THE LEAF 



91 



0-" 



5-ranked arrangement : 80, 

 shoot with its leaves 5-ranked, 

 the sixth leaf over the first, as 

 in the Apple Tree ; 81, diagram 

 of this arrangement. 



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 two- 

 fifths of the circumference of the 

 stem. 



165. The above arrangements 



of spirally placed leaves are the 80-81. 

 most common. A three-eighths 

 or five-thirteenths divergence is 

 not uncommon. It will be noted 

 that the precise arrangement may 

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

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

 the f, T 5 ^, 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 f, 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 

 \.*)Y of the preceding, and therefore under the 



^~Jj intervals of the pair or whorl next above. 



fj 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 j gj w horls of two leaves only, are far com- 



crossi'gTachoth'er moner thau whorls of three or four or more 

 at right angles. members. 



