890 THE SHAPES OF HORNS [ch. 



principle that a much twisted rope is stiffer than a slackly twisted 

 one), and is thus indirectly benefited so as to be able to pass over 

 inequalities in its spiral ascent, and to carry its own weight when 

 allowed to revolve freely." The mechanical explanation would 

 appear to be very simple, and such as to render the teleological 

 hypothesis unnecessary. In the case of the roughened support, 

 there is a temporary adhesion or "clinging" between it and the 

 growing stem which twines around it; and a system of forces is 

 thus set up, producing a "couple," just as it was in the case of the 

 ram's or antelope's horn through direct adhesion of the bony core 

 to the surrounding sheath. The twist is the direct result of this 

 couple, and it disappears when the support is so smooth that no 

 such force comes to be exerted. 



Another important class of climbers includes the so-called "leaf- 

 climbers." In these, some portion of the leaf, generally the petiole, 

 sometimes (as' in the fumitory) the elongated midrib, curls round 

 a support; and a phenomenon of like nature occurs in many, though 

 not all, of the so-called "tendril-bearers." Except that a different 

 part of the plant, leaf or tendril instead of stem, is concerned in the 

 twining process, the phenomenon here is strictly analogous to our 

 former case ; but in the resulting helix there is, as a rul^, this obvious 

 difference, that, while the twining stem, for instance of the hop, 

 makes a slow revolution about its support, the typical leaf-climber 

 makes a close, firm coil: the axis of the latter is nearly perpendicular 

 and parallel to the axis of its support, while in the twining stem the 

 angle between the two axes is comparatively small. Mathematically 

 speaking, the difference merely amounts to this, that the component 

 in the direction of the vertical axis is large in the one case, and the 

 corresponding component is small, if not absent, in the other; in 

 other words, we have in the climbing stem a considerable vertical 

 component, due to its own tendency to grow in height, while this 

 longitudinal or vertical extension of the whole system is not apparent, 

 or little apparent, in the other cases. But from the fact that the 

 twining stem tends to run obliquely to its support, and the coiling 

 petiole of the leaf-climber tends to run transversely to the axis of 

 its support, there immediately follows this marked difference, that 

 the phenomenon of torsion, so manifest in the former case, will be 

 absent in the latter. 



