104 A TEXTBOOK OF GENERAL BOTANY 
Series of divergences. The divergences for alternate leaves 
can be arranged in the following series: 1/2, 1/3, 2/5, 3/8, 5/13, 
8/21, 13/34, 21/55, etc. Each fraction represents the part of 
the way around the stem that one leaf is from the next in age. 
In each fraction the denominator represents the number of 
internodes between suc- 
cessive leaves that are 
situated in the same ver- 
tical row, and also the 
number of vertical rows 
of leaves on the stem, 
while the numerator 
shows the number of 
turns of the spiral be- 
tween two successive 
leaves in the same ver- 
tical row. It should be 
noted that the numera- 
tor and denominator for 
every divergence can be 
Fie. 101. Diagram showing a divergence obtained by adding to- 
of alternate leaves, expressed in degrees of 

gether those of the two 
; preceding fractions in 
All divergences lie between 1/3 = 120° and 1/2= wee 
180°, while all members of the series higher than LOO eaAeee ; 
2/5 lie between 2/5 = 144° and 3/8 = 135°. The The first figure in 
members higher than 5/18 lie so close to the theo- the series, 1/25 is the 
retical limit of 137° 30’ that it is not practicable 
to show them on a diagram of this size 
circumference 
greatest divergence that 
occurs with alternate 
leaves; the second figure, 1/3, is the smallest; the third figure, 
2/5, is the second largest; the fourth figure, 3/8, is the second 
smallest; the fifth figure, 5/13, is the third largest; the sixth 
figure, 8/21, is the third smallest; the seventh figure, 13/34, is 
the fourth largest; and the eighth figure, 21/55, is the fourth 
smallest, etc. This can be expressed in a different way. If we 
take the first figure in the series and then every second figure, 
we obtain the following descending series of divergences: 1/2, 

