a nearly rectilinear {562} triangle in Lithocardium, and a curvilinear triangle in Mactra. Many apparently diverse but more or less related forms may be shewn to be deformations of a common type, by a simple application of the mathôÙeôÙmatôÙiôÙcal theory of ãTransformations,ã which we shall have to study in a later chapter. In such a series as is furnished, for instance, by Gervillea, Perna, Avicula, Modiola, Mytilus, etc., a ãsimple shearã accounts for most, if not all, of the apparent differences.
Upon the surface of the bivalve shell we usually see with great clearness the ãlines of growthã which represent the successive margins of the shell, or in other words the successive positions assumed during growth by the growing generating curve; and we have a good illustration, accordingly, of how it is charôÙacôÙterôÙisôÙtic of the generating curve that it should constantly increase, while never altering its geometric similarity.
Underlying these ãlines of growth,ã which are so charôÙacôÙterôÙisôÙtic of a molluscan shell (and of not a few other organic formations), there is, then, a ãlaw of growthã which we may attempt to enquire into and which may be illustrated in various ways. The simplest cases are those in which we can study the lines of growth on a more or less flattened shell, such as the one valve of an oyster, a Pecten or a Tellina, or some such bivalve mollusc. Here around an origin, the so-called ãumboã of the shell, we have a series of curves, sometimes nearly circular, sometimes elliptical, and often asymmetrical; and such curves are obviously not ãconcentric,ã though we are often apt to call them so, but are always ãco-axial.ã This manner of arrangement may be illustrated by various analogies. We might for instance compare it to a series of waves, radiating outwards from a point, through a medium which offered a resistance increasing, with the angle of divergence, according