184 EXTERNAL CONFORMATION OF PLANTS. 



but in such a manner that the two halves of the member do not He exactly 

 opposite to one another like reflected images. Thus, for example, the oblique 

 leaves of Begonia are not symmetrical, although bilateral ; the one half to the 

 right of the mid-rib of the lamina is larger and of somewhat different shape to 

 the other half to the left of the mid-rib; and the same is the case with the elm. 

 A shoot with alternating leaves in two rows is also simply bilateral without being 

 monosymmetrical ; if it is divided at right angles to the common median plane 

 of all the leaves, the two halves bear each one row of leaves ; but the one is not 

 the reflected image of the other, since the leaves of the two rows spring from 

 difterent 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. 



The same relationship occurs between polysymmetry and multilateral arrange- 

 ment as between monosymmetry and bilateral arrangement ; polysymmetry must 

 also be considered only as a particular case of the multilateral structure. This latter 

 is always present when several pairs of halves can be produced by axial longitu- 

 dinal 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, the cones of species of Pinus 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 in 

 a spiral manner, 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 three-, four-, five-, eight-, thirteen-sided, &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 circular transverse sections, 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 be usually 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 

 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 gravity, light, pressure, and external circumstances. 



If the members of a plant are compared with one another, it is seen, for ex- 

 ample, that the principal sections of all the leaves may lie in one plane on opposite 

 sides of the stem, in wh"ich 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 



