Fig. 129. Arachnophyllum pentagonum. (After Nicholson.) Fig. 130. Heliolites. (After Woods.)
When, as happens in certain corals, the peripheral walls or ãthecaeã of the individual polypes remain undeveloped but the radiating septa are formed and calcified, then we obtain new and beautiful mathôÙeôÙmatôÙiôÙcal conôÙfiôÙgurôÙaôÙtions (Fig. 131). For the radiating septa are no longer confined to the circular or hexagonal bounds of a polypite, but tend to meet and become confluent with their neighbours on every side; and, tending to assume positions of equiôÙlibôÙrium, or of minimal area, under the restraints to which they are subject, they fall into congruent curves; and these correspond, in a striking manner, to the lines of force running, in a common field of force, between a number of secondary centres. Similar patterns may be produced in various ways, by the play of osmotic or magnetic forces; and a particular and very curious case is to be found in those complicated forms of nuclear division {327} known as triasters, polyasters, etc., whose relation to a field of force Hartog has explained25. It is obvious that, in our corals, these curving septa are all orthogonal to the non-existent hexagonal boundaries. As the phenomenon is wholly due to the imperfect development or non-existence of a thecal wall, it is not surprising that we find identical conôÙfiôÙgurôÙaôÙtions among various corals, or families of corals, not otherwise related to one another; we find the same or very similar patterns displayed, for instance, in Synhelia (Oculinidae), in Phillipsastraea (Rugosa), in Thamnastraea (Fungida), and in many more.
The most famous of all hexagonal conformations and perhaps the most beautiful is that of the beeãs cell. Here we have, as in
