THE ALTERNATE OR SPIRAL ARRANGEMENT 



197 



Orthostachy. Thus, if leaf No. 4 is the next in the orthostachy, to 

 which leaf No. 1 belongs (Fig. 574), three leaves will belong to that 

 cycle. A cycle containing three leaves makes but one turn of the stem. 

 A cycle is expressed in the form of a fraction, its numerator indicating 

 the number of times it encircles the stem, its denominator the number 

 of leaves which it includes, so that the cycle last described must be 

 indicated by the fraction one-thu'd. The angular divergence of its leaves 

 is 120 degrees. If the next leaf in the same orthostachy as No. 1 be 

 No. 6 (Fig. 572), then that cycle will contain five leaves. A cycle 

 containing five leaves makes two circuits of the stem, so that its exponent 



Fig. 570. Decussating opposite leaves. 571. Alternate or spiral leaf-arrangement. 572. Diagram 

 of the same, the i^ arrangement. 573. Diagram of 570, showing its 4 orthostachies. 574. The ^ spiral. 

 575. The ^ spiral. 



will be two-fifths. If the second leaf of the orthostachy were No. 9, the 

 appropriate fraction would be three-eighths, the cycle making three 

 turns and containing eight leaves (Fig. 575). It will thus be observed 

 that these fractions form a series, in which each possesses a numerator 

 equal to the sum of the numerators of the two preceding and a denom- 

 inator equal to the sum of the denominators of the two preceding. No 

 cycles occur among the higher plants with which we are concerned, 

 which can be indicated by any fraction not thus formed. 



Noticing these fractions still further, we observe that the denomi- 

 nators will indicate the number of orthostachies upon the stems which 



