14 



PART I. MORPHOLOGY. 



[6 



is a certain fraction of the circumference. In the simplest case, 

 when the divergence is i (Fig. 6 A\ starting with any leaf 0, the 

 insertion of the next leaf, in succession on the stem, which may 

 be numbered 1, will be on the opposite side to that of the leaf ; 

 and the next leaf, numbered 2, will be opposite to 1 and exactly 

 above 0. Thus there are two orthostichies. But since each leaf 

 is at a different level, in proceeding from leaf to 1, 2, 3, and so 

 on, always in the same direction, the circumference of the stem 

 is traversed in a spiral which, in the course of each whole turn, 

 touches the bases of two leaves and intersects the same orthostichy. 

 This spiral will pass through the insertion of every leaf, and as it 

 does so in the order of their development, it is known as the, 

 (jcnetic spiral. The number of leaves through which the genetic 



spiral passes in its course 

 between any two on the 

 same orthostichy is termed 

 a spire. When the di- 

 vergence is ^, the leaf 

 numbered 3 comes exactly 

 above leaf 0, 4 over 1, 

 5 over 2, and so on : and 

 there are three orthosti- 

 chous lines, the spire being 

 composed of three leaves. 

 It might be said with 

 equal accuracy that the di- 



FIG. 7. Diagram of a stem with a constant di- Vergence is -|, since leaf 1 

 vergence of |: I. II, III, etc., the orthostichous is distant f of the cirCUm- 

 lines. (After Sachs.) 3 



ference from leaf 0, if the 



spiral be followed in the other direction. If it be continued in this 

 direction, it will pass round the stem twice in each spire. For the 

 sake of simplicity, the spiral is not traced in this longer way, but 

 in the shorter way. When the numerator of the fraction of diver- 

 gence is not 1, but some other rational number, the spiral passes 

 round the stem more than once within the spire, in fact, just as 

 many times as is expressed by the numerator of the fraction of 

 divergence ; the denominator of the fraction expresses the number 

 of the orthostichies. In Figs. 7 and 8, which represent a constant 

 livergence of --, it is easy to see that eight orthostichies are pres- 

 ent, leaf y being over 1, 10 over 2, and so on ; also that the spiral 

 returns to a leaf on the same orthostichy after three turns, and 

 thus goes thrice round the stem in one spire. 



