134 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



to a considerable degree, but it caimot go ou for ever. The system 

 has a hmit, and the system of progressive growth comes into conflict 

 with the demand for the production of a mass of flowers approxi- 

 mately simultaneously. 



To limit the series, the system must therefore be broken at 

 certain intervals, and a lower series of curves, implying that the 

 bulk-ratio has been raised, will be the sign of such modification. 



Gynara Scolymus may be taken as a type (fig. 53a, 6). The 

 large capitulum commences formation of disk-florets with the ratio 

 (55-1-89), and this is continued as shown by the shorter curves for 

 8-10 members along these paths — that is to say, for an aggregate of 

 about 9x89 = 800 florets. Since the meshes of the log. spiral net- 

 work have all this time been getting smaller, though a theoretical 

 construction diagram shows that the difference is almost imper- 

 ceptible, a point is now reached at which adjustments in the lateral 

 primordia can no longer be strained, and an alteration of the system 

 correlated with a marked modification of the bulk-ratio is required. 

 While the 55 long curves are thus carried on, the 89 short ones 

 break off and present an approximate reduction to 34 still longer 

 spirals — that is to say, the system is now (34-1-55) and the set of 

 the parastichies reversed. The transition is, however, not clearly 

 marked, and it cannot be traced with sufficient accuracy to show 

 whether it is rapid or irregular, owing to the fact that the actual 

 leaves are absent. The point to note is that a Fibonacci ratio is 

 soon regained. The " 34 " curves are carried almost to the centre 

 of the disk, but at about six florets along the " 55 " curves these in 

 turn break away, suggesting a reduction to 21, and implying there- 

 fore a second reversal to (21-1-34). The central part of the disk 

 becomes still more obscure. 



The phenomena of falling phyllotaxis in Gynara somewhat re- 

 sembles the rising phyllotaxis of the same capitulum, but with 

 diminished accuracy. Expansion followed normal lines, but re- 

 duction gives discontinuous systems. 



In the same way Helianthics presents reduction reversals, but 

 they are less marked. For example, the head (34-1-55), taken as a 

 type (fig. 15), shows the short curves remaining unbroken for 11-12 

 members. The number of florets in which small adjustments were 



