The very numerous examples of spiral conformation which we meet with in our studies of organic form are peculiarly adapted to mathôÙeôÙmatôÙiôÙcal methods of inôÙvesôÙtiôÙgaôÙtion. But ere we begin to study them, we must take care to define our terms, and we had better also attempt some rough preliminary clasôÙsiôÙfiôÙcaôÙtion of the objects with which we shall have to deal.
In general terms, a Spiral Curve is a line which, starting from a point of origin, continually diminishes in curvature as it recedes from that point; or, in other words, whose radius of curvature continually increases. This definition is wide enough to include a number of different curves, but on the other hand it excludes at least one which in popular speech we are apt to confuse with a true spiral. This latter curve is the simple Screw, or cylindrical Helix, which curve, as is very evident, neither starts from a definite origin, nor varies in its curvature as it proceeds. The ãspiralã thickening of a woody plant-cell, the ãspiralã thread within an insectãs tracheal tube, or the ãspiralã twist and twine of a climbing stem are not, mathôÙeôÙmatôÙiôÙcally speaking, spirals at all, but screws or helices. They belong to a distinct, though by no means very remote, family of curves. Some of these helical forms we have just now treated of, briefly and parenthetically, under the subject of Geodetics.
Of true organic spirals we have no lackÿ£¢1. We think at once of the beautiful spiral curves of the horns of ruminants, and of the still more varied, if not more beautiful, spirals of molluscan shells. Closely related spirals may be traced in the arrangement {494} of the florets in the sunflower; a true spiral, though not, by the way, so easy of inôÙvesôÙtiôÙgaôÙtion, is presented to us by the outline of a cordate leaf; and yet again, we can recognise typical though transitory