The Principles of Phyllotaxis. 



BY 



ARTHUR H. CHURCH, M.A., D.Sc, 



Lecturer in Natural Science, Jesus College, Oxford. 

 With seven Figures in the Text. 



IN a preliminary note published some time ago ^ exception was taken 

 to the conventional methods adopted for the description and even 

 interpretation of phyllotaxis phenomena, and a suggestion was made 

 that appeared to be not only more in accord with modern conceptions 

 of the phenomena of energy distribution, but it was further indicated that 

 such a theory when carried to its mathematical limits threw a strong light 

 both on the mechanism of shoot production and the inherent mathematical 

 properties of the lateral appendage usually described as a 'leaf-member,' 

 as opposed to any secondary and subsidiary biological adaptations. 



As publication of the entire paper has been delayed, and the new 

 standpoint has not received any special support from botanists to whom 

 the mathematical setting proved possibly a deterrent, the object of the 

 present note is to place the entire argument of the original paper in as 

 concise a form as possible ^. The prehminary discussion is sufficiently 

 familiar ^. 



The conventional account of phyllotaxis phenomena involves a system 

 of ' fractional expressions ' which become interpreted into angular diver- 

 gences ; and in practice the appearance of ' orthostichies ' has been taken 

 as a guide to the determination of the proper 'fractional expression.' 

 This method, elaborated by Schimper (1830-5), has more or less held 

 the field to the present time ; and, for want of something better, has 

 received the assent, though often unwilling, of such great investigators 

 as Hofmeister and Sachs, to say nothing of lesser lights. Although 

 elaborated into a system by Schimper and Braun, who added the peculiar 

 mathematical properties of the Fibonacci series to the academical account 



' Note on Phyllotaxis, Annals of Botany, xv, p. 481, 1901. 



" On the Relation of Phyllotaxis to Mechanical Laws. Part I, Construction by Orthogonal 

 Trajectories, 1901. Part II, Asymmetry and Symmetry, 1902. 



' Descriptive Morphology-Phyllotaxis. New Phytologist, i, p. 49. 



[Annals of Botany, Vol. XVni. No. LXX. April, 1904.] 



