50 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



the plant actually selects such an arrangement in order to secure 

 this gain of concentration, the fact remains that the system is the 

 one found in the vast majority of whorled types, which are again 

 regarded as secondary derivatives from an ancestral asymmetrical 

 condition. 



In selecting this alternative whorled construction (fig. 22), note 

 that — 



(1) The system remains orthogonal, and is thus equally de- 

 pendent on lines of equal pressure. 



(2) No additional pressure is required beyond those already in 

 action in arrangement A. 



(3) However great the growth pressures of the equally developing 

 component primordia, no hexagonal packing will be produced, but 

 the circles will approach square rhombs, unless, as before, growth is 

 unequal, or takes place inside a closed system. 



Again, since the whole bulk remains constant, the arrangement 

 is not due to any condensation, implying packing, but may be 

 perhaps better expressed by the term concentration. 



When expressed in the form of a plane circular diagram (fig. 22), 

 the diagonals become orthogonally intersecting log. spirals in that 

 they cross the radii at a constant angle, and a suitable number of 

 these paired spirals will in turn map out the system by their 

 orthogonal intersections, which will give figures which are in the 

 limit squares with inscribed circles. 



5. Arrangement D. 



The general case of spiral phyllotaxis is now reached by taking the 

 asymmetrical expression of the construction C. The whole system 

 remains orthogonal, but is expressed by a spiral vortex-construction 

 in which the genetic spiral remains as in B the grand log. spiral 

 current line. The radial '' orthostichies '•' will intersect this spiral 

 orthogonally. The two symmetrical log. spirals which mark out 

 the paths along which the members are actually laid down in a 

 concentration system become an asymmetrical pair and form the 

 Contact- Parastichies of the system. When the genetic spirals 



