270 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



growth at a uniform radial distribution from a growth-centre 

 implies the uniform action of various surrounding stimuli, which 

 in the vast majority of cases are unequally distributed, the 

 wonder remains that centric growth should be on the whole so 

 closely approximated that it appeals to the senses sufficiently to 

 justify this simple mathematical conception as a general starting- 

 point. Thus, although the majority of tree trunks and branches 

 may be fairly circular in section, few would show an even 

 approximately central pith, while the eccentricity of large starch 

 grains becomes the type. That the growth-centre of a shoot 

 exposed to varying environment should become eccentric is 

 therefore not to be wondered at ; but the degree of eccentricity 

 can only be judged by the after effects and by the eye, so that a 

 slight alteration of the system would not necessarily be noticed, 

 and it becomes very difficult to draw any sharp line between what 

 may be taken as sufficiently centric and constructions which are 

 obviously eccentric. 



Such cases of eccentricity and their relations as expressed in 

 the phyllotaxis systems may, however, be as readily followed by 

 geometrical constructions as the allied cases of the centric and 

 eccentric tree trunk, or the centric and eccentric starch grain, 

 the construction lines of which are generally accepted as being 

 represented by orthogonal trajectories (Sachs), though it is true 

 that no absolute proof has yet been given. Further, it becomes 

 possible, by geometrical constructions similar to those already put 

 forward as explanatory of the relations of symmetric (whorled) 

 and asymmetric (spiral) centric phyllotaxis systems, to deduce the 

 properties of the same system when the whole growth-system 

 becomes eccentric : the whole series of phenomena representing, 

 in fact, definite mathematical cases of growth construction which 

 would naturally be expected to occur in organisms exhibiting 

 growth under different aspects. 



Just as, in dealing with the growth and phyllotaxis of the main 

 shoot axis, the chances would appear to lie mathematically in 

 favour of asymmetry rather than symmetry as the fundamental 

 case, so that perfectly symmetrical construction, as exhibited in 

 the (2 -I- 2) or decussate system, or the (5 -f- 5) symmetry of flowers 



