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CHAPTER XI THE LOGARITHMIC SPIRAL

very fact of its being a spiral soon ceases to be apparent (Figs. 271, 272). Suppose one whorl to be an inch in breadth, then, if the angle of the spiral were 80ô¯, the {535} next whorl would (as we have just seen) be about three inches broad; if it were 70ô¯, the next whorl would be nearly ten inches, and if it were 60ô¯, the next whorl would be nearly four feet broad. If the angle were 28ô¯, the next whorl would be a mile and a half in breadth; and if it were 17ô¯, the next would be some 15,000 miles broad.

A mathematical figure showing two logarithmic spirals originating from a common pole, labeled 60° and 50°.

In other words, the spiral shells of gentle curvature, or of small constant angle, such as Dentalium or Nodosaria, are true logarithmic spirals, just as are those of Nautilus or Rotalia: from which they differ only in degree, in the magnitude of an angular constant. But this diminished magnitude of the angle causes

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