The distinction between protists and histons is much more important than the familiar division of organisms into plants and animals, in respect of their fundamental forms and their configuration. For the protists, the unicellular organisms (without tissue) exhibit a much greater freedom and variety in the development of their fundamental forms than the histons, the multicellular tissue-forming organisms. In the protists (both protophyta and protozoa) the constructive force of the elementary organism, the individual cell, determines the symmetry of the typical form and the special form of its supplementation; but in the histons (both metaphyta and metazoa) it is the plasticity of the tissue, made up of a number of socially combined cells, that determines this. On the ground of this tectological distinction we may divide the whole organic world into four kingdoms (or sub-kingdoms), as the morphological system in the seventh table shows. In respect of the general science of fundamental forms (promorphology), the most interesting and varied group of living things is the class of the radiolaria. All the various fundamental forms that can be distinguished and defined mathematically are found realized in the graceful flinty skeletons of these unicellular sea-dwelling protozoa. I have distinguished more than four thousand forms of them, and illustrated by one hundred and forty plates, in my monograph on the _Challenger_ radiolaria [translated]. Only a very few organic forms seem to be quite irregular, without any trace of symmetry, or constantly changing their formless shape, as we find, for instance, in the amœbæ and the similar amœboid cells of the plasmodia. The great majority of organic bodies show a certain regularity both in their outer configuration and the construction of their various parts, which we may call "symmetry" in the wider sense of the word. The regularity of this symmetrical construction often expresses itself at first sight in the arrangement side by side of similar parts in a certain number and of a certain size, and in the possibility of distinguishing certain ideal axes and planes cutting each other at measurable angles. In this respect many organic forms are like inorganic crystals. The important branch of mineralogy that describes these crystalline forms, and gives them mathematical formulæ, is called crystallography. There is a parallel branch of the science of biological forms, promorphology, which has been greatly neglected. These two branches of investigation have the common aim of detecting an ideal law of symmetry in the bodies they deal with and expressing this in a definite mathematical formula.