1899] CONSIDERATIONS CONCERNING SYMMETRY 99 



It is evident that a limit to the exercise of the compressing force may 

 be set by the elasticity of the cell contents resisting any further com- 

 pression, or extreme pressure may paralyse the cells. Then light, heat, 

 and electric phenomena, as well as gravity, are agents that may 

 influence the demeanour of the cells. The radiate symmetry of a 

 hexagonal prism body or element is easy to understand, but the prism 

 may be divided bilaterally by six planes that pass through the axis, 

 and notably by three directed through the axis and opposite angles. 

 Skeletal structures laid down along the lines of certain radii, where 

 circumstances favour the deposit, establish the character of the 

 symmetry, and these radial structures (composed of lignin, lime salts, 

 cellulose, or other substances) leave between them avenues which 

 protoplasm and fluids keep free. The skeleton, like many another tissue, 

 is advantageously regarded as an excretion, such as might be cast off 

 by some organisms, but is retained by its possessor. This structure, of 

 seeming advantage at first as a protecting and supporting framework, 

 grows so large sometimes as to interfere with the activity of the tissue 

 by which it has been produced. There are apparently no limits to the 

 possibilities in the interior structure of cylindrical organisms. The 

 number of radii may be many or few, and the cylinder may be of small 

 or large diameter. 



The trimerous and pentamerous symmetry of plants excited much 

 interest when first established as a plant law. The fixity and nature 

 of growth of the higher plants favour a radiate cylindrical symmetry. 1 

 There are well-known cases of an apparent bilateral symmetry, in the 

 ovary and other parts, and a spurious quadrilateral in others. The in- 

 crease in information with reference to the effects of light, heat, gravity, 

 etc., forces most people to be cautious in drawing conclusions. Dr. 

 William Allman, formerly Professor of Botany in the University of 

 Dublin, sought to connect the structure of exogens with the penta- 

 merous arrangement of the parts of the flower, and that of the so-called 

 endogens with the trimerous arrangement, by means of the cellular 

 structure of the plants. Starting with the hypothesis that plant-cells 

 in mass have a tendency under the influence of an all round pressure 

 to assume figures intermediate between the sphere and regular solid, 

 he refers to the fact that the regular solids are : the tetrahedron (4 

 sides), cube (6 sides), octohedron (8 sides), dodecahedron, with penta- 

 gonal faces (12 sides), icosahedron (20 sides). He proceeds to show 

 that the two latter forms appear to agree best with the forms of cells 

 in plants, the dodecahedrons would best explain the pentagonal 

 arrangement of the exogens, and the icosahedrons the trimerous form 

 of endogens. The cubical form was regarded as more prevalent 

 amongst the acotyledons. Allman supposed the young shoot of a 



1 The term symmetrical is used sometimes by authors when bilaterally symmetrical is 

 meant. The word is also used to indicate certain relationships between sepals, petals, 

 stamens, etc. 



