OCCULT CHEMISTRY 4

	OCCULT CHEMISTRY 4

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). [Illustration] 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. [Illustration: PLATE XV.] 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 [Illustration: PLATE XVI.] 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. [Illustration: PLATE XVII.] Here, for the first time, we find ourselves a little at issue with the accepted system of chemistry. Fluorine stands at the head of a group--called the inter-periodic--whereof the remaining members are (see Crookes' table, p. 28), manganese, iron, cobalt, nickel; ruthenium, rhodium, palladium; osmium, iridium, platinum. If we take all these as group V, we find that fluorine and manganese are violently forced into company with which they have hardly any points of relationship, and that they intrude into an otherwise very harmonious group of closely similar composition. Moreover, manganese reproduces the characteristic lithium "spike" and not the bars of those into whose company it is thrust, and it is thus allied with lithium, with which indeed it is almost identical. But lithium is placed by Crookes at the head of a group, the other members of which are potassium, rubidium and cæsium (the last not examined). Following these identities of composition, I think it is better to remove manganese and fluorine from their incongruous companions and place them with lithium and its allies as V _a_, the Spike Groups, marking, by the identity of number, similarities of arrangement which exist, and by the separation the differences of composition. It is worth while noting what Sir William Crookes, in his "Genesis of the Elements," remarks on the relations of the interperiodic group with its neighbours. He says: "These bodies are interperiodic because their atomic weights exclude them from the small periods into which the other elements fall, and because their chemical relations with some members of the neighbouring groups show that they are probably interperiodic in the sense of being in transition stages." Group V in every case shows fourteen bars radiating from a centre as shown in iron, Plate IV, 1. While the form remains unchanged throughout, the increase of weight is gained by adding to the number of atoms contained in a bar. The group is made up, not of single chemical elements, as in all other cases, but of sub-groups, each containing three elements, and the relations within each sub-group are very close; moreover the weights only differ by two atoms per bar, making a weight difference of twenty-eight in the whole. Thus we have per bar:-- 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.) [Illustration: PLATE XVIII.] The next sub-group, ruthenium, rhodium, and palladium, has nothing to detain us. It will be observed that each bar contains eight segments, instead of the six of cobalt and nickel; that ruthenium and palladium have the same number of atoms in their upper ovoids, although in ruthenium a triplet and quartet represent the septet of palladium; and that in ruthenium and rhodium the lower ovoids are identical, though one has the order: sixteen, fourteen, sixteen, fourteen; and the other: fourteen, sixteen, fourteen, sixteen. One constantly asks oneself: What is the significance of these minute changes? Further investigators will probably discover the answer.       14 bars of 132 atoms              1848       Atomic weight                   100.91       Number weight 1848/18           102.66 RUTHENIUM (Plate XVIII, 1):       14 bars of 134 atoms              1876       Atomic weight                   102.23       Number weight 1876/18           104.22 RHODIUM (Plate XVII, 2):       14 bars of 136 atoms              1904       Atomic weight                   105.74       Number weight 1904/18           105.77 PALLADIUM (XVIII, 3): The third sub-group, osmium, iridium and platinum, is, of course, more complicated in its composition, but its builders succeed in preserving the bar form, gaining the necessary increase by a multiplication of contained spheres within the ovoids. Osmium has one peculiarity: the ovoid marked _a_ (XVIII, 4) takes the place of axis in the upper half of the bar, and the three ovoids, marked _b_, revolve round it. In the lower half, the four ovoids, _c_, revolve round the central axis. In platinum, we have marked two forms as platinum A and platinum B, the latter having two four-atomed spheres (XVIII, 6 _b_) in the place of the two triplets marked a. It may well be that what we have called platinum B is not a variety of platinum, but a new element, the addition of two atoms in a bar being exactly that which separates the other elements within each of the sub-groups. It will be noticed that the four lower sections of the bars are identical in all the members of this sub-group, each ovoid containing thirty atoms. The upper ring of ovoids in iridium and platinum A are also identical, but for the 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. [Illustration: PLATE XIX.] LITHIUM (Plate IV, 2 and Plate XIX, 1) is a striking and beautiful form, with its upright cone, or spike, its eight radiating petals (_x_) at the base of the cone, and the plate-like support in the centre of which is a globe, on which the spike rests. The spike revolves swiftly on its axis, carrying the petals with it; the plate revolves equally swiftly in the opposite direction. Within the spike are two globes and a long ovoid; the spheres within the globe revolve as a cross; within the ovoid are four spheres containing atoms arranged on tetrahedra, and a central sphere with an axis of three atoms surrounded by a spinning wheel of six. LITHIUM: Spike of 63 atoms                 63          8 petals of 6 atoms               48          Central globe of 16 atoms         16                                          ----                                Total      127                                          ----          Atomic weight                   6.98          Number weight 127/18            7.05 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). [Illustration] 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). [Illustration] 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). [Illustration] 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). [Illustration] 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). [Illustration] 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. [Illustration: PLATE XX.] 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 [Illustration: PLATE XXI.] 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. [Illustration: PLATE XXII.] 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.