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: 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
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
4 c of 212 atoms 848
12 d of 36 " 432
Central globe 128
----
Total 1624
----
Atomic weight 89.85
Number weight 90.22
Atomic weight 28.18
Number weight 520/18 28.88
Central globe 52
----
Total 1300
----
Atomic weight 71.93
Number weight 1300/18 72.22
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:—
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.
Atomic weight 55.47
Number weight 1008/18 56.00
Atomic weight 57.70
Number weight 1036/18 57.55
Atomic weight 58.30
Number weight 1064/18 59.11
(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.
Atomic weight 100.91
Number weight 1848/18 102.66
Atomic weight 102.23
Number weight 1876/18 104.22
Atomic weight 105.74
Number weight 1904/18 105.77
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.
Atomic weight 189.55
Number weight 3430/18 190.55
Atomic weight 191.11
Number weight 3458/18 192.11
Atomic weight 193.66
Number weight 3486/18 193.34
Atomic weight ------
Number weight 3514/18 195.22
V a.—The Spike Groups.
I place within this group lithium, potassium, 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. Potassium 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, potassium 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.
8 petals of 6 atoms 48
Central globe of 16 atoms 16
----
Total 127
----
Atomic weight 6.98
Number weight 127/18 7.05
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.)
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.
2 balloons 220
----
Total 340
----
Atomic weight 18.90
Number weight 340/18 18.88
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).
Carbon is the typical octahedron, and a clear understanding of this will enable us to follow easily the constitution 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 titanium 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.
Titanium (Plate III, 6, and XV, 2, 3).
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 titanium. On the meta level, c (titanium 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 sextet, 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 titanium, 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 sextet and an octet. The d ovoid liberates five bodies, four of which we have already seen in titanium, as the crosses and sextet of sodium, and which are figured under titanium; the four quartets within the larger globe also follow a sodium model, and are given again.
Silicon (Plate XVI, 1).
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, pass along their usual course. The quintet and quartet remain together, and form a nine-atomed body on the meta level, yielding a sextet 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 titanium. 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.
Tin (Plate XVI, 3, 4).
Here we have only the spike to consider, as the funnels are the same as in germanium, and the central globe is that of titanium, omitting the eight atomed centre. The cone of the spike we have had in silver (see p. 729, May), and it is set free on the proto level. The spike, as in zinc, becomes a large sphere, with the single septet in the centre, the remaining six bodies circling round it on differing planes. They break up as shown. (Tin is Sn.)