26 RELATION OP PHYLLOTAXIS TO MECHANICAL LAWS. 



bracts and subtended flowers are developed centripetally (i.e., in 

 normal series), and by a Tvonderful correlation of growth in the 

 whole capitulum, the receptacle extends laterally and symmetri- 

 cally as new flowers are added, expand, and pass on into the 

 fruiting condition. The result is that the head in fruit exhibits 

 practically the same structure as in its early stages, but on a large 

 discoid area. 



Such capitula admit of ready observation. By taking a head in 

 which the last flowers are withering, and clearing away the corolla 

 tubes, the developing ovaries are seen to mark out rhomboidal 

 facets (fig. 10), and when the fruits are ripened and have been 

 shed, the subtending bracts still form rhomboidal sockets (fig. 11). 



These sockets, with or without fruits, form series of intersecting 

 curves (" parastichies " of Braun, " contact-lines " of Schwendener), 

 identical with those of the Pine cone, only reduced to a horizontal 

 plane. 



A fairly large head, 5-6 inches in diameter in the fruiting 

 condition, will show exactly 55 long curves crossing 89 shorter 

 ones (fig. 12). A head slightly smaller, 3-5 inches across the disk, 

 exactly 34 long and 55 short (figs. 10, 11) ; very large 11 inch heads 

 give 89 long and 144 short (fig. 13): the smallest tertiary heads 

 reduce to 21-|-34, and ultimately 13-f-21 may be found; but these 

 being developed late in the season are frequently distorted and do 

 not set fruit well.* 



A record head grown at Oxford in 1899 measured 22 inches in 

 diameter, and, though it was not counted, there is every reason to 

 believe that its parastichies belonged to a still higher series 

 (144 -f 233). The Sunflower is thus limited in its inflorescence to 

 certain set patterns (according to the strength of the inflorescence 

 axis,) e.g., jf , §J, ||, f f , ^^. These were first observed by Braun,-j- 

 and translated into terms of the Schimper-Braim series they would 

 correspond to divergences of ^|, fj, f f, ^, and ^^^ respectively. 



* Gf. A. Weisse : " Die Zalil der Eandbliitlieii an Compositenkopfchen in 

 ihrer Bezieliuiig zur Blattstellung und Ernahrung (JPring. Jahrb.', xxx. 453). 

 Complete data for 140 specimens are tabulated ; out of 61 poorly nourished 

 pot-cultures 27 produced (13 + 21) terminal capitula. 



t Flora, 1835, p. 157, 



