one another within that plane, they also tend to diverge by successive equal angles from that plane of reference; and by this means, there will be superposed upon the logarithmic spiral a helicoid twist or screw. And, in the particular case where this latter angle of divergence is just equal to 180ô¯, or two right angles, the successive shoots will once more come to lie in a plane, but they will appear to come off from one another on alternate sides, as in Fig. 243ã₤A. This is the Schraubel or Bostryx of Schimper, the cyme unipare hûˋlicoide of Bravais. The logarithmic spiral is still latent in it, as in the other; but is concealed from view by the deformation resulting from the helicoid. The confusion of nomenclature would seem to have arisen from the fact that many botanists did not recognise (as the brothers Bravais did) the mathôÙeôÙmatôÙiôÙcal significance of the latter case; but were led, by the snail-like spiral of the scorpioid cyme, to transfer the name ãhelicoidã to it.
In the study of such curves as these, then, we speak of the point of origin as the pole (O); a straight line having its extremity in the pole and revolving about it, is called the radius vector; {503} and a point (P) which is conceived as travelling along the radius vector under definite conditions of velocity, will then describe our spiral curve.
Of several mathôÙeôÙmatôÙiôÙcal curves whose form and development may be so conceived, the two most important (and the only two with which we need deal), are those which are known as (1) the equable spiral, or spiral of Archimedes, and (2) the logarithmic, or equiangular spiral.
The former may be illustrated by the spiral coil in which a sailor coils a rope upon the deck; as the rope is of