THE LEAF 



91 



164. Five-ranked is the next in series, and the most common. It 

 is seen in the Apple (Fig. 80), Cherry, Poplar, and the greater number 

 of trees and shrubs. In this case 



the line traced from leaf to leaf 

 will pass twice round the stem 

 before it reaches a leaf situated 

 directly over any below. Here 

 the sixth leaf is over the first; 

 the leaves stand in five perpen- 

 dicular ranks, with equal angular 

 distance from each other; and 

 this distance between any two 

 successive leaves is just tw'o- 

 fifths of the circumference of the 

 stem. 



165. The above arrangements 

 of spirally placed leaves are the 80-81. 5-ranked arrangement: 80, 

 most common. A three-eighths ^^oot with its leaves o-rauked, 

 or five-thirteenths divergence is f^e sixth leaf over the first, as 



o in the Apple Iree; 81, diagram 



not uncommon. It will be noted of this arrangement. 



that the precise arrangement may 



be indicated by a fraction, thus : the two-ranked by \, the three-ranked 



by i, the five-ranked by f, and so on with 

 the I, y\, and other arrangements, the whole 

 fraction indicating the angular divergence of 

 the leaves, while the denominator shows the 

 number of vertical ranks. It will be seen 

 that, beginning with |, any one of the frac- 

 tions may be derived by adding the numera- 

 tors of the two preceding fractions for the 

 following numerator, and in like manner 

 adding the two preceding denominators for 

 the new denominator. 



166. Phyllotaxy of opposite and whorled 

 leaves. — This is simple and comparatively 

 uniform. The leaves of each pair or whorl 

 are placed over the intervals between those 

 of the preceding, and therefore under the 

 intervals of the pair or whorl next above. 

 The whorls or pairs alternate or cross each 

 82. Opposite leaves of Eu- other, usually at right angles, that is, they 

 onymus, or Spindle decussate (Fig. 82). Opposite leaves, that 

 Tree, showing the ig^ ^^i^q.^Is of two leaves onlv, are far com- 

 successive pairs ,, ^ ^ o ,^ " t- 



crossing each other i^oi^er than whorls oi three or four or more 



at right angles. members. 



