aragus_ has been figured at p. 14.

Very often the leaves are produced in a spiral line round the stem, as
in a specimen of _Dracocephalum speciosum_ described and figured by C.
Morren. The leaves of this plant are naturally rectiserial and
decussate, but, in the twisted stem the leaves were curviserial, and
arranged according to the 5/13 plan. Now, referring to the ordinary
notation of alternate leaves, we shall have the first leaf covered by
the fifth, with two turns of the spiral; since decussate leaves result
from two conjugate lines, the formula will be necessarily 2/5. The
fraction 5/13 hence comes regularly into the 2/5 series (2/5, 3/8,
5/13). Thus, the leaves in assuming a new phyllotaxy, take one quite
analogous to the normal one.

One of the most curious instances that have fallen under the writer's
own observation occurred in the stem of _Dipsacus fullonum_. (See
'Proceedings of the Linnean Society,' March 6, 1855, vol. ii, p. 370).
The stem was distended, and hollow, and twisted on itself; its fibres,
moreover, were arranged in an oblique or spiral direction; the branches
or leaf-stalks, which usually are arranged in an opposite and decussate
manner, were, in this case, disposed in a linear series, one over the
other, following the line of curvature of the stem. When the course of
the fibres was traced from the base of one of the stalks, upward around
the stem, a spiral was found to be completed at the base of the second
stalk, above that which was made the starting point. Now, if opposite
leaves depend on the shortened condition of the internode between the
two leaves, then, in the teazel-stem just described, each turn of the
spiral would represent a lengthened internode; and, if the fibres of
this specimen could be untwisted, and made to assume the vertical
direction, and, at the same time, the internodes were shortened, the
result would be the opposition of the branches and the decussation of
the pairs; this explanation is borne out by the similar twisting which
takes place so frequently in the species of _Galium_ and other
_Rubiaceae_.

[Illustration: FIG. 172.--Twisted stem of _Dipsacus fullonum_.]

G. Franc[358] was one of the first to notice this twisting in _Galium_,
and M. Duchartre,[359] in mentioning a similar instance, gives the
following explanation of the appearance which will be found to apply to
most of these cases. In the normal stem of _Galium Mollugo_ the
branches are opposite in each