187 



leaf, which may affect secondary displacements, the so-called 

 metatopies. When we now consider e. g. a pentamerous whorled 

 phyllotaxis with regular alternation of the whorls, this must be 

 understood in this way that every leaf of a whorl is determined in 

 its position by the two nearest leaves of the lower whorl; in using 

 the notation of Church^ this may be expressed by denoting the 

 System as 5 + 5. 



A ^/s calyx on the contrary must be a cycle of a normal phyllo- 

 taxis of the Fibonacci séries, and may be a 1 -f 2 System with 

 144'' divergence. 



Floral morphology has taught as further that most floral penta- 

 merous whorls, which are not discernible from a 5 + 5 system, 

 must be derived from a 1 +2 system, or at least from a system of 

 the normal séries. Now it is clear that a given phyllotaxis can 

 originate as 5 + 5 or as 1—2 but not as both at the same time. For 

 a leaf the position of which has been determined by two lower 

 leaves, cannot at the same time originate through the influence of 

 two others; at the utmost the other leaves can afterwards cause a 

 metatopy of the said leaf. 



The changes required to make a 5 + 5 system out of a ! +2 system 

 arevery considérable, and so the f ollowmg two questions may be put : 



Are ail floral whcrls really derived from spiral Systems, or is it 

 possible that there are two kinds of floral whorls, real whorls and 

 altered spireil Systems? 



The second question is: by what processes are the metatopies 

 induced, which change a spiral system into a whorled one? In 

 respect to the first question, it may be remembered that Eichler 

 has tried^ to make a distinction between real floral whorls and 

 false ones. He considered as characteristics of the false ones that 

 the members originate in a spiral order and show différences in 

 bulk or other peculiarities, connected with the same spiral order, 

 and that this whorls are generally not alternating, but superposed. 

 As true whorls on the contrary be considered those that are composed 



^ A. H. Church.On the relation of phyllotaxis to mechanical laws, London 1904. 

 ■^ A. W. Eichler, Blùthendiagramme, Leipzig, 1875—78, part I, p. 8. 



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