220 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



II. Rhythm. 



In previous chapters a general theory of growth was enunciated, 

 according to which the production of new members might be 

 capable of mathematical expression and of geometrical representa- 

 tion in a diagrammatic form. That growth is distributed at the 

 apex of a shoot in such a manner that its transverse component may 

 be expressed by a plane circular construction around a central 

 point (the growth-centre) is sufficiently clear, in that the circular 

 section of the vast majority of plant axes is evidently the outcome 

 of such a regular and symmetrical distribution from the " growing- 

 point " : so much so, in fact, that any stem which is not circular 

 in section is generally recognised as the result of secondary 

 inequalities in the rate of transverse growth. On the other hand, 

 it is clear that such a generalisation is based on an unexpressed 

 physical conception of radial growth ; and although it is thus 

 possible to imagine a stem which will be mathematically circular 

 in section, it does not necessarily follow that such a stem ever 

 occurs in nature ; nor would it be expected, owing to the recognised 

 frequency of secondary irregularities in every growth-system. The 

 fact that no stem is mathematically circular in section does not 

 affect this well-established generalisation ; but it is necessary to 

 point out that such ideas involve a physical conception which, as 

 in other cases, must ever be the basis of any system of morphology. 

 Exceptional cases, apart from the production of angular and 

 ridged stems, and the band-like forms produced by uneven 

 secondary growth in thickness, may be included under three 

 types :— 



