PHYLLOTAXIS. 



39 



assumed first leaf). Thus : for the pentastichous, as we have seen, it is at 

 an angular distance of 144° ; for the § divergence the second leaf is at an 

 angular distance of 135°, while the positions of the second leaves of the 

 spirals, represented by the consecutive fractions -f^, ^ T , -^J, &c. gradually 

 approximate to some intermediate point on the arc, but which no known 

 example ever reaches. That point will be understood by mathematicians 

 to represent the " limiting" value of the continued fraction given above, 

 or 3 -^ 5 of 360°, or 137° 30' 28" + . 



Occasionally other fractions must be constructed to indicate peculiar 

 arrangements, and which cannot be represented by any one of the 

 fractions of the primary series. I discovered the Jerusalem Artichoke to 

 be a plant which, unlike most species having their own peculiar 



180° 



0 



Fig. 1. 



arrangements constantly the same, offered the most singular varieties. 

 Not only were some leaves opposite, i.e. in pairs at right angles, but also 

 in threes, all on the same level ; and when this was the case they 

 followed the same law regulating their positions, as already mentioned in 

 the case of opposite or decussate leaves, viz. that the leaves of each group 

 of three alternate in position with those of the groups above and below 

 them ; I have called * this arrangement tricussate. But besides these 

 two kinds the leaves on many stems were arranged alternately, and could 

 be represented by the fractions }, f, &o. But more than this ; for 

 I found that the fractions f, and others were likewise to be 



frequently obtained. Now these latter are obviously part of an analogous 

 or secondary series; and if continued would stand thus : ^, -f, j\, nr, 



* Op. cit. 



