159 



if all' 



the 



in:; indeed the prototype of the most -< -m r.il jxriodical distn- 

 u t ion of equal things in unlimited number. I'.ut vet then must 

 I)|H ,ir to be a striking difference between the arrangement of living 

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

 all conditions in phyllotaxis were really such as pictured here, 

 he di vergencies 

 which occur would 

 such that their 

 umerical symbols 

 uld be only ratio- 

 l numbers, 

 u<t in the same way 

 .s the possible cd- 

 ;es of a crystal are 

 ways determined 

 y the direction of 

 me straight line 

 ining the angular 

 ints of each net- 

 lane. 



However, as we 

 ive seen, it is found 

 >y experience that 

 m\y symbols clo- 

 jly related to those 

 )f the series men- 

 tioned above occur 



living nature, and that there is thus rather a tendency towards 

 the irrational ratio of the "aurea sectio" in living nature, which 

 to some extent goes parallel to the preference for true pentagonal 

 symmetry stated in the preceding chapters of this book. 

 Wulff tries to show that this contrast is only an apparent one, 

 )inting to the fact that even in such a crystallographically admit- 

 table space-lattice, irrational "limit "-values might be indicated. *) 

 If a straight line for instance joins the angular point of such a net- 

 plane, which has the coordinates (8,21), with the origin (= o, o), 

 it passes alternately above and beneath the angular points 0" /.;), 

 (3,8), (25), etc., of the net-plane, and it approaches the closer 



Fig. 128. 



Genetic spiral (laevogyrate) . 

 Parastichies (8 + 13). 



1) G. \V. Wulff, loco cit. 



