STRUCTURAL BOTANY. 83 



fourtli leaf commeuces a second one. This is the tristl- 

 chous^ or ^-ranked arrangement ; it is seen in Carex, 

 Scu'pus, Alnus, Betula, etc. 



160. A CYCLE is a system of leaves, in which, after 

 one or more turns of the spiral, we come to a leaf situated 

 directly above the one from which the spiral started. 



161, If on a brancli of the Oak we form a spiral, so 

 that it shall touch the insertion of the leaves, the sixtli 

 leaf, as stated above, will be found to be directly above 

 the first. In this case the leaves are disposed on five 

 equidistant verticals, and the circumference of the axis 

 (the branch) is then divided into five equal portions, each 

 of them an arc representing one fifth of the circumference. 

 "We notice, however, that the leaf which follows the first 

 is placed not on the second but on the third vertical. 

 Hence we say, that this vertical is two fifths the circum- 

 ference distant from the first. While in the ti'istichoiis 

 arrangement, the spiral, rising from the first leaf below, 

 described one turn only, to arrive at a leaf (the fourtli) 

 directly above the first, in the present case, it must describe 

 two turns or revolutions around the axis, to reach a leaf 

 (the sixth), situated vertically above the first (lowest) of the 

 five lower leaves. This arrangement, in which the dis- 

 tance between the verticals is two fifths of the circum- 

 ference of the axis, is the jpentastichous^ qidncuncial, or 

 t>-raiiked, and by far the most usual in alternate-leaved 

 exogens. 



16^. The ^-rariked arrangement is also frequently met 

 with, as in Aconite, Flax, Plantain, Holly, etc. Here the 

 ninth leaf is situated vertically over the first ; and the arc 

 between the verticals of two successive leaves is f of the 

 circumference of the axis. 



