BROMINE (Plate V, 3).

Three additional bodies appear at the top of the funnel, which otherwise repeats that of chlorine. The connecting rod is the same and may be disregarded. The central globes become more complex. The additions are, however, of very easy types, and hence are readily dealt with. Each of the three similar ovoid bodies contains two triplets—each a triangle and a quintet—a four-sided pyramid. These are the same, as may be seen in the connecting rod of chlorine, and we need not repeat them. Only the globe remains. This does not break up as a proto-compound but is merely set free, a and the 2 bs whirling in a plane vertical to the paper and the two smaller bodies, cc, whirling on a plane at right angles to the other. These two disengage themselves, forming a quartet as a meta-compound, while a makes a whirling cross and bb a single sextet; these further dissociate themselves into four pairs and two triplets.

IODINE (Plate V, 4).



Iodine has nothing new to give us, except five similar ovoid bodies at the top of each funnel, and two quartets instead of two pairs in the central globe. The ovoid bodies become spheres when the funnels are thrown off, and a crystalline form is indicated within the sphere. The atoms are arranged in two tetrahedra with a common apex, and the relationship is maintained in the meta-body, a septet. The latter breaks up into two triplets and a unit on the hyper-level. In the central globes, the a of bromine is repeated twice instead of the pairs in cc.

COPPER (Plate VI, 3).

We have already disposed of occultum, on this plate, and of sodium, which lies at the root of both groups. Copper, we now find, is also very largely off our hands, as the funnel provides us with only two new types—two spheres—each containing five atoms in a new arrangement, and the triangular body at the mouth with its ten atoms. This triangular body, with an increased number of atoms, reappears in various other chemical elements. The central globes are different from any we have had before, in their internal arrangement, but the constituents are familiar; there are two contained spheres with four atoms each, the a in the globe of bromine (see above) and 2 "cigars." The "cigars" may be followed under occultum (see above). The connecting rod is as in chlorine, bromine and iodine.

The atoms in the bodies a and b are curiously arranged. A consists of two square-based pyramids turned so as to meet at their apices, and breaks up into two quartet rings and a duad. B is again two four-sided pyramids, but the bases are in contact and set at right angles to each other; the second apex is not seen, as it is directly below the first. The pyramids separate as meta-bodies, and the atoms assume the peculiar arrangement indicated and then break up into four pairs and two units on the hyper level.

* * * * *

IV.

SILVER (Plate VI, 4 and Ag below).

Silver presents us with only two new bodies, and even these are only new by slight additions to old models. The triangular shaped body at the apex of the funnel, containing 21 atoms, is intermediate between the similar bodies in copper and iron. As a proto-element it becomes three triangles, joined at their apices, in fact a tetrahedron in which no atoms are distributed on the fourth face. The faces separate on the meta level and give three seven-atomed figures, and each of these breaks up into two triplets and a unit. The central globe only differs from that of bromine by the addition of one atom, which gives the familiar four-sided pyramid with a square base as in chlorine (see p. 46).

GOLD (Plate VII and Au below).



The disintegration of gold first yields forty-seven bodies on the proto-level; the twenty-four funnels separate, and the central globes which hold each twelve together set free their six contained globes (c, d), thirty bodies being thus liberated. The sixteen bodies on the central inclined planes, marked b, break away, their central globe, with its four contained globes, remaining unchanged. But this condition does not last. The motion of the funnels changes and thus the funnels cease to exist and their contents are set free, each funnel thus liberating nine independent bodies; the sixteen b separate into two each; the four a liberate five each; the two c set free thirteen each; the four d finally liberate two each: 302 proto elements in all.

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 caesium (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.

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.



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 POTASSIUM (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.

POTASSIUM: 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 sextet—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).



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.)

IRON (Plate IV, I, and XVII, 3).



We have already dealt with the affinities of this peculiar group, and we shall see, in the disintegration, even more clearly, the close relationships which exist according to the classification which we here follow.

The fourteen bars of iron break asunder on the proto level, and each sets free its contents—a cone and three ovoids, which as usual, become spheres. The twenty-eight-atomed cone becomes a four-sided figure, and the ovoids show crystalline contents. They break up, on the meta level as shown in the diagram, and are all reduced to triplets and duads on the hyper level.

COBALT (Plate XVII, 4).

The ovoids in cobalt are identical with those of iron; the higher ovoids, which replace the cone of iron, show persistently the crystalline forms so noticeable throughout this group.

NICKEL (Plate XVII, 5).

The two additional atoms in a bar, which alone separate nickel from cobalt, are seen in the upper sphere of the central ovoid.

RUTHENIUM (Plate XVIII, 1).

The lower ovoids in ruthenium are identical in composition, with those of iron, cobalt and nickel and may be studied under Iron. The upper ones only differ by the addition of a triplet.

RHODIUM (Plate XVIII, 2).

Rhodium has a septet, which is to be seen in the c of titanium (see k in the titanium diagram) and differs only in this from its group.

PALLADIUM (Plate XVIII, 3).

In palladium this septet appears as the upper sphere in every ovoid of the upper ring.

OSMIUM (Plate XVIII, 4).

We have here no new constituents; the ovoids are set free on the proto level and the contained globes on the meta, all being of familiar forms. The cigars, as usual, break free on the proto level, and leave their ovoid with only four contained spheres, which unite into two nine-atomed bodies as in silicon (see above).

IRIDIUM (Plate XVIII, 5.)

The twenty-one-atomed cone of silver here reappears, and its proceedings may be followed under that metal (see diagram, p. 729, May). The remaining bodies call for no remark.

PLATINUM (Plate XVIII, 6).

Again the silver cone is with us. The remaining bodies are set free on the proto level, and their contained spheres on the meta.

LITHIUM (Plate IV, 2, and XIX, 1).



Here we have some new combinations, which recur persistently in its allies. The bodies a, in Plate XIX, 1, are at the top and bottom of the ellipse; they come to right and left of it in the proto state, and each makes a twelve-atomed body on the meta level.

The five bodies within the ellipse, three monads and two sextets, show two which we have had before: d, which behaves like the quintet and quartet in silicon, after their junction, and b, which we have had in iron. The two bodies c are a variant of the square-based pyramid, one atom at the apex, and two at each of the other angles. The globe, e, is a new form, the four tetrahedra of the proto level making a single twelve-atomed one on the meta. The body a splits up into triplets on the hyper; b and d follow their iron and silicon models; c yields four duads and a unit; e breaks into four quartets.

POTASSIUM (Plate XIX, 2).

Potassium repeats the lithium spike; the central globe shows the "nitrogen balloon," which we already know, and which is surrounded on the proto level with six tetrahedra, which are set free on the meta and behave as in cobalt. Hence we have nothing new.

RUBIDIUM (Plate XIX, 3).

Again the lithium spike, modified slightly by the introduction of an ovoid, in place of the top sphere; the forms here are somewhat unusual, and the triangles of the sextet revolve round each other on the meta level; all the triads break up on the hyper level into duads and units.

FLUORINE (Plate IV, 3, and Plate XVII, 1).

The reversed funnels of fluorine split asunder on the proto level, and are set free, the "balloons" also floating off independently. The funnels, as usual, become spheres, and on the meta level set free their contained bodies, three quartets and a triplet from each of the eight. The balloons disintegrate in the usual way.

MANGANESE (Plate XVII, 2).

Manganese offers us nothing new, being composed of "lithium spikes" and "nitrogen balloons."

* * * * *

X.

VI.—THE STAR GROUPS.

We have now reached the last of the groups as arranged on Sir William Crookes' lemniscates, that forming the "neutral" column; it is headed by helium, which is sui generis. The remainder are in the form of a flat star (see Plate IV, 4), with a centre formed of five intersecting and "cigar"-bearing tetrahedra, and six radiating arms. Ten of these have been observed, five pairs in which the second member differs but slightly from the first; they are: Neon, Meta-neon; Argon, Metargon; Krypton, Meta-krypton; Xenon, Meta-xenon; Kalon, Meta-kalon; the last pair and the meta forms are not yet discovered by chemists. These all show the presence of a periodic law; taking an arm of the star in each of the five pairs, we find the number of atoms to be as follows :—

40 99 224 363 489 47 106 231 370 496 It will be observed that the meta form in each case shows seven more atoms than its fellow.



HELIUM (Plate III, 5, and Plate XX, 1) shows two "cigar"-bearing tetrahedra, and two hydrogen triangles, the tetrahedra revolving round an egg-shaped central body, and the triangles spinning on their own axes while performing a similar revolution. The whole has an attractively airy appearance, as of a fairy element.

HELIUM: Two tetrahedra of 24 atoms 48 Two triangles of 9 atoms 18 Central egg 6 —— Total 72 —— Atomic weight 3.94 Number weight 72/18 4.00 NEON (Plate XX, 2 and 6) has six arms of the pattern shown in 2, radiating from the central globe.

NEON: Six arms of 40 atoms 240 Central tetrahedra 120

—— Total 360 —— Atomic weight 19.90 Number weight 360/18 20.00 META-NEON (Plate XX, 3 and 6) differs from its comrade by the insertion of an additional atom in each of the groups included in the second body within its arm, and substituting a seven-atomed group for one of the triplets in neon.

META-NEON: Six arms of 47 atoms 282 Central tetrahedra 120 —— Total 402 —— Atomic weight —— Number weight 402/18 22.33 ARGON (Plate XX, 4, 6 and 7) shows within its arms the b 63 which we met in nitrogen, yttrium, vanadium and niobium, but not the "balloon," which we shall find with it in krypton and its congeners.

ARGON: Six arms of 99 atoms 594 Central tetrahedra 120 —— Total 714 —— Atomic weight 39.60 Number weight 714/18 39.66 METARGON (Plate XX, 5, 6 and 7) again shows only an additional seven atoms in each arm.

METARGON: Six arms of 106 atoms 636 Central tetrahedra 120 —— Total 756 —— Atomic weight —— Number weight 756/18 42

KRYPTON (Plate XXI, 1 and 4, and Plate XX, 6 and 7) contains the nitrogen "balloon," elongated by its juxtaposition to b 63. The central tetrahedra appear as usual.

KRYPTON: Six arms of 224 atoms 1344 Central tetrahedra 120 ——- Total 1464 ——- Atomic weight 81.20 Number weight 1464/18 81.33 META-KRYPTON differs only from krypton by the substitution of z for y in each arm of the star.

META-KRYPTON: Six arms of 231 atoms 1386 Central tetrahedra 120 ——- Total 1506 ——- Atomic weight ——- Number weight 1506/18 83.66 XENON (Plate XXI, 2 and 4, and Plate XX, 6 and 7) has a peculiarity shared only by kalon, that x and y are asymmetrical, the centre of one having three atoms and the centre of the other two. Is this done in order to preserve the difference of seven from its comrade?

XENON: Six arms of 363 atoms 2178 Central tetrahedra 120 ——- Total 2298 ——- Atomic weight 127.10 Number weight 2298/18 127.66 META-XENON differs from xenon only by the substitution of two z's for x and y.

META-XENON: Six arms of 370 atoms 2220 Central tetrahedra 120 ——- Total 2340 ——- Atomic weight ——- Number weight 2340/18 130 KALON (Plate XXI, 3 and 4, and Plate XX, 6 and 7) has a curious cone, possessing a kind of tail which we have not observed elsewhere; x and y show the same asymmetry as in xenon.

KALON: Six arms of 489 atoms 2934 Central tetrahedra 120 —— Total 3054 —— Atomic weight —— Number weight 3054/18 169.66 META-KALON again substitutes two z's for x and y.

META-KALON: Six arms of 496 atoms 2976 Central tetrahedra 120 —— Total 3096 —— Atomic weight —— Number weight 3096/18 172 Only a few atoms of kalon and meta-kalon have been found in the air of a fair-sized room.

It does not seem worth while to break up these elements, for their component parts are so familiar. The complicated groups—a 110, b 63 and c 120—have all been fully dealt with in preceding pages.

* * * * *

There remains now only radium, of the elements which we have, so far, examined, and that will be now described and will bring to an end this series of observations. A piece of close and detailed work of this kind, although necessarily imperfect, will have its value in the future, when science along its own lines shall have confirmed these researches.

It will have been observed that our weights, obtained by counting, are almost invariably slightly in excess of the orthodox ones: it is interesting that in the latest report of the International Commission (November 13, 1907), printed in the Proceedings of the Chemical Society of London, Vol. XXIV, No. 33, and issued on January 25, 1908, the weight of hydrogen is now taken at 1.008 instead of at 1. This would slightly raise all the orthodox weights; thus aluminium rises from 26.91 to 27.1, antimony from 119.34 to 120.2, and so on.

* * * * *

XI.

RADIUM.



Radium has the form of a tetrahedron, and it is in the tetrahedral groups (see article IV) that we shall find its nearest congeners; calcium, strontium, chromium, molybdenum resemble it most closely in general internal arrangements, with additions from zinc and cadmium. Radium has a complex central sphere (Plate XXII), extraordinarily vivid and living; the whirling motion is so rapid that continued accurate observation is very difficult; the sphere is more closely compacted than the centre-piece in other elements, and is much larger in proportion to the funnels and spikes than is the case with the elements above named; reference to Plate VIII will show that in these the funnels are much larger than the centres, whereas in radium the diameter of the sphere and the length of the funnel or spike are about equal. Its heart consists of a globe containing seven atoms, which assume on the proto level the prismatic form shown in cadmium, magnesium and selenium. This globe is the centre of two crosses, the arms of which show respectively three-atomed and two-atomed groups. Round this sphere are arranged, as on radii, twenty-four segments, each containing five bodies—four quintets and a septet—and six loose atoms, which float horizontally across the mouth of the segment; the whole sphere has thus a kind of surface of atoms. On the proto level these six atoms in each segment gather together and form a "cigar." In the rush of the streams presently to be described one of these atoms is occasionally torn away, but is generally, if not always, replaced by the capture of another which is flung into the vacated space.

Each of the four funnels opens, as usual, on one face of the tetrahedron, and they resemble the funnels of strontium and molybdenum but contain three pillars instead of four (Plate XXIII). They stand within the funnel as though at the angles of a triangle, not side by side. The contained bodies, though numerous, contain forms which are all familiar.

The spikes alternate with the funnels, and point to the angles of the tetrahedron as in zinc and cadmium; each spike contains three "lithium spikes" (see Plate XIX) with a ten-atomed cone or cap at the top, floating above the three (Plate XXIV). The "petals" or "cigars" of lithium exist in the central globe in the floating atoms, and the four-atomed groups which form the lithium "plate" may be seen in the funnels, so that the whole of lithium appears in radium.

So much for its composition. But a very peculiar result, so far unobserved elsewhere, arises from the extraordinarily rapid whirling of the central sphere. A kind of vortex is formed, and there is a constant and powerful indraught through the funnels. By this, particles are drawn in from without, and these are swept round with the sphere, their temperature becoming much raised, and they are then violently shot out through the spikes. It is these jets which occasionally sweep away an atom from the surface of the sphere. These "particles" may be atoms, or they may be bodies from any of the etheric levels; in some cases these bodies break up and form new combinations. In fact lithium seems like a kind of vortex of creative activity, drawing in, breaking up, recombining, shooting forth—a most extraordinary element.

RADIUM: 4 funnels of 618 atoms 2472 4 spikes of 199 atoms 796 Central sphere 819 —— Total 4087 —— Atomic weight —— Number weight 4087/18 227.05



* * * * *

APPENDIX.

THE AETHER OF SPACE.

Much discussion has taken place, especially between physicists and chemists, over the nature of the substances with which all space must, according to scientific hypothesis, be filled. One side contends that it is infinitely thinner than the thinnest gas, absolutely frictionless and without weight; the other asserts that it is denser than the densest solid. In this substance the ultimate atoms of matter are thought to float, like motes in a sunbeam, and light, heat and electricity are supposed to be its vibrations.

Theosophical investigators, using methods not at the disposal of physical science, have found that this hypothesis includes under one head two entirely different and widely separated sets of phenomena. They have been able to deal with states of matter higher than the gaseous and have observed that it is by means of vibrations of this finer matter that light, heat and electricity manifest themselves to us. Seeing that matter in these higher states thus performs the functions attributed to the ether of science, they have (perhaps unadvisedly) called these states etheric, and have thus left themselves without a convenient name for that substance which fulfils the other part of the scientific requirements.

Let us for the moment name this substance koilon, since it fills what we are in the habit of calling empty space. What mulaprakrti, or "mother-matter," is to the inconceivable totality of universes, koilon is to our particular universe—not to our solar system merely but to the vast unit which includes all visible suns. Between koilon and mulaprakrti there must be various stages, but we have at present no direct means of estimating their number or of knowing anything whatever about them.

In an ancient occult treatise, however, we read of a "colorless spiritual fluid" "which exists everywhere and forms the first foundation on which our solar system is built. Outside the latter, it is found in its pristine purity only between the stars [suns] of the universe.... As its substance is of a different kind from that known on earth, the inhabitants of the latter, seeing through it, believe, in their illusion and ignorance, that it is empty space. There is not one finger's breadth of void space in the whole boundless universe."[21] "The mother-substance" is said, in this treatise, to produce this aether of space as its seventh grade of density, and all objective suns are said to have this for their "substance."

To any power of sight which we can bring to bear upon it, this koilon appears to be homogeneous, though it is probably nothing of the kind, since homogeneity can belong to the mother-substance alone. It is out of all proportion denser than any other substance known to us, infinitely denser—if we may be pardoned the expression; so much denser that it seems to belong to another type, or order, of density. But now comes the startling part of the investigation: we might expect matter to be a densification of this koilon; it is nothing of the kind. Matter is not koilon, but the absence of koilon, and at first sight, matter and space appear to have changed places, and emptiness has become solidity, solidity has become emptiness.

To help us to understand this clearly let us examine the ultimate atom of the physical plane (see pp. 21-23). It is composed of ten rings or wires, which lie side by side, but never touch one another. If one of these wires be taken away from the atom, and be, as it were, untwisted from its peculiar spiral shape and laid out on a flat surface, it will be seen that it is a complete circle—a tightly twisted endless coil. This coil is itself a spiral containing 1680 turns; it can be unwound, and it will then make a much larger circle. This process of unwinding may be again performed, and a still bigger circle obtained, and this can be repeated till the seven sets of spirillae are all unwound, and we have a huge circle of the tiniest imaginable dots, like pearls threaded on an invisible string. These dots are so inconceivably small that many millions of them are needed to make one ultimate physical atom, and while the exact number is not readily ascertainable, several different lines of calculation agree in indicating it as closely approximate to the almost inconceivable total of fourteen thousand millions. Where figures are so huge, direct counting is obviously impossible, but fortunately the different parts of the atom are sufficiently alike to enable us to make an estimate in which the margin of error is not likely to be very great. The atom consists of ten wires, which divide themselves naturally into two groups—the three which are thicker and more prominent, and the seven thinner ones which correspond to the colors and planets. These latter appear to be identical in constitution though the forces flowing through them must differ, since each responds most readily to its own special set of vibrations. By actual counting it has been discovered that the numbers of coils or spirillae of the first order in each wire is 1680; and the proportion of the different orders of spirillae to one another is equal in all cases that have been examined, and correspond with the number of dots in the ultimate spirillae of the lowest order. The ordinary sevenfold rule works quite accurately with the thinner coils, but there is a very curious variation with regard to the set of three. As may be seen from the drawings, these are obviously thicker and more prominent, and this increase of size is produced by an augmentation (so slight as to be barely perceptible) in the proportion to one another of the different orders of spirillae and in the number of dots in the lowest. This augmentation, amounting at present to not more than .00571428 of the whole of each case, suggests the unexpected possibility that this portion of the atom may be somehow actually undergoing a change—may in fact be in process of growth, as there is reason to suppose that these three thicker spirals originally resembled the others.

Since observation shows us that each physical atom is represented by forty-nine astral atoms, each astral atom by forty-nine mental atoms, and each mental atom by forty-nine of those on the buddhic plane, we have here evidently several terms of a regular progressive series, and the natural presumption is that the series continues where we are no longer able to observe it. Further probability is lent to this assumption by the remarkable fact that—if we assume one dot to be what corresponds to an atom on the seventh or highest of our planes (as is suggested in The Ancient Wisdom, p. 42) and then suppose the law of multiplication to begin its operation, so that 49 dots shall form the atom of the next or sixth plane, 2401 that of the fifth, and so on—we find that the number indicated for the physical atom (496) corresponds almost exactly with the calculation based upon the actual counting of the coils. Indeed, it seems probable that but for the slight growth of the three thicker wires of the atom the correspondence would have been perfect.

It must be noted that a physical atom cannot be directly broken up into astral atoms. If the unit of force which whirls those millions of dots into the complicated shape of a physical atom be pressed back by an effort of will over the threshold of the astral plane, the atom disappears instantly, for the dots are released. But the same unit of force, working now upon a higher level, expresses itself not through one astral atom, but through a group of 49. If the process of pressing back the unit of force is repeated, so that it energises upon the mental plane, we find the group there enlarged to the number of 2401 of those higher atoms. Upon the buddhic plane the number of atoms formed by the same amount of force is very much greater still—probably the cube of 49 instead of the square, though they have not been actually counted. Therefore one physical atom is not composed of forty-nine astral or 2401 mental atoms, but corresponds to them, in the sense that the force which manifests through it would show itself on those higher planes by energising respectively those numbers of atoms.

The dots, or beads, seem to be the constituents of all matter of which we, at present, know anything; astral, mental and buddhic atoms are built of them, so we may fairly regard them as fundamental units, the basis of matter.

These units are all alike, spherical and absolutely simple in construction. Though they are the basis of all matter, they are not themselves matter; they are not blocks but bubbles. They do not resemble bubbles floating in the air, which consist of a thin film of water separating the air within them from the air outside, so that the film has both an outer and an inner surface. Their analogy is rather with the bubbles that we see rising in water, before they reach the surface, bubbles which may be said to have only one surface—that of the water which is pushed back by the contained air. Just as such bubbles are not water, but are precisely the spots from which water is absent, so these units are not koilon, but the absence of koilon—the only spots where it is not—specks of nothingness floating in it, so to speak, for the interior of these space-bubbles is an absolute void to the highest power of vision that we can turn upon them.

That is the startling, well-nigh incredible, fact. Matter is nothingness, the space obtained by pressing back an infinitely dense substance; Fohat "digs holes in space" of a verity, and the holes are the airy nothingnesses, the bubbles, of which "solid" universes are built.

What are they, then, these bubbles, or rather, what is their content, the force which can blow bubbles in a substance of infinite density? The ancients called that force "the Breath," a graphic symbol, which seems to imply that they who used it had seen the kosmic process, had seen the LOGOS when He breathed into the "waters of space," and made the bubbles which build universes. Scientists may call this "Force" by what names they will—names are nothing; to us, Theosophists, it is the Breath of the LOGOS, we know not whether of the LOGOS of this solar system or of a yet mightier Being; the latter would seem the more likely, since in the above-quoted occult treatise all visible suns are said to have this as their substance.

The Breath of the LOGOS, then, is the force which fills these spaces; His the force which holds them open against the tremendous pressure of the koilon; they are full of His Life, of Himself, and everything we call matter, on however high or low a plane, is instinct with divinity; these units of force, of life, the bricks with which He builds His universe, are His very life scattered through space; truly is it written: "I established this universe with a portion of myself." And when He draws in His breath, the waters of space will close in again, and the universe will have disappeared. It is only a breath.

The outbreathing which makes these bubbles is quite distinct from, and long antecedent to, the three outpourings, or Life-Waves, so familiar to the theosophical student. The first Life-Wave catches up these bubbles, and whirls them into the various arrangements which we call the atoms of the several planes, and aggregates them into the molecules, and on the physical plane into the chemical elements. The worlds are built out of these voids, these emptinesses, which seem to us "nothing" but are divine force. It is matter made from the privation of matter. How true were H.P.B.'s statements in "The Secret Doctrine": "Matter is nothing but an aggregation of atomic forces" (iii, 398); "Buddha taught that the primitive substance is eternal and unchangeable. Its vehicle is the pure luminous aether, the boundless infinite space, not a void, resulting from the absence of all forms, but on the contrary, the foundation of all forms" (iii, 402).

How vividly, how unmistakably this knowledge brings home to us the great doctrine of Maya, the transitoriness and unreality of earthly things, the utterly deceptive nature of appearances! When the candidate for initiation sees (not merely believes, remember, but actually sees) that what has always before seemed to him empty space is in reality a solid mass of inconceivable density, and that the matter which has appeared to be the one tangible and certain basis of things is not only by comparison tenuous as gossamer (the "web" spun by "Father-Mother"), but is actually composed of emptiness and nothingness—is itself the very negation of matter—then for the first time he thoroughly appreciates the valuelessness of the physical senses as guides to the truth. Yet even more clearly still stands out the glorious certainty of the immanence of the Divine; not only is everything ensouled by the LOGOS, but even its visible manifestation is literally part of Him, is built of His very substance, so that Matter as well as Spirit becomes sacred to the student who really understands.