THE LATER RESEARCHES.
The first difficulty that faced us was the identification of the forms seen
on focusing the sight on gases.[2] We could only proceed tentatively. Thus,
a very common form in the air had a sort of dumb-bell shape (see Plate I);
we examined this, comparing our rough sketches, and counted its atoms;
these, divided by 18--the number of ultimate atoms in hydrogen--gave us
23.22 as atomic weight, and this offered the presumption that it was
sodium. We then took various substances--common salt, etc.--in which we
knew sodium was present, and found the dumb-bell form in all. In other
cases, we took small fragments of metals, as iron, tin, zinc, silver, gold;
in others, again, pieces of ore, mineral waters, etc., etc., and, for the
rarest substances, Mr. Leadbeater visited a mineralogical museum. In all,
57 chemical elements were examined, out of the 78 recognized by modern
chemistry.
In addition to these, we found 3 chemical waifs: an unrecognized stranger
between hydrogen and helium which we named occultum, for purposes of
reference, and 2 varieties of one element, which we named kalon and
meta-kalon, between xenon and osmium; we also found 4 varieties of 4
recognized elements and prefixed meta to the name of each, and a second
form of platinum, that we named Pt. B. Thus we have tabulated in all 65
chemical elements, or chemical atoms, completing three of Sir William
Crookes' lemniscates, sufficient for some amount of generalization.
[Illustration: PLATE I. SODIUM.]
In counting the number of ultimate atoms in a chemical elemental atom, we
did not count them throughout, one by one; when, for instance, we counted
up the ultimate atoms in sodium, we dictated the number in each convenient
group to Mr. Jinarâjadâsa, and he multiplied out the total, divided by 18,
and announced the result. Thus: sodium (_see_ Plate I) is composed of an
upper part, divisible into a globe and 12 funnels; a lower part, similarly
divided; and a connecting rod. We counted the number in the upper part:
globe--10; the number in two or three of the funnels--each 16; the number
of funnels--12; the same for the lower part; in the connecting rod--14. Mr.
Jinarâjadâsa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418:
divided by 18 = 23.22 recurring. By this method we guarded our counting
from any prepossession, as it was impossible for us to know how the various
numbers would result on addition, multiplication and division, and the
exciting moment came when we waited to see if our results endorsed or
approached any accepted weight. In the heavier elements, such as gold, with
3546 atoms, it would have been impossible to count each atom without quite
unnecessary waste of time, when making a preliminary investigation. Later,
it may be worth while to count each division separately, as in some we
noticed that two groups, at first sight alike, differed by 1 or 2 atoms,
and some very slight errors may, in this way, have crept into our
calculations.
In the following table is a list of the chemical elements examined; the
first column gives the names, the asterisk affixed to some indicating that
they have not yet been discovered by orthodox chemistry. The second column
gives the number of ultimate physical atoms contained in one chemical atom
of the element concerned. The third column gives the weight as compared
with hydrogen, taken as 18, and this is obtained by dividing the calculated
number of ultimate atoms by 18. The fourth column gives the recognized
weight-number, mostly according to the latest list of atomic weights, the
"International List" of 1905, given in Erdmann's "Lehrbuch der
Unorganischen Chemie." These weights differ from those hitherto accepted,
and are generally lighter than those given in earlier text-books. It is
interesting to note that our counting endorses the earlier numbers, for the
most part, and we must wait to see if later observations will endorse the
last results of orthodox chemistry, or confirm ours.
--------------------------------------------
Hydrogen | 18 | 1 | 1
*Occultum | 54 | 3 | --
Helium | 72 | 4 | 3.94
Lithium | 127 | 7.06 | 6.98
Baryllium | 164 | 9.11 | 9.01
Boron | 200 | 11.11 | 10.86
Carbon | 216 | 12 | 11.91
Nitrogen | 261 | 14.50 | 14.01
Oxygen | 290 | 16.11 | 15.879
Fluorine | 340 | 18.88 | 18.90
Neon | 360 | 20 | 19.9
*Meta-Neon | 402 | 22.33 | --
Sodium | 418 | 23.22 | 22.88
Magnesium | 432 | 24 | 24.18
Aluminium | 486 | 27 | 26.91
Silicon | 520 | 28.88 | 28.18
Phosphorus | 558 | 31 | 30.77
Sulphur | 576 | 32 | 31.82
Chlorine | 639 | 35.50 | 35.473
Potassium | 701 | 38.944 | 38.85
Argon | 714 | 39.66 | 39.60
Calcium | 720 | 40 | 39.74
*Metargon | 756 | 42 | --
Scandium | 792 | 44 | 43.78
Titanium | 864 | 48 | 47.74
Vanadium | 918 | 51 | 50.84
Chromium | 936 | 52 | 51.74
Manganese | 992 | 55.11 | 54.57
Iron | 1008 | 56 | 55.47
Cobalt | 1036 | 57.55 | 57.7
Nickel | 1064 | 59.ll | 58.30
Copper | 1139 | 63.277 | 63.12
Zinc | 1170 | 65 | 64.91
Gallium | 1260 | 70 | 69.50
Germanium | 1300 | 72.22 | 71.93
Arsenic | 1350 | 75 | 74.45
Selenium | 1422 | 79 | 78.58
Bromine | 1439 | 79.944 | 79.953
Krypton | 1464 | 81.33 | 81.20
*Meta-Krypton | 1506 | 83.66 | --
Rubidium | 1530 | 85 | 84.85
Strontium | 1568 | 87.11 | 86.95
Yttrium | 1606 | 89.22 | 88.34
Zirconium | 1624 | 90.22 | 89.85
Niobium | 1719 | 95.50 | 93.25
Molybdenum | 1746 | 97 | 95.26
Ruthenium | 1848 | 102.66 | 100.91
Rhodium | 1876 | 104.22 | 102.23
Palladium | 1904 | 105.77 | 105.74
Silver | 1945 | 108.055 | 107.93
Cadmium | 2016 | 112 | 111.60
Indium | 2052 | 114 | 114.05
Tin | 2124 | 118 | 118.10
Antimony | 2169 | 120.50 | 119.34
Tellurium | 2223 | 123.50 | 126.64
Iodine | 2287 | 127.055 | 126.01
Xenon | 2298 | 127.66 | 127.10
*Meta-Xenon | 2340 | 130 | --
*Kalon | 3054 | 169.66 | --
*Meta-Kalon | 3096 | 172 | --
Osmium | 3430 | 190.55 | 189.55
Iridium | 3458 | 192.11 | 191.56
Platinum A | 3486 | 193.66 | 193.34
*Platinum B | 3514 | 195.22 | --
Gold | 3546 | 197 | 195.74
--------------------------------------------
[Illustration: PLATE II. MALE (left) and FEMALE (right).]
As the words "ultimate physical atom" must frequently occur, it is
necessary to state what we mean by the phrase. Any gaseous chemical atom
may be dissociated into less complicated bodies; these, again, into still
less complicated; these, again, into yet still less complicated. These will
be dealt with presently. After the third dissociation but one more is
possible; the fourth dissociation gives the ultimate physical atom.[3] This
may vanish from the physical plane, but it can undergo no further
dissociation on it. In this ultimate state of physical matter two types of
atoms have been observed; they are alike in everything save the direction
of their whorls and of the force which pours through them. In the one case
force pours in from the "outside," from fourth-dimensional space,[4] and
passing through the atom, pours into the physical world. In the second, it
pours in from the physical world, and out through the atom into the
"outside" again,[4] _i.e._, vanishes from the physical world. The one is
like a spring, from which water bubbles out; the other is like a hole, into
which water disappears. We call the atoms from which force comes out
_positive_ or _male_; those through which it disappears, _negative_ or
_female_. All atoms, so far as observed, are of one or other of these two
forms. (Plate II.)
It will be seen that the atom is a sphere, slightly flattened, and there is
a depression at the point where the force flows in, causing a heart-like
form. Each atom is surrounded by a field, formed of the atoms of the four
higher planes, which surround and interpenetrate it.
The atom can scarcely be said to be a "thing," though it is the material
out of which all things physical are composed. It is formed by the flow of
the life-force[5] and vanishes with its ebb. When this force arises in
"space"[6]--the apparent void which must be filled with substance of some
kind, of inconceivable tenuity--atoms appear; if this be artificially
stopped for a single atom, the atom disappears; there is nothing left.
Presumably, were that flow checked but for an instant, the whole physical
world would vanish, as a cloud melts away in the empyrean. It is only the
persistence of that flow[7] which maintains the physical basis of the
universe.[8]
In order to examine the construction of the atom, a space is artificially
made[9]; then, if an opening be made in the wall thus constructed, the
surrounding force flows in, and three whorls immediately appear,
surrounding the "hole" with their triple spiral of two and a half coils,
and returning to their origin by a spiral within the atom; these are at
once followed by seven finer whorls, which following the spiral of the
first three on the outer surface, and returning to their origin by a spiral
within that, flowing in the opposite direction--form a caduceus with the
first three. Each of the three coarser whorls, flattened out, makes a
closed circle; each of the seven finer ones, similarly flattened out, makes
a closed circle. The forces which flow in them, again, come from "outside,"
from a fourth-dimensional space.[10] Each of the finer whorls is formed of
seven yet finer ones, set successively at right angles to each other, each
finer than its predecessor; these we call spirillæ.[11]
It will be understood from the foregoing, that the atom cannot be said to
have a wall of its own, unless these whorls of force can be so designated;
its "wall" is the pressed back "space." As said in 1895, of the chemical
atom, the force "clears itself a space, pressing back the undifferentiated
matter of the plane, and making to itself a whirling wall of this matter."
The wall belongs to space, not to the atom.
In the three whorls flow currents of different electricities; the seven
vibrate in response to etheric waves of all kinds--to sound, light, heat,
etc.; they show the seven colours of the spectrum; give out the seven
sounds of the natural scale; respond in a variety of ways to physical
vibration--flashing, singing, pulsing bodies, they move incessantly,
inconceivably beautiful and brilliant.[12]
The atom has--as observed so far--three proper motions, _i.e._, motions of
its own, independent of any imposed upon it from outside. It turns
incessantly upon its own axis, spinning like a top; it describes a small
circle with its axis, as though the axis of the spinning top moved in a
small circle; it has a regular pulsation, a contraction and expansion, like
the pulsation of the heart. When a force is brought to bear upon it, it
dances up and down, flings itself wildly from side to side, performs the
most astonishing and rapid gyrations, but the three fundamental motions
incessantly persist. If it be made to vibrate, as a whole, at the rate
which gives any one of the seven colors, the whorl belonging to that color
glows out brilliantly.
[Illustration]
An electric current brought to bear upon the atoms checks their proper
motions, _i.e._, renders them slower; the atoms exposed to it arrange
themselves in parallel lines, and in each line the heart-shaped depression
receives the flow, which passes out through the apex into the depression of
the next, and so on. The atoms always set themselves to the current. The
well-known division of diamagnetic and paramagnetic depends generally on
this fact, or on an analogous action on molecules, as may be seen in the
accompanying diagrams.[13]
Two atoms, positive and negative, brought near to each other, attract each
other, and then commence to revolve round each other, forming a relatively
stable duality; such a molecule is neutral. Combinations of three or more
atoms are positive, negative or neutral, according to the internal
molecular arrangement; the neutral are relatively stable, the positive and
negative are continually in search of their respective opposites, with a
view to establishing a relatively permanent union.
Three states of matter exist between the atomic state and the gaseous--the
state in which the chemical atoms are found, the recognized chemical
elements; for our purposes we may ignore the liquid and solid states. For
the sake of clearness and brevity in description, we have been obliged to
name these states; we call the atomic state of the chemist _elemental_; the
state which results from breaking up chemical elements, _proto-elemental_;
the next higher, _meta-proto-elemental_; the next higher,
_hyper-meta-proto-elemental_; then comes the atomic state. These are
briefly marked as El., Proto., Meta., and Hyper.[14]
The simplest unions of atoms, never, apparently consisting of more than
seven, form the first molecular state of physical matter.
[Illustration: TYPES OF HYPER-META-PROTO-ELEMENTAL MATTER.]
Here are some characteristic combinations of the Hyper state; the atom is
conventional, with the depression emphasised; the lines, always entering at
the depression and coming out at the apex, show the resultants of lines of
force; where no line appears entering the depression, the force wells up
from fourth-dimensional space; where no line appears leaving the apex, the
force disappears into fourth-dimensional space; where the point of entry
and departure is outside the atoms, it is indicated by a dot.[15]
The molecules show all kinds of possible combinations; the combinations
spin, turn head over heels, and gyrate in endless ways. Each aggregation is
surrounded with an apparent cell-wall, the circle or oval, due to the
pressure on the surrounding matter caused by its whirling motion; they
strike on each other[16] and rebound, dart hither and thither, for reasons
we have not distinguished.
[Illustration: TYPES OF META-PROTO-ELEMENTAL MATTER.]
The Meta state, in some of its combinations, appears at first sight to
repeat those of the Hyper state; the only obvious way of distinguishing to
which some of the molecules of less complexity belong is to pull them out
of the "cell-wall"; if they are Hyper molecules they at once fly off as
separate atoms; if they are Meta molecules they break up into two or more
molecules containing a smaller number of atoms. Thus one of the Meta
molecules of iron, containing seven atoms, is identical in appearance with
a Hyper heptad, but the latter dissociates into seven atoms, the former
into two triads and a single atom. Long-continued research into the
detailed play of forces and their results is necessary; we are here only
able to give preliminary facts and details--are opening up the way. The
following may serve as characteristic Meta types:--
These are taken from constituents of the various elements; 1 from Gl; 2 and
3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12
from Li; 13 and 14 from Na. Others will be seen in the course of breaking
up the elements.
The Proto state preserves many of the forms in the elements, modified by
release from the pressure to which they are subjected in the chemical atom.
In this state various groups are thus recognizable which are characteristic
of allied metals.
[Illustration: TYPES OF PROTO-ELEMENTAL MATTER.]
These are taken from the products of the first disintegration of the
chemical atom, by forcibly removing it from its hole. The groups fly apart,
assuming a great variety of forms often more or less geometrical; the lines
between the constituents of the groups, where indicated, no longer
represent lines of force, but are intended to represent the impression of
form, _i.e._, of the relative position and motion of the constituents, made
on the mind of the observer. They are elusive, for there are no lines, but
the appearance of lines is caused by the rapid motion of the costituents up
and down, or along them backwards and forwards. The dots represent atoms,
or groups of atoms, within the proto-elements. 1 is found in C; 2 and 3 in
He; 4 in Fl; 5 in Li; 6 in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe;
12 in Se. We shall return to these when analysing the elements, and shall
meet many other proto-elemental groupings.
The first thing which is noticed by the observer, when he turns his
attention to the chemical atoms, is that they show certain definite forms,
and that within these forms, modified in various ways, sub-groupings are
observable which recur in connexion with the same modified form. The main
types are not very numerous, and we found that, when we arranged the atoms
we had observed, according to their external forms, they fell into natural
classes; when these, in turn, were compared with Sir William Crookes'
classification, they proved to be singularly alike. Here is his arrangement
of the elements, as it appeared in the _Proceedings of the Royal Society_,
in a paper read on June 9th, 1898.
[Illustration]
This is to be read, following the lines of the "figures of eight": H, He,
Li, Gl, B, C, N, and so on, each successive element being heavier than the
one preceding it in order. The disks which fall immediately below each
other form a class; thus: H, Cl, Br, I; these resemble each other in
various ways, and, as we shall presently see, the same forms and groupings
re-appear.
Another chart--taken from Erdmann's _Lehrbuch_--arranges the elements on a
curved line, which curiously resembles the curves within the shell of a
nautilus. The radiating lines show the classes, the whole diameter building
up a family; it will be observed that there is an empty radius between
hydrogen and helium, and we have placed occultum there; on the opposite
radius, iron, rubidium and osmium are seen.
[Illustration]
The external forms may be classified as follows; the internal details will
be dealt with later :--
[Illustration: PLATE III.]
1. _The Dumb-bell._--The characteristics of this are a higher and lower
group, each showing 12 projecting funnels, grouped round a central body,
and a connecting rod. It appears in sodium, copper, silver, and gold,[17]
and gold is given (1 on Plate III) as the most extremely modified example
of this form. The 12 almond-like projections, above and below, are
severally contained in shadowy funnels, impossible to reproduce in the
drawing; the central globe contains three globes, and the connecting
portion has swollen out into an egg, with a very complicated central
arrangement. The dumb-bell appears also in chlorine, bromine and iodine,
but there is no trace of it in hydrogen, the head of the group. We have not
met it elsewhere. It may be remarked that, in Sir William Crookes' scheme,
in which they are all classed as monads, these two groups are the nearest
to the neutral line, on the ingoing and outgoing series, and are
respectively positive and negative.
II and IIa. _The Tetrahedron._--The characteristics of this form are four
funnels, containing ovoid bodies, opening on the face of a tetrahedron. The
funnels generally, but not always, radiate from a central globe. We give
beryllium (glucinum) as the simplest example (2 on Plate III), and to this
group belong calcium and strontium. The tetrahedron is the form of chromium
and molybdenum, but not that of the head of their group, oxygen, which is,
like hydrogen, _sui generis_. These two groups are marked in orthodox
chemistry as respectively positive and negative, and are closely allied.
Another pair of groups show the same tetrahedral form: magnesium, zinc and
cadmium, positive; sulphur, selenium and tellurium, negative. Selenium is a
peculiarly beautiful element, with a star floating across the mouth of each
funnel; this star is extremely sensitive to light, and its rays tremble
violently and bend if a beam of light falls on it. All these are dyads.
The tetrahedron is not confined to the external form of the above atoms; it
seems to be one of the favourite forms of nature, and repeatedly appears in
the internal arrangements. There is one tetrahedron within the unknown
element occultum; two appear in helium (3 on Plate III); yttrium has also
two within its cube, as has germanium; five, intersecting, are found in
neon, meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon,
kalon, meta-kalon, tin, titanium and zirconium. Gold contains no less than
twenty tetrahedra.
III. _The Cube._--The cube appears to be the form of triads. It has six
funnels, containing ovoids, and opening on the faces of the cube. Boron is
chosen as an example (4 on Plate III). Its group members, scandium and
yttrium, have the same form; we have not examined the fourth; the group is
positive. Its negative complement consists of nitrogen, vanadium and
niobium, and we have again to note that nitrogen, like hydrogen and oxygen,
departs from its group type. Two other triad groups, the positive
aluminium, gallium and indium (the fourth unexamined) and the negative
phosphorus, arsenic and antimony (the fourth unexamined), have also six
funnels opening on the faces of a cube.
IV. _The Octahedron._--The simplest example of this is carbon (5 on Plate
III). We have again the funnel with its ovoids, but now there are eight
funnels opening on the eight faces of the octahedron. In titanium (6 on
Plate III) the form is masked by the protruding arms, which give the
appearance of the old Rosicrucian Cross and Rose, but when we look into the
details later, the carbon type comes out clearly. Zirconium is exactly like
titanium in form, but contains a large number of atoms. We did not examine
the remaining two members of this group. The group is tetratomic and
positive. Its negative pendant shows the same form in silicon, germanium
and tin; again, the fourth was unexamined.
[Illustration: PLATE IV.]
V. _The Bars._--These characterise a set of closely allied groups, termed
"inter-periodic." Fourteen bars (or seven crossed) radiate from a centre,
as in iron (1 on Plate IV), and the members of each group--iron, nickel,
cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum--differ
from each other by the weight of each bar, increasing in orderly
succession; the details will be given later. Manganese is often grouped
with iron, nickel, and cobalt (_see_ Crookes' lemniscates), but its
fourteen protruding bodies repeat the "lithium spike" (proto-element 5) and
are grouped round a central ovoid. This would appear to connect it with
lithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with
which it is often classed. The "lithium spike" re-appears in potassium and
rubidium. These details, again, will come out more clearly later.
VI. _The Star._--A flat star, with five interpenetrating tetrahedra in the
centre, is the characteristic of neon and its allies (4 on Plate IV)
leaving apart helium, which, as may be seen by referring to 3, Plate IV,
has an entirely different form.
There are thus six clearly defined forms, typical of classes, with
two--lithium and fluorine--of doubtful affinities. It is worthy of notice
that in diatomic elements _four_ funnels open on the faces of tetrahedra;
in triatomic, _six_ funnels on the faces of cubes; in tetratomic, _eight_
funnels on the faces of octahedra.
Thus we have a regular sequence of the platonic solids, and the question
suggests itself, will further evolution develop elements shaped to the
dodecahedron and the icosahedron?
* * * * *
II.
We now pass from the consideration of the outer forms of the chemical
elements to a study of their internal structure, the arrangement within the
element of more or less complicated groups--proto-elements--capable of
separate, independent existence; these, once more, may be dissociated into
yet simpler groups--hyper-meta-proto-elements--equally capable of separate,
independent existence, and resolvable into single ultimate physical atoms,
the irreducible substratum of the physical world (see _Theosophist_, 1908,
pp. 354-356).[18]
We shall have to study the general internal structure, and then the
breaking up of each element, and the admirable diagrams, patiently worked
out by Mr. Jinarâjadâsa, will make the study comparatively easy to carry
on.
The diagrams, of course, can only give a very general idea of the facts
they represent; they give groupings and show relations, but much effort of
the imagination is needed to transform the two-dimensional diagram into the
three-dimensional object. The wise student will try to visualize the figure
from the diagram. Thus the two triangles of hydrogen are not in one plane;
the circles are spheres, and the atoms within them, while preserving to
each other their relative positions, are in swift movement in
three-dimensional space. Where five atoms are seen, as in bromine and
iodine, they are generally arranged with the central atom above the four,
and their motion indicates lines which erect four plane triangles--meeting
at their apices--on a square base, forming a square-based four-sided
pyramid. Each dot represents a single ultimate atom. The enclosing lines
indicate the impression of form made on the observer, and the groupings of
the atoms; the groups will divide along these lines, when the element is
broken up, so that the lines have significance, but they do not exist as
stable walls or enclosing films, but rather mark limits, not lines, of
vibrations. It should be noted that it is not possible to show five of the
prisms in the five intersecting tetrahedra of prisms, and 30 atoms must,
therefore, be added in counting.
The diagrams are not drawn to scale, as such drawing would be impossible;
the dot representing the atom is enormously too large compared with the
enclosures, which are absurdly too small; a scale drawing would mean an
almost invisible dot on a sheet of many yards square.
The use of the words "positive" and "negative" needs to be guarded by the
following paragraphs from the article on "Chemistry" in the _Encyclopædia
Britannica_. We use the words in their ordinary text-book meaning, and have
not, so far, detected any characteristics whereby an element can be
declared, at sight, to be either positive or negative:--
"When binary compounds, or compounds of two elements, are decomposed by an
electric current, the two elements make their appearance at opposite poles.
These elements which are disengaged at the negative pole are termed
electro-positive or positive or basylous elements, while those disengaged
at the positive pole are termed electro-negative or negative or chlorous
elements. But the difference between these two classes of elements is one
of degree only, and they gradually merge into each other; moreover the
electric relations of elements are not absolute, but vary according to the
state of combination in which they exist, so that it is just as impossible
to divide the elements into two classes according to this property as it is
to separate them into two distinct classes of metals and non-metals."
We follow here the grouping according to external forms, and the student
should compare it with the groups marked in the lemniscate arrangement
shown in Article II (p. 377, properly p. 437, February), reading the group
by the disks that fall below each other; thus the first group is H, Cl, Br,
I (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered
element. The elements grow denser in descending order; thus hydrogen is an
invisible gas; chlorine a denser gas visible by its colour; bromine is a
liquid; iodine is a solid--all, of course, when temperature and pressure
are normal. By the lowering of temperature and the increase of pressure, an
element which is normally gaseous becomes a liquid, and then a solid.
Solid, liquid, gaseous, are three interchangeable states of matter, and an
element does not alter its constitution by changing its state. So far as a
chemical "atom" is concerned, it matters not whether it be drawn for
investigation from a solid, a liquid, or a gas; but the internal
arrangements of the "atoms" become much more complicated as they become
denser and denser, as is seen by the complex arrangements necessitated by
the presence of the 3546 ultimate atoms contained in the chemical "atom" of
gold, as compared with the simple arrangement of the 18 ultimate atoms of
hydrogen.
According to the lemniscate arrangement, we should commence with hydrogen
as the head of the first negative group, but as it differs wholly from
those placed with it, it is better to take it by itself. Hydrogen is the
lightest of the known elements, and is therefore taken as 1 in ordinary
chemistry, and all atomic weights are multiples of this. We take it as 18,
because it contains eighteen ultimate atoms, the smallest number we have
found in a chemical element. So our "number-weights" are obtained by
dividing the total number of atoms in an element by 18 (see p. 349,
January).
[Illustration: PLATE V.]
HYDROGEN (Plate V, 1).--Hydrogen not only stands apart from its reputed
group by not having the characteristic dumb-bell shape, well shown in
sodium (Plate I, opposite p. 349, January), but it also stands apart in
being positive, serving as a base, not as a chlorous, or acid, radical,
thus "playing the part of a metal," as in hydrogen chloride (hydrochloric
acid), hydrogen sulphate (sulphuric acid), etc.
It is most curious that hydrogen, oxygen and nitrogen, the most widely
spread gases, all differ fundamentally in form from the groups they
reputedly head.[19] Hydrogen was the first chemical element examined by us,
nearly thirteen years ago, and I reproduce here the substance of what I
wrote in November, 1895, for we have nothing to add to nor amend in it.
Hydrogen consists of six small bodies, contained in an egg-like form (the
outer forms are not given in the diagrams). The six little bodies are
arranged in two sets of three, forming two triangles which are not
interchangeable, but are related to each other as object and image. The six
bodies are not all alike; they each contain three ultimate physical atoms,
but in four of the bodies the three atoms are arranged in a triangle, and
in the remaining two in a line.
HYDROGEN: 6 bodies of 3 18
Atomic weight 1
Number weight 18/18 1
I.--THE DUMB-BELL GROUP.
I a.--This group consists of Cl, Br, and I (chlorine, bromine and iodine);
they are monads, diamagnetic and negative.
CHLORINE (Plate V, 2).--As already said, the general form is that of the
dumb-bell, the lower and upper parts each consisting of twelve funnels, six
sloping upwards and six downwards, the funnels radiating outwards from a
central globe, and these two parts being united by a connecting rod (see,
again, sodium, Plate I).
The funnel (shown flat as an isosceles triangle, standing on its apex) is a
somewhat complicated structure, of the same type as that in sodium (Plate
VI, 2), the difference consisting in the addition of one more globe,
containing nine additional atoms. The central globe is the same as in
sodium, but the connecting rod differs. We have here a regular arrangement
of five globes, containing three, four, five, four, three atoms
respectively, whereas sodium has only three bodies, containing four, six,
four. But copper and silver, its congeners, have their connecting rods of
exactly the same pattern as the chlorine rod, and the chlorine rod
reappears in both bromine and iodine. These close similarities point to
some real relation between these groups of elements, which are placed, in
the lemniscates, equi-distant from the central line, though one is on the
swing which is going towards that line and the other is on the swing away
from it.
CHLORINE: Upper part {12 funnels of 25 atoms 300
{Central globe 10
Lower part same 310
Connecting rod 19
----
Total 639
----
Atomic weight 35.473
Number weight 639/18 35.50
(The Atomic Weights are mostly from Erdmann, and the Number Weights are
those ascertained by us by counting the atoms as described on p. 349,
January, and dividing by 18. Prof. T.W. Richards, in _Nature_, July 18,
1907, gives 35.473.)
BROMINE (Plate V, 3).--In bromine, each funnel has three additional bodies,
ovoid in shape, an addition of 33 atoms being thus made without any
disturbance of form; two pairs of atoms are added to the central globe, and
a rearrangement of the atoms is effected by drawing together and lessening
the swing of the pair of triplets, thus making symmetrical room for the
newcomers. The connecting rod remains unchanged. The total number of atoms
is thus raised from the 639 of chlorine to 1439. Over and over again, in
these investigations, were we reminded of Tyndall's fascinating description
of crystal building, and his fancy of the tiny, ingenious builders busied
therein. Truly are there such builders, and the ingenuity and effectiveness
of their devices are delightful to see.[20]
BROMINE: Upper part {12 funnels of 58 atoms 696
{Central globe 14
Lower part same 710
Connecting rod 19
----
Total 1439
----
Atomic weight 79.953
Number weight 1459/18 79.944
IODINE (Plate V, 4).--We find herein that the central globe gains 4 atoms,
the two pairs becoming 2 quartets; the connecting rod exactly reproduces
the rods of chlorine and bromine; the funnel is also that of bromine,
except that five bodies, containing 35 atoms, are added to it. The 1439
atoms of bromine are thus raised to 2887.
IODINE: Upper Part {12 funnels of 90 atoms 1116
{Central globe 18
Lower part same 1134
Connecting rod 19
----
Total 2287
----
Atomic weight 126.01
Number weight 2287/18 127.055
The plan underlying the building up of groups is here clearly shown; a
figure is built up on a certain plan, in this case a dumb-bell; in the
succeeding members of the group additional atoms are symmetrically
introduced, modifying the appearance, but following the general idea; in
this case the connecting rod remains unaltered, while the two ends become
larger and larger, more and more overshadowing it, and causing it to become
shorter and thicker. Thus a group is gradually formed by additional
symmetrical additions. In the undiscovered remaining member of the group we
may suppose that the rod will have become still more egg-like, as in the
case of gold.
I b.--The corresponding positive group to that which we have been
considering consists of Na, Cu, Ag, and Au (sodium, copper, silver and
gold), with an empty disk between silver and gold, showing where an element
ought to be. These four elements are monads, diamagnetic, and positive, and
they show the dumb-bell arrangement, although it is much modified in gold;
we may presume that the undiscovered element between silver and gold would
form a link between them.
[Illustration: PLATE VI.]
SODIUM (Plate VI, 2) has been already described (p. 349, January), as a
type of the group, so we need only refer to its internal arrangement in
order to note that it is the simplest of the dumb-bell group. Its twelve
funnels show only four enclosed bodies, the same as we see in chlorine,
bromine, iodine, copper and silver, and which is very little modified in
gold. Its central globe is the simplest of all, as is its connecting rod.
We may therefore take it that sodium is the ground-plan of the whole group.
SODIUM: Upper part
{ 12 funnels of 16 each 192
{ Central globe 10
Lower part same 202
Connecting rod 14
----
Total 418
----
Atomic weight 23.88
Number weight 418/19 23.22
COPPER (Plate VI, 3) introduces an addition in the funnel, that we shall
find elsewhere, _e.g._, in silver, gold, iron, platinum, zinc, tin, the
triangular arrangement near the mouth of the funnel and adds to the ten
atoms in this nineteen more in three additional enclosed bodies, thus
raising the number of atoms in a funnel from the sixteen of sodium to
forty-five. The number in the central globe is doubled, and we meet for the
first time the peculiar cigar or prism-shaped six-atomed arrangement, that
is one of the most common of atomic groups. It ought to imply some definite
quality, with its continual recurrence. The central column is the three,
four, five, four, three, arrangement already noted.
COPPER: Upper part {12 funnels of 45 atoms 540
{Central globe 20
Lower part same 560
Connecting rod 19
----
Total 1139
----
Atomic weight 63.12
Number weight 1139/18 63.277
SILVER (Plate VI, 4) follows copper in the constitution of five of the
bodies enclosed in the funnels. But the triangular group contains
twenty-one atoms as against ten, and three ovoids, each containing three
bodies with eleven atoms, raise the number of atoms in a funnel to
seventy-nine. The central globe is decreased by five, and the prisms have
disappeared. The connecting rod is unaltered.
SILVER: Upper part {12 funnels of 79 atoms 948
{Central globe 15
Lower part same 963
Connecting rod 19
----
Total 1945
----
Atomic weight 107.93
Number weight 1945/18 108.055
(This atomic weight is given by Stas, in _Nature_, August 29, 1907, but it
has been argued later that the weight should not be above 107.883.)
[Illustration: PLATE VII.]
GOLD (Plate VII) is so complicated that it demands a whole plate to itself.
It is difficult to recognize the familiar dumb-bell in this elongated egg,
but when we come to examine it, the characteristic groupings appear. The
egg is the enormously swollen connecting rod, and the upper and lower parts
with their central globes are the almond-like projections above and below,
with the central ovoid. Round each almond is a shadowy funnel (not drawn in
the diagram), and within the almond is the collection of bodies shown in
_e_, wherein the two lowest bodies are the same as in every other member of
the negative and positive groups; the third, ascending, is a very slight
modification of the other thirds; the fourth is a union and re-arrangement
of the fourth and fifth; the fifth, of four ovoids, adds one to the three
ovoids of bromine, iodine and silver; the triangular group is like that in
copper and silver, though with 28 atoms instead of 10 or 21, and it may be
noted that the cone in iron has also 28. The central body in the ovoid is
very complicated, and is shown in _c_, the bodies on each side, _d_, are
each made up of two tetrahedra, one with four six-atomed prisms at its
angles, and the other with four spheres, a pair with four atoms and a pair
with three. We then come to the connecting rod. One of the four similar
groups in the centre is enlarged in _a_, and one of the sixteen circling
groups is enlarged in b. These groups are arranged in two planes inclined
to one another.
GOLD: Upper part
{ 12 funnels of 97 atoms 1164
{ Central ovoid {c 101
{2 d, 38 76
Lower part same 1341
Connecting rod { 4 a 84 336
{16 b 33 528
----
Total 3546
----
Atomic weight 195.74
Number weight 3546/18 197
It may be noted that the connecting rod is made up of exactly sixteen atoms
of occultum, and that sixteen such atoms contain 864 ultimate atoms, the
exact member of atoms in titanium.
* * * * *
III.
Occultum was observed by us in 1895, and, finding that it was so light, and
so simple in its composition, we thought that it might be helium, of which
we were unable, at the time, to obtain a sample. When, however, helium
itself came under observation in 1907, it proved to be quite different from
the object before observed, so we dubbed the unrecognised object Occultum,
until orthodox science shall find it and label it in proper fashion.
OCCULTUM (Plate VI, 1).
We here meet the tetrahedron for the first time, with each angle occupied
by a six-atomed group, the atoms arranged as on the end triangles of a
prism. This form recurs very often, and was noted, last month, as seen in
copper (Plate VI, 3); it revolves with extreme rapidity around its
longitudinal axis, and looks like a pencil sharpened at both ends, or a
cigar tapering at both ends; we habitually spoke of it as "the cigar." It
appears to be strongly coherent, for, as will be seen below, its six atoms
remain attached to each other as meta-compounds and even when divided into
two triplets as hyper-compounds, they revolve round each other.
Above the tetrahedron is a balloon-shaped figure, apparently drawn into
shape by the attraction of the tetrahedron. The body below the tetrahedron
looks like a coil of rope, and contains fifteen atoms; they are arranged on
a slanting disk in a flat ring, and the force goes in at the top of one
atom, and out of the bottom of it into the top of the next, and so on,
making a closed circuit. The two little spheres, each containing a triplet,
are like fill-up paragraphs to a compositor--they seem to be kept standing
and popped in where wanted. The sphere marked _x_ is a proto-compound, the
balloon when set free.
As was noted under gold (p. 41), sixteen occultum bodies, re-arranged, make
up the connecting rod in gold:--
OCCULTUM: Tetrahedron 24
Balloon 9
Triplets 6
Rope-circle 15
----
Total 54
----
Atomic weight Not known
Number weight 54/18 3
DISSOCIATION OF ATOMS.
Before proceeding to the study of other chemical atoms, as to their general
internal arrangements, it is desirable to follow out, in those already
shown, the way in which these atoms break up into simpler forms, yielding
successively what we have called proto-, meta-, and hyper-compounds. It is
naturally easier to follow these in the simpler atoms than in the more
complex, and if the earlier dissociations are shown, the latter can be more
readily and more intelligibly described.
The first thing that happens on removing a gaseous atom from its "hole"
(see pp. 21 to 23) or encircling "wall," is that the contained bodies are
set free, and, evidently released from tremendous pressure, assume
spherical or ovoid forms, the atoms within each re-arranging themselves,
more or less, within the new "hole" or "wall." The figures are, of course,
three-dimensional, and often remind one of crystals; tetrahedral,
octagonal, and other like forms being of constant occurrence. In the
diagrams of the proto-compounds, the constituent atoms are shown by dots.
In the diagrams of the meta-compounds the dot becomes a heart, in order to
show the resultants of the lines of force. In the diagrams of the
hyper-compounds the same plan is followed. The letters _a_, _b_, _c_, &c.,
enable the student to follow the breaking up of each group through its
successive stages.
HYDROGEN (Plate V, 1).
[Illustration]
The six bodies contained in the gaseous atom instantaneously re-arrange
themselves within two spheres; the two linear triplets unite with one
triangular triplet, holding to each other relative positions which, if
connected by three right lines, would form a triangle with a triplet at
each angle; the remaining three triangular triplets similarly arrange
themselves in the second sphere. These form the proto-compounds of
hydrogen.
In the dissociation of these, each group breaks up into two, the two linear
triplets joining each other and setting free their triangular comrade,
while two of the triangular triplets similarly remain together, casting out
the third, so that hydrogen yields four meta-compounds.
In the hyper-condition, the connexion between the double triplets is
broken, and they become four independent groups, two like ix, in the
hyper-types (p. 25), and two remaining linear, but rearranging their
internal relations; the two remaining groups break up into two pairs and a
unit.
The final dissociation sets all the atoms free.
OCCULTUM (Plate VI, 1).
[Illustration]
On the first dissociation of the component parts of occultum, the
tetrahedron separates as a whole, with its four "cigars," flattening itself
out within its hole, _a_; two "cigars" are positive and two negative,
marked respectively _a_ and _a'_. The rope becomes a ring within a sphere,
_b_, and the two bodies _d_ _d_, which are loose in the gaseous atom, come
within this ring. The balloon becomes a sphere.
On further dissociation, the "cigars" go off independently, showing two
types, and these again each divide into triplets, as meta-compounds. _B_,
on the meta-level, casts out the two _d_ bodies, which become independent
triplets, and the "rope" breaks into two, a close ring of seven atoms and a
double cross of eight. These subdivide again to form hyper-compounds, the
ring yielding a quintet and a pair, and the double cross separating into
its two parts.
The balloon, _c_, becomes much divided, the cohesion of its parts being
slight; it forms two triplets, a pair and a unit, and these set free, on
further dissociation, no less than five separate atoms and two duads.
The two triplets of _d_ each cast out an atom on dissociation, and form two
pairs and two units.
SODIUM (Plate VI, 2).
It is convenient to consider sodium next, because it is the basic pattern
on which not only copper, silver and gold are formed, but also chlorine,
bromine and iodine.
[Illustration]
When sodium is set free from its gaseous condition, it divides up into
thirty-one bodies--twenty-four separate funnels, four bodies derived from
the two central globes, and three from the connecting rod. The funnels
become spheres, and each contains four enclosed spheres, with more or less
complicated contents. Each central globe yields a sextet and a quartet, and
the rod sets free two quartets and a peculiarly formed sextet.
When the proto-compounds are dissociated, the funnel-sphere sets free: (1)
the contents of _a_, rearranged into two groups of four within a common
sphere; the sphere yields four duads as hyper-compounds; (2) the contents
of _b_, which unite themselves into a quartet, yielding two duads as
hyper-compounds; and (3) the contents of the two spheres, _c_, which
maintain their separation as meta-compounds, and become entirely
independent, the atoms within the sphere revolving round each other, but
the spheres ceasing their revolution round a common axis, and going off in
different directions. The atoms break off from each other, and gyrate in
independent solitude as hyper-"compounds." Thus each funnel yields finally
ten hyper-bodies.
The part of the central globe, marked _d_, with its six atoms, whirling
round a common centre, becomes two triplets, at the meta-stage, preparing
for the complete separation of these as hyper-bodies. The second part of
the same globe, marked _e_, a whirling cross, with an atom at each point,
becomes a quartet in the meta-state, in which three atoms revolve round a
fourth, and in the hyper-state this central atom is set free, leaving a
triplet and a unit.
Each of the two bodies marked _f_, liberated from the connecting rod, shows
four atoms whirling round a common centre, exactly resembling _e_ in
appearance; but there must be some difference of inner relations, for, in
the meta-state, they re-arrange themselves as two pairs, and divide into
two as hyper-bodies.
The body marked _g_ is a four-sided pyramid, with two closely joined atoms
at its apex; these still cling to each in mutual revolution as a meta-body,
encircled by a ring of four, and this leads to a further dissociation into
three pairs on the hyper-level.
CHLORINE (Plate V, 2).
[Illustration]
The description of the funnel of sodium applies to that of chlorine, until
we come to the body nearest the mouth, the sphere containing three
additional bodies; this remains within the funnel in the first
dissociation, so that again we have twenty-four separate funnels as
proto-compounds; the central globes are the same as in sodium, and yield
the same four bodies; the connecting rod sets free five bodies, of which
two are the same; we have thus thirty-three separate bodies as the result
of the dissociation of chlorine into its proto-compounds. As all the
compounds which are in sodium break up in the same way into meta- and
hyper-compounds, we need not repeat the process here. We have only to
consider the new meta- and hyper-compounds of the highest sphere within the
funnel, and the two triplets and one quintet from the connecting rod.
The additional body within the proto-funnel is of a very simple character,
three contained triangles within the flattened sphere. On release from the
funnel, on the meta-level, the atoms rearrange themselves in a whirling set
of three triplets, and these break off from each other as hyper-compounds.
The two triplets from the connecting rod, also, are of the simplest
character and need not delay us. The five-atomed body, a four-sided pyramid
as a proto-compound, becomes a ring whirling round a centre on the meta,
and two pairs with a unit on the hyper.
BROMINE (Plate V, 3).
Three additional bodies appear at the top of the funnel, which otherwise
repeats that of chlorine. The connecting rod is the same and may be
disregarded. The central globes become more complex. The additions are,
however, of very easy types, and hence are readily dealt with. Each of the
three similar ovoid bodies contains two triplets--each a triangle and a
quintet--a four-sided pyramid. These are the same, as may be seen in the
connecting rod of chlorine, and we need not repeat them. Only the globe
remains. This does not break up as a proto-compound but is merely set free,
_a_ and the 2 _bs_ whirling in a plane vertical to the paper and the two
smaller bodies, _cc_, whirling on a plane at right angles to the other.
These two disengage themselves, forming a quartet as a meta-compound, while
_a_ makes a whirling cross and _bb_ a single sextet; these further
dissociate themselves into four pairs and two triplets.
IODINE (Plate V, 4).
[Illustration]
Iodine has nothing new to give us, except five similar ovoid bodies at the
top of each funnel, and two quartets instead of two pairs in the central
globe. The ovoid bodies become spheres when the funnels are thrown off, and
a crystalline form is indicated within the sphere. The atoms are arranged
in two tetrahedra with a common apex, and the relationship is maintained in
the meta-body, a septet. The latter breaks up into two triplets and a unit
on the hyper-level. In the central globes, the _a_ of bromine is repeated
twice instead of the pairs in _cc_.
COPPER (Plate VI, 3).
We have already disposed of occultum, on this plate, and of sodium, which
lies at the root of both groups. Copper, we now find, is also very largely
off our hands, as the funnel provides us with only two new types--two
spheres--each containing five atoms in a new arrangement, and the
triangular body at the mouth with its ten atoms. This triangular body, with
an increased number of atoms, reappears in various other chemical elements.
The central globes are different from any we have had before, in their
internal arrangement, but the constituents are familiar; there are two
contained spheres with four atoms each, the _a_ in the globe of bromine
(see above) and 2 "cigars." The "cigars" may be followed under occultum
(see above). The connecting rod is as in chlorine, bromine and iodine.
The atoms in the bodies _a_ and _b_ are curiously arranged. _A_ consists of
two square-based pyramids turned so as to meet at their apices, and breaks
up into two quartet rings and a duad. _B_ is again two four-sided pyramids,
but the bases are in contact and set at right angles to each other; the
second apex is not seen, as it is directly below the first. The pyramids
separate as meta-bodies, and the atoms assume the peculiar arrangement
indicated and then break up into four pairs and two units on the hyper
level.
* * * * *
IV.
SILVER (Plate VI, 4 and Ag below).
Silver presents us with only two new bodies, and even these are only new by
slight additions to old models. The triangular shaped body at the apex of
the funnel, containing 21 atoms, is intermediate between the similar bodies
in copper and iron. As a proto-element it becomes three triangles, joined
at their apices, in fact a tetrahedron in which no atoms are distributed on
the fourth face. The faces separate on the meta level and give three
seven-atomed figures, and each of these breaks up into two triplets and a
unit. The central globe only differs from that of bromine by the addition
of one atom, which gives the familiar four-sided pyramid with a square base
as in chlorine (see p. 46).
GOLD (Plate VII and Au below).
[Illustration]
The disintegration of gold first yields forty-seven bodies on the
proto-level; the twenty-four funnels separate, and the central globes which
hold each twelve together set free their six contained globes (_c_, _d_),
thirty bodies being thus liberated. The sixteen bodies on the central
inclined planes, marked _b_, break away, their central globe, with its four
contained globes, remaining unchanged. But this condition does not last.
The motion of the funnels changes and thus the funnels cease to exist and
their contents are set free, each funnel thus liberating nine independent
bodies; the sixteen _b_ separate into two each; the four _a_ liberate five
each; the two _c_ set free thirteen each; the four _d_ finally liberate two
each: 302 proto elements in all.
The funnel is almost that of iodine, re-arranged. Four of the first ring in
the iodine funnel are replaced by the triangular body, which becomes a
four-sided pyramid with an occupied base. The second ring of three ovoids
in iodine becomes four in gold, but the internal arrangement of each ovoid
is the same. The next two spheres in the iodine funnel coalesce into one
sphere, with similar contents, in the gold funnel. The fifth in iodine is
slightly rearranged to form the fourth in descent in gold, and the
remaining two are the same. _B_ has been broken up under occultum (p. 628)
and can be followed there. The sixteen rings set free from the four _a_,
after gyrating round the central body, now become a sphere, break up, as in
occultum (see p. 44) into a meta seven-atomed ring and an eight-atomed
double cross, and so on to the hyper level. The sphere with its two
contained bodies breaks up into eight triangles on the meta level, and each
of these, on the hyper, into a duad and a unit. The twelve septets of _c_
assume the form of prisms as in iodine (see p. 48) and pursue the same
course, while its central body, a four-sided pyramid with its six
attendants, divides on the meta level into six duads, revolving round a
ring with a central atom as in chlorine (p. 47), the duads going off
independently on the hyper-level and the ring breaking up as in chlorine.
The "cigar" tetrahedron of _d_ follows its course as in occultum, and the
other sets free two quartets and two triplets on the meta level, yielding
six duads and two units as hyper compounds. It will be seen that, complex
as gold is, it is composed of constituents already familiar, and has iodine
and occultum as its nearest allies.
II AND IIa.--THE TETRAHEDRAL GROUPS.
II.--This group consists of beryllium (glucinum), calcium, strontium and
barium, all diatomic, paramagnetic and positive. The corresponding group
consists of oxygen, chromium, molybdenum, wolfram (tungsten) and uranium,
with a blank disk between wolfram and uranium: these are diatomic,
paramagnetic, and negative. We have not examined barium, wolfram, or
uranium.
[Illustration: PLATE VIII.]
BERYLLIUM (Plate III, 2, and Plate VIII, 1). In the tetrahedron four
funnels are found, the mouth of each funnel opening on one of its faces.
The funnels radiate from a central globe, and each funnel contains four
ovoids each with ten atoms within it arranged in three spheres. In the
accompanying diagrams one funnel with its four ovoids is shown and a single
ovoid with its three spheres, containing severally three, four, and three
atoms, is seen at the left-hand corner of the plate (7 _a_). The members of
this group are alike in arrangement, differing only in the increased
complexity of the bodies contained in the funnels. Beryllium, it will be
observed, is very simple, whereas calcium and strontium are complicated.
BERYLLIUM: 4 funnels of 40 atoms 160
Central globe 4
----
Total 164
----
Atomic weight 9.01
Number weight 164/18 9.11
CALCIUM (Plate VIII, 2) shows in each funnel three contained spheres, of
which the central one has within it seven ovoids identical with those of
beryllium, and the spheres above and below it contain each five ovoids (7
_b_) in which the three contained spheres have, respectively, two, five,
and two atoms. The central globe is double, globe within globe, and is
divided into eight segments, radiating from the centre like an orange; the
internal part of the segment belonging to the inner globe has a triangular
body within it, containing four atoms (7 _c_), and the external part,
belonging to the encircling globe, shows the familiar "cigar" (7 _d_). In
this way 720 atoms are packed into the simple beryllium type.
CALCIUM: 4 funnels of 160 atoms 640
Central globe 80
----
Total 720
----
Atomic weight 39.74
Number weight 720/18 40.00
STRONTIUM (Plate VIII, 3) shows a still further complication within the
funnels, no less than eight spheres being found within each. Each of the
highest pair contains four subsidiary spheres, with five, seven, seven,
five atoms, respectively (7 _e_, _g_, _f_). The _g_ groups are identical
with those in gold, but difference of pressure makes the containing body
spherical instead of ovoid; similar groups are seen in the top ring of the
iodine funnel, where also the "hole" is ovoid in form. The second pair of
spheres contains ten ovoids (7 _b_) identical with those of calcium. The
third pair contains fourteen ovoids (7 _a_) identical with those of
beryllium, while the fourth pair repeats the second, with the ovoids
re-arranged. The internal divisions of the double sphere of the central
globe are the same as in calcium, but the contents differ. The "cigars" in
the external segments are replaced by seven-atomed ovoids (7 _h_)--the
iodine ovoids--and the external segments contain five-atomed triangles (7
_i_). Thus 1,568 atoms have been packed into the beryllium type, and our
wonder is again aroused by the ingenuity with which a type is preserved
while it is adapted to new conditions.
STRONTIUM: 4 funnels of 368 atoms 1472
Central globe 96
----
Total 1568
----
Atomic weight 86.95
Number weight 1568/18 87.11
The corresponding group, headed by oxygen--oxygen, chromium, molybdenum,
wolfram and uranium--offers us another problem in its first member.
OXYGEN (Plate VIII, 4). This was examined by us in 1895, and the
description may be reproduced here with a much improved diagram of its very
peculiar constitution. The gaseous atom is an ovoid body, within which a
spirally-coiled snake-like body revolves at a high velocity, five brilliant
points of light shining on the coils. The appearance given in the former
diagram will be obtained by placing the five septets on one side on the top
of those on the other, so that the ten become in appearance five, and thus
doubling the whole, the doubling point leaving eleven duads on each side.
The composition is, however, much better seen by flattening out the whole.
On the proto level the two snakes separate and are clearly seen.
OXYGEN: Positive snake
{ 55 spheres of 2 atoms }
{ + 5 disks of 7 atoms } 145
Negative snake " 145
----
Total 290
----
Atomic weight 15.87
Number weight 290/18 16.11
CHROMIUM (Plate VIII, 5) "reverts to the ancestral type," the tetrahedron;
the funnel is widened by the arrangement of its contents, three spheres
forming its first ring, as compared with the units in beryllium and
calcium, and the pairs in strontium and molybdenum. Two of these spheres
are identical in their contents--two quintets (7 _f_), a quintet (7 _j_),
and two quintets (7 _e_), _e_ and _f_ being to each other as object and
image. The remaining sphere (7 _b_) is identical with the highest in the
calcium funnel. The remaining two spheres, one below the other, are
identical with the corresponding two spheres in calcium. The central globe,
as regards its external segments, is again identical with that of calcium,
but in the internal segments a six-atomed triangle (7 _k_) is substituted
for the calcium four-atomed one (7 _e_).
CHROMIUM: 4 funnels of 210 atoms 840
Central globe 96
-----
Total 936
-----
Atomic weight 51.74
Number weight 936/18 52.00
MOLYBDENUM (Plate VIII, 6) very closely resembles strontium, differing from
it only in the composition of the highest pair of spheres in the funnels
and in the presence of a little sphere, containing two atoms only, in the
middle of the central globe. The topmost spheres contain no less than eight
subsidiary spheres within each; the highest of these (7 _e_) has four atoms
in it; the next three have four, seven and four (7 _e_ _g_ _e_),
respectively; the next three are all septets (7 _g_), and the last has
four--making in all for these two spheres 88 atoms, as against the 48 in
corresponding spheres of strontium, making a difference of 160 in the four
funnels.
MOLYBDENUM: 4 funnels of 408 atoms 1632
Central globe 98
-----
Total 1730
-----
Atomic weight 95.26
Number weight 1730/18 96.11
II a.--This group contains magnesium, zinc, cadmium, and mercury, with an
empty disk between cadmium and mercury; we did not examine mercury. All are
diatomic, diamagnetic and positive; the corresponding group consists of
sulphur, selenium and tellurium, also all diatomic and diamagnetic, but
negative. The same characteristics of four funnels opening on the faces of
a tetrahedron are found in all, but magnesium and sulphur have no central
globe, and in cadmium and tellurium the globe has become a cross.
[Illustration: PLATE IX.]
MAGNESIUM (Plate IX, 1) introduces us to a new arrangement: each group of
three ovoids forms a ring, and the three rings are within a funnel; at
first glance, there are three bodies in the funnel; on examination each of
these is seen to consist of three, with other bodies, spheres, again within
them. Apart from this, the composition is simple enough, all the ovoids
being alike, and composed of a triplet, a septet and a duad.
MAGNESIUM: 4 funnels of 108 atoms 432
Atomic weight 24.18
Number weight 432/18 24.00
ZINC (Plate IX, 2) also brings a new device: the funnel is of the same type
as that of magnesium, while septets are substituted for the triplets, and
36 additional atoms are thus slipped in. Then we see four spikes,
alternating with the funnels and pointing to the angles, each adding 144
atoms to the total. The spikes show the ten-atomed triangle, already met
with in other metals, three very regular pillars, each with six spheres,
containing two, three, four, four, three, two atoms, respectively. The
supporting spheres are on the model of the central globe, but contain more
atoms. Funnels and spikes alike radiate from a simple central globe, in
which five contained spheres are arranged crosswise, preparing for the
fully developed cross of cadmium. The ends of the cross touch the bottoms
of the funnels.
ZINC: 4 funnels of 144 atoms 576
4 spikes of 144 atoms 576
Central globe 18
-----
Total 1170
-----
Atomic weight 64.91
Number weight 1170/18 65.00
CADMIUM (Plate IX, 3) has an increased complexity of funnels; the diagram
shows one of the three similar segments which lie within the funnels as
cylinders; each of these contains four spheres, three pillars and three
ovoids, like the spike of zinc turned upside down, and the zinc ten-atomed
triangle changed into three ten-atomed ovoids. The centre-piece is a new
form, though prefigured in the central globe of zinc.
CADMIUM: 3 segments of 164 atoms = 492
4 funnels of 492 atoms 1968
Central body 48
-----
Total 2016
-----
Atomic weight 111.60
Number weight 2016/18 112.00
The corresponding negative group is headed by
[Illustration: PLATE X.]
SULPHUR (Plate X, 1), which, like magnesium, has no central globe, and
consists simply of the zinc funnels, much less compressed than zinc but the
same in composition.
SULPHUR: 4 funnels of 144 atoms 576
Atomic weight 31.82
Number weight 576/18 32.00
SELENIUM (Plate X, 2) is distinguished by the exquisite peculiarity,
already noticed, of a quivering star, floating across the mouth of each
funnel, and dancing violently when a ray of light falls upon it. It is
known that the conductivity of selenium varies with the intensity of the
light falling upon it, and it may be that the star is in some way connected
with its conductivity. It will be seen that the star is a very complicated
body, and in each of its six points the two five-atomed spheres revolve
round the seven-atomed cone. The bodies in the funnels resemble those in
magnesium, but a reversed image of the top one is interposed between itself
and the small duad, and each pair has its own enclosure. The central globe
is the same as that of zinc.
SELENIUM: 4 funnels of 198 atoms 792
4 stars of 153 atoms 612
Central globe 18
-----
Total 1422
-----
Atomic weight 78.58
Number weight 1422/18 79.00
TELLURIUM (Plate X, 3), it will be seen, closely resembles cadmium, and has
three cylindrical segments--of which one is figured--making up the funnel.
The contained bodies in the pillars run three, four, five, four, three,
two, instead of starting with two; and a quartet replaces a duad in the
globes above. The central cross only differs from that of cadmium in having
a seven-atomed instead of a four-atomed centre. So close a similarity is
striking.
TELLURIUM: 3 segments of 181 atoms = 543
4 funnels of 543 atoms 2172
Central body 51
-----
Total 2223
-----
Atomic weight 126.64
Number weight 2223/18 123.50
* * * * *
V.
We must now consider the ways in which the members of the tetrahedral
groups break up, and as we proceed with this study we shall find how
continual are the repetitions, and how Nature, with a limited number of
fundamental methods, creates by varied combinations her infinite variety of
forms.
BERYLLIUM (Plate III, 2, and VIII, 1).
[Illustration]
Beryllium offers us four similar funnels and a central globe, and the
proto-elements consist of these five bodies, set free. The funnel, released
from pressure, assumes a spherical form, with its four ovoids spinning
within it, and the central globe remains a sphere, containing a whirling
cross. On the meta level, the ovoids are set free, and two from each funnel
are seen to be positive, two negative--sixteen bodies in all, _plus_ the
cross, in which the resultant force-lines are changed, preparatory to its
breaking into two duads on the hyper level. On that level, the decades
disintegrate into two triplets and a quartet, the positive with the
depressions inward, the negative with the depressions outward.
CALCIUM (Plate VIII, 2).
The funnels, as usual, assume a spherical form on the proto level, and
show, in each case, three spheres containing ovoids. These spheres, still
on the proto level, break free from their containing funnel, as in the case
of gold (p. 49), twelve bodies being thus liberated, while the central
globe breaks up into eight segments, each of which becomes globular, and
contains within it a "cigar" and a somewhat heart-shaped body. Four
spheres, each containing seven ten-atomed ovoids, are identical with those
in beryllium, and can be followed in its diagram. Eight spheres, each
containing five nine-atomed ovoids of a different type, set free, on the
meta level, eighty duads--forty positive and forty negative--and forty
quintets, which are identical with those in chlorine. On the hyper level,
the duads become single atoms, within a sphere, and the central atom from
the quintet is also set free, one hundred and twenty in all. The remaining
four atoms of the quintet divide into two duads.
The central globe, dividing into eight, becomes eight six-atomed spheres on
the meta, the "cigar" behaving as usual, four "cigars" being positive and
four negative, and becoming dissociated into triplets; the four atoms
within the heart-shaped body appear as a tetrahedron, remain together on
the meta level, and break up into duads on the hyper.
STRONTIUM (PLATE VIII, 3).
The third member of this group repeats the _a_ groups of beryllium and the
_b_ groups of calcium, and they dissociate into the bodies already
described under these respectively. The two upper globes in each funnel
repeat each other, but each globe contains four smaller spheres showing
three varieties of forms. The two marked _g_, which are repeated in the
central globe as _h_, are seven-atomed, and appear as spheres or ovoids
according to pressure. They are figured on p. 48, under iodine; _e_ and _f_
are related as object and image, and we have already seen them in copper
(pp. 38 and 48); in each case, as in copper, they unite into a ten-atomed
figure; on the meta level the pair of fours form a ring, and the remaining
two atoms form a duad; _i_, which repeats _f_, makes a ring with the fifth
in the centre, as in the five-atomed _b_ of calcium, as shown above. There
is, thus, nothing new in strontium, but only repetitions of forms already
studied.
OXYGEN (PLATE VIII, 4).
[Illustration]
The disintegration of oxygen as given in 1895 may be repeated here, and the
better presentation given on p. 54 renders it easier to follow the process.
On the proto level the two "snakes" divide; the brilliant disks are
seven-atomed, but are differently arranged, the positive snake having the
atoms arranged as in the iodine ovoids, whereas the negative snake has them
arranged as in a capital H. The snakes show the same extraordinary activity
on the proto level as on the gaseous, twisting and writhing, darting and
coiling. The body of the snake is of two-atomed beads, positive and
negative. On the meta level the snakes break into ten fragments, each
consisting of a disk, with six beads on one side and five on the other,
remaining as lively as the original snake. They shiver into their
constituent disks, and beads on the hyper level, there yielding the ten
disks, five positive and five negative, and the 110 beads, fifty-five
positive and fifty-five negative.
CHROMIUM (PLATE VIII, 5).
When we go on to chromium and molybdenum, we return to our familiar funnels
and central globes, and the secondary spheres within the funnels--quickly
set free, as before, on the proto level--give us no new combinations in
their contained spheres and ovoids. The _a_ of beryllium, the _b_ of
calcium and strontium, and _d_ of calcium, the _e_ and _f_ of strontium,
are all there; _j_ in chromium is the same as the central sphere in the _b_
ovoid. In the central globe, _k_, is a pair of triangles as in hydrogen,
consisting of only six atoms, which on the meta level revolve round each
other, and break up into two duads and two units on the hyper.
MOLYBDENUM (PLATE VIII, 6).
Molybdenum presents us with only two new forms, and these are merely
four-atomed tetrahedra, occurring in pairs as object and image. All the
other bodies have already been analysed.
II a.--We come now to the second great tetrahedral group, which though very
much complicated, is yet, for the most part, a repetition of familiar
forms.
MAGNESIUM (PLATE IX, 1).
[Illustration]
We are still among tetrahedra, so have to do with four funnels, but each
funnel contains three rings, and each ring three ovoids; on the proto level
a triple dissociation takes place, for the funnels let free the rings as
large spheres, in each of which rotate three twelve-atomed ovoids, and then
the ovoids break loose from the spheres, and themselves become spherical,
so that we have finally thirty-six proto compounds from the tetrahedron. On
the meta level the contained bodies, a triplet, Mg _a_, a septet, Mg _b_,
and a duad, Mg _c_, are set free from each globe, thus yielding one hundred
and eight meta compounds. On the hyper level the triplet becomes a duad and
a unit; the duad becomes two units; and the septet a triplet and a quartet.
ZINC (PLATE IX, 2).
We can leave aside the funnel, for the only difference between it and the
magnesium funnel is the substitution of a second septet for the triplet,
and the septet is already shown in the magnesium diagram. We have,
therefore, only to consider the spikes, pointing to the angles of the
enclosing tetrahedron, and the central globe. These are set free on the
proto level and the spikes immediately release their contents, yielding
thus thirty-two separate bodies.
The triangular arrangement at the top of the spike is the same as occurs in
copper (_b_ on p. 48), and can be there followed. One of the three similar
pillars is shown in the accompanying diagram under Zn a. The compressed
long oval becomes a globe, with six bodies revolving within it in a rather
peculiar way: the quartets turn round each other in the middle; the
triplets revolve round them in a slanting ellipse; the duads do the same on
an ellipse slanting at an angle with the first, somewhat as in gold (_a_
and _b_, p. 40). The spheres within the globes at the base of the spikes,
Zn _b_, behave as a cross--the cross is a favourite device in the II _a_
groups. Finally, the central globe, Zn _c_, follows the same cruciform line
of disintegration.
CADMIUM (Plate IX, 3).
[Illustration]
Cadmium follows very closely on the lines of zinc; the pillars of the zinc
spike are reproduced in the rings of the cadmium funnel; the globes are
also the globes of cadmium; so neither of these needs attention. We have
only to consider the three ten-atomed ovoids, which are substituted for the
one ten-atomed triangle of zinc, and the central cross. The ovoids become
spheres (Cd _a_, _b_), the contained bodies revolving within them, _a_
whirling on a diameter of the sphere, cutting it in halves, as it were, and
_b_ whirling round it at right angles; the cross also becomes a sphere (Cd
_c_), but the cruciform type is maintained within it by the relative
positions of the contained spheres in their revolution. The subsequent
stages are shown in the diagram.
SULPHUR (Plate XI, 1).
Sulphur has nothing new, but shows only the funnels already figured in
magnesium, with the substitution of a second septet for the triplet, as in
zinc.
SELENIUM (Plate X, 2).
[Illustration]
The funnel of selenium is a re-arrangement of the twelve-atomed ovoids of
magnesium and the ten-atomed ovoids of cadmium. The funnels, on
disintegrating, set free twelve groups, each containing nine spheres. On
the meta level the ten-atomed bodies are set free, and the twelve-atomed
divide into duads and decads, thus yielding seventy-two decads and
thirty-six duads; the duads, however, at once recombine into hexads, thus
giving only twelve meta elements, or eighty-four in all from the funnels.
The central globe holds together on the proto level, but yields five meta
elements. The star also at first remains a unit on the proto level, and
then shoots off into seven bodies, the centre keeping together, and the six
points becoming spheres, within which the two cones, base to base, whirl in
the centre, and the globes circle round them. On the meta level all the
thirty bodies contained in the star separate from each other, and go on
their independent ways.
Selenium offers a beautiful example of the combination of simple elements
into a most exquisite whole.
TELLURIUM (Plate X, 3).
Tellurium very closely resembles cadmium, and they are, therefore placed on
the same diagram. The pillars are the same as in chlorine and its
congeners, with a duad added at the base. The ten-atomed ovoid is the same
as in cadmium and follows the same course in breaking up. It would be
interesting to know why this duad remains as a duad in selenium and breaks
up into a septad and triad in the other members of the group. It may be due
to the greater pressure to which it is subjected in selenium, or there may
be some other reason. The cross in tellurium is identical with that in
cadmium, except that the centre is seven-atomed instead of four-atomed.
* * * * *
VI.
III AND IIIa.--THE CUBE GROUPS.
We have here four groups to consider, all the members of which are triads,
and have six funnels, opening on the six faces of a cube.
III.--Boron, scandium and yttrium were examined; they are all triatomic,
paramagnetic, and positive. The corresponding group consists of nitrogen,
vanadium and niobium; they are triatomic, paramagnetic, and negative. We
have not examined the remaining members of these groups. In these two
groups nitrogen dominates, and in order to make the comparison easy the
nitrogen elements are figured on both Plate XI and Plate XII. It will be
seen that scandium and yttrium, of the positive group, differ only in
details from vanadium and niobium, of the negative group; the ground-plan
on which they are built is the same. We noted a similar close resemblance
between the positive strontium and the negative molybdenum.
[Illustration: PLATE XI.]
BORON (Plate III, 4, and Plate XI, 1). We have here the simplest form of
the cube; the funnels contain only five bodies--four six-atomed ovoids and
one six-atomed "cigar." The central globe has but four five-atomed spheres.
It is as simple in relation to its congeners as is beryllium to its
group-members.
BORON: 6 funnels of 30 atoms 180
Central globe 20
----
Total 200
----
Atomic weight 10.86
Number weight 200/18 11.11
SCANDIUM (Plate XI, 2). For the first time we meet funnels of different
types, A and B, three of each kind; A appear to be positive and B negative,
but this must be stated with reserve.
In A the boron funnel is reproduced, the "cigar" having risen above its
companion ovoids; but the most important matter to note in respect to this
funnel is our introduction to the body marked _a_ 110. This body was
observed by us first in nitrogen, in 1895, and we gave it the name of the
"nitrogen balloon," for in nitrogen it takes the balloon form, which it
also often assumes in other gaseous elements. Here it appears as a
sphere--the form always assumed on the proto level--and it will be seen, on
reference to the detailed diagram 4 _a_, to be a complicated body,
consisting of six fourteen-atomed globes arranged round a long ovoid
containing spheres with three, four, six, six, four, three, atoms
respectively. It will be observed that this balloon appears in every member
of these two groups, except boron.
The B funnel runs largely to triads, _c_ and _b_, _b_ (see 4 _b_) having
not only a triadic arrangement of spheres within its contained globes, but
each sphere has also a triplet of atoms. In _c_ (see 4 _c_) there is a
triadic arrangement of spheres, but each contains duads. B is completed by
a five-atomed sphere at the top of the funnel. It should be noted that _a_,
_b_ and _c_ all are constituents of nitrogen.
The central globe repeats that of boron, with an additional four-atomed
sphere in the middle.
SCANDIUM: 3 funnels (A) of 140 atoms 420
3 " (B) of 116 " 348
Centre globe 24
----
Total 792
----
Atomic weight 43.78
Number weight 792/18 44.00
YTTRIUM (Plate XI, 3). Here we have a quite new arrangement of bodies
within the funnel--the funnel being of one type only. Two "cigars" whirl on
their own axes in the centre near the top, while four eight-atomed globes
(see 4 _e_) chase each other in a circle round them, spinning madly on
their own axes--this axial spinning seems constant in all contained
bodies--all the time. Lower down in the funnel, a similar arrangement is
seen, with a globe (see 4 _d_)--a nitrogen element--replacing the "cigars,"
and six-atomed ovoids replacing the globes.
The "nitrogen balloon" occupies the third place in the funnel, now showing
its usual shape in combination, while the _b_ globe (see 4 _b_) of scandium
takes on a lengthened form below it.