RISING PHYLLOTAXIS. 115 



shows that the involucral region is here much more developed than 

 in Relianthus, while two complete transitions are included in the 

 construction. 



The relation of two such transitional systems to one another 

 therefore remains to be considered. Does the transition take place 

 rapidly and with a minimum number of members, or is it irregular 

 and spread over a large number? In Cynara the number of 

 members observed is very large, and in absence of further data 

 either method may be possible ; the remarkable accuracy with 

 which the transition has been planned for Helianthus suggests that 

 the latter plant may be taken as a type. 



Before passing on to the case of the double transition, the 

 mechanism of the normal expansion of Helianthus capitulum re- 

 quires to be carefully considered. As already noted, such a 

 transitional system presents the appearance of a cell-segmentation, 

 or even a process by means of which primordia are as it were 

 separated out along specially formed lines of cleavage. The whole 

 construction is influenced rather by the preceding parastichy lines 

 than by a definite genetic spiral, and the system grows throughout 

 along its pre-established paths of asymmetry. This agrees with the 

 facts observed in the actual ontogeny, so many new members being 

 formed simultaneously that the genetic spiral is hopelessly lost 

 sight of, and can only be traced by numbering the members. 



It would appear now that the genetic spiral as a line of building 

 has lost its significance ; the question of phyllotaxis becomes one of 

 continuing an expansive development along similar curved paths, 

 and the plant continues to work out a definite pattern quite 

 mechanically. 



It is clear that while such expansion may be pursued indefi- 

 nitely, the same ratio system will always be constantly maintained, 

 and constructions in the very highest terms of the Fibonacci series 

 thus "become conceivable, not by accuracy of the building-mechanism 

 however, which in such case would come down to a question of 

 working at an angle correct to minutes and seconds, but by simply 

 following up a system of construction which maintains at all stages 

 an approximately identical degree of symmetry. 



The method of employing this expanding mechanism may now 



