108 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



{Podocarpus, etc.), become obscured rather than explained ; while 

 the assumption of true circular symmetry from a spiral construction 

 is an entirely anomalous proceeding. 



On the other hand, the second standpoint, that the parastichies 

 are the controlling featxire, certainly gives broader views of the 

 whole range of phyUotaxis phenomena, in that it— 



(1) Allows for addition or loss of curves to such an extent that it 

 is immaterial whether the system works out as one or many 

 "genetic spirals." 



(2) It suggests a simple transition to true symmetry by equalisa- 

 tion of the number of curves in either direction. 



(3) It also presents a clear view of aU transitional systems, and 

 especially those included under the term "expansion systems," 

 which will now be considered. 



Putting on one side, therefore, any discussion as to what is, after all, 

 to be regarded as the prime cause of the asymmetrical growth which 

 thus expresses itself in terms of subjective spirals, it is so far clear 

 that as a matter of practical observation of the phenomena, as well 

 as the discussion and tabulation of the results, this method of t9- 

 garding the parastichy ratio as being the more immediate controlling 

 factor not only affords more accurate information from a theoretical 

 standpoint, but is even simpler practically than the established 

 method of genetic spiral and so-called " orthostichies " as a means 

 of determining, tabulating, and reproducing the constructions. 



