164 



and if the forms of the parastichies on a cylindrical stem be supposed 

 to agree with that of the ordinary Archimedian spirals (p = a.i), 

 the development of the system of parastichies on the cylindrical 

 surface in a plane will give a system of parallelogram-shaped 

 meshes, at the corners of which are placed the different leaves. 

 Such a plane drawing, showing the arrangement of the bracts and 



berries observed in a 

 part of the multiple 

 fruit of Ananassa 

 sativa, is reprodu- 

 ced in fig. i jo. 



As Wulff 1 ) first 

 pointed out, the 

 distribution of these 

 organs is, at least 

 in principle, exactly 

 comparable with the 

 space-lattice-struc- 

 ture met with in 

 crystalline matter, 

 this form of struc- 

 ture being, indeed, 

 the prototype of the 

 most general perio- 



Fig. 130. 



.... Genetic spiral (laevogyratory) . 

 Parastichies (* -f- 13) . 



dical distribution of 

 equal things in unli- 

 mited number. But 

 yet there must ap- 

 pear to be a striking difference between the arrangement of living 

 objects in one case, and that of the molecules in the other. For 

 if all conditions in phyllotaxis were really such as pictured here, 

 the divergencies which occur would be such, that their numerical 

 symbols Could be only rational numbers, just in the same way 

 as the possible edges of a crystal are always determined by the 

 direction of some straight line joining the angular points of each 

 netplane. 



However, as we have seen, it is found by experience, that only 

 symbols closely related to those of the series mentioned above occur 



l ) G. W. Wulff, CHMMETPlfl H Efl HPOJ1B71EH1E Bb'llPHPCVlfc. (Symmetry and Its 

 Manifestations in Nature), (Russian), Moscou, (1907), p. 119. etc. 



