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nydus/On Growth and FormPublic
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CHAPTER XI THE LOGARITHMIC SPIRAL

traces on the surface of the operculum {522} (Fig. 264, 1), which traces have the form of curved lines in Turbo, and of straight lines in (e.g.) Nerita (Fig. 264, 2); that is to say, apart from the side constituting the outer edge of the operculum (which side is always and of necessity curved) the successive increments constitute curvilinear triangles in the one case, and rectilinear triangles in the other. The sides of these triangles are tangents to the spiral line of the operculum, and may be supposed to generate it by their consecutive intersections.

Two geometric diagrams showing logarithmic spirals radiating from a central point P, illustrating shell growth patterns.

In a number of such opercula, Moseley measured the breadths of the successive whorls along a radius vector14, just in the same way as he did with the entire shell in the foregoing cases; and here is one example of his results.

Operculum of Turbo sp.; breadth (in inches) of successive whorls, measured from the pole.
DistanceRatioDistanceRatioDistanceRatioDistanceRatio
ôñ24ôñ16ôñ2〇ôñ18
2ôñ282ôñ312ôñ302ôñ30
ôñ55ôñ37ôñ6〇ôñ42
2ôñ322ôñ302ôñ302ôñ24
1ôñ28ôñ851ôñ38ôñ94

The ratio is apôÙproxôÙiôÙmateôÙly constant, and this spiral also is, therefore, a logarithmic spiral.

545