LEAVES 13 



there is one leaf at each node, and each leaf is inserted on the 

 side exactly opposite to that on which the leaf at the next node 

 is attached ; consequently we have to travel half-way round the 

 stem (as well as go higher up) in order to reach the single leaf 

 at the next higher node : the divergence, or angular distance, 

 is described as being ^. Again, in some Hazel-shoots (fig. 12) 

 we have to travel one-third of the way round the stem in 

 passing from one leaf to its predecessor or successor, and 

 the divergence is said to be -g-. On the stems of the Oak, 

 Red Currant, Pear, Poplar, Musk Rose, the divergence is 

 ■|. The consequence of this constancy of the divergence 

 between the leaves of the successive nodes of a stem is 

 that the above-mentioned longitudinal rows of leaves are 

 formed. In the Grasses and most Hazel-shoots with ^ diver- 

 gence, the leaves are ranged in two rows ; in the Hazel-shoots 

 with ^ divergence, in three rows ; on Pear-trees, etc., with f 

 divergence, in five rows. Thus in each case the numerator of 

 the fraction denotes the number of longitudinal rows of leaves. 

 And the numerator of the fraction represents the number of 

 times it is necessary to travel round the stem in passing from 

 one leaf on a stem to the next one vertically above it, at the 

 same time touching all the leaves on the way thither. This 

 gives us an easy method for determining the exact leaf- 

 arrangement of a shoot. The commonest series are repre- 

 sented by the fractions ^, ^, f, f, j%. This series can be 

 remembered with ease if we note that — 



i + i_ 2 i + 2_ 3 2 + 3 _ 5 



2 + 3 5' 3 + 5 8' s-f-8 13- 



Possibly the most simple way to understand the 'Spiral method 

 of arrangement of leaves is to look at the cone of a Pine- 

 tree, or to remember that the leaves are distributed like the 

 steps of a spiral staircase. 



Diagrams to represent the leaf-arrangement. — We can denote 

 the method of arrangement of the leaves on a stem by a plan 

 or map, representing a side view of the surface of the stem 

 unrolled into one plane, much as we show the surface of the 

 spherical earth with its two hemispheres extended on a single 

 flat map. Or, on the other hand, we can for a moment imagine 

 that a shoot is like a large bud, and that we are looking down 



