GEOMETRY OF SHELLS.
There is a mechanical uniformity observable in the description of shells of the same species which at once suggests the probability that the generating figure of each increases, and that the spiral chamber of each expands itself, according to some simple geometrical law common to all. To the determination of this law the operculum lends itself, in certain classes of shells, with remarkable facility. Continually enlarged by the animal, as the construction of its shell advances so as to fill up its mouth, the operculum measures the progressive widening of the spiral chamber by the progressive stages of its growth.
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The animal, as he advances in the construction of his shell, increases continually his operculum, so as to adjust it to his mouth. He increases it, however, not by additions made at the same time all round its margin, but by additions made only on one side of it at once. One edge of the operculum thus remains unaltered as it is advanced into each new position, and placed in a newly-formed section of the chamber similar to the last but greater than it.
That the same edge which fitted a portion of the first less section should be capable of adjustment so as to fit a portion of the next similar but greater section, supposes a geometrical provision in the curved form of the chamber of great complication and difficulty. But God hath bestowed upon this humble architect the practical skill of the learned geometrician; and he makes this provision with admirable precision in that curvature of the logarithmic spiral which he gives to the section of the shell. This curvature obtaining, he has only to turn his operculum slightly round in its own place, as he advances it into each newly-formed portion of his chamber, to adapt one margin of it to a new and larger surface and a different curvature, leaving the space to be filled up by increasing the operculum wholly on the outer margin.
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Why the Mollusks, who inhabit turbinated and discoid shells, should, in the progressive increase of their spiral dwellings, affect the peculiar law of the logarithmic spiral, is easily to be understood. Providence has subjected the instinct which shapes out each to a rigid uniformity of operation.—Professor Mosely: Philos. Trans. 1838.