CONTENTS. 



VU 



V. Bilateral! ty of Appendages: Structure of a Foliage- 

 bud; Phenomena of Sliding-Growth ; Displacements 

 and Keadj ustments ; Spiral of Uorsiventrality ; 

 Spiral of Phyllody ; Kepresentation of Extreme 

 Bilaterality ; Contact-Cycles . . 290-315 



VI. Varying Growth in Lateral Members : Retention or 

 Obliteration of the Primary Pattern ; Pinus ; 

 Sempervivum ; Production of a Normal Foliage-leaf . 316-326 



MATHEMATICAL NOTES ON LOG: SPIRAL SYSTEMS AND 

 THEIR APPLICATION TO PHYLLOTAXIS PHENOMENA. 



I. General Equation to the Quasi-Cirole inscribed in a 

 Log. Spiral Quasi- Square Mesh: Bilaterality; 



Dorsiventrality ; Isophylly . 329-333 



II. Mathematical Orthostichies in Log. Spiral Systems . 334-335 



III. The Form of the " Ovoid " Curve . . . 335-337 



IV. Bulk-Ratio ...... 338-339 



V. The Oscillation Angle .... 339-341 



VI. The Fibonacci Series . ... 341-344 



VII. Continued Fractions . ... 344 



VIII. Sliding-Growth . . . 345-347 



General Conclusions . . . 348-349 



Errata and Notes to Part I. . . . . 213 



Errata and Notes to Part II. : Pine-Cones ; Dichotomy 



of Helianlhus annuus . . 361 



