On this subject the Rev. J. F. Brake observes,* “If we 
take any fixed point in relation to the shell—say, a point in 
its surface or in the centre of its apertures—that point will 
describe a curve with the growth of the shell; and if this 
curve be projected on a plane, it nearly forms the well-known 
equiangular spiral.’ Not exactly, however, because the 
growth does not begin from a point, as it should, but from the 
circumference of the embryo; and it has, therefore, been 
proposed by Mr. Naumann to call it a ‘concho-spiral.’ Taking, 
however, the former curve as an approximation to the form 
produced, we know 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, there- 
fore, inan Ammonite which is coiled on one plane it is necessary 
to go back an exact revolution of 360° to reach the part of the 
* “The Yorkshire Lias,” p. 262. 
