logarithmic spiral (though it is one of small angle) gives its own character to the structure, and causes the little carapace to partake of the charôÙacôÙterôÙisôÙtic conformation of the molluscan shell.
The essential simplicity, as well as the great regularity of the ãcurves of growthã which result in the familiar conôÙfiôÙgurôÙaôÙtions of our bivalve shells, sufficiently explain, in a general way, the ease with which they may be imitated, as for instance in the so-called ãartificial shellsã which Kappers has produced from the conchoidal form and lamination of lumps of melted and quickly cooled paraffin32.
In the above account of the mathôÙeôÙmatôÙiôÙcal form of the bivalve shell, we have supposed, for simplicityãs sake, that the pole or origin of the system is at a point where all the successive curves touch one another. But such an arrangement is neither theoretically probable, nor is it actually the case; for it would mean that in a certain direction growth fell, not merely to a minimum, but to zero. As a matter of fact, the centre of the system (the ãumboã of the conchologists) lies not at the edge of the system, but very near to it; in other words, there is a certain amount of growth all round. But to take account of this condition would involve more troublesome mathematics, and it is obvious that the foregoing illustrations are a sufficiently near approximation to the actual case. {567}
Among the bivalves the spiral angle (öÝ) is very small in the flattened shells, such as Orthis, Lingula or Anomia. It is larger, as a rule, in the Lamellibranchs than in the Brachiopods, but in the latter it is of considerable magnitude among the Pentameri. Among the Lamellibranchs it is largest in such forms as Isocardia and Diceras, and in the very curious genus Caprinella; in all of these last-named genera its magnitude leads to the production of