84 THE VEGETABLE WORLD. 
changed into scales, a transformation of which we have an example 
in the Asparagus plant, Fig. 113; into tendrils, as we have already 
observed in the Pea, Fig. 111; and into spines, as in the Barberry 
(Berberis), Fig. 115, for spines would have become branches under 
other evolutions of the axillary leaf-bud. 
Now what is the source of this disposition of leaves upon the 
_ stems and branches which carry them? Are they thrown at 
random upon the axes of the vegetable? The most superficial 
examination suffices to satisfy us that the leaves are always placed in 
( 
%, 
= A 
n 
e 
Fig. 110.—Acecia heterophylla. 
the same manner and in a fixed order for every species of plant. 10 
other words, that their relative distance and time are rigorously : 
fixed by nature. A more profound examination leads to the con- 
viction that this order is subject to certain laws, and may 
expressed by an arithmetical formula. If we examine a branch of 
the Elm (Fig. 116), of the Willow, or the Cherry-tree, we observe 
at once that the leaves are all inserted at different heights. In 
