110 A First Study of Natural Selection in Clamilia laniinata 
apparently reached through practically its whole length, the section exposed will 
be very near indeed to that containing the real axis of the spire. Such a section 
will have the appearance shown in Fig. 1 ; and from it Ave can ascertain the 
elements which determine the " pitch " and certain other characters of the spire. 
The shell is of course essentially a tube, coiled round an axis so that the 
successive coils are in contact. The wall of the tube nearest to the axis forms the 
columella ; that remote from the axis forms the outer surface of the shell. Where 
the successive whorls are in contact, a double septum is formed, running from the 
columella to the outer surface of the shell. The line of contact of successive whorls 
along the outside of the shell describes what we will call the "peripheral spiral" ; 
the line of contact along the axial wall may be called the " coluniellar spiral*." If 
we know the pitch of these two spirals, and their distance apart at every point, we 
know the elements which determine all the important characters of the spire, 
except the " ventricosity," which is measured by the longitudinal curvature of the 
outer walls, for example by the convexity of the portion BDE in Fig. 1. 
A 
Fig. 1. 
Now in a median longitudinal section through the shell, the relations of any 
point on the peripheral spiral, such as B, Fig. 1, to the corresponding point on the 
C(^lumellar spiral, C, and to the apex of the shell A, are fully determined if we 
know the lengths of the sides of the triangle formed by joining the three points 
A, B and G. If such a triangle be supposed to revolve round the columella, the 
length of each side changing as it revolves, while the angle A remains always 
I have deliberately used the word "spiral" to describe a curve in three-dimensional space, which 
mathematicians would call a " helix," in order to use a term which may be applied to pulmonates 
generally, without the inconvenience which would result from speaking for example of the " helix " 
of Helix ui<pcrsa. 
