vary, within the limits of a genus, from somewhere about 35ô¯ to somewhere about 125ô¯.
The angle of retardation (öý) is very small in Dentalium and Patella; it is very large in Haliotis. It becomes infinite in Argonauta and in Cypraea. Connected with the angle of retardation are the various possibilities of contact or separation, in various degrees, between adjacent whorls in the discoid, and between both adjacent and opposite whorls in the turbinated shell. But with these phenomena we have already dealt sufficiently.
Of Bivalve Shells.
Hitherto we have dealt only with univalve shells, and it is in these that all the mathôÙeôÙmatôÙiôÙcal problems connected with the spiral, or helico-spiral, are best illustrated. But the case of the bivalve shell, of Lamellibranchs or of Brachiopods, presents no essential difference, save only that we have here to do with two conjugate spirals, whose two axes have a definite relation to one another, and some freedom of rotatory movement relatively to one another.
The generating curve is particularly well seen in the bivalve, where it simply constitutes what we call ãthe outline of the shell.ã It is for the most part a plane curve, but not always; for there are forms, such as Hippopus, Tridacna and many Cockles, or Rhynchonella and Spirifer among the Brachiopods, in which the edges of the two valves interlock, and others, such as Pholas, Mya, etc., where in part they fail to meet. In such cases as these the generating curves are conjugate, having a similar relation, but of opposite sign, to a median plane of reference. A great variety of form is exhibited by these generating curves among the bivalves. In a good many cases the curve is apôÙproxôÙiôÙmateôÙly circular, as in Anomia, Cyclas, Artemis, Isocardia; it is nearly semi-circular in Argiope. It is apôÙproxôÙiôÙmateôÙly elliptical in Orthis and in Anodon; it may be called semi-elliptical in Spirifer. It is