XI] OF THE MOLLUSCAN SHELL 787 



ako, though somewhat roughly, be determined. For instance, in 

 Terebra dimidiata the apical angle was found to be 13°, the sutural 

 angle 109°, and so forth. 



It was at once obvious that, in such a shell as is represented in 

 Figs. 369 and 375 the entire outUne (always excepting that of 

 the immediate neighbourhood of the mouth) could be restored from 

 a broken fragment. For if we draw our tangents to the cone, it 

 follows from the symmetry of the figure that we can continue the 

 projection of the sutural hne, and so mark off the successive whorls, 

 by simply drawing a' series of consecutive parallels, and by then 

 filling into the quadrilaterals so marked off a series of curves similar 

 to one another, and to the whorls which are still intact in the broken 

 shell. But the use of the hehcometer soon shewed that it was 

 by no means universally the case that one and the same cone was 

 tangent to all the turbinate whorls; in other words, there was not 

 always one specific apical angle which held good for the entire 

 system. In the great majority of cases, it is true, the same tangent 

 touches all the whorls, and is a straight Hne. But in others, as in 

 the large Cerithium nodosum, such a hne is sKghtly concave to the 

 axis of the shell; and in the short spire of Doliumj for instance, 

 the concavity is marked, ^nd the apex of the spire is a distinct 

 cusp. On the other hand, in Pupa and Clausilia the conmion 

 tangent is convex to the axis of the shell. 



So also is it, as we shall presently see, among the Ammonites: 

 where there are some species in which the ratio of whorl to whorl 

 remains, to all appearance, perfectly constant; others in which 

 it gi^dually though only shghtly increases; and others again in 

 which it slightly and gradually falls away. It is obvious that, 

 among the manifold possibihties of growth, such conditions as 

 these are very easily conceivable. It is much more remarkable 

 that, among these shells, the relative velocities of growth in various 

 dimensions should be as constant as they are than that there 

 should be an occasional departure from perfect regularity. In these 

 latter cases the logarithmic law of growth is only approximately 

 true. The shell is no longer to be represented simply as a cone which 

 has been rolled up, but as a cone which (while rolling up) had grown 

 trumpet-shaped, or conversely whose mouth had narrowed in, and 

 which in longitudinal section is a curvilinear instead of a rectihnear 



