Origin and Development of the Compositce. 133 
Chapter VIII. 
PHYLLOTAXIS OF THE COMPOSITE. 
HE vegetative part of the plant in the Compositae varies so 
markedly that it is of little use in taxonomy or phylogeny 
apart from the special vegetative organs of the capitulum which 
have been considered in Chapters VI and VII. Nevertheless it is of 
interest to consider the occurrence of opposite and alternate leaves 
throughout the family, as even this variable character agrees in 
several points with previous phyletic conclusions; this is done in 
Section B. In addition the phyllotaxis of the capitulum is of con¬ 
siderable interest and is discussed in Section A of the present 
chapter. A brief summary of the phyletic data obtained in the 
study of the phyllotaxis of the family is given in Section C. 
A. Phyllotaxis of the Capitulum. 
The variation of the number of the ray florets in the Compositae, 
being easily observed, has furnished a basis for much of the work on 
the significance of the Fibonacci series. 
History. For a full account of the salient features in the history 
of phyllotaxis in general, readers are referred to Church (1, Pt. I). 
Wydler (29) seems to have been the first to consider phyllotaxis 
in the Compositae in any detail and he gives the data for the capitula 
and leaves of many species. Ludwig (15-18) gives maxima for the 
ray florets at 5, 8, 13, 21 and others of the Fibonacci series. He 
used the Schimper-Braun accessory series to explain the secondary 
and tertiary modes observed (18). A little later Haacke (6) found 
similar monomodal variation curves, but the modes in many cases 
did not fall in the Fibonacci series and from his data he concluded 
that the number of rays florets varied with the locality and the 
nutrition of the plants. Haacke thus anticipated the modern work 
on place-constants and seasonal variation. 
About the same time Weisse (25) published a long account of 
the phenomenon, with a good bibliography and a summary of the 
periodicity theory as given by Ludwig. Weisse also considered the 
phyllotaxis of the disc florets, describing it in terms of curve systems 
(cp. Church). He pointed out that the rays come at the ends of 
the long curves, e.g., a capitulum with a 21 : 34 curve system has 
21 rays. He agreed with Haacke in regarding the multimodal 
curves obtained from uncultivated material as due to nutrition and 
not to the presence of true races. This same author has also given 
a brief account (26) of Schwendener’s mechanical theory of 
