928 ON LEAF-ARRANGEMENT [ch. 



as another. In a fire-cone one particular series, or rather two 

 conjugate series, are always conspicuous, but the related series may 

 be sought and found with httle difficulty. The spruce-fir is com- 

 monly said to have a phyllotaxis of 8/13; but we may count still 



Fig. 452. 



steeper and nearly vertical rows of scales to the number of 13/21; 

 and if we take pains to number all the scales consecutively, we may 

 find the lower series, 5/8, 3/5, and even 1/2, with ease and certainty. 

 The phenomenon is illustrated by Fig. 452, a-d. The ground-plan 

 of all these diagrams is identically the same. The generating spiral 



