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 t.i.tanium, of five intersecting tetrahedra, carrying twenty "cigars"; the latter, however, omits the eight-atomed centre of the globe that was found in t.i.tanium, 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, s.e.xtet, septet, s.e.xtet, 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.

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

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 pota.s.sium, rubidium and caesium (the last not examined). Following these ident.i.ties 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 ident.i.ty 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 s.e.xton, in _Nature_, August 1, 1907, give the weight, as the result of their experiments, as 57.7.)

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

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 subst.i.tution, 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.

I place within this group lithium, pota.s.sium, rubidium, fluorine, and manganese, because of their similarity in internal composition. Manganese has fourteen spikes, arranged as in the iron group, but radiating from a central globe. Pota.s.sium has nine, rubidium has sixteen, in both cases radiating from a central globe. Lithium (Plate IV, 2) and fluorine (Plate IV, 3) are the two types which dominate the group, lithium supplying the spike which is reproduced in all of them, and fluorine the "nitrogen balloon" which appears in all save lithium. It will be seen that the natural affinities are strongly marked. They are all monads and paramagnetic; lithium, pota.s.sium and rubidium are positive, while fluorine and manganese are negative. We seem thus to have a pair, corresponding with each other, as in other cases, and the interperiodic group is left interperiodic and congruous within itself.

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

LITHIUM (Plate IV, 2 and Plate XIX, 1) is a striking and beautiful form, with its upright cone, or spike, its eight radiating petals (_x_) at the base of the cone, and the plate-like support in the centre of which is a globe, on which the spike rests. The spike revolves swiftly on its axis, carrying the petals with it; the plate revolves equally swiftly in the opposite direction. Within the spike are two globes and a long ovoid; the spheres within the globe revolve as a cross; within the ovoid are four spheres containing atoms arranged on tetrahedra, and a central sphere with an axis of three atoms surrounded by a spinning wheel of six.

LITHIUM: Spike of 63 atoms 63 8 petals of 6 atoms 48 Central globe of 16 atoms 16 ---- Total 127 ---- Atomic weight 6.98 Number weight 127/18 7.05 POTa.s.sIUM (Plate XIX, 2) consists of nine radiating lithium spikes, but has not petals; its central globe contains one hundred and thirty-four atoms, consisting of the "nitrogen balloon," encircled by six four-atomed spheres.

POTa.s.sIUM: 9 bars of 63 atoms 567 Central globe 134 ---- Total 701 ---- Atomic weight 38.94 Number weight 701/18 38.85 (The weight, as determined by Richards [_Nature_, July 18, 1907] is 39.114.)

RUBIDIUM: (Plate XIX, 3) adds an ovoid, containing three spheres--two triplets and a s.e.xtet--to the lithium spike, of which it has sixteen, and its central globe is composed of three "balloons."

RUBIDIUM: 16 spikes of 75 atoms 1200 Central globe 330 ---- Total 1530 ---- Atomic weight 84.85 Number weight 1530/18 85.00 The corresponding negative group consists only of fluorine and manganese, so far as our investigations have gone.

FLUORINE (Plate IV, 3, and Plate XVII, 1) is a most peculiar looking object like a projectile, and gives one the impression of being ready to shoot off on the smallest provocation. The eight spikes, reversed funnels, coming to a point, are probably responsible for this warlike appearance. The remainder of the body is occupied by two "balloons."

FLUORINE: 8 spikes of 15 atoms 120 2 balloons 220 ---- Total 340 ---- Atomic weight 18.90 Number weight 340/18 18.88 MANGANESE (Plate XVII, 2) has fourteen spikes radiating from a central "balloon."

MANGANESE: 14 spikes of 63 atoms 882 Central balloon 110 ---- Total 992 ---- Atomic weight 54.57 Number weight 992/18 55.11 * * * * *

IX.

We have now to consider the breaking up of the octahedral groups, and more and more, as we proceed, do we find that the most complicated arrangements are reducible to simple elements which are already familiar.

CARBON (Plate III, 5, and XV, 1).

[Ill.u.s.tration]

Carbon is the typical octahedron, and a clear understanding of this will enable us to follow easily the const.i.tution and disintegration of the various members of these groups. Its appearance as a chemical atom is shown on Plate III, and see XV, 1. On the proto level the chemical atom breaks up into four segments, each consisting of a pair of funnels connected by a single atom; this is the proto element which appears at the end of each arm of the cross in t.i.tanium and zirconium. On the meta level the five six-atomed "cigars" show two neutral combinations, and the truncated "cigar" of five atoms is also neutral; the "leaves" yield two forms of triplet, five different types being thus yielded by each pair of funnels, exclusive of the linking atom. The hyper level has triplets, duads and units.

t.i.tANIUM (Plate III, 6, and XV, 2, 3).

[Ill.u.s.tration]

On the proto level, the cross breaks up completely, setting free the pairs of funnels with the linking atom (_a_ and _b_), as in carbon, the four bodies marked _c_, the twelve marked _d_, and the central globe marked e.

The latter breaks up again, setting free its five intersecting cigar-bearing tetrahedra, which follow their usual course (see Occultum, p.

44). The eight-atomed body in the centre makes a ring of seven atoms round a central one, like that in occultum (see p. 44, diagram B), from which it only differs in having the central atom, and breaks up similarly, setting the central atom free. The ovoid _c_ sets free its four contained globes, and the ovoid _d_ sets free the three within it. Thus sixty-one proto elements are yielded by t.i.tanium. On the meta level, _c_ (t.i.tanium 3) breaks up into star-like and cruciform bodies; the component parts of these are easily followed; on the hyper level, of the four forms of triplets one behaves as in carbon, and the others are shown, _a_, _b_ and _f_; the cruciform quintet yields a triplet and a duad, _c_ and _d_; the tetrahedra yield two triplets _g_ and _h_, and two units; the septet, a triplet _k_ and a quartet _j_. On the meta level, the bodies from _d_ behave like their equivalents in sodium, each _d_ shows two quartets and a s.e.xtet, breaking up, on the hyper level, into four duads and two triads.

ZIRCONIUM (Plate XV, 2, 5).

Zirconium reproduces in its _c_ the four forms that we have already followed in the corresponding _c_ of t.i.tanium, and as these are set free on the proto level, and follow the same course on the meta and hyper levels, we need not repeat them. The central globe of zirconium _c_ sets free its nine contained bodies; eight of these are similar and are figured in the diagram; it will be observed that the central body is the truncated "cigar"

of carbon; their behaviour on the meta and hyper levels is easily followed there. The central sphere is also figured; the cigar follows its usual course, and its companions unite into a s.e.xtet and an octet. The _d_ ovoid liberates five bodies, four of which we have already seen in t.i.tanium, as the crosses and s.e.xtet of sodium, and which are figured under t.i.tanium; the four quartets within the larger globe also follow a sodium model, and are given again.

SILICON (Plate XVI, 1).

[Ill.u.s.tration]

In silicon, the ovoids are set free from the funnels on the proto level, and the truncated "cigar," playing the part of a leaf, is also liberated.

This, and the four "cigars," which escape from their ovoids, pa.s.s along their usual course. The quintet and quartet remain together, and form a nine-atomed body on the meta level, yielding a s.e.xtet and a triplet on the hyper.

GERMANIUM (Plate XVI, 2, 4).

The central globe, with its two "cigar"-bearing tetrahedra, need not delay us; the tetrahedra are set free and follow the occultum disintegration, and the central four atoms is the sodium cross that we had in t.i.tanium. The ovoids (XVI, 4) are liberated on the proto level, and the "cigar," as usual, bursts its way through and goes along its accustomed path. The others remain linked on the meta level, and break up into two triangles and a quintet on the hyper.