the spiral to dilate with such immense rapidity that, so to speak, ãit never comes roundã; and so, in such a shell as Dentalium, we never see but a small portion of the initial whorl.
We might perhaps be inclined to suppose that, in such a shell as Dentalium, the lack of a visible spiral convolution was only due to our seeing but a small portion of the curve, at a distance from the pole, and when, therefore, its {536} curvature had already greatly diminished. That is to say we might suppose that, however small the angle a, and however rapidly the whorls accordingly increased, there would nevertheless be a manifest spiral convolution in the immediate neighbourhood of the pole, as the starting point of the curve. But it may be shewn that this is not so.
For, taking the formula
this, for any given spiral, is equivalent to aöçÿ£¢kö¡ã₤.
Therefore
or,