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.
[Illustration: PLATE XII.]
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.
[Illustration: PLATE XIII.]
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.
[Illustration: PLATE XIV.]
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).
[Illustration]
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).
[Illustration]
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).
[Illustration]
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).
[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.
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
[Illustration: PLATE XXIV.]
[Illustration: PLATE XXIII.]
* * * * *
APPENDIX.
THE ÆTHER 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 mûlaprakrti, 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 mûlaprakrti 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 æther 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 spirillæ 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 spirillæ of the first
order in each wire is 1680; and the proportion of the different orders of
spirillæ to one another is equal in all cases that have been examined, and
correspond with the number of dots in the ultimate spirillæ 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 spirillæ 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 æther, 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 Mâyâ, 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.
The koilon in which all these bubbles are formed undoubtedly represents a
part, and perhaps the principal part, of what science describes as the
luminiferous æther. Whether it is actually the bearer of the vibrations of
light and heat through interplanetary space is as yet undetermined. It is
certain that these vibrations impinge upon and are perceptible to our
bodily senses only through the etheric matter of the physical plane. But
this by no means proves that they are conveyed through space in the same
manner, for we know very little of the extent to which the physical etheric
matter exists in interplanetary and interstellar space, though the
examination of meteoric matter and kosmic dust shows that at least some of
it is scattered there.
The scientific theory is that the æther has some quality which enables it
to transmit at a certain definite velocity transverse waves of all lengths
and intensities--that velocity being what is commonly called the speed of
light, 190,000 miles per second. Quite probably this may be true of koilon,
and if so it must also be capable of communicating those waves to bubbles
or aggregations of bubbles, and before the light can reach our eyes there
must be a downward transference from plane to plane similar to that taking
place when a thought awakens emotion or causes action.
In a recent pamphlet on "The Density of Æther," Sir Oliver Lodge remarks:--
"Just as the ratio of mass to volume is small in the case of a solar system
or a nebula or a cobweb, I have been driven to think that the observed
mechanical density of matter is probably an excessively small fraction of
the total density of the substance or æther contained in the space which it
thus partially occupies--the substance of which it may hypothetically be
held to be composed.
"Thus, for instance, consider a mass of platinum, and assume that its atoms
are composed of electrons, or of some structures not wholly dissimilar: the
space which these bodies actually fill, as compared with the whole space
which in a sense they 'occupy,' is comparable to one ten-millionth of the
whole, even inside each atom; and the fraction is still smaller if it
refers to the visible mass. So that a kind of minimum estimate of ætherial
density, on this basis, would be something like ten thousand million times
that of platinum."
And further on he adds that this density may well turn out to be fifty
thousand million times that of platinum. "The densest matter known," he
says, "is trivial and gossamer-like compared with the unmodified æther in
the same space."
Incredible as this seems to our ordinary ideas, it is undoubtedly an
understatement rather than an exaggeration of the true proportion as
observed in the case of koilon. We shall understand how this can be so if
we remember that koilon seems absolutely homogeneous and solid even when
examined by a power of magnification which makes physical atoms appear in
size and arrangement like cottages scattered over a lonely moor, and when
we further add to this the recollection that the bubbles of which these
atoms in turn are composed are themselves what may be not inaptly called
fragments of nothingness.
In the same pamphlet Sir Oliver Lodge makes a very striking estimate of the
intrinsic energy of the æther. He says: "The total output of a
million-kilowatt power station for thirty million years exists permanently,
and at present inaccessibly in every cubic millimetre of space." Here again
he is probably underestimating the stupendous truth.
It may naturally be asked how, if all this be so, it is possible that we
can move about freely in a solid ten thousand million times denser, as Sir
Oliver Lodge says, than platinum. The obvious answer is that, where
densities differ sufficiently, they can move through each other with
perfect freedom; water or air can pass through cloth; air can pass through
water; an astral form passes unconsciously through a physical wall, or
through an ordinary human body; many of us have seen an astral form walk
through a physical, neither being conscious of the passage; it does not
matter whether we say that a ghost has passed through a wall, or a wall has
passed through a ghost. A gnome passes freely through a rock, and walks
about within the earth, as comfortably as we walk about in the air. A
deeper answer is that consciousness can recognize only consciousness, that
since we are of the nature of the LOGOS we can sense only those things
which are also of His nature. These bubbles are His essence, His life, and,
therefore, we, who also are part of Him, can see the matter which is built
of his substance, for all forms are but manifestations of Him. The koilon
is to us non-manifestation, because we have not unfolded powers which
enable us to cognise it, and it may be the manifestation of a loftier order
of LOGOI, utterly beyond our ken.
As none of our investigators can raise his consciousness to the highest
plane of our universe, the âdi-tattva plane, it may be of interest to
explain how it is possible for them to see what may very probably be the
atom of that plane. That this may be understood it is essential to remember
that the power of magnification by means of which these experiments are
conducted is quite apart from the faculty of functioning upon one or other
of the planes. The latter is the result of a slow and gradual unfoldment of
the Self, while the former is merely a special development of one of the
many powers latent in man. All the planes are round us here, just as much
as any other point in space, and if a man sharpens his sight until he can
see their tiniest atoms he can make a study of them, even though he may as
yet be far from the level necessary to enable him to understand and
function upon the higher planes as a whole, or to come into touch with the
glorious Intelligences who gather those atoms into vehicles for Themselves.
A partial analogy may be found in the position of the astronomer with
regard to the stellar universe, or let us say the Milky Way. He can observe
its constituent parts and learn a good deal about them along various lines,
but it is absolutely impossible for him to see it as a whole from outside,
or to form any certain conception of its true shape, and to know what it
really is. Suppose that the universe is, as many of the ancients thought,
some inconceivably vast Being, it is utterly impossible for us, here in the
midst of it, to know what that Being is or is doing, for that would mean
raising ourselves to a height comparable with His; but we may make
extensive and detailed examination of such particles of His body as happen
to be within our reach, for that means only the patient use of powers and
machinery already at our command.
Let it not be supposed that, in thus unfolding a little more of the wonders
of Divine Truth by pushing our investigations to the very farthest point at
present possible to us, we in any way alter or modify all that has been
written in theosophical books of the shape and constitution of the physical
atom, and of the wonderful and orderly arrangements by which it is grouped
into the various chemical molecules; all this remains entirely unaffected.
Nor is any change introduced as regards the three outpourings from the
LOGOS, and the marvellous facility with which the matter of the various
planes is by them moulded into forms for the service of the evolving life.
But if we wish to have a right view of the realities underlying
manifestation in this universe, we must to a considerable extent reverse
the ordinary conception as to what this matter essentially is. Instead of
thinking of its ultimate constituents as solid specks floating in a void,
we must realise that it is the apparent void itself which is solid, and
that the specks are but bubbles on it. That fact once grasped, all the rest
remains as before. The relative position of what we have hitherto called
matter and force is still for us the same as ever; it is only that, on
closer examination, both of these conceptions prove to be variants of
force, the one ensouling combinations of the other, and the real "matter,"
koilon, is seen to be something which has hitherto been altogether outside
our scheme of thought.
In view of this marvellous distribution of Himself in "space," the familiar
concept of the "sacrifice of the LOGOS" takes on a new depth and splendour;
this is His "dying in matter," His "perpetual sacrifice," and it may be the
very glory of the LOGOS that He can sacrifice Himself to the uttermost by
thus permeating and making Himself one with that portion of koilon which He
chooses as the field of His universe.
What koilon is, what its origin, whether it is itself changed by the Divine
Breath which is poured into it--does "Dark Space" thus become "Bright
Space" at the beginning of a manifestation?--these are questions to which
we cannot at present even indicate answers. Perchance an intelligent study
of the great Scriptures of the world may yield replies.
* * * * *
NOTES
[1] See footnote in next Chapter.
[2] The drawings of the elements were done by two Theosophical artists,
Herr Hecker and Mrs. Kirby, whom we sincerely thank; the diagrams, showing
the details of the construction of each "element," we owe to the most
painstaking labour of Mr. Jinarâjadâsa, without whose aid it would have
been impossible for us to have presented clearly and definitely the
complicated arrangements by which the chemical elements are built up. We
have also to thank him for a number of most useful notes, implying much
careful research, which are incorporated in the present series, and without
which we could not have written these papers.
[3] The atomic sub-plane.
[4] The astral plane.
[5] Known to Theosophists as Fohat, the force of which all the physical
plane forces--electricities--are differentiations.
[6] When Fohat "digs holes in space."
[7] The first life-wave, the work of the third Logos.
[8] A mâyâ, truly.
[9] By a certain action of the will, known to students, it is possible to
make such a space by pressing back and walling off the matter of space.
[10] Again the astral world.
[11] Each spirilla is animated by the life-force of a plane, and four are
at present normally active, one for each round. Their activity in an
individual may be prematurely forced by yoga practice.
[12] "The ten numbers of the sun. These are called Dis--in reality
space--the forces spread in space, three of which are contained in the
Sun's Atman, or seventh principle, and seven are the rays shot out by the
Sun." The atom is a sun in miniature in its own universe of the
inconceivably minute. Each of the seven whorls is connected with one of the
Planetary Logoi, so that each Planetary Logos has a direct influence
playing on the very matter of which all things are constructed. It may be
supposed that the three, conveying electricity, a differentiation of Fohat,
are related to the Solar Logoi.
[13] The action of electricity opens up ground of large extent, and cannot
be dealt with here. Does it act on the atoms themselves, or on molecules,
or sometimes on one and sometimes on the other? In soft iron, for instance,
are the internal arrangements of the chemical atom forcibly distorted, and
do they elastically return to their original relations when released? and
in steel is the distortion permanent? In all the diagrams the heart-shaped
body, exaggerated to show the depression caused by the inflow and the point
caused by the outflow, is a single atom.
[14] These sub-planes are familiar to the Theosophist as gaseous, etheric,
super-etheric, sub-atomic, atomic; or as Gas, Ether 4, Ether 3, Ether 2,
Ether 1.
[15] It must be remembered that the diagrams represent three-dimensional
objects, and the atoms are not all on a plane, necessarily.
[16] That is, the surrounding magnetic fields strike on each other.
[17] The fifth member of this group was not sought for.
[18] This, with references which appear later (pp. 32, 33, 50, etc.),
relates to articles which appeared in the _Theosophist_, 1908.
[19] Since writing the above I have noticed, in the _London, Edinburgh and
Dublin Philosophical Magazine and Journal of Science_, conducted by Dr.
John Joly and Mr. William Francis, in an article entitled "Evolution and
Devolution of the Elements," the statement that it is probable that in "the
nebulous state of matter there are four substances, the first two being
unknown upon earth, the third being hydrogen and the fourth ... helium. It
also seems probable that ... hydrogen, the two unknown elements, and helium
are the four original elements from which all the other elements form. To
distinguish them from the others we will term them protons." This is
suggestive as regards hydrogen, but does not help us with regard to oxygen
and nitrogen.
[20] Theosophists call them Nature-Spirits, and often use the mediæval term
Elementals. Beings concerned with the elements truly are they, even with
chemical elements.
[21] Quoted in "The Secret Doctrine." H.P. Blavatsky, i, 309.