ON LEAVES. 87 
two leaves there are four others diversely placed. All these leaves 
are placed upon the line of an ideal spiral, which commences in 
one leaf and terminates 
in the leaf on the line 
unit of the spiral may 
consist of one or more 
revolutions of the spiral. 
round the axis. Fixing 
on any leaf and ascend- 
ing the branch till the 
is found, by counting all 
the intermediate ones the 
number constituting the 
unit or cycle is arrived at. 
In the Peach and Plum- 
tree the cycle embraces / 
five leaves, and the spiral 
goes twice round the @y 
branch. This 
is expressed in 
botani lan- 
guage by the 
| ‘| fractional for- ) 
if mula a the nu- Fig. 117.—Branch of the Peach 
‘| merator indicating the number of turns the spiral makes 
on the cycle, the denomimator the number of leaves 
which constitute the cycle, as in Fig. 118. In the Alder 
(Alnus glutinosa), Fig. 119, three leaves constitute the 
cycle ; and the spiral only describing a single turn on the 
stem, the disposition of its leaves is represented by the 
fraction }, as exhibited in Fig. 120. 
fi In the Elm (Udnus), as we have seen in Fig. 116, and 
Big. us, he in the Lime-tree, two leaves only constitute the cycle, in 
Peach leaves. which case they are represented by the fraction 4. Let 
us write these three fractions in a single line, 4, 3, 3, and we find 
the fraction 3 is the sum of the two first fractions. Let us add the _ 
e 
Ay ye 
4 
