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 a.n.a.lysed.

II a.--We come now to the second great tetrahedral group, which though very much complicated, is yet, for the most part, a repet.i.tion of familiar forms.

MAGNESIUM (PLATE IX, 1).

[Ill.u.s.tration]

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 subst.i.tution 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).

[Ill.u.s.tration]

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 subst.i.tuted 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 subst.i.tution of a second septet for the triplet, as in zinc.

SELENIUM (Plate X, 2).

[Ill.u.s.tration]

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.

[Ill.u.s.tration: PLATE XI.]

BORON (Plate III, 4, and Plate XI, 1). We have here the simplest form of the cube; the funnels contain only five bodies--four six-atomed ovoids and one six-atomed "cigar." The central globe has but four five-atomed spheres.

It is as simple in relation to its congeners as is beryllium to its group-members.

BORON: 6 funnels of 30 atoms 180 Central globe 20 ---- Total 200 ---- Atomic weight 10.86 Number weight 200/18 11.11 SCANDIUM (Plate XI, 2). For the first time we meet funnels of different types, A and B, three of each kind; A appear to be positive and B negative, but this must be stated with reserve.

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 a.s.sumes in other gaseous elements. Here it appears as a sphere--the form always a.s.sumed 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 const.i.tuents of nitrogen.

The central globe repeats that of boron, with an additional four-atomed sphere in the middle.

SCANDIUM: 3 funnels (A) of 140 atoms 420 3 " (B) of 116 " 348 Centre globe 24 ---- Total 792 ---- Atomic weight 43.78 Number weight 792/18 44.00 YTTRIUM (Plate XI, 3). Here we have a quite new arrangement of bodies within the funnel--the funnel being of one type only. Two "cigars" whirl on their own axes in the centre near the top, while four eight-atomed globes (see 4 _e_) chase each other in a circle round them, spinning madly on their own axes--this axial spinning seems constant in all contained bodies--all the time. Lower down in the funnel, a similar arrangement is seen, with a globe (see 4 _d_)--a nitrogen element--replacing the "cigars,"

and six-atomed ovoids replacing the globes.

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 subst.i.tution 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.

YTTRIUM: 6 funnels of 261 atoms 1566 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 const.i.tuent parts, which we are able only to describe.

[Ill.u.s.tration: PLATE XII.]

NITROGEN (Plate XII, 1) does not a.s.sume the cubical form of its relatives, but is in shape like an egg. Referring again to our 1895 investigations, I quote from them. The balloon-shaped body (see 4 _a_) floats in the middle of the egg, containing six small spheres in two horizontal rows, and a long ovoid in the midst; this balloon-shaped body is positive, and is drawn down towards the negative body _b_ (see 4 _b_) with its seven contained spheres, each of which has nine atoms within it--three triads. Four spheres are seen, in addition to the two larger bodies; two of these (see 4 _d_), each containing five smaller globes, are positive, and two (see 4 _c_) containing four smaller globes, are negative.

NITROGEN: Balloon 110 Oval 63 2 bodies of 20 atoms 40 2 " " 24 " 48 ---- Total 261 ---- Atomic weight 14.01 Number weight 261/18 14.50 VANADIUM (Plate XII, 2) closely follows scandium, having two types of funnels. Funnel A only differs from that of scandium by having a globe (see 4 _d_) inserted in the ring of four ovoids; funnel B has a six-atomed, instead of a five-atomed globe at the top, and slips a third globe containing twenty atoms (see 4 _d_) between the two identical with those of scandium (see 4 _c_). The central globe has seven atoms in its middle body instead of four. In this way does vanadium succeed in overtopping scandium by 126 atoms.

VANADIUM: 3 funnels (A) of 160 atoms 480 3 " (B) " 137 " 411 Central globe 27 ---- Total 918 ---- Atomic weight 50.84 Number weight 918/18 51.00 NIOBIUM (Plate XII, 3) is as closely related to yttrium as is vanadium to scandium. The little globes that scamper round the "cigars" contain twelve atoms instead of eight (see 4 _e_).

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.

NIOBIUM: 6 funnels of 277 atoms 1662 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, a.r.s.enic and antimony: bis.m.u.th also belongs to it, but was not examined; they are triatomic, diamagnetic and negative. They have no central globes.

[Ill.u.s.tration: PLATE XIII.]

ALUMINIUM (Plate XIII, 1), the head of the group, is, as usual, simple.

There are six similar funnels, each containing eight ovoids, below which is a globe.

ALUMINIUM: 6 funnels of 81 atoms 486 Atomic weight 26.91 Number weight 486/18 27.00 GALLIUM (Plate XIII, 2) has two segments in every funnel; in the segment to the left a "cigar" balances a globe, equally six-atomed, in that of the right, and the globes to right and left are four-atomed as against three-atomed. In the next row, the smaller contained globes have six atoms as against four, and the cones have respectively seven and five. By these little additions the left-hand funnel boasts one hundred and twelve atoms as against ninety-eight.

GALLIUM: Left segment 112 atoms } Right segment 98 " } = 210 6 funnels of 210 atoms 1260 ---- Atomic weight 69.50 Number weight 1260/18 70.00 INDIUM (Plate XIII, 3) repeats the segments of gallium exactly, save in the subst.i.tution of a sixteen-atomed body for the seven-atomed cone of the left-hand segment, and a fourteen-atomed body for the five-atomed corresponding one in gallium. But each funnel now has three segments instead of two; three funnels out of the six contain two segments of type A and one of type B; the remaining three contain two of type B, and one of type A.

INDIUM: Segment A 121 atoms 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, a.r.s.enic, and antimony, run on very similar lines to those we have just examined.