mark the symmetry, not of cells merely, but of the parts and organs of entire animals. The phenomena are not ãfunctions,ã or specific characters, of this or that tissue or organism, but involve general principles which lie within the province of the mathematician.
The theory of space-partitioning, to which the segmentation of the egg gives us an easy practical introduction, is illustrated in much more complex ways in other fields of natural history. A very beautiful but immensely complicated case is furnished by the ãvenationã of the wings of insects. Here we have sometimes (as in the dragon-flies), a general reticulum of small, more or less hexagonal ãcellsã: but in most other cases, in flies, bees, butterflies, etc., we have a moderate number of cells, whose partitions always impinge upon one another three by three, and whose arrangement, therefore, includes of necessity a number of small intermediate partitions, analogous to our polar furrows. I think {386} that a mathôÙeôÙmatôÙiôÙcal study of these, including an inôÙvesôÙtiôÙgaôÙtion of the ãdeformationã of the wing (that is to say, of the changes in shape and changes in the form of its ãcellsã which it undergoes during the life of the individual, and from one species to another) would be of great interest. In very many cases, the entomologist relies upon this venation, and upon the occurrence of this or that intermediate vein, for his clasôÙsiôÙfiôÙcaôÙtion, and therefore for his hypothetical phylogeny of particular groups; which latter procedure hardly commends itself to the physicist or the mathematician.
Another case, geometrically akin but biologically very different, is to be found in the little diatoms of the genus Asterolampra, and their immediate congeners13. In Asterolampra we have a little disc, in which we see (as it were) radiating spokes of one material, alternating with intervals occupied on the flattened wheel-like disc by another (Fig. 171). The spokes vary in number, but