THE LEAF. 



43 



form two perpendicular rows. Such leaves are termed distichous or 

 two-ranked (tig. 44) ; examples of which are found in the Grasses. 



If the second leaf is not opposite to the first, but at a point dis- 

 tant from it one third of the circumference of the stem, and the 

 third leaf one third further round, the fourth leaf, likewise distant 

 one third from the preceding, will stand over the first. Leaves so 

 arranged form three perpendicular rows, constituting the tristichous 

 or three-ranked arrangement, which is common among the Mono- 

 cotyledons (fig. 46). 



Now when a line is drawn round the stem so as to pass regu- 

 larly from leaf to leaf, we find that its course is spiral. In the 

 distichous case the spiral line starting from any given leaf com- 

 pletes one circuit and then commences a new one at the third leaf ; 

 in the tristichous arrangement the spiral completes one circuit and 

 begins a new one with the fourth leaf (fig. 46). The series of 

 leaves included by the spiral line in passing from the first leaf to 

 that which stands directly above it is called a cycle (fig. 47) ; the 

 fraction of the circumference of the stem which measures the 

 angular distance between any two succeeding leaves in a cycle 

 when projected on a plane is termed the angular divergence. In 



Fig. 48. 



F g. 46. Projection of the ^ arrangement. 



Fig. 47. Horizontal projection of a cycle of the ^ arrangement. 



Fig. 48. Projection of the f arrangement. 



Fig. 49. Horizontal projection of a cycle of the f arrangement. 



the distichous, represented by the fraction j, it is one half of 360, 

 or 180; in the tristichous, or j, it is 1^0. 



These fractions not only represent the angular divergence, but 



