V.
We must now consider the ways in which the members of the tetrahedral groups break up, and as we proceed with this study we shall find how continual are the repetitions, and how Nature, with a limited number of fundamental methods, creates by varied combinations her infinite variety of forms.
Beryllium ([Plate III], 2, and [VIII], 1).
Beryllium offers us four similar funnels and a central globe, and the proto-elements consist of these five bodies, set free. The funnel, released from pressure, assumes a spherical form, with its four ovoids spinning within it, and the central globe remains a sphere, containing a whirling cross. On the meta level, the ovoids are set free, and two from each funnel are seen to be positive, two negative—sixteen bodies in all, plus the cross, in which the resultant force-lines are changed, preparatory to its breaking into two duads on the hyper level. On that level, the decades disintegrate into two triplets and a quartet, the positive with the depressions inward, the negative with the depressions outward.
Calcium ([Plate VIII], 2).
The funnels, as usual, assume a spherical form on the proto level, and show, in each case, three spheres containing ovoids. These spheres, still on the proto level, break free from their containing funnel, as in the case of gold ([p. 49]), twelve bodies being thus liberated, while the central globe breaks up into eight segments, each of which becomes globular, and contains within it a "cigar" and a somewhat heart-shaped body. Four spheres, each containing seven ten-atomed ovoids, are identical with those in beryllium, and can be followed in its diagram. Eight spheres, each containing five nine-atomed ovoids of a different type, set free, on the meta level, eighty duads—forty positive and forty negative—and forty quintets, which are identical with those in chlorine. On the hyper level, the duads become single atoms, within a sphere, and the central atom from the quintet is also set free, one hundred and twenty in all. The remaining four atoms of the quintet divide into two duads.
The central globe, dividing into eight, becomes eight six-atomed spheres on the meta, the "cigar" behaving as usual, four "cigars" being positive and four negative, and becoming dissociated into triplets; the four atoms within the heart-shaped body appear as a tetrahedron, remain together on the meta level, and break up into duads on the hyper.
Strontium ([Plate VIII], 3).
The third member of this group repeats the a groups of beryllium and the b groups of calcium, and they dissociate into the bodies already described under these respectively. The two upper globes in each funnel repeat each other, but each globe contains four smaller spheres showing three varieties of forms. The two marked g, which are repeated in the central globe as h, are seven-atomed, and appear as spheres or ovoids according to pressure. They are figured on [p. 48], under iodine; e and f are related as object and image, and we have already seen them in copper ([pp. 38] and [48]); in each case, as in copper, they unite into a ten-atomed figure; on the meta level the pair of fours form a ring, and the remaining two atoms form a duad; i, which repeats f, makes a ring with the fifth in the centre, as in the five-atomed b of calcium, as shown above. There is, thus, nothing new in strontium, but only repetitions of forms already studied.
Oxygen ([Plate VIII], 4).
The disintegration of oxygen as given in 1895 may be repeated here, and the better presentation given on [p. 54] renders it easier to follow the process. On the proto level the two "snakes" divide; the brilliant disks are seven-atomed, but are differently arranged, the positive snake having the atoms arranged as in the iodine ovoids, whereas the negative snake has them arranged as in a capital H. The snakes show the same extraordinary activity on the proto level as on the gaseous, twisting and writhing, darting and coiling. The body of the snake is of two-atomed beads, positive and negative. On the meta level the snakes break into ten fragments, each consisting of a disk, with six beads on one side and five on the other, remaining as lively as the original snake. They shiver into their constituent disks, and beads on the hyper level, there yielding the ten disks, five positive and five negative, and the 110 beads, fifty-five positive and fifty-five negative.
Chromium ([Plate VIII], 5).
When we go on to chromium and molybdenum, we return to our familiar funnels and central globes, and the secondary spheres within the funnels—quickly set free, as before, on the proto level—give us no new combinations in their contained spheres and ovoids. The a of beryllium, the b of calcium and strontium, and d of calcium, the e and f of strontium, are all there; j in chromium is the same as the central sphere in the b ovoid. In the central globe, k, is a pair of triangles as in hydrogen, consisting of only six atoms, which on the meta level revolve round each other, and break up into two duads and two units on the hyper.
Molybdenum ([Plate VIII], 6).
Molybdenum presents us with only two new forms, and these are merely four-atomed tetrahedra, occurring in pairs as object and image. All the other bodies have already been analysed.
II a.—We come now to the second great tetrahedral group, which though very much complicated, is yet, for the most part, a repetition of familiar forms.
Magnesium ([Plate IX], 1).
We are still among tetrahedra, so have to do with four funnels, but each funnel contains three rings, and each ring three ovoids; on the proto level a triple dissociation takes place, for the funnels let free the rings as large spheres, in each of which rotate three twelve-atomed ovoids, and then the ovoids break loose from the spheres, and themselves become spherical, so that we have finally thirty-six proto compounds from the tetrahedron. On the meta level the contained bodies, a triplet, Mg a, a septet, Mg b, and a duad, Mg c, are set free from each globe, thus yielding one hundred and eight meta compounds. On the hyper level the triplet becomes a duad and a unit; the duad becomes two units; and the septet a triplet and a quartet.
Zinc ([Plate IX], 2).
We can leave aside the funnel, for the only difference between it and the magnesium funnel is the substitution of a second septet for the triplet, and the septet is already shown in the magnesium diagram. We have, therefore, only to consider the spikes, pointing to the angles of the enclosing tetrahedron, and the central globe. These are set free on the proto level and the spikes immediately release their contents, yielding thus thirty-two separate bodies.
The triangular arrangement at the top of the spike is the same as occurs in copper (b on [p. 48]), and can be there followed. One of the three similar pillars is shown in the accompanying diagram under Zn a. The compressed long oval becomes a globe, with six bodies revolving within it in a rather peculiar way: the quartets turn round each other in the middle; the triplets revolve round them in a slanting ellipse; the duads do the same on an ellipse slanting at an angle with the first, somewhat as in gold (a and b, [p. 40]). The spheres within the globes at the base of the spikes, Zn b, behave as a cross—the cross is a favourite device in the II a groups. Finally, the central globe, Zn c, follows the same cruciform line of disintegration.
Cadmium ([Plate IX], 3).
Cadmium follows very closely on the lines of zinc; the pillars of the zinc spike are reproduced in the rings of the cadmium funnel; the globes are also the globes of cadmium; so neither of these needs attention. We have only to consider the three ten-atomed ovoids, which are substituted for the one ten-atomed triangle of zinc, and the central cross. The ovoids become spheres (Cd a, b), the contained bodies revolving within them, a whirling on a diameter of the sphere, cutting it in halves, as it were, and b whirling round it at right angles; the cross also becomes a sphere (Cd c), but the cruciform type is maintained within it by the relative positions of the contained spheres in their revolution. The subsequent stages are shown in the diagram.
Sulphur ([Plate XI], 1).
Sulphur has nothing new, but shows only the funnels already figured in magnesium, with the substitution of a second septet for the triplet, as in zinc.
Selenium ([Plate X], 2).
The funnel of selenium is a re-arrangement of the twelve-atomed ovoids of magnesium and the ten-atomed ovoids of cadmium. The funnels, on disintegrating, set free twelve groups, each containing nine spheres. On the meta level the ten-atomed bodies are set free, and the twelve-atomed divide into duads and decads, thus yielding seventy-two decads and thirty-six duads; the duads, however, at once recombine into hexads, thus giving only twelve meta elements, or eighty-four in all from the funnels. The central globe holds together on the proto level, but yields five meta elements. The star also at first remains a unit on the proto level, and then shoots off into seven bodies, the centre keeping together, and the six points becoming spheres, within which the two cones, base to base, whirl in the centre, and the globes circle round them. On the meta level all the thirty bodies contained in the star separate from each other, and go on their independent ways.
Selenium offers a beautiful example of the combination of simple elements into a most exquisite whole.
Tellurium ([Plate X], 3).
Tellurium very closely resembles cadmium, and they are, therefore placed on the same diagram. The pillars are the same as in chlorine and its congeners, with a duad added at the base. The ten-atomed ovoid is the same as in cadmium and follows the same course in breaking up. It would be interesting to know why this duad remains as a duad in selenium and breaks up into a septad and triad in the other members of the group. It may be due to the greater pressure to which it is subjected in selenium, or there may be some other reason. The cross in tellurium is identical with that in cadmium, except that the centre is seven-atomed instead of four-atomed.