turns of the spiral will depend, not only on the length of the spicule, but on the relative dimensions of the ellipsoidal cell, as well as upon the angle by which the spicule is inclined to the ellipsoid axes; but a very common case will probably be that in which the spicule looks at first sight to be {442} a plane C-shaped figure, but is discovered, on more careful inspection, to lie not in one plane but in a more complicated spiral twist.
This inôÙvesôÙtiôÙgaôÙtion includes a series of forms which are abundantly represented among actual sponge-spicules, as illustrated in
Figs. 211 and 212. If the spicule be not restricted to linear growth, but have a tendency to expand, or to branch out from a main axis, we shall obtain a series of more complex figures, all related to the geodetic system of curves. A very simple case will arise where the spicule occupies, in the first instance, the axis of the containing cell, and then, on reaching its boundary, tends to branch or spread outwards. We shall now get various figures, in some of which the spicule will appear as an axis expanding into a disc or wheel at either end; and in other cases, the