7 
106 <A TEXTBOOK OF GENERAL BOTANY 
a divergence of 137° 30! 28’. The above figures for the ascend- 
ing and descending series show that all members of the original 
series have values which lie within the limits 1/2 and 1/3. Like- 
wise, the values for higher members than 3/8 lie between 2/5 and 
3/8, and the values for higher members than 8/21 lie between 
5/13 and 8/21. The difference between the divergences 13/34 
and 21/55 is only 12’, 
or 1/5 of a degree, and 
the difference between all 
higher members of the 
series must be less than 
‘this. There is, therefore, 
very little difference be- 
tween. the divergences of 
the higher members of the 
series. This relationship 
is shown in Fig. 101. 
The phyllotaxy is fre- 
quently obscured by a 
twisting of the stem. A 
very striking case is that 
of the umbrella plant. 
Here the leaves are in 

is so twisted that the 
Fic. 104. Excurrent crown of Casuarina leaves radiate in all di- 
rections (Fig. 102). 
Branching. Many stems branch and thereby increase the num- 
ber of leaves and flowers which they can advantageously support. 
Since buds grow in the axils of the leaves, the arrangement of the 
branches would be the same as that of the leaves if all buds pro- 
duced branches. Usually, however, many of the buds fail to 
grow. Some plants, as is the case with numerous palms (Fig. 108), 
do not branch at all. In many species the main stem continues 
to grow throughout the life of the plant and is very much more 
vigorous than any of the branches (Fig. 104). Plants that have 
three rows, but the stem > 
