224 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



circular meshwork of quasi-squares, in which all the similar 

 meshes are produced in equal times — it being evident, as pre- 

 viously pointed out, that the consideration of an ideal condition 

 of uniform growth should precede any attempt at a closer 

 approximation to the facts of growth actually presented by 

 living organisms. While, again, this geometrical presentation 

 of uniform growth is so far simple in its radially symmetrical 

 relations, a geometrical device admits of homologous cases of 

 asymmetrical growth also being plotted, thus giving, as already 

 described, a figure identical with the geometrical representa- 

 tion of lines of equal pressure and paths of flow in a spiral 

 vortex. 



In such a system the introduction of lateral growth-centres 

 may be next considered. That such a secondary growth-centre 

 should repeat the construction of the primary centre appears 

 fully warranted as a sound hypothesis. The phenomenon of a 

 lateral growth-centre is thus to be similarly planned by a circular 

 meshwork of quasi-squares, and the figure illustrates similar 

 relations expressed in terms of equal time-units. It may thus 

 be taken that a lateral growth-centre may be similarly represented 

 either by a true circle, or possibly by the homologue of a circle : 

 the two cases may be subsequently distinguished. 



In the arrangement of such lateral members, again, one of two 

 conditions must obtain : either the system is wholly irregular, 

 or it is regular and systematic. The former case is apparently 

 presented in certain specialised inflorescences {Ficus) and floral 

 axes {Clematis), androecium {Paeonia, Cereus), but not in 

 positions in which it can present any claim to be regarded as 

 representative of a phylogenetically primitive arrangement; and 

 when the construction is thus irregular, little can be said about 

 it beyond the fact that the impulses apparently obey no law 

 which can be formulated, other than the statement that they 

 appear to be very approximately equidistant. 



On the other hand, in the vast majority of plants, especially 

 in unmodified vegetative shoots, as previously pointed out, the 

 regularity of phyllotaxis formations is their most remarkable 

 and distinctive feature ; and this clearly implies at least an equal 



