As the words "ultimate physical atom" must frequently occur, it is necessary to state what we mean by the phrase. Any gaseous chemical atom may be dissociated into less complicated bodies; these, again, into still less complicated; these, again, into yet still less complicated. These will be dealt with presently. After the third dissociation but one more is possible; the fourth dissociation gives the ultimate physical atom.^[3] This may vanish from the physical plane, but it can undergo no further dissociation on it. In this ultimate state of physical matter two types of atoms have been observed; they are alike in everything save the direction of their whorls and of the force which pours through them. In the one case force pours in from the "outside," from fourth-dimensional space,^[4] and passing through the atom, pours into the physical world. In the second, it pours in from the physical world, and out through the atom into the "outside" again,^[4] i.e., vanishes from the physical world. The one is like a spring, from which water bubbles out; the other is like a hole, into which water disappears. We call the atoms from which force comes out positive or male; those through which it disappears, negative or female. All atoms, so far as observed, are of one or other of these two forms. (Plate II.)

It will be seen that the atom is a sphere, slightly flattened, and there is a depression at the point where the force flows in, causing a heart-like form. Each atom is surrounded by a field, formed of the atoms of the four higher planes, which surround and interpenetrate it.

The atom can scarcely be said to be a "thing," though it is the material out of which all things physical are composed. It is formed by the flow of the life-force^[5] and vanishes with its ebb. When this force arises in "space"^[6]—the apparent void which must be filled with substance of some kind, of inconceivable tenuity—atoms appear; if this be artificially stopped for a single atom, the atom disappears; there is nothing left. Presumably, were that flow checked but for an instant, the whole physical world would vanish, as a cloud melts away in the empyrean. It is only the persistence of that flow^[7] which maintains the physical basis of the universe.^[8]

In order to examine the construction of the atom, a space is artificially made^[9]; then, if an opening be made in the wall thus constructed, the surrounding force flows in, and three whorls immediately appear, surrounding the "hole" with their triple spiral of two and a half coils, and returning to their origin by a spiral within the atom; these are at once followed by seven finer whorls, which following the spiral of the first three on the outer surface, and returning to their origin by a spiral within that, flowing in the opposite direction—form a caduceus with the first three. Each of the three coarser whorls, flattened out, makes a closed circle; each of the seven finer ones, similarly flattened out, makes a closed circle. The forces which flow in them, again, come from "outside," from a fourth-dimensional space.^[10] Each of the finer whorls is formed of seven yet finer ones, set successively at right angles to each other, each finer than its predecessor; these we call spirillæ.^[11]

It will be understood from the foregoing, that the atom cannot be said to have a wall of its own, unless these whorls of force can be so designated; its "wall" is the pressed back "space." As said in 1895, of the chemical atom, the force "clears itself a space, pressing back the undifferentiated matter of the plane, and making to itself a whirling wall of this matter." The wall belongs to space, not to the atom.

In the three whorls flow currents of different electricities; the seven vibrate in response to etheric waves of all kinds—to sound, light, heat, etc.; they show the seven colours of the spectrum; give out the seven sounds of the natural scale; respond in a variety of ways to physical vibration—flashing, singing, pulsing bodies, they move incessantly, inconceivably beautiful and brilliant.^[12]

The atom has—as observed so far—three proper motions, i.e., motions of its own, independent of any imposed upon it from outside. It turns incessantly upon its own axis, spinning like a top; it describes a small circle with its axis, as though the axis of the spinning top moved in a small circle; it has a regular pulsation, a contraction and expansion, like the pulsation of the heart. When a force is brought to bear upon it, it dances up and down, flings itself wildly from side to side, performs the most astonishing and rapid gyrations, but the three fundamental motions incessantly persist. If it be made to vibrate, as a whole, at the rate which gives any one of the seven colors, the whorl belonging to that color glows out brilliantly.

An electric current brought to bear upon the atoms checks their proper motions, i.e., renders them slower; the atoms exposed to it arrange themselves in parallel lines, and in each line the heart-shaped depression receives the flow, which passes out through the apex into the depression of the next, and so on. The atoms always set themselves to the current. The well-known division of diamagnetic and paramagnetic depends generally on this fact, or on an analogous action on molecules, as may be seen in the accompanying diagrams.^[13]

Two atoms, positive and negative, brought near to each other, attract each other, and then commence to revolve round each other, forming a relatively stable duality; such a molecule is neutral. Combinations of three or more atoms are positive, negative or neutral, according to the internal molecular arrangement; the neutral are relatively stable, the positive and negative are continually in search of their respective opposites, with a view to establishing a relatively permanent union.

Three states of matter exist between the atomic state and the gaseous—the state in which the chemical atoms are found, the recognized chemical elements; for our purposes we may ignore the liquid and solid states. For the sake of clearness and brevity in description, we have been obliged to name these states; we call the atomic state of the chemist elemental; the state which results from breaking up chemical elements, proto-elemental; the next higher, meta-proto-elemental; the next higher, hyper-meta-proto-elemental; then comes the atomic state. These are briefly marked as El., Proto., Meta., and Hyper.^[14]

The simplest unions of atoms, never, apparently consisting of more than seven, form the first molecular state of physical matter.

Here are some characteristic combinations of the Hyper state; the atom is conventional, with the depression emphasised; the lines, always entering at the depression and coming out at the apex, show the resultants of lines of force; where no line appears entering the depression, the force wells up from fourth-dimensional space; where no line appears leaving the apex, the force disappears into fourth-dimensional space; where the point of entry and departure is outside the atoms, it is indicated by a dot.^[15]

The molecules show all kinds of possible combinations; the combinations spin, turn head over heels, and gyrate in endless ways. Each aggregation is surrounded with an apparent cell-wall, the circle or oval, due to the pressure on the surrounding matter caused by its whirling motion; they strike on each other^[16] and rebound, dart hither and thither, for reasons we have not distinguished.

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 constituents 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.

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, assuming a great variety of forms often more or less geometrical; the lines between the constituents 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 constituents, 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 costituents 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 analysing 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 classes; when these, in turn, were compared with Sir William Crookes' classification, 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.

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 class; 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 shell of a nautilus. The radiating lines show the classes, 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.

The external forms may be classified as follows; the internal details will be dealt with later :—

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 classed 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, titanium 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, arsenic 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 titanium (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 titanium 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.

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 classed. The "lithium spike" re-appears in potassium 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 classes, 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 pass 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. Jinarâjadâsa, 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 space. 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 Encyclopædia 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 classes 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 classes according to this property as it is to separate them into two distinct classes 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 constitution 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).

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.

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.

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.

(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.)

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.

(This atomic weight is given by Stas, in Nature, August 29, 1907, but it has been argued later that the weight should not be above 107.883.)