CHAPTER XIV 



ON LEAF-ARRANGEMENT, OR PHYLLOTAXIS 



The beautiful configurations produced by the orderly arrange- 

 ment of leaves or florets on a stem have long been an object of 

 admiration and curiosity. Leonardo da Vinci would seem, as Sir 

 Theodore Cook tells us, to have been the first to record his thoughts 

 upon this subject; but the old Greek and Egyptian geometers 

 are not likely to have left unstudied or unobserved the spiral 

 traces of the leaves upon a palm-stem, or the spiral curves of the 

 petals of a lotus or the florets in a sunflower. 



The spiral leaf-order has been regarded by many learned 

 botanists as involving a fundamental law of growth, of the deepest 

 and most far-reaching importance; while others, such as Sachs, 

 have looked upon the whole doctrine of " phyllotaxis " as " a sort 

 of geometrical or arithmetical playing with ideas," and "the 

 spiral theory as a mode of view gratuitously introduced into the 

 plant." Sachs even goes so far as to declare this doctrine "in 

 direct opposition to scientific investigation, and based upon the 

 idealistic direction of the Naturphilosophie," — the mystical biology 

 of Oken and his school. 



The essential facts of the case are not difficult to understand ; 

 but the theories built upon them are so varied, so conflicting, and 

 sometimes so obscure, that we must not attempt to submit them 

 to detailed analysis and criticism. There are two chief ways by 

 which we may approach the question, according to whether we 

 regard, as the more fundamental and typical, one or other of the 

 two chief modes in which the phenomenon presents itself. That 

 is to say, we may hold that the phenomenon is displayed in its 

 essential simplicity by the corkscrew spirals, or helices, which 

 mark the position of the leaves upon a cylindrical stem or on an 



