CHAP, iv.] Metamorphosis and of the Spiral Theory. 169 



thing coming into being in time and according to natural laws, 

 how profoundly he despised the principles of modern natural 

 science is shown in his judgment of Darwin's theory of descent 

 and of the modern atomic theory, the coarseness of which is 

 the more surprising, because Schimper was a man of refined and 

 even poetic feeling. ' Darwin's doctrine of breeding,' he says, 

 'is, as I discovered at once and could not help perceiving 

 more and more after repeated and careful perusal, the most 

 shortsighted possible, most stupidly mean and brutal, much 

 more paltry even than that of the tesselated atoms with which 

 a modern buffoon and hired forger has tried to entertain us.' 

 Here is the old platonic view of nature flying at modern 

 science; the sternest 'opposites' that culture has ever pro- 

 duced. 



The theory of Schimper, which should rather be called the 

 theory of Schimper and Braun, considering the active part 

 which Braun took from the first in framing and applying it, 

 was capable of further development only in the mathematical 

 and formal direction, as was shown especially in Naumann's 

 essay, ' Ueber den Quincunx als Grundgesetz der Blattstellung 

 vieler Pflanzen ' (1845). The defects above described, but not 

 the merits of the theory, were shared by the doctrine of phyl- 

 lotaxis laid down about ten years later by the brothers Louis 

 and Auguste Bravais. Their theory makes use of mathematical 

 formulae to even a greater extent than that of Schimper with- 

 out paying any attention to genetic conditions, and yet it is 

 less consistent with itself, for it assumes two thoroughly different 

 kinds of phyllotaxis, the positions in which are arranged in a 

 straight and in a curved line; for the latter without any 

 apparent reason a purely ideal original divergence is assumed 

 which stands in irrational relation to the circumference of the 

 stem, and from it all other divergences should be derivable ; 

 and this ultimately degenerates into mere playing with figures 

 which in this form afford no deeper insight into the causes 

 of the relations of position. As regards serviceableness in the 



