KHYTHM. 227 



developed androecium derived from a circular zone of growth 

 (Paeonia, Gereus), shows that such secondary influences will only 

 increase the primary irregularity. 



Since, as hypothecated, the geometrical construction of a circular 

 meshwork of quasi-squares indicates a time-diagram, that is to 

 say, one expressed in terms of rate of growth, and the above 

 constructions follow the lines of such a diagram or its asymmetrical 

 homologues, it is clear that the system must be first interpreted 

 in terms of time, and that the regularity of the system is the 

 expression of a remarkably beautiful periodicity or rhythm in 

 member production. 



That regular phyllotaxis phenomena are really the expression of 

 such accurate periodicity in member production will be readily 

 granted ; but such a statement does not take one very far, since it 

 is only another way of expressing an obvious fact. The point is, 

 — to what is this periodicity due, and will it afford any further 

 insight into the phenomena ? Thus, once such periodicity is 

 granted, it is clear that the phenomena of "rising" and "falling " 

 phyllotaxis may be very elegantly expressed from this standpoint, 

 in that a rising phyllotaxis and high ratios would imply an in- 

 creased activity of production of new growth-centres on a given 

 area, correlated with an increased vigour in the axis ; while falling 

 phyllotaxis and low ratios become a sign of enfeebled growth — 

 that is to say, growth-centres are only produced at greater in- 

 tervals of time, with the result that they each influence a wider 

 tract, and thus give rise to members of relatively greater bulk, 

 so that the system presents the subjective appearance of a smaller 

 number of intersecting curves. But, on the other hand, it affords 

 little further insight into the causes affecting other phenomena of 

 symmetry, bijugate systems, etc. Thus, in dealing with symmetri- 

 cal as opposed to asymmetrical systems, periodicity can go no 

 further than the expression of the simple fact that in the former 

 ease several members are simultaneously produced at equal in- 

 tervals of time, while in the latter case only single members are 

 produced at equal intervals. 



There must, in fact, be some still more hidden meaning in the 

 construction, from which the periodicity as expressed in a time- 



