PHYLLOTAXY, OR LEAP ARRANGEMENT. 49 



231. THE ALDER CYCLE. In the alder, birch, sedges, &c., the cjcle is not com- 

 plete until the fourth leaf is reached. The fourth leaf stands over the first, the fifth 

 over the second, &c., forming three vertical rows. Here call the cycle $ ; 1 denotes 

 the turns, 3 the leaves, and this fraction itself the angular distance ($ of 360). 



232. THE CHERRY CYCLE. In the cherry, apple, peach, oak, willow, etc., neither 

 the third nor the fourth leaf, but the sixth, stands over the first ; and in order to 

 reach it the thread makes two turns around the stem. The sixth leaf is over the 

 first, the seventh over the second, &c., forming five vertical rows. Call this the f 

 cycle ; 2 denotes the turns, 5 the leaves in the cycle, and the fraction itself the an- 

 gular distance ( of 360). 



233. THE OSAGE-ORANGE CYCLE. In the common hedge plant, Osage-orange, 

 the holly, evening primrose, flax, etc., we find no leaf exactly over the first until we 

 come to the 9th, and in reaching it the spiral makes three turns. Here the leaves 

 form eight vertical rows. It is a f cycle ; 3 the number of turns, 8 the number of 

 leaves, and the fraction the angular distance between the leaves ( of 360). 



234. THE CYCLES COMPARED. These several fractions which represent the above 

 cycles form a series as follows : , &, |, f , in which each term is the sum of the two 

 preceding. The fifth terms in order will, therefore, be J^ ; and this arrangement is 

 actually realized in 



96, Phyllotaxy of the cone (cycle -^) of Finns serotina. 9T, cherry cycle (f), as seen from 

 above, forming necessarily that kind of aestivation called quincuntial. 



235. THE WHITE PINE CYCLE. In the young shoots of the white pine, in cones 

 of most pines, in flea-bane (Erigeron Canadense), etc., the fourteenth leaf stands over 

 the first, the fifteenth over the second, etc. The spiral thread makes five revolu- 

 tions to complete the cycle, which is, therefore, truly expressed by -A. 



236. THE HOUSELEEK CYCLE is next in order, expressed by the fraction (g^) 

 JL having eight turns and twenty-one leaves. Examples are found in the Scotch 

 pine, houseleek, &c. 



237. How TO DETERMINE THE HIGHER CYCLES. To trace the course of the for- 

 mative spiral in these higher cycles becomes difficult on account of the close prox- 

 imity of the leaves. In the pine cone (Fig. 96, Pinus serotina) several sets of sec- 

 ondary spirals are seen ; one set of five parallel spirals turning right (1 6 11 16, 



