186 



a hitherto unexplained différence between those two kinds of whorls 

 exists, is in my opinion quite certainly the case, and a well-establis- 

 hed theory of phyllotaxis should explain this remarkable différence. 



Schimper and Braun did net try to explain the phenomena 

 they described; Braun especially was inclined to think that any 

 further step after the description of facts was impossible as thèse 

 phenomena were the expression of ideas mherent to the living 

 plant. Schimper was obviously more bent towards physiological 

 conceptions and he promised to go „tiefer ins Physiologische" m 

 his large work on phyllotaxis that was announced several times'^ 

 but unfortunately has never been published. 



Since that time, many investigators hâve studied the phenomena 

 of phyllotaxis and many attempts to explain them on a more or 

 less physiological base hâve been undertaken; but it is very re- 

 markable that thèse attempts hardi y bore on whorled phyllotaxis 

 and chiefly endeavoured to make us understand the cause of the 

 prédominance of the numbers of the Fibonacci séries. 



Apart from a short paper of GoebeP, in which whorls are 

 denved from spirals in a phylogenetical way, no defimte study of 

 whorled phyllotaxis seems ever to hâve been undertaken. 



This is the more surprising, as the whorled condition of phyllo- 

 taxis offers a very temptmg problem, which morphologists as well 

 as systematists often must hâve come across. The said problem is 

 as follows. Since Hofmeister^ in 1868 rejected the spiral-theory 

 of Schimper and Braun, and expressed the opinion that leaves 

 originate in the largest space between two lower leaves, this so- 

 called law of Hof meister has been the base of almost ail théories 

 on phyllotaxis. If this law holds true, the place of a leaf is deter- 

 mined by the position of two lower leaves, or if there are no lower 

 leaves, by the boundaries of available space. Besides there may 

 be various causes which act during the developmental stages of the 



1 Symphytum 1. c. p. 119; Flora 18, 1, 1833, p. 39. ibid. p. 745. 

 ^ K. Goebel, Morphologischeund biologischeBemerkungen, 21, Scheinwirtel, 

 Flora 1912, 105. p. 71. 



3 W. Hofmeister, Allgemeine Morphologie der Gewachse, Leipzig 1868. 



