196 THE LEAF 



a direct relation is to be traced between the definite arrangements of 

 foliage and floral leaves, as will be considered under Phjdlotaxy, and 

 the arrangement of the parts of the flower itself; so the characteristics 

 or praefloration are seen to be directly dependent upon the phyllotaxy 

 and praefoliation. 



Phyllotaxy. — In view of the established fact that the development 

 of the branches follows that of the leaves, it becomes clear that the 

 arrangement of the latter determines the entire symmetry of the 

 plant, with all the far-reaching consequences in connection with both 

 vegetation and reproduction. Certain definite laws of phyllotaxy 

 having been ascertained, the forms resulting become, in their different 

 manifestations, of nearly fundamental importance in classification and 

 in diagnosis. 



The Whorled Arrangement. — We find that either one or more than one 

 leaf is developed from a node. In the latter case the arrangement is 

 called Verticillate or Whorled, and the circle a Whorl or Verticil. If 

 the Whorl contain but two members, they are called Opposite — that 

 is, the centers of their points of insertion are separated by one-half the 

 circumference, or their Divergence is 180 degrees. Usually the other 

 nodes are similarly clothed, except that in all of the higher plants the 

 leaves of each pair Decussate with those of each adjacent pair — that is, a 

 leaf of one whorl is over the center of the sinus of that next below (Fig. 

 570). Four vertical rows (Orthostachies) of leaves thus appear upon 

 such a stem (Fig. 573). If, instead, there be three leaves to the whorl, 

 six orthostachies will result; if four, eight; and so on. It frequently 

 happens that the number of leaves in the upper or lower whorls will 

 contain only half the number of leaves in the others, and still higher 

 up the whorled arrangement may be lost, the leaves becoming arranged 

 as in the form next considered. 



The Alternate or Spiral Arrangement. — By the other arrangement the 

 nodes produce solitary leaves, so that each leaf is successively produced 

 at a higher level. If a line be traced from the point of origin of one 

 leaf to that of the one next above, and continued in the same direction, 

 so that it exactly meets the point of insertion of another, and then of 

 another, and so on, it will at length meet one exactly over the point of 

 starting — that is, a second leaf in the same Orthostachy (Fig. 571). 

 It will then be found that the line followed is a spiral, which has passed 

 once or more around the stem. Such a spiral is cafled a Cycle, and if its 

 line be continued, it will form other similar cycles above and below. It 

 is observed that a cycle will be limited by two adjacent leaves of one 



