DZSTRIBCTION OF THE GREEN LEAVES ON THE STEM. 407 



from the first by the circumference, in consequence of the torsion of the 

 stem, d 1S placed about t the circumference (60); that is to say, exactly so 

 tha lt now separated from the first by half the circumference (180' S 

 pabular alteratum can be very well seen in the developing branch s of beeches 

 hornbeams hasels, and many other trees and shrubs. In the buds the leaves ha"e" 

 a one-third Arrangement, in the fully formed, now woody branches the phyllotaxil 

 appears to be one-half. Since, as a rule, amongst buds, the simplest cases f espec Tally 



Fig. 102. Displacement of the leaf-positions in consequence of torsion of the stem. 

 Transformation of the one-third into the two-fifths phyllotaxis. Dot 2 is displaced by torsion to 2'; dot S to V, Ac. 



the one-third arrangement, are most frequently observed, it appears probable that 

 the number of original phyllotaxes is really only very small, and that complicated 

 leaf arrangements, which are represented by fractions whose numerator consists of 

 two figures, frequently are produced by torsion of the individual parts of the stem 

 during their growth. It still remains to point out here that the phyllotaxis becomes 

 the more complicated, the less the amount of torsion undergone by an internode, which 

 is, indeed, evident from the preceding representation. It is also worthy of note, that 

 in plants whose foliage-leaves originate 2, 3, or more together at the same height on 

 the stem (which therefore possess whorled leaves), such torsions of the inter-nodes, 

 and alterations of the phyllotaxis dependent upon them, very frequently occur. 



