4 stars of 153 atoms 612
Central globe 18
-----
Total 1422
-----
Atomic weight 78.58
Number weight 1422/18 79.00
4 funnels of 543 atoms 2172
Central body 51
-----
Total 2223
-----
Atomic weight 126.64
Number weight 2223/18 123.50
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.
VI.
III and IIIa.—The Cube Groups.
We have here four groups to consider, all the members of which are triads, and have six funnels, opening on the six faces of a cube.
III.—Boron, scandium and yttrium were examined; they are all triatomic, paramagnetic, and positive. The corresponding group consists of nitrogen, vanadium and niobium; they are triatomic, paramagnetic, and negative. We have not examined the remaining members of these groups. In these two groups nitrogen dominates, and in order to make the comparison easy the nitrogen elements are figured on both Plate XI and Plate XII. It will be seen that scandium and yttrium, of the positive group, differ only in details from vanadium and niobium, of the negative group; the ground-plan on which they are built is the same. We noted a similar close resemblance between the positive strontium and the negative molybdenum.
Central globe 20
----
Total 200
----
Atomic weight 10.86
Number weight 200/18 11.11
In A the boron funnel is reproduced, the "cigar" having risen above its companion ovoids; but the most important matter to note in respect to this funnel is our introduction to the body marked a 110. This body was observed by us first in nitrogen, in 1895, and we gave it the name of the "nitrogen balloon," for in nitrogen it takes the balloon form, which it also often assumes in other gaseous elements. Here it appears as a sphere—the form always assumed on the proto level—and it will be seen, on reference to the detailed diagram 4 a, to be a complicated body, consisting of six fourteen-atomed globes arranged round a long ovoid containing spheres with three, four, six, six, four, three, atoms respectively. It will be observed that this balloon appears in every member of these two groups, except boron.
The B funnel runs largely to triads, c and b, b (see 4 b) having not only a triadic arrangement of spheres within its contained globes, but each sphere has also a triplet of atoms. In c (see 4 c) there is a triadic arrangement of spheres, but each contains duads. B is completed by a five-atomed sphere at the top of the funnel. It should be noted that a, b and c all are constituents of nitrogen.
The central globe repeats that of boron, with an additional four-atomed sphere in the middle.
3 " (B) of 116 " 348
Centre globe 24
----
Total 792
----
Atomic weight 43.78
Number weight 792/18 44.00
The "nitrogen balloon" occupies the third place in the funnel, now showing its usual shape in combination, while the b globe (see 4 b) of scandium takes on a lengthened form below it.
The central globe presents us with two tetrahedra, recalling one of the combinations in gold (see Plate VII d), and differing from that only by the substitution of two quartets for the two triplets in gold.
One funnel of yttrium contains exactly the same number of atoms as is contained in a gaseous atom of nitrogen. Further, a, b, and d are all nitrogen elements. We put on record these facts, without trying to draw any conclusions from them. Some day, we—or others—may find out their significance, and trace through them obscure relations.
Central globe 40
----
Total 1606
----
Atomic weight 88.34
Number weight 1606/18 89.22
The corresponding negative group, of nitrogen, vanadium and niobium, is rendered particularly interesting by the fact that it is headed by nitrogen, which—like the air, of which it forms so large a part—pervades so many of the bodies we are studying. What is there in nitrogen which renders it so inert as to conveniently dilute the fiery oxygen and make it breathable, while it is so extraordinarily active in some of its compounds that it enters into the most powerful explosives? Some chemist of the future, perhaps, will find the secret in the arrangement of its constituent parts, which we are able only to describe.
Oval 63
2 bodies of 20 atoms 40
2 " " 24 " 48
----
Total 261
----
Atomic weight 14.01
Number weight 261/18 14.50
3 " (B) " 137 " 411
Central globe 27
----
Total 918
----
Atomic weight 50.84
Number weight 918/18 51.00
The rest of the funnel is the same. In the central globe both the tetrahedra have "cigars," and a central nine-atomed globe spins round in the centre (see 4 f), seventeen atoms being thus added.
Central globe 57
----
Total 1719
----
Atomic weight 93.25
Number weight 1719/18 95.50
III a.—Aluminium, gallium and indium were examined from this group. They are triatomic, diamagnetic, and positive. The corresponding group contains phosphorus, arsenic and antimony: bismuth also belongs to it, but was not examined; they are triatomic, diamagnetic and negative. They have no central globes.
Atomic weight 26.91
Number weight 486/18 27.00
Right segment 98 " } = 210
6 funnels of 210 atoms 1260
----
Atomic weight 69.50
Number weight 1260/18 70.00
Segment B 107 "
3 funnels of 2 A and 1 B ([242 + 107] 3) 1047
3 " " 2 B and 1 A ([214 + 121] 3) 1005
----
Total 2052
----
Atomic weight 114.05
Number weight 2052/18 114.00
The corresponding negative group, phosphorus, arsenic, and antimony, run on very similar lines to those we have just examined.
Right segment 43 "
--
93
6 funnels of 93 atoms 558
Atomic weight 30.77
Number weight 558/18 31.00
Atomic weight 74.45
Number weight 1350/18 75.00
Segment B 113 atoms
3 funnels of 2 A and 1 B ([256 + 113]3) 1107
3 " " 2 B and 1 A ([226 + 128]3) 1056
----
Total 2163
----
Atomic weight 119.34
Number weight 120.16
VII.
Boron (Plate III, 4, and Plate XI, 1).
The disintegration of boron is very simple: the funnels are set free and assume the spherical form, showing a central "cigar" and four globes each containing two triplets. The central globe is also set free with its four quintets, and breaks at once in two. On the meta level the "cigar" breaks up as usual, and the triplets separate. On the hyper level, the "cigar" follows its usual course, and the triplets become duads and units. The globe forms two quintets on the meta level, and these are resolved into triplets and duads.
Scandium (Plate XI, 2).
In funnel A the "cigar" and the ovoids behave as in boron, but the "balloon," a 110 (XI, 4), escapes from the funnel as it changes to a sphere, and holds together on the proto level; on the meta, it yields six globes each containing seven duads, and these are all set free as duads on the hyper level; the ovoid is also set free on the meta level becoming a sphere, and on the hyper level liberates its contained bodies, as two triplets, two quartets and two sextets.
In funnel B there is a quintet, that behaves like those in the globe of boron, on escaping from the funnel, in which the bodies remain on the proto level, with the exception of b 63, which escapes. On the meta level, c (Plate XI, 4), c assumes a tetrahedral form with six atoms at each point, and these hold together as sextets on the hyper level. At the meta stage, b (Plate XI, 4 b) sets free seven nine-atomed bodies, which become free triplets on the hyper. The central globe shows a cross at its centre, with the four quintets whirling round it, on the proto level. On the meta, the quintets are set free, and follow the boron type, while the cross becomes a quartet on the meta level, and two duads on the hyper.
Yttrium (Plate XI, 3).
In yttrium, on the proto level, a 110 and b 63 both escape from the funnel, and behave as in scandium. The ovoids and "cigars," set free on the meta level, behave as in boron. The central globe breaks up as in gold (pp. 49 and 50), four quartets being set free instead of two quartets and two triplets. We have only to consider e 8 and d 20 (Plate XI, 4). E 8 is a tetrahedral arrangement of duads on the meta level, set free as duads on the hyper. D 20 is an arrangement of pairs of duads at the angles of a square-based pyramid on the meta, and again free duads on the hyper.
Nitrogen (Plate XII, 1).
Nitrogen has nothing new to show us, all its constituents having appeared in scandium and yttrium.
Vanadium (Plate XII, 2).
The A funnel of vanadium repeats the A funnel of scandium, with the addition of d 20, already studied. In the B funnel scandium B is repeated, with an addition of d 20 and a sextet for a quintet; the sextet is the c of the "nitrogen balloon." The central globe follows boron, save that it has a septet for its centre; this was figured in iodine (p. 48).
Niobium (Plate XII, 3).
Niobium only differs from yttrium by the introduction of triplets for duads in e; on the meta level we have therefore triplets, and on the hyper each triplet yields a duad and a unit. The only other difference is in the central globe. The tetrahedra separate as usual, but liberate eight "cigars" instead of four with four quartets; the central body is simple, becoming three triads at the angles of a triangle on the meta level, and three duads and three units on the hyper.
Aluminium (Plate XIII, 1).