24 NEW ZEALAND NATURE-STUDY BOOK 
an! 
that it passes over five leaves; hence the numerator of 
the fraction denotes the number of times it is necessary 
to pass round the stem in travelling from one leaf to 
the next vertically above it, at the same time touching all 
the leaves between these two. 
Importance of Leaf Arrangement. A little 
thought will convince the observer that the arrangement 
which we have been describing is admirably adapted for 
enabling the plant to obtain the maximum amount of light, 
which, as we have already seen, is a matter of the first 
importance to healthy and rapid growth. Not only are 
leaves arranged on the branches with this object, but the 
branches themselves grow in such a way as to aid the 
leaves in securing it, where leaves, as in the case of the 
Daisy or Primrose, all spring from nearly the same level, 
the base of the leaf is cut away where shut off from the 
light. If this were not so, one leaf would overlap the other 
and, preventing the passage of light, would render the 
shaded portions useless. 
The Position of Branches. We have already seen 
that buds from which branches develop occur only in the 
axils of leaves — axillary buds ; or at the end of growing 
shoots—terminal buds. Hence the ultimate arrangement 
of branches on a stem must depend to some extent on the 
position of the leaves. It will be found that this is the 
case ; but, as all the buds do not develop, it frequently 
happens that the final arrangement of the branches is by no 
means regular. Still, although the positions of the leaves 
do not absolutely control the branch system, they have a 
good deal to do withit. We do not, for instance, find opposite 
branches on a tree whose leaves are arranged on the alternate 
system. If the branches are opposite, the leaf arrangement 
must have been opposite or whorled, for wherever we find a 
branch growing, there must at one time have been a leaf 
