LEAF ARRANGEMENT 23 
Rata. In this case there will be just twice as many rows of 
leaves as there are leaves at each node. 
Spiral Arrangement. When only one leaf is inserted 
at each node, the arrangement is said to be spiral. If a 
piece of cotton be fastened to a leaf on a twig of Hazel and 
be taken along the stem passing over the bases of successive 
leaves, it will be found to trace out a spiral path. In this 
case the leaves form rows just as they do when occurring in 
whorls. Moreover each leaf, though separated from the one 
immediately above or below by a variable distance along 
the stem, is placed in such a way that its angular distance 
round the stem from either of the others is the same. For 
instance, in the Mako-mako, each leaf is inserted on the side 
opposite to that on which the leaf at the next higher node is 
attached, so that a piece of cotton would have to wind half 
way round the stem in passing from any one leaf to the next 
and once round the stem before reaching the leaf vertically 
above the first. In this case the divergence of arrangement 
is one-half. In other cases we might have to travel one-third 
of the distance round the stem in going from one leaf tc 
the next, or of course once round the stem before reaching 
the leaf vertically above the first—-one-third divergence seen 
in the Mahoe. It will readily be seen during the operation 
that a twig with a divergence of one-half will have two rows 
. of leaves, and one with one-third divergence, three rows of 
leaves. Thus the denominator of the fraction indicates the 
number of rows of leaves. Ifa Wallflower or an Oak branch 
be operated on in the same way, the thread will wind twice 
round the stem before reaching a leaf vertically over the 
first and moreover will pass five leaves—two-fifths diver- 
gence. It will be noticed when the divergence is one-half 
that the thread, in travelling round the stem to a leaf 
vertically above the first, passes over two leaves ; when one- 
third, that it passes over three leaves ; when two-fifths, 
