86o MECHANICS OF GROWTH. 



hibit torsions about their axis of growth ; the striations on the surface of the organ 

 are not parallel to its axis of growth, but run round it in the form of more or less 

 oblique spiral lines, as if the organ were fastened at one end, and then twisted at the 

 other. Torsions of this kind occur in the unicellular internodes of Nitella ; they are 

 common in the elongated multicellular internodes of the erect stems of Dicoty- 

 ledons, universal in climbing internodes ; the setae of Mosses are generally very 

 strongly twisted. Even in flat leaves, as Wichura has shown, torsions of the lamina 

 occur very commonly; they behave like strips of paper fastened at one end and 

 twisted by the other round their median line. These torsions are particularly con- 

 spicuous in the leaves of many Grasses, o^ Allium ursinum^ species oi Alstroemerta, 

 &c., causing the under side of the lamina to lie uppermost towards the apex^. 



Since the striae on a twisted organ run spirally round the axis, they must exceed 

 the axis in length ; if therefore the torsion is the result of growth, the growth of the 

 outer layers of cylindrical, conical, or prismatic organs (internodes, roots, &c.) must 

 be more rapid or must last longer than that of the inner layers ; and in twisted 

 leaves there must be the same difference as respects the growth of the mid-rib in 

 comparison to that of the margins. The fact that at the time of most rapid growth 

 the inner layers generally grow more rapidly than the outer ones (Sect. 13), thus 

 preventing the possibility of torsion, the additional fact that torsion does not gener- 

 ally take place until growth is ceasing, and lastly, the circumstance that etiolated 

 internodes, which in a normal state do not exhibit torsion, usually manifest this 

 phenomenon at the close of their growth, lead to the conclusion that torsion is the 

 result of growth continuing in the outer layers after it has ceased or begun to cease 

 in the inner layers. In twisted leaves, especially those oi Ahtroemeria, the torsion 

 however begins earlier. If the growth of the outer layers, besides being greater, 

 were also exactly parallel to the axis, and if the resistance to the strain thus caused 

 of the outer against the inner layers were exactly in the direction of the axis, there 

 would be no torsion, but only a longitudinal tension between them, which would 

 be directly opposed to the tension of the layers already described. It is however 

 evident that this would be possible only if all the parts were arranged with mathe- 

 matical precision ; but that any irregularity, however small, must give a lateral direc- 

 tion to the strain in the outer layers, and thus cause a torsion 2. 



Torsions are also very often the result of an increase in diameter or are made 

 more evident as the formation of wood advances, as is often seen in the bark of old 

 stems of Dicotyledons and Conifers, and more clearly in the oblique course of the 

 fibro-vascular bundles. It may be concluded with probability that the phenomenon 

 is the result of the small but powerful increase in length of the young wood-cells ; 

 if these did not increase at all in length no torsion would take place. 



^ [Similar torsions occur in petals as Cyclamen, fruits as Ailanthus malaharica, and not unfre- 

 quently in pedicels or inferior ovaries as Orchidese, causing the anterior part of the flower to become 

 apparently posterior, and vice versa.l 



^ This can easily be made clear to the student in the following way. If an india-rubber tube 

 is strongly stretched, and another tube only a little wider is drawn over it, and the first is then 

 released, it contracts and is then too short for the outer tube. If the two tubes were perfectly 

 uniform in structure in the longitudinal and transverse directions, the only result would be 

 a longitudinal tension ; but torsion takes place also because a transverse is combined with the 

 longitudinal tension. 



