DIRECTIONS OF GROWTH, 
205 
of the other, since the leaves of the two rows spring from different heights. Where 
a true monosymmetrical structure occurs, it may be considered a particular case of 
the bilateral; the latter, therefore, being the more common, is the more important 
phenomenon. 
There is the same relationship between polysymmetry and multilateral arrange- 
ment as between monosymmetry and bilateral arrangement; polysymmetry must be 
considered only as a particular case of the multilateral structure. This latter always 
occurs where several pairs of halves can be produced by axial longitudinal sections, 
so that the two halves of each pair are very similar to one another, but not exactly 
alike, like an object and its reflected image. Thus the short stems of Sempervivum^ 
the leaf-rosettes of ionium, and fir-cones with their scales, can be easily halved by 
numerous longitudinal sections, but the halves thus formed are never symmetrical, 
because the leaves and scales are arranged spirally, and a spiral can never be divided 
symmetrically ; but in so far as the spirally arranged leaves stand in three, four, five, 
eight, thirteen, &c. orthostichies, the shoot itself may be said to be tri-, quadri-, 
quinqui- octo-, trideci-lateral, &c. 
The most common distinction is between bilateral and multilateral structures ; 
in both cases the lateral arrangement may rise into symmetry, the former into 
monosymmetry, the latter into polysymmetry. The extremes are seen on the one 
side in roots with a circular transverse section, on the other side in most leaves and 
leaf- like shoots with only two symmetrical halves. If, however, in the case of roots 
regard is paid to the number of their fibro-vascular bundles, the apparently infinite 
number of their planes of symmetry may usually be reduced to two, three, four, 
or five. 
To obtain a convenient mode of expression for relationships of this kind, each 
longitudinal section which produces two similar halves may be termed a principal 
section or principal plane ; and if the two halves are symmetrical it is a symmetrical 
section or plane. Thus bilateral structures have one principal section, multilateral 
structures two or more principal sections. 
(5) Lateral arrangement and relationships of symmetry may be looked at from 
two important points of view, according as the members of a plant are compared 
with one another, or are considered in reference to their relation with the external 
world, with gravitation, light, or the pressure of external objects. 
If the members of a plant are compared w^ith one another, it is seen, for ex- 
ample, that the principal sections of all the leaves, though on opposite sides of the 
stem, may lie in one plane, in which case the shoot itself is bilateral ; or they may lie 
in two planes crossing one another at right angles, when the shoot is quadrilateral, 
as, for instance, when it bears decussate whorls of two members, a case which, in 
reference to other relationships, is very near to that of bilateral arrangements, and 
may be termed a double bilateral arrangement. In these cases the principal sections 
of the leaves are also at the same time principal sections of the stem. In Sahnnia, 
Marsilea, Polypodium aureu?n, and Pteris aquiUna^ on the contrary, the principal 
sections of the leaves, forming two rectilineal series, lie right and left of the 
singll principal section of the bilateral stem, an arrangement which is in these 
cases dependent on the horizontal growth. 
The relationship of lateral arrangement and symmetry to the external envi- 
