Origin and Development of the Compositee. 135 
leaves into the calyculus is, therefore, gradual. The passage from the 
(8 + 13) system of the calyculus into the (21 +34) of the disc occurs 
in the pericline, the 21 members of which are transitional and 
subtend the 21 ray florets at the ends of the long spirals. 
In the cases mentioned in Chap. VI, B, where the calyculus 
passes gradually into the pericline the change from the lower to 
the higher curve system is not accomplished in the minimum 
number of members as it is in Helianthus and the transition begins 
with the inner members of the calyculus and continues in the outer 
members of the pericline. The two parts of the involucre in these 
cases belong to the same curve system and appear, therefore, to 
pass gradually into each other. 
Fio. 22. Expansion system : log. gpiral scheme for the introduction of 
new paths which determine the rise of phyllotaxis ratios in the capitulum of 
Helianthus animus from (8+13) to (21+34). A small capitulum is taken as a 
type ; the genetic spiral winds left ; the small amount of unavoidable error in 
the construction is admitted in the (8+13) system. (Figure and legend after 
Church.) 
Another case is exemplified by Cynara Scolymus (op. cit., Pt. 
II, p. 119) where the distinction between the foliage leaves and 
