1899] CONSIDERATIONS CONCERNING SYMMETRY 101 
The flow of nutrient fluid in the plant conjoins with the active 
protoplasm to make new tissue. Year after year new additions are 
added to the stem, but these are laid down in accordance with the 
laws of plant growth. Whatever may be the resolution of these forces, 
it is evident that the form, shape, and nature of the grouping of bundles, 
and the succession, as well as the shape of the conjoined bundles and 
packing tissue that form stems or leaves, are the results of not merely 
internal forces, physical and organic, but external forces of great 
constancy, if not of great magnitude. 
A collapsing cylinder is said to assume often the form of a three- 
sided prism, and a sphere the form of a tetrahedron, There can be no 
harm in placing side by side with this statement the record of trimerous 
symmetry in plants. One would require to take a note of several hollow 
cylinders in the latter case, perhaps, which renders the comparison 
more difficult ; five, six, or eight-angled prisms might also be allowed 
to be within the powers of plant manufacture,—columns not to be 
formed as a battalion of soldiers, from the outside alone, but by the 
. addition of new rows between the already formed lines. W. Allman 
pointed out a connection between the icosahedron and dodecahedron ; if 
the latter be inscribed in a sphere, tangent planes at the angles will 
constitute an icosahedron, just as a cube in a sphere similarly treated 
will give rise to an octohedron, and a tetrahedron to a figure like itself. 
It may be noted here, that, if we compare the pentamerous symmetry 
with the trimerous, it will appear at once that five equilateral triangles ' 
meeting by their apices and arranged so that each is separated from 
his neighbour by twelve degrees, will leave chinks which in triangular 
prisms would serve for young tissues. Account is rather taken here of 
the collective tissue groups (vascular and cellular). The flower or leaf 
parts, if followed to the large stems, are not so easy to marshal. Six 
equilateral triangles meeting in the centre by their apices, and lying in 
the same plane, would leave no spaces for the reception of cells or 
fibres; in this case the exterior of the composite bundle might be 
regarded as the chief generating tissue. Then eight equal equilateral 
triangles with the apices turned in would require to stand well out 
in the same plane in order that their external angles might even fit 
to one another. Eight equal equilateral triangular prisms may be 
adjusted, with their long axes parallel to one another, and with 
their edges on radial planes that divide the cylinder into equal 
segments. One face pointing out in each, and one edge looking 
in, will, if the prisms stand, leave interspaces internally wide and 
externally narrow. These prisms, if the first to develop out, 
might determine the course of future tissues. The arrangement of the 
leaves on the stem suggests other schemes for plant bundles, but there 
is clear enough proof of a predominant radial symmetry, and it ddes 
1 The triangles are here taken to represent sections of prisms. No account is taken of 
any twisting the stem or bundles may experience in the course of development. 
