Another case, geometrically akin but biologically very different, is to be found in the little diatoms of the genus Asterolampra, and their immediate congeners[399]. 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 the general appearance is in a high degree suggestive of the Chladni figures produced by the vibration of a circular plate. The spokes broaden out towards the centre, and interlock by visible junctions, which obey the rule of triple intersection, and accordingly exemplify the partition-figures with which we are dealing. But whereas we have found the particular arrangement in which one cell is in contact with all the rest to be unstable, according to Roux’s oil-drop experiments, and to be conspicuous {387} by its absence from our diagrams of segmenting eggs, here in Asterolampra, on the other hand, it occurs frequently, and is indeed the commonest arrangement[400] (Fig. [171], B). In all probability, we are entitled to consider this marked difference natural enough. For we may suppose that in Asterolampra (unlike the case of the segmenting egg) the tendency is to perfect radial symmetry, all the spokes emanating from a point in the centre: such a condition would be eminently unstable, and would break down under the least asymmetry. A very simple, perhaps the simplest case, would be that one single spoke should differ slightly from the rest, and should so tend to be drawn in amid the others, these latter remaining similar and symmetrical among themselves. Such a configuration would be vastly less unstable than the original one in which all the boundaries meet in a point; and the fact that further progress is not made towards other configurations of still greater stability may be sufficiently accounted for by viscosity, rapid solidification, or other conditions of restraint. A perfectly stable condition would of course be obtained if, as in the case of Roux’s oil-drop (Fig. [170], 6), one of the cellular spaces passed into the centre of the system, the other partitions radiating outwards from its circular wall to the periphery of the whole system. Precisely such a condition occurs among our diatoms; but when it does so, it is looked upon as the mark and characterisation of the allied genus Arachnoidiscus.
Fig. 172. Section of Alcyonarian polype.
In a diagrammatic section of an Alcyonarian polype (Fig. [172]), we have eight chambers set, symmetrically, about a ninth, which constitutes the “stomach.” In this arrangement there is no difficulty, for it is obvious that, throughout the system, three boundaries meet (in plane section) in a point. In many corals we have as {388} simple, or even simpler conditions, for the radiating calcified partitions either converge upon a central chamber, or fail to meet it and end freely. But in a few cases, the partitions or “septa” converge to meet one another, there being no central chamber on which they may impinge; and here the manner in which contact is effected becomes complicated, and involves problems identical with those which we are now studying.
Fig. 173. Heterophyllia angulata. (After Nicholson.)
In the great majority of corals we have as simple or even simpler conditions than those of Alcyonium; for as a rule the calcified partitions or septa of the coral either converge upon a central chamber (or central “columella”), or else fail to meet it and end freely. In the latter case the problem of space-partitioning does not arise; in the former, however numerous the septa be, their separate contacts with the wall of the central chamber comply with our fundamental rule according to which three lines and no more meet in a point, and from this simple and symmetrical arrangement there is little tendency to variation. But in a few cases, the septal partitions converge to meet one another, there being no central chamber on which they may impinge; and here the manner in which contact is effected becomes complicated, and involves problems of space-partitioning identical with those which we are now studying. In the genus Heterophyllia and in a few allied forms we have such conditions, and students of the Coelenterata have found them very puzzling. McCoy[401], their first discoverer, pronounced these corals to be “totally unlike” any other group, recent or fossil; and Professor Martin Duncan, writing a memoir on Heterophyllia and its allies[402], described them as “paradoxical in their anatomy.”
Fig. 174. Heterophyllia sp. (After Martin Duncan.)