Considered as an exceptional occurrence, it occurs frequently in certain plants, and, when it affects the stem or branches, necessarily causes some changes in the arrangement of the parts attached to them; thus, spiral torsion of the axial organs is generally accompanied by displacement of the leaves, whorled leaves becoming alternate, and opposite or whorled leaves becoming arranged on one side of the stem only. Frequently also this condition is associated with fasciation, or, at least, with a distended or dilated state. An illustration of this in _Asparagus_ 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_.]