42 MOEPHOLOGICAL BOTANY. 



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

 the angular divergence is three-eighths there being eight vertical ranks 

 and three turns of the spiral. 



In the next case, the angular divergence is five-thirteenths, the four- 

 teenth leaf being placed vertically over the first ; there_ are thirteen 

 vertical ranks and five turns of the spiral. 



Then follow such divergences as $£, ■§§, etc. If the preceeding fractions 

 representing angular divergences are carefully observed, it will be seen 

 that a certain relation exists between them; thus the sum of any two 

 preceeding numerators is the numerator of the next succeeding fraction, 

 and the same is true of the denominators. Therefore, the series of 

 fractions representing the angular divergence may be expressed by the 

 continued fraction, 



1 



a + 1 



1 +_1_ 



1 + J-,etc. 

 1 



——(simplest angular divergence). 



2 



— = _— (next angular divergence). 



2 + 1 o 



_ = — = — •= — (next angular divergence). 



2 +J_ 2 +J_ _5_ 5 v 5 5 ' 



1 + 1 2 2 



12 2 

 There are still other divergences, but not common, as——, — , — -, etc. 



3. KINDS OF FOLIAGE LEAVES IN REFERENCE TO 

 THEIR COMPOSITION. 



Some foliage leaves have only one lamina and never 

 more than one articulation at the base, as in the Mume 

 and Sakura (Fig. 16) ; while others have two or more 

 laminae, as in the Fuji (Wistaria chinensis) (Fig. 48) and 

 Akebi (Ahebia quinata) (Fig. 49), or one lamina and two 

 articulations, as in the Yudzu (Fig. 47) and Megi. Those 

 of the former kind are called Simple Leaves and those of 

 the latter Compound. 



