The number of ideal fundamental forms, to which we may reduce the symmetries of the innumerable living organisms, is comparatively small. Formerly it was thought sufficient to distinguish two or three chief groups: (1) radial (or actinomorphic) types, (2) bilateral (or zygomorphic) types, and (3) irregular (or amorphic) types. But when we study the distinctive marks and differences of these types more closely, and take due account of the relations of the ideal axes and their poles, we are led to distinguish the nine groups or types which are found in the sixth table. In this promorphological system the determining factor is the disposition of the parts to the natural middle of the body. On this basis we make a first distinction into four classes or types: (1) the centrostigma have a _point_ as the natural middle of the body; (2) the centraxonia a straight line (axis); (3) the centroplana a plane (median plane); and (4) the centraporia (acentra or anaxonia), the wholly irregular forms, have no distinguishable middle or symmetry. I. CENTROSTIGMATIC TYPES.--The natural middle of the body is a mathematical point. Properly speaking, only one form is of this type, and that is the most regular of all, the sphere or ball. We may, however, distinguish two sub-classes, the smooth sphere and the flattened sphere. The smooth sphere (_holospœra_) is a mathematically pure sphere, in which all points at the surface are equally distant from the centre, and all axes drawn through the centre are of equal length. We find this realized in its purity in the ovum of many animals (for instance, that of man and the mammals) and the pollen cells of many plants; also cells that develop freely floating in a liquid, the simplest forms of the radiolaria (_actissa_), the spherical cœnobia of the volvocina and catallacta, and the corresponding pure embryonic form of the _blastula_. The smooth sphere is particularly important, because it is the only absolutely regular type, the sole form with a perfectly stable equilibrium, and at the same time the sole organic form which is susceptible of direct physical explanation. Inorganic fluids (drops of quicksilver, water, etc.) similarly assume the purely spherical form, as drops of oil do, for instance, when put in a watery fluid of the same specific weight (as a mixture of alcohol and water).