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James Small. 
phyllotaxis. Church (1, Pt. 1, p. 16) remarks of this theory that 
“ it superimposes a second doubtful hypothesis on the original 
unsatisfactory one of Schimper and Braun.” 
Most of the more modern work agrees in finding seasonal and 
local changes in the number of ray florets, the modes not being 
confined to the Fibonacci series (see VI 13, VI 14 ; 5, 12, 13,14,19, 
23, 24, 27). Strickland (22) in one of the most recent notes on the 
subject returned to the concentric circles of the Schimper-Braun 
hypothesis, but was answered within a month by Henslow (11), who 
referred to his own observations on phyllotaxis (7-10). In spite of 
the variation observed, a monomodal curve with the mode at 21 is 
very common in the Composite (cp. 20, 28). 
Church's work. This author, in addition to various notes (2-4) on 
the simpler aspects of phyllotaxis, has published the most complete 
exposition of phyllotaxis in general and of the phyllotaxis of the 
capitulum in particular (1). Some of the points explained by Church 
which are directly relevant will now be given, but as the phyletic 
value in the Composite of these very interesting data is rather 
restricted readers are referred to the original for details. Indeed, 
for the proper comprehension of what occurs in the capitulum a 
close study of ChurclTs monograph is essential and all previous 
work may be regarded as more or less superficial when compared 
with that author’s fundamental exposition of the subject. 
Involucre. The involucral scales, according to Church, show 
a “ rising phyllotaxis ” and the phyllotaxis cannot, here or elsewhere 
in the capitulum, be given a real value in the fractional system of 
Schimper and Braun. In dealing with the phyllotaxis of Helianthus 
(op. cit, Pt. I, p. 25) he says “ the vegetative leaves pass gradually 
by reduction into an involucre of leaf-base scales.” The study of 
the phyllotaxis of the capitulum confirms, therefore, the theory of 
the origin of the calyculus from the cauline leaves by suppression of 
the internodes (cp. Chap. VI). 
In Helianthus the difference between the uniseriate pericline 
and the multiseriate calyculus is very distinct. Taking the case 
figured (op. cit., Pt. II, Fig. 50), the whole plant shows a rising 
phyllotaxis, from the (3 + 5) of the foliage leaves and the (8 + 13) 
of the foliage leaves and calyculus to the (21+34) of the disc. The 
transition from the (3 + 5) of the lower cauline leaves to the (8+13) 
of the upper foliage leaves and calyculus occurs below the calyculus 
so that the leaves of that part of the capitulum have the same 
phyllotaxis as the upper foliage leaves. The passage of the foliage 
