The method by which we have hitherto arranged the univalve shells of our cabinets rests upon a foundation of convenience rather than of Nature. Linnaeus, whose Systema Naturæ has governed our classifications these twenty years past, proposed a division based upon the form of the aperture — a scheme elegant in its simplicity, yet one that fails to account for the deeper geometry of the shell itself. I do not write to dismiss his labours, but to suggest that the spiral, not the mouth, ought to be our first consideration.
The Spiral as First Principle
I spent the greater part of last winter at the cabinet of a private collector in Kensington, examining some three hundred specimens of the genus Turbo with compass and rule. What I discovered there has convinced me that the logarithmic spiral — that curve which Descartes described in his correspondence with Mersenne, and which Bernoulli admired to the point of requesting it engraved upon his tombstone — constitutes the true ordering principle of the turbinidæ.