36 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS 



The same will hold good for the radial longitudinal section, and 

 since lines of equal action are here marked out by orthogonally 

 intersecting cell-membranes, it is possible, though not at all essential, 

 that these curves may be parabolas. 



But although in deahng with a semi-fluid protoplasmic mass in 

 which movements are undoubtedly taking place one is tempted 

 to use the terminology of lines of equal pressure and flow, it is 

 clear that no definite movements, implying any considerable trans- 

 fer of material along any radial or circular paths, can be estab- 

 lished throughout the midticellular apex characteristic of vascular 

 plants, or even in the coenocytic apex of the Siphoneae. The 

 same orthogonal paths would in a plane system of electrical con- 

 duction mark out lines of equipotential and current flow, the two 

 sets of phenomena being in fact only special cases of the general 

 proposition of the distribution of energy along interchangeable 

 orthogonal paths. 



The more ambiguous term, paths of equal " action" may there- 

 fore be used in preference to any other terminology, although in 

 mapping out such systems the phenomena of the more obvious 

 vortex-motion of a fluid may be used metaphoricall]/, and as a term 

 implying a definite geometrical construction. 



Again, circular symmetry is clearly secondary ; all lower plants, 

 the majority of Algae, Bryophyta, and to a certain extent Vascular 

 Cryptogams, present asymmetrical growth at the apex, due to the 

 fact that new lateral members, in the form of single cells, can 

 only be added one at a time ; this being especially well seen in the 

 growth of filamentous cellular algae. 



A transition to a more bulky stage is accompanied by the de- 

 velopment of an initial cell cutting off segments in serial lateral 

 order, the three-sided apical cell of the Fucaceae and most Mosses and 

 Ferns being the most typical case. 



Primarily, then, it may be said plants possess asymmetrical growth 

 as a necessary consequence of the limitation of new members to 

 serial succession of individual units, and that the symmetrical con- 

 dition, in which new cells are added at the apex in all directions 

 contemporaneously, is a secondary phenomenon, evolved > as a 

 distinct improvement on the older method in correlation with the 



