INTRODtrCTION. 15 



and the relationship of members is thus readily tabulated and 

 placed in diagrammatic form, as in the construction of floral 

 diagrams, it affords ■ no explanation of the fact why, for example, a 

 § divergence maybe continued indefinitely, and then, when it does 

 rise, passes into a | or even directly into a ^-, as in the construction 

 usually given for the nectaries of Helleborus niger. One begins to 

 regard with suspicion the convention which infers from five 

 members a f spiral, and from thirteen members a f^ spiral, while a 

 fall to five carpels may be interpreted as a reversion to a | spiral 

 again. The conventions do not explain anything; and it is not 

 clear, if angular distances cannot be checked, what criterion can 

 distinguish between five members of a § spiral and the first five, for 

 example, of an ^ series. 



Schwendener in his constructions accepts the divergences as 

 standard quantities, and proposes figures of transition in which the 

 varying bulk of the elements is taken into account. The point of 

 view adopted here will be that, in the case of normal and phylo- 

 genetically primitive inodes of growth, the divergences themselves 

 convey an erroneous impression, and that all theories which include 

 their acceptance must necessarily fall to the ground. 



Nothing is more striking, in dealing with the subject of phyllo- 

 taxis, than the large number of hypotheses put forward which are 

 almost equally incapable of direct proof or disproof ; and the 

 difficulty of the problem consists in determining a sure foundation 

 on which subsequent theories may be elaborated. 



The hypothesis of Schimper and Braun does not satisfy the 

 demands of modern investigation, in that its premises do not admit 

 of strict observation and measurement, and for similar reasons 

 Schwendener's views on mechanical contact-pressures are incapable 

 of direct proof.* 



. That such contact-pressures exist, and operate to a very consider- 

 able extent in producing secondary changes, is undoubted ; but it 

 does not follow that they are so pre-eminently important and lead 

 to such great disturbances of the original construction, since it is 

 possible that by being equally distributed the disturbing effect 



* Cf. K. Schumann, Morphologische Studim, Heft 2, 1899, p. 312 ; C. de 

 Candolle, Consid^ations sur P^tvde de la Phyllotaxie, 1881, p. 27. 



