626 THE SHAPES OF HORNS [ch. 



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 un- 

 necessary. 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 rule, 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 com- 

 ponent 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 



