INTRODUCTION. 



13 



on direct observations of plants, and the results are so far logically 

 carried out along Schimper-Braun lines of argument. 



If these arrangements are regarded as the reductio ad absurdum 

 of the whole subject, it follows that the original premises are 

 possibly incorrect. It is so far only necessary to point out that 

 these cases are relatively much less numerous, and occur in plants 

 which exhibit marked adaptations to special biological environ- 

 ment, or, in modern phraseology, are markedly xerophytic, as for 

 example, Dipsacus, Sedum, Pothos, Bromelia, Gadacem. 



By adopting the following 

 construction, and using the 



usual terminology, a very 



plausible diagram, which con- 

 veys a useful summary of the 

 Schimper-Braun theory, may 

 be plotted out (fig. 1). If it 

 be granted that, given a con- 

 stant type of lateral member, 

 the phyllotaxis would rise, as 

 expressed in the fractional 

 series, with successive increase 

 in the diameter of the axis, it 

 might also follow that it would 

 fall on a constant axis if the 

 members increased in bulk, or 

 rise if they were diminished, 

 according to the number of 

 members which would fill a 

 cycle round the stem. 



Again, since members pack 

 more or less together, spheres to a certain degree extending into 

 the rows adjacent to them, while rhomboid figures each press one 

 half their length into adjacent cycles ; and since, to take the general 

 ease, the plant commences growth from two symmetrically placed 

 cotyledons (divergence J), it would pass on to a spiral arrangement 

 in the simplest manner by placing one member on one side and two 

 on the other ( = divergence ^). With no further increase in the 



Fig.l. — General scheme for the orientation of 

 the cycles of the Schimper-Braun hypothesis. 



