4.] 



CHAPTER I. GENERAL MORPHOLOGY. 



27 



However, this example will serve to indicate the relation between 

 the construction of the spiral and the fraction which is used to 

 express the divergence. The denominator of this fraction gives 

 the number of the orthostichies, the numerator the number of 

 turns of the spiral in the cycle. 



Another very common divergence is --, the geometrical condi- 

 tions of which are readily intelligible. From the Figures 14 and 

 15, which represent a divergence -of f, it is easy to see that in this 

 case there are eight orthostichies, that 

 number 9 stands over 1, 10 over 2, and so 

 on, and further, that the spiral passes 

 through the insertion of a member at every 

 third orthostichy, and turns three times 

 round the axis in the course of one cycle. 



If, for instance, it is required to determine 

 the arrangement of the leaves (phyllotaxis) 

 on a stem, it is necessary to find the leaf 

 which is exactly above the one, numbered 0, 

 selected as a starting-point, and then to 

 count the number of leaves which are met 

 with in following the shorter spiral round 

 the stem between these two leaves. The 

 number of the leaf which lies in the same 

 orthostichy is the denominator of the frac- 

 tion of divergence, and the numerator is the 

 number of turns made by the spiral be- 

 tween the two leaves. 



When the number of orthostichies is 

 greater than eight, it becomes very diffi- 

 cult to detect them, particularly when the 

 lateral members are closely arranged, as the 

 leaves in the rosettes of the House-leek, as 

 the flowers in the capitulum of the Sun- 

 flower, or as the scales in a fir-cone. 

 Another set of lines, lying obliquely, then 

 strike the eye, called parastichies, which 

 also run round the stem in a spiral, but 

 touch only some of the lateral members ; 



vif 



FIG. 15. Diagram of an 

 axis, the lateral members of 

 which have the constant di- 

 vergence of | : those of the 

 anterior surface are indi- 

 cated by their insertions, 

 those of the posterior by 

 circles ; they are connected 

 by the genetic spiral. I, 

 I, II, III, etc. , are the eight 

 orthostichies. 



for instance, in Fig. 15, a line which con- 

 nects the members 3, 6, 9, and 12. It is evident that the number 

 of parallel parastichies must be as great as the difference between 



