128 ESSAY ON CLASSIFICATION. Part I. 



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 maxi- 

 mum and the minimum divergence between two single successive leaves. The 

 normal series of fractious which expresses the various combinations most frequently 

 observed among the leaves of plants, is as follows: I, |, |, |, y\, -^j, ||, ||^, etc. 

 Now, upon comparing this arrangement of the leaves in plants with the revolu- 

 tions 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 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 fractions expressing the law of the jihyUotaxis. 



Neptune, . . 60,129 . . 62,000 



Uranus, . . . 30,687 . . . 31,000 ... J 



Saturn, . . 10,759 . . 10,333 . . i 



Jupiter, . . . 4,333 . . . 4,133 . . . f 



Asteroids, . . 1,200 to 2,000 . 1,550 . . | 



Mars, . . . 687 . . . 596 ... /j 



Earth, . . 365 . . 366 



Venus, . . . 225 . . . 227 . 



Mercury, . . 88 . . 87 . . J| 



4! J 



In this series the Earth forms a break ; but this apparent irregularity admits 

 of an easy explanation. The fractions |, |, |, f, -j^g, -^\, -||, etc., as expressing the 

 position of successive leaves ujjon an axis, by the short way of ascent along the 

 spiral, are identical, as far as their meanmg is concerned, with the fractions express- 

 ing these same positions, by the long way, namely, |, |, |, f, ^^3, ^|, |{, etc. 



Let us, therefore, repeat our diagram m another form, the third column giving 

 the theoretical time of revolution. 



60,129 



30,687 



* See the works quoted above, p. 18, note 3. 



