161 



i\vn one, a fact already stated in some exceptional cases by 

 l r. iv a is. All so-called "orthostichies" seem to be really curviserial 

 les, especially in the higher divergencies. But then they cannot 

 distinguished principally from parastichies, and therewith one 

 >t the premises of the Schimper-Braun-theory has lost its value. 

 Church concludes that only the number of intersecting parastichies, 

 txtro-, or laevogyrate, determines the numerical character of the arran- 

 t, as already suggested by Braun. Moreover he points to the 

 ict already stated by Hofmeister, De Candolle and Sachs, 

 lat the phyllotaxis-fraction, whatever numerical value is given 

 it, must appear greater or smaller in the same rate, as the axis 

 ibout which the leaves are arranged, is shortened or lengthened, 

 ic phenomena of varying phyllotaxis therefore being partially 

 msed by the varying rates of growth 1 ). De Candolle *) has drawn 

 ittention to the same fact; according to this author the character 

 )f the phyllotaxis, even if a constant angular divergence between 

 msecutive members be supposed, -- must vary when the ratio: 



1.V 



- of the stem during the process of growth changes appre- 

 iiamcter 



:iably. In condensed and multiple fruits and inflorescences (Pinus, 

 [nanassa, Helianthus, etc.) a change of the ratio between longitudinal 

 id transversal growth does not occur ; hence the laws of phyllotaxis 

 re best studied in the case of such multiple fruits and inflorescences, 

 the capitulum of the sunflower, in the cones of Pinus, in termi- 

 buds, etc. It is therefore absolutely necessary to draw attention 

 lore exclusively to the study of the growing apex of the plant: the 

 'irst zone of growth in the terminal bud must, in the opinion of this 

 mthor, reveal the phenomena of phyllotaxis in their most pure and 

 idisturbed form. The explanation to be given of it must moreover 

 ;ally satisfy the requirements of ontogenetic observation. Thus, 

 tarting from Sachs' theory of cell-formation and of the orthogonal 

 itersection of cell-walls 2 ) in the terminal bud, he comes to the 

 >n elusion that the parastichies must have the shape of logarithmic 



1) Cf.: G. v. Iterson Jr., Mathematische und Mikroskopisch-anatomische 

 Studien uber Blattstellungen, Jena, (1907), p. 222. C. de Candolle, Considerations 

 sur 1'Etude de la Phyllotaxie, Geneve, (1881), p. 47, 29, 52. There seem to be however 

 a number of other important causes, acting during the first design of the lateral 

 organs, which govern this phenomenon of varying phyllotaxis. 



2) J. Sachs, loco cit. p. 253; Cf. also: L. Errera, Bull, de la Soc. beige de 

 Microscopic, 18. 1. (1886). 



II 



