140 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



metrical constructions only, — the (2 + 3) and the (3 + 5), from both 

 of which pentamerous forms may be obtained. 



I. The rules for constant phyllotaxis may be observed ; e.g., in 

 Delphinium Ajacis, (3 + 5) throughout; Galycanthus, (5 + 8) 

 throughout. 



II. Normal expansion types are general among the primitive 

 forms; e.g., Eanunculaceae and allied families exhibiting very 

 commonly (2 + 3) (5 + 8), Nigella, Magnolia; (3 + 5) (8 + 13) 

 Hellehorus, Aeonitum Napellus. 



III. The symmetrical variations of the form, — 



(2 + 3) becomes (2 + 2) or (3 + 3), 

 (3 + 5) becomes (3 + 3) or (5 + 5),. 



follow normal lines of production, by the equalisation of the 



parastichy curves ; the full 

 © type thus commences by 



adding normally to the long 

 curves, but remains station- 

 ary on the first attainment of 

 symmetry, while true dimery 

 and trimery are seen to be 

 secondary, as dicliny also un- 

 doubtedly is as well. 



IV. The case of falliug 

 phyllotaxis is rendered espe- 

 cially interesting, in that such 

 a reduced series naturally 

 closes the production of 

 lateral members at the end 

 of the floral axis and will be 

 noticed usually in the mem- 

 bers of the gynoecium (Ean- 



Fig. 1.— Symmetrical version of falling Unculaceae). 



phyllotaxis in terms of circular con- The general phenomena of 

 struction instead of spiral. g^c^ a falling phyllotaxis hav- 



ing been described as theoretically representing a fall of the Fibonacci 

 ratios along their normal sequence 2, 1, 2, 1, 2, etc., the scheme 



