i 3 6 
James Small 
calyculus is very marked, as is the case in most Compositae. Here 
there is one transition from the foliage leaves (3 + 5) to the “ outer 
involucre” (8+13), a second transition from the “outer involucre” 
to the “ inner involucre ” (21+34) and a third to the disc florets 
(55 + 89). The outer and inner parts of the involucre may be 
considered calyculus and pericline respectively and the transition 
which occurs to give the calyculus marks off the involucre very 
definitely from the cauline leaves. 
These few examples will be sufficient to show that the morpho¬ 
logical distinction drawn between the two parts of the involucre is 
confirmed by the phyllotaxis. 
Ray Florets. Most of the work on the phyllotaxis and 
biometrics of the capitulum has been done on the ray florets and 
one of the most interesting points in the whole of the literature of 
phyllotaxis is the geometrical construction given by Church, which 
explains the number and position of the rays. The chief points 
can be seen in Fig. 22, 1 —for the method of construction the reader is 
referred to the original monograph (1, Pt. II, pp. 116 sqq.). The 
method consists in adding one long and one short curve to each of 
the first 13 members of the (8 + 13) cycle and one short curve to 
the remaining 8 members of the complete cycle. 
The ray florets are marked black and it will be seen that they 
fill in the corners left by the transitional members of the involucre or 
pericline which are all more oblong than square and thus differ from 
the quasi-squares of the disc and the outer involucral members or 
calyculus. The members of the pericline are thus quite definitely 
indicated and it will be noted that according to this construction 
the ray florets are always more or less to one side of the sub¬ 
tending bract. This displacement of the floret from the median 
position is more marked with the outer bracts. It should also be 
noted that the ray florets occur at the ends of the long spirals, e.g. t 
there are no rays at the ends of the short spirals marked 22, 25, 30, 
etc. Starting from the bract numbered 1 (Fig. 22) and counting 
from left to right round the lower part of the circle it will be noticed 
that the ray florets are grouped thus 2: 1:2: 1:2:2: 1:2: 1:2:2: 
1:2. As there are 21 long spirals there are 21 ray florets, so that 
the number and position of the rays follows from the geometrical 
construction adopted. 
1 I am much indebted to Dr. A. H. Church for his kindness in lending 
me the blocks for Figs. 22 24, which are Figs. 44-46 in the original. 
