PHYLLOTAXIS OR LEAF- ARRANGEMENT. 



91 



through 3, 11, 19, 27, 35, 43, and so on. Thus it is that, by counting 

 the secondary spirals, all the scales may be numbered, and, by this 

 means, the generating spiral may be discovered. 



173. The primitive or generating spiral may pass either from right 

 to left or from left to right. It sometimes follows a different direction 

 in the branches from that pursued in the stem. When it follows the 

 same course in the stem and branches, they are homodromous (oftoi'o?, 

 similar, and dj&^oj, a course) ; when the direction differs, they are 

 heterodromous (trigo;, another). In different species of the same genus 

 the phyllotaxis frequently varies. 



174. Considering alternation as the usual leaf-arrangement, some 

 have supposed that opposite leaves are owing to the development of 

 two spirals in opposite directions, while others look upon them as pro- 

 duced by two nodes coming close together without an internode. A 

 verticil, in the latter view, will be the result of the non-development of 

 more than one internode. Thus, in fig. 195, if the space between 1 

 and 2 were obliterated, or the internode, m, not developed, the leaves 

 would be opposite. In fig. 198, if the spaces between each of the 

 leaves were obliterated, there would be a verticil of five leaves. In 

 many plants there is a law of arrestment of development, by which 

 opposite and verticillate leaves are naturally produced : but in such 



Fig. 200. Cycle of thirteen leaves placed closely together so as to form a rosette, as in Sem- 

 pervivum. A, is the very short axis to which the leaves are attached. The leaves are numbered 

 in their order, from below upwards. The circles in the centre indicate the five turns of the 

 spiral, and show the insertion of each of the leaves. The divergence is expressed by the fraction 



T%- 



Fig. 201. Cone of Pinus alba, with the scales or modified leaves numbered in the order of their 

 arrangement on the axis of the cone. The lines indicate a rectilinear series of scales, and two 

 lateral secondary spirals, one turning from left to right, the other from right to left. 



