VASCULAR CRYPTOGAMS. 
■ The phyllotaxis of Ferns sometimes corresponds to the rectilinear arrangement 
of the segments of the apical cell. Thus the distichous arrangement of the leaves 
of Pteris aqinlina, Niphobolus rupestris, and of some species of Polypodium, corre- 
sponds to the biseriate segmentation of the apical cell of the stem. But where the 
phyllotaxis is complicated and spiral, and the apical cell a three-sided pyramid, as 
occurs in Aspidium Filix-mas, the same processes may take place as in those Mosses 
which have their leaves arranged in many rows with a trilateral apical cell, such 
as Polyirichum \ 
The Terminal Branching of the stem is considered by Hofmeister to be 
dichotomous in all Ferns ^ The branches arise very near the end of the stem, and 
are, at least at first, equivalent to the primary stem, so that the branching is a 
bifurcation. That the branches are independent of the leaves is inferred by this 
writer from the fact that the ends of the stem of Pteris aquilina, which are leafless 
and often several inches long, regularly bifurcate. These branches are, in this 
and in many other cases, not axillary ; and where, in other Ferns, they appear 
axillary, we must assume, with Hofmeister, that the bifurcation has taken place 
immediately in front of a youngest leaf, and that the limb of the fork which stands 
before the leaf developes to a smaller, while the other (the prolongation of the primary 
stem) does so to a greater extent. The branching at the end of the stem does not 
necessarily take place in the same plane as the insertion of the leaf immediately pre- 
ceding ; when it does, the branch stands laterally on the stem beside the leaf. To this 
class belongs, according to Mettenius's description, the extra-axillary branching of those 
Hymenophyllacese which have their leaves in two rows. That which distinguishes 
Ferns from Phanerogams with axillary branching, especially Angiosperms, is the 
rarity of terminal branching. While in the latter every leaf-axil, at least in the 
vegetative region, bears a bud, even the apparently axillary branches of creeping 
Ferns with long internodes occur mostly only at great distances, being wanting in 
a number of intermediate leaves. In those Ferns where the growth of the stem is 
slow and the apical region of considerable size, especially in erect species like Aspi- 
dium Filix-mas and the Tree-ferns, terminal branching of the stem is reduced to 
a minimum, or is entirely absent, or occurs only in abnormal cases. 
The formation of new shoots from the bases of leaf-stalks must be distinguished 
from the normal terminal branching of the stem. These have nothing to do 
genetically with the stem, any more than the formation of adventitious shoots from 
the lamina of the leaves {vide infra). 
The Developfnejit of the Leaf^ is exclusively basifugal and apical, the further 
growth being also basifugal. The leaf-stalk is first formed; at its apex the lamina 
begins subsequently to show itself ; its lowest parts are formed first, its higher parts 
in basifugal succession. The extraordinary slowness of this growth is very re- 
^ See Hofmeister, Allgemeine Morphologie, p. 509; and Bot. Zeitg. 1870, p. 441. 
^ [According to Mettenius (Ueb. Seitenknospen bei Farnen, Abhdl. d. kgl. sächs. Ges. d. Wiss. 
V, 1 86 1, this is not the case. Mettenius' view has been recently confirmed by Prantl, who has 
found that the branching in many Ferns, such as Cystopteris montaiia, Phegopteris v/dgaris, Dryopteris 
calcarea, is effected by lateral buds (Flora, 1875). Ceratopteris appears to be the only Fern which 
does not produce them (Kny, loc. cit.y] 
2 [See Sadebeck, Ueb, d. Entwick. d. Farnblattes ; Verhandl. d. bot. Ver. d. prov. Branden- 
burg, 1874.] 
