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 steins 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 l 

 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 does 



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. 



