COMBINATION OF RELATIONS. 193 



Thus far we have been considering chiefly the contrasts 

 existing between the organic and inorganic worlds. 1 At 

 this stage of our investigation it may not be out of place 

 to take a glance at some of the coincidences which may 

 be traced between them, especially as they afford direct 

 evidence that the physical world has been ordained 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 2 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 frequently observed among the leaves 

 of plants, is as follows : |, i, f, %, rV, -&, if, H> etc. 

 Now, upon comparing this arrangement of the leaves in 

 plants with the revolutions of the members of our solar 

 system, Pierce 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 suc- 

 cessive planets, expressed in days, the third column the 

 successive 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 frac- 

 tions expressing the law of the phyllotaxis. 



1 Compare Sects. 24, 25, 26, 27, 28, 24, note 3. WRIGHT (C.), On the 

 29, and 30. Phyllotaxis, Astr. Jonvn., vol. 5, Dec. 



2 See the works quoted above, p. 1856. 



O 



