similar to St Venantãs diagram of the cross-section of a twisted triangular prism; and this is especially the case in the neighbourhood of the sharp angle of our prismatic section. That in parts the diagram is somewhat asymmetrical is not to be wondered at: and (apart from inaccuracies due to the somewhat rough means by which it was made) this asymmetry can be sufficiently accounted for by anisotropy of the material, by inequalities in thickness of different parts of the horny sheath, and especially (I think) by unequal distributions of rigidity due to the presence of the smaller corrugations of the {624} horn. It is apparently on account of these minor corrugations that, in such horns as the Highland ramãs, where they are strongly marked, the main St Venant effect is not nearly so well shewn as in the smoother horns such as those of O. Ammon and its immediate congeners6.
A further Note upon Torsion.
The phenomenon of torsion, to which we have been thus introduced, opens up many wide questions in connection with form. Some of the associated phenomena are admirably illustrated in the case of climbing plants; but we can only deal with these still more briefly and parenthetically.
The subject of climbing plants has been elaborately dealt with not only in Darwinãs books7, but also by a very large number of earlier and later writers. In ãtwiningã plants, which constitute the greater number of ãclimbers,ã the essential phenomenon is a tendency of the growing shoot to revolve about a vertical axisãa tendency long ago discussed and investigated by such writers as Palm, H. von Mohl and Dutrochet8. This tendency to revolutionããcircumvolution,ã as Darwin calls it, ãrevolving nutation,ã as Sachs puts itãis very closely comparable to the process by which an antelopeãs horn (such as the koodooãs) grows into its spiral or rather helicoid form; and it is simply due, in like manner, to inequalities in the rate of growth on different sides of the growing stem. There is only this difference between the two cases, that in the antelopeãs horn the zone of active growth is confined to the base of the horn, while in the climbing stem the same phenomenon is at work throughout the whole length of the growing structure. This growth is in the main due to ãturgescence,ã that is to the extension, or elongation, of ready-formed cells through the imbibition of water; it is a phenomenon due to osmotic pressure. The particular stimuli to which these movements (that is to say, these inequalities of growth) have been {625} ascribed, such as contact (thigmotaxis), exposure to light (heliotropism), and so forth, need not be discussed here9.
A simple stem growing upright in the dark, or in uniformly diffused light, would be in a position of equiôÙlibôÙrium to a field of force radially symmetrical about its vertical axis. But this complete radial symmetry will not often occur; and the radial anomalies may be such as arise intrinsically from structural peculiarities in the stem itself, or externally to it by reason of unequal illumination or through various other localised forces. The essential fact, so far as we are concerned, is that in twining plants we have a very marked tendency to inequalities in longitudinal growth on different aspects of the stemãa tendency which is but an exaggerated manifestation of one which is more or less present, under certain conditions, in all plants whatsoever. Just as in the case of the ruminantsã horns so we find here, that this inequality may be, so to speak, positive or negative, the maximum lying to the one side or the other of the twining stem; and so it comes to pass that some climbers twine to the one side and some to the other: the hop and the honeysuckle following the sun, and the field-convolvulus twining in the reverse direction; there are also some, like the woody nightshade (Solanum Dulcamara) which twine indifferently either way.
Together with this circumnutatory movement, there is very generally to be seen an actual torsion of the twining stemãa twist, that is to say, about its own axis; and Mohl made the curious observation, confirmed