NORMAL FIBONACCI PHYLLOTAXIS. 



89 



the sine of half the angle subtended, the previous series be- 

 comes : — 



There is reason to believe, however, that these highest systems 

 are never formed directly at the apex of a young axis, but are 

 gradually built up along similar curve systems ; and the occurrence 

 of such a system as (8-1-13) as a direct formation is the limit of 

 the capacity of the plant. When such a system is regarded as 

 composed of primordia each subtending an arc of 23°, the possi- 

 bility of a range of error amounting to even more than one degree 

 is at once apparent. It will not be necessary so far to regard the 

 plant as working to any divergence angle of very exact degree, 

 and the approximation in building the system to such an angle as 

 137° '5 may be very rough. This becomes still more obvious when 

 the ease with which the primordia make very considerable adjust- 

 ments is taken into consideration. 



* Gf. Maihematical Notes, IV. 



