84 



MA.NUAL OF BOTANY 



third being in like manner opposite to the second, it is placed 

 vertically over the first, and thus completes the cycle, which 

 here consists of but two leaves ; the fourth leaf again is over the 

 second, and the fifth over the third and first, thus completing a 

 second cycle : and so on with the successive leaves. Here one 

 turn completes the spiral, so that the distance between the leaves 

 is J the circumference of a circle, and the angular divergence is 

 180°- This arrangement is the normal one in all Grasses, and 

 many other Monocotyledons ; the Lime-tree {Jig- 165) and 

 other Dicotyledons exhibit a similar arrangement. 



A third varietv of arrangement in alternate leaves is the 



FiGf. 165. 



Fig. 165. Portion of a branch of tlie Lime-tree, with four leaves arranged in 



a distichous or two-ranked manner. Fig. 166. Portion of a brancli with 



tliebase of the leaves of a species of Car^.f; showing the tristiclious or three- 

 ranlced arrangement. The numbers indicate the succesyive bases of the 

 leaves. 



tristiclious or tln-cc-raiilteil (fig- 166). In this variety, if we start 

 with any leaf and mark it No. 1, and then pass to 2, 3, and 4, we 

 shall find that we shall make one turn round the stem before 

 coming to a leaf vertically over the first, which will be the fourth 

 in order, and thus complete a cycle composed of three leaves. 

 In like manner, the fifth leaf will be over the second, the sixth 

 over the third, and the seventh over the fourth and first, thus 

 completing a second cycle ; and so on with the succeeding leaves. 

 Here the angular divergence is j of 360° = 120° This arrange- 

 ment is by far the most common one among Monocotyledons. 



A fourth variety of Phyllotaxis in alternate leaves is the 

 octostichous or eight-ranked. Examples of this variety are 



