4 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



Four types were established : the cases of opposite leaves, whorled, 

 alternate and scattered (feuilles ^parses) respectively; the 

 definition of the last named being that it included all instances in 

 which the members were arranged in no constant order. 



Linnaeus scarcely went farther than this. In his Fhilosophia 

 Botanica, 1751, the types are increased to nine ; Bispositio sparsa 

 being extended to Conferta, Imlricata, and Fasciculata : the 

 definition of sparsa being again "sine ordine." 



Bonnet first determined a spiral arrangement, and his observa- 

 tions contain the germs of all subsequent spiral theories 

 (Becherches swr I'usage des Feuilles dans les plantes, 1754, p. 159). 



He classified leaf arrangement according to five types : 



(1) Alternating, 



(2) Decussate (Faires croissees), 



(3) Whorled, 



(4) Quineuncial, 



(5) Multiple Spirals (Spirales redoubles) : 



the last two of these being the ones which present the essential 

 points of interest. 



Not only did Bonnet thus originate the spiral construction, but 

 he claimed to have discovered the "final cause" of the arrange- 

 ment of leaves, and his generalization, that " Transpiration which 

 takes place in the leaves demands that avr should- circulate freely 

 aroimd them, and that they should overlap as little as possible," 

 has had a remarkably persistent influence on subsequent in- 

 vestigators. 



Omitting this physiological standpoint, the morphological 

 generalizations of Bonnet were sufficiently striking. In this fourth 

 type, he included the true f spiral as we now understand it, in 

 which a spiral makes two revolutions to insert five members, thus 

 ultimately producing five vertical rows on the axis; and this 

 arrangement he checked on sixty-one species of plants. The term 

 quincumcial, thus defined, became limited to a special type of spiral 

 phyllotaxis quite apart from its original signification. He further 

 noted the tendency of the f phyUotaxis to vary to vertical rows of 3 

 or 8 on the same species : the variation in the rise of the spiral 



