88 THE VEGETABLE WORLD. 
term of the 4 and 2, we obtain $. Do the same for 2 and 3, and 
we obtain ;‘;, In this manner the terms 4, 4, 2, 3, i%s, $4, are 
obtained. Singularly enough these fractional formulas express 
precisely the disposition of leaves which nature realises. The 
denominators of these fractions, in giving the leaves of each cyele, 
indicate at the same time the vertical lines following which the 
leaves are ranged. 
Thus in the Elm and 
in the Lime-tree, the 
leaves are disposed 
in two rows, and are 
said to be distichous, 
in which it agrees 
with the Ivy (Hedera 
helix), and the Yew 
(Tazus banata). In 
cum autumnale), the 
leaves are disposed in 
=<.\ three rows, and said 
Fig. 119.—Branch of the Alder 
are disposed 
in five rows, they are said to be guincuncial. “The 
distribution of leaves upon the branches,” says De 
Candolle, “is in accord with their functions, which are 
almost exclusively determined by the action of the sun. [| 
In order that this action should exercise itself properly, 4 . 
it is necessary that the leaves be wide apart one from & 
the other. We have seen that in all the systems by Ete eag 
which the positions of the leaves are arranged, it results ee ee of the 
that the leaves which bear immediately above others are j 
never covered. In cases the least favourable, the third only covers — 
the first, and the fourth the second. In another case it is the © 
