Contents 



PART I. 

 CONSTRUCTION BY ORTHOGONAL TRAJECTORIES. 



PAGES 



I. Introduction : Historical Sketch, Fibonacci, Bonnet, 



The Spiral Theory of Schimper, Bravais, Sachs . 1-16 



II. General Observations: 1. Orthostichies; 2. Parastichies, 

 Pinus Pinea ; 3. Eupliorhia Wulfenii ; 4. Cynara 

 Scolymus ; 5. Helianihus annuus . . , 17-29 



III. Geometrical Representation of Growth : The First 



Zone of Growth ; Vortex Representation ; Geometry 



of Uniform Growth Expansion . . . 30-44 



IV. Application of Spiral- Vortex Construction ; Possible 



Arrangements; Concentration-Systems; Construction 

 of Log. Spiral Curves ; Application to Helianthus 

 Capitulum ; Helices and Spirals of Archimedes . 45-65 



V. Ideal Angles : Suggestions of Wiesner . . 66-74 



VI. Asymmetry . .... 75-78 



PART II. 



ASYMMETRICAL AND SYMMETRICAL PHYLLOTAXIS. 



I. Normal Fibonacci Phyllotaxis : Conception of Bulk- 

 Rath) ...... 83-89 



II. Constant Phyllotaxis : Arauearia, Podocarpus . 90-108 



V 



