104 



PHYLLOTAXIS OE LEAF-AEEANGEMENT. 



of turns, and the denominator the number of leaves in the spiral 

 cycle. Thus, in fig. 214, ab, the cycle consists of five leaves, the 6th 

 leaf being placed vertically over the 1st, 

 the 7th over the 2d, and so on ; while 

 the number of turns between the 1st 

 and 6th leaf is two : hence, this arrange- 

 ment is indicated by the fraction |. In 

 other words, the distance or divergence 

 between the first and second leaf, ex- 

 pressed in parts of a circle, is | of a 

 circle, or 360° -M = 144°. In fig. 211, 

 a b, the spiral is ^, i.e. one turn and two 

 leaves ; the third leaf being placed verti- 

 cally over the first, and the divergence 

 between the first and second leaf being 

 one-half the circumference of a circle, 

 360° -H J = 180°. Again, in fig. 215, 

 a b, the number is i, or one turn and 

 three leaves, the angular divergence being 

 120°. 



The general forms of Phyllotaxy may be brought out by a con- 

 tinued fraction — 



1 



Fig. 215. 



a+l + l + l + 1, etc., 



where a may have the values 1, 2, 3, or 4, etc. 

 The actual fractions thus resulting are — when 



« = 1-* -I f * A, etc. 

 » = 2,..i i i 1 A> etc. 



Each fraction being obtained by adding together the numerator and 

 denominator in the two preceding fractions. 



When the leaves or scales are alternate, and run in a single series, 

 they are unijugate ; when the leaves are opposite, and there are two 

 parallel rows produced, the arrangement is bijugate, while in the case 

 of whorled leaves the arrangement may be trijugate or quadrijugate. 



Fig. 215. — ^Young plant of Cyperus esculentus, wil^ii leaves in three rows, or tristichous, 

 expressed by the fraction i, or one turn and three leaves, a, The plant, with its leaves 

 numbered in their order. ■ i. Magnified representation of the stem, showing the insertion of 

 the leaves and their spiral arrangement. 



