LEAF-AR11ANGEMENT. 



89 



the cycle is not complete until the fourth leaf is readied. The 

 fourth leaf stands over the first, the fifth over the second, etc., 

 forming three vertical rows. Here call the cycle ^ ; 1 denotes 

 the turns, 3 the leaves, and the fraction itself the angulai dis- 

 tance (^ of 360). 



266. 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, etc., forming five vertical 

 rows. Call this the f cycle ; 2 denotes the turns, 5 the leaves in 

 the cycle, and the fraction itself the angular distance (f of 360). 



295, 296, 297, Showing the course of the spiral thread and the order of the leaf-succession in the hxs ol 

 Elm, Alder, and Cherry. 298, Axis ol Osage-orange with a section of the bark peeled, displaying the 

 order of the leaf-scars (cycle %). 



267. 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 be- 

 tween the leaves (f of 360). 



268. These several fractions which represent the above cycles 

 form a series as follows : , J, f, |, in which each term is the 



