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Title: Occult Chemistry: Clairvoyant Observations on the Chemical
Elements

Author: Annie Besant
C. W. Leadbeater

Editor: A. P. Sinnett

Release date: June 14, 2005 [eBook #16058]
Most recently updated: December 11, 2020

Language: English

Other information and formats: www.gutenberg.org/ebooks/16058

Credits: E-text prepared by Clare Boothby, Keith Edkins, and the Project
Gutenberg Online Distributed Proofreading Team

*** START OF THE PROJECT GUTENBERG EBOOK OCCULT
CHEMISTRY: CLAIRVOYANT OBSERVATIONS ON THE CHEMICAL
ELEMENTS ***

E-text prepared by Clare Boothby, Keith Edkins,
and the Project Gutenberg Online Distributed Proofreading Team

OCCULT CHEMISTRY

Clairvoyant Observations on the
Chemical Elements

BY

ANNIE BESANT, p.t.s.

AND

CHARLES W. LEADBEATER

Revised Edition edited by A.P. Sinnett

London

THEOSOPHICAL PUBLISHING HOUSE

1, Upper Woburn Place, W.C. 1.

1919

EDITOR'S PREFACE.

When undertaking to prepare a new edition of this book I received
permission from the authors to "throw it into the form in which you think it
would be most useful at the present time." It was left to my discretion,
"What to use and what to omit." I have not found it necessary to avail
myself to any considerable extent of this latter permission. But as the
contents of the book were originally arranged the reader was ill-prepared to
appreciate the importance of the later research for want of introductory
matter explaining how it began, and how the early research led up to the
later investigation. I have therefore contributed an entirely new preliminary
chapter which will, I hope, help the reader to realise the credibility of the
results attained when the molecular forms and constitution of the numerous
bodies examined were definitely observed. I have not attempted to revise
the records of the later research in which I had no personal share, so from
the beginning of Chapter III to the end the book in its present form is
simply a reprint of the original edition except for the correction of a few
trifling misprints.
I have thus endeavoured to bring into clear prominence at the outset the
scientific value of the light the book sheds on the constitution of matter. The
world owes a debt to scientific men of the ordinary type that cannot be
over-estimated, but though they have hitherto preferred to progress
gradually, from point to point, disliking leaps in the dark, the leap now
made is only in the dark for those who will not realise that the progress to
be accomplished by means of instrumental research must sooner or later be
supplemented by subtler methods. Physical science has reached the
conception that the atoms of the bodies hitherto called the chemical
elements are each composed of minor atoms. Instrumental research cannot
determine by how many, in each case. Occult research ascertained the
actual number in some cases by direct observation and then discovered the
law governing the numbers in all cases, and the relation of these numbers to
atomic weights. The law thus unveiled is a demonstration of the accuracy of
the first direct observations, and this principle once established the
credibility of accounts now given as to the arrangement of minor atoms in

the molecules of the numerous elements examined, seems to me advanced
to a degree approximating to proof.
It remains to be seen—not how far, but rather how soon the scientific world
at large will accept the conclusions of this volume as a definite contribution
to science, blending the science of the laboratory with that variety that has
hitherto been called occult.

CONTENTS.

I.—A Preliminary Survey

II.—Details of the Early Research

The Platonic Solids

III.—The Later Researches

OCCULT CHEMISTRY.
CHAPTER I.

A PRELIMINARY SURVEY.

The deep interest and importance of the research which this book describes
will best be appreciated if introduced by an account of the circumstances
out of which it arose. The first edition, consisting mainly of articles
reprinted from the Theosophist, dealt at once with the later phases of the
research in a way which, though intelligible to the occult student, must have
been rather bewildering to the ordinary reader. These later phases, however,
endow the earlier results with a significance that in the beginning could
only be vaguely conjectured. I am the better entitled to perform the task that
has been assigned to me—that of preparing the present edition—by reason
of the fact that it was in my presence and at my instigation that the first
efforts were made to penetrate the mystery previously enshrouding the
ultimate molecule of matter.
I remember the occasion vividly. Mr. Leadbeater was then staying at my
house, and his clairvoyant faculties were frequently exercised for the
benefit of myself, my wife and the theosophical friends around us. I had
discovered that these faculties, exercised in the appropriate direction, were
ultra-microscopic in their power. It occurred to me once to ask Mr.
Leadbeater if he thought he could actually see a molecule of physical
matter. He was quite willing to try, and I suggested a molecule of gold as
one which he might try to observe. He made the appropriate effort, and
emerged from it saying the molecule in question was far too elaborate a
structure to be described. It evidently consisted of an enormous number of
some smaller atoms, quite too many to count; quite too complicated in their
arrangement to be comprehended. It struck me at once that this might be
due to the fact that gold was a heavy metal of high atomic weight, and that
observation might be more successful if directed to a body of low atomic
weight, so I suggested an atom of hydrogen as possibly more manageable.

Mr. Leadbeater accepted the suggestion and tried again. This time he found
the atom of hydrogen to be far simpler than the other, so that the minor
atoms constituting the hydrogen atom were countable. They were arranged
on a definite plan, which will be rendered intelligible by diagrams later on,
and were eighteen in number.
We little realized at the moment the enormous significance of this
discovery, made in the year 1895, long before the discovery of radium
enabled physicists of the ordinary type to improve their acquaintance with
the "electron." Whatever name is given to that minute body it is recognised
now by ordinary science as well as by occult observation, as the
fundamental unit of physical matter. To that extent ordinary science has
overtaken the occult research I am dealing with, but that research rapidly
carried the occult student into regions of knowledge whither, it is perfectly
certain, the ordinary physicist must follow him at no distant date.
The research once started in the way I have described was seen to be
intensely interesting. Mrs. Besant almost immediately co-operated with Mr.
Leadbeater in its further progress. Encouraged by the success with
hydrogen, the two important gases, oxygen and nitrogen, were examined.
They proved to be rather more difficult to deal with than hydrogen but were
manageable. Oxygen was found to consist of 290 minor atoms and nitrogen
of 261. Their grouping will be described later on. The interest and
importance of the whole subject will best be appreciated by a rough
indication of the results first attained. The reader will then have more
patience in following the intricacies of the later discoveries.
The figures just quoted were soon perceived to have a possible significance.
The atomic weight of oxygen is commonly taken as 16. That is to say, an
atom of oxygen is sixteen times heavier than an atom of hydrogen. In this
way, all through the table of atomic weights, hydrogen is taken as unity,
without any attempt being made to estimate its absolute weight. But now
with the atom of hydrogen dissected, so to speak, and found to consist of 18
somethings, while the atom of oxygen consisted of 290 of the same things,
the sixteen to one relationship reappears: 290 divided by 18 gives us 16 and
a minute decimal fraction. Again the nitrogen number divided by 18 gives
us 14 and a minute fraction as the result, and that is the accepted atomic
weight of nitrogen. This gave us a glimpse of a principle that might run all

through the table of atomic weights. For reasons having to do with other
work, it was impossible for the authors of this book to carry on the research
further at the time it was begun. The results already sketched were
published as an article in the magazine then called Lucifer, in November,
1895, and reprinted as a separate pamphlet bearing the title "Occult
Chemistry," a pamphlet the surviving copies of which will one day be a
recognised vindication of the method that will at some time in the future be
generally applied to the investigation of Nature's mysteries. For the later
research which this volume deals with does establish the principle with a
force that can hardly be resisted by any fair-minded reader. With patience
and industry—the authors being assisted in the counting in a way that will
be described (and the method adopted involved a check upon the accuracy
of the counting)—the minor atoms of almost all the known chemical
elements, as they are commonly called, were counted and found to bear the
same relation to their atomic weights as had been suggested by the cases of
oxygen and nitrogen. This result throws back complete proof on the original
estimate of the number of minor atoms in hydrogen, a figure which ordinary
research has so far entirely failed to determine. The guesses have been
widely various, from unity to many hundreds, but, unacquainted with the
clairvoyant method, the ordinary physicist has no means of reaching the
actual state of the facts.
Before going on with the details of the later research some very important
discoveries arising from the early work must first be explained. As I have
already said clairvoyant faculty of the appropriate order directed to the
minute phenomena of Nature is practically infinite in its range. Not content
with estimating the number of minor atoms in physical molecules, the
authors proceeded to examine the minor atoms individually. They were
found to be themselves elaborately complicated structures which, in this
preliminary survey of the whole subject, I will not stop to explain (full
explanation will be found later on) and they are composed of atoms
belonging to an ultra-physical realm of Nature with which the occultist has
long been familiar and describes as "the Astral Plane." Some rather pedantic
critics have found fault with the term, as the "plane" in question is of course
really a sphere entirely surrounding the physical globe, but as all occultists
understand the word, "plane" simply signifies a condition of nature. Each
condition, and there are many more than the two under consideration,

blends with its neighbour, via atomic structure. Thus the atoms of the Astral
plane in combination give rise to the finest variety of physical matter, the
ether of space, which is not homogeneous but really atomic in its character,
and the minute atoms of which physical molecules are composed are atoms
of ether, "etheric atoms," as we have now learned to call them.
Many physicists, though not all, will resent the idea of treating the ether of
space as atomic. But at all events the occultist has the satisfaction of
knowing that the great Russian chemist, Mendeleef, preferred the atomic
theory. In Sir William Tilden's recent book entitled "Chemical Discovery
and Invention in the Twentieth Century," I read that Mendeleef,
"disregarding conventional views," supposed the ether to have a molecular
or atomic structure, and in time all physicists must come to recognise that
the Electron is not, as so many suppose at present, an atom of electricity,
but an atom of ether carrying a definite unit charge of electricity.
Long before the discovery of radium led to the recognition of the electron
as the common constituent of all the bodies previously described as
chemical elements, the minute particles of matter in question had been
identified with the cathode rays observed in Sir William Crookes' vacuum
tubes. When an electric current is passed through a tube from which the air
(or other gas it may contain) has been almost entirely exhausted, a luminous
glow pervades the tube manifestly emanating from the cathode or negative
pole of the circuit. This effect was studied by Sir William Crookes very
profoundly. Among other characteristics it was found that, if a minute
windmill was set up in the tube before it was exhausted, the cathode ray
caused the vanes to revolve, thus suggesting the idea that they consisted of
actual particles driven against the vanes; the ray being thus evidently
something more than a mere luminous effect. Here was a mechanical
energy to be explained, and at the first glance it seemed difficult to
reconcile the facts observed with the idea creeping into favour, that the
particles, already invested with the name "electron," were atoms of
electricity pure and simple. Electricity was found, or certain eminent
physicists thought they had found, that electricity per se had inertia. So the
windmills in the Crookes' vacuum tubes were supposed to be moved by the
impact of electric atoms.

Then in the progress of ordinary research the discovery of radium by
Madame Curie in the year 1902 put an entirely new face upon the subject of
electrons. The beta particles emanating from radium were soon identified
with the electrons of the cathode ray. Then followed the discovery that the
gas helium, previously treated as a separate element, evolved itself as one
consequence of the disintegration of radium. Transmutation, till then
laughed at as a superstition of the alchemist, passed quietly into the region
of accepted natural phenomena, and the chemical elements were seen to be
bodies built up of electrons in varying number and probably in varying
arrangements. So at last ordinary science had reached one important result
of the occult research carried on seven years earlier. It has not yet reached
the finer results of the occult research—the structure of the hydrogen atom
with its eighteen etheric atoms and the way in which the atomic weights of
all elements are explained by the number of etheric atoms entering into
their constitution.
The ether of space, though defying instrumental examination, comes within
scope of the clairvoyant faculty, and profoundly interesting discoveries
were made during what I have called the early research in connexion with
that branch of the inquiry. Etheric atoms combine to form molecules in
many different ways, but combinations involving fewer atoms than the
eighteen which give rise to hydrogen, make no impression on the physical
senses nor on physical instruments of research. They give rise to varieties of
molecular ether, the comprehension of which begins to illuminate realms of
natural mystery as yet entirely untrodden by the ordinary physicist.
Combinations below 18 in number give rise to three varieties of molecular
ether, the functions of which when they come to be more fully studied will
constitute a department of natural knowledge on the threshold of which we
already stand. Some day we may perhaps be presented with a volume on
Occult Physics as important in its way as the present dissertation on Occult
Chemistry.

CHAPTER II.

DETAILS OF THE EARLY RESEARCH.

The article detailing the results of the research carried on in the year 1895
(see the November issue for that year of the magazine then called Lucifer),
began with some general remarks about the clairvoyant faculty, already
discussed in the preceding chapter. The original record then goes on as
follows:—
The physical world is regarded as being composed of between sixty and
seventy chemical elements, aggregated into an infinite variety of
combinations. These combinations fall under the three main heads of solids,
liquids and gases, the recognised substates of physical matter, with the
theoretical ether scarcely admitted as material. Ether, to the scientist, is not
a substate or even a state of matter, but is a something apart by itself. It
would not be allowed that gold could be raised to the etheric condition as it
might be to the liquid and gaseous; whereas the occultist knows that the
gaseous is succeeded by the etheric, as the solid is succeeded by the liquid,
and he knows also that the word "ether" covers four substates as distinct
from each other as are the solids, liquids and gases, and that all chemical
elements have their four etheric substates, the highest being common to all,
and consisting of the ultimate physical atoms to which all elements are
finally reducible. The chemical atom is regarded as the ultimate particle of
any element, and is supposed to be indivisible and unable to exist in a free
state. Mr. Crookes' researches have led the more advanced chemists to
regard the atoms as compound, as a more or less complex aggregation of
protyle.
To astral vision ether is a visible thing, and is seen permeating all
substances and encircling every particle. A "solid" body is a body composed
of a vast number of particles suspended in ether, each vibrating backwards
and forwards in a particular field at a high rate of velocity; the particles are
attracted towards each other more strongly than they are attracted by
external influences, and they "cohere," or maintain towards each other a
definite relation in space. Closer examination shows that the ether is not
homogeneous but consists of particles of numerous kinds, differing in the
aggregations of the minute bodies composing them; and a careful and more
detailed method of analysis reveals that it has four distinct degrees, giving
us, with the solid, liquid and gaseous, seven instead of four substates of
matter in the physical world.

These four etheric substates will be best understood if the method be
explained by which they were studied. This method consisted of taking
what is called an atom of gas, and breaking it up time after time, until what
proved to be the ultimate physical atom was reached, the breaking up of this
last resulting in the production of astral, and no longer physical matter.
It is, of course, impossible to
convey by words the clear
conceptions that are gained by
direct vision of the objects of
study, and the accompanying
diagram—cleverly drawn from
the description given by the
investigators—is offered as a
substitute, however poor, for the
lacking vision of the readers. The
horizontal lines separate from
each other the seven substates of
matter; solid, liquid, gas, ether 4,
ether 3, ether 2, ether 1. On the
gas level are represented three
chemical atoms, one of hydrogen
(H), one of oxygen (O), one of
nitrogen (N). The successive
changes undergone by each
chemical atom are shown in the
compartments vertically above it,
the left-hand column showing the
breaking up of the hydrogen
atom, the middle column that of
the oxygen atom, the right-hand
column, that of the nitrogen atom.
The ultimate physical atom is
marked a, and is drawn only
once, although it is the same
throughout. The numbers 18, 290

and 261 are the numbers of the ultimate physical atoms found to exist in a
chemical atom.
The dots indicate the lines along which force is observed to be playing, and
the arrowheads show the direction of the force. No attempt has been made
to show this below E 2 except in the case of the hydrogen. The letters given
are intended to help the reader to trace upwards any special body; thus d in
the oxygen chemical atom on the gas level may be found again on E 4, E 3,
and E 2. It must be remembered that the bodies shown diagrammatically in
no way indicate relative size; as a body is raised from one substate to the
one immediately above it, it is enormously magnified for the purpose of
investigation, and the ultimate atom on E 1 is represented by the dot a on
the gaseous level.
The first chemical atom selected for this examination was an atom of
hydrogen (H). On looking carefully at it, it was seen to consist of six small
bodies, contained in an egg-like form. It rotated with great rapidity on its
own axis, vibrating at the same time, and the internal bodies performed
similar gyrations. The whole atom spins and quivers, and has to be steadied
before exact observation is possible. The six little bodies are arranged in
two sets of three, forming two triangles that are not interchangeable, but are
related to each other as object and image. (The lines in the diagram of it on
the gaseous sub-plane are not lines of force, but show the two triangles; on
a plane surface the interpenetration of the triangles cannot be clearly
indicated.) Further, the six bodies are not all alike; they each contain three
smaller bodies—each of these being an ultimate physical atom—but in two
of them the three atoms are arranged in a line, while in the remaining four
they are arranged in a triangle.
The wall of the limiting spheroid in which the bodies are enclosed being
composed of the matter of the third, or gaseous, kind, drops away when the
gaseous atom is raised to the next level, and the six bodies are set free. They
at once re-arrange themselves in two triangles, each enclosed by a limiting
sphere; the two marked b in the diagram unite with one of those marked b'
to form a body which shows a positive character, the remaining three
forming a second body negative in type. These form the hydrogen particles
of the lowest plane of ether, marked E 4—ether 4—on the diagram. On
raising these further, they undergo another disintegration, losing their

limiting walls; the positive body of E 4, on losing its wall, becomes two
bodies, one consisting of the two particles, marked b, distinguishable by the
linear arrangement of the contained ultimate atoms, enclosed in a wall, and
the other being the third body enclosed in E 4 and now set free. The
negative body of E 4 similarly, on losing its wall, becomes two bodies, one
consisting of the two particles marked b', and the second the remaining
body, being set free. These free bodies do not remain on E 3 but pass
immediately to E 2, leaving the positive and negative bodies, each
containing two particles, as the representatives of hydrogen on E 3. On
taking these bodies a step higher their wall disappears, and the internal
bodies are set free, those containing the atoms arranged lineally being
positive, and those with the triangular arrangement being negative. These
two forms represent hydrogen on E 2, but similar bodies of this state of
matter are found entering into other combinations, as may be seen by
referring to f on E 2 of nitrogen (N). On raising these bodies yet one step
further, the falling away of the walls sets the contained atoms free, and we
reach the ultimate physical atom, the matter of E 1. The disintegration of
this sets free particles of astral matter, so that we have reached in this the
limit of physical matter. The Theosophical reader will notice with interest
that we can thus observe seven distinct substates of physical matter, and no
more.
The ultimate atom, which is the same in all the observed cases, is an
exceedingly complex body, and only its main characteristics are given in
the diagram. It is composed entirely of spirals, the spiral being in its turn
composed of spirillæ, and these again of minuter spirillæ. A fairly accurate
drawing is given in Babbitt's "Principles of Light and Colour," p. 102. The
illustrations there given of atomic combinations are entirely wrong and
misleading, but if the stove-pipe run through the centre of the single atom
be removed, the picture may be taken as correct, and will give some idea of
the complexity of this fundamental unit of the physical universe.
Turning to the force side of the atom and its combinations, we observe that
force pours in the heart-shaped depression at the top of the atom, and issues
from the point, and is changed in character by its passage; further, force
rushes through every spiral and every spirilla, and the changing shades of
colour that flash out from the rapidly revolving and vibrating atom depend
on the several activities of the spirals; sometimes one, sometimes another, is

thrown into more energetic action, and with the change of activity from one
spiral to another the colour changes.
The building of a gaseous atom of hydrogen may be traced downward from
E 1, and, as stated above, the lines given in the diagram are intended to
indicate the play of the forces which bring about the several combinations.
Speaking generally, positive bodies are marked by their contained atoms
setting their points towards each other and the centre of their combination,
and repelling each other outwards; negative bodies are marked by the heart-
shaped depressions being turned inwards, and by a tendency to move
towards each other instead of away. Every combination begins by a welling
up of force at a centre, which is to form the centre of the combination; in
the first positive hydrogen combination, E 2, an atom revolving at right
angles to the plane of the paper and also revolving on its own axis, forms
the centre, and force, rushing out at its lower point, rushes in at the
depressions of two other atoms, which then set themselves with their points
to the centre; the lines are shown in +b, right-hand figure. (The left-hand
figure indicates the revolution of the atoms each by itself.) As this atomic
triad whirls round, it clears itself a space, pressing back the undifferentiated
matter of the plane, and making to itself a whirling wall of this matter, thus
taking the first step towards building up the chemical hydrogen atom. A
negative atomic triad is similarly formed, the three atoms being
symmetrically arranged round the centre of out-welling force. These atomic
triads then combine, two of the linear arrangement being attracted to each
other, and two of the triangular, force again welling up and forming a centre
and acting on the triads as on a single atom, and a limiting wall being again
formed as the combination revolves round its centre. The next stage is
produced by each of these combinations on E 3 attracting to itself a third
atomic triad of the triangular type from E 2, by the setting up of a new
centre of up-welling force, following the lines traced in the combinations of
E 4. Two of these uniting, and their triangles interpenetrating, the chemical
atom is formed, and we find it to contain in all eighteen ultimate physical
atoms.
The next substance investigated was oxygen, a far more complicated and
puzzling body; the difficulties of observation were very much increased by
the extraordinary activity shown by this element and the dazzling brilliancy
of some of its constituents. 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 snake appears to be a solid
rounded body, but on raising the atom to E 4 the snake splits lengthwise
into two waved bodies, and it is seen that the appearance of solidity is due
to the fact that these spin round a common axis in opposite directions, and
so present a continuous surface, as a ring of fire can be made by whirling a
lighted stick. The brilliant bodies seen in the atom are on the crests of the
waves in the positive snake, and in the hollows in the negative one; the
snake itself consists of small bead-like bodies, eleven of which interpose
between the larger brilliant spots. On raising these bodies to E 3 the snakes
break up, each bright spot carrying with it six beads on one side and five on
the other; these twist and writhe about still with the same extraordinary
activity, reminding one of fire-flies stimulated to wild gyrations. It can been
seen that the larger brilliant bodies each enclose seven ultimate atoms,
while the beads each enclose two. (Each bright spot with its eleven beads is
enclosed in a wall, accidentally omitted in the diagram.) On the next stage,
E 2, the fragments of the snakes break up into their constituent parts; the
positive and negative bodies, marked d and d', showing a difference of
arrangement of the atoms contained in them. These again finally
disintegrate, setting free the ultimate physical atoms, identical with those
obtained from hydrogen. The number of ultimate atoms contained in the
gaseous atom of oxygen is 290, made up as follows:—

2 in each bead, of which there are 110:
7 in each bright spot, of which there are 10;
2 x 110 + 70 = 290.

When the observers had worked out this, they compared it with the number
of ultimate atoms in hydrogen:—

290 / 18 = 16.11 +

The respective number of ultimate atoms contained in a chemical atom of
these two bodies are thus seen to closely correspond with their accepted
weight-numbers.
It may be said in passing that a chemical atom of ozone appears as an oblate
spheroid, with the contained spiral much compressed and widened in the

centre; the spiral consists of three snakes, one positive and two negative,
formed in a single revolving body. On raising the chemical atom to the next
plane, the snake divides into three, each being enclosed in its own egg.
The chemical atom of nitrogen was the third selected by the students for
examination, as it seemed comparatively quiet in contrast with the ever-
excited oxygen. It proved, however, to be the most complicated of all in its
internal arrangements, and its quiet was therefore a little deceptive. Most
prominent was the balloon-shaped body in the middle, with six smaller
bodies in two horizontal rows and one large egg-shaped one in the midst,
contained in it. Some chemical atoms were seen in which the internal
arrangement of these contained bodies was changed and the two horizontal
rows became vertical; this change seemed to be connected with a greater
activity of the whole body, but the observations on this head are too
incomplete to be reliable. The balloon-shaped body is positive, and is
apparently drawn downwards towards the negative egg-shaped body below
it, containing seven smaller particles. In addition to these large bodies, four
small ones are seen, two positive and two negative, the positive containing
five and the negative four minuter spots. On raising the gaseous atom to
E 4, the falling away of the wall sets free the six contained bodies, and both
the balloon and the egg round themselves, apparently with the removal of
their propinquity, as though they had exercised over each other some
attractive influence. The smaller bodies within the egg—marked q on E 4—
are not on one plane, and those within n and o form respectively square-
based and triangular-based pyramids. On raising all these bodies to E 3 we
find the walls fall away as usual, and the contents of each "cell" are set free:
p of E 4 contains six small bodies marked k, and these are shown in k of
E 3, as containing each seven little bodies—marked e—each of which has
within it two ultimate atoms; the long form of p E 4—marked l—appears as
the long form l on E 3, and this has three pairs of smaller bodies within it, f',
g and h, containing respectively three, four and six ultimate atoms; q of E 4,
with its seven contained particles, m, has three particles m on E 3, each
showing three ultimate atoms within them; e from n of E 4 becomes i of
E 3, with contained bodies, e, showing two ultimate atoms in each; while e'
from o of E 4 becomes j of E 3, each having three smaller bodies within it,
e', with two ultimate atoms in each. On E 2, the arrangement of these
ultimate atoms is shown, and the pairs, f', g and h are seen with the lines of

force indicated; the triads in f—from m of E 3—are similarly shown, and
the duads in e and e'—from i and j of E 3—are given in the same way.
When all these bodies are raised to E 1, the ultimate physical atoms are set
free, identical, of course, with that previously described. Reckoning up the
number of ultimate physical atoms in a chemical atom of nitrogen we find
they amount to 261, thus divided:—

62 + bodies with 2 ultimate atoms, 62 x 2
= 124
24 - " " 2 " " 24 x 2
= 48
21 - " " 3 " " 21 x 3
= 63
2 + " " 3 " " 2 x 3
= 6
2 + " " 4 " " 2 x 4
= 8
2 + " " 4 " " 2 x 6
= 12

----

261

This again approaches closely the weight-number assigned to nitrogen:—

261 / 18 =14.44 +

This is interesting as checking the observations, for weight-numbers are
arrived at in so very different a fashion, and especially in the case of
nitrogen the approximation is noteworthy, from the complexity of the
bodies which yield the number on analysis.
Some other observations were made which went to show that as weight-
numbers increased, there was a corresponding increase in the number of
bodies discerned within the chemical atom; thus, gold showed forty-seven
contained bodies; but these observations need repetition and checking.

Investigation of a molecule of water revealed the presence of twelve bodies
from hydrogen and the characteristic snake of oxygen, the encircling walls
of the chemical atoms being broken away. But here again, further
observations are necessary to substantiate details. The present paper is only
offered as a suggestion of an inviting line of research, promising interesting
results of a scientific character; the observations recorded have been
repeated several times and are not the work of a single investigator, and
they are believed to be correct so far as they go.

THE PLATONIC SOLIDS.

Some of our readers may be glad to have a drawing of the Platonic solids,
since they play so large a part in the building up of elements. The regular
solids are five, and five only; in each:

(1) The lines are equal.
(2) The angles are equal.
(3) The surfaces are equal.

It will be seen that the tetrahedron
is the fundamental form, the
three-sided pyramid on a
triangular base, i.e., a solid figure
formed from four triangles. Two
of these generate the cube and the
octahedron; five of these generate
the dodecahedron and the
icosahedron.
The rhombic dodecahedron is not
regular, for though the lines and
surfaces are equal, the angles are
not.

NOTES.

Mr. C. Jinarâjadâsa[1] writes:

The asterisk put before metargon in the list of elements should be omitted,
for metargon had been discovered by Sir William Ramsey and Mr. Travers
at the same time as neon (see Proceedings of the Royal Society, vol. lxiii, p.
411), and therefore before it was observed clairvoyantly. It is not, however,
given in the latest list of elements in the Report of November 13, 1907, of
the International Atomic Weights Commission, so it would seem as though
it were not yet fully recognised.
Neon was discovered in 1898 by Ramsey and Travers, and the weight given
to it was 22. This almost corresponds with our weight for meta-neon, 22.33;
the latest weight given to neon is 20, and that corresponds within one-tenth
to our weight, 19.9. From this it would seem that neon was examined in the
later investigations and meta-neon in the earlier.
He says further on a probable fourth Interperiodic Group:
Thinking over the diagrams, it seemed to me likely that a fourth group
exists, coming on the paramagnetic side, directly under iron, cobalt, nickel,
just one complete swing of the pendulum after rhodium, ruthenium,
palladium. This would make four interperiodic groups, and they would
come also periodically in the table too.
I took the diagram for Osmium, and in a bar postulated only three columns
for the first element of the new groups, i.e., one column less than in
Osmium. This would make 183 atoms in a bar; the new group then would
follow in a bar, 183, 185, 187. Here I found to my surprise that the third
postulated group would have a remarkable relation to Os, Ir, Pt.
Thus

Os.--245 (in a bar); less 60 =
185
Ir. 247 less 60 =
187
Pt. 249 less 60 =
189

But strange to say also

Ruthenium (bar) 132 less 60--72
Rhodium 134 less 60--74
Palladium 136 less 60--76

But 72, 74, 76, are Iron, Cobalt and Nickel.
So there does probably exist a new group with bars (183), 185, 187, 189,
with atomic weights.

X=bar 185; atoms 2590, wt. 143.3
Y= 187, 2618, wt. 145.4
Z= 189, 2646, wt. 147.0.

They come probably among the rare earths. Probably also Neodymium and
Praseodymium are two of them, for their weights are 143.6, 140.5.

CHAPTER III.

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.
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 Plate I. Sodium.

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
--------------------------------------------

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
PLATE II. MALE (left) and FEMALE (right).
be dealt with presently. After the
third dissociation but one more is
possible; the fourth dissociation gives the ultimate physical atom.[3] This
may vanish from the physical plane, but it can undergo no further
dissociation on it. In this ultimate state of physical matter two types of
atoms have been observed; they are alike in everything save the direction of
their whorls and of the force which pours through them. In the one case
force pours in from the "outside," from fourth-dimensional space,[4] and
passing through the atom, pours into the physical world. In the second, it
pours in from the physical world, and out through the atom into the
"outside" again,[4] i.e., vanishes from the physical world. The one is like a
spring, from which water bubbles out; the other is like a hole, into which
water disappears. We call the atoms from which force comes out positive or
male; those through which it disappears, negative or female. All atoms, so
far as observed, are of one or other of these two forms. (Plate II.)

It will be seen that the atom is a sphere, slightly flattened, and there is a
depression at the point where the force flows in, causing a heart-like form.
Each atom is surrounded by a field, formed of the atoms of the four higher
planes, which surround and interpenetrate it.
The atom can scarcely be said to be a "thing," though it is the material out
of which all things physical are composed. It is formed by the flow of the
life-force[5] and vanishes with its ebb. When this force arises in "space"[6]—
the apparent void which must be filled with substance of some kind, of
inconceivable tenuity—atoms appear; if this be artificially stopped for a
single atom, the atom disappears; there is nothing left. Presumably, were
that flow checked but for an instant, the whole physical world would
vanish, as a cloud melts away in the empyrean. It is only the persistence of
that flow[7] which maintains the physical basis of the universe.[8]
In order to examine the construction of the atom, a space is artificially
made[9]; then, if an opening be made in the wall thus constructed, the
surrounding force flows in, and three whorls immediately appear,
surrounding the "hole" with their triple spiral of two and a half coils, and
returning to their origin by a spiral within the atom; these are at once
followed by seven finer whorls, which following the spiral of the first three
on the outer surface, and returning to their origin by a spiral within that,
flowing in the opposite direction—form a caduceus with the first three.
Each of the three coarser whorls, flattened out, makes a closed circle; each
of the seven finer ones, similarly flattened out, makes a closed circle. The
forces which flow in them, again, come from "outside," from a fourth-
dimensional space.[10] Each of the finer whorls is formed of seven yet finer
ones, set successively at right angles to each other, each finer than its
predecessor; these we call spirillæ.[11]
It will be understood from the foregoing, that the atom cannot be said to
have a wall of its own, unless these whorls of force can be so designated; its
"wall" is the pressed back "space." As said in 1895, of the chemical atom,
the force "clears itself a space, pressing back the undifferentiated matter of
the plane, and making to itself a whirling wall of this matter." The wall
belongs to space, not to the atom.

In the three whorls flow currents of different electricities; the seven vibrate
in response to etheric waves of all kinds—to sound, light, heat, etc.; they
show the seven colours of the spectrum; give out the seven sounds of the
natural scale; respond in a variety of ways to physical vibration—flashing,
singing, pulsing bodies, they move incessantly, inconceivably beautiful and
brilliant.[12]
The atom has—as observed so far—three proper motions, i.e., motions of
its own, independent of any imposed upon it from outside. It turns
incessantly upon its own axis, spinning like a top; it describes a small circle
with its axis, as though the axis of the spinning top moved in a small circle;
it has a regular pulsation, a contraction and expansion, like the pulsation of
the heart. When a force is brought to bear upon it, it dances up and down,
flings itself wildly from side to side, performs the most astonishing and
rapid gyrations, but the three fundamental motions incessantly persist. If it
be made to vibrate, as a whole, at the rate which gives any one of the seven
colors, the whorl belonging to that color glows out brilliantly.
An electric current brought to
bear upon the atoms checks their
proper motions, i.e., renders them
slower; the atoms exposed to it
arrange themselves in parallel
lines, and in each line the heart-
shaped depression receives the
flow, which passes out through
the apex into the depression of the next, and so on. The atoms always set
themselves to the current. The well-known division of diamagnetic and
paramagnetic depends generally on this fact, or on an analogous action on
molecules, as may be seen in the accompanying diagrams.[13]
Two atoms, positive and negative, brought near to each other, attract each
other, and then commence to revolve round each other, forming a relatively
stable duality; such a molecule is neutral. Combinations of three or more
atoms are positive, negative or neutral, according to the internal molecular
arrangement; the neutral are relatively stable, the positive and negative are
continually in search of their respective opposites, with a view to
establishing a relatively permanent union.

Three states of matter exist between the atomic state and the gaseous—the
state in which the chemical atoms are found, the recognized chemical
elements; for our purposes we may ignore the liquid and solid states. For
the sake of clearness and brevity in description, we have been obliged to
name these states; we call the atomic state of the chemist elemental; the
state which results from breaking up chemical elements, proto-elemental;
the next higher, meta-proto-elemental; the next higher, hyper-meta-proto-
elemental; then comes the atomic state. These are briefly marked as El.,
Proto., Meta., and Hyper.[14]
The simplest unions of atoms, never, apparently consisting of more than
seven, form the first molecular state of physical matter.
Here are some characteristic
combinations of the Hyper state;
the atom is conventional, with the
depression emphasised; the lines,
always entering at the depression
and coming out at the apex, show
the resultants of lines of force;
where no line appears entering the
Types of Hyper-Meta-Proto-Elemental
depression, the force wells up Matter.
from fourth-dimensional space;
where no line appears leaving the apex, the force disappears into fourth-
dimensional space; where the point of entry and departure is outside the
atoms, it is indicated by a dot.[15]
The molecules show all kinds of possible combinations; the combinations
spin, turn head over heels, and gyrate in endless ways. Each aggregation is
surrounded with an apparent cell-wall, the circle or oval, due to the pressure
on the surrounding matter caused by its whirling motion; they strike on
each other[16] and rebound, dart hither and thither, for reasons we have not
distinguished.
The Meta state, in some of its combinations, appears at first sight to repeat
those of the Hyper state; the only obvious way of distinguishing to which
some of the molecules of less complexity belong is to pull them out of the
"cell-wall"; if they are Hyper molecules they at once fly off as separate

atoms; if they are Meta molecules
they break up into two or more
molecules containing a smaller
number of atoms. Thus one of the
Meta molecules of iron,
containing seven atoms, is
identical in appearance with a
Hyper heptad, but the latter
dissociates into seven atoms, the
Types of Meta-Proto-Elemental Matter.
former into two triads and a
single atom. Long-continued
research into the detailed play of forces and their results is necessary; we
are here only able to give preliminary facts and details—are opening up the
way. The following may serve as characteristic Meta types:—
These are taken from constituents of the various elements; 1 from Gl; 2 and
3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12
from Li; 13 and 14 from Na. Others will be seen in the course of breaking
up the elements.
The Proto state preserves many of the forms in the elements, modified by
release from the pressure to which they are subjected in the chemical atom.
In this state various groups are thus recognizable which are characteristic of
allied metals.
These are taken from the products
of the first disintegration of the
chemical atom, by forcibly
removing it from its hole. The
groups fly apart, assuming a great
variety of forms often more or
less geometrical; the lines
between the constituents of the
groups, where indicated, no Types of Proto-Elemental Matter.
longer represent lines of force,
but are intended to represent the impression of form, i.e., of the relative
position and motion of the constituents, made on the mind of the observer.
They are elusive, for there are no lines, but the appearance of lines is caused

by the rapid motion of the costituents up and down, or along them
backwards and forwards. The dots represent atoms, or groups of atoms,
within the proto-elements. 1 is found in C; 2 and 3 in He; 4 in Fl; 5 in Li; 6
in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe; 12 in Se. We shall return to
these when analysing the elements, and shall meet many other proto-
elemental groupings.
The first thing which is noticed by the observer, when he turns his attention
to the chemical atoms, is that they show certain definite forms, and that
within these forms, modified in various ways, sub-groupings are observable
which recur in connexion with the same modified form. The main types are
not very numerous, and we found that, when we arranged the atoms we had
observed, according to their external forms, they fell into natural classes;
when these, in turn, were compared with Sir William Crookes'
classification, they proved to be singularly alike. Here is his arrangement of
the elements, as it appeared in the Proceedings of the Royal Society, in a
paper read on June 9th, 1898.

This is to be read, following the lines of the "figures of eight": H, He, Li,
Gl, B, C, N, and so on, each successive element being heavier than the one
preceding it in order. The disks which fall immediately below each other
form a class; thus: H, Cl, Br, I; these resemble each other in various ways,
and, as we shall presently see, the same forms and groupings re-appear.
Another chart—taken from Erdmann's Lehrbuch—arranges the elements on
a curved line, which curiously resembles the curves within the shell of a

nautilus. The radiating lines show the classes, the whole diameter building
up a family; it will be observed that there is an empty radius between
hydrogen and helium, and we have placed occultum there; on the opposite
radius, iron, rubidium and osmium are seen.

The external forms may be classified as follows; the internal details will be
dealt with later :—
1. The Dumb-bell.—The characteristics of this are a higher and lower
group, each showing 12 projecting funnels, grouped round a central body,
and a connecting rod. It appears in sodium, copper, silver, and gold,[17] and
gold is given (1 on Plate III) as the most extremely modified example of
this form. The 12 almond-like projections, above and below, are severally
contained in shadowy funnels, impossible to reproduce in the drawing; the
central globe contains three globes, and the connecting portion has swollen
out into an egg, with a very complicated central arrangement. The dumb-
bell appears also in chlorine, bromine and iodine, but there is no trace of it
in hydrogen, the head of the group. We have not met it elsewhere. It may be
remarked that, in Sir William Crookes' scheme, in which they are all classed
as monads, these two groups are the nearest to the neutral line, on the
ingoing and outgoing series, and are respectively positive and negative.

II and IIa. The Tetrahedron.—The
characteristics of this form are
four funnels, containing ovoid
bodies, opening on the face of a
tetrahedron. The funnels
generally, but not always, radiate
from a central globe. We give
beryllium (glucinum) as the
simplest example (2 on Plate III),
and to this group belong calcium
and strontium. The tetrahedron is
the form of chromium and
molybdenum, but not that of the
head of their group, oxygen,
which is, like hydrogen, sui
generis. These two groups are
marked in orthodox chemistry as
respectively positive and
negative, and are closely allied.
Another pair of groups show the
same tetrahedral form: Plate III.

magnesium, zinc and cadmium,
positive; sulphur, selenium and tellurium, negative. Selenium is a peculiarly
beautiful element, with a star floating across the mouth of each funnel; this
star is extremely sensitive to light, and its rays tremble violently and bend if
a beam of light falls on it. All these are dyads.
The tetrahedron is not confined to the external form of the above atoms; it
seems to be one of the favourite forms of nature, and repeatedly appears in
the internal arrangements. There is one tetrahedron within the unknown
element occultum; two appear in helium (3 on Plate III); yttrium has also
two within its cube, as has germanium; five, intersecting, are found in neon,
meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon,
kalon, meta-kalon, tin, titanium and zirconium. Gold contains no less than
twenty tetrahedra.
III. The Cube.—The cube appears to be the form of triads. It has six
funnels, containing ovoids, and opening on the faces of the cube. Boron is

chosen as an example (4 on Plate III). Its group members, scandium and
yttrium, have the same form; we have not examined the fourth; the group is
positive. Its negative complement consists of nitrogen, vanadium and
niobium, and we have again to note that nitrogen, like hydrogen and
oxygen, departs from its group type. Two other triad groups, the positive
aluminium, gallium and indium (the fourth unexamined) and the negative
phosphorus, arsenic and antimony (the fourth unexamined), have also six
funnels opening on the faces of a cube.
IV. The Octahedron.—The simplest example of this is carbon (5 on Plate
III). We have again the funnel with its ovoids, but now there are eight
funnels opening on the eight faces of the octahedron. In titanium (6 on Plate
III) the form is masked by the protruding arms, which give the appearance
of the old Rosicrucian Cross and Rose, but when we look into the details
later, the carbon type comes out clearly. Zirconium is exactly like titanium
in form, but contains a large number of atoms. We did not examine the
remaining two members of this group. The group is tetratomic and positive.
Its negative pendant shows the same form in silicon, germanium and tin;
again, the fourth was unexamined.
V. The Bars.—These characterise a set of closely allied groups, termed
"inter-periodic." Fourteen bars (or seven crossed) radiate from a centre, as
in iron (1 on Plate IV), and the members of each group—iron, nickel,
cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum—differ
from each other by the weight of each bar, increasing in orderly succession;
the details will be given later. Manganese is often grouped with iron, nickel,
and cobalt (see Crookes' lemniscates), but its fourteen protruding bodies
repeat the "lithium spike" (proto-element 5) and are grouped round a central
ovoid. This would appear to connect it with lithium (2 on Plate IV) rather
than with fluorine (3 in Plate IV), with which it is often classed. The
"lithium spike" re-appears in potassium and rubidium. These details, again,
will come out more clearly later.
VI. The Star.—A flat star, with five interpenetrating tetrahedra in the centre,
is the characteristic of neon and its allies (4 on Plate IV) leaving apart
helium, which, as may be seen by referring to 3, Plate IV, has an entirely
different form.

There are thus six clearly defined
forms, typical of classes, with two
—lithium and fluorine—of
doubtful affinities. It is worthy of
notice that in diatomic elements
four funnels open on the faces of
tetrahedra; in triatomic, six
funnels on the faces of cubes; in
tetratomic, eight funnels on the
faces of octahedra.
Thus we have a regular sequence
of the platonic solids, and the
question suggests itself, will
further evolution develop
elements shaped to the
dodecahedron and the
icosahedron?
Plate IV.

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).
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. Plate V.

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.
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, Plate VI.
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.)
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 Plate VII.
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).

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

Copper (Plate VI, 3).
We have already disposed of occultum, on this plate, and of sodium, which
lies at the root of both groups. Copper, we now find, is also very largely off
our hands, as the funnel provides us with only two new types—two spheres
—each containing five atoms in a new arrangement, and the triangular body
at the mouth with its ten atoms. This triangular body, with an increased
number of atoms, reappears in various other chemical elements. The central
globes are different from any we have had before, in their internal
arrangement, but the constituents are familiar; there are two contained
spheres with four atoms each, the a in the globe of bromine (see above) and
2 "cigars." The "cigars" may be followed under occultum (see above). The
connecting rod is as in chlorine, bromine and iodine.
The atoms in the bodies a and b are curiously arranged. A consists of two
square-based pyramids turned so as to meet at their apices, and breaks up
into two quartet rings and a duad. B is again two four-sided pyramids, but
the bases are in contact and set at right angles to each other; the second

apex is not seen, as it is directly below the first. The pyramids separate as
meta-bodies, and the atoms assume the peculiar arrangement indicated and
then break up into four pairs and two units on the hyper level.

IV.

Silver (Plate VI, 4 and Ag below).
Silver presents us with only two new bodies, and even these are only new
by slight additions to old models. The triangular shaped body at the apex of
the funnel, containing 21 atoms, is intermediate between the similar bodies
in copper and iron. As a proto-element it becomes three triangles, joined at
their apices, in fact a tetrahedron in which no atoms are distributed on the
fourth face. The faces separate on the meta level and give three seven-
atomed figures, and each of these breaks up into two triplets and a unit. The
central globe only differs from that of bromine by the addition of one atom,
which gives the familiar four-sided pyramid with a square base as in
chlorine (see p. 46).

Gold (Plate VII and Au below).
The disintegration of gold first
yields forty-seven bodies on the
proto-level; the twenty-four
funnels separate, and the central
globes which hold each twelve
together set free their six
contained globes (c, d), thirty
bodies being thus liberated. The
sixteen bodies on the central
inclined planes, marked b, break
away, their central globe, with its four contained globes, remaining
unchanged. But this condition does not last. The motion of the funnels
changes and thus the funnels cease to exist and their contents are set free,

each funnel thus liberating nine independent bodies; the sixteen b separate
into two each; the four a liberate five each; the two c set free thirteen each;
the four d finally liberate two each: 302 proto elements in all.
The funnel is almost that of iodine, re-arranged. Four of the first ring in the
iodine funnel are replaced by the triangular body, which becomes a four-
sided pyramid with an occupied base. The second ring of three ovoids in
iodine becomes four in gold, but the internal arrangement of each ovoid is
the same. The next two spheres in the iodine funnel coalesce into one
sphere, with similar contents, in the gold funnel. The fifth in iodine is
slightly rearranged to form the fourth in descent in gold, and the remaining
two are the same. B has been broken up under occultum (p. 628) and can be
followed there. The sixteen rings set free from the four a, after gyrating
round the central body, now become a sphere, break up, as in occultum (see
p. 44) into a meta seven-atomed ring and an eight-atomed double cross, and
so on to the hyper level. The sphere with its two contained bodies breaks up
into eight triangles on the meta level, and each of these, on the hyper, into a
duad and a unit. The twelve septets of c assume the form of prisms as in
iodine (see p. 48) and pursue the same course, while its central body, a four-
sided pyramid with its six attendants, divides on the meta level into six
duads, revolving round a ring with a central atom as in chlorine (p. 47), the
duads going off independently on the hyper-level and the ring breaking up
as in chlorine. The "cigar" tetrahedron of d follows its course as in
occultum, and the other sets free two quartets and two triplets on the meta
level, yielding six duads and two units as hyper compounds. It will be seen
that, complex as gold is, it is composed of constituents already familiar, and
has iodine and occultum as its nearest allies.

II and IIa.—The Tetrahedral Groups.
II.—This group consists of beryllium (glucinum), calcium, strontium and
barium, all diatomic, paramagnetic and positive. The corresponding group
consists of oxygen, chromium, molybdenum, wolfram (tungsten) and
uranium, with a blank disk between wolfram and uranium: these are
diatomic, paramagnetic, and negative. We have not examined barium,
wolfram, or uranium.

Beryllium (Plate III, 2, and Plate
VIII, 1). In the tetrahedron four
funnels are found, the mouth of
each funnel opening on one of its
faces. The funnels radiate from a
central globe, and each funnel
contains four ovoids each with ten
atoms within it arranged in three
spheres. In the accompanying
diagrams one funnel with its four
ovoids is shown and a single
ovoid with its three spheres,
containing severally three, four,
and three atoms, is seen at the
left-hand corner of the plate (7 a).
The members of this group are
alike in arrangement, differing
only in the increased complexity
of the bodies contained in the Plate VIII.
funnels. Beryllium, it will be
observed, is very simple, whereas calcium and strontium are complicated.

BERYLLIUM: 4 funnels of 40 atoms 160
Central globe 4
----
Total 164
----
Atomic weight 9.01
Number weight 164/18 9.11

Calcium (Plate VIII, 2) shows in each funnel three contained spheres, of
which the central one has within it seven ovoids identical with those of
beryllium, and the spheres above and below it contain each five ovoids (7
b) in which the three contained spheres have, respectively, two, five, and
two atoms. The central globe is double, globe within globe, and is divided
into eight segments, radiating from the centre like an orange; the internal

part of the segment belonging to the inner globe has a triangular body
within it, containing four atoms (7 c), and the external part, belonging to the
encircling globe, shows the familiar "cigar" (7 d). In this way 720 atoms are
packed into the simple beryllium type.

CALCIUM: 4 funnels of 160 atoms 640
Central globe 80
----
Total 720
----
Atomic weight 39.74
Number weight 720/18 40.00

Strontium (Plate VIII, 3) shows a still further complication within the
funnels, no less than eight spheres being found within each. Each of the
highest pair contains four subsidiary spheres, with five, seven, seven, five
atoms, respectively (7 e, g, f). The g groups are identical with those in gold,
but difference of pressure makes the containing body spherical instead of
ovoid; similar groups are seen in the top ring of the iodine funnel, where
also the "hole" is ovoid in form. The second pair of spheres contains ten
ovoids (7 b) identical with those of calcium. The third pair contains
fourteen ovoids (7 a) identical with those of beryllium, while the fourth pair
repeats the second, with the ovoids re-arranged. The internal divisions of
the double sphere of the central globe are the same as in calcium, but the
contents differ. The "cigars" in the external segments are replaced by seven-
atomed ovoids (7 h)—the iodine ovoids—and the external segments contain
five-atomed triangles (7 i). Thus 1,568 atoms have been packed into the
beryllium type, and our wonder is again aroused by the ingenuity with
which a type is preserved while it is adapted to new conditions.

STRONTIUM: 4 funnels of 368 atoms 1472
Central globe 96
----
Total 1568
----

Atomic weight 86.95
Number weight 1568/18 87.11

The corresponding group, headed by oxygen—oxygen, chromium,
molybdenum, wolfram and uranium—offers us another problem in its first
member.
Oxygen (Plate VIII, 4). This was examined by us in 1895, and the
description may be reproduced here with a much improved diagram of its
very peculiar constitution. The gaseous atom is an ovoid body, within which
a spirally-coiled snake-like body revolves at a high velocity, five brilliant
points of light shining on the coils. The appearance given in the former
diagram will be obtained by placing the five septets on one side on the top
of those on the other, so that the ten become in appearance five, and thus
doubling the whole, the doubling point leaving eleven duads on each side.
The composition is, however, much better seen by flattening out the whole.
On the proto level the two snakes separate and are clearly seen.

OXYGEN: Positive snake
{ 55 spheres of 2 atoms }
{ + 5 disks of 7 atoms } 145
Negative snake " 145
----
Total 290
----
Atomic weight 15.87
Number weight 290/18 16.11

Chromium (Plate VIII, 5) "reverts to the ancestral type," the tetrahedron; the
funnel is widened by the arrangement of its contents, three spheres forming
its first ring, as compared with the units in beryllium and calcium, and the
pairs in strontium and molybdenum. Two of these spheres are identical in
their contents—two quintets (7 f), a quintet (7 j), and two quintets (7 e), e
and f being to each other as object and image. The remaining sphere (7 b) is
identical with the highest in the calcium funnel. The remaining two spheres,
one below the other, are identical with the corresponding two spheres in
calcium. The central globe, as regards its external segments, is again

identical with that of calcium, but in the internal segments a six-atomed
triangle (7 k) is substituted for the calcium four-atomed one (7 e).

CHROMIUM: 4 funnels of 210 atoms 840
Central globe 96
-----
Total 936
-----
Atomic weight 51.74
Number weight 936/18 52.00

Molybdenum (Plate VIII, 6) very closely resembles strontium, differing
from it only in the composition of the highest pair of spheres in the funnels
and in the presence of a little sphere, containing two atoms only, in the
middle of the central globe. The topmost spheres contain no less than eight
subsidiary spheres within each; the highest of these (7 e) has four atoms in
it; the next three have four, seven and four (7 e g e), respectively; the next
three are all septets (7 g), and the last has four—making in all for these two
spheres 88 atoms, as against the 48 in corresponding spheres of strontium,
making a difference of 160 in the four funnels.

MOLYBDENUM: 4 funnels of 408 atoms 1632
Central globe 98
-----
Total 1730
-----
Atomic weight 95.26
Number weight 1730/18 96.11

II a.—This group contains magnesium, zinc, cadmium, and mercury, with
an empty disk between cadmium and mercury; we did not examine
mercury. All are diatomic, diamagnetic and positive; the corresponding
group consists of sulphur, selenium and tellurium, also all diatomic and
diamagnetic, but negative. The same characteristics of four funnels opening
on the faces of a tetrahedron are found in all, but magnesium and sulphur

have no central globe, and in cadmium and tellurium the globe has become
a cross.
Magnesium (Plate IX, 1)
introduces us to a new
arrangement: each group of three
ovoids forms a ring, and the three
rings are within a funnel; at first
glance, there are three bodies in
the funnel; on examination each
of these is seen to consist of three,
with other bodies, spheres, again
within them. Apart from this, the
composition is simple enough, all
the ovoids being alike, and
composed of a triplet, a septet and
a duad.

MAGNESIUM: 4 funnels
of 108 atoms 432 Plate IX.
Atomic
weight 24.18
Number weight 432/18 24.00

Zinc (Plate IX, 2) also brings a new device: the funnel is of the same type as
that of magnesium, while septets are substituted for the triplets, and 36
additional atoms are thus slipped in. Then we see four spikes, alternating
with the funnels and pointing to the angles, each adding 144 atoms to the
total. The spikes show the ten-atomed triangle, already met with in other
metals, three very regular pillars, each with six spheres, containing two,
three, four, four, three, two atoms, respectively. The supporting spheres are
on the model of the central globe, but contain more atoms. Funnels and
spikes alike radiate from a simple central globe, in which five contained
spheres are arranged crosswise, preparing for the fully developed cross of
cadmium. The ends of the cross touch the bottoms of the funnels.

ZINC: 4 funnels of 144 atoms 576
4 spikes of 144 atoms 576
Central globe 18
-----
Total 1170
-----
Atomic weight 64.91
Number weight 1170/18 65.00

Cadmium (Plate IX, 3) has an increased complexity of funnels; the diagram
shows one of the three similar segments which lie within the funnels as
cylinders; each of these contains four spheres, three pillars and three ovoids,
like the spike of zinc turned upside down, and the zinc ten-atomed triangle
changed into three ten-atomed ovoids. The centre-piece is a new form,
though prefigured in the central globe of zinc.

CADMIUM: 3 segments of 164 atoms = 492
4 funnels of 492 atoms 1968
Central body 48
-----
Total 2016
-----
Atomic weight 111.60
Number weight 2016/18 112.00

The corresponding negative group is headed by
Sulphur (Plate X, 1), which, like magnesium, has no central globe, and
consists simply of the zinc funnels, much less compressed than zinc but the
same in composition.

SULPHUR: 4 funnels of 144 atoms 576
Atomic weight 31.82
Number weight 576/18 32.00

Selenium (Plate X, 2) is distinguished by the exquisite peculiarity, already
noticed, of a quivering star, floating across the mouth of each funnel, and
dancing violently when a ray of light falls upon it. It is known that the
conductivity of selenium varies with the intensity of the light falling upon
it, and it may be that the star is in some way connected with its
conductivity. It will be seen that the star is a very complicated body, and in
each of its six points the two five-atomed spheres revolve round the seven-
atomed cone. The bodies in the funnels resemble those in magnesium, but a
reversed image of the top one is interposed between itself and the small
duad, and each pair has its own enclosure. The central globe is the same as
that of zinc.

SELENIUM: 4 funnels of 198 atoms 792
4 stars of 153 atoms 612
Central globe 18
-----
Total 1422
-----
Atomic weight 78.58
Number weight 1422/18 79.00

Tellurium (Plate X, 3), it will be seen, closely resembles cadmium, and has
three cylindrical segments—of which one is figured—making up the
funnel. The contained bodies in the pillars run three, four, five, four, three,
two, instead of starting with two; and a quartet replaces a duad in the globes
above. The central cross only differs from that of cadmium in having a
seven-atomed instead of a four-atomed centre. So close a similarity is
striking.

TELLURIUM: 3 segments of 181 atoms = 543
4 funnels of 543 atoms 2172
Central body 51
-----
Total 2223
-----

Atomic weight 126.64
Number weight 2223/18 123.50

V.

We must now consider the ways in which the members of the tetrahedral
groups break up, and as we proceed with this study we shall find how
continual are the repetitions, and how Nature, with a limited number of
fundamental methods, creates by varied combinations her infinite variety of
forms.

Beryllium (Plate III, 2, and VIII, 1).
Beryllium offers us four similar
funnels and a central globe, and
the proto-elements consist of
these five bodies, set free. The
funnel, released from pressure,
assumes a spherical form, with its
four ovoids spinning within it,
and the central globe remains a
sphere, containing a whirling
cross. On the meta level, the
ovoids are set free, and two from
each funnel are seen to be positive, two negative—sixteen bodies in all,
plus the cross, in which the resultant force-lines are changed, preparatory to
its breaking into two duads on the hyper level. On that level, the decades
disintegrate into two triplets and a quartet, the positive with the depressions
inward, the negative with the depressions outward.

Calcium (Plate VIII, 2).
The funnels, as usual, assume a spherical form on the proto level, and show,
in each case, three spheres containing ovoids. These spheres, still on the

proto level, break free from their containing funnel, as in the case of gold
(p. 49), twelve bodies being thus liberated, while the central globe breaks
up into eight segments, each of which becomes globular, and contains
within it a "cigar" and a somewhat heart-shaped body. Four spheres, each
containing seven ten-atomed ovoids, are identical with those in beryllium,
and can be followed in its diagram. Eight spheres, each containing five
nine-atomed ovoids of a different type, set free, on the meta level, eighty
duads—forty positive and forty negative—and forty quintets, which are
identical with those in chlorine. On the hyper level, the duads become
single atoms, within a sphere, and the central atom from the quintet is also
set free, one hundred and twenty in all. The remaining four atoms of the
quintet divide into two duads.
The central globe, dividing into eight, becomes eight six-atomed spheres on
the meta, the "cigar" behaving as usual, four "cigars" being positive and
four negative, and becoming dissociated into triplets; the four atoms within
the heart-shaped body appear as a tetrahedron, remain together on the meta
level, and break up into duads on the hyper.

Strontium (Plate VIII, 3).
The third member of this group repeats the a groups of beryllium and the b
groups of calcium, and they dissociate into the bodies already described
under these respectively. The two upper globes in each funnel repeat each
other, but each globe contains four smaller spheres showing three varieties
of forms. The two marked g, which are repeated in the central globe as h,
are seven-atomed, and appear as spheres or ovoids according to pressure.
They are figured on p. 48, under iodine; e and f are related as object and
image, and we have already seen them in copper (pp. 38 and 48); in each
case, as in copper, they unite into a ten-atomed figure; on the meta level the
pair of fours form a ring, and the remaining two atoms form a duad; i,
which repeats f, makes a ring with the fifth in the centre, as in the five-
atomed b of calcium, as shown above. There is, thus, nothing new in
strontium, but only repetitions of forms already studied.

Oxygen (Plate VIII, 4).

The disintegration of oxygen as
given in 1895 may be repeated
here, and the better presentation
given on p. 54 renders it easier to
follow the process. On the proto
level the two "snakes" divide; the
brilliant disks are seven-atomed,
but are differently arranged, the
positive snake having the atoms
arranged as in the iodine ovoids,
whereas the negative snake has
them arranged as in a capital H. The snakes show the same extraordinary
activity on the proto level as on the gaseous, twisting and writhing, darting
and coiling. The body of the snake is of two-atomed beads, positive and
negative. On the meta level the snakes break into ten fragments, each
consisting of a disk, with six beads on one side and five on the other,
remaining as lively as the original snake. They shiver into their constituent
disks, and beads on the hyper level, there yielding the ten disks, five
positive and five negative, and the 110 beads, fifty-five positive and fifty-
five negative.

Chromium (Plate VIII, 5).
When we go on to chromium and molybdenum, we return to our familiar
funnels and central globes, and the secondary spheres within the funnels—
quickly set free, as before, on the proto level—give us no new combinations
in their contained spheres and ovoids. The a of beryllium, the b of calcium
and strontium, and d of calcium, the e and f of strontium, are all there; j in
chromium is the same as the central sphere in the b ovoid. In the central
globe, k, is a pair of triangles as in hydrogen, consisting of only six atoms,
which on the meta level revolve round each other, and break up into two
duads and two units on the hyper.

Molybdenum (Plate VIII, 6).

Molybdenum presents us with only two new forms, and these are merely
four-atomed tetrahedra, occurring in pairs as object and image. All the other
bodies have already been analysed.
II a.—We come now to the second great tetrahedral group, which though
very much complicated, is yet, for the most part, a repetition of familiar
forms.

Magnesium (Plate IX, 1).
We are still among tetrahedra, so
have to do with four funnels, but
each funnel contains three rings,
and each ring three ovoids; on the
proto level a triple dissociation
takes place, for the funnels let
free the rings as large spheres, in
each of which rotate three twelve-
atomed ovoids, and then the
ovoids break loose from the
spheres, and themselves become
spherical, so that we have finally thirty-six proto compounds from the
tetrahedron. On the meta level the contained bodies, a triplet, Mg a, a
septet, Mg b, and a duad, Mg c, are set free from each globe, thus yielding
one hundred and eight meta compounds. On the hyper level the triplet
becomes a duad and a unit; the duad becomes two units; and the septet a
triplet and a quartet.

Zinc (Plate IX, 2).
We can leave aside the funnel, for the only difference between it and the
magnesium funnel is the substitution of a second septet for the triplet, and
the septet is already shown in the magnesium diagram. We have, therefore,
only to consider the spikes, pointing to the angles of the enclosing
tetrahedron, and the central globe. These are set free on the proto level and
the spikes immediately release their contents, yielding thus thirty-two
separate bodies.

The triangular arrangement at the top of the spike is the same as occurs in
copper (b on p. 48), and can be there followed. One of the three similar
pillars is shown in the accompanying diagram under Zn a. The compressed
long oval becomes a globe, with six bodies revolving within it in a rather
peculiar way: the quartets turn round each other in the middle; the triplets
revolve round them in a slanting ellipse; the duads do the same on an ellipse
slanting at an angle with the first, somewhat as in gold (a and b, p. 40). The
spheres within the globes at the base of the spikes, Zn b, behave as a cross
—the cross is a favourite device in the II a groups. Finally, the central
globe, Zn c, follows the same cruciform line of disintegration.

Cadmium (Plate IX, 3).
Cadmium follows very closely on
the lines of zinc; the pillars of the
zinc spike are reproduced in the
rings of the cadmium funnel; the
globes are also the globes of
cadmium; so neither of these
needs attention. We have only to
consider the three ten-atomed
ovoids, which are substituted for
the one ten-atomed triangle of
zinc, and the central cross. The ovoids become spheres (Cd a, b), the
contained bodies revolving within them, a whirling on a diameter of the
sphere, cutting it in halves, as it were, and b whirling round it at right
angles; the cross also becomes a sphere (Cd c), but the cruciform type is
maintained within it by the relative positions of the contained spheres in
their revolution. The subsequent stages are shown in the diagram.

Sulphur (Plate XI, 1).
Sulphur has nothing new, but shows only the funnels already figured in
magnesium, with the substitution of a second septet for the triplet, as in
zinc.

Selenium (Plate X, 2).
The funnel of selenium is a re-
arrangement of the twelve-atomed
ovoids of magnesium and the ten-
atomed ovoids of cadmium. The
funnels, on disintegrating, set free
twelve groups, each containing
nine spheres. On the meta level
the ten-atomed bodies are set free,
and the twelve-atomed divide into
duads and decads, thus yielding
seventy-two decads and thirty-six
duads; the duads, however, at once recombine into hexads, thus giving only
twelve meta elements, or eighty-four in all from the funnels. The central
globe holds together on the proto level, but yields five meta elements. The
star also at first remains a unit on the proto level, and then shoots off into
seven bodies, the centre keeping together, and the six points becoming
spheres, within which the two cones, base to base, whirl in the centre, and
the globes circle round them. On the meta level all the thirty bodies
contained in the star separate from each other, and go on their independent
ways.
Selenium offers a beautiful example of the combination of simple elements
into a most exquisite whole.

Tellurium (Plate X, 3).
Tellurium very closely resembles cadmium, and they are, therefore placed
on the same diagram. The pillars are the same as in chlorine and its
congeners, with a duad added at the base. The ten-atomed ovoid is the same
as in cadmium and follows the same course in breaking up. It would be
interesting to know why this duad remains as a duad in selenium and breaks
up into a septad and triad in the other members of the group. It may be due
to the greater pressure to which it is subjected in selenium, or there may be
some other reason. The cross in tellurium is identical with that in cadmium,
except that the centre is seven-atomed instead of four-atomed.

VI.

III and IIIa.—The Cube Groups.
We have here four groups to consider, all the members of which are triads,
and have six funnels, opening on the six faces of a cube.
III.—Boron, scandium and yttrium were examined; they are all triatomic,
paramagnetic, and positive. The corresponding group consists of nitrogen,
vanadium and niobium; they are triatomic, paramagnetic, and negative. We
have not examined the remaining members of these groups. In these two
groups nitrogen dominates, and in order to make the comparison easy the
nitrogen elements are figured on both Plate XI and Plate XII. It will be seen
that scandium and yttrium, of the positive group, differ only in details from
vanadium and niobium, of the negative group; the ground-plan on which
they are built is the same. We noted a similar close resemblance between
the positive strontium and the negative molybdenum.
Boron (Plate III, 4, and Plate XI,
1). We have here the simplest
form of the cube; the funnels
contain only five bodies—four
six-atomed ovoids and one six-
atomed "cigar." The central globe
has but four five-atomed spheres.
It is as simple in relation to its
congeners as is beryllium to its
group-members.

BORON: 6 funnels of 30
atoms 180
Central globe
20

---- Plate XI.

Total 200
----
Atomic weight 10.86
Number weight 200/18 11.11

Scandium (Plate XI, 2). For the first time we meet funnels of different
types, A and B, three of each kind; A appear to be positive and B negative,
but this must be stated with reserve.
In A the boron funnel is reproduced, the "cigar" having risen above its
companion ovoids; but the most important matter to note in respect to this
funnel is our introduction to the body marked a 110. This body was
observed by us first in nitrogen, in 1895, and we gave it the name of the
"nitrogen balloon," for in nitrogen it takes the balloon form, which it also
often assumes in other gaseous elements. Here it appears as a sphere—the
form always assumed on the proto level—and it will be seen, on reference
to the detailed diagram 4 a, to be a complicated body, consisting of six
fourteen-atomed globes arranged round a long ovoid containing spheres
with three, four, six, six, four, three, atoms respectively. It will be observed
that this balloon appears in every member of these two groups, except
boron.
The B funnel runs largely to triads, c and b, b (see 4 b) having not only a
triadic arrangement of spheres within its contained globes, but each sphere
has also a triplet of atoms. In c (see 4 c) there is a triadic arrangement of
spheres, but each contains duads. B is completed by a five-atomed sphere at
the top of the funnel. It should be noted that a, b and c all are constituents of
nitrogen.
The central globe repeats that of boron, with an additional four-atomed
sphere in the middle.

SCANDIUM: 3 funnels (A) of 140 atoms 420
3 " (B) of 116 " 348
Centre globe 24

----
Total 792
----
Atomic weight 43.78
Number weight 792/18 44.00

Yttrium (Plate XI, 3). Here we have a quite new arrangement of bodies
within the funnel—the funnel being of one type only. Two "cigars" whirl on
their own axes in the centre near the top, while four eight-atomed globes
(see 4 e) chase each other in a circle round them, spinning madly on their
own axes—this axial spinning seems constant in all contained bodies—all
the time. Lower down in the funnel, a similar arrangement is seen, with a
globe (see 4 d)—a nitrogen element—replacing the "cigars," and six-
atomed ovoids replacing the globes.
The "nitrogen balloon" occupies the third place in the funnel, now showing
its usual shape in combination, while the b globe (see 4 b) of scandium
takes on a lengthened form below it.
The central globe presents us with two tetrahedra, recalling one of the
combinations in gold (see Plate VII d), and differing from that only by the
substitution of two quartets for the two triplets in gold.
One funnel of yttrium contains exactly the same number of atoms as is
contained in a gaseous atom of nitrogen. Further, a, b, and d are all nitrogen
elements. We put on record these facts, without trying to draw any
conclusions from them. Some day, we—or others—may find out their
significance, and trace through them obscure relations.

YTTRIUM: 6 funnels of 261 atoms 1566
Central globe 40
----
Total 1606
----
Atomic weight 88.34
Number weight 1606/18 89.22

The corresponding negative group, of nitrogen, vanadium and niobium, is
rendered particularly interesting by the fact that it is headed by nitrogen,
which—like the air, of which it forms so large a part—pervades so many of
the bodies we are studying. What is there in nitrogen which renders it so
inert as to conveniently dilute the fiery oxygen and make it breathable,
while it is so extraordinarily active in some of its compounds that it enters
into the most powerful explosives? Some chemist of the future, perhaps,
will find the secret in the arrangement of its constituent parts, which we are
able only to describe.
Nitrogen (Plate XII, 1) does not
assume the cubical form of its
relatives, but is in shape like an
egg. Referring again to our 1895
investigations, I quote from them.
The balloon-shaped body (see 4
a) floats in the middle of the egg,
containing six small spheres in
two horizontal rows, and a long
ovoid in the midst; this balloon-
shaped body is positive, and is
drawn down towards the negative
body b (see 4 b) with its seven
contained spheres, each of which
has nine atoms within it—three
triads. Four spheres are seen, in
addition to the two larger bodies;
Plate XII.
two of these (see 4 d), each
containing five smaller globes,
are positive, and two (see 4 c) containing four smaller globes, are negative.

NITROGEN: Balloon 110
Oval 63
2 bodies of 20 atoms 40
2 " " 24 " 48
----
Total 261

----
Atomic weight 14.01
Number weight 261/18 14.50

Vanadium (Plate XII, 2) closely follows scandium, having two types of
funnels. Funnel A only differs from that of scandium by having a globe (see
4 d) inserted in the ring of four ovoids; funnel B has a six-atomed, instead
of a five-atomed globe at the top, and slips a third globe containing twenty
atoms (see 4 d) between the two identical with those of scandium (see 4 c).
The central globe has seven atoms in its middle body instead of four. In this
way does vanadium succeed in overtopping scandium by 126 atoms.

VANADIUM: 3 funnels (A) of 160 atoms 480
3 " (B) " 137 " 411
Central globe 27
----
Total 918
----
Atomic weight 50.84
Number weight 918/18 51.00

Niobium (Plate XII, 3) is as closely related to yttrium as is vanadium to
scandium. The little globes that scamper round the "cigars" contain twelve
atoms instead of eight (see 4 e).
The rest of the funnel is the same. In the central globe both the tetrahedra
have "cigars," and a central nine-atomed globe spins round in the centre
(see 4 f), seventeen atoms being thus added.

NIOBIUM: 6 funnels of 277 atoms 1662
Central globe 57
----
Total 1719
----
Atomic weight 93.25
Number weight 1719/18 95.50

III a.—Aluminium, gallium and indium were examined from this group.
They are triatomic, diamagnetic, and positive. The corresponding group
contains phosphorus, arsenic and antimony: bismuth also belongs to it, but
was not examined; they are triatomic, diamagnetic and negative. They have
no central globes.
Aluminium (Plate XIII, 1), the
head of the group, is, as usual,
simple. There are six similar
funnels, each containing eight
ovoids, below which is a globe.

ALUMINIUM: 6 funnels
of 81 atoms 486
Atomic
weight
26.91
Number
weight 486/18
27.00

Gallium (Plate XIII, 2) has two
segments in every funnel; in the Plate XIII.
segment to the left a "cigar"
balances a globe, equally six-atomed, in that of the right, and the globes to
right and left are four-atomed as against three-atomed. In the next row, the
smaller contained globes have six atoms as against four, and the cones have
respectively seven and five. By these little additions the left-hand funnel
boasts one hundred and twelve atoms as against ninety-eight.

GALLIUM: Left segment 112 atoms }
Right segment 98 " } = 210
6 funnels of 210 atoms 1260
----
Atomic weight 69.50
Number weight 1260/18 70.00

Indium (Plate XIII, 3) repeats the segments of gallium exactly, save in the
substitution of a sixteen-atomed body for the seven-atomed cone of the left-
hand segment, and a fourteen-atomed body for the five-atomed
corresponding one in gallium. But each funnel now has three segments
instead of two; three funnels out of the six contain two segments of type A
and one of type B; the remaining three contain two of type B, and one of
type A.

INDIUM: Segment A 121 atoms
Segment B 107 "
3 funnels of 2 A and 1 B ([242 + 107] 3)
1047
3 " " 2 B and 1 A ([214 + 121] 3)
1005

----
Total
2052

----
Atomic weight
114.05
Number weight 2052/18
114.00

The corresponding negative group, phosphorus, arsenic, and antimony, run
on very similar lines to those we have just examined.
Phosphorus (Plate XIV, 1) offers us a very curious arrangement of atoms,
which will give some new forms in breaking up. Two segments are in each
funnel, in fact the only two of group III a which do not show this
arrangement, or a modification thereof, are aluminium and arsenic.

PHOSPHORUS: Left segment 50 atoms
Right segment 43 "
--

93
6 funnels
of 93 atoms 558
Atomic
weight
30.77
Number
weight 558/18
31.00

Arsenic (Plate XIV, 2) resembles
aluminium in having eight
internal sub-divisions in a funnel,
and the ovoids which form the top
ring are identical, save for a
minute difference that in
aluminium the ovoids stand the Plate XIV.
reverse way from those in arsenic.
It will be noted that in the former the top and bottom triangles of atoms
have the apices upwards, and the middle one has its apex downwards. In
arsenic, the top and bottom ones point downwards, and the middle one
upwards. Arsenic inserts sixteen spheres between the ovoids and globe
shown in aluminium, and thus adds no less than one hundred and forty-four
atoms to each funnel.

ARSENIC: 6 funnels of 225 atoms 1350
Atomic weight 74.45
Number weight 1350/18 75.00

Antimony (Plate XIV, 3) is a close copy of indium, and the arrangement of
types A and B in the funnels is identical. In the middle rings of both A and
B a triplet is substituted for a unit at the centre of the larger globe. In the
lowest body of type A the "cigar" has vanished, and is represented by a
seven-atomed crystalline form.

ANTIMONY: Segment A 128 atoms
Segment B 113 atoms
3 funnels of 2 A and 1 B ([256 + 113]3)
1107
3 " " 2 B and 1 A ([226 + 128]3)
1056
--
--
Total
2163
--
--
Atomic weight
119.34
Number weight
120.16

VII.

Boron (Plate III, 4, and Plate XI, 1).
The disintegration of boron is
very simple: the funnels are set
free and assume the spherical
form, showing a central "cigar"
and four globes each containing
two triplets. The central globe is
also set free with its four quintets,
and breaks at once in two. On the
meta level the "cigar" breaks up
as usual, and the triplets separate.
On the hyper level, the "cigar" follows its usual course, and the triplets

become duads and units. The globe forms two quintets on the meta level,
and these are resolved into triplets and duads.

Scandium (Plate XI, 2).
In funnel A the "cigar" and the ovoids behave as in boron, but the "balloon,"
a 110 (XI, 4), escapes from the funnel as it changes to a sphere, and holds
together on the proto level; on the meta, it yields six globes each containing
seven duads, and these are all set free as duads on the hyper level; the ovoid
is also set free on the meta level becoming a sphere, and on the hyper level
liberates its contained bodies, as two triplets, two quartets and two sextets.
In funnel B there is a quintet, that behaves like those in the globe of boron,
on escaping from the funnel, in which the bodies remain on the proto level,
with the exception of b 63, which escapes. On the meta level, c (Plate XI,
4), c assumes a tetrahedral form with six atoms at each point, and these hold
together as sextets on the hyper level. At the meta stage, b (Plate XI, 4 b)
sets free seven nine-atomed bodies, which become free triplets on the hyper.
The central globe shows a cross at its centre, with the four quintets whirling
round it, on the proto level. On the meta, the quintets are set free, and
follow the boron type, while the cross becomes a quartet on the meta level,
and two duads on the hyper.

Yttrium (Plate XI, 3).
In yttrium, on the proto level, a
110 and b 63 both escape from the
funnel, and behave as in
scandium. The ovoids and
"cigars," set free on the meta
level, behave as in boron. The
central globe breaks up as in gold
(pp. 49 and 50), four quartets
being set free instead of two
quartets and two triplets. We have
only to consider e 8 and d 20 (Plate XI, 4). E 8 is a tetrahedral arrangement
of duads on the meta level, set free as duads on the hyper. D 20 is an

arrangement of pairs of duads at the angles of a square-based pyramid on
the meta, and again free duads on the hyper.

Nitrogen (Plate XII, 1).
Nitrogen has nothing new to show us, all its constituents having appeared in
scandium and yttrium.

Vanadium (Plate XII, 2).
The A funnel of vanadium repeats the A funnel of scandium, with the
addition of d 20, already studied. In the B funnel scandium B is repeated,
with an addition of d 20 and a sextet for a quintet; the sextet is the c of the
"nitrogen balloon." The central globe follows boron, save that it has a septet
for its centre; this was figured in iodine (p. 48).

Niobium (Plate XII, 3).
Niobium only differs from yttrium by the introduction of triplets for duads
in e; on the meta level we have therefore triplets, and on the hyper each
triplet yields a duad and a unit. The only other difference is in the central
globe. The tetrahedra separate as usual, but liberate eight "cigars" instead of
four with four quartets; the central body is simple, becoming three triads at
the angles of a triangle on the meta level, and three duads and three units on
the hyper.

Aluminium (Plate XIII, 1).
The funnels let go the globes, but the eight ovoids remain within them, so
that seven bodies are let loose on the proto level. When the ovoids are set
free at the meta stage they become spherical and a nine-atomed body is
produced, which breaks up into triangles on the hyper level. The globe
becomes a cross at the meta stage, with one atom from the duads at each
arm in addition to its own, and these form four duads on the hyper, and a
unit from the centre.

Gallium (Plate XIII, 2).
In gallium the funnel disappears
on the proto level, setting free its
two contained segments, each of
which forms a cylinder, thus
yielding twelve bodies on the
proto level. On the meta, the three
upper globes in each left-hand
segment are set free, and soon
vanish, each liberating a cigar and
two septets, the quartet and triad uniting. On the hyper the quartet yields
two duads but the triangle persists. The second set of bodies divide on the
meta level, forming a sextet and a cross with a duad at each arm; these on
the hyper level divide into two triangles, four duads and a unit. The seven-
atomed cone becomes two triangles united by a single atom, and on the
meta level these form a ring round the unit; on the hyper they form three
duads and a unit.
In the right-hand segment, the same policy is followed, the four triads
becoming two sextets, while the central body adds a third to the number.
The second ring has a quartet instead of the sextet, but otherwise breaks up
as does that of the left; the quintet at the base follows that of boron.

Indium (Plate XIII, 3).
The complication of three segments of different types in each funnel does
not affect the process of breaking up, and indium needs little attention. A is
exactly the same as the left-hand funnel of gallium, save for the substitution
of a globe containing the familiar "cigar" and two square-based pyramids. B
is the same as the right-hand funnel of gallium, except that its lowest body
consists of two square-based pyramids and a tetrahedron. All these are
familiar.

Phosphorus (Plate XIV, 1).

The atoms in the six similar
spheres in the segments of the
phosphorus funnel are arranged
on the eight angles of a cube, and
the central one is attached to all of
them. On the meta level five of
the nine atoms hold together and
place themselves on the angles of
a square-based pyramid; the
remaining four set themselves on
the angle of a tetrahedron. They yield, on the hyper level, two triads, a
duad, and a unit. The remaining bodies are simple and familiar.

Arsenic (Plate XIV, 2).
Arsenic shows the same ovoids and globe as have already been broken up
in aluminium (see ante); the remaining sixteen spheres form nine-atomed
bodies on the meta level, all similar to those of aluminium, thus yielding
twelve positive and twelve negative; the globe also yields a nine-atomed
body, twenty-five bodies of nine.

Antimony (Plate XIV, 3).
Antimony follows closely in the track of gallium and indium, the upper ring
of spheres being identical. In the second ring, a triplet is substituted for the
unit, and this apparently throws the cross out of gear, and we have a new
eleven-atomed figure, which breaks up into a triplet and two quartets on the
hyper level. The lowest seven-atomed sphere of the three at the base is the
same as we met with in copper.

VIII.

IV.—The Octahedral Groups.

These groups are at the turns of the spiral in Sir William Crookes'
lemniscates (see p. 28). On the one side is carbon, with below it titanium
and zirconium; on the other silicon, with germanium and tin. The
characteristic form is an octahedron, rounded at the angles and a little
depressed between the faces in consequence of the rounding; in fact, we did
not, at first, recognize it as an octahedron, and we called it the "corded
bale," the nearest likeness that struck us. The members of the group are all
tetrads, and have eight funnels, opening on the eight faces of the
octahedron. The first group is paramagnetic and positive; the corresponding
one is diamagnetic and negative. The two groups are not closely allied in
composition, though both titanium and tin have in common the five
intersecting tetrahedra at their respective centres.
Carbon (Plate III, 5, and XV, 1)
gives us the fundamental
octahedral form, which becomes
so masked in titanium and
zirconium. As before said (p. 30),
the protrusion of the arms in these
suggests the old Rosicrucian
symbol of the cross and rose, but
they show at their ends the eight
carbon funnels with their
characteristic contents, and thus
justify their relationship. The
funnels are in pairs, one of each
pair showing three "cigars," and
having as its fellow a funnel in
which the middle "cigar" is
truncated, thus loosing one atom.
Plate XV.
Each "cigar" has a leaf-like body
at its base, and in the centre of the
octahedron is a globe containing four atoms, each within its own wall; these
lie on the dividing lines of the faces, and each holds a pair of the funnels
together. It seems as though this atom had been economically taken from
the "cigar" to form a link. This will be more clearly seen when we come to
separate the parts from each other. It will be noticed that the atoms in the

"leaves" at the base vary in arrangement, being alternately in a line and in a
triangle.

{ left 27
CARBON: One pair of funnels { right 22
{ centre 1
--
54
4 pairs of funnels of 54 atoms 216
Atomic weight 11.91
Number weight 216/18 12.00

Titanium (Plate III, 6, and XV, 2) has a complete carbon atom distributed
over the ends of its four arms, a pair of funnels with their linking atom
being seen in each. Then, in each arm, comes the elaborate body shown as 3
c, with its eighty-eight atoms. A ring of twelve ovoids (3 d) each holding
within itself fourteen atoms, distributed among three contained globes—two
quartets and a sextet—is a new device for crowding in material. Lastly
comes the central body (4 e) of five intersecting tetrahedra, with a "cigar" at
each of their twenty points—of which only fifteen can be shown in the
diagram—and a ring of seven atoms round an eighth, that forms the minute
centre of the whole. Into this elaborate body one hundred and twenty-eight
atoms are built.

TITANIUM: One carbon atom 216
4 c of 88 atoms 352
12 d of 14 " 168
Central globe 128
----
Total 864
----
Atomic weight 47.74
Number weight 864/18 48.00

Zirconium (Plate XV, 3) has exactly the same outline as titanium, the
carbon atom is similarly distributed, and the central body is identical. Only

in 5 c and d do we find a difference on comparing them with 4 c and d. The
c ovoid in zirconium shows no less than fifteen secondary globes within the
five contained in the ovoid, and these, in turn, contain altogether sixty-nine
smaller spheres, with two hundred and twelve atoms within them, arranged
in pairs, triplets, quartets, quintets, a sextet and septets. Finally, the ovoids
of the ring are also made more elaborate, showing thirty-six atoms instead
of fourteen. In this way the clever builders have piled up in zirconium no
less than 1624 atoms.

ZIRCONIUM: One Carbon atom 216
4 c of 212 atoms 848
12 d of 36 " 432
Central globe 128
----
Total 1624
----
Atomic weight 89.85
Number weight 90.22

Silicon (Plate XVI, 1) is at the
head of the group which
corresponds to carbon on the
opposite turn of the lemniscate. It
has the usual eight funnels,
containing four ovoids in a circle,
and a truncated "cigar" but no
central body of any kind. All the
funnels are alike.

SILICON: 8 funnels of
65 atoms 520
Atomic weight
28.18
Number weight
520/18 28.88

Germanium (Plate XVI, 2) shows Plate XVI.
the eight funnels, containing each
four segments (XVI, 4), within which are three ovoids and a "cigar." In this
case the funnels radiate from a central globe, formed of two intersecting
tetrahedra, with "cigars" at each point enclosing a four-atomed globe.

GERMANIUM: 8 funnels of 156 atoms 1248
Central globe 52
----
Total 1300
----
Atomic weight 71.93
Number weight 1300/18 72.22

Tin (Plate XVI, 3) repeats the funnel of germanium, and the central globe
we met with in titanium, of five intersecting tetrahedra, carrying twenty
"cigars"; the latter, however, omits the eight-atomed centre of the globe that
was found in titanium, and hence has one hundred and twenty atoms therein
instead of one hundred and twenty-eight. Tin, to make room for the
necessary increase of atoms, adopts the system of spikes, which we met
with in zinc (see Plate IX, 2); these spikes, like the funnels, radiate from the
central globe, but are only six in number. The twenty-one-atomed cone at
the head of the spike we have already seen in silver, and we shall again find
it in iridium and platinum; the pillars are new in detail though not in
principle, the contained globes yielding a series of a triplet, quintet, sextet,
septet, sextet, quintet, triplet.

TIN: 8 funnels of 156 atoms 1248
6 spikes of 126 " 756
Central globe 120
----
Total 2124
----
Atomic weight 118.10
Number weight 2124/18 118.00

V.—The Bars Groups.
Here, for the first time, we find
ourselves a little at issue with the
accepted system of chemistry.
Fluorine stands at the head of a
group—called the inter-periodic
—whereof the remaining
members are (see Crookes' table,
p. 28), manganese, iron, cobalt,
nickel; ruthenium, rhodium,
palladium; osmium, iridium,
platinum. If we take all these as
group V, we find that fluorine and
manganese are violently forced
into company with which they
have hardly any points of
relationship, and that they intrude
into an otherwise very
harmonious group of closely Plate XVII.
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.
Iron (Plate IV, 1, and XVII, 3):

14 bars of 72 atoms 1008
Atomic weight 55.47
Number weight 1008/18 56.00

Cobalt (Plate XVII, 4):

14 bars of 74 atoms 1036

Atomic weight 57.70
Number weight 1036/18 57.55

Nickel (Plate XVII, 4):

14 bars of 76 atoms 1064
Atomic weight 58.30
Number weight 1064/18 59.11

(The weight of cobalt, as given in Erdmann's Lehrbuch, is 58.55, but
Messrs. Parker and Sexton, in Nature, August 1, 1907, give the weight, as
the result of their experiments, as 57.7.)
The next sub-group, ruthenium,
rhodium, and palladium, has
nothing to detain us. It will be
observed that each bar contains
eight segments, instead of the six
of cobalt and nickel; that
ruthenium and palladium have the
same number of atoms in their
upper ovoids, although in
ruthenium a triplet and quartet
represent the septet of palladium;
and that in ruthenium and
rhodium the lower ovoids are
identical, though one has the
order: sixteen, fourteen, sixteen,
fourteen; and the other: fourteen,
sixteen, fourteen, sixteen. One
constantly asks oneself: What is
the significance of these minute
Plate XVIII.
changes? Further investigators
will probably discover the answer.
Ruthenium (Plate XVIII, 1):

14 bars of 132 atoms 1848
Atomic weight 100.91
Number weight 1848/18 102.66

Rhodium (Plate XVII, 2):

14 bars of 134 atoms 1876
Atomic weight 102.23
Number weight 1876/18 104.22

Palladium (XVIII, 3):

14 bars of 136 atoms 1904
Atomic weight 105.74
Number weight 1904/18 105.77

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.

Osmium (Plate XVIII, 4):

14 bars of 245 atoms 3430
Atomic weight 189.55
Number weight 3430/18 190.55

Iridium (Plate XVIII, 5):

14 bars of 247 atoms 3458
Atomic weight 191.11
Number weight 3458/18 192.11

Platinum A (Plate XVIII, 6 a):

14 bars of 249 atoms 3486
Atomic weight 193.66
Number weight 3486/18 193.34

Platinum B (Plate XVIII, 6 b):

14 bars of 251 atoms 3514
Atomic weight ------
Number weight 3514/18 195.22

V a.—The Spike Groups.
I place within this group lithium, potassium, rubidium, fluorine, and
manganese, because of their similarity in internal composition. Manganese
has fourteen spikes, arranged as in the iron group, but radiating from a
central globe. Potassium has nine, rubidium has sixteen, in both cases
radiating from a central globe. Lithium (Plate IV, 2) and fluorine (Plate IV,
3) are the two types which dominate the group, lithium supplying the spike
which is reproduced in all of them, and fluorine the "nitrogen balloon"
which appears in all save lithium. It will be seen that the natural affinities

are strongly marked. They are all monads and paramagnetic; lithium,
potassium and rubidium are positive, while fluorine and manganese are
negative. We seem thus to have a pair, corresponding with each other, as in
other cases, and the interperiodic group is left interperiodic and congruous
within itself.
Lithium (Plate IV, 2 and Plate
XIX, 1) is a striking and beautiful
form, with its upright cone, or
spike, its eight radiating petals (x)
at the base of the cone, and the
plate-like support in the centre of
which is a globe, on which the
spike rests. The spike revolves
swiftly on its axis, carrying the
petals with it; the plate revolves
equally swiftly in the opposite
direction. Within the spike are
two globes and a long ovoid; the
spheres within the globe revolve
as a cross; within the ovoid are
four spheres containing atoms
arranged on tetrahedra, and a
central sphere with an axis of
three atoms surrounded by a
Plate XIX.
spinning wheel of six.

LITHIUM: Spike of 63 atoms 63
8 petals of 6 atoms 48
Central globe of 16 atoms 16
----
Total 127
----
Atomic weight 6.98
Number weight 127/18 7.05

Potassium (Plate XIX, 2) consists of nine radiating lithium spikes, but has
not petals; its central globe contains one hundred and thirty-four atoms,
consisting of the "nitrogen balloon," encircled by six four-atomed spheres.

POTASSIUM: 9 bars of 63 atoms 567
Central globe 134
----
Total 701
----
Atomic weight 38.94
Number weight 701/18 38.85

(The weight, as determined by Richards [Nature, July 18, 1907] is 39.114.)
Rubidium: (Plate XIX, 3) adds an ovoid, containing three spheres—two
triplets and a sextet—to the lithium spike, of which it has sixteen, and its
central globe is composed of three "balloons."

RUBIDIUM: 16 spikes of 75 atoms 1200
Central globe 330
----
Total 1530
----
Atomic weight 84.85
Number weight 1530/18 85.00

The corresponding negative group consists only of fluorine and manganese,
so far as our investigations have gone.
Fluorine (Plate IV, 3, and Plate XVII, 1) is a most peculiar looking object
like a projectile, and gives one the impression of being ready to shoot off on
the smallest provocation. The eight spikes, reversed funnels, coming to a
point, are probably responsible for this warlike appearance. The remainder
of the body is occupied by two "balloons."

FLUORINE: 8 spikes of 15 atoms 120
2 balloons 220
----
Total 340
----
Atomic weight 18.90
Number weight 340/18 18.88

Manganese (Plate XVII, 2) has fourteen spikes radiating from a central
"balloon."

MANGANESE: 14 spikes of 63 atoms 882
Central balloon 110
----
Total 992
----
Atomic weight 54.57
Number weight 992/18 55.11

IX.

We have now to consider the breaking up of the octahedral groups, and
more and more, as we proceed, do we find that the most complicated
arrangements are reducible to simple elements which are already familiar.

Carbon (Plate III, 5, and XV, 1).
Carbon is the typical octahedron, and a clear understanding of this will
enable us to follow easily the constitution and disintegration of the various
members of these groups. Its appearance as a chemical atom is shown on
Plate III, and see XV, 1. On the proto level the chemical atom breaks up into
four segments, each consisting of a pair of funnels connected by a single

atom; this is the proto element
which appears at the end of each
arm of the cross in titanium and
zirconium. On the meta level the
five six-atomed "cigars" show
two neutral combinations, and the
truncated "cigar" of five atoms is
also neutral; the "leaves" yield
two forms of triplet, five different
types being thus yielded by each
pair of funnels, exclusive of the
linking atom. The hyper level has triplets, duads and units.

Titanium (Plate III, 6, and XV, 2, 3).
On the proto level, the cross
breaks up completely, setting free
the pairs of funnels with the
linking atom (a and b), as in
carbon, the four bodies marked c,
the twelve marked d, and the
central globe marked e. The latter
breaks up again, setting free its
five intersecting cigar-bearing
tetrahedra, which follow their
usual course (see Occultum, p.
44). The eight-atomed body in the centre makes a ring of seven atoms round
a central one, like that in occultum (see p. 44, diagram B), from which it
only differs in having the central atom, and breaks up similarly, setting the
central atom free. The ovoid c sets free its four contained globes, and the
ovoid d sets free the three within it. Thus sixty-one proto elements are
yielded by titanium. On the meta level, c (titanium 3) breaks up into star-
like and cruciform bodies; the component parts of these are easily followed;
on the hyper level, of the four forms of triplets one behaves as in carbon,
and the others are shown, a, b and f; the cruciform quintet yields a triplet
and a duad, c and d; the tetrahedra yield two triplets g and h, and two units;
the septet, a triplet k and a quartet j. On the meta level, the bodies from d

behave like their equivalents in sodium, each d shows two quartets and a
sextet, breaking up, on the hyper level, into four duads and two triads.

Zirconium (Plate XV, 2, 5).
Zirconium reproduces in its c the four forms that we have already followed
in the corresponding c of titanium, and as these are set free on the proto
level, and follow the same course on the meta and hyper levels, we need not
repeat them. The central globe of zirconium c sets free its nine contained
bodies; eight of these are similar and are figured in the diagram; it will be
observed that the central body is the truncated "cigar" of carbon; their
behaviour on the meta and hyper levels is easily followed there. The central
sphere is also figured; the cigar follows its usual course, and its companions
unite into a sextet and an octet. The d ovoid liberates five bodies, four of
which we have already seen in titanium, as the crosses and sextet of
sodium, and which are figured under titanium; the four quartets within the
larger globe also follow a sodium model, and are given again.

Silicon (Plate XVI, 1).
In silicon, the ovoids are set free
from the funnels on the proto
level, and the truncated "cigar,"
playing the part of a leaf, is also
liberated. This, and the four
"cigars," which escape from their
ovoids, pass along their usual
course. The quintet and quartet
remain together, and form a nine-
atomed body on the meta level,
yielding a sextet and a triplet on
the hyper.

Germanium (Plate XVI, 2, 4).

The central globe, with its two "cigar"-bearing tetrahedra, need not delay
us; the tetrahedra are set free and follow the occultum disintegration, and
the central four atoms is the sodium cross that we had in titanium. The
ovoids (XVI, 4) are liberated on the proto level, and the "cigar," as usual,
bursts its way through and goes along its accustomed path. The others
remain linked on the meta level, and break up into two triangles and a
quintet on the hyper.

Tin (Plate XVI, 3, 4).
Here we have only the spike to consider, as the funnels are the same as in
germanium, and the central globe is that of titanium, omitting the eight
atomed centre. The cone of the spike we have had in silver (see p. 729,
May), and it is set free on the proto level. The spike, as in zinc, becomes a
large sphere, with the single septet in the centre, the remaining six bodies
circling round it on differing planes. They break up as shown. (Tin is Sn.)

Iron (Plate IV, I, and XVII, 3).
We have already dealt with the
affinities of this peculiar group,
and we shall see, in the
disintegration, even more clearly,
the close relationships which exist
according to the classification
which we here follow.
The fourteen bars of iron break
asunder on the proto level, and
each sets free its contents—a cone
and three ovoids, which as usual, become spheres. The twenty-eight-atomed
cone becomes a four-sided figure, and the ovoids show crystalline contents.
They break up, on the meta level as shown in the diagram, and are all
reduced to triplets and duads on the hyper level.

Cobalt (Plate XVII, 4).

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

Nickel (Plate XVII, 5).
The two additional atoms in a bar, which alone separate nickel from cobalt,
are seen in the upper sphere of the central ovoid.

Ruthenium (Plate XVIII, 1).
The lower ovoids in ruthenium are identical in composition, with those of
iron, cobalt and nickel and may be studied under Iron. The upper ones only
differ by the addition of a triplet.

Rhodium (Plate XVIII, 2).
Rhodium has a septet, which is to be seen in the c of titanium (see k in the
titanium diagram) and differs only in this from its group.

Palladium (Plate XVIII, 3).
In palladium this septet appears as the upper sphere in every ovoid of the
upper ring.

Osmium (Plate XVIII, 4).
We have here no new constituents; the ovoids are set free on the proto level
and the contained globes on the meta, all being of familiar forms. The
cigars, as usual, break free on the proto level, and leave their ovoid with
only four contained spheres, which unite into two nine-atomed bodies as in
silicon (see above).

Iridium (Plate XVIII, 5.)

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

Platinum (Plate XVIII, 6).
Again the silver cone is with us. The remaining bodies are set free on the
proto level, and their contained spheres on the meta.

Lithium (Plate IV, 2, and XIX, 1).
Here we have some new
combinations, which recur
persistently in its allies. The
bodies a, in Plate XIX, 1, are at
the top and bottom of the ellipse;
they come to right and left of it in
the proto state, and each makes a
twelve-atomed body on the meta
level.
The five bodies within the ellipse,
three monads and two sextets, show two which we have had before: d,
which behaves like the quintet and quartet in silicon, after their junction,
and b, which we have had in iron. The two bodies c are a variant of the
square-based pyramid, one atom at the apex, and two at each of the other
angles. The globe, e, is a new form, the four tetrahedra of the proto level
making a single twelve-atomed one on the meta. The body a splits up into
triplets on the hyper; b and d follow their iron and silicon models; c yields
four duads and a unit; e breaks into four quartets.

Potassium (Plate XIX, 2).
Potassium repeats the lithium spike; the central globe shows the "nitrogen
balloon," which we already know, and which is surrounded on the proto

level with six tetrahedra, which are set free on the meta and behave as in
cobalt. Hence we have nothing new.

Rubidium (Plate XIX, 3).
Again the lithium spike, modified slightly by the introduction of an ovoid,
in place of the top sphere; the forms here are somewhat unusual, and the
triangles of the sextet revolve round each other on the meta level; all the
triads break up on the hyper level into duads and units.

Fluorine (Plate IV, 3, and Plate XVII, 1).
The reversed funnels of fluorine split asunder on the proto level, and are set
free, the "balloons" also floating off independently. The funnels, as usual,
become spheres, and on the meta level set free their contained bodies, three
quartets and a triplet from each of the eight. The balloons disintegrate in the
usual way.

Manganese (Plate XVII, 2).
Manganese offers us nothing new, being composed of "lithium spikes" and
"nitrogen balloons."

X.

VI.—The Star Groups.
We have now reached the last of the groups as arranged on Sir William
Crookes' lemniscates, that forming the "neutral" column; it is headed by
helium, which is sui generis. The remainder are in the form of a flat star
(see Plate IV, 4), with a centre formed of five intersecting and "cigar"-
bearing tetrahedra, and six radiating arms. Ten of these have been observed,
five pairs in which the second member differs but slightly from the first;

they are: Neon, Meta-neon; Argon, Metargon; Krypton, Meta-krypton;
Xenon, Meta-xenon; Kalon, Meta-kalon; the last pair and the meta forms
are not yet discovered by chemists. These all show the presence of a
periodic law; taking an arm of the star in each of the five pairs, we find the
number of atoms to be as follows :—

40 99 224 363 489
47 106 231 370 496

It will be observed that the meta form in each case shows seven more atoms
than its fellow.
Helium (Plate III, 5, and Plate
XX, 1) shows two "cigar"-bearing
tetrahedra, and two hydrogen
triangles, the tetrahedra revolving
round an egg-shaped central body,
and the triangles spinning on their
own axes while performing a
similar revolution. The whole has
an attractively airy appearance, as
of a fairy element.

HELIUM: Two tetrahedra
of 24 atoms 48
Two triangles
of 9 atoms 18
Central egg
6
Plate XX.

----
Total 72
----
Atomic weight 3.94
Number weight 72/18 4.00

Neon (Plate XX, 2 and 6) has six arms of the pattern shown in 2, radiating
from the central globe.

NEON: Six arms of 40 atoms 240
Central tetrahedra 120

----
Total 360
----
Atomic weight 19.90
Number weight 360/18 20.00

Meta-neon (Plate XX, 3 and 6) differs from its comrade by the insertion of
an additional atom in each of the groups included in the second body within
its arm, and substituting a seven-atomed group for one of the triplets in
neon.

META-NEON: Six arms of 47 atoms 282
Central tetrahedra 120
----
Total 402
----
Atomic weight ----
Number weight 402/18 22.33

Argon (Plate XX, 4, 6 and 7) shows within its arms the b 63 which we met
in nitrogen, yttrium, vanadium and niobium, but not the "balloon," which
we shall find with it in krypton and its congeners.

ARGON: Six arms of 99 atoms 594
Central tetrahedra 120
----
Total 714
----

Atomic weight 39.60
Number weight 714/18 39.66

Metargon (Plate XX, 5, 6 and 7) again shows only an additional seven
atoms in each arm.

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

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

KRYPTON: Six arms of
224 atoms
1344
Central
tetrahedra
120

-----

Total 1464
Plate XXI.
-----
Atomic weight 81.20
Number weight 1464/18 81.33

Meta-Krypton differs only from krypton by the substitution of z for y in
each arm of the star.

META-KRYPTON: Six arms of 231 atoms 1386
Central tetrahedra 120
-----
Total 1506
-----
Atomic weight -----
Number weight 1506/18 83.66

Xenon (Plate XXI, 2 and 4, and Plate XX, 6 and 7) has a peculiarity shared
only by kalon, that x and y are asymmetrical, the centre of one having three
atoms and the centre of the other two. Is this done in order to preserve the
difference of seven from its comrade?

XENON: Six arms of 363 atoms 2178
Central tetrahedra 120
-----
Total 2298
-----
Atomic weight 127.10
Number weight 2298/18 127.66

Meta-Xenon differs from xenon only by the substitution of two z's for x and
y.

META-XENON: Six arms of 370 atoms 2220
Central tetrahedra 120
-----
Total 2340
-----
Atomic weight -----
Number weight 2340/18 130

Kalon (Plate XXI, 3 and 4, and Plate XX, 6 and 7) has a curious cone,
possessing a kind of tail which we have not observed elsewhere; x and y
show the same asymmetry as in xenon.

KALON: Six arms of 489 atoms 2934
Central tetrahedra 120
----
Total 3054
----
Atomic weight ----
Number weight 3054/18 169.66

Meta-Kalon again substitutes two z's for x and y.

META-KALON: Six arms of 496 atoms 2976
Central tetrahedra 120
----
Total 3096
----
Atomic weight ----
Number weight 3096/18 172

Only a few atoms of kalon and meta-kalon have been found in the air of a
fair-sized room.
It does not seem worth while to break up these elements, for their
component parts are so familiar. The complicated groups—a 110, b 63 and
c 120—have all been fully dealt with in preceding pages.

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

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

XI.

Radium.
Radium has the form of a
tetrahedron, and it is in the
tetrahedral groups (see article IV)
that we shall find its nearest
congeners; calcium, strontium,
chromium, molybdenum resemble
it most closely in general internal
arrangements, with additions
from zinc and cadmium. Radium
has a complex central sphere
(Plate XXII), extraordinarily
vivid and living; the whirling
motion is so rapid that continued
accurate observation is very
difficult; the sphere is more Plate XXII.
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

Plate XXIII.

Plate XXIV.

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.

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