168 



the radii of all-sided growth. The "diagonal" arrangement corres- 

 ponds to the special supposition, that a new member takes its place 

 exactly in the cavity left between two members already present. 



The radial arrangement is in 

 agreement with the radial direc- 

 tion of transversal growth (De 

 Candolle, loco cit. p. 29). Now 

 the concentric circles indicating 

 the successive zones, are substi- 

 tuted by a logarithmic spiral as 

 "genetic" line, "like the line of 

 current in a spiral vortex", and 

 the radii likewise substituted by 

 parastichies of the same shape 

 Fig. 132. wound in one or in the opposite 



direction. 



Thus, in the case of "diagonal" orientation, the asymmetrical 

 system of fig, 132 

 appears; and how 

 closely these con- 

 structions, which 

 can, moreover, be 

 performed in a sim- 

 ple geometrical way, 

 - lead to arrange- 

 ments correspon- 

 ding with what is 

 actually observed in 

 nature, may be 

 seen by comparison 

 of Church's fig. 133, 

 which represents 

 the configuration of 

 fruits in the capi- 

 tulum of Helianthus 

 annuus as deduced church 

 from his theory, - 

 with the arrange- 

 ment of the fruits really observed, as represented in fig. 128. In this 

 construction the whole system remains orthogonal, as was original- 



Fig. 133. 



construction of the Configuration of the 

 fruits in the Capitulum of Helianthus annuus. 



