THE LEAF 



91 



V, 



80-81. 5-ranked arrangement : SO, 

 shoot with its leaves Ti-ranked, 

 the sixth leal' over the first, as 

 in the Apple Tree ; 81, diagram 

 of this arrangement. 



164. Five-ranked is the uexl in .series, and the most coiniiion. It 

 is seen in the Apple (Fig. 80), Clierry, PopLai', and tlie greater number 

 of trees and shrubs. In this case 

 the line traced frum leaf to leaf 

 will pass twice round tlie stem 

 before it readies a leaf situated 

 directly over any below. Here 

 the sixth leaf is over the first; 

 the leaves sttind in five perpen- 

 dicular ranks, with ecpial 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 letives are the 

 most common. A three-eighths 

 or five-thirteenths divergence is 

 not uncommon. It will be noted 

 tliat the preci.se arrangement may 



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

 by ], tlio five-ranked by 5, and so on with 

 the J, (J, and oilier ai'rangements, 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 m.anner 

 adding the two preceding denominators for 

 the new denominator. 



166. Phyllotaxy of opposite and whorled 

 leaves. — This is simpile and comparatively 

 uniform. The leaves of each pair or whorl 

 are placed over tiie intervals between those 



Tof the preceding, and therefore under the 

 intervals of the pair or wlioii next above. 

 The whorls or pairs alternate or cross each 

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

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

 Tree, showing the jg^ whorls of two leaves only, are far com- 

 successive pairs ,, 1 1 -f iv j- 



crossing each other '"O"*^'' ^'^'"^ ^^'''°''^« "^ t^"''=« °i' ^O"'' O'' '""^'e 

 at right angles. members. 



