THE PRINCIPLE OF NUMBER. 11 



found that the an-augement of the latter is almost invariably 

 represented by the | type. It is secured by developing inter- 

 nodes between the two opposite leaves of each pair, and by 

 shifting their positions so as to acquire ultimately an angular 

 divergence of 144°.* 



The feature to be especially observed in the transitions 

 from opposite to alternate arrangements is the order in which 

 the opposite leaves separate so as to assume successive 

 positions on the continuous spiral line passing through their 

 insertions, when they have become alternate. This will be 

 understood from the accompanying diagram, in which the 

 numbers represent the order which the leaves will ultimately 

 assume on the f type ; tlioagh they ai'e placed as if still 

 opposite and decussate. The numbers 1 and 2, 3 and 4, 5 

 and 6, etc., represent the successive pairs of opposite leaves, 

 the arrows showing the direction of the spiral. 



It will be at once ob- 

 served that the numbers 6, 

 9, 14, and 22 are in the 

 same row, and correspond to 

 the divergences |, |, -/g, 

 ^V No. 17 falls into the 

 series |, and completes the 

 second cycle of that type 

 from No. 1. 



It may be observed 

 here, as occasion will arise 

 for a fuller allusion to the 

 significance of the fact, that, with the sole exception of the 



* I have fully explained this in my paper, On the Variations of the 

 Angular Divergences of the Leaves of Helianthns Tuberosus, Trans. Lin. 

 Soc, vol. xxvi,, p. 647. See also On the Origin of the Prevailing Systems 

 of Phyllotaxis, I.e., 2nd series, vol. i. p. 37. 



