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.* 
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, 
ete., 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, ete. 
