REJUVENESCENCE IN NATURE. 117 



Naumann, which, originally scattered through' Leohhard 

 and Bronn's 'Jahrbuch der Mineralogie' (1842), and 

 Poggendorff's 'Annalen' (1842-43), were subsequently 

 collected by the author -into an independent treatise 

 (Ueber den Quincunx als Grundgesetz der Blattstellung,' 

 1845). Since I have indicated the occurrence of simpler 

 and more complicated conditions of the arrangement of 

 leaves, and a determinate cycle in which these appear in 

 the plant, I may be permitted to introduce here inci- 

 dentally an observation on the actual existence of series 

 of different conditions of arrangement, as asserted in 

 Schimper's, and my own works, but questioned in the 

 essays of the brothers Bravais. I feel the greater in- 

 clination thereto from a remark of Schleiden (' Grundz.,' 

 p. 1 76 ; ' Principles,' p. 265), who characterises the theory 

 of the Bravais, who sought to trace back to a single, 

 irrational angle of divergence, alike for all, the modes of 

 arrangement regarded by us as different and expressed 

 by a series of rational divergences, as far preferable, 

 since it indicates a simplicity of the law, and under like 

 possibilities that explanation is always to be preferred 

 which embraces the greatest number of cases under one 

 point of view. But the theory of rational divergences 

 which first recognised as such the multiformity of the 

 cases which observation reveals, and then strove to 

 subordinate them to a general law, should have been 

 upheld on this very ground, in opposition to a theory 

 which, in contradiction to itself, first denies the multi- 

 formity of the cases, to insinuate under them an ab- 

 stract unity, and subsequently (in the second part) 

 cannot avoid admitting that the rational and in reality 

 dissimilar cases do occur in plants. To deny the multi- 

 formity of nature without sufficient proof is certainly not 

 the right way to introduce unity of law into phenomena. 

 The assertion of the Bravais that all supposable arrange- 

 ments of leaves of the main chain are formed on a plan of 

 equal irrational divergence, is just as contrary to nature 

 as a system of crystallography would be that denied the 



