torsion, than were those from which we evolved them; and this is a very curious physical or mathôÙeôÙmatôÙiôÙcal fact. So a cylinder, which is especially resistant to torsion, is very easily bent or flexed; while projecting ribs or angles, such as an engineer makes in a bar or pillar of iron for the purpose of greatly increasing its strength in the way of resistance to bending, actually make it much weaker than before (for the same amount of metal per unit length) in the way of resistance to torsion.
In the hop itself, and in a very considerable number of other twining and twisting stems, the ribbed or channelled form of the stem is a conspicuous feature. We may safely take it, (1) that {628} such stems are especially susceptible of torsion; and (2) that the effect of torsion will be to intensify any such peculiarities of sectional outline which they may possess, though not to initiate them in an originally cylindrical structure. In the leaf-climbers the case does not present itself, for there, as we have seen, torsion itself is not, or is very slightly, manifested. There are very distinct traces of the phenomenon in the horns of certain antelopes, but the reason why it is not a more conspicuous feature of the antelopeãs horn or of the ramãs is apparently a very simple one: namely, that the presence of the bony core within tends to check that deformation which is perpendicular, while it permits that which is parallel, to the axis of the horn.
Of Deerãs Antlers.
But let us return to our subject of the shapes of horns, and consider briefly our last class of these structures, namely the bony antlers of the various species of elk and deer10. The problems which these present to us are very different from those which we have had to do with in the antelope or the sheep.
With regard to its structure, it is plain that the bony antler corresponds, upon the whole, to the bony core of the antelopeãs horn; while in place of the hard horny sheath of the latter, we have the soft ãvelvet,ã which every season covers the new growing antler, and protects the large nutrient blood-vessels by help of which the antler grows11. The main difference lies in the fact that, in the one case, the bony core, imprisoned within its sheath, is rendered incapable of branching and incapable also of lateral expansion, and the whole horn is only permitted to grow in length, while retaining a sectional contour that is identical with (or but little altered from) that which it possesses at its growing base: {629} but in the antler, on the other hand, no such restraint is imposed, and the living, growing fabric of bone may expand into a broad flattened plate over which the blood-vessels run. In the immediate neighbourhood of the main blood-vessels growth will be most active; in the interspaces between, it may wholly fail: with the result that we may have great notches cut out of the flattened plate, or may at length find it reduced to the form of a simple branching structure. The main point, as it seems to me, is that the ãhornã is essentially an axial rod, while the ãantlerã is