30 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



III. Geometrical Bepreseutation of Growth. 



Structuee of the First Zone of G-rowth. 



If spiral phyllotaxis is thus reducible to a function of the first zone 

 of growth, and is, for example, wholly independent of the circum- 

 nutation spiral which is a function of the second zone of growth,* 

 often exhibited most clearly in stems with a symmetrical arrange- 

 ment of leaves, it is necessary before deducing constructions for 

 phyllotaxis to determine as far as possible the various agencies in 

 operation in the former zone. 



The conception of the first zone of growth, as elaborated by Sachs, 



* Tlie same observation applies to the theory proposed by Airy (Proceedings 

 of the Royal Society, vol. xxii., 1874, p. 297, 307), in which a strong condensing 

 force was supposed to act with a telescoping effect on a simple whorled series 

 with a tendency to lateral displacement ! Such a condensing force, considered 

 possible as a phenomenon of arrested development of the axis, would be clearly 

 a property of the second zone, and though it may come under the head of 

 secondary changes, will have no influence whatever on the actual origin of the 

 new centres of growth in Zone I. 



Schwendener's theory (Mechamsche Theorie der Blattstellimgen, 1878) of a 

 vertical compressing force resembles in many points that of Airy ; his pressure 

 is again derived from the 'mutual contact of the primordia at their bases after 

 they are formed. But such alterations, again, must obviously belong to the 

 second zone of growth, and will, if the pressures are unequal, induce packing of 

 the primordia in close hexagonal series. 



Lastly, it may not be amiss to point out that the correspondence of vascular 

 bundles (Bonnet), the shape of the pith (Palisot de Beauvais, 1812), or the 

 presence of ridges on the stem (Naumann), being phenomena originated in the 

 third zone of differentiation, have still less importance as indicating any relation 

 whatever to the actual arrangement of the new centres of grovrth in the 

 embryonic protoplasm of Zone I. 



