114 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



that this belongs to member 0, and represents a case of the 

 fertility of the last involucral member. The fact that the number 

 of sterile ray-florets is not absolutely constant is thus illustrated, 

 while it may be noted that such irregularities will also affect 

 the observed number of involucral scales as a constant quantity. 



Deviations from theoretical construction are seen to be due 

 merely to :■ — (1) The assumption of dorsiventral symmetry by the 

 sterile involucral scales, which further exhibit sliding growth over 

 one another in the tangential direction to such an extent that 

 a ray-floret is sometimes isolated from its subtending bract, while 

 the members themselves are greatly flattened radially. (2) Owing 

 to the sharp line of demarcation between these dorsiventral 

 members and the fertile bracts, which with their enclosed radiaUy- 

 symmetrical florets retain their original relative volume, the edge 

 of the disk becomes a fairly rigid circular boundary againpt which 

 the decadent ray-florets are subsequently pressed. The ultimate 

 assumption by these latter of a form adjusted to the room allotted 

 them in the bud is thus not due to the fact that they are subtended 

 by members of transition ; while since the same influences may act 

 to a greater or less extent in other peripheral florets, the number 

 of ray-florets is not absolutely constant, although the approximation 

 to the theoretical number is very close.* 



Transition to a higher scale of phyllotaxis, on an axis which is 

 rapidly expanding without correlated expansion in the lateral 

 members, thus takes place in alternate stages of the ratio series. 



Thus in the specimen of Cynara Scolyrmis figured, the large 

 involucral scales (figs. 9, 52) showed on the sides of the capitulum 

 the obviftus parastichies (8-1-13), and these are further seen to be 

 contact parastichies in section of the head. After production of 

 79 of these the phyllotaxis rose to (21-)- 34) and 102 smaller 

 sterile scales were laid down, while at the edge of the disk the 

 phyllotaxis rises to (55-)- 89), with which curve-construction the 

 disk-florets are produced without subtending bracts (fig. 52). 



The total number of sterile scales (181) being relatively large, 

 and greater than the number of florets in one complete cycle (144), 



* Of. Weisse, Variation Curves, p. 480, tables ; Lndwig, Ueber Variations- 

 kurven, Bot. Centralb., Ixiv. p. 102. 



