86 MANUAL OF BOTANY 



its torsion is reversed at the conclusion of each complete cycle. 

 Sometimes, again, the spiral changes as the axis gets older, the 

 earliest leaves, or perhaps the youngest, being of a different order 

 from the rest. Sometimes by the suppression of the internodes 

 of a spiral cycle the leaves are apparently whorled or opposite. 



It should be mentioned with respect to the laws of Phyllo- 

 taxis, that they are frequently interfered with by accidental 

 causes which produce corresponding interruptions of growth, so 

 that it is then difficult, or altogether impossible, to discover the 

 regular condition. Thus in the case of axes whose internodes 

 are much elongated, the arrangement is sometimes apparently 

 altered by torsion of the stem or branch. This may also be seen 

 with short internodes, though less frequently. The direction of 

 the torsion of the axis may be uniform, or may change in 

 different regions of it. 



In Pandanus there are usually three vertical orthostichies 

 which pass straight down the stem, but sometimes a torsion of 

 the latter makes them spiral instead of straight. A singular case 

 of torsion is seen in Baptisia perfoliata, whose leaves, which 

 are normally in two ranks, become in the upper part of the stem 

 arranged in a single rank, owing to a twist of the successive 

 internodes, first to the right and then to the left. 



All the above varieties of PhyUotaxis in which the angular 

 divergence is such that the orthostichies are vertical, and the 

 leaves completing the cycles are thus directly over those com- 

 mencing them, are called rectiserial ; while those in which the 

 divergence is such that the orthostichies themselves are slightly 

 twisted spirally are termed curviserial. The first forms of 

 arrangement are looked upon as the normal ones ; the latter 

 will show the impossibility of bringing organic forms and 

 arrangements, in all cases, under exact mathematical laws. 



We have thus endeavoured to show that when leaves are 

 alternate, the successive leaves form a spiral round the axis. 

 The spire may turn either from right to left, or from left to 

 right. In the majority of cases, its direction in both stem 

 and branches is the same, and it is then said to be homodromous ; 

 but instances also occasionally occur in which its direction is 

 not the same in both, when it is called heterodromous. 



2. Opposite and Whorled Leaves. — We have already observed 

 with regard to these naodifications of arrangement, that each suc- 

 cessive pair, or whorl, of leaves, as they succeed each other, 

 is not commonly inserted immediately over the preceding one, 

 but that the second pair (fig. 162), or whorl, is placed over 



