RrsiNG PHYLLOTAXIS. 109 



III. Bising Fhyllotaxis. 



As previously indicated, any definite alteration of the system of a 

 constant phyllotaxis must result in a distortion of the parastichy 

 curves. The case of Dipsacus in which, with a constant lateral 

 member and varying axis, new members were added or lost to 

 compensate this change in the bulk-ratio, to the very slight extent 

 of losiug or adding one or two curved rows, shows that the dis- 

 tortion effect may be considerable (figs. 38a, 6); and it is clear 

 that the same law of adding one member at a time to the system, 

 which controls the asymmetry of the whole construction, must also 

 result in the addition of such compensatory rows one at a time, if 

 the whole system is to change from one curve-ratio to another. If 

 now these changes are initiated on a rapidly expanding apex, such 

 as that presented by the developing capitulum of Helianthus, there 

 can evidently be no attainment of symmetry resembling that which 

 previously obtained in the apex, until every member of the cycle has 

 similarly divided, all round the axis. 



A " Zone of Transition " must thus be intercalated between the 

 two systems, and will form the outward sign of the passage of one 

 system of asymmetry to another with the same approximate curve 

 construction. Previous considerations have further shown that, if 

 the curves remain constant in direction, and the ontogenetic spiral 

 is also constant, change can only take place between alternate 

 members of the ratio series; thus (5-)- 8) rises with a minimum 

 effort and least distortion to (13-1-21) ; {cf. table in fig. 34). 



Confirmation of such a view is very obvious in ffelianthus, in 

 which the ratio of the contact-curves of the inner sterile involucral 

 scales of the capitulum, bears constantly this relation to the para- 



