9U ON LEAF-ARRANGEMENT [ch. 



the other be the better, or even whether one be not positively correct 

 and the other radically wrong, has been vehemently debated ; but as 

 a matter of fact they are, both mathematically and biologically, 

 inseparable and even identical phenomena. For the face of the 

 sunflower is but a shortened stem, and the curves upon its 



Fig. 449. A cauliflower, its composite inflorescence shewing spiral patterns 

 of the first and second order. 



surfaces are but the projection on a plane of a more elongated 

 inflorescence. 



We speak, as botanists are wont to do, of these spirals of sunflower, 

 cauliflower and the rest as logarithmic spirals, but not without 

 hesitation. They doubtless resemble the logarithmic or equiangular 

 spiral, but different spirals may look much alike; and these are 

 ill-suited to the careful admeasurement and rigorous verification 



