272 M. WICHURA ON THE WINDING OF LEAVES. 



sented in figure 3, may serve as an example. If we draw a 

 straight line from the extreme point of this to its stalk, it will 

 cut through the substance of the leaf in its whole course. The 

 parts of the fruit lying in this direction consequently form a 

 straight line and consequently the fixed axis, around which the 

 halves on the right and left appear wound in the shape of a screw. 

 But if, on the contrary, the axis of the helix which the leaf 

 describes lies outside the latter, all parts of the leaf share in the 

 heliacal winding, and the leaf then resembles a band wound in 

 a heliacal direction round an invisible cylinder or cone, where 

 one side of the band is always turned towards the said cylinder 

 or cone. The axis of the heliacal winding in this case coincides 

 with that of the imaginary cylinder or cone. Leaves of this kind 

 occur much more frequently than the others. Some examples 

 are represented in figures 8 & 9. 



§ 20. 



The angle of inclination of the heliacal winding, i, e. the angle 

 formed when a line is drawn through the helix parallel to its axis, is 

 in many leaves so small as to be imperceptible, for example in the 

 "aestivatio contorta;" in others it rises, judging from simple 

 inspection, which indeed leaves a wide field for error, to 30°, 40°, 

 or even 45°. It therefore falls short of 90°, the highest degree 

 mathematically possible, which would flatten the helix into a 

 plane. 



§21. 



Lastly, the length of the helix is dependent on the length of 

 the leaf, or when only a part of this winds, on the length of 

 this portion. 



§22. 



The sum of all these elements of the heHx gives the number of 

 revolutions. The magnitude of the angle of inclination and the 

 length of the helix stand in direct, and its distance from the axis 

 in inverse, proportion thereto. The greater the angle of inclination 

 and the longer the helix, the higher the number ; the greater the 

 distance of the helix from the axis, the smaller the number of re- 

 volutions. Under otherwise like circumstances a broad leaf can 

 never complete so many revolutions as a narrow one, because the 



