102 



Ae 
+ 
Fig. 99. Diagram show- 
ing the arrangement of 
five-ranked leaves 
In this diagram the top of 
the cylinder is divided into 
five equal sectors, while 
from the end of each di- 
viding line runsalinedown 
the stem through a row of 
leaves, showing that the 
leaves are in five rows. 
The five vertical lines di- 
vide the stem into five 
equal parts, so that the 
distance around the stem 
that one leaf is from the 
next in age (as from leaf 
2 to leaf 3) can be deter- 
mined. This distance is 
two fifths of the circum- 
ference, so that the diver- 
gence is 2/5. Between two 
consecutive leaves in the 
same vertical row there 
are two turns of the spiral 
A TEXTBOOK OF GENERAL BOTANY 
are irregularities in the whorls. If only 
one leaf occurs at a node, the leaves are 
said to be alternate (Fig. 110). Alternate 
leaves are arranged in a spiral around. 
the stems, and the leaves have a definite 
location in the spiral. This location varies 
with different species. 
Phyllotaxy of alternate leaves. In 
some cases alternate leaves occur only on 
two sides of the stem, so that every leaf 
is above the second one below (Fig. 68). 
Such leaves are in two rows (two-ranked), 
and each leaf is halfway around the stem 
from the next in age (Fig. 97). 
Another arrangement is in three ranks, 
in which the point of attachment of every 
leaf is directly above that of the third 
leaf below (Fig. 98) and there is a com- 
plete turn of the spiral for every three 
leaves. If we include the leaf which be- 
gins a turn of a spiral and also the one 
which ends it, there are, of course, four 
leaves ; but when we take into considera- 
tion the whole length of the stem, there 
will be noted a turn for every three leaves. 
The commonest arrangement is in five 
ranks, with the point of attachment of 
each leaf 2/5 of the way around the stem 
from that of the leaf next in age (Figs. 
99,110). In such arrangement the point 
of attachment of every leaf is directly 
above that of the fifth leaf below, and 
there are two turns in the spiral for every 
five leaves. 
Still another method of arrangement 
is in eight ranks, with the point of 
