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 produced.
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 phyllotaxis 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 without 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
