ORGANS AND SYSTEMS OF ORGANS. 



173 



The mimerator 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 

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

 which represents tlie divergence 

 t. 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 fiat. 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 



Fig. 102. 



(After Sachs.) 



Fig. 103. 



direction ah (Fig, 103) this number is five, in the direction cri it 

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

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



