ANGULAR DIVERGENCE. 



41 



In the simplest case of alternate leaves (Fig.. 44), the leaf at the second 

 node is above and exactly opposite to the leaf at the first node, and that 

 at the third node is disposed vertically over the leaf at the first node. 

 Hence, the angular divergence is here one-half of the circumference, and 

 there are two vertical ranks of leaves. Now if we connect the bases of the 

 leaves with a line from below upwards always in the same direction, 

 a spiral will be drawn. As this spiral passes through the bases of . leaves 

 in the order of their development, it is called the Genetic Spiral. By the 

 fraction J, not only the angular divergence is expressed, but also the 

 numerator 1 denotes that there is one turn of the genetic spiral from one 

 leaf to another which is disposed directly above, and the denominator 

 2 denotes that there are two vertical ranks. 



In the next simpler case of alternate leaves, the fourth leaf that is one 

 at the. fourth node is placed vertically over the first leaf (Pig. 45) ; so that 



Fig. 46. 



Fig. 46. — Diagram of a stem bearing alternate leaves with a divergence 

 •of f ; I, II, III, etc., the vertical lines. (Sachs.) 



the angular divergence is one-third of the circumference, vertical ranks 

 are three, and the genetic spiral makes one turn round the stem from the 

 first leaf to -the fourth. 



In the next case, the sixth leaf is placed directly above the first, so that 

 the angular divergence is two-fifths, there being five vertical ranks and 

 -the genetic spiral making two turns. 



