M. WICHURA ON THE WINDING OF LEAVES. 275 



VI. Mechanical Constituents of the Movement : Revolution round 

 the Axis and Curvature, 



§29. 



The movement of winding is in all cases founded on a revolu- 

 tion of the leaf around the straight line which may be imagined 

 to pass from the point to the middle of its base. I call this the 

 axis of the leaf, to distinguish it from the axis of the helix, which, 

 as we have seen, may lie outside the substance of the leaf. This 

 revolution round the axis, with the resistance, increasing from 

 the freely moveable point down to the fixed base of the leaf, 

 which is opposed to it within the parts of the leaf itself, causes 

 a change in the relation of the direction of the parts of the leaf 

 to one another. Under its influence, the substance of the leaf, 

 originally expanded in a rectilinear plane, becomes converted 

 into a body wound in the form of a helix, within which only the 

 median line of the leaf, as the fixed axis around which the two 

 laterally situated halves revolve, retains its original position. 

 The forms of twisted leaves mentioned in § 19, in which the axis 

 of the heliacal winding coincides with the axis of the leaf, are 

 consequently fully explained by the mere assumption of a re- 

 volution of the leaf round the axis. 



§30. 



Very frequently a curvature of the leaf is added to the revolu- 

 tion round the axis. Then a mixed movement is produced, 

 whence result the heliacally wound leaves with the axis of the 

 helix lying outside the leaf. That it is so may be strictly proved 

 mathematically by the aid of analysis. But a conviction of the 

 importance of the explanation given may be also readily obtained 

 in the empirical way, by holding a riband-shaped piece of wax 

 by one end, and twisting it around its long axis while curving it 

 at the same time toward one of its flat surfaces. In this way 

 are produced heliacal bands which agree in all essential points 

 with the forms of leaf represented in figures 8 and 9. 



18* 



