We have already disposed of occultum, on this plate, and of sodium, which lies at the root of both groups. Copper, we now find, is also very largely off our hands, as the funnel provides us with only two new types--two spheres--each containing five atoms in a new arrangement, and the triangular body at the mouth with its ten atoms. This triangular body, with an increased number of atoms, reappears in various other chemical elements.

The central globes are different from any we have had before, in their internal arrangement, but the const.i.tuents are familiar; there are two contained spheres with four atoms each, the _a_ in the globe of bromine (see above) and 2 "cigars." The "cigars" may be followed under occultum (see above). The connecting rod is as in chlorine, bromine and iodine.

The atoms in the bodies _a_ and _b_ are curiously arranged. _A_ consists of two square-based pyramids turned so as to meet at their apices, and breaks up into two quartet rings and a duad. _B_ is again two four-sided pyramids, but the bases are in contact and set at right angles to each other; the second apex is not seen, as it is directly below the first. The pyramids separate as meta-bodies, and the atoms a.s.sume the peculiar arrangement indicated and then break up into four pairs and two units on the hyper level.

IV.

SILVER (Plate VI, 4 and Ag below).

Silver presents us with only two new bodies, and even these are only new by slight additions to old models. The triangular shaped body at the apex of the funnel, containing 21 atoms, is intermediate between the similar bodies in copper and iron. As a proto-element it becomes three triangles, joined at their apices, in fact a tetrahedron in which no atoms are distributed on the fourth face. The faces separate on the meta level and give three seven-atomed figures, and each of these breaks up into two triplets and a unit. The central globe only differs from that of bromine by the addition of one atom, which gives the familiar four-sided pyramid with a square base as in chlorine (see p. 46).

GOLD (Plate VII and Au below).

[Ill.u.s.tration]

The disintegration of gold first yields forty-seven bodies on the proto-level; the twenty-four funnels separate, and the central globes which hold each twelve together set free their six contained globes (_c_, _d_), thirty bodies being thus liberated. The sixteen bodies on the central inclined planes, marked _b_, break away, their central globe, with its four contained globes, remaining unchanged. But this condition does not last.

The motion of the funnels changes and thus the funnels cease to exist and their contents are set free, each funnel thus liberating nine independent bodies; the sixteen _b_ separate into two each; the four _a_ liberate five each; the two _c_ set free thirteen each; the four _d_ finally liberate two each: 302 proto elements in all.

The funnel is almost that of iodine, re-arranged. Four of the first ring in the iodine funnel are replaced by the triangular body, which becomes a four-sided pyramid with an occupied base. The second ring of three ovoids in iodine becomes four in gold, but the internal arrangement of each ovoid is the same. The next two spheres in the iodine funnel coalesce into one sphere, with similar contents, in the gold funnel. The fifth in iodine is slightly rearranged to form the fourth in descent in gold, and the remaining two are the same. _B_ has been broken up under occultum (p. 628) and can be followed there. The sixteen rings set free from the four _a_, after gyrating round the central body, now become a sphere, break up, as in occultum (see p. 44) into a meta seven-atomed ring and an eight-atomed double cross, and so on to the hyper level. The sphere with its two contained bodies breaks up into eight triangles on the meta level, and each of these, on the hyper, into a duad and a unit. The twelve septets of _c_ a.s.sume the form of prisms as in iodine (see p. 48) and pursue the same course, while its central body, a four-sided pyramid with its six attendants, divides on the meta level into six duads, revolving round a ring with a central atom as in chlorine (p. 47), the duads going off independently on the hyper-level and the ring breaking up as in chlorine.

The "cigar" tetrahedron of _d_ follows its course as in occultum, and the other sets free two quartets and two triplets on the meta level, yielding six duads and two units as hyper compounds. It will be seen that, complex as gold is, it is composed of const.i.tuents already familiar, and has iodine and occultum as its nearest allies.

II AND IIa.--THE TETRAHEDRAL GROUPS.

II.--This group consists of beryllium (glucinum), calcium, strontium and barium, all diatomic, paramagnetic and positive. The corresponding group consists of oxygen, chromium, molybdenum, wolfram (tungsten) and uranium, with a blank disk between wolfram and uranium: these are diatomic, paramagnetic, and negative. We have not examined barium, wolfram, or uranium.

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

BERYLLIUM (Plate III, 2, and Plate VIII, 1). In the tetrahedron four funnels are found, the mouth of each funnel opening on one of its faces.

The funnels radiate from a central globe, and each funnel contains four ovoids each with ten atoms within it arranged in three spheres. In the accompanying diagrams one funnel with its four ovoids is shown and a single ovoid with its three spheres, containing severally three, four, and three atoms, is seen at the left-hand corner of the plate (7 _a_). The members of this group are alike in arrangement, differing only in the increased complexity of the bodies contained in the funnels. Beryllium, it will be observed, is very simple, whereas calcium and strontium are complicated.

BERYLLIUM: 4 funnels of 40 atoms 160 Central globe 4 ---- Total 164 ---- Atomic weight 9.01 Number weight 164/18 9.11 CALCIUM (Plate VIII, 2) shows in each funnel three contained spheres, of which the central one has within it seven ovoids identical with those of beryllium, and the spheres above and below it contain each five ovoids (7 _b_) in which the three contained spheres have, respectively, two, five, and two atoms. The central globe is double, globe within globe, and is divided into eight segments, radiating from the centre like an orange; the internal part of the segment belonging to the inner globe has a triangular body within it, containing four atoms (7 _c_), and the external part, belonging to the encircling globe, shows the familiar "cigar" (7 _d_). In this way 720 atoms are packed into the simple beryllium type.

CALCIUM: 4 funnels of 160 atoms 640 Central globe 80 ---- Total 720 ---- Atomic weight 39.74 Number weight 720/18 40.00 STRONTIUM (Plate VIII, 3) shows a still further complication within the funnels, no less than eight spheres being found within each. Each of the highest pair contains four subsidiary spheres, with five, seven, seven, five atoms, respectively (7 _e_, _g_, _f_). The _g_ groups are identical with those in gold, but difference of pressure makes the containing body spherical instead of ovoid; similar groups are seen in the top ring of the iodine funnel, where also the "hole" is ovoid in form. The second pair of spheres contains ten ovoids (7 _b_) identical with those of calcium. The third pair contains fourteen ovoids (7 _a_) identical with those of beryllium, while the fourth pair repeats the second, with the ovoids re-arranged. The internal divisions of the double sphere of the central globe are the same as in calcium, but the contents differ. The "cigars" in the external segments are replaced by seven-atomed ovoids (7 _h_)--the iodine ovoids--and the external segments contain five-atomed triangles (7 _i_). Thus 1,568 atoms have been packed into the beryllium type, and our wonder is again aroused by the ingenuity with which a type is preserved while it is adapted to new conditions.

STRONTIUM: 4 funnels of 368 atoms 1472 Central globe 96 ---- Total 1568 ---- Atomic weight 86.95 Number weight 1568/18 87.11 The corresponding group, headed by oxygen--oxygen, chromium, molybdenum, wolfram and uranium--offers us another problem in its first member.

OXYGEN (Plate VIII, 4). This was examined by us in 1895, and the description may be reproduced here with a much improved diagram of its very peculiar const.i.tution. The gaseous atom is an ovoid body, within which a spirally-coiled snake-like body revolves at a high velocity, five brilliant points of light shining on the coils. The appearance given in the former diagram will be obtained by placing the five septets on one side on the top of those on the other, so that the ten become in appearance five, and thus doubling the whole, the doubling point leaving eleven duads on each side.

The composition is, however, much better seen by flattening out the whole.

On the proto level the two snakes separate and are clearly seen.

OXYGEN: Positive snake { 55 spheres of 2 atoms } { + 5 disks of 7 atoms } 145 Negative snake " 145 ---- Total 290 ---- Atomic weight 15.87 Number weight 290/18 16.11 CHROMIUM (Plate VIII, 5) "reverts to the ancestral type," the tetrahedron; the funnel is widened by the arrangement of its contents, three spheres forming its first ring, as compared with the units in beryllium and calcium, and the pairs in strontium and molybdenum. Two of these spheres are identical in their contents--two quintets (7 _f_), a quintet (7 _j_), and two quintets (7 _e_), _e_ and _f_ being to each other as object and image. The remaining sphere (7 _b_) is identical with the highest in the calcium funnel. The remaining two spheres, one below the other, are identical with the corresponding two spheres in calcium. The central globe, as regards its external segments, is again identical with that of calcium, but in the internal segments a six-atomed triangle (7 _k_) is subst.i.tuted for the calcium four-atomed one (7 _e_).

CHROMIUM: 4 funnels of 210 atoms 840 Central globe 96 ----- Total 936 ----- Atomic weight 51.74 Number weight 936/18 52.00 MOLYBDENUM (Plate VIII, 6) very closely resembles strontium, differing from it only in the composition of the highest pair of spheres in the funnels and in the presence of a little sphere, containing two atoms only, in the middle of the central globe. The topmost spheres contain no less than eight subsidiary spheres within each; the highest of these (7 _e_) has four atoms in it; the next three have four, seven and four (7 _e_ _g_ _e_), respectively; the next three are all septets (7 _g_), and the last has four--making in all for these two spheres 88 atoms, as against the 48 in corresponding spheres of strontium, making a difference of 160 in the four funnels.

MOLYBDENUM: 4 funnels of 408 atoms 1632 Central globe 98 ----- Total 1730 ----- Atomic weight 95.26 Number weight 1730/18 96.11 II a.--This group contains magnesium, zinc, cadmium, and mercury, with an empty disk between cadmium and mercury; we did not examine mercury. All are diatomic, diamagnetic and positive; the corresponding group consists of sulphur, selenium and tellurium, also all diatomic and diamagnetic, but negative. The same characteristics of four funnels opening on the faces of a tetrahedron are found in all, but magnesium and sulphur have no central globe, and in cadmium and tellurium the globe has become a cross.

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

MAGNESIUM (Plate IX, 1) introduces us to a new arrangement: each group of three ovoids forms a ring, and the three rings are within a funnel; at first glance, there are three bodies in the funnel; on examination each of these is seen to consist of three, with other bodies, spheres, again within them. Apart from this, the composition is simple enough, all the ovoids being alike, and composed of a triplet, a septet and a duad.

MAGNESIUM: 4 funnels of 108 atoms 432 Atomic weight 24.18 Number weight 432/18 24.00 ZINC (Plate IX, 2) also brings a new device: the funnel is of the same type as that of magnesium, while septets are subst.i.tuted for the triplets, and 36 additional atoms are thus slipped in. Then we see four spikes, alternating with the funnels and pointing to the angles, each adding 144 atoms to the total. The spikes show the ten-atomed triangle, already met with in other metals, three very regular pillars, each with six spheres, containing two, three, four, four, three, two atoms, respectively. The supporting spheres are on the model of the central globe, but contain more atoms. Funnels and spikes alike radiate from a simple central globe, in which five contained spheres are arranged crosswise, preparing for the fully developed cross of cadmium. The ends of the cross touch the bottoms of the funnels.

ZINC: 4 funnels of 144 atoms 576 4 spikes of 144 atoms 576 Central globe 18 ----- Total 1170 ----- Atomic weight 64.91 Number weight 1170/18 65.00 CADMIUM (Plate IX, 3) has an increased complexity of funnels; the diagram shows one of the three similar segments which lie within the funnels as cylinders; each of these contains four spheres, three pillars and three ovoids, like the spike of zinc turned upside down, and the zinc ten-atomed triangle changed into three ten-atomed ovoids. The centre-piece is a new form, though prefigured in the central globe of zinc.

CADMIUM: 3 segments of 164 atoms = 492 4 funnels of 492 atoms 1968 Central body 48 ----- Total 2016 ----- Atomic weight 111.60 Number weight 2016/18 112.00 The corresponding negative group is headed by

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

SULPHUR (Plate X, 1), which, like magnesium, has no central globe, and consists simply of the zinc funnels, much less compressed than zinc but the same in composition.

SULPHUR: 4 funnels of 144 atoms 576 Atomic weight 31.82 Number weight 576/18 32.00 SELENIUM (Plate X, 2) is distinguished by the exquisite peculiarity, already noticed, of a quivering star, floating across the mouth of each funnel, and dancing violently when a ray of light falls upon it. It is known that the conductivity of selenium varies with the intensity of the light falling upon it, and it may be that the star is in some way connected with its conductivity. It will be seen that the star is a very complicated body, and in each of its six points the two five-atomed spheres revolve round the seven-atomed cone. The bodies in the funnels resemble those in magnesium, but a reversed image of the top one is interposed between itself and the small duad, and each pair has its own enclosure. The central globe is the same as that of zinc.

SELENIUM: 4 funnels of 198 atoms 792 4 stars of 153 atoms 612 Central globe 18 ----- Total 1422 ----- Atomic weight 78.58 Number weight 1422/18 79.00 TELLURIUM (Plate X, 3), it will be seen, closely resembles cadmium, and has three cylindrical segments--of which one is figured--making up the funnel.

The contained bodies in the pillars run three, four, five, four, three, two, instead of starting with two; and a quartet replaces a duad in the globes above. The central cross only differs from that of cadmium in having a seven-atomed instead of a four-atomed centre. So close a similarity is striking.

TELLURIUM: 3 segments of 181 atoms = 543 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 repet.i.tions, 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).

[Ill.u.s.tration]

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, a.s.sumes 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, a.s.sume 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 repet.i.tions of forms already studied.

OXYGEN (PLATE VIII, 4).

[Ill.u.s.tration]

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 const.i.tuent 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.