On the Relation of Phyllotaxis to Mechanical 



Laws. 



By 



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



Lecturer in Natural Science, Jesus Gollege, Oxford. 



PART II. 



ASYMMETRICAL AND SYMMETRICAL PHYLLOTAXIS. 



In the previously published chapters,* the theory was elaborated 

 that the arrangement of lateral members on a shoot-apex was 

 possibly the expression of the symmetrical or asymmetrical distri- 

 bution of growth-energy in the growing apex, and in a system 

 for which uniform growth was postulated, the appearances were 

 to be mapped in terms of the phenomena of vortex construction, 

 and represented graphically by the same geometrical construction 

 as the lines of equal pressure and flow in circular or spiral vortices 

 respectively.^ 



That such conditions of uniform growth do not obtain to any 

 great extent in a plant-apex is sufficiently obvious, siace the apex 

 is never absolutely plane, nor again do the curves seen in a 



* On the Relation of Phyllotaxis to Mechanical Laws. Part I. Construction by 

 Orthogonal Trajectories ; A. H. Churcli, 1901, pp. 1-78. Of. Note on Phyllotaxis, 

 Annals of Botany, vol. xv. p. 481, 1901. 



t The relation of logarithmic spirals to phenomena of growth is very neatly 

 expressed in a mathematical form, in that in two dimensions the logarithmic 

 spiral is the only curve in which one part differs from another in size only but 

 not in shape. This property naturally follows from the definition of an equi- 

 angular spiral, but it brings out very vividly the essential character of such 

 a curve as a line of growth, 



F 



