30 



OBQANOGBAPHT. 



instance, the numerator and denominator of any fraction 

 may be obtained by adding respectively the numerators 

 and denominators of the two preceding fractions. The 

 numerator of any fraction is the same as the denominator 

 of the second preceding fraction. Spirals may be con- 

 structed which will show the arrangements indicated by 

 the several fractions, and exhibit at the same time the 

 angular divergence of the leaves (Figs. 30-33). Such 



a view may actu- 

 ally be obtained by 

 looking from above 

 at the shoot in the 

 direction of its 

 axis. 



33. If a num- 

 ber of leaf-buds be 

 dissected it will 

 be found that a 

 difference prevails 

 in regard to the 

 vernation (Lat. 

 '^^° ver. Spring), or the 

 disposition of the 

 scales or leaves in the bud. The arrangement of these 

 leaves in reference to each other is, in general, like their 

 arrangement on the stem, but more will be said of this 

 hereafter, when treating of flower-buds. Each separate 

 leaf is generally bent or folded or rolled up. When the 

 upper part is bent down upon the lower (e.g. Tulip-tree) 

 it is said to be inflexed, or recline. When the two 

 halves are folded together, face to face, it is conduplicate 



Figs. 30-33. Spirals showing angular divergence of leaves, }, i, i, j. 



