r 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 €ach pair are very similar to one another, but not exactly 

 alike, like an object and its reflected imag'C. 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 bundies, 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 with 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. \xi Salvinia^ 

 Marsilea, Polypodium aureum, and Pterts aquilina^ on the contrary, the principal 

 sections of the leaves, forming two rectilineal series, lie right and left of the 

 single 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- 



