MORPHOLOGY OF ANGIOSPERMS. 



119 



subsequent leaves are arranged according to a different order in 

 these several plants, but in a definite manner in each. In the elm, 

 the distribution of the leaves is such that the third leaf is directly 

 above the first ; in the beech, the fourth leaf is above the first, and 

 in the oak, the sixth leaf is above the first. If these leaves are con- 

 nected in the order of their development, it will be seen that they 

 describe a spiral in their arrangement, and it will also be found 

 that one or more circuits of the stem are made between the super- 

 imposed leaves. Ftirthermore, it will be found that this arrange- 

 ment constitutes, a mathematical series which may be expressed 

 in degrees, or the parts of a circle that the leaves are from each 

 other, this measure being known as divergence ; or by the number 

 of perpendicular rows of leaves on the stem, which are known as 



ORTHOSTICHIES. 



The following may serve to illustrate the terms used : 



If we examine the fractions used, we will find that the numer- 

 ator indicates the number of turns around the stem before encoun- 

 tering a superimposed leaf, and that the denominator indicates 

 the number of leaves found ; the latter also expresses the number 

 of orthostichies. On adding the numerators and denominators of 

 any two successive fractions, a fraction is obtained which ex- 

 presses the next highest arrangement, as 



1 J- 1 



2 T^ 3 



1 _|_ 2 3 



8 T -5" 'g'' 



In quite a number of plants two leaves arise at the nodes, as 

 in the Labiatae. These are invariably situated opposite each other 

 on the stem, and the successive pairs alternate with one another, 

 forming the decussate arrangement of leaves (Figs. 67, 74, 

 168, 172). 



