ORGANS AND SYSTEMS OF VKGANS. 



172 



The numerator indicates the number of turns about the stem, begin- 

 ning with one leaf and terminating at the first leaf vertically above ; 

 the denominator indicates the number of vertical rows. 



There are two methods for representing the leaf-divergence 

 graphically: first, projection upon a horizontal plane, as in Fig. 102, 

 which represents the divergence 

 J- . This method shows the verti- 

 cal rows very clearly. The other 

 method is that of representing 

 it upon the plane of a cylinder 

 rolled out flat. This brings out 

 the spiral lines very beautifully, 

 as shown in Fig. 103, which illus- 

 trates the divergence f. 



The number of vertical rows 

 also gives the number of leaves 

 between two successive members 

 of a series, as will be seen from a 

 close inspection of the figures ; 

 for example, in Fig. 103 eight vertical rows are shown, hence the 

 name eight-ranked. 



Likewise the parallel diagonal lines cutting the leaf-organs also- 

 indicate the number of intervening leaves. For example, in the 



PIG. 102. 



(After Sachs.) 



FIG. 103. 



direction ab (Fig. 103) this number is five, in the direction cd it 

 is three. These relations can be very easily studied in the cones of 

 conifers. It must be borne in mind that this numerical relation 



