M. WICHURA ON THE WINDING OF LEAVES. 307 



remains over, and draws the leaf downward from the point where 

 the revolution of the axis takes place. The results are various, 

 according as the leaf is strong enough to oppose a resistance to 

 the pressure burdening it, or not. In the former case the re- 

 volution of the axis is limited to the degree admitted by the 

 extensibility of the fibre, which is so slight that the movement 

 of winding possible under such conditions will remain almost 

 invisible to our eyes. But if the leaf gives, and curves, there 

 arises, as we have seen above, § 30, from the combination of 

 revolution of the axis and curvature, a new movement, which is 

 very essentially distinguished from mere revolution of the axis, 

 insomuch that now all parts of the leaf, its axis included, take 

 share in the heliacal winding around an ideal axis lying outside 

 the substance of the leaf. The contrast which appears between 

 axis and margins in a leaf wound round its own axis, is com- 

 pletely removed, and it no longer requires a predominating 

 longitudinal development of the lateral parts of the leaf to render 

 the heliacal winding possible. In this way the obstacles opposed 

 to revolution of the axis are removed by the curvature of the 

 leaf, after the revolution of the leaf having itself previously pro- 

 duced the curvature. The two movements then act as reciprocal 

 causes, and the result is that revolution of the axis and curvature 

 of the leaf are mostly combined ; winding leaves not curled are, 

 on the contrary, very rare. 



§ 128. 



At the same time it is true, that in the curled winding leaf, 

 two other contrasts, likewise accompanied by an unequal tension 

 in the substance of the leaf, present themselves in the place of 

 the contrast between the axis and margins of the leaf, removed 

 by the curvature. Under supposed equal longitudinal develop- 

 ment of both surfaces of the leaf, in the first place, the surface 

 turned outwards must be rendered more tense, since it describes 

 a larger arc, than the surface turned to the interior of the helix, 

 and this in the greater proportion as the leaf is thicker. Se- 

 condly, from mechanical causes which it would occupy too much 

 space to discuss here, one margin of the leaf, — namely in left- 

 wound leaves with the upper face turned inwards, and in right- 

 wound leaves with the lower surface turned inwards, the right 



20* 



