similar quadrilaterals. And, when we consider the quadrilateral AEDB as having infinitesimal sides, AE and BD , the angle ö° tends to öÝ, the constant angle of an equiangular spiral which passes through the points AEG , and of a similar spiral which passes through the points BDF ; and the point C is the pole of both of these spirals. In a particular limiting case, when our quadrilaterals are all equal as well as similar,ãwhich will be the case when the angle ö° (or the angles EAC , etc.) is a {502} right angle,ãthe ãspiralã curve will be a circular arc, C being the centre of the circle.
Another, and a very simple illustration may be drawn from the ãcymose inflorescencesã of the botanists, though the actual mode of development of some of these structures is open to dispute, and their nomenclature is involved in extraordinary historical confusion2.
In Fig. 243B (which represents the Cicinnus of Schimper, or cyme unipare scorpioide of Bravais, as seen in the Borage), we begin with a primary shoot from which is given off, at a certain definite angle, a secondary shoot: and from that in turn, on the same side and at the same angle, another shoot, and so on. The deflection, or curvature, is continuous and progressive, for it is caused by no external force but only by causes intrinsic in the system. And the whole system is symmetrical: the angles at which the successive shoots are given off being all equal, and the lengths of the shoots diminishing in constant ratio. The result is that the successive shoots, or successive increments of growth, are tangents to a curve, and this curve is a true logarithmic spiral. But while, in this simple case, the successive shoots are depicted as lying in a plane, it may also happen that, in addition to their successive angular divergence from