CHAPTER XIV 



ON LEAF-ARRANGEMENT, OR PHYLLOTAXIS 



The beautiful configurations produced by the orderly arrangement 

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

 and curiosity; and not the least curious feature of the case is the 

 limited, even the small number of possible arrangements which we 

 observe and recognise. 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 order of the petals of a lotus or the 

 florets in a sunflower. For so, as old Nehemiah Grew says, "from 

 the contemplation of Plants, men might first be invited to Mathe- 

 matical Enquirys*." 



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 

 went so far as to declare this doctrine to be "in direct opposition 

 to scientific investigation, and based upon the idealism 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 said to be 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 

 two chief modes in which the phenomenon presents itself. That is 

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



* N. Grew, The Anatomy of Plants, 1682, p. 152. 



