228 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



diagram, and in actual ontogeny, follows as naturally as does the 

 geometrical construction by logarithmic spirals from, the addition of 

 similar members. 



The perfect regularity of the system shows that it is not the 

 ultimate shape or the lateral contact of the members which is the 

 essential controlling feature ; the form may vary with subsequent 

 growth changes, and the similarity of the contact-relations is again 

 only the expression of regular periodicity of formation. Whatever 

 subsequent changes take place, the primary curves drawn through 

 the centres of construction of the lateral members, in the great 

 majority of cases, retain their numerical relations, the only differ- 

 ence being in the form of the curves themselves. Still more 

 remarkable is the fact that in many cases even the secondary 

 lateral axes subtended by these primary members (Helianthus), 

 or emergences based on them (Pine-cone), maintain the original 

 curve system with such constancy that phyllotaxis theories are 

 discussed from the standpoint of these structures, which have only 

 a secondary relation to the true lateral members.* 



The essential point to note is that in order to produce such a 

 degree of regularity the actual centres of lateral growth must 

 have been initiated at definitely established points ; that is to say, 

 an infinite number of causes might produce secondary irregulari- 

 ties once a system were laid down : the fact that any system can 

 be traced in the adult condition implies that the initial impulses 

 must have been not only equally regularly placed, but presumably 

 far more so. 



Thus, in the postulated construction of circular growth-centres 

 plotted along orthogonally intersecting log. spirals, the numbers of 

 which are taken from observation of the plant, it follows that 

 these initial centres must also have been laid down at the inter- 

 section of orthogonally intersecting log. spirals of the same ratio. 

 The main question at issue, therefore, is to determine why these 

 points should be found at the intersection of certain orthogonal 



* Gf. Jost, Bot. Zeitung, 1902, p. 21, "Die Theorie der Verschiebung 

 seitliclier organe duroh. ihren gegenseitigen Druck " ; Leisering, Flora, 1902, 

 p. 378, " Die Verschiebungen an Helianthuskopfen in Verlaufe ihrer Entwicke- 

 lung vom Aufbliihen bis zur Reife." 



