TORSION. 771 



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 

 direction to the strain in the outer layers, and thus cause a torsion \ 



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. 



The examples of torsion we have been considering so far are produced solely 

 by internal causes ; the direction in which the striae run round the axis is usually 

 constant in the same species ; but other instances of torsion frequently occur which 

 result from external and accidental circumstances. It is evident that when any 

 weight is attached to the side of an organ growing in a horizontal or oblique 

 direction, such as an internode, leaf, or tendril, the tendency will be to produce a 

 twisting of the organ round its axis. If the organ which is twisted in this manner is 

 very elastic, the torsion will disappear when the weight is removed ; but if it is only 

 very imperfectly elastic, the torsion will remain permanently, as in a twisted thread 

 of wax ; and this will be the case if the organ is in a growing state. This does 

 in fact occur in growing internodcs, petioles, the mid-ribs of leaves, &c. If an 

 organ of this kind is laid horizontally in wet sand, after a pin slightly weighted on 

 one side, as by a drop of sealing-wax, has been passed horizontally through its 

 summit, the small twisting force is sufficient, as de Vries has shown, to cause a 

 permanent torsion in the growing part. The same result will of course ensue if a 

 leaf or branch instead of a pin is attached to the side of the organ. Branches which 

 grow horizontally and bear decussate pairs of leaves usually exhibit alternate tor- 

 sions of their internodes to the right and left, so that the leaves all stand in two 

 rows along the branch instead of four. De Vries has shown that this is occasioned 

 by the unequal twisting force of the leaves of each pair. If the young leaves 

 are cut away no torsion results ; if only one of each pair is removed, the torsion is 

 determined by the weight of the remaining leaf. 



Torsions of this kind also occur frequently when leafy shoots rise in consequence 

 of geotropism from a horizontal position, and are caused by the unequal distribution 

 of the weight of the leaves, and by their various geotropic and heliotropic curvatures 

 twisting the stem as it becomes erect. Very clear instances are furnished by long 

 petioles as those of Cucurbita, when the branch from which they spring is fixed in 



^ 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 ; hut torsion takes place also because a transverse is combined with the longitudinal 

 tension. 



3 D 2 



