RELATIVE POSITIONS OF LATERAL MEMBERS, I99 



three rows, so that each new division-wall of the apical cell is parallel to the last 

 division-wall but two, as in Foniinalis, three rows of leaves result, arranged spirally 

 with the constant divergence \. Whem the apical cell is a three-sided pyramid, 

 but the new walls which are formed in it are not parallel to those already in existence^ 

 but oblique, so that, for example, all the segments are broader on the anodic than 

 on the kathodic side, then the segments no longer lie in three straight rows, but 

 either three spirals or one only can be recognised encircling the axis 3 and since each 

 < segment' in this case {e.g. in Pdlylnchum, Calharinea, and Sphagnum'^) developes 

 into a leaf, the leaves are formed in spiral phyllotaxes, with divergences depending 

 on the obliquity of the principal walls of the segments to one another'^. These 

 phenomena show clearly that when each segment produces a leaf, the phyllotaxis 

 depends on the manner in which the new principal walls of the segments arise ; and 

 since the direction taken by the segmentation of the apical cell depends again on 

 causes of which we are at present ignorant, the phyllotaxis must also finally be 

 referred to these unknown causes. In certain cases a reason may be given why, when 

 the mode of segmentation of the apical cell is the same, the positions at which the leaves 

 are formed are nevertheless variable. The segments of the apical cell, both in 

 Fontinalis and in Equisetuniy lie in three straight rows ; but in Fontinalis the solitary 

 leaves stand in straight rows and are arranged spirally with the constant divergence 

 J, while in EquisetunL, on the contrary, alternating whorls of leaves arise which have 

 grown together in the form of a sheath ; because here, as Rees has shown ^, the three 

 segments of each cycle, arranged originally in a spiral manner, are finally placed, in 

 consequence of the growth not being uniform, on the same zone. From this a cir- 

 cular projection next grows out, on which the sheath-teeth are formed. From the 

 want of uniformity in the growth of the segments, the causes of which are at present 

 unknown, still further differences, as compared with FontinaliSy are introduced, in 

 consequence of which the development of the whorls themselves becomes alternate 

 instead of superposed, as might be the case. If the processes which take place in 

 Marsilea^ as Hanstein has described them *, are compared with this, it is seen that the 

 segmentation of the apical cell of the stem, agrees in the main with that of Fontinalis 

 and Equisetum ; it is in three rows with a divergence \. As in Fontinalis, the leaves 

 originate by a curving outwards of the segment-cells ; but the leaves are in this case 

 not arranged in three rows as in Fontinalis, nor in whorls as in Equisetum, but in two 

 rows. The immediate cause of this must be sought in the fact that the stem, together 

 with the growing point, lies in a horizontal position ; it has an upper and an under 

 side. The segments of the apical cell form two rows on the upper and one on the under 

 side ; but the former produce leaves, the latter roots. The horizontal position of the 

 stem and its bilateral development are here perhaps the cause why the upper side 



* Compare the admirable description by Leitgeb in the case of Sphagnum, in the Sitzungsber* 

 der kais. Akad, der Wissenschaften, Wien, March 1869. 



^ See Hofmeisler, Allg, Morph. p. 494; and Miiller, Eine algemeine morphologische Studie, 

 Bot. Zeitg. 1869, t. IX. fig. 24. In such cases the behaviour of the apical cell may be represented by 

 imagining it to rotate on its axis, as I expressed it in my first edition. The description there given 

 does not however uomt appear to me suited to the beginner. 



^ Rees, Jahrb. fiir wissen. Bot. vol. VI. p. 216. 



* Hanstein, in Jahrb. fiir wissen. Bot. vol. IV. p. 252. 



