64 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



For expressing the facts of actual development, Archimedean 

 spirals are therefore absolutely useless. But while this is so, the 

 progressive flattening of the rhombs at the periphery of the system 

 bears a remarkable similarity to the phenomena observed in the 

 progressive dorsiventrality of foliage leaves, and it is to this fact, 



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Fig. 33. 



-Geometrical construction for spirals of Archimedes, asymmetrical 

 and symmetrical pairs, a=2, 3, 6, 8, 13, 21, 34. 



combined with the production of members which attain a fairly con- 

 stant bulk, that the close approximation to an appearance of Archi- 

 medean spirals is due as the members attain their adult form. 



In fact these spirals appeal to the eye, in the macroscopic 

 appearance of such a plant as Sempenivmn, or the cone of Pinus, 

 because the members observed cover a fairly uniform area; and 

 the parastichies approach Archimedean spirals in a transverse view 



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