Chapter III: The Later Researches (2)

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_ assume 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 constituents 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.

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 constitution. 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 substituted 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.

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 substituted 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

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 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.

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 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.

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 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.

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 constituent parts, which we are able only to describe.

NITROGEN (Plate XII, 1) does not assume 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, arsenic and antimony: bismuth also belongs to it, but was not
examined; they are triatomic, diamagnetic and negative. They have no
central globes.

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 substitution 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, arsenic, and antimony, run on
very similar lines to those we have just examined.

PHOSPHORUS (Plate XIV, 1) offers us a very curious arrangement of atoms, which will give some new forms in breaking up. Two segments are in each funnel, in fact the only two of group III _a_ which do not show this arrangement, or a modification thereof, are aluminium and arsenic.

PHOSPHORUS: Left segment 50 atoms Right segment 43 " -- 93 6 funnels of 93 atoms 558 Atomic weight 30.77 Number weight 558/18 31.00 ARSENIC (Plate XIV, 2) resembles aluminium in having eight internal sub-divisions in a funnel, and the ovoids which form the top ring are identical, save for a minute difference that in aluminium the ovoids stand the reverse way from those in arsenic. It will be noted that in the former the top and bottom triangles of atoms have the apices upwards, and the middle one has its apex downwards. In arsenic, the top and bottom ones point downwards, and the middle one upwards. Arsenic inserts sixteen spheres between the ovoids and globe shown in aluminium, and thus adds no less than one hundred and forty-four atoms to each funnel.

ARSENIC: 6 funnels of 225 atoms 1350 Atomic weight 74.45 Number weight 1350/18 75.00 ANTIMONY (Plate XIV, 3) is a close copy of indium, and the arrangement of types A and B in the funnels is identical. In the middle rings of both A and B a triplet is substituted for a unit at the centre of the larger globe. In the lowest body of type A the "cigar" has vanished, and is represented by a seven-atomed crystalline form.

ANTIMONY: Segment A 128 atoms
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).

The funnels let go the globes, but the eight ovoids remain within them, so that seven bodies are let loose on the proto level. When the ovoids are set free at the meta stage they become spherical and a nine-atomed body is produced, which breaks up into triangles on the hyper level. The globe becomes a cross at the meta stage, with one atom from the duads at each arm in addition to its own, and these form four duads on the hyper, and a unit from the centre.

GALLIUM (Plate XIII, 2).

In gallium the funnel disappears on the proto level, setting free its two contained segments, each of which forms a cylinder, thus yielding twelve bodies on the proto level. On the meta, the three upper globes in each left-hand segment are set free, and soon vanish, each liberating a cigar and two septets, the quartet and triad uniting. On the hyper the quartet yields two duads but the triangle persists. The second set of bodies divide on the meta level, forming a sextet and a cross with a duad at each arm; these on the hyper level divide into two triangles, four duads and a unit. The seven-atomed cone becomes two triangles united by a single atom, and on the meta level these form a ring round the unit; on the hyper they form three duads and a unit.

In the right-hand segment, the same policy is followed, the four triads becoming two sextets, while the central body adds a third to the number. The second ring has a quartet instead of the sextet, but otherwise breaks up as does that of the left; the quintet at the base follows that of boron.

INDIUM (Plate XIII, 3).

The complication of three segments of different types in each funnel does not affect the process of breaking up, and indium needs little attention. A is exactly the same as the left-hand funnel of gallium, save for the substitution of a globe containing the familiar "cigar" and two square-based pyramids. B is the same as the right-hand funnel of gallium, except that its lowest body consists of two square-based pyramids and a tetrahedron. All these are familiar.

PHOSPHORUS (Plate XIV, 1).

The atoms in the six similar spheres in the segments of the phosphorus funnel are arranged on the eight angles of a cube, and the central one is attached to all of them. On the meta level five of the nine atoms hold together and place themselves on the angles of a square-based pyramid; the remaining four set themselves on the angle of a tetrahedron. They yield, on the hyper level, two triads, a duad, and a unit. The remaining bodies are simple and familiar.

ARSENIC (Plate XIV, 2).

Arsenic shows the same ovoids and globe as have already been broken up in aluminium (see _ante_); the remaining sixteen spheres form nine-atomed bodies on the meta level, all similar to those of aluminium, thus yielding twelve positive and twelve negative; the globe also yields a nine-atomed body, twenty-five bodies of nine.

ANTIMONY (Plate XIV, 3).

Antimony follows closely in the track of gallium and indium, the upper ring of spheres being identical. In the second ring, a triplet is substituted for the unit, and this apparently throws the cross out of gear, and we have a new eleven-atomed figure, which breaks up into a triplet and two quartets on the hyper level. The lowest seven-atomed sphere of the three at the base is the same as we met with in copper.

* * * * *

VIII.

IV.--THE OCTAHEDRAL GROUPS.

These groups are at the turns of the spiral in Sir William Crookes' lemniscates (see p. 28). On the one side is carbon, with below it titanium and zirconium; on the other silicon, with germanium and tin. The characteristic form is an octahedron, rounded at the angles and a little depressed between the faces in consequence of the rounding; in fact, we did not, at first, recognize it as an octahedron, and we called it the "corded bale," the nearest likeness that struck us. The members of the group are all tetrads, and have eight funnels, opening on the eight faces of the octahedron. The first group is paramagnetic and positive; the corresponding one is diamagnetic and negative. The two groups are not closely allied in composition, though both titanium and tin have in common the five intersecting tetrahedra at their respective centres.

CARBON (Plate III, 5, and XV, 1) gives us the fundamental octahedral form, which becomes so masked in titanium and zirconium. As before said (p. 30), the protrusion of the arms in these suggests the old Rosicrucian symbol of the cross and rose, but they show at their ends the eight carbon funnels with their characteristic contents, and thus justify their relationship. The funnels are in pairs, one of each pair showing three "cigars," and having as its fellow a funnel in which the middle "cigar" is truncated, thus loosing one atom. Each "cigar" has a leaf-like body at its base, and in the centre of the octahedron is a globe containing four atoms, each within its own wall; these lie on the dividing lines of the faces, and each holds a pair of the funnels together. It seems as though this atom had been economically taken from the "cigar" to form a link. This will be more clearly seen when we come to separate the parts from each other. It will be noticed that the atoms in the "leaves" at the base vary in arrangement, being alternately in a line and in a triangle.

{ left 27 CARBON: One pair of funnels { right 22 { centre 1 -- 54 4 pairs of funnels of 54 atoms 216 Atomic weight 11.91 Number weight 216/18 12.00 TITANIUM (Plate III, 6, and XV, 2) has a complete carbon atom distributed over the ends of its four arms, a pair of funnels with their linking atom being seen in each. Then, in each arm, comes the elaborate body shown as 3 _c_, with its eighty-eight atoms. A ring of twelve ovoids (3 _d_) each holding within itself fourteen atoms, distributed among three contained globes--two quartets and a sextet--is a new device for crowding in material. Lastly comes the central body (4 _e_) of five intersecting tetrahedra, with a "cigar" at each of their twenty points--of which only fifteen can be shown in the diagram--and a ring of seven atoms round an eighth, that forms the minute centre of the whole. Into this elaborate body one hundred and twenty-eight atoms are built.

TITANIUM: One carbon atom 216 4 _c_ of 88 atoms 352 12 _d_ of 14 " 168 Central globe 128 ---- Total 864 ---- Atomic weight 47.74 Number weight 864/18 48.00 ZIRCONIUM (Plate XV, 3) has exactly the same outline as titanium, the carbon atom is similarly distributed, and the central body is identical. Only in 5 _c_ and _d_ do we find a difference on comparing them with 4 _c_ and d. The _c_ ovoid in zirconium shows no less than fifteen secondary globes within the five contained in the ovoid, and these, in turn, contain altogether sixty-nine smaller spheres, with two hundred and twelve atoms within them, arranged in pairs, triplets, quartets, quintets, a sextet and septets. Finally, the ovoids of the ring are also made more elaborate, showing thirty-six atoms instead of fourteen. In this way the clever builders have piled up in zirconium no less than 1624 atoms.

ZIRCONIUM: One Carbon atom 216
4 _c_ of 212 atoms 848
12 _d_ of 36 " 432
Central globe 128
----
Total 1624
----
Atomic weight 89.85
Number weight 90.22

SILICON (Plate XVI, 1) is at the head of the group which corresponds to carbon on the opposite turn of the lemniscate. It has the usual eight funnels, containing four ovoids in a circle, and a truncated "cigar" but no central body of any kind. All the funnels are alike.

SILICON: 8 funnels of 65 atoms 520 Atomic weight 28.18 Number weight 520/18 28.88 GERMANIUM (Plate XVI, 2) shows the eight funnels, containing each four segments (XVI, 4), within which are three ovoids and a "cigar." In this case the funnels radiate from a central globe, formed of two intersecting tetrahedra, with "cigars" at each point enclosing a four-atomed globe.

GERMANIUM: 8 funnels of 156 atoms 1248 Central globe 52 ---- Total 1300 ---- Atomic weight 71.93 Number weight 1300/18 72.22 TIN (Plate XVI, 3) repeats the funnel of germanium, and the central globe we met with in titanium, of five intersecting tetrahedra, carrying twenty "cigars"; the latter, however, omits the eight-atomed centre of the globe that was found in titanium, and hence has one hundred and twenty atoms therein instead of one hundred and twenty-eight. Tin, to make room for the necessary increase of atoms, adopts the system of spikes, which we met with in zinc (see Plate IX, 2); these spikes, like the funnels, radiate from the central globe, but are only six in number. The twenty-one-atomed cone at the head of the spike we have already seen in silver, and we shall again find it in iridium and platinum; the pillars are new in detail though not in principle, the contained globes yielding a series of a triplet, quintet, sextet, septet, sextet, quintet, triplet.

TIN: 8 funnels of 156 atoms 1248
6 spikes of 126 " 756
Central globe 120
----
Total 2124
----
Atomic weight 118.10
Number weight 2124/18 118.00
V.--THE BARS GROUPS.

Here, for the first time, we find ourselves a little at issue with the accepted system of chemistry. Fluorine stands at the head of a group--called the inter-periodic--whereof the remaining members are (see Crookes' table, p. 28), manganese, iron, cobalt, nickel; ruthenium, rhodium, palladium; osmium, iridium, platinum. If we take all these as group V, we find that fluorine and manganese are violently forced into company with which they have hardly any points of relationship, and that they intrude into an otherwise very harmonious group of closely similar composition. Moreover, manganese reproduces the characteristic lithium "spike" and not the bars of those into whose company it is thrust, and it is thus allied with lithium, with which indeed it is almost identical. But lithium is placed by Crookes at the head of a group, the other members of which are potassium, rubidium and cæsium (the last not examined). Following these identities of composition, I think it is better to remove manganese and fluorine from their incongruous companions and place them with lithium and its allies as V _a_, the Spike Groups, marking, by the identity of number, similarities of arrangement which exist, and by the separation the differences of composition. It is worth while noting what Sir William Crookes, in his "Genesis of the Elements," remarks on the relations of the interperiodic group with its neighbours. He says: "These bodies are interperiodic because their atomic weights exclude them from the small periods into which the other elements fall, and because their chemical relations with some members of the neighbouring groups show that they are probably interperiodic in the sense of being in transition stages."

Group V in every case shows fourteen bars radiating from a centre as shown in iron, Plate IV, 1. While the form remains unchanged throughout, the increase of weight is gained by adding to the number of atoms contained in a bar. The group is made up, not of single chemical elements, as in all other cases, but of sub-groups, each containing three elements, and the relations within each sub-group are very close; moreover the weights only differ by two atoms per bar, making a weight difference of twenty-eight in the whole. Thus we have per bar:--

Iron 72 Palladium 136 Nickel 74 Osmium 245 Cobalt 76 Iridium 247 Ruthenium 132 Platinum A 249 Rhodium 134 Platinum B 257 It will be noticed (Plate XVII, 3, 4, 5,) that each bar has two sections, and that the three lower sections in iron, cobalt and nickel are identical; in the upper sections, iron has a cone of twenty-eight atoms, while cobalt and nickel have each three ovoids, and of these the middle ones alone differ, and that only in their upper globes, this globe being four-atomed in cobalt and six-atomed in nickel.

The long ovoids within each bar revolve round the central axis of the bar, remaining parallel with it, while each spins on its own axis; the iron cone spins round as though impaled on the axis.

14 bars of 72 atoms 1008
Atomic weight 55.47
Number weight 1008/18 56.00
IRON (Plate IV, 1, and XVII, 3):

14 bars of 74 atoms 1036
Atomic weight 57.70
Number weight 1036/18 57.55
COBALT (Plate XVII, 4):

14 bars of 76 atoms 1064
Atomic weight 58.30
Number weight 1064/18 59.11
NICKEL (Plate XVII, 4):

(The weight of cobalt, as given in Erdmann's _Lehrbuch_, is 58.55, but Messrs. Parker and Sexton, in _Nature_, August 1, 1907, give the weight, as the result of their experiments, as 57.7.)

The next sub-group, ruthenium, rhodium, and palladium, has nothing to detain us. It will be observed that each bar contains eight segments, instead of the six of cobalt and nickel; that ruthenium and palladium have the same number of atoms in their upper ovoids, although in ruthenium a triplet and quartet represent the septet of palladium; and that in ruthenium and rhodium the lower ovoids are identical, though one has the order: sixteen, fourteen, sixteen, fourteen; and the other: fourteen, sixteen, fourteen, sixteen. One constantly asks oneself: What is the significance of these minute changes? Further investigators will probably discover the answer.

14 bars of 132 atoms 1848
Atomic weight 100.91
Number weight 1848/18 102.66
RUTHENIUM (Plate XVIII, 1):

14 bars of 134 atoms 1876
Atomic weight 102.23
Number weight 1876/18 104.22
RHODIUM (Plate XVII, 2):

14 bars of 136 atoms 1904
Atomic weight 105.74
Number weight 1904/18 105.77
PALLADIUM (XVIII, 3):

The third sub-group, osmium, iridium and platinum, is, of course, more complicated in its composition, but its builders succeed in preserving the bar form, gaining the necessary increase by a multiplication of contained spheres within the ovoids. Osmium has one peculiarity: the ovoid marked _a_ (XVIII, 4) takes the place of axis in the upper half of the bar, and the three ovoids, marked _b_, revolve round it. In the lower half, the four ovoids, _c_, revolve round the central axis. In platinum, we have marked two forms as platinum A and platinum B, the latter having two four-atomed spheres (XVIII, 6 _b_) in the place of the two triplets marked a. It may well be that what we have called platinum B is not a variety of platinum, but a new element, the addition of two atoms in a bar being exactly that which separates the other elements within each of the sub-groups. It will be noticed that the four lower sections of the bars are identical in all the members of this sub-group, each ovoid containing thirty atoms. The upper ring of ovoids in iridium and platinum A are also identical, but for the substitution, in platinum A, of a quartet for a triplet in the second and third ovoids; their cones are identical, containing twenty-one atoms, like those of silver and tin.

14 bars of 245 atoms 3430
Atomic weight 189.55
Number weight 3430/18 190.55
OSMIUM (Plate XVIII, 4):

14 bars of 247 atoms 3458
Atomic weight 191.11
Number weight 3458/18 192.11
IRIDIUM (Plate XVIII, 5):

14 bars of 249 atoms 3486
Atomic weight 193.66
Number weight 3486/18 193.34
PLATINUM A (Plate XVIII, 6 _a_):

14 bars of 251 atoms 3514
Atomic weight ------
Number weight 3514/18 195.22
PLATINUM B (Plate XVIII, 6 _b_):

V a.--THE SPIKE GROUPS.