122 PHYLLOTAXY, OK LEAF-ARRANGEMENT. 



follow each other in the ascending order upon different sides of 

 the axis : it also secures an advantageous spacing of the leaves 

 over the whole length of the axis. Their vertical distance from 

 each other of course depends on the length which the internodes 

 attain, which is a matter of growth and is very variable ; but 

 their angular distance is fixed in the kind or numerical plan of 

 the particular phyllotaxy, and is uniform throughout. 



238. The leaves are said to be alternate, because they come 

 one after another, now on this side, then on that, as they ascend 

 the stem. The arrangement is said to be spiral, because if a line 

 be drawn or a thread extended from the base or insertion of one 

 leaf to that of the next higher, and so on, taking in all the leaves, 

 it forms a helix, more or less loose or close according to the 

 development of the internodes. (See Fig. 242.) This imagined 

 spiral line ascends continuous!}', without a break ; and on it the 

 leaves are equably laid down. 1 



239. Almost all the ordinary instances of spiral plryllotaxy 

 belong to one series, having very simple arithmetical relations. 

 So that this may be taken as the type, and the few others re- 

 garded as exceptions or sometimes as modifications of it. The 

 kinds are simply designated by the number of vertical ranks of 

 leaves : the}' are technically named by prefixing the proper 

 Greek numeral to the word meaning row or rank. The arrange- 

 ment called 



Distichous, or Two-ranked, is the simplest and among the com- 

 ynonest, occurring, as it does, in all Grasses and many other 

 /nonocotyledonous plants, in Lindens, Elms, and many dico- 

 tyledonous genera. Here the leaves are disposed alternately on 

 exactly opposite sides of the stem (as in Fig. 1 ) ; the second 

 leaf being the farthest possible from the first, as is the third from 

 the second ; the third therefore over the first, and the fourth over 

 the second, and so on, thus forming two vertical ranks. The 

 angular divergence is here half the circumference, or 180 ; and 

 the phyllotaxy may be represented by the fraction J, which desig- 

 nates the angular divergence, while its denominator expresses 

 the number of vertical ranks formed. 



Tristichous, or Three-ranked, is the next in the series, and is 



1 But when we reach a leaf which stands directly over a lower and older 

 one, we say that one set or spire is completed, and that this leaf is the first 

 of a succeeding set or spire. From analogy of such an open spire to the 

 closed cycle of a whorl of leaves, it is not unusual to designate the former 

 likewise as a cycle. Yet it is better (with Eichler) to restrict that term, and 

 the adjective cyclical, to verticillate phyllotaxy, or to whorls, to which it 

 properly and etymologically belongs. 



