[Ill.u.s.tration: TYPES OF META-PROTO-ELEMENTAL MATTER.]

The Meta state, in some of its combinations, appears at first sight to repeat those of the Hyper state; the only obvious way of distinguishing to which some of the molecules of less complexity belong is to pull them out of the "cell-wall"; if they are Hyper molecules they at once fly off as separate atoms; if they are Meta molecules they break up into two or more molecules containing a smaller number of atoms. Thus one of the Meta molecules of iron, containing seven atoms, is identical in appearance with a Hyper heptad, but the latter dissociates into seven atoms, the former into two triads and a single atom. Long-continued research into the detailed play of forces and their results is necessary; we are here only able to give preliminary facts and details--are opening up the way. The following may serve as characteristic Meta types:--

These are taken from const.i.tuents of the various elements; 1 from Gl; 2 and 3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12 from Li; 13 and 14 from Na. Others will be seen in the course of breaking up the elements.

The Proto state preserves many of the forms in the elements, modified by release from the pressure to which they are subjected in the chemical atom.

In this state various groups are thus recognizable which are characteristic of allied metals.

[Ill.u.s.tration: TYPES OF PROTO-ELEMENTAL MATTER.]

These are taken from the products of the first disintegration of the chemical atom, by forcibly removing it from its hole. The groups fly apart, a.s.suming a great variety of forms often more or less geometrical; the lines between the const.i.tuents of the groups, where indicated, no longer represent lines of force, but are intended to represent the impression of form, _i.e._, of the relative position and motion of the const.i.tuents, made on the mind of the observer. They are elusive, for there are no lines, but the appearance of lines is caused by the rapid motion of the cost.i.tuents up and down, or along them backwards and forwards. The dots represent atoms, or groups of atoms, within the proto-elements. 1 is found in C; 2 and 3 in He; 4 in Fl; 5 in Li; 6 in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe; 12 in Se. We shall return to these when a.n.a.lysing the elements, and shall meet many other proto-elemental groupings.

The first thing which is noticed by the observer, when he turns his attention to the chemical atoms, is that they show certain definite forms, and that within these forms, modified in various ways, sub-groupings are observable which recur in connexion with the same modified form. The main types are not very numerous, and we found that, when we arranged the atoms we had observed, according to their external forms, they fell into natural cla.s.ses; when these, in turn, were compared with Sir William Crookes'

cla.s.sification, they proved to be singularly alike. Here is his arrangement of the elements, as it appeared in the _Proceedings of the Royal Society_, in a paper read on June 9th, 1898.

[Ill.u.s.tration]

This is to be read, following the lines of the "figures of eight": H, He, Li, Gl, B, C, N, and so on, each successive element being heavier than the one preceding it in order. The disks which fall immediately below each other form a cla.s.s; thus: H, Cl, Br, I; these resemble each other in various ways, and, as we shall presently see, the same forms and groupings re-appear.

Another chart--taken from Erdmann's _Lehrbuch_--arranges the elements on a curved line, which curiously resembles the curves within the sh.e.l.l of a nautilus. The radiating lines show the cla.s.ses, the whole diameter building up a family; it will be observed that there is an empty radius between hydrogen and helium, and we have placed occultum there; on the opposite radius, iron, rubidium and osmium are seen.

[Ill.u.s.tration]

The external forms may be cla.s.sified as follows; the internal details will be dealt with later :--

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

1. _The Dumb-bell._--The characteristics of this are a higher and lower group, each showing 12 projecting funnels, grouped round a central body, and a connecting rod. It appears in sodium, copper, silver, and gold,[17]

and gold is given (1 on Plate III) as the most extremely modified example of this form. The 12 almond-like projections, above and below, are severally contained in shadowy funnels, impossible to reproduce in the drawing; the central globe contains three globes, and the connecting portion has swollen out into an egg, with a very complicated central arrangement. The dumb-bell appears also in chlorine, bromine and iodine, but there is no trace of it in hydrogen, the head of the group. We have not met it elsewhere. It may be remarked that, in Sir William Crookes' scheme, in which they are all cla.s.sed as monads, these two groups are the nearest to the neutral line, on the ingoing and outgoing series, and are respectively positive and negative.

II and IIa. _The Tetrahedron._--The characteristics of this form are four funnels, containing ovoid bodies, opening on the face of a tetrahedron. The funnels generally, but not always, radiate from a central globe. We give beryllium (glucinum) as the simplest example (2 on Plate III), and to this group belong calcium and strontium. The tetrahedron is the form of chromium and molybdenum, but not that of the head of their group, oxygen, which is, like hydrogen, _sui generis_. These two groups are marked in orthodox chemistry as respectively positive and negative, and are closely allied.

Another pair of groups show the same tetrahedral form: magnesium, zinc and cadmium, positive; sulphur, selenium and tellurium, negative. Selenium is a peculiarly beautiful element, with a star floating across the mouth of each funnel; this star is extremely sensitive to light, and its rays tremble violently and bend if a beam of light falls on it. All these are dyads.

The tetrahedron is not confined to the external form of the above atoms; it seems to be one of the favourite forms of nature, and repeatedly appears in the internal arrangements. There is one tetrahedron within the unknown element occultum; two appear in helium (3 on Plate III); yttrium has also two within its cube, as has germanium; five, intersecting, are found in neon, meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon, kalon, meta-kalon, tin, t.i.tanium and zirconium. Gold contains no less than twenty tetrahedra.

III. _The Cube._--The cube appears to be the form of triads. It has six funnels, containing ovoids, and opening on the faces of the cube. Boron is chosen as an example (4 on Plate III). Its group members, scandium and yttrium, have the same form; we have not examined the fourth; the group is positive. Its negative complement consists of nitrogen, vanadium and niobium, and we have again to note that nitrogen, like hydrogen and oxygen, departs from its group type. Two other triad groups, the positive aluminium, gallium and indium (the fourth unexamined) and the negative phosphorus, a.r.s.enic and antimony (the fourth unexamined), have also six funnels opening on the faces of a cube.

IV. _The Octahedron._--The simplest example of this is carbon (5 on Plate III). We have again the funnel with its ovoids, but now there are eight funnels opening on the eight faces of the octahedron. In t.i.tanium (6 on Plate III) the form is masked by the protruding arms, which give the appearance of the old Rosicrucian Cross and Rose, but when we look into the details later, the carbon type comes out clearly. Zirconium is exactly like t.i.tanium in form, but contains a large number of atoms. We did not examine the remaining two members of this group. The group is tetratomic and positive. Its negative pendant shows the same form in silicon, germanium and tin; again, the fourth was unexamined.

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

V. _The Bars._--These characterise a set of closely allied groups, termed "inter-periodic." Fourteen bars (or seven crossed) radiate from a centre, as in iron (1 on Plate IV), and the members of each group--iron, nickel, cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum--differ from each other by the weight of each bar, increasing in orderly succession; the details will be given later. Manganese is often grouped with iron, nickel, and cobalt (_see_ Crookes' lemniscates), but its fourteen protruding bodies repeat the "lithium spike" (proto-element 5) and are grouped round a central ovoid. This would appear to connect it with lithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with which it is often cla.s.sed. The "lithium spike" re-appears in pota.s.sium and rubidium. These details, again, will come out more clearly later.

VI. _The Star._--A flat star, with five interpenetrating tetrahedra in the centre, is the characteristic of neon and its allies (4 on Plate IV) leaving apart helium, which, as may be seen by referring to 3, Plate IV, has an entirely different form.

There are thus six clearly defined forms, typical of cla.s.ses, with two--lithium and fluorine--of doubtful affinities. It is worthy of notice that in diatomic elements _four_ funnels open on the faces of tetrahedra; in triatomic, _six_ funnels on the faces of cubes; in tetratomic, _eight_ funnels on the faces of octahedra.

Thus we have a regular sequence of the platonic solids, and the question suggests itself, will further evolution develop elements shaped to the dodecahedron and the icosahedron?

II.

We now pa.s.s from the consideration of the outer forms of the chemical elements to a study of their internal structure, the arrangement within the element of more or less complicated groups--proto-elements--capable of separate, independent existence; these, once more, may be dissociated into yet simpler groups--hyper-meta-proto-elements--equally capable of separate, independent existence, and resolvable into single ultimate physical atoms, the irreducible substratum of the physical world (see _Theosophist_, 1908, pp. 354-356).[18]

We shall have to study the general internal structure, and then the breaking up of each element, and the admirable diagrams, patiently worked out by Mr. Jinarajadasa, will make the study comparatively easy to carry on.

The diagrams, of course, can only give a very general idea of the facts they represent; they give groupings and show relations, but much effort of the imagination is needed to transform the two-dimensional diagram into the three-dimensional object. The wise student will try to visualize the figure from the diagram. Thus the two triangles of hydrogen are not in one plane; the circles are spheres, and the atoms within them, while preserving to each other their relative positions, are in swift movement in three-dimensional s.p.a.ce. Where five atoms are seen, as in bromine and iodine, they are generally arranged with the central atom above the four, and their motion indicates lines which erect four plane triangles--meeting at their apices--on a square base, forming a square-based four-sided pyramid. Each dot represents a single ultimate atom. The enclosing lines indicate the impression of form made on the observer, and the groupings of the atoms; the groups will divide along these lines, when the element is broken up, so that the lines have significance, but they do not exist as stable walls or enclosing films, but rather mark limits, not lines, of vibrations. It should be noted that it is not possible to show five of the prisms in the five intersecting tetrahedra of prisms, and 30 atoms must, therefore, be added in counting.

The diagrams are not drawn to scale, as such drawing would be impossible; the dot representing the atom is enormously too large compared with the enclosures, which are absurdly too small; a scale drawing would mean an almost invisible dot on a sheet of many yards square.

The use of the words "positive" and "negative" needs to be guarded by the following paragraphs from the article on "Chemistry" in the _Encyclopaedia Britannica_. We use the words in their ordinary text-book meaning, and have not, so far, detected any characteristics whereby an element can be declared, at sight, to be either positive or negative:--

"When binary compounds, or compounds of two elements, are decomposed by an electric current, the two elements make their appearance at opposite poles.

These elements which are disengaged at the negative pole are termed electro-positive or positive or basylous elements, while those disengaged at the positive pole are termed electro-negative or negative or chlorous elements. But the difference between these two cla.s.ses of elements is one of degree only, and they gradually merge into each other; moreover the electric relations of elements are not absolute, but vary according to the state of combination in which they exist, so that it is just as impossible to divide the elements into two cla.s.ses according to this property as it is to separate them into two distinct cla.s.ses of metals and non-metals."

We follow here the grouping according to external forms, and the student should compare it with the groups marked in the lemniscate arrangement shown in Article II (p. 377, properly p. 437, February), reading the group by the disks that fall below each other; thus the first group is H, Cl, Br, I (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered element. The elements grow denser in descending order; thus hydrogen is an invisible gas; chlorine a denser gas visible by its colour; bromine is a liquid; iodine is a solid--all, of course, when temperature and pressure are normal. By the lowering of temperature and the increase of pressure, an element which is normally gaseous becomes a liquid, and then a solid.

Solid, liquid, gaseous, are three interchangeable states of matter, and an element does not alter its const.i.tution by changing its state. So far as a chemical "atom" is concerned, it matters not whether it be drawn for investigation from a solid, a liquid, or a gas; but the internal arrangements of the "atoms" become much more complicated as they become denser and denser, as is seen by the complex arrangements necessitated by the presence of the 3546 ultimate atoms contained in the chemical "atom" of gold, as compared with the simple arrangement of the 18 ultimate atoms of hydrogen.

According to the lemniscate arrangement, we should commence with hydrogen as the head of the first negative group, but as it differs wholly from those placed with it, it is better to take it by itself. Hydrogen is the lightest of the known elements, and is therefore taken as 1 in ordinary chemistry, and all atomic weights are multiples of this. We take it as 18, because it contains eighteen ultimate atoms, the smallest number we have found in a chemical element. So our "number-weights" are obtained by dividing the total number of atoms in an element by 18 (see p. 349, January).

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

HYDROGEN (Plate V, 1).--Hydrogen not only stands apart from its reputed group by not having the characteristic dumb-bell shape, well shown in sodium (Plate I, opposite p. 349, January), but it also stands apart in being positive, serving as a base, not as a chlorous, or acid, radical, thus "playing the part of a metal," as in hydrogen chloride (hydrochloric acid), hydrogen sulphate (sulphuric acid), etc.

It is most curious that hydrogen, oxygen and nitrogen, the most widely spread gases, all differ fundamentally in form from the groups they reputedly head.[19] Hydrogen was the first chemical element examined by us, nearly thirteen years ago, and I reproduce here the substance of what I wrote in November, 1895, for we have nothing to add to nor amend in it.

Hydrogen consists of six small bodies, contained in an egg-like form (the outer forms are not given in the diagrams). The six little bodies are arranged in two sets of three, forming two triangles which are not interchangeable, but are related to each other as object and image. The six bodies are not all alike; they each contain three ultimate physical atoms, but in four of the bodies the three atoms are arranged in a triangle, and in the remaining two in a line.

HYDROGEN: 6 bodies of 3 18 Atomic weight 1 Number weight 18/18 1 I.--THE DUMB-BELL GROUP.

I a.--This group consists of Cl, Br, and I (chlorine, bromine and iodine); they are monads, diamagnetic and negative.

CHLORINE (Plate V, 2).--As already said, the general form is that of the dumb-bell, the lower and upper parts each consisting of twelve funnels, six sloping upwards and six downwards, the funnels radiating outwards from a central globe, and these two parts being united by a connecting rod (see, again, sodium, Plate I).

The funnel (shown flat as an isosceles triangle, standing on its apex) is a somewhat complicated structure, of the same type as that in sodium (Plate VI, 2), the difference consisting in the addition of one more globe, containing nine additional atoms. The central globe is the same as in sodium, but the connecting rod differs. We have here a regular arrangement of five globes, containing three, four, five, four, three atoms respectively, whereas sodium has only three bodies, containing four, six, four. But copper and silver, its congeners, have their connecting rods of exactly the same pattern as the chlorine rod, and the chlorine rod reappears in both bromine and iodine. These close similarities point to some real relation between these groups of elements, which are placed, in the lemniscates, equi-distant from the central line, though one is on the swing which is going towards that line and the other is on the swing away from it.

CHLORINE: Upper part {12 funnels of 25 atoms 300 {Central globe 10 Lower part same 310 Connecting rod 19 ---- Total 639 ---- Atomic weight 35.473 Number weight 639/18 35.50 (The Atomic Weights are mostly from Erdmann, and the Number Weights are those ascertained by us by counting the atoms as described on p. 349, January, and dividing by 18. Prof. T.W. Richards, in _Nature_, July 18, 1907, gives 35.473.)

BROMINE (Plate V, 3).--In bromine, each funnel has three additional bodies, ovoid in shape, an addition of 33 atoms being thus made without any disturbance of form; two pairs of atoms are added to the central globe, and a rearrangement of the atoms is effected by drawing together and lessening the swing of the pair of triplets, thus making symmetrical room for the newcomers. The connecting rod remains unchanged. The total number of atoms is thus raised from the 639 of chlorine to 1439. Over and over again, in these investigations, were we reminded of Tyndall's fascinating description of crystal building, and his fancy of the tiny, ingenious builders busied therein. Truly are there such builders, and the ingenuity and effectiveness of their devices are delightful to see.[20]

BROMINE: Upper part {12 funnels of 58 atoms 696 {Central globe 14 Lower part same 710 Connecting rod 19 ---- Total 1439 ---- Atomic weight 79.953 Number weight 1459/18 79.944 IODINE (Plate V, 4).--We find herein that the central globe gains 4 atoms, the two pairs becoming 2 quartets; the connecting rod exactly reproduces the rods of chlorine and bromine; the funnel is also that of bromine, except that five bodies, containing 35 atoms, are added to it. The 1439 atoms of bromine are thus raised to 2887.

IODINE: Upper Part {12 funnels of 90 atoms 1116 {Central globe 18 Lower part same 1134 Connecting rod 19 ---- Total 2287 ---- Atomic weight 126.01 Number weight 2287/18 127.055 The plan underlying the building up of groups is here clearly shown; a figure is built up on a certain plan, in this case a dumb-bell; in the succeeding members of the group additional atoms are symmetrically introduced, modifying the appearance, but following the general idea; in this case the connecting rod remains unaltered, while the two ends become larger and larger, more and more overshadowing it, and causing it to become shorter and thicker. Thus a group is gradually formed by additional symmetrical additions. In the undiscovered remaining member of the group we may suppose that the rod will have become still more egg-like, as in the case of gold.

I b.--The corresponding positive group to that which we have been considering consists of Na, Cu, Ag, and Au (sodium, copper, silver and gold), with an empty disk between silver and gold, showing where an element ought to be. These four elements are monads, diamagnetic, and positive, and they show the dumb-bell arrangement, although it is much modified in gold; we may presume that the undiscovered element between silver and gold would form a link between them.

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