128 ESSAY ON CLASSIFICATION 



in conformity with laws which obtain also among living beings, and 

 disclose in both spheres equally plainly the workings of a reflective 

 mind. It is well known that the arrangement of the leaves in plants^^^ 

 may be expressed by very simple series of fractions, all of which are 

 gradual approximations to, or the natural means between | or ^, 

 which two fractions are themselves the maximum and the minimum 

 divergence between two single successive leaves. The normal series 

 of fractions which expresses the various combinations most fre- 

 quently observed among the leaves of plants is as follows: |, ^, f, f, 

 TS) inr? Mj fi' etc. Now upon comparing this arrangement of the 

 leaves in plants with the revolutions of the members of our solar 

 system, Peirce has discovered the most perfect identity between the 

 fundamental laws which regulate both, as may be at once seen by the 

 following diagram, in which the first column gives the names of 

 the planets, the second column indicates the actual time of revolution 

 of the successive planets, expressed in days; the third column, the suc- 

 cessive times of revolution of the planets, which are derived from the 

 hypothesis that each time of revolution should have a ratio to those 

 upon each side of it, which shall be one of the ratios of the law of 

 phyllotaxis; and the fourth column, finally, gives the normal series 

 of fractions expressing the law of the phyllotaxis. ^^^ 



^**Johann Wolfgang von Gothe, Zur Naturwissenschaft uherhaupt, besonders zur 

 Morphologic (2 vols., Stuttgart, 1817-1824), and Oeuvres d'histoire naturelle, com- 

 prenant divers memoires d'anatomie comparee, de botanique et de geologic . . . (Paris, 

 1837); Augustin P. de CandoUe, Organographie vegetale (2 vols., Paris, 1827); Braun, 

 Das Individuum der Pflanze. 



1" [Agassiz tried to interest Americans in this concept, an idea typical of German 

 speculative biology and one that he had been much impressed with since his student 

 days at the University of Munich. See Asa Gray, "On the Composition of the Plant by 

 Phytons, and Some Applications of Phyllotaxis," Proceedings, AAAS, II (1850), 438- 

 444, and Benjamin Peirce, "Mathematical Investigations of the Fractions Which Oc- 

 cur in Phyllotaxis," in ibid., AAA-A^l . Gray was never entirely convinced of the validity 

 of this ideal conception. He subsequently encouraged Chauncey Wright to examine the 

 problem of leaf arrangement, with the result that such facts were shown to be under- 

 standable in terms of the principle of natural selection.] 



