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+The Project Gutenberg eBook, Occult Chemistry, by Annie Besant and Charles
+W. Leadbeater, Edited by A. P. Sinnett
+
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+
+
+
+Title: Occult Chemistry
+       Clairvoyant Observations on the Chemical Elements
+
+
+Author: Annie Besant and Charles W. Leadbeater
+
+Editor: A. P. Sinnett
+
+Release Date: June 14, 2005  [eBook #16058]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+
+***START OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY***
+
+
+E-text prepared by Clare Boothby, Keith Edkins, and the Project Gutenberg
+Online Distributed Proofreading Team
+
+
+
+Note: Project Gutenberg also has an HTML version of this
+      file which includes the original illustrations.
+      See 16058-h.htm or 16058-h.zip:
+      (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h/16058-h.htm)
+      or
+      (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h.zip)
+
+
+
+
+
+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.
+
+[Illustration]
+
+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 spirillę, and these again of minuter spirillę. 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.
+
+[Illustration]
+
+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. Jinarājadāsa[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.
+
+[Illustration: PLATE I. SODIUM.]
+
+In counting the number of ultimate atoms in a chemical elemental atom, we
+did not count them throughout, one by one; when, for instance, we counted
+up the ultimate atoms in sodium, we dictated the number in each convenient
+group to Mr. Jinarājadāsa, and he multiplied out the total, divided by 18,
+and announced the result. Thus: sodium (_see_ Plate I) is composed of an
+upper part, divisible into a globe and 12 funnels; a lower part, similarly
+divided; and a connecting rod. We counted the number in the upper part:
+globe--10; the number in two or three of the funnels--each 16; the number
+of funnels--12; the same for the lower part; in the connecting rod--14. Mr.
+Jinarājadāsa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418:
+divided by 18 = 23.22 recurring. By this method we guarded our counting
+from any prepossession, as it was impossible for us to know how the various
+numbers would result on addition, multiplication and division, and the
+exciting moment came when we waited to see if our results endorsed or
+approached any accepted weight. In the heavier elements, such as gold, with
+3546 atoms, it would have been impossible to count each atom without quite
+unnecessary waste of time, when making a preliminary investigation. Later,
+it may be worth while to count each division separately, as in some we
+noticed that two groups, at first sight alike, differed by 1 or 2 atoms,
+and some very slight errors may, in this way, have crept into our
+calculations.
+
+In the following table is a list of the chemical elements examined; the
+first column gives the names, the asterisk affixed to some indicating that
+they have not yet been discovered by orthodox chemistry. The second column
+gives the number of ultimate physical atoms contained in one chemical atom
+of the element concerned. The third column gives the weight as compared
+with hydrogen, taken as 18, and this is obtained by dividing the calculated
+number of ultimate atoms by 18. The fourth column gives the recognized
+weight-number, mostly according to the latest list of atomic weights, the
+"International List" of 1905, given in Erdmann's "Lehrbuch der
+Unorganischen Chemie." These weights differ from those hitherto accepted,
+and are generally lighter than those given in earlier text-books. It is
+interesting to note that our counting endorses the earlier numbers, for the
+most part, and we must wait to see if later observations will endorse the
+last results of orthodox chemistry, or confirm ours.
+
+--------------------------------------------
+Hydrogen       |    18   |   1     |   1
+*Occultum      |    54   |   3     |   --
+Helium         |    72   |   4     |   3.94
+Lithium        |   127   |   7.06  |   6.98
+Baryllium      |   164   |   9.11  |   9.01
+Boron          |   200   |  11.11  |  10.86
+Carbon         |   216   |  12     |  11.91
+Nitrogen       |   261   |  14.50  |  14.01
+Oxygen         |   290   |  16.11  |  15.879
+Fluorine       |   340   |  18.88  |  18.90
+Neon           |   360   |  20     |  19.9
+*Meta-Neon     |   402   |  22.33  |   --
+Sodium         |   418   |  23.22  |  22.88
+Magnesium      |   432   |  24     |  24.18
+Aluminium      |   486   |  27     |  26.91
+Silicon        |   520   |  28.88  |  28.18
+Phosphorus     |   558   |  31     |  30.77
+Sulphur        |   576   |  32     |  31.82
+Chlorine       |   639   |  35.50  |  35.473
+Potassium      |   701   |  38.944 |  38.85
+Argon          |   714   |  39.66  |  39.60
+Calcium        |   720   |  40     |  39.74
+*Metargon      |   756   |  42     |   --
+Scandium       |   792   |  44     |  43.78
+Titanium       |   864   |  48     |  47.74
+Vanadium       |   918   |  51     |  50.84
+Chromium       |   936   |  52     |  51.74
+Manganese      |   992   |  55.11  |  54.57
+Iron           |  1008   |  56     |  55.47
+Cobalt         |  1036   |  57.55  |  57.7
+Nickel         |  1064   |  59.ll  |  58.30
+Copper         |  1139   |  63.277 |  63.12
+Zinc           |  1170   |  65     |  64.91
+Gallium        |  1260   |  70     |  69.50
+Germanium      |  1300   |  72.22  |  71.93
+Arsenic        |  1350   |  75     |  74.45
+Selenium       |  1422   |  79     |  78.58
+Bromine        |  1439   |  79.944 |  79.953
+Krypton        |  1464   |  81.33  |  81.20
+*Meta-Krypton  |  1506   |  83.66  |   --
+Rubidium       |  1530   |  85     |  84.85
+Strontium      |  1568   |  87.11  |  86.95
+Yttrium        |  1606   |  89.22  |  88.34
+Zirconium      |  1624   |  90.22  |  89.85
+Niobium        |  1719   |  95.50  |  93.25
+Molybdenum     |  1746   |  97     |  95.26
+Ruthenium      |  1848   | 102.66  | 100.91
+Rhodium        |  1876   | 104.22  | 102.23
+Palladium      |  1904   | 105.77  | 105.74
+Silver         |  1945   | 108.055 | 107.93
+Cadmium        |  2016   | 112     | 111.60
+Indium         |  2052   | 114     | 114.05
+Tin            |  2124   | 118     | 118.10
+Antimony       |  2169   | 120.50  | 119.34
+Tellurium      |  2223   | 123.50  | 126.64
+Iodine         |  2287   | 127.055 | 126.01
+Xenon          |  2298   | 127.66  | 127.10
+*Meta-Xenon    |  2340   | 130     |   --
+*Kalon         |  3054   | 169.66  |   --
+*Meta-Kalon    |  3096   | 172     |   --
+Osmium         |  3430   | 190.55  | 189.55
+Iridium        |  3458   | 192.11  | 191.56
+Platinum A     |  3486   | 193.66  | 193.34
+*Platinum B    |  3514   | 195.22  |   --
+Gold           |  3546   | 197     | 195.74
+--------------------------------------------
+[Illustration: PLATE II. MALE (left) and FEMALE (right).]
+
+As the words "ultimate physical atom" must frequently occur, it is
+necessary to state what we mean by the phrase. Any gaseous chemical atom
+may be dissociated into less complicated bodies; these, again, into still
+less complicated; these, again, into yet still less complicated. These will
+be dealt with presently. After the third dissociation but one more is
+possible; the fourth dissociation gives the ultimate physical atom.[3] This
+may vanish from the physical plane, but it can undergo no further
+dissociation on it. In this ultimate state of physical matter two types of
+atoms have been observed; they are alike in everything save the direction
+of their whorls and of the force which pours through them. In the one case
+force pours in from the "outside," from fourth-dimensional space,[4] and
+passing through the atom, pours into the physical world. In the second, it
+pours in from the physical world, and out through the atom into the
+"outside" again,[4] _i.e._, vanishes from the physical world. The one is
+like a spring, from which water bubbles out; the other is like a hole, into
+which water disappears. We call the atoms from which force comes out
+_positive_ or _male_; those through which it disappears, _negative_ or
+_female_. All atoms, so far as observed, are of one or other of these two
+forms. (Plate II.)
+
+It will be seen that the atom is a sphere, slightly flattened, and there is
+a depression at the point where the force flows in, causing a heart-like
+form. Each atom is surrounded by a field, formed of the atoms of the four
+higher planes, which surround and interpenetrate it.
+
+The atom can scarcely be said to be a "thing," though it is the material
+out of which all things physical are composed. It is formed by the flow of
+the life-force[5] and vanishes with its ebb. When this force arises in
+"space"[6]--the apparent void which must be filled with substance of some
+kind, of inconceivable tenuity--atoms appear; if this be artificially
+stopped for a single atom, the atom disappears; there is nothing left.
+Presumably, were that flow checked but for an instant, the whole physical
+world would vanish, as a cloud melts away in the empyrean. It is only the
+persistence of that flow[7] which maintains the physical basis of the
+universe.[8]
+
+In order to examine the construction of the atom, a space is artificially
+made[9]; then, if an opening be made in the wall thus constructed, the
+surrounding force flows in, and three whorls immediately appear,
+surrounding the "hole" with their triple spiral of two and a half coils,
+and returning to their origin by a spiral within the atom; these are at
+once followed by seven finer whorls, which following the spiral of the
+first three on the outer surface, and returning to their origin by a spiral
+within that, flowing in the opposite direction--form a caduceus with the
+first three. Each of the three coarser whorls, flattened out, makes a
+closed circle; each of the seven finer ones, similarly flattened out, makes
+a closed circle. The forces which flow in them, again, come from "outside,"
+from a fourth-dimensional space.[10] Each of the finer whorls is formed of
+seven yet finer ones, set successively at right angles to each other, each
+finer than its predecessor; these we call spirillę.[11]
+
+It will be understood from the foregoing, that the atom cannot be said to
+have a wall of its own, unless these whorls of force can be so designated;
+its "wall" is the pressed back "space." As said in 1895, of the chemical
+atom, the force "clears itself a space, pressing back the undifferentiated
+matter of the plane, and making to itself a whirling wall of this matter."
+The wall belongs to space, not to the atom.
+
+In the three whorls flow currents of different electricities; the seven
+vibrate in response to etheric waves of all kinds--to sound, light, heat,
+etc.; they show the seven colours of the spectrum; give out the seven
+sounds of the natural scale; respond in a variety of ways to physical
+vibration--flashing, singing, pulsing bodies, they move incessantly,
+inconceivably beautiful and brilliant.[12]
+
+The atom has--as observed so far--three proper motions, _i.e._, motions of
+its own, independent of any imposed upon it from outside. It turns
+incessantly upon its own axis, spinning like a top; it describes a small
+circle with its axis, as though the axis of the spinning top moved in a
+small circle; it has a regular pulsation, a contraction and expansion, like
+the pulsation of the heart. When a force is brought to bear upon it, it
+dances up and down, flings itself wildly from side to side, performs the
+most astonishing and rapid gyrations, but the three fundamental motions
+incessantly persist. If it be made to vibrate, as a whole, at the rate
+which gives any one of the seven colors, the whorl belonging to that color
+glows out brilliantly.
+
+[Illustration]
+
+An electric current brought to bear upon the atoms checks their proper
+motions, _i.e._, renders them slower; the atoms exposed to it arrange
+themselves in parallel lines, and in each line the heart-shaped depression
+receives the flow, which passes out through the apex into the depression of
+the next, and so on. The atoms always set themselves to the current. The
+well-known division of diamagnetic and paramagnetic depends generally on
+this fact, or on an analogous action on molecules, as may be seen in the
+accompanying diagrams.[13]
+
+Two atoms, positive and negative, brought near to each other, attract each
+other, and then commence to revolve round each other, forming a relatively
+stable duality; such a molecule is neutral. Combinations of three or more
+atoms are positive, negative or neutral, according to the internal
+molecular arrangement; the neutral are relatively stable, the positive and
+negative are continually in search of their respective opposites, with a
+view to establishing a relatively permanent union.
+
+Three states of matter exist between the atomic state and the gaseous--the
+state in which the chemical atoms are found, the recognized chemical
+elements; for our purposes we may ignore the liquid and solid states. For
+the sake of clearness and brevity in description, we have been obliged to
+name these states; we call the atomic state of the chemist _elemental_; the
+state which results from breaking up chemical elements, _proto-elemental_;
+the next higher, _meta-proto-elemental_; the next higher,
+_hyper-meta-proto-elemental_; then comes the atomic state. These are
+briefly marked as El., Proto., Meta., and Hyper.[14]
+
+The simplest unions of atoms, never, apparently consisting of more than
+seven, form the first molecular state of physical matter.
+
+[Illustration: TYPES OF HYPER-META-PROTO-ELEMENTAL MATTER.]
+
+Here are some characteristic combinations of the Hyper state; the atom is
+conventional, with the depression emphasised; the lines, always entering at
+the depression and coming out at the apex, show the resultants of lines of
+force; where no line appears entering the depression, the force wells up
+from fourth-dimensional space; where no line appears leaving the apex, the
+force disappears into fourth-dimensional space; where the point of entry
+and departure is outside the atoms, it is indicated by a dot.[15]
+
+The molecules show all kinds of possible combinations; the combinations
+spin, turn head over heels, and gyrate in endless ways. Each aggregation is
+surrounded with an apparent cell-wall, the circle or oval, due to the
+pressure on the surrounding matter caused by its whirling motion; they
+strike on each other[16] and rebound, dart hither and thither, for reasons
+we have not distinguished.
+
+[Illustration: TYPES OF META-PROTO-ELEMENTAL MATTER.]
+
+The Meta state, in some of its combinations, appears at first sight to
+repeat those of the Hyper state; the only obvious way of distinguishing to
+which some of the molecules of less complexity belong is to pull them out
+of the "cell-wall"; if they are Hyper molecules they at once fly off as
+separate atoms; if they are Meta molecules they break up into two or more
+molecules containing a smaller number of atoms. Thus one of the Meta
+molecules of iron, containing seven atoms, is identical in appearance with
+a Hyper heptad, but the latter dissociates into seven atoms, the former
+into two triads and a single atom. Long-continued research into the
+detailed play of forces and their results is necessary; we are here only
+able to give preliminary facts and details--are opening up the way. The
+following may serve as characteristic Meta types:--
+
+These are taken from constituents of the various elements; 1 from Gl; 2 and
+3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12
+from Li; 13 and 14 from Na. Others will be seen in the course of breaking
+up the elements.
+
+The Proto state preserves many of the forms in the elements, modified by
+release from the pressure to which they are subjected in the chemical atom.
+In this state various groups are thus recognizable which are characteristic
+of allied metals.
+
+[Illustration: TYPES OF PROTO-ELEMENTAL MATTER.]
+
+These are taken from the products of the first disintegration of the
+chemical atom, by forcibly removing it from its hole. The groups fly apart,
+assuming a great variety of forms often more or less geometrical; the lines
+between the constituents of the groups, where indicated, no longer
+represent lines of force, but are intended to represent the impression of
+form, _i.e._, of the relative position and motion of the constituents, made
+on the mind of the observer. They are elusive, for there are no lines, but
+the appearance of lines is caused by the rapid motion of the costituents up
+and down, or along them backwards and forwards. The dots represent atoms,
+or groups of atoms, within the proto-elements. 1 is found in C; 2 and 3 in
+He; 4 in Fl; 5 in Li; 6 in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe;
+12 in Se. We shall return to these when analysing the elements, and shall
+meet many other proto-elemental groupings.
+
+The first thing which is noticed by the observer, when he turns his
+attention to the chemical atoms, is that they show certain definite forms,
+and that within these forms, modified in various ways, sub-groupings are
+observable which recur in connexion with the same modified form. The main
+types are not very numerous, and we found that, when we arranged the atoms
+we had observed, according to their external forms, they fell into natural
+classes; when these, in turn, were compared with Sir William Crookes'
+classification, they proved to be singularly alike. Here is his arrangement
+of the elements, as it appeared in the _Proceedings of the Royal Society_,
+in a paper read on June 9th, 1898.
+
+[Illustration]
+
+This is to be read, following the lines of the "figures of eight": H, He,
+Li, Gl, B, C, N, and so on, each successive element being heavier than the
+one preceding it in order. The disks which fall immediately below each
+other form a class; thus: H, Cl, Br, I; these resemble each other in
+various ways, and, as we shall presently see, the same forms and groupings
+re-appear.
+
+Another chart--taken from Erdmann's _Lehrbuch_--arranges the elements on a
+curved line, which curiously resembles the curves within the shell of a
+nautilus. The radiating lines show the classes, the whole diameter building
+up a family; it will be observed that there is an empty radius between
+hydrogen and helium, and we have placed occultum there; on the opposite
+radius, iron, rubidium and osmium are seen.
+
+[Illustration]
+
+The external forms may be classified as follows; the internal details will
+be dealt with later :--
+
+[Illustration: PLATE III.]
+
+1. _The Dumb-bell._--The characteristics of this are a higher and lower
+group, each showing 12 projecting funnels, grouped round a central body,
+and a connecting rod. It appears in sodium, copper, silver, and gold,[17]
+and gold is given (1 on Plate III) as the most extremely modified example
+of this form. The 12 almond-like projections, above and below, are
+severally contained in shadowy funnels, impossible to reproduce in the
+drawing; the central globe contains three globes, and the connecting
+portion has swollen out into an egg, with a very complicated central
+arrangement. The dumb-bell appears also in chlorine, bromine and iodine,
+but there is no trace of it in hydrogen, the head of the group. We have not
+met it elsewhere. It may be remarked that, in Sir William Crookes' scheme,
+in which they are all classed as monads, these two groups are the nearest
+to the neutral line, on the ingoing and outgoing series, and are
+respectively positive and negative.
+
+II and IIa. _The Tetrahedron._--The characteristics of this form are four
+funnels, containing ovoid bodies, opening on the face of a tetrahedron. The
+funnels generally, but not always, radiate from a central globe. We give
+beryllium (glucinum) as the simplest example (2 on Plate III), and to this
+group belong calcium and strontium. The tetrahedron is the form of chromium
+and molybdenum, but not that of the head of their group, oxygen, which is,
+like hydrogen, _sui generis_. These two groups are marked in orthodox
+chemistry as respectively positive and negative, and are closely allied.
+Another pair of groups show the same tetrahedral form: magnesium, zinc and
+cadmium, positive; sulphur, selenium and tellurium, negative. Selenium is a
+peculiarly beautiful element, with a star floating across the mouth of each
+funnel; this star is extremely sensitive to light, and its rays tremble
+violently and bend if a beam of light falls on it. All these are dyads.
+
+The tetrahedron is not confined to the external form of the above atoms; it
+seems to be one of the favourite forms of nature, and repeatedly appears in
+the internal arrangements. There is one tetrahedron within the unknown
+element occultum; two appear in helium (3 on Plate III); yttrium has also
+two within its cube, as has germanium; five, intersecting, are found in
+neon, meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon,
+kalon, meta-kalon, tin, titanium and zirconium. Gold contains no less than
+twenty tetrahedra.
+
+III. _The Cube._--The cube appears to be the form of triads. It has six
+funnels, containing ovoids, and opening on the faces of the cube. Boron is
+chosen as an example (4 on Plate III). Its group members, scandium and
+yttrium, have the same form; we have not examined the fourth; the group is
+positive. Its negative complement consists of nitrogen, vanadium and
+niobium, and we have again to note that nitrogen, like hydrogen and oxygen,
+departs from its group type. Two other triad groups, the positive
+aluminium, gallium and indium (the fourth unexamined) and the negative
+phosphorus, arsenic and antimony (the fourth unexamined), have also six
+funnels opening on the faces of a cube.
+
+IV. _The Octahedron._--The simplest example of this is carbon (5 on Plate
+III). We have again the funnel with its ovoids, but now there are eight
+funnels opening on the eight faces of the octahedron. In titanium (6 on
+Plate III) the form is masked by the protruding arms, which give the
+appearance of the old Rosicrucian Cross and Rose, but when we look into the
+details later, the carbon type comes out clearly. Zirconium is exactly like
+titanium in form, but contains a large number of atoms. We did not examine
+the remaining two members of this group. The group is tetratomic and
+positive. Its negative pendant shows the same form in silicon, germanium
+and tin; again, the fourth was unexamined.
+
+[Illustration: PLATE IV.]
+
+V. _The Bars._--These characterise a set of closely allied groups, termed
+"inter-periodic." Fourteen bars (or seven crossed) radiate from a centre,
+as in iron (1 on Plate IV), and the members of each group--iron, nickel,
+cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum--differ
+from each other by the weight of each bar, increasing in orderly
+succession; the details will be given later. Manganese is often grouped
+with iron, nickel, and cobalt (_see_ Crookes' lemniscates), but its
+fourteen protruding bodies repeat the "lithium spike" (proto-element 5) and
+are grouped round a central ovoid. This would appear to connect it with
+lithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with
+which it is often classed. The "lithium spike" re-appears in potassium and
+rubidium. These details, again, will come out more clearly later.
+
+VI. _The Star._--A flat star, with five interpenetrating tetrahedra in the
+centre, is the characteristic of neon and its allies (4 on Plate IV)
+leaving apart helium, which, as may be seen by referring to 3, Plate IV,
+has an entirely different form.
+
+There are thus six clearly defined forms, typical of classes, with
+two--lithium and fluorine--of doubtful affinities. It is worthy of notice
+that in diatomic elements _four_ funnels open on the faces of tetrahedra;
+in triatomic, _six_ funnels on the faces of cubes; in tetratomic, _eight_
+funnels on the faces of octahedra.
+
+Thus we have a regular sequence of the platonic solids, and the question
+suggests itself, will further evolution develop elements shaped to the
+dodecahedron and the icosahedron?
+
+       *       *       *       *       *
+
+II.
+
+We now pass from the consideration of the outer forms of the chemical
+elements to a study of their internal structure, the arrangement within the
+element of more or less complicated groups--proto-elements--capable of
+separate, independent existence; these, once more, may be dissociated into
+yet simpler groups--hyper-meta-proto-elements--equally capable of separate,
+independent existence, and resolvable into single ultimate physical atoms,
+the irreducible substratum of the physical world (see _Theosophist_, 1908,
+pp. 354-356).[18]
+
+We shall have to study the general internal structure, and then the
+breaking up of each element, and the admirable diagrams, patiently worked
+out by Mr. Jinarājadāsa, 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 _Encyclopędia
+Britannica_. We use the words in their ordinary text-book meaning, and have
+not, so far, detected any characteristics whereby an element can be
+declared, at sight, to be either positive or negative:--
+
+"When binary compounds, or compounds of two elements, are decomposed by an
+electric current, the two elements make their appearance at opposite poles.
+These elements which are disengaged at the negative pole are termed
+electro-positive or positive or basylous elements, while those disengaged
+at the positive pole are termed electro-negative or negative or chlorous
+elements. But the difference between these two classes of elements is one
+of degree only, and they gradually merge into each other; moreover the
+electric relations of elements are not absolute, but vary according to the
+state of combination in which they exist, so that it is just as impossible
+to divide the elements into two classes according to this property as it is
+to separate them into two distinct classes of metals and non-metals."
+
+We follow here the grouping according to external forms, and the student
+should compare it with the groups marked in the lemniscate arrangement
+shown in Article II (p. 377, properly p. 437, February), reading the group
+by the disks that fall below each other; thus the first group is H, Cl, Br,
+I (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered
+element. The elements grow denser in descending order; thus hydrogen is an
+invisible gas; chlorine a denser gas visible by its colour; bromine is a
+liquid; iodine is a solid--all, of course, when temperature and pressure
+are normal. By the lowering of temperature and the increase of pressure, an
+element which is normally gaseous becomes a liquid, and then a solid.
+Solid, liquid, gaseous, are three interchangeable states of matter, and an
+element does not alter its constitution by changing its state. So far as a
+chemical "atom" is concerned, it matters not whether it be drawn for
+investigation from a solid, a liquid, or a gas; but the internal
+arrangements of the "atoms" become much more complicated as they become
+denser and denser, as is seen by the complex arrangements necessitated by
+the presence of the 3546 ultimate atoms contained in the chemical "atom" of
+gold, as compared with the simple arrangement of the 18 ultimate atoms of
+hydrogen.
+
+According to the lemniscate arrangement, we should commence with hydrogen
+as the head of the first negative group, but as it differs wholly from
+those placed with it, it is better to take it by itself. Hydrogen is the
+lightest of the known elements, and is therefore taken as 1 in ordinary
+chemistry, and all atomic weights are multiples of this. We take it as 18,
+because it contains eighteen ultimate atoms, the smallest number we have
+found in a chemical element. So our "number-weights" are obtained by
+dividing the total number of atoms in an element by 18 (see p. 349,
+January).
+
+[Illustration: PLATE V.]
+
+HYDROGEN (Plate V, 1).--Hydrogen not only stands apart from its reputed
+group by not having the characteristic dumb-bell shape, well shown in
+sodium (Plate I, opposite p. 349, January), but it also stands apart in
+being positive, serving as a base, not as a chlorous, or acid, radical,
+thus "playing the part of a metal," as in hydrogen chloride (hydrochloric
+acid), hydrogen sulphate (sulphuric acid), etc.
+
+It is most curious that hydrogen, oxygen and nitrogen, the most widely
+spread gases, all differ fundamentally in form from the groups they
+reputedly head.[19] Hydrogen was the first chemical element examined by us,
+nearly thirteen years ago, and I reproduce here the substance of what I
+wrote in November, 1895, for we have nothing to add to nor amend in it.
+
+Hydrogen consists of six small bodies, contained in an egg-like form (the
+outer forms are not given in the diagrams). The six little bodies are
+arranged in two sets of three, forming two triangles which are not
+interchangeable, but are related to each other as object and image. The six
+bodies are not all alike; they each contain three ultimate physical atoms,
+but in four of the bodies the three atoms are arranged in a triangle, and
+in the remaining two in a line.
+
+HYDROGEN: 6 bodies of 3            18
+          Atomic weight             1
+          Number weight 18/18       1
+I.--THE DUMB-BELL GROUP.
+
+I a.--This group consists of Cl, Br, and I (chlorine, bromine and iodine);
+they are monads, diamagnetic and negative.
+
+CHLORINE (Plate V, 2).--As already said, the general form is that of the
+dumb-bell, the lower and upper parts each consisting of twelve funnels, six
+sloping upwards and six downwards, the funnels radiating outwards from a
+central globe, and these two parts being united by a connecting rod (see,
+again, sodium, Plate I).
+
+The funnel (shown flat as an isosceles triangle, standing on its apex) is a
+somewhat complicated structure, of the same type as that in sodium (Plate
+VI, 2), the difference consisting in the addition of one more globe,
+containing nine additional atoms. The central globe is the same as in
+sodium, but the connecting rod differs. We have here a regular arrangement
+of five globes, containing three, four, five, four, three atoms
+respectively, whereas sodium has only three bodies, containing four, six,
+four. But copper and silver, its congeners, have their connecting rods of
+exactly the same pattern as the chlorine rod, and the chlorine rod
+reappears in both bromine and iodine. These close similarities point to
+some real relation between these groups of elements, which are placed, in
+the lemniscates, equi-distant from the central line, though one is on the
+swing which is going towards that line and the other is on the swing away
+from it.
+
+CHLORINE: Upper part {12 funnels of 25 atoms  300
+                     {Central globe            10
+          Lower part same                     310
+          Connecting rod                       19
+                                             ----
+                           Total              639
+                                             ----
+          Atomic weight                     35.473
+          Number weight 639/18              35.50
+(The Atomic Weights are mostly from Erdmann, and the Number Weights are
+those ascertained by us by counting the atoms as described on p. 349,
+January, and dividing by 18. Prof. T.W. Richards, in _Nature_, July 18,
+1907, gives 35.473.)
+
+BROMINE (Plate V, 3).--In bromine, each funnel has three additional bodies,
+ovoid in shape, an addition of 33 atoms being thus made without any
+disturbance of form; two pairs of atoms are added to the central globe, and
+a rearrangement of the atoms is effected by drawing together and lessening
+the swing of the pair of triplets, thus making symmetrical room for the
+newcomers. The connecting rod remains unchanged. The total number of atoms
+is thus raised from the 639 of chlorine to 1439. Over and over again, in
+these investigations, were we reminded of Tyndall's fascinating description
+of crystal building, and his fancy of the tiny, ingenious builders busied
+therein. Truly are there such builders, and the ingenuity and effectiveness
+of their devices are delightful to see.[20]
+
+BROMINE:  Upper part {12 funnels of 58 atoms   696
+                     {Central globe             14
+          Lower part same                      710
+          Connecting rod                        19
+                                              ----
+                           Total              1439
+                                              ----
+          Atomic weight                      79.953
+          Number weight 1459/18              79.944
+IODINE (Plate V, 4).--We find herein that the central globe gains 4 atoms,
+the two pairs becoming 2 quartets; the connecting rod exactly reproduces
+the rods of chlorine and bromine; the funnel is also that of bromine,
+except that five bodies, containing 35 atoms, are added to it. The 1439
+atoms of bromine are thus raised to 2887.
+
+IODINE:   Upper Part {12 funnels of 90 atoms  1116
+                     {Central globe             18
+          Lower part same                     1134
+          Connecting rod                        19
+                                              ----
+                           Total              2287
+                                              ----
+          Atomic weight                     126.01
+          Number weight  2287/18            127.055
+The plan underlying the building up of groups is here clearly shown; a
+figure is built up on a certain plan, in this case a dumb-bell; in the
+succeeding members of the group additional atoms are symmetrically
+introduced, modifying the appearance, but following the general idea; in
+this case the connecting rod remains unaltered, while the two ends become
+larger and larger, more and more overshadowing it, and causing it to become
+shorter and thicker. Thus a group is gradually formed by additional
+symmetrical additions. In the undiscovered remaining member of the group we
+may suppose that the rod will have become still more egg-like, as in the
+case of gold.
+
+I b.--The corresponding positive group to that which we have been
+considering consists of Na, Cu, Ag, and Au (sodium, copper, silver and
+gold), with an empty disk between silver and gold, showing where an element
+ought to be. These four elements are monads, diamagnetic, and positive, and
+they show the dumb-bell arrangement, although it is much modified in gold;
+we may presume that the undiscovered element between silver and gold would
+form a link between them.
+
+[Illustration: PLATE VI.]
+
+SODIUM (Plate VI, 2) has been already described (p. 349, January), as a
+type of the group, so we need only refer to its internal arrangement in
+order to note that it is the simplest of the dumb-bell group. Its twelve
+funnels show only four enclosed bodies, the same as we see in chlorine,
+bromine, iodine, copper and silver, and which is very little modified in
+gold. Its central globe is the simplest of all, as is its connecting rod.
+We may therefore take it that sodium is the ground-plan of the whole group.
+
+SODIUM:   Upper part
+              { 12 funnels of 16 each    192
+              { Central globe             10
+          Lower part same                202
+          Connecting rod                  14
+                                        ----
+                      Total              418
+                                        ----
+          Atomic weight                23.88
+          Number weight 418/19         23.22
+COPPER (Plate VI, 3) introduces an addition in the funnel, that we shall
+find elsewhere, _e.g._, in silver, gold, iron, platinum, zinc, tin, the
+triangular arrangement near the mouth of the funnel and adds to the ten
+atoms in this nineteen more in three additional enclosed bodies, thus
+raising the number of atoms in a funnel from the sixteen of sodium to
+forty-five. The number in the central globe is doubled, and we meet for the
+first time the peculiar cigar or prism-shaped six-atomed arrangement, that
+is one of the most common of atomic groups. It ought to imply some definite
+quality, with its continual recurrence. The central column is the three,
+four, five, four, three, arrangement already noted.
+
+COPPER:   Upper part {12 funnels of 45 atoms  540
+                     {Central globe            20
+          Lower part same                     560
+          Connecting rod                       19
+                                             ----
+                           Total             1139
+                                             ----
+          Atomic weight                     63.12
+          Number weight 1139/18             63.277
+SILVER (Plate VI, 4) follows copper in the constitution of five of the
+bodies enclosed in the funnels. But the triangular group contains
+twenty-one atoms as against ten, and three ovoids, each containing three
+bodies with eleven atoms, raise the number of atoms in a funnel to
+seventy-nine. The central globe is decreased by five, and the prisms have
+disappeared. The connecting rod is unaltered.
+
+SILVER:   Upper part {12 funnels of 79 atoms   948
+                     {Central globe             15
+          Lower part same                      963
+          Connecting rod                        19
+                                              ----
+                           Total              1945
+                                              ----
+          Atomic weight                     107.93
+          Number weight 1945/18             108.055
+(This atomic weight is given by Stas, in _Nature_, August 29, 1907, but it
+has been argued later that the weight should not be above 107.883.)
+
+[Illustration: PLATE VII.]
+
+GOLD (Plate VII) is so complicated that it demands a whole plate to itself.
+It is difficult to recognize the familiar dumb-bell in this elongated egg,
+but when we come to examine it, the characteristic groupings appear. The
+egg is the enormously swollen connecting rod, and the upper and lower parts
+with their central globes are the almond-like projections above and below,
+with the central ovoid. Round each almond is a shadowy funnel (not drawn in
+the diagram), and within the almond is the collection of bodies shown in
+_e_, wherein the two lowest bodies are the same as in every other member of
+the negative and positive groups; the third, ascending, is a very slight
+modification of the other thirds; the fourth is a union and re-arrangement
+of the fourth and fifth; the fifth, of four ovoids, adds one to the three
+ovoids of bromine, iodine and silver; the triangular group is like that in
+copper and silver, though with 28 atoms instead of 10 or 21, and it may be
+noted that the cone in iron has also 28. The central body in the ovoid is
+very complicated, and is shown in _c_, the bodies on each side, _d_, are
+each made up of two tetrahedra, one with four six-atomed prisms at its
+angles, and the other with four spheres, a pair with four atoms and a pair
+with three. We then come to the connecting rod. One of the four similar
+groups in the centre is enlarged in _a_, and one of the sixteen circling
+groups is enlarged in b. These groups are arranged in two planes inclined
+to one another.
+
+GOLD: Upper part
+          { 12 funnels of 97 atoms      1164
+          { Central ovoid {c             101
+                          {2 d, 38        76
+      Lower part same                   1341
+      Connecting rod { 4 a 84            336
+                     {16 b 33            528
+                                        ----
+                      Total             3546
+                                        ----
+      Atomic weight                   195.74
+      Number weight 3546/18           197
+It may be noted that the connecting rod is made up of exactly sixteen atoms
+of occultum, and that sixteen such atoms contain 864 ultimate atoms, the
+exact member of atoms in titanium.
+
+       *       *       *       *       *
+
+III.
+
+Occultum was observed by us in 1895, and, finding that it was so light, and
+so simple in its composition, we thought that it might be helium, of which
+we were unable, at the time, to obtain a sample. When, however, helium
+itself came under observation in 1907, it proved to be quite different from
+the object before observed, so we dubbed the unrecognised object Occultum,
+until orthodox science shall find it and label it in proper fashion.
+
+OCCULTUM (Plate VI, 1).
+
+We here meet the tetrahedron for the first time, with each angle occupied
+by a six-atomed group, the atoms arranged as on the end triangles of a
+prism. This form recurs very often, and was noted, last month, as seen in
+copper (Plate VI, 3); it revolves with extreme rapidity around its
+longitudinal axis, and looks like a pencil sharpened at both ends, or a
+cigar tapering at both ends; we habitually spoke of it as "the cigar." It
+appears to be strongly coherent, for, as will be seen below, its six atoms
+remain attached to each other as meta-compounds and even when divided into
+two triplets as hyper-compounds, they revolve round each other.
+
+Above the tetrahedron is a balloon-shaped figure, apparently drawn into
+shape by the attraction of the tetrahedron. The body below the tetrahedron
+looks like a coil of rope, and contains fifteen atoms; they are arranged on
+a slanting disk in a flat ring, and the force goes in at the top of one
+atom, and out of the bottom of it into the top of the next, and so on,
+making a closed circuit. The two little spheres, each containing a triplet,
+are like fill-up paragraphs to a compositor--they seem to be kept standing
+and popped in where wanted. The sphere marked _x_ is a proto-compound, the
+balloon when set free.
+
+As was noted under gold (p. 41), sixteen occultum bodies, re-arranged, make
+up the connecting rod in gold:--
+
+OCCULTUM: Tetrahedron                  24
+          Balloon                       9
+          Triplets                      6
+          Rope-circle                  15
+                                     ----
+                     Total             54
+                                     ----
+          Atomic weight         Not known
+          Number weight 54/18           3
+DISSOCIATION OF ATOMS.
+
+Before proceeding to the study of other chemical atoms, as to their general
+internal arrangements, it is desirable to follow out, in those already
+shown, the way in which these atoms break up into simpler forms, yielding
+successively what we have called proto-, meta-, and hyper-compounds. It is
+naturally easier to follow these in the simpler atoms than in the more
+complex, and if the earlier dissociations are shown, the latter can be more
+readily and more intelligibly described.
+
+The first thing that happens on removing a gaseous atom from its "hole"
+(see pp. 21 to 23) or encircling "wall," is that the contained bodies are
+set free, and, evidently released from tremendous pressure, assume
+spherical or ovoid forms, the atoms within each re-arranging themselves,
+more or less, within the new "hole" or "wall." The figures are, of course,
+three-dimensional, and often remind one of crystals; tetrahedral,
+octagonal, and other like forms being of constant occurrence. In the
+diagrams of the proto-compounds, the constituent atoms are shown by dots.
+In the diagrams of the meta-compounds the dot becomes a heart, in order to
+show the resultants of the lines of force. In the diagrams of the
+hyper-compounds the same plan is followed. The letters _a_, _b_, _c_, &c.,
+enable the student to follow the breaking up of each group through its
+successive stages.
+
+HYDROGEN (Plate V, 1).
+
+[Illustration]
+
+The six bodies contained in the gaseous atom instantaneously re-arrange
+themselves within two spheres; the two linear triplets unite with one
+triangular triplet, holding to each other relative positions which, if
+connected by three right lines, would form a triangle with a triplet at
+each angle; the remaining three triangular triplets similarly arrange
+themselves in the second sphere. These form the proto-compounds of
+hydrogen.
+
+In the dissociation of these, each group breaks up into two, the two linear
+triplets joining each other and setting free their triangular comrade,
+while two of the triangular triplets similarly remain together, casting out
+the third, so that hydrogen yields four meta-compounds.
+
+In the hyper-condition, the connexion between the double triplets is
+broken, and they become four independent groups, two like ix, in the
+hyper-types (p. 25), and two remaining linear, but rearranging their
+internal relations; the two remaining groups break up into two pairs and a
+unit.
+
+The final dissociation sets all the atoms free.
+
+OCCULTUM (Plate VI, 1).
+
+[Illustration]
+
+On the first dissociation of the component parts of occultum, the
+tetrahedron separates as a whole, with its four "cigars," flattening itself
+out within its hole, _a_; two "cigars" are positive and two negative,
+marked respectively _a_ and _a'_. The rope becomes a ring within a sphere,
+_b_, and the two bodies _d_ _d_, which are loose in the gaseous atom, come
+within this ring. The balloon becomes a sphere.
+
+On further dissociation, the "cigars" go off independently, showing two
+types, and these again each divide into triplets, as meta-compounds. _B_,
+on the meta-level, casts out the two _d_ bodies, which become independent
+triplets, and the "rope" breaks into two, a close ring of seven atoms and a
+double cross of eight. These subdivide again to form hyper-compounds, the
+ring yielding a quintet and a pair, and the double cross separating into
+its two parts.
+
+The balloon, _c_, becomes much divided, the cohesion of its parts being
+slight; it forms two triplets, a pair and a unit, and these set free, on
+further dissociation, no less than five separate atoms and two duads.
+
+The two triplets of _d_ each cast out an atom on dissociation, and form two
+pairs and two units.
+
+SODIUM (Plate VI, 2).
+
+It is convenient to consider sodium next, because it is the basic pattern
+on which not only copper, silver and gold are formed, but also chlorine,
+bromine and iodine.
+
+[Illustration]
+
+When sodium is set free from its gaseous condition, it divides up into
+thirty-one bodies--twenty-four separate funnels, four bodies derived from
+the two central globes, and three from the connecting rod. The funnels
+become spheres, and each contains four enclosed spheres, with more or less
+complicated contents. Each central globe yields a sextet and a quartet, and
+the rod sets free two quartets and a peculiarly formed sextet.
+
+When the proto-compounds are dissociated, the funnel-sphere sets free: (1)
+the contents of _a_, rearranged into two groups of four within a common
+sphere; the sphere yields four duads as hyper-compounds; (2) the contents
+of _b_, which unite themselves into a quartet, yielding two duads as
+hyper-compounds; and (3) the contents of the two spheres, _c_, which
+maintain their separation as meta-compounds, and become entirely
+independent, the atoms within the sphere revolving round each other, but
+the spheres ceasing their revolution round a common axis, and going off in
+different directions. The atoms break off from each other, and gyrate in
+independent solitude as hyper-"compounds." Thus each funnel yields finally
+ten hyper-bodies.
+
+The part of the central globe, marked _d_, with its six atoms, whirling
+round a common centre, becomes two triplets, at the meta-stage, preparing
+for the complete separation of these as hyper-bodies. The second part of
+the same globe, marked _e_, a whirling cross, with an atom at each point,
+becomes a quartet in the meta-state, in which three atoms revolve round a
+fourth, and in the hyper-state this central atom is set free, leaving a
+triplet and a unit.
+
+Each of the two bodies marked _f_, liberated from the connecting rod, shows
+four atoms whirling round a common centre, exactly resembling _e_ in
+appearance; but there must be some difference of inner relations, for, in
+the meta-state, they re-arrange themselves as two pairs, and divide into
+two as hyper-bodies.
+
+The body marked _g_ is a four-sided pyramid, with two closely joined atoms
+at its apex; these still cling to each in mutual revolution as a meta-body,
+encircled by a ring of four, and this leads to a further dissociation into
+three pairs on the hyper-level.
+
+CHLORINE (Plate V, 2).
+
+[Illustration]
+
+The description of the funnel of sodium applies to that of chlorine, until
+we come to the body nearest the mouth, the sphere containing three
+additional bodies; this remains within the funnel in the first
+dissociation, so that again we have twenty-four separate funnels as
+proto-compounds; the central globes are the same as in sodium, and yield
+the same four bodies; the connecting rod sets free five bodies, of which
+two are the same; we have thus thirty-three separate bodies as the result
+of the dissociation of chlorine into its proto-compounds. As all the
+compounds which are in sodium break up in the same way into meta- and
+hyper-compounds, we need not repeat the process here. We have only to
+consider the new meta- and hyper-compounds of the highest sphere within the
+funnel, and the two triplets and one quintet from the connecting rod.
+
+The additional body within the proto-funnel is of a very simple character,
+three contained triangles within the flattened sphere. On release from the
+funnel, on the meta-level, the atoms rearrange themselves in a whirling set
+of three triplets, and these break off from each other as hyper-compounds.
+The two triplets from the connecting rod, also, are of the simplest
+character and need not delay us. The five-atomed body, a four-sided pyramid
+as a proto-compound, becomes a ring whirling round a centre on the meta,
+and two pairs with a unit on the hyper.
+
+BROMINE (Plate V, 3).
+
+Three additional bodies appear at the top of the funnel, which otherwise
+repeats that of chlorine. The connecting rod is the same and may be
+disregarded. The central globes become more complex. The additions are,
+however, of very easy types, and hence are readily dealt with. Each of the
+three similar ovoid bodies contains two triplets--each a triangle and a
+quintet--a four-sided pyramid. These are the same, as may be seen in the
+connecting rod of chlorine, and we need not repeat them. Only the globe
+remains. This does not break up as a proto-compound but is merely set free,
+_a_ and the 2 _bs_ whirling in a plane vertical to the paper and the two
+smaller bodies, _cc_, whirling on a plane at right angles to the other.
+These two disengage themselves, forming a quartet as a meta-compound, while
+_a_ makes a whirling cross and _bb_ a single sextet; these further
+dissociate themselves into four pairs and two triplets.
+
+IODINE (Plate V, 4).
+
+[Illustration]
+
+Iodine has nothing new to give us, except five similar ovoid bodies at the
+top of each funnel, and two quartets instead of two pairs in the central
+globe. The ovoid bodies become spheres when the funnels are thrown off, and
+a crystalline form is indicated within the sphere. The atoms are arranged
+in two tetrahedra with a common apex, and the relationship is maintained in
+the meta-body, a septet. The latter breaks up into two triplets and a unit
+on the hyper-level. In the central globes, the _a_ of bromine is repeated
+twice instead of the pairs in _cc_.
+
+COPPER (Plate VI, 3).
+
+We have already disposed of occultum, on this plate, and of sodium, which
+lies at the root of both groups. Copper, we now find, is also very largely
+off our hands, as the funnel provides us with only two new types--two
+spheres--each containing five atoms in a new arrangement, and the
+triangular body at the mouth with its ten atoms. This triangular body, with
+an increased number of atoms, reappears in various other chemical elements.
+The central globes are different from any we have had before, in their
+internal arrangement, but the constituents are familiar; there are two
+contained spheres with four atoms each, the _a_ in the globe of bromine
+(see above) and 2 "cigars." The "cigars" may be followed under occultum
+(see above). The connecting rod is as in chlorine, bromine and iodine.
+
+The atoms in the bodies _a_ and _b_ are curiously arranged. _A_ consists of
+two square-based pyramids turned so as to meet at their apices, and breaks
+up into two quartet rings and a duad. _B_ is again two four-sided pyramids,
+but the bases are in contact and set at right angles to each other; the
+second apex is not seen, as it is directly below the first. The pyramids
+separate as meta-bodies, and the atoms assume the peculiar arrangement
+indicated and then break up into four pairs and two units on the hyper
+level.
+
+       *       *       *       *       *
+
+IV.
+
+SILVER (Plate VI, 4 and Ag below).
+
+Silver presents us with only two new bodies, and even these are only new by
+slight additions to old models. The triangular shaped body at the apex of
+the funnel, containing 21 atoms, is intermediate between the similar bodies
+in copper and iron. As a proto-element it becomes three triangles, joined
+at their apices, in fact a tetrahedron in which no atoms are distributed on
+the fourth face. The faces separate on the meta level and give three
+seven-atomed figures, and each of these breaks up into two triplets and a
+unit. The central globe only differs from that of bromine by the addition
+of one atom, which gives the familiar four-sided pyramid with a square base
+as in chlorine (see p. 46).
+
+GOLD (Plate VII and Au below).
+
+[Illustration]
+
+The disintegration of gold first yields forty-seven bodies on the
+proto-level; the twenty-four funnels separate, and the central globes which
+hold each twelve together set free their six contained globes (_c_, _d_),
+thirty bodies being thus liberated. The sixteen bodies on the central
+inclined planes, marked _b_, break away, their central globe, with its four
+contained globes, remaining unchanged. But this condition does not last.
+The motion of the funnels changes and thus the funnels cease to exist and
+their contents are set free, each funnel thus liberating nine independent
+bodies; the sixteen _b_ separate into two each; the four _a_ liberate five
+each; the two _c_ set free thirteen each; the four _d_ finally liberate two
+each: 302 proto elements in all.
+
+The funnel is almost that of iodine, re-arranged. Four of the first ring in
+the iodine funnel are replaced by the triangular body, which becomes a
+four-sided pyramid with an occupied base. The second ring of three ovoids
+in iodine becomes four in gold, but the internal arrangement of each ovoid
+is the same. The next two spheres in the iodine funnel coalesce into one
+sphere, with similar contents, in the gold funnel. The fifth in iodine is
+slightly rearranged to form the fourth in descent in gold, and the
+remaining two are the same. _B_ has been broken up under occultum (p. 628)
+and can be followed there. The sixteen rings set free from the four _a_,
+after gyrating round the central body, now become a sphere, break up, as in
+occultum (see p. 44) into a meta seven-atomed ring and an eight-atomed
+double cross, and so on to the hyper level. The sphere with its two
+contained bodies breaks up into eight triangles on the meta level, and each
+of these, on the hyper, into a duad and a unit. The twelve septets of _c_
+assume the form of prisms as in iodine (see p. 48) and pursue the same
+course, while its central body, a four-sided pyramid with its six
+attendants, divides on the meta level into six duads, revolving round a
+ring with a central atom as in chlorine (p. 47), the duads going off
+independently on the hyper-level and the ring breaking up as in chlorine.
+The "cigar" tetrahedron of _d_ follows its course as in occultum, and the
+other sets free two quartets and two triplets on the meta level, yielding
+six duads and two units as hyper compounds. It will be seen that, complex
+as gold is, it is composed of constituents already familiar, and has iodine
+and occultum as its nearest allies.
+
+II AND IIa.--THE TETRAHEDRAL GROUPS.
+
+II.--This group consists of beryllium (glucinum), calcium, strontium and
+barium, all diatomic, paramagnetic and positive. The corresponding group
+consists of oxygen, chromium, molybdenum, wolfram (tungsten) and uranium,
+with a blank disk between wolfram and uranium: these are diatomic,
+paramagnetic, and negative. We have not examined barium, wolfram, or
+uranium.
+
+[Illustration: PLATE VIII.]
+
+BERYLLIUM (Plate III, 2, and Plate VIII, 1). In the tetrahedron four
+funnels are found, the mouth of each funnel opening on one of its faces.
+The funnels radiate from a central globe, and each funnel contains four
+ovoids each with ten atoms within it arranged in three spheres. In the
+accompanying diagrams one funnel with its four ovoids is shown and a single
+ovoid with its three spheres, containing severally three, four, and three
+atoms, is seen at the left-hand corner of the plate (7 _a_). The members of
+this group are alike in arrangement, differing only in the increased
+complexity of the bodies contained in the funnels. Beryllium, it will be
+observed, is very simple, whereas calcium and strontium are complicated.
+
+BERYLLIUM: 4 funnels of 40 atoms    160
+           Central globe              4
+                                   ----
+                           Total    164
+                                   ----
+Atomic weight                      9.01
+Number weight  164/18              9.11
+CALCIUM (Plate VIII, 2) shows in each funnel three contained spheres, of
+which the central one has within it seven ovoids identical with those of
+beryllium, and the spheres above and below it contain each five ovoids (7
+_b_) in which the three contained spheres have, respectively, two, five,
+and two atoms. The central globe is double, globe within globe, and is
+divided into eight segments, radiating from the centre like an orange; the
+internal part of the segment belonging to the inner globe has a triangular
+body within it, containing four atoms (7 _c_), and the external part,
+belonging to the encircling globe, shows the familiar "cigar" (7 _d_). In
+this way 720 atoms are packed into the simple beryllium type.
+
+CALCIUM: 4 funnels of 160 atoms      640
+         Central globe                80
+                                    ----
+                          Total      720
+                                    ----
+         Atomic weight             39.74
+         Number weight 720/18      40.00
+STRONTIUM (Plate VIII, 3) shows a still further complication within the
+funnels, no less than eight spheres being found within each. Each of the
+highest pair contains four subsidiary spheres, with five, seven, seven,
+five atoms, respectively (7 _e_, _g_, _f_). The _g_ groups are identical
+with those in gold, but difference of pressure makes the containing body
+spherical instead of ovoid; similar groups are seen in the top ring of the
+iodine funnel, where also the "hole" is ovoid in form. The second pair of
+spheres contains ten ovoids (7 _b_) identical with those of calcium. The
+third pair contains fourteen ovoids (7 _a_) identical with those of
+beryllium, while the fourth pair repeats the second, with the ovoids
+re-arranged. The internal divisions of the double sphere of the central
+globe are the same as in calcium, but the contents differ. The "cigars" in
+the external segments are replaced by seven-atomed ovoids (7 _h_)--the
+iodine ovoids--and the external segments contain five-atomed triangles (7
+_i_). Thus 1,568 atoms have been packed into the beryllium type, and our
+wonder is again aroused by the ingenuity with which a type is preserved
+while it is adapted to new conditions.
+
+STRONTIUM: 4 funnels of 368 atoms       1472
+           Central globe                  96
+                                        ----
+                            Total       1568
+                                        ----
+           Atomic weight               86.95
+           Number weight 1568/18       87.11
+The corresponding group, headed by oxygen--oxygen, chromium, molybdenum,
+wolfram and uranium--offers us another problem in its first member.
+
+OXYGEN (Plate VIII, 4). This was examined by us in 1895, and the
+description may be reproduced here with a much improved diagram of its very
+peculiar constitution. The gaseous atom is an ovoid body, within which a
+spirally-coiled snake-like body revolves at a high velocity, five brilliant
+points of light shining on the coils. The appearance given in the former
+diagram will be obtained by placing the five septets on one side on the top
+of those on the other, so that the ten become in appearance five, and thus
+doubling the whole, the doubling point leaving eleven duads on each side.
+The composition is, however, much better seen by flattening out the whole.
+On the proto level the two snakes separate and are clearly seen.
+
+OXYGEN: Positive snake
+        { 55 spheres of 2 atoms }
+        {  + 5 disks of 7 atoms }    145
+        Negative snake     "         145
+                                    ----
+                        Total        290
+                                    ----
+        Atomic weight              15.87
+        Number weight 290/18       16.11
+CHROMIUM (Plate VIII, 5) "reverts to the ancestral type," the tetrahedron;
+the funnel is widened by the arrangement of its contents, three spheres
+forming its first ring, as compared with the units in beryllium and
+calcium, and the pairs in strontium and molybdenum. Two of these spheres
+are identical in their contents--two quintets (7 _f_), a quintet (7 _j_),
+and two quintets (7 _e_), _e_ and _f_ being to each other as object and
+image. The remaining sphere (7 _b_) is identical with the highest in the
+calcium funnel. The remaining two spheres, one below the other, are
+identical with the corresponding two spheres in calcium. The central globe,
+as regards its external segments, is again identical with that of calcium,
+but in the internal segments a six-atomed triangle (7 _k_) is substituted
+for the calcium four-atomed one (7 _e_).
+
+CHROMIUM: 4 funnels of 210 atoms      840
+          Central globe                96
+                                    -----
+                   Total              936
+                                    -----
+          Atomic weight             51.74
+          Number weight 936/18      52.00
+MOLYBDENUM (Plate VIII, 6) very closely resembles strontium, differing from
+it only in the composition of the highest pair of spheres in the funnels
+and in the presence of a little sphere, containing two atoms only, in the
+middle of the central globe. The topmost spheres contain no less than eight
+subsidiary spheres within each; the highest of these (7 _e_) has four atoms
+in it; the next three have four, seven and four (7 _e_ _g_ _e_),
+respectively; the next three are all septets (7 _g_), and the last has
+four--making in all for these two spheres 88 atoms, as against the 48 in
+corresponding spheres of strontium, making a difference of 160 in the four
+funnels.
+
+MOLYBDENUM: 4 funnels of 408 atoms     1632
+            Central globe                98
+                                      -----
+                          Total        1730
+                                      -----
+            Atomic weight             95.26
+            Number weight 1730/18     96.11
+II a.--This group contains magnesium, zinc, cadmium, and mercury, with an
+empty disk between cadmium and mercury; we did not examine mercury. All are
+diatomic, diamagnetic and positive; the corresponding group consists of
+sulphur, selenium and tellurium, also all diatomic and diamagnetic, but
+negative. The same characteristics of four funnels opening on the faces of
+a tetrahedron are found in all, but magnesium and sulphur have no central
+globe, and in cadmium and tellurium the globe has become a cross.
+
+[Illustration: PLATE IX.]
+
+MAGNESIUM (Plate IX, 1) introduces us to a new arrangement: each group of
+three ovoids forms a ring, and the three rings are within a funnel; at
+first glance, there are three bodies in the funnel; on examination each of
+these is seen to consist of three, with other bodies, spheres, again within
+them. Apart from this, the composition is simple enough, all the ovoids
+being alike, and composed of a triplet, a septet and a duad.
+
+MAGNESIUM: 4 funnels of 108 atoms     432
+           Atomic weight            24.18
+           Number weight 432/18     24.00
+ZINC (Plate IX, 2) also brings a new device: the funnel is of the same type
+as that of magnesium, while septets are substituted for the triplets, and
+36 additional atoms are thus slipped in. Then we see four spikes,
+alternating with the funnels and pointing to the angles, each adding 144
+atoms to the total. The spikes show the ten-atomed triangle, already met
+with in other metals, three very regular pillars, each with six spheres,
+containing two, three, four, four, three, two atoms, respectively. The
+supporting spheres are on the model of the central globe, but contain more
+atoms. Funnels and spikes alike radiate from a simple central globe, in
+which five contained spheres are arranged crosswise, preparing for the
+fully developed cross of cadmium. The ends of the cross touch the bottoms
+of the funnels.
+
+ZINC: 4 funnels of 144 atoms        576
+      4 spikes of 144 atoms         576
+      Central globe                  18
+                                  -----
+                        Total      1170
+                                  -----
+         Atomic weight            64.91
+         Number weight 1170/18    65.00
+CADMIUM (Plate IX, 3) has an increased complexity of funnels; the diagram
+shows one of the three similar segments which lie within the funnels as
+cylinders; each of these contains four spheres, three pillars and three
+ovoids, like the spike of zinc turned upside down, and the zinc ten-atomed
+triangle changed into three ten-atomed ovoids. The centre-piece is a new
+form, though prefigured in the central globe of zinc.
+
+CADMIUM:  3 segments of 164 atoms = 492
+          4 funnels of 492 atoms          1968
+          Central body                      48
+                                         -----
+                             Total        2016
+                                         -----
+          Atomic weight                 111.60
+          Number weight 2016/18         112.00
+The corresponding negative group is headed by
+
+[Illustration: PLATE X.]
+
+SULPHUR (Plate X, 1), which, like magnesium, has no central globe, and
+consists simply of the zinc funnels, much less compressed than zinc but the
+same in composition.
+
+SULPHUR: 4 funnels of 144 atoms       576
+         Atomic weight              31.82
+         Number weight 576/18       32.00
+SELENIUM (Plate X, 2) is distinguished by the exquisite peculiarity,
+already noticed, of a quivering star, floating across the mouth of each
+funnel, and dancing violently when a ray of light falls upon it. It is
+known that the conductivity of selenium varies with the intensity of the
+light falling upon it, and it may be that the star is in some way connected
+with its conductivity. It will be seen that the star is a very complicated
+body, and in each of its six points the two five-atomed spheres revolve
+round the seven-atomed cone. The bodies in the funnels resemble those in
+magnesium, but a reversed image of the top one is interposed between itself
+and the small duad, and each pair has its own enclosure. The central globe
+is the same as that of zinc.
+
+SELENIUM: 4 funnels of 198 atoms     792
+          4 stars of 153 atoms       612
+          Central globe               18
+                                   -----
+                         Total      1422
+                                   -----
+          Atomic weight            78.58
+          Number weight 1422/18    79.00
+TELLURIUM (Plate X, 3), it will be seen, closely resembles cadmium, and has
+three cylindrical segments--of which one is figured--making up the funnel.
+The contained bodies in the pillars run three, four, five, four, three,
+two, instead of starting with two; and a quartet replaces a duad in the
+globes above. The central cross only differs from that of cadmium in having
+a seven-atomed instead of a four-atomed centre. So close a similarity is
+striking.
+
+TELLURIUM: 3 segments of 181 atoms = 543
+           4 funnels of 543 atoms          2172
+           Central body                      51
+                                          -----
+                            Total          2223
+                                          -----
+           Atomic weight                 126.64
+           Number weight 2223/18         123.50
+       *       *       *       *       *
+
+V.
+
+We must now consider the ways in which the members of the tetrahedral
+groups break up, and as we proceed with this study we shall find how
+continual are the repetitions, and how Nature, with a limited number of
+fundamental methods, creates by varied combinations her infinite variety of
+forms.
+
+BERYLLIUM (Plate III, 2, and VIII, 1).
+
+[Illustration]
+
+Beryllium offers us four similar funnels and a central globe, and the
+proto-elements consist of these five bodies, set free. The funnel, released
+from pressure, assumes a spherical form, with its four ovoids spinning
+within it, and the central globe remains a sphere, containing a whirling
+cross. On the meta level, the ovoids are set free, and two from each funnel
+are seen to be positive, two negative--sixteen bodies in all, _plus_ the
+cross, in which the resultant force-lines are changed, preparatory to its
+breaking into two duads on the hyper level. On that level, the decades
+disintegrate into two triplets and a quartet, the positive with the
+depressions inward, the negative with the depressions outward.
+
+CALCIUM (Plate VIII, 2).
+
+The funnels, as usual, assume a spherical form on the proto level, and
+show, in each case, three spheres containing ovoids. These spheres, still
+on the proto level, break free from their containing funnel, as in the case
+of gold (p. 49), twelve bodies being thus liberated, while the central
+globe breaks up into eight segments, each of which becomes globular, and
+contains within it a "cigar" and a somewhat heart-shaped body. Four
+spheres, each containing seven ten-atomed ovoids, are identical with those
+in beryllium, and can be followed in its diagram. Eight spheres, each
+containing five nine-atomed ovoids of a different type, set free, on the
+meta level, eighty duads--forty positive and forty negative--and forty
+quintets, which are identical with those in chlorine. On the hyper level,
+the duads become single atoms, within a sphere, and the central atom from
+the quintet is also set free, one hundred and twenty in all. The remaining
+four atoms of the quintet divide into two duads.
+
+The central globe, dividing into eight, becomes eight six-atomed spheres on
+the meta, the "cigar" behaving as usual, four "cigars" being positive and
+four negative, and becoming dissociated into triplets; the four atoms
+within the heart-shaped body appear as a tetrahedron, remain together on
+the meta level, and break up into duads on the hyper.
+
+STRONTIUM (PLATE VIII, 3).
+
+The third member of this group repeats the _a_ groups of beryllium and the
+_b_ groups of calcium, and they dissociate into the bodies already
+described under these respectively. The two upper globes in each funnel
+repeat each other, but each globe contains four smaller spheres showing
+three varieties of forms. The two marked _g_, which are repeated in the
+central globe as _h_, are seven-atomed, and appear as spheres or ovoids
+according to pressure. They are figured on p. 48, under iodine; _e_ and _f_
+are related as object and image, and we have already seen them in copper
+(pp. 38 and 48); in each case, as in copper, they unite into a ten-atomed
+figure; on the meta level the pair of fours form a ring, and the remaining
+two atoms form a duad; _i_, which repeats _f_, makes a ring with the fifth
+in the centre, as in the five-atomed _b_ of calcium, as shown above. There
+is, thus, nothing new in strontium, but only repetitions of forms already
+studied.
+
+OXYGEN (PLATE VIII, 4).
+
+[Illustration]
+
+The disintegration of oxygen as given in 1895 may be repeated here, and the
+better presentation given on p. 54 renders it easier to follow the process.
+On the proto level the two "snakes" divide; the brilliant disks are
+seven-atomed, but are differently arranged, the positive snake having the
+atoms arranged as in the iodine ovoids, whereas the negative snake has them
+arranged as in a capital H. The snakes show the same extraordinary activity
+on the proto level as on the gaseous, twisting and writhing, darting and
+coiling. The body of the snake is of two-atomed beads, positive and
+negative. On the meta level the snakes break into ten fragments, each
+consisting of a disk, with six beads on one side and five on the other,
+remaining as lively as the original snake. They shiver into their
+constituent disks, and beads on the hyper level, there yielding the ten
+disks, five positive and five negative, and the 110 beads, fifty-five
+positive and fifty-five negative.
+
+CHROMIUM (PLATE VIII, 5).
+
+When we go on to chromium and molybdenum, we return to our familiar funnels
+and central globes, and the secondary spheres within the funnels--quickly
+set free, as before, on the proto level--give us no new combinations in
+their contained spheres and ovoids. The _a_ of beryllium, the _b_ of
+calcium and strontium, and _d_ of calcium, the _e_ and _f_ of strontium,
+are all there; _j_ in chromium is the same as the central sphere in the _b_
+ovoid. In the central globe, _k_, is a pair of triangles as in hydrogen,
+consisting of only six atoms, which on the meta level revolve round each
+other, and break up into two duads and two units on the hyper.
+
+MOLYBDENUM (PLATE VIII, 6).
+
+Molybdenum presents us with only two new forms, and these are merely
+four-atomed tetrahedra, occurring in pairs as object and image. All the
+other bodies have already been analysed.
+
+II a.--We come now to the second great tetrahedral group, which though very
+much complicated, is yet, for the most part, a repetition of familiar
+forms.
+
+MAGNESIUM (PLATE IX, 1).
+
+[Illustration]
+
+We are still among tetrahedra, so have to do with four funnels, but each
+funnel contains three rings, and each ring three ovoids; on the proto level
+a triple dissociation takes place, for the funnels let free the rings as
+large spheres, in each of which rotate three twelve-atomed ovoids, and then
+the ovoids break loose from the spheres, and themselves become spherical,
+so that we have finally thirty-six proto compounds from the tetrahedron. On
+the meta level the contained bodies, a triplet, Mg _a_, a septet, Mg _b_,
+and a duad, Mg _c_, are set free from each globe, thus yielding one hundred
+and eight meta compounds. On the hyper level the triplet becomes a duad and
+a unit; the duad becomes two units; and the septet a triplet and a quartet.
+
+ZINC (PLATE IX, 2).
+
+We can leave aside the funnel, for the only difference between it and the
+magnesium funnel is the substitution of a second septet for the triplet,
+and the septet is already shown in the magnesium diagram. We have,
+therefore, only to consider the spikes, pointing to the angles of the
+enclosing tetrahedron, and the central globe. These are set free on the
+proto level and the spikes immediately release their contents, yielding
+thus thirty-two separate bodies.
+
+The triangular arrangement at the top of the spike is the same as occurs in
+copper (_b_ on p. 48), and can be there followed. One of the three similar
+pillars is shown in the accompanying diagram under Zn a. The compressed
+long oval becomes a globe, with six bodies revolving within it in a rather
+peculiar way: the quartets turn round each other in the middle; the
+triplets revolve round them in a slanting ellipse; the duads do the same on
+an ellipse slanting at an angle with the first, somewhat as in gold (_a_
+and _b_, p. 40). The spheres within the globes at the base of the spikes,
+Zn _b_, behave as a cross--the cross is a favourite device in the II _a_
+groups. Finally, the central globe, Zn _c_, follows the same cruciform line
+of disintegration.
+
+CADMIUM (Plate IX, 3).
+
+[Illustration]
+
+Cadmium follows very closely on the lines of zinc; the pillars of the zinc
+spike are reproduced in the rings of the cadmium funnel; the globes are
+also the globes of cadmium; so neither of these needs attention. We have
+only to consider the three ten-atomed ovoids, which are substituted for the
+one ten-atomed triangle of zinc, and the central cross. The ovoids become
+spheres (Cd _a_, _b_), the contained bodies revolving within them, _a_
+whirling on a diameter of the sphere, cutting it in halves, as it were, and
+_b_ whirling round it at right angles; the cross also becomes a sphere (Cd
+_c_), but the cruciform type is maintained within it by the relative
+positions of the contained spheres in their revolution. The subsequent
+stages are shown in the diagram.
+
+SULPHUR (Plate XI, 1).
+
+Sulphur has nothing new, but shows only the funnels already figured in
+magnesium, with the substitution of a second septet for the triplet, as in
+zinc.
+
+SELENIUM (Plate X, 2).
+
+[Illustration]
+
+The funnel of selenium is a re-arrangement of the twelve-atomed ovoids of
+magnesium and the ten-atomed ovoids of cadmium. The funnels, on
+disintegrating, set free twelve groups, each containing nine spheres. On
+the meta level the ten-atomed bodies are set free, and the twelve-atomed
+divide into duads and decads, thus yielding seventy-two decads and
+thirty-six duads; the duads, however, at once recombine into hexads, thus
+giving only twelve meta elements, or eighty-four in all from the funnels.
+The central globe holds together on the proto level, but yields five meta
+elements. The star also at first remains a unit on the proto level, and
+then shoots off into seven bodies, the centre keeping together, and the six
+points becoming spheres, within which the two cones, base to base, whirl in
+the centre, and the globes circle round them. On the meta level all the
+thirty bodies contained in the star separate from each other, and go on
+their independent ways.
+
+Selenium offers a beautiful example of the combination of simple elements
+into a most exquisite whole.
+
+TELLURIUM (Plate X, 3).
+
+Tellurium very closely resembles cadmium, and they are, therefore placed on
+the same diagram. The pillars are the same as in chlorine and its
+congeners, with a duad added at the base. The ten-atomed ovoid is the same
+as in cadmium and follows the same course in breaking up. It would be
+interesting to know why this duad remains as a duad in selenium and breaks
+up into a septad and triad in the other members of the group. It may be due
+to the greater pressure to which it is subjected in selenium, or there may
+be some other reason. The cross in tellurium is identical with that in
+cadmium, except that the centre is seven-atomed instead of four-atomed.
+
+       *       *       *       *       *
+
+VI.
+
+III AND IIIa.--THE CUBE GROUPS.
+
+We have here four groups to consider, all the members of which are triads,
+and have six funnels, opening on the six faces of a cube.
+
+III.--Boron, scandium and yttrium were examined; they are all triatomic,
+paramagnetic, and positive. The corresponding group consists of nitrogen,
+vanadium and niobium; they are triatomic, paramagnetic, and negative. We
+have not examined the remaining members of these groups. In these two
+groups nitrogen dominates, and in order to make the comparison easy the
+nitrogen elements are figured on both Plate XI and Plate XII. It will be
+seen that scandium and yttrium, of the positive group, differ only in
+details from vanadium and niobium, of the negative group; the ground-plan
+on which they are built is the same. We noted a similar close resemblance
+between the positive strontium and the negative molybdenum.
+
+[Illustration: PLATE XI.]
+
+BORON (Plate III, 4, and Plate XI, 1). We have here the simplest form of
+the cube; the funnels contain only five bodies--four six-atomed ovoids and
+one six-atomed "cigar." The central globe has but four five-atomed spheres.
+It is as simple in relation to its congeners as is beryllium to its
+group-members.
+
+BORON: 6 funnels of 30 atoms    180
+       Central globe             20
+                               ----
+                         Total  200
+                               ----
+       Atomic weight          10.86
+       Number weight 200/18   11.11
+SCANDIUM (Plate XI, 2). For the first time we meet funnels of different
+types, A and B, three of each kind; A appear to be positive and B negative,
+but this must be stated with reserve.
+
+In A the boron funnel is reproduced, the "cigar" having risen above its
+companion ovoids; but the most important matter to note in respect to this
+funnel is our introduction to the body marked _a_ 110. This body was
+observed by us first in nitrogen, in 1895, and we gave it the name of the
+"nitrogen balloon," for in nitrogen it takes the balloon form, which it
+also often assumes in other gaseous elements. Here it appears as a
+sphere--the form always assumed on the proto level--and it will be seen, on
+reference to the detailed diagram 4 _a_, to be a complicated body,
+consisting of six fourteen-atomed globes arranged round a long ovoid
+containing spheres with three, four, six, six, four, three, atoms
+respectively. It will be observed that this balloon appears in every member
+of these two groups, except boron.
+
+The B funnel runs largely to triads, _c_ and _b_, _b_ (see 4 _b_) having
+not only a triadic arrangement of spheres within its contained globes, but
+each sphere has also a triplet of atoms. In _c_ (see 4 _c_) there is a
+triadic arrangement of spheres, but each contains duads. B is completed by
+a five-atomed sphere at the top of the funnel. It should be noted that _a_,
+_b_ and _c_ all are constituents of nitrogen.
+
+The central globe repeats that of boron, with an additional four-atomed
+sphere in the middle.
+
+SCANDIUM: 3 funnels (A) of 140 atoms   420
+          3    "    (B) of 116   "     348
+          Centre globe                  24
+                                      ----
+                               Total   792
+                                      ----
+          Atomic weight              43.78
+          Number weight 792/18       44.00
+YTTRIUM (Plate XI, 3). Here we have a quite new arrangement of bodies
+within the funnel--the funnel being of one type only. Two "cigars" whirl on
+their own axes in the centre near the top, while four eight-atomed globes
+(see 4 _e_) chase each other in a circle round them, spinning madly on
+their own axes--this axial spinning seems constant in all contained
+bodies--all the time. Lower down in the funnel, a similar arrangement is
+seen, with a globe (see 4 _d_)--a nitrogen element--replacing the "cigars,"
+and six-atomed ovoids replacing the globes.
+
+The "nitrogen balloon" occupies the third place in the funnel, now showing
+its usual shape in combination, while the _b_ globe (see 4 _b_) of scandium
+takes on a lengthened form below it.
+
+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.
+
+[Illustration: PLATE XII.]
+
+NITROGEN (Plate XII, 1) does not assume the cubical form of its relatives,
+but is in shape like an egg. Referring again to our 1895 investigations, I
+quote from them. The balloon-shaped body (see 4 _a_) floats in the middle
+of the egg, containing six small spheres in two horizontal rows, and a long
+ovoid in the midst; this balloon-shaped body is positive, and is drawn down
+towards the negative body _b_ (see 4 _b_) with its seven contained spheres,
+each of which has nine atoms within it--three triads. Four spheres are
+seen, in addition to the two larger bodies; two of these (see 4 _d_), each
+containing five smaller globes, are positive, and two (see 4 _c_)
+containing four smaller globes, are negative.
+
+NITROGEN: Balloon                         110
+          Oval                             63
+          2 bodies of 20 atoms             40
+          2   "    "  24   "               48
+                                         ----
+                              Total       261
+                                         ----
+          Atomic weight                 14.01
+          Number weight 261/18          14.50
+VANADIUM (Plate XII, 2) closely follows scandium, having two types of
+funnels. Funnel A only differs from that of scandium by having a globe (see
+4 _d_) inserted in the ring of four ovoids; funnel B has a six-atomed,
+instead of a five-atomed globe at the top, and slips a third globe
+containing twenty atoms (see 4 _d_) between the two identical with those of
+scandium (see 4 _c_). The central globe has seven atoms in its middle body
+instead of four. In this way does vanadium succeed in overtopping scandium
+by 126 atoms.
+
+VANADIUM: 3 funnels (A) of 160 atoms      480
+          3    "    (B) "  137   "        411
+          Central globe                    27
+                                         ----
+                              Total       918
+                                         ----
+          Atomic weight                 50.84
+          Number weight 918/18          51.00
+NIOBIUM (Plate XII, 3) is as closely related to yttrium as is vanadium to
+scandium. The little globes that scamper round the "cigars" contain twelve
+atoms instead of eight (see 4 _e_).
+
+The rest of the funnel is the same. In the central globe both the
+tetrahedra have "cigars," and a central nine-atomed globe spins round in
+the centre (see 4 _f_), seventeen atoms being thus added.
+
+NIOBIUM: 6 funnels of 277 atoms        1662
+         Central globe                   57
+                                       ----
+                             Total     1719
+                                       ----
+         Atomic weight                93.25
+         Number weight 1719/18        95.50
+III a.--Aluminium, gallium and indium were examined from this group. They
+are triatomic, diamagnetic, and positive. The corresponding group contains
+phosphorus, arsenic and antimony: bismuth also belongs to it, but was not
+examined; they are triatomic, diamagnetic and negative. They have no
+central globes.
+
+[Illustration: PLATE XIII.]
+
+ALUMINIUM (Plate XIII, 1), the head of the group, is, as usual, simple.
+There are six similar funnels, each containing eight ovoids, below which is
+a globe.
+
+ALUMINIUM: 6 funnels of 81 atoms        486
+           Atomic weight              26.91
+           Number weight 486/18       27.00
+GALLIUM (Plate XIII, 2) has two segments in every funnel; in the segment to
+the left a "cigar" balances a globe, equally six-atomed, in that of the
+right, and the globes to right and left are four-atomed as against
+three-atomed. In the next row, the smaller contained globes have six atoms
+as against four, and the cones have respectively seven and five. By these
+little additions the left-hand funnel boasts one hundred and twelve atoms
+as against ninety-eight.
+
+GALLIUM: Left segment 112 atoms }
+         Right segment 98   "   } = 210
+         6 funnels of 210 atoms         1260
+                                        ----
+         Atomic weight                 69.50
+         Number weight 1260/18         70.00
+INDIUM (Plate XIII, 3) repeats the segments of gallium exactly, save in the
+substitution of a sixteen-atomed body for the seven-atomed cone of the
+left-hand segment, and a fourteen-atomed body for the five-atomed
+corresponding one in gallium. But each funnel now has three segments
+instead of two; three funnels out of the six contain two segments of type A
+and one of type B; the remaining three contain two of type B, and one of
+type A.
+
+INDIUM: Segment A 121 atoms
+        Segment B 107   "
+        3 funnels of 2 A and 1 B ([242 + 107] 3)    1047
+        3    "    "  2 B and 1 A ([214 + 121] 3)    1005
+                                                    ----
+                                         Total      2052
+                                                    ----
+        Atomic weight                             114.05
+        Number weight 2052/18                     114.00
+The corresponding negative group, phosphorus, arsenic, and antimony, run on
+very similar lines to those we have just examined.
+
+[Illustration: PLATE XIV.]
+
+PHOSPHORUS (Plate XIV, 1) offers us a very curious arrangement of atoms,
+which will give some new forms in breaking up. Two segments are in each
+funnel, in fact the only two of group III _a_ which do not show this
+arrangement, or a modification thereof, are aluminium and arsenic.
+
+PHOSPHORUS: Left segment  50 atoms
+            Right segment 43   "
+                          --
+                          93
+            6 funnels of 93 atoms       558
+            Atomic weight             30.77
+            Number weight 558/18      31.00
+ARSENIC (Plate XIV, 2) resembles aluminium in having eight internal
+sub-divisions in a funnel, and the ovoids which form the top ring are
+identical, save for a minute difference that in aluminium the ovoids stand
+the reverse way from those in arsenic. It will be noted that in the former
+the top and bottom triangles of atoms have the apices upwards, and the
+middle one has its apex downwards. In arsenic, the top and bottom ones
+point downwards, and the middle one upwards. Arsenic inserts sixteen
+spheres between the ovoids and globe shown in aluminium, and thus adds no
+less than one hundred and forty-four atoms to each funnel.
+
+ARSENIC: 6 funnels of 225 atoms    1350
+         Atomic weight            74.45
+         Number weight 1350/18    75.00
+ANTIMONY (Plate XIV, 3) is a close copy of indium, and the arrangement of
+types A and B in the funnels is identical. In the middle rings of both A
+and B a triplet is substituted for a unit at the centre of the larger
+globe. In the lowest body of type A the "cigar" has vanished, and is
+represented by a seven-atomed crystalline form.
+
+ANTIMONY: Segment A 128 atoms
+          Segment B 113 atoms
+      3 funnels of 2 A and 1 B ([256 + 113]3)   1107
+      3   "     "  2 B and 1 A ([226 + 128]3)   1056
+                                                ----
+                                     Total      2163
+                                                ----
+      Atomic weight                           119.34
+      Number weight                           120.16
+       *       *       *       *       *
+
+VII.
+
+BORON (Plate III, 4, and Plate XI, 1).
+
+[Illustration]
+
+The disintegration of boron is very simple: the funnels are set free and
+assume the spherical form, showing a central "cigar" and four globes each
+containing two triplets. The central globe is also set free with its four
+quintets, and breaks at once in two. On the meta level the "cigar" breaks
+up as usual, and the triplets separate. On the hyper level, the "cigar"
+follows its usual course, and the triplets become duads and units. The
+globe forms two quintets on the meta level, and these are resolved into
+triplets and duads.
+
+SCANDIUM (Plate XI, 2).
+
+In funnel A the "cigar" and the ovoids behave as in boron, but the
+"balloon," _a_ 110 (XI, 4), escapes from the funnel as it changes to a
+sphere, and holds together on the proto level; on the meta, it yields six
+globes each containing seven duads, and these are all set free as duads on
+the hyper level; the ovoid is also set free on the meta level becoming a
+sphere, and on the hyper level liberates its contained bodies, as two
+triplets, two quartets and two sextets.
+
+In funnel B there is a quintet, that behaves like those in the globe of
+boron, on escaping from the funnel, in which the bodies remain on the proto
+level, with the exception of _b_ 63, which escapes. On the meta level, _c_
+(Plate XI, 4), _c_ assumes a tetrahedral form with six atoms at each point,
+and these hold together as sextets on the hyper level. At the meta stage,
+_b_ (Plate XI, 4 _b_) sets free seven nine-atomed bodies, which become free
+triplets on the hyper. The central globe shows a cross at its centre, with
+the four quintets whirling round it, on the proto level. On the meta, the
+quintets are set free, and follow the boron type, while the cross becomes a
+quartet on the meta level, and two duads on the hyper.
+
+YTTRIUM (Plate XI, 3).
+
+[Illustration]
+
+In yttrium, on the proto level, _a_ 110 and _b_ 63 both escape from the
+funnel, and behave as in scandium. The ovoids and "cigars," set free on the
+meta level, behave as in boron. The central globe breaks up as in gold (pp.
+49 and 50), four quartets being set free instead of two quartets and two
+triplets. We have only to consider _e_ 8 and _d_ 20 (Plate XI, 4). _E_ 8 is
+a tetrahedral arrangement of duads on the meta level, set free as duads on
+the hyper. _D_ 20 is an arrangement of pairs of duads at the angles of a
+square-based pyramid on the meta, and again free duads on the hyper.
+
+NITROGEN (Plate XII, 1).
+
+Nitrogen has nothing new to show us, all its constituents having appeared
+in scandium and yttrium.
+
+VANADIUM (Plate XII, 2).
+
+The A funnel of vanadium repeats the A funnel of scandium, with the
+addition of _d_ 20, already studied. In the B funnel scandium B is
+repeated, with an addition of _d_ 20 and a sextet for a quintet; the sextet
+is the _c_ of the "nitrogen balloon." The central globe follows boron, save
+that it has a septet for its centre; this was figured in iodine (p. 48).
+
+NIOBIUM (Plate XII, 3).
+
+Niobium only differs from yttrium by the introduction of triplets for duads
+in _e_; on the meta level we have therefore triplets, and on the hyper each
+triplet yields a duad and a unit. The only other difference is in the
+central globe. The tetrahedra separate as usual, but liberate eight
+"cigars" instead of four with four quartets; the central body is simple,
+becoming three triads at the angles of a triangle on the meta level, and
+three duads and three units on the hyper.
+
+ALUMINIUM (Plate XIII, 1).
+
+[Illustration]
+
+The funnels let go the globes, but the eight ovoids remain within them, so
+that seven bodies are let loose on the proto level. When the ovoids are set
+free at the meta stage they become spherical and a nine-atomed body is
+produced, which breaks up into triangles on the hyper level. The globe
+becomes a cross at the meta stage, with one atom from the duads at each arm
+in addition to its own, and these form four duads on the hyper, and a unit
+from the centre.
+
+GALLIUM (Plate XIII, 2).
+
+In gallium the funnel disappears on the proto level, setting free its two
+contained segments, each of which forms a cylinder, thus yielding twelve
+bodies on the proto level. On the meta, the three upper globes in each
+left-hand segment are set free, and soon vanish, each liberating a cigar
+and two septets, the quartet and triad uniting. On the hyper the quartet
+yields two duads but the triangle persists. The second set of bodies divide
+on the meta level, forming a sextet and a cross with a duad at each arm;
+these on the hyper level divide into two triangles, four duads and a unit.
+The seven-atomed cone becomes two triangles united by a single atom, and on
+the meta level these form a ring round the unit; on the hyper they form
+three duads and a unit.
+
+In the right-hand segment, the same policy is followed, the four triads
+becoming two sextets, while the central body adds a third to the number.
+The second ring has a quartet instead of the sextet, but otherwise breaks
+up as does that of the left; the quintet at the base follows that of boron.
+
+INDIUM (Plate XIII, 3).
+
+The complication of three segments of different types in each funnel does
+not affect the process of breaking up, and indium needs little attention. A
+is exactly the same as the left-hand funnel of gallium, save for the
+substitution of a globe containing the familiar "cigar" and two
+square-based pyramids. B is the same as the right-hand funnel of gallium,
+except that its lowest body consists of two square-based pyramids and a
+tetrahedron. All these are familiar.
+
+PHOSPHORUS (Plate XIV, 1).
+
+[Illustration]
+
+The atoms in the six similar spheres in the segments of the phosphorus
+funnel are arranged on the eight angles of a cube, and the central one is
+attached to all of them. On the meta level five of the nine atoms hold
+together and place themselves on the angles of a square-based pyramid; the
+remaining four set themselves on the angle of a tetrahedron. They yield, on
+the hyper level, two triads, a duad, and a unit. The remaining bodies are
+simple and familiar.
+
+ARSENIC (Plate XIV, 2).
+
+Arsenic shows the same ovoids and globe as have already been broken up in
+aluminium (see _ante_); the remaining sixteen spheres form nine-atomed
+bodies on the meta level, all similar to those of aluminium, thus yielding
+twelve positive and twelve negative; the globe also yields a nine-atomed
+body, twenty-five bodies of nine.
+
+ANTIMONY (Plate XIV, 3).
+
+Antimony follows closely in the track of gallium and indium, the upper ring
+of spheres being identical. In the second ring, a triplet is substituted
+for the unit, and this apparently throws the cross out of gear, and we have
+a new eleven-atomed figure, which breaks up into a triplet and two quartets
+on the hyper level. The lowest seven-atomed sphere of the three at the base
+is the same as we met with in copper.
+
+       *       *       *       *       *
+
+VIII.
+
+IV.--THE OCTAHEDRAL GROUPS.
+
+These groups are at the turns of the spiral in Sir William Crookes'
+lemniscates (see p. 28). On the one side is carbon, with below it titanium
+and zirconium; on the other silicon, with germanium and tin. The
+characteristic form is an octahedron, rounded at the angles and a little
+depressed between the faces in consequence of the rounding; in fact, we did
+not, at first, recognize it as an octahedron, and we called it the "corded
+bale," the nearest likeness that struck us. The members of the group are
+all tetrads, and have eight funnels, opening on the eight faces of the
+octahedron. The first group is paramagnetic and positive; the corresponding
+one is diamagnetic and negative. The two groups are not closely allied in
+composition, though both titanium and tin have in common the five
+intersecting tetrahedra at their respective centres.
+
+[Illustration: PLATE XV.]
+
+CARBON (Plate III, 5, and XV, 1) gives us the fundamental octahedral form,
+which becomes so masked in titanium and zirconium. As before said (p. 30),
+the protrusion of the arms in these suggests the old Rosicrucian symbol of
+the cross and rose, but they show at their ends the eight carbon funnels
+with their characteristic contents, and thus justify their relationship.
+The funnels are in pairs, one of each pair showing three "cigars," and
+having as its fellow a funnel in which the middle "cigar" is truncated,
+thus loosing one atom. Each "cigar" has a leaf-like body at its base, and
+in the centre of the octahedron is a globe containing four atoms, each
+within its own wall; these lie on the dividing lines of the faces, and each
+holds a pair of the funnels together. It seems as though this atom had been
+economically taken from the "cigar" to form a link. This will be more
+clearly seen when we come to separate the parts from each other. It will be
+noticed that the atoms in the "leaves" at the base vary in arrangement,
+being alternately in a line and in a triangle.
+
+                            { left  27
+CARBON: One pair of funnels { right 22
+                            { centre 1
+                                    --
+                                    54
+        4 pairs of funnels of 54 atoms   216
+        Atomic weight                  11.91
+        Number weight 216/18           12.00
+TITANIUM (Plate III, 6, and XV, 2) has a complete carbon atom distributed
+over the ends of its four arms, a pair of funnels with their linking atom
+being seen in each. Then, in each arm, comes the elaborate body shown as 3
+_c_, with its eighty-eight atoms. A ring of twelve ovoids (3 _d_) each
+holding within itself fourteen atoms, distributed among three contained
+globes--two quartets and a sextet--is a new device for crowding in
+material. Lastly comes the central body (4 _e_) of five intersecting
+tetrahedra, with a "cigar" at each of their twenty points--of which only
+fifteen can be shown in the diagram--and a ring of seven atoms round an
+eighth, that forms the minute centre of the whole. Into this elaborate body
+one hundred and twenty-eight atoms are built.
+
+TITANIUM: One carbon atom               216
+          4 _c_ of 88 atoms        352
+          12 _d_ of 14  "          168
+          Central globe                 128
+                                       ----
+                            Total       864
+                                       ----
+          Atomic weight               47.74
+          Number weight 864/18        48.00
+ZIRCONIUM (Plate XV, 3) has exactly the same outline as titanium, the
+carbon atom is similarly distributed, and the central body is identical.
+Only in 5 _c_ and _d_ do we find a difference on comparing them with 4 _c_
+and d. The _c_ ovoid in zirconium shows no less than fifteen secondary
+globes within the five contained in the ovoid, and these, in turn, contain
+altogether sixty-nine smaller spheres, with two hundred and twelve atoms
+within them, arranged in pairs, triplets, quartets, quintets, a sextet and
+septets. Finally, the ovoids of the ring are also made more elaborate,
+showing thirty-six atoms instead of fourteen. In this way the clever
+builders have piled up in zirconium no less than 1624 atoms.
+
+ZIRCONIUM: One Carbon atom              216
+           4 _c_ of 212 atoms      848
+           12 _d_ of 36   "        432
+           Central globe                128
+                                       ----
+                              Total    1624
+                                       ----
+           Atomic weight              89.85
+           Number weight              90.22
+[Illustration: PLATE XVI.]
+
+SILICON (Plate XVI, 1) is at the head of the group which corresponds to
+carbon on the opposite turn of the lemniscate. It has the usual eight
+funnels, containing four ovoids in a circle, and a truncated "cigar" but no
+central body of any kind. All the funnels are alike.
+
+SILICON: 8 funnels of 65 atoms          520
+         Atomic weight                28.18
+         Number weight 520/18         28.88
+GERMANIUM (Plate XVI, 2) shows the eight funnels, containing each four
+segments (XVI, 4), within which are three ovoids and a "cigar." In this
+case the funnels radiate from a central globe, formed of two intersecting
+tetrahedra, with "cigars" at each point enclosing a four-atomed globe.
+
+GERMANIUM: 8 funnels of 156 atoms     1248
+           Central globe                52
+                                      ----
+                   Total              1300
+                                      ----
+           Atomic weight             71.93
+           Number weight 1300/18     72.22
+TIN (Plate XVI, 3) repeats the funnel of germanium, and the central globe
+we met with in titanium, of five intersecting tetrahedra, carrying twenty
+"cigars"; the latter, however, omits the eight-atomed centre of the globe
+that was found in titanium, and hence has one hundred and twenty atoms
+therein instead of one hundred and twenty-eight. Tin, to make room for the
+necessary increase of atoms, adopts the system of spikes, which we met with
+in zinc (see Plate IX, 2); these spikes, like the funnels, radiate from the
+central globe, but are only six in number. The twenty-one-atomed cone at
+the head of the spike we have already seen in silver, and we shall again
+find it in iridium and platinum; the pillars are new in detail though not
+in principle, the contained globes yielding a series of a triplet, quintet,
+sextet, septet, sextet, quintet, triplet.
+
+TIN: 8 funnels of 156 atoms           1248
+     6 spikes  of 126   "              756
+     Central globe                     120
+                                      ----
+                      Total           2124
+                                      ----
+     Atomic weight                  118.10
+     Number weight 2124/18          118.00
+V.--THE BARS GROUPS.
+
+[Illustration: PLATE XVII.]
+
+Here, for the first time, we find ourselves a little at issue with the
+accepted system of chemistry. Fluorine stands at the head of a
+group--called the inter-periodic--whereof the remaining members are (see
+Crookes' table, p. 28), manganese, iron, cobalt, nickel; ruthenium,
+rhodium, palladium; osmium, iridium, platinum. If we take all these as
+group V, we find that fluorine and manganese are violently forced into
+company with which they have hardly any points of relationship, and that
+they intrude into an otherwise very harmonious group of closely similar
+composition. Moreover, manganese reproduces the characteristic lithium
+"spike" and not the bars of those into whose company it is thrust, and it
+is thus allied with lithium, with which indeed it is almost identical. But
+lithium is placed by Crookes at the head of a group, the other members of
+which are potassium, rubidium and cęsium (the last not examined). Following
+these identities of composition, I think it is better to remove manganese
+and fluorine from their incongruous companions and place them with lithium
+and its allies as V _a_, the Spike Groups, marking, by the identity of
+number, similarities of arrangement which exist, and by the separation the
+differences of composition. It is worth while noting what Sir William
+Crookes, in his "Genesis of the Elements," remarks on the relations of the
+interperiodic group with its neighbours. He says: "These bodies are
+interperiodic because their atomic weights exclude them from the small
+periods into which the other elements fall, and because their chemical
+relations with some members of the neighbouring groups show that they are
+probably interperiodic in the sense of being in transition stages."
+
+Group V in every case shows fourteen bars radiating from a centre as shown
+in iron, Plate IV, 1. While the form remains unchanged throughout, the
+increase of weight is gained by adding to the number of atoms contained in
+a bar. The group is made up, not of single chemical elements, as in all
+other cases, but of sub-groups, each containing three elements, and the
+relations within each sub-group are very close; moreover the weights only
+differ by two atoms per bar, making a weight difference of twenty-eight in
+the whole. Thus we have per bar:--
+
+Iron             72        Palladium       136
+Nickel           74        Osmium          245
+Cobalt           76        Iridium         247
+Ruthenium       132        Platinum A      249
+Rhodium         134        Platinum B      257
+It will be noticed (Plate XVII, 3, 4, 5,) that each bar has two sections,
+and that the three lower sections in iron, cobalt and nickel are identical;
+in the upper sections, iron has a cone of twenty-eight atoms, while cobalt
+and nickel have each three ovoids, and of these the middle ones alone
+differ, and that only in their upper globes, this globe being four-atomed
+in cobalt and six-atomed in nickel.
+
+The long ovoids within each bar revolve round the central axis of the bar,
+remaining parallel with it, while each spins on its own axis; the iron cone
+spins round as though impaled on the axis.
+
+        14 bars of 72 atoms            1008
+        Atomic weight                 55.47
+        Number weight 1008/18         56.00
+IRON (Plate IV, 1, and XVII, 3):
+
+        14 bars of 74 atoms            1036
+        Atomic weight                 57.70
+        Number weight 1036/18         57.55
+COBALT (Plate XVII, 4):
+
+        14 bars of 76 atoms             1064
+        Atomic weight                  58.30
+        Number weight 1064/18          59.11
+NICKEL (Plate XVII, 4):
+
+(The weight of cobalt, as given in Erdmann's _Lehrbuch_, is 58.55, but
+Messrs. Parker and Sexton, in _Nature_, August 1, 1907, give the weight, as
+the result of their experiments, as 57.7.)
+
+[Illustration: PLATE XVIII.]
+
+The next sub-group, ruthenium, rhodium, and palladium, has nothing to
+detain us. It will be observed that each bar contains eight segments,
+instead of the six of cobalt and nickel; that ruthenium and palladium have
+the same number of atoms in their upper ovoids, although in ruthenium a
+triplet and quartet represent the septet of palladium; and that in
+ruthenium and rhodium the lower ovoids are identical, though one has the
+order: sixteen, fourteen, sixteen, fourteen; and the other: fourteen,
+sixteen, fourteen, sixteen. One constantly asks oneself: What is the
+significance of these minute changes? Further investigators will probably
+discover the answer.
+
+      14 bars of 132 atoms              1848
+      Atomic weight                   100.91
+      Number weight 1848/18           102.66
+RUTHENIUM (Plate XVIII, 1):
+
+      14 bars of 134 atoms              1876
+      Atomic weight                   102.23
+      Number weight 1876/18           104.22
+RHODIUM (Plate XVII, 2):
+
+      14 bars of 136 atoms              1904
+      Atomic weight                   105.74
+      Number weight 1904/18           105.77
+PALLADIUM (XVIII, 3):
+
+The third sub-group, osmium, iridium and platinum, is, of course, more
+complicated in its composition, but its builders succeed in preserving the
+bar form, gaining the necessary increase by a multiplication of contained
+spheres within the ovoids. Osmium has one peculiarity: the ovoid marked _a_
+(XVIII, 4) takes the place of axis in the upper half of the bar, and the
+three ovoids, marked _b_, revolve round it. In the lower half, the four
+ovoids, _c_, revolve round the central axis. In platinum, we have marked
+two forms as platinum A and platinum B, the latter having two four-atomed
+spheres (XVIII, 6 _b_) in the place of the two triplets marked a. It may
+well be that what we have called platinum B is not a variety of platinum,
+but a new element, the addition of two atoms in a bar being exactly that
+which separates the other elements within each of the sub-groups. It will
+be noticed that the four lower sections of the bars are identical in all
+the members of this sub-group, each ovoid containing thirty atoms. The
+upper ring of ovoids in iridium and platinum A are also identical, but for
+the substitution, in platinum A, of a quartet for a triplet in the second
+and third ovoids; their cones are identical, containing twenty-one atoms,
+like those of silver and tin.
+
+       14 bars of 245 atoms            3430
+       Atomic weight                 189.55
+       Number weight 3430/18         190.55
+OSMIUM (Plate XVIII, 4):
+
+       14 bars of 247 atoms            3458
+       Atomic weight                 191.11
+       Number weight 3458/18         192.11
+IRIDIUM (Plate XVIII, 5):
+
+       14 bars of 249 atoms            3486
+       Atomic weight                 193.66
+       Number weight 3486/18         193.34
+PLATINUM A (Plate XVIII, 6 _a_):
+
+       14 bars of 251 atoms            3514
+       Atomic weight                 ------
+       Number weight 3514/18         195.22
+PLATINUM B (Plate XVIII, 6 _b_):
+
+V a.--THE SPIKE GROUPS.
+
+I place within this group lithium, potassium, rubidium, fluorine, and
+manganese, because of their similarity in internal composition. Manganese
+has fourteen spikes, arranged as in the iron group, but radiating from a
+central globe. Potassium has nine, rubidium has sixteen, in both cases
+radiating from a central globe. Lithium (Plate IV, 2) and fluorine (Plate
+IV, 3) are the two types which dominate the group, lithium supplying the
+spike which is reproduced in all of them, and fluorine the "nitrogen
+balloon" which appears in all save lithium. It will be seen that the
+natural affinities are strongly marked. They are all monads and
+paramagnetic; lithium, potassium and rubidium are positive, while fluorine
+and manganese are negative. We seem thus to have a pair, corresponding with
+each other, as in other cases, and the interperiodic group is left
+interperiodic and congruous within itself.
+
+[Illustration: PLATE XIX.]
+
+LITHIUM (Plate IV, 2 and Plate XIX, 1) is a striking and beautiful form,
+with its upright cone, or spike, its eight radiating petals (_x_) at the
+base of the cone, and the plate-like support in the centre of which is a
+globe, on which the spike rests. The spike revolves swiftly on its axis,
+carrying the petals with it; the plate revolves equally swiftly in the
+opposite direction. Within the spike are two globes and a long ovoid; the
+spheres within the globe revolve as a cross; within the ovoid are four
+spheres containing atoms arranged on tetrahedra, and a central sphere with
+an axis of three atoms surrounded by a spinning wheel of six.
+
+LITHIUM: Spike of 63 atoms                 63
+         8 petals of 6 atoms               48
+         Central globe of 16 atoms         16
+                                         ----
+                               Total      127
+                                         ----
+         Atomic weight                   6.98
+         Number weight 127/18            7.05
+POTASSIUM (Plate XIX, 2) consists of nine radiating lithium spikes, but has
+not petals; its central globe contains one hundred and thirty-four atoms,
+consisting of the "nitrogen balloon," encircled by six four-atomed spheres.
+
+POTASSIUM: 9 bars of 63 atoms             567
+           Central globe                  134
+                                         ----
+                              Total       701
+                                         ----
+           Atomic weight                38.94
+           Number weight 701/18         38.85
+(The weight, as determined by Richards [_Nature_, July 18, 1907] is
+39.114.)
+
+RUBIDIUM: (Plate XIX, 3) adds an ovoid, containing three spheres--two
+triplets and a sextet--to the lithium spike, of which it has sixteen, and
+its central globe is composed of three "balloons."
+
+RUBIDIUM: 16 spikes of 75 atoms          1200
+          Central globe                   330
+                                         ----
+                            Total        1530
+                                         ----
+          Atomic weight                 84.85
+          Number weight 1530/18         85.00
+The corresponding negative group consists only of fluorine and manganese,
+so far as our investigations have gone.
+
+FLUORINE (Plate IV, 3, and Plate XVII, 1) is a most peculiar looking object
+like a projectile, and gives one the impression of being ready to shoot off
+on the smallest provocation. The eight spikes, reversed funnels, coming to
+a point, are probably responsible for this warlike appearance. The
+remainder of the body is occupied by two "balloons."
+
+FLUORINE: 8 spikes of 15 atoms            120
+          2 balloons                      220
+                                         ----
+                             Total        340
+                                         ----
+          Atomic weight                 18.90
+          Number weight 340/18          18.88
+MANGANESE (Plate XVII, 2) has fourteen spikes radiating from a central
+"balloon."
+
+MANGANESE: 14 spikes of 63 atoms          882
+           Central balloon                110
+                                         ----
+                           Total          992
+                                         ----
+           Atomic weight                54.57
+           Number weight 992/18         55.11
+       *       *       *       *       *
+
+IX.
+
+We have now to consider the breaking up of the octahedral groups, and more
+and more, as we proceed, do we find that the most complicated arrangements
+are reducible to simple elements which are already familiar.
+
+CARBON (Plate III, 5, and XV, 1).
+
+[Illustration]
+
+Carbon is the typical octahedron, and a clear understanding of this will
+enable us to follow easily the constitution and disintegration of the
+various members of these groups. Its appearance as a chemical atom is shown
+on Plate III, and see XV, 1. On the proto level the chemical atom breaks up
+into four segments, each consisting of a pair of funnels connected by a
+single atom; this is the proto element which appears at the end of each arm
+of the cross in titanium and zirconium. On the meta level the five
+six-atomed "cigars" show two neutral combinations, and the truncated
+"cigar" of five atoms is also neutral; the "leaves" yield two forms of
+triplet, five different types being thus yielded by each pair of funnels,
+exclusive of the linking atom. The hyper level has triplets, duads and
+units.
+
+TITANIUM (Plate III, 6, and XV, 2, 3).
+
+[Illustration]
+
+On the proto level, the cross breaks up completely, setting free the pairs
+of funnels with the linking atom (_a_ and _b_), as in carbon, the four
+bodies marked _c_, the twelve marked _d_, and the central globe marked e.
+The latter breaks up again, setting free its five intersecting
+cigar-bearing tetrahedra, which follow their usual course (see Occultum, p.
+44). The eight-atomed body in the centre makes a ring of seven atoms round
+a central one, like that in occultum (see p. 44, diagram B), from which it
+only differs in having the central atom, and breaks up similarly, setting
+the central atom free. The ovoid _c_ sets free its four contained globes,
+and the ovoid _d_ sets free the three within it. Thus sixty-one proto
+elements are yielded by titanium. On the meta level, _c_ (titanium 3)
+breaks up into star-like and cruciform bodies; the component parts of these
+are easily followed; on the hyper level, of the four forms of triplets one
+behaves as in carbon, and the others are shown, _a_, _b_ and _f_; the
+cruciform quintet yields a triplet and a duad, _c_ and _d_; the tetrahedra
+yield two triplets _g_ and _h_, and two units; the septet, a triplet _k_
+and a quartet _j_. On the meta level, the bodies from _d_ behave like their
+equivalents in sodium, each _d_ shows two quartets and a sextet, breaking
+up, on the hyper level, into four duads and two triads.
+
+ZIRCONIUM (Plate XV, 2, 5).
+
+Zirconium reproduces in its _c_ the four forms that we have already
+followed in the corresponding _c_ of titanium, and as these are set free on
+the proto level, and follow the same course on the meta and hyper levels,
+we need not repeat them. The central globe of zirconium _c_ sets free its
+nine contained bodies; eight of these are similar and are figured in the
+diagram; it will be observed that the central body is the truncated "cigar"
+of carbon; their behaviour on the meta and hyper levels is easily followed
+there. The central sphere is also figured; the cigar follows its usual
+course, and its companions unite into a sextet and an octet. The _d_ ovoid
+liberates five bodies, four of which we have already seen in titanium, as
+the crosses and sextet of sodium, and which are figured under titanium; the
+four quartets within the larger globe also follow a sodium model, and are
+given again.
+
+SILICON (Plate XVI, 1).
+
+[Illustration]
+
+In silicon, the ovoids are set free from the funnels on the proto level,
+and the truncated "cigar," playing the part of a leaf, is also liberated.
+This, and the four "cigars," which escape from their ovoids, pass along
+their usual course. The quintet and quartet remain together, and form a
+nine-atomed body on the meta level, yielding a sextet and a triplet on the
+hyper.
+
+GERMANIUM (Plate XVI, 2, 4).
+
+The central globe, with its two "cigar"-bearing tetrahedra, need not delay
+us; the tetrahedra are set free and follow the occultum disintegration, and
+the central four atoms is the sodium cross that we had in titanium. The
+ovoids (XVI, 4) are liberated on the proto level, and the "cigar," as
+usual, bursts its way through and goes along its accustomed path. The
+others remain linked on the meta level, and break up into two triangles and
+a quintet on the hyper.
+
+TIN (Plate XVI, 3, 4).
+
+Here we have only the spike to consider, as the funnels are the same as in
+germanium, and the central globe is that of titanium, omitting the eight
+atomed centre. The cone of the spike we have had in silver (see p. 729,
+May), and it is set free on the proto level. The spike, as in zinc, becomes
+a large sphere, with the single septet in the centre, the remaining six
+bodies circling round it on differing planes. They break up as shown. (Tin
+is Sn.)
+
+IRON (Plate IV, I, and XVII, 3).
+
+[Illustration]
+
+We have already dealt with the affinities of this peculiar group, and we
+shall see, in the disintegration, even more clearly, the close
+relationships which exist according to the classification which we here
+follow.
+
+The fourteen bars of iron break asunder on the proto level, and each sets
+free its contents--a cone and three ovoids, which as usual, become spheres.
+The twenty-eight-atomed cone becomes a four-sided figure, and the ovoids
+show crystalline contents. They break up, on the meta level as shown in the
+diagram, and are all reduced to triplets and duads on the hyper level.
+
+COBALT (Plate XVII, 4).
+
+The ovoids in cobalt are identical with those of iron; the higher ovoids,
+which replace the cone of iron, show persistently the crystalline forms so
+noticeable throughout this group.
+
+NICKEL (Plate XVII, 5).
+
+The two additional atoms in a bar, which alone separate nickel from cobalt,
+are seen in the upper sphere of the central ovoid.
+
+RUTHENIUM (Plate XVIII, 1).
+
+The lower ovoids in ruthenium are identical in composition, with those of
+iron, cobalt and nickel and may be studied under Iron. The upper ones only
+differ by the addition of a triplet.
+
+RHODIUM (Plate XVIII, 2).
+
+Rhodium has a septet, which is to be seen in the _c_ of titanium (see _k_
+in the titanium diagram) and differs only in this from its group.
+
+PALLADIUM (Plate XVIII, 3).
+
+In palladium this septet appears as the upper sphere in every ovoid of the
+upper ring.
+
+OSMIUM (Plate XVIII, 4).
+
+We have here no new constituents; the ovoids are set free on the proto
+level and the contained globes on the meta, all being of familiar forms.
+The cigars, as usual, break free on the proto level, and leave their ovoid
+with only four contained spheres, which unite into two nine-atomed bodies
+as in silicon (see above).
+
+IRIDIUM (Plate XVIII, 5.)
+
+The twenty-one-atomed cone of silver here reappears, and its proceedings
+may be followed under that metal (see diagram, p. 729, May). The remaining
+bodies call for no remark.
+
+PLATINUM (Plate XVIII, 6).
+
+Again the silver cone is with us. The remaining bodies are set free on the
+proto level, and their contained spheres on the meta.
+
+LITHIUM (Plate IV, 2, and XIX, 1).
+
+[Illustration]
+
+Here we have some new combinations, which recur persistently in its allies.
+The bodies _a_, in Plate XIX, 1, are at the top and bottom of the ellipse;
+they come to right and left of it in the proto state, and each makes a
+twelve-atomed body on the meta level.
+
+The five bodies within the ellipse, three monads and two sextets, show two
+which we have had before: _d_, which behaves like the quintet and quartet
+in silicon, after their junction, and _b_, which we have had in iron. The
+two bodies _c_ are a variant of the square-based pyramid, one atom at the
+apex, and two at each of the other angles. The globe, _e_, is a new form,
+the four tetrahedra of the proto level making a single twelve-atomed one on
+the meta. The body _a_ splits up into triplets on the hyper; _b_ and _d_
+follow their iron and silicon models; _c_ yields four duads and a unit; _e_
+breaks into four quartets.
+
+POTASSIUM (Plate XIX, 2).
+
+Potassium repeats the lithium spike; the central globe shows the "nitrogen
+balloon," which we already know, and which is surrounded on the proto level
+with six tetrahedra, which are set free on the meta and behave as in
+cobalt. Hence we have nothing new.
+
+RUBIDIUM (Plate XIX, 3).
+
+Again the lithium spike, modified slightly by the introduction of an ovoid,
+in place of the top sphere; the forms here are somewhat unusual, and the
+triangles of the sextet revolve round each other on the meta level; all the
+triads break up on the hyper level into duads and units.
+
+FLUORINE (Plate IV, 3, and Plate XVII, 1).
+
+The reversed funnels of fluorine split asunder on the proto level, and are
+set free, the "balloons" also floating off independently. The funnels, as
+usual, become spheres, and on the meta level set free their contained
+bodies, three quartets and a triplet from each of the eight. The balloons
+disintegrate in the usual way.
+
+MANGANESE (Plate XVII, 2).
+
+Manganese offers us nothing new, being composed of "lithium spikes" and
+"nitrogen balloons."
+
+       *       *       *       *       *
+
+X.
+
+VI.--THE STAR GROUPS.
+
+We have now reached the last of the groups as arranged on Sir William
+Crookes' lemniscates, that forming the "neutral" column; it is headed by
+helium, which is _sui generis_. The remainder are in the form of a flat
+star (see Plate IV, 4), with a centre formed of five intersecting and
+"cigar"-bearing tetrahedra, and six radiating arms. Ten of these have been
+observed, five pairs in which the second member differs but slightly from
+the first; they are: Neon, Meta-neon; Argon, Metargon; Krypton,
+Meta-krypton; Xenon, Meta-xenon; Kalon, Meta-kalon; the last pair and the
+meta forms are not yet discovered by chemists. These all show the presence
+of a periodic law; taking an arm of the star in each of the five pairs, we
+find the number of atoms to be as follows :--
+
+40       99      224      363      489
+47      106      231      370      496
+It will be observed that the meta form in each case shows seven more atoms
+than its fellow.
+
+[Illustration: PLATE XX.]
+
+HELIUM (Plate III, 5, and Plate XX, 1) shows two "cigar"-bearing
+tetrahedra, and two hydrogen triangles, the tetrahedra revolving round an
+egg-shaped central body, and the triangles spinning on their own axes while
+performing a similar revolution. The whole has an attractively airy
+appearance, as of a fairy element.
+
+HELIUM: Two tetrahedra of 24 atoms   48
+        Two triangles of 9 atoms     18
+        Central egg                   6
+                                   ----
+                 Total               72
+                                   ----
+        Atomic weight              3.94
+        Number weight 72/18        4.00
+NEON (Plate XX, 2 and 6) has six arms of the pattern shown in 2, radiating
+from the central globe.
+
+NEON: Six arms of 40 atoms       240
+      Central tetrahedra         120
+
+                                ----
+                   Total         360
+                                ----
+      Atomic weight            19.90
+      Number weight 360/18     20.00
+META-NEON (Plate XX, 3 and 6) differs from its comrade by the insertion of
+an additional atom in each of the groups included in the second body within
+its arm, and substituting a seven-atomed group for one of the triplets in
+neon.
+
+META-NEON: Six arms of 47 atoms    282
+           Central tetrahedra      120
+                                  ----
+Total                              402
+                                  ----
+Atomic weight                     ----
+Number weight 402/18             22.33
+ARGON (Plate XX, 4, 6 and 7) shows within its arms the _b_ 63 which we met
+in nitrogen, yttrium, vanadium and niobium, but not the "balloon," which we
+shall find with it in krypton and its congeners.
+
+ARGON: Six arms of 99 atoms     594
+       Central tetrahedra       120
+                               ----
+                 Total          714
+                               ----
+       Atomic weight          39.60
+       Number weight 714/18   39.66
+METARGON (Plate XX, 5, 6 and 7) again shows only an additional seven atoms
+in each arm.
+
+METARGON: Six arms of 106 atoms   636
+          Central tetrahedra      120
+                                 ----
+                      Total       756
+                                 ----
+Atomic weight                    ----
+Number weight 756/18               42
+[Illustration: PLATE XXI.]
+
+KRYPTON (Plate XXI, 1 and 4, and Plate XX, 6 and 7) contains the nitrogen
+"balloon," elongated by its juxtaposition to _b_ 63. The central tetrahedra
+appear as usual.
+
+KRYPTON:  Six arms of 224 atoms             1344
+          Central tetrahedra                 120
+                                           -----
+                               Total        1464
+                                           -----
+          Atomic weight                    81.20
+          Number weight 1464/18            81.33
+META-KRYPTON differs only from krypton by the substitution of _z_ for _y_
+in each arm of the star.
+
+META-KRYPTON:  Six arms of 231 atoms        1386
+               Central tetrahedra            120
+                                           -----
+                               Total        1506
+                                           -----
+               Atomic weight               -----
+               Number weight 1506/18       83.66
+XENON (Plate XXI, 2 and 4, and Plate XX, 6 and 7) has a peculiarity shared
+only by kalon, that _x_ and _y_ are asymmetrical, the centre of one having
+three atoms and the centre of the other two. Is this done in order to
+preserve the difference of seven from its comrade?
+
+XENON:  Six arms of 363 atoms               2178
+        Central tetrahedra                   120
+                                           -----
+                               Total        2298
+                                           -----
+        Atomic weight                     127.10
+        Number weight 2298/18             127.66
+META-XENON differs from xenon only by the substitution of two _z_'s for _x_
+and _y_.
+
+META-XENON:  Six arms of 370 atoms          2220
+            Central tetrahedra               120
+                                           -----
+                               Total        2340
+                                           -----
+            Atomic weight                  -----
+            Number weight 2340/18            130
+KALON (Plate XXI, 3 and 4, and Plate XX, 6 and 7) has a curious cone,
+possessing a kind of tail which we have not observed elsewhere; _x_ and _y_
+show the same asymmetry as in xenon.
+
+KALON: Six arms of 489 atoms          2934
+       Central tetrahedra              120
+                                      ----
+                            Total     3054
+                                      ----
+       Atomic weight                  ----
+       Number weight 3054/18        169.66
+META-KALON again substitutes two _z_'s for _x_ and _y_.
+
+META-KALON: Six arms of 496 atoms           2976
+            Central tetrahedra               120
+                                            ----
+                            Total           3096
+                                            ----
+            Atomic weight                   ----
+            Number weight 3096/18            172
+Only a few atoms of kalon and meta-kalon have been found in the air of a
+fair-sized room.
+
+It does not seem worth while to break up these elements, for their
+component parts are so familiar. The complicated groups--_a_ 110, _b_ 63
+and _c_ 120--have all been fully dealt with in preceding pages.
+
+       *       *       *       *       *
+
+There remains now only radium, of the elements which we have, so far,
+examined, and that will be now described and will bring to an end this
+series of observations. A piece of close and detailed work of this kind,
+although necessarily imperfect, will have its value in the future, when
+science along its own lines shall have confirmed these researches.
+
+It will have been observed that our weights, obtained by counting, are
+almost invariably slightly in excess of the orthodox ones: it is
+interesting that in the latest report of the International Commission
+(November 13, 1907), printed in the _Proceedings of the Chemical Society of
+London_, Vol. XXIV, No. 33, and issued on January 25, 1908, the weight of
+hydrogen is now taken at 1.008 instead of at 1. This would slightly raise
+all the orthodox weights; thus aluminium rises from 26.91 to 27.1, antimony
+from 119.34 to 120.2, and so on.
+
+       *       *       *       *       *
+
+XI.
+
+RADIUM.
+
+[Illustration: PLATE XXII.]
+
+Radium has the form of a tetrahedron, and it is in the tetrahedral groups
+(see article IV) that we shall find its nearest congeners; calcium,
+strontium, chromium, molybdenum resemble it most closely in general
+internal arrangements, with additions from zinc and cadmium. Radium has a
+complex central sphere (Plate XXII), extraordinarily vivid and living; the
+whirling motion is so rapid that continued accurate observation is very
+difficult; the sphere is more closely compacted than the centre-piece in
+other elements, and is much larger in proportion to the funnels and spikes
+than is the case with the elements above named; reference to Plate VIII
+will show that in these the funnels are much larger than the centres,
+whereas in radium the diameter of the sphere and the length of the funnel
+or spike are about equal. Its heart consists of a globe containing seven
+atoms, which assume on the proto level the prismatic form shown in cadmium,
+magnesium and selenium. This globe is the centre of two crosses, the arms
+of which show respectively three-atomed and two-atomed groups. Round this
+sphere are arranged, as on radii, twenty-four segments, each containing
+five bodies--four quintets and a septet--and six loose atoms, which float
+horizontally across the mouth of the segment; the whole sphere has thus a
+kind of surface of atoms. On the proto level these six atoms in each
+segment gather together and form a "cigar." In the rush of the streams
+presently to be described one of these atoms is occasionally torn away, but
+is generally, if not always, replaced by the capture of another which is
+flung into the vacated space.
+
+Each of the four funnels opens, as usual, on one face of the tetrahedron,
+and they resemble the funnels of strontium and molybdenum but contain three
+pillars instead of four (Plate XXIII). They stand within the funnel as
+though at the angles of a triangle, not side by side. The contained bodies,
+though numerous, contain forms which are all familiar.
+
+The spikes alternate with the funnels, and point to the angles of the
+tetrahedron as in zinc and cadmium; each spike contains three "lithium
+spikes" (see Plate XIX) with a ten-atomed cone or cap at the top, floating
+above the three (Plate XXIV). The "petals" or "cigars" of lithium exist in
+the central globe in the floating atoms, and the four-atomed groups which
+form the lithium "plate" may be seen in the funnels, so that the whole of
+lithium appears in radium.
+
+So much for its composition. But a very peculiar result, so far unobserved
+elsewhere, arises from the extraordinarily rapid whirling of the central
+sphere. A kind of vortex is formed, and there is a constant and powerful
+indraught through the funnels. By this, particles are drawn in from
+without, and these are swept round with the sphere, their temperature
+becoming much raised, and they are then violently shot out through the
+spikes. It is these jets which occasionally sweep away an atom from the
+surface of the sphere. These "particles" may be atoms, or they may be
+bodies from any of the etheric levels; in some cases these bodies break up
+and form new combinations. In fact lithium seems like a kind of vortex of
+creative activity, drawing in, breaking up, recombining, shooting forth--a
+most extraordinary element.
+
+RADIUM: 4 funnels of 618 atoms          2472
+        4 spikes of 199 atoms            796
+        Central sphere                   819
+                                        ----
+                             Total      4087
+                                        ----
+        Atomic weight                   ----
+        Number weight 4087/18         227.05
+[Illustration: PLATE XXIV.]
+
+[Illustration: PLATE XXIII.]
+
+       *       *       *       *       *
+
+APPENDIX.
+
+THE ĘTHER 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 mūlaprakrti, 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 mūlaprakrti 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 ęther 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 spirillę 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 spirillę of the first
+order in each wire is 1680; and the proportion of the different orders of
+spirillę to one another is equal in all cases that have been examined, and
+correspond with the number of dots in the ultimate spirillę 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 spirillę 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 ęther, 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 Māyā, 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 ęther. 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 ęther 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 Ęther," 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 ęther 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 ętherial
+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 ęther 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 ęther. 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 ādi-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. Jinarājadāsa, 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 māyā, 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 medięval 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.
+
+
+
+***END OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY***
+
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+<h1>The Project Gutenberg eBook, Occult Chemistry, by Annie Besant and Charles
+W. Leadbeater, Edited by A. P. Sinnett</h1>
+<pre class="pg">
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at <a href = "https://www.gutenberg.org">www.gutenberg.org</a></pre>
+<p>Title: Occult Chemistry</p>
+<p>       Clairvoyant Observations on the Chemical Elements</p>
+<p>Author: Annie Besant and Charles W. Leadbeater</p>
+<p>Editor: A. P. Sinnett</p>
+<p>Release Date: June 14, 2005  [eBook #16058]</p>
+<p>Language: English</p>
+<p>Character set encoding: ISO-8859-1</p>
+<p>***START OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY***</p>
+<p>&nbsp;</p>
+<h3>E-text prepared by Clare Boothby, Keith Edkins,<br />
+    and the Project Gutenberg Online Distributed Proofreading Team</h3>
+<p>&nbsp;</p>
+<hr class="full" />
+<p>&nbsp;</p>
+<p>&nbsp;</p>
+<h2>OCCULT CHEMISTRY</h2>
+
+<p class="center" style="margin-top: 2em;">Clairvoyant Observations on the<br />
+Chemical Elements</p>
+
+<p class="center" style="margin-top: 2em;">BY</p>
+
+<h3>ANNIE BESANT, <font class="sc">p.t.s.</font></h3>
+
+<p class="center" style="margin-top: 2em;">AND</p>
+
+<h3>CHARLES W. LEADBEATER</h3>
+
+  <br clear="all" />
+<hr class="short" />
+
+<p class="center" style="margin-top: 2em;"><i>Revised Edition edited by</i> A.P. <font class="sc">Sinnett</font></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">London</font></p>
+
+<h3>THEOSOPHICAL PUBLISHING HOUSE</h3>
+
+<p class="center" style="margin-top: 2em;">1, <font class="sc">Upper Woburn Place</font>, W.C. 1.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>1919</h3>
+
+  <br clear="all" />
+<hr />
+
+<h3>EDITOR'S PREFACE.</h3>
+
+  <br clear="all" />
+<hr class="short" />
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>It remains to be seen&mdash;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.</p>
+
+  <br clear="all" />
+<hr />
+
+<h3>CONTENTS.</h3>
+
+  <div class="contents">
+    <div class="stanza">
+      <p>I.&mdash;<a href="#chap1"><font class="sc">A Preliminary Survey</font></a></p>
+    </div>
+
+    <div class="stanza">
+      <p>II.&mdash;<a href="#chap2"><font class="sc">Details of the Early Research</font></a></p>
+    </div>
+
+    <div class="stanza">
+      <p class="i4"><a href="#chap2b"><font class="sc">The Platonic Solids</font></a></p>
+    </div>
+
+    <div class="stanza">
+      <p>III.&mdash;<a href="#chap3"><font class="sc">The Later Researches</font></a></p>
+    </div>
+  </div>
+  <br clear="all" />
+<hr />
+
+  <p><a name="chap1"></a></p>
+
+<h2>OCCULT CHEMISTRY.</h2>
+
+<h3>CHAPTER I.</h3>
+
+<h3>A PRELIMINARY SURVEY.</h3>
+
+  <p>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 <i>Theosophist</i>, 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&mdash;that of preparing the present edition&mdash;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.</p>
+
+  <p>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 <i>see</i> 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.</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>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 <i>Lucifer</i>, 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&mdash;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)&mdash;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.</p>
+
+  <p>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,
+  <i>via</i> 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.</p>
+
+  <p>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.</p>
+
+  <p>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
+  <i>per se</i> had inertia. So the windmills in the Crookes' vacuum tubes
+  were supposed to be moved by the impact of electric atoms.</p>
+
+  <p>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&mdash;the <i>structure</i> 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.</p>
+
+  <p>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.</p>
+
+  <br clear="all" />
+<hr />
+
+  <p><a name="chap2"></a></p>
+
+<h3>CHAPTER II.</h3>
+
+<h3>DETAILS OF THE EARLY RESEARCH.</h3>
+
+  <p>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 <i>Lucifer</i>), began with some general remarks about the
+  clairvoyant faculty, already discussed in the preceding chapter. The
+  original record then goes on as follows:&mdash;</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p><a name="UltAtom"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-001.png" target="_blank"><img width="100%" src="images/oc-001.png"
+      alt="Substates of matter for hydrogen, oxygen and nitrogen." /></a>
+  </div>
+  <p>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&mdash;cleverly drawn from the description given by
+  the investigators&mdash;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 <i>a</i>, 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.</p>
+
+  <p>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&nbsp;2 except in the case of the hydrogen.
+  The letters given are intended to help the reader to trace upwards any
+  special body; thus <i>d</i> in the oxygen chemical atom on the gas level
+  may be found again on E&nbsp;4, E&nbsp;3, and E&nbsp;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&nbsp;1 is represented by the dot <i>a</i> on the gaseous level.</p>
+
+  <p>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&mdash;each of these being an ultimate physical atom&mdash;but in
+  two of them the three atoms are arranged in a line, while in the
+  remaining four they are arranged in a triangle.</p>
+
+  <p>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 <i>b</i> in the diagram
+  unite with one of those marked <i>b'</i> 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&nbsp;4&mdash;ether 4&mdash;on the diagram. On raising these further,
+  they undergo another disintegration, losing their limiting walls; the
+  positive body of E&nbsp;4, on losing its wall, becomes two bodies, one
+  consisting of the two particles, marked <i>b</i>, distinguishable by the
+  linear arrangement of the contained ultimate atoms, enclosed in a wall,
+  and the other being the third body enclosed in E&nbsp;4 and now set free. The
+  negative body of E&nbsp;4 similarly, on losing its wall, becomes two bodies,
+  one consisting of the two particles marked <i>b'</i>, and the second the
+  remaining body, being set free. These free bodies do not remain on E&nbsp;3
+  but pass immediately to E&nbsp;2, leaving the positive and negative bodies,
+  each containing two particles, as the representatives of hydrogen on E&nbsp;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&nbsp;2, but similar bodies
+  of this state of matter are found entering into other combinations, as
+  may be seen by referring to <i>f</i> on E&nbsp;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&nbsp;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.</p>
+
+  <p>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 spirillę, and these again of minuter spirillę. 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.</p>
+
+  <p>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.</p>
+
+  <p>The building of a gaseous atom of hydrogen may be traced downward from
+  E&nbsp;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&nbsp;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&nbsp;3 attracting to itself a
+  third atomic triad of the triangular type from E&nbsp;2, by the setting up of
+  a new centre of up-welling force, following the lines traced in the
+  combinations of E&nbsp;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.</p>
+
+  <p>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&nbsp;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&nbsp;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&nbsp;2, the fragments of the snakes break up into their constituent
+  parts; the positive and negative bodies, marked <i>d</i> and <i>d'</i>,
+  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:&mdash;</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>2 in each bead, of which there are 110:</p>
+      <p>7 in each bright spot, of which there are 10;</p>
+      <p>2 x 110 + 70 = 290.</p>
+    </div>
+  </div>
+  <p>When the observers had worked out this, they compared it with the
+  number of ultimate atoms in hydrogen:&mdash;</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>290 / 18 = 16.11 +</p>
+    </div>
+  </div>
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>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&nbsp;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&mdash;marked <i>q</i> on E&nbsp;4&mdash;are not on one plane,
+  and those within <i>n</i> and <i>o</i> form respectively square-based and
+  triangular-based pyramids. On raising all these bodies to E&nbsp;3 we find the
+  walls fall away as usual, and the contents of each "cell" are set free:
+  <i>p</i> of E&nbsp;4 contains six small bodies marked <i>k</i>, and these are
+  shown in <i>k</i> of E&nbsp;3, as containing each seven little
+  bodies&mdash;marked <i>e</i>&mdash;each of which has within it two
+  ultimate atoms; the long form of <i>p</i> E&nbsp;4&mdash;marked
+  <i>l</i>&mdash;appears as the long form <i>l</i> on E&nbsp;3, and this has
+  three pairs of smaller bodies within it, <i>f'</i>, <i>g</i> and
+  <i>h</i>, containing respectively three, four and six ultimate atoms;
+  <i>q</i> of E&nbsp;4, with its seven contained particles, <i>m</i>, has three
+  particles <i>m</i> on E&nbsp;3, each showing three ultimate atoms within them;
+  <i>e</i> from <i>n</i> of E&nbsp;4 becomes <i>i</i> of E&nbsp;3, with contained
+  bodies, <i>e</i>, showing two ultimate atoms in each; while <i>e'</i>
+  from <i>o</i> of E&nbsp;4 becomes <i>j</i> of E&nbsp;3, each having three smaller
+  bodies within it, <i>e'</i>, with two ultimate atoms in each. On E&nbsp;2, the
+  arrangement of these ultimate atoms is shown, and the pairs, <i>f'</i>,
+  <i>g</i> and <i>h</i> are seen with the lines of force indicated; the
+  triads in <i>f</i>&mdash;from <i>m</i> of E&nbsp;3&mdash;are similarly shown,
+  and the duads in <i>e</i> and <i>e'</i>&mdash;from <i>i</i> and <i>j</i>
+  of E&nbsp;3&mdash;are given in the same way. When all these bodies are raised
+  to E&nbsp;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:&mdash;</p>
+
+<pre>
+        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
+</pre>
+  <p>This again approaches closely the weight-number assigned to
+  nitrogen:&mdash;</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>261 / 18 =14.44 +</p>
+    </div>
+  </div>
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p><a name="chap2b"></a></p>
+
+<h3>THE PLATONIC SOLIDS.</h3>
+
+  <p>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:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>(1) The lines are equal.</p>
+      <p>(2) The angles are equal.</p>
+      <p>(3) The surfaces are equal.</p>
+    </div>
+  </div>
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-002.png" target="_blank"><img width="100%" src="images/oc-002.png"
+      alt="The five Platonic solids." /></a>
+  </div>
+  <p>It will be seen that the tetrahedron is the fundamental form, the
+  three-sided pyramid on a triangular base, <i>i.e.</i>, 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.</p>
+
+  <p>The rhombic dodecahedron is not regular, for though the lines and
+  surfaces are equal, the angles are not.</p>
+
+<h3>NOTES.</h3>
+
+  <p>Mr. C. Jinarājadāsa<a name="NtA_1" href="#Nt_1"><sup>[1]</sup></a>
+  writes:</p>
+
+  <p>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 <i>Proceedings of the Royal
+  Society</i>, 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.</p>
+
+  <p>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.</p>
+
+  <p>He says further on a probable <i>fourth</i> Interperiodic Group:</p>
+
+  <p>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 <i>periodically</i> in the table too.</p>
+
+  <p>I took the diagram for Osmium, and in a bar postulated only three
+  columns for the first element of the new groups, <i>i.e.</i>, 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.</p>
+
+  <p>Thus</p>
+
+<pre>
+        Os.--245     (in a bar);      less 60 = 185
+        Ir.  247                      less 60 = 187
+        Pt.  249                      less 60 = 189
+</pre>
+  <p>But strange to say <i>also</i></p>
+
+<pre>
+    Ruthenium (bar) 132              less 60--72
+    Rhodium         134              less 60--74
+    Palladium       136              less 60--76
+</pre>
+  <p>But 72, 74, 76, are Iron, Cobalt and Nickel.</p>
+
+  <p>So there does probably exist a new group with bars (183), 185, 187,
+  189, with atomic weights.</p>
+
+<pre>
+    X=bar 185;      atoms      2590, wt. 143.3
+    Y=    187,                 2618, wt. 145.4
+    Z=    189,                 2646, wt. 147.0.
+</pre>
+  <p>They come probably among the rare earths. Probably also Neodymium and
+  Praseodymium are two of them, for their weights are 143.6, 140.5.</p>
+
+  <br clear="all" />
+<hr />
+
+  <p><a name="chap3"></a></p>
+
+<h3>CHAPTER III.</h3>
+
+<h3>THE LATER RESEARCHES.</h3>
+
+  <p>The first difficulty that faced us was the identification of the forms
+  seen on focusing the sight on gases.<a name="NtA_2"
+  href="#Nt_2"><sup>[2]</sup></a> We could only proceed tentatively. Thus,
+  a very common form in the air had a sort of dumb-bell shape (see <a
+  href="#PlateI">Plate I</a>); we examined this, comparing our rough
+  sketches, and counted its atoms; these, divided by 18&mdash;the number of
+  ultimate atoms in hydrogen&mdash;gave us 23.22 as atomic weight, and this
+  offered the presumption that it was sodium. We then took various
+  substances&mdash;common salt, etc.&mdash;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.</p>
+
+  <p>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.</p>
+
+  <p><a name="PlateI"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-003.png" target="_blank"><img width="100%" src="images/oc-003.png"
+      alt="Plate I. Sodium." /></a>
+    <font class="sc">Plate I. Sodium</font>.
+  </div>
+  <p>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. Jinarājadāsa, and he multiplied out the total,
+  divided by 18, and announced the result. Thus: sodium (<i>see</i> 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&mdash;10; the number in two or three of
+  the funnels&mdash;each 16; the number of funnels&mdash;12; the same for
+  the lower part; in the connecting rod&mdash;14. Mr. Jinarājadāsa
+  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.</p>
+
+  <p>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.</p>
+
+<pre>
+--------------------------------------------
+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
+--------------------------------------------
+</pre>
+  <p><a name="PlateII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-004.png" target="_blank"><img width="100%" src="images/oc-004.png"
+      alt="Plate II - Ultimate physical atoms." /></a>
+    PLATE II. MALE (left) and FEMALE (right).
+  </div>
+  <p>As the words "ultimate physical atom" must frequently occur, it is
+  necessary to state what we mean by the phrase. Any gaseous chemical atom
+  may be dissociated into less complicated bodies; these, again, into still
+  less complicated; these, again, into yet still less complicated. These
+  will be dealt with presently. After the third dissociation but one more
+  is possible; the fourth dissociation gives the ultimate physical atom.<a
+  name="NtA_3" href="#Nt_3"><sup>[3]</sup></a> 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,<a name="NtA_4"
+  href="#Nt_4"><sup>[4]</sup></a> 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,<a
+  href="#Nt_4"><sup>[4]</sup></a> <i>i.e.</i>, 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 <i>positive</i> or <i>male</i>; those through which it
+  disappears, <i>negative</i> or <i>female</i>. All atoms, so far as
+  observed, are of one or other of these two forms. (Plate II.)</p>
+
+  <p>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.</p>
+
+  <p>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<a name="NtA_5" href="#Nt_5"><sup>[5]</sup></a>
+  and vanishes with its ebb. When this force arises in "space"<a
+  name="NtA_6" href="#Nt_6"><sup>[6]</sup></a>&mdash;the apparent void
+  which must be filled with substance of some kind, of inconceivable
+  tenuity&mdash;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<a name="NtA_7" href="#Nt_7"><sup>[7]</sup></a> which maintains the
+  physical basis of the universe.<a name="NtA_8"
+  href="#Nt_8"><sup>[8]</sup></a></p>
+
+  <p>In order to examine the construction of the atom, a space is
+  artificially made<a name="NtA_9" href="#Nt_9"><sup>[9]</sup></a>; 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&mdash;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.<a name="NtA_10"
+  href="#Nt_10"><sup>[10]</sup></a> 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 spirillę.<a name="NtA_11"
+  href="#Nt_11"><sup>[11]</sup></a></p>
+
+  <p>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.</p>
+
+  <p>In the three whorls flow currents of different electricities; the
+  seven vibrate in response to etheric waves of all kinds&mdash;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&mdash;flashing, singing, pulsing bodies, they move
+  incessantly, inconceivably beautiful and brilliant.<a name="NtA_12"
+  href="#Nt_12"><sup>[12]</sup></a></p>
+
+  <p>The atom has&mdash;as observed so far&mdash;three proper motions,
+  <i>i.e.</i>, 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.</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-005.png" target="_blank"><img width="100%" src="images/oc-005.png"
+      alt="Arrangement of atoms in an electric current." /></a>
+  </div>
+  <p>An electric current brought to bear upon the atoms checks their proper
+  motions, <i>i.e.</i>, 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.<a name="NtA_13"
+  href="#Nt_13"><sup>[13]</sup></a></p>
+
+  <p>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.</p>
+
+  <p>Three states of matter exist between the atomic state and the
+  gaseous&mdash;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 <i>elemental</i>; the state which results from breaking up
+  chemical elements, <i>proto-elemental</i>; the next higher,
+  <i>meta-proto-elemental</i>; the next higher,
+  <i>hyper-meta-proto-elemental</i>; then comes the atomic state. These are
+  briefly marked as El., Proto., Meta., and Hyper.<a name="NtA_14"
+  href="#Nt_14"><sup>[14]</sup></a></p>
+
+  <p>The simplest unions of atoms, never, apparently consisting of more
+  than seven, form the first molecular state of physical matter.</p>
+
+  <p><a name="Hyper"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-006.png" target="_blank"><img width="100%" src="images/oc-006.png"
+      alt="Types of Hyper-Meta-Proto-Elemental Matter." /></a>
+    <font class="sc">Types of Hyper-Meta-Proto-Elemental Matter</font>.
+  </div>
+  <p>Here are some characteristic combinations of the Hyper state; the atom
+  is conventional, with the depression emphasised; the lines, always
+  entering at the depression and coming out at the apex, show the
+  resultants of lines of force; where no line appears entering the
+  depression, the force wells up from fourth-dimensional space; where no
+  line appears leaving the apex, the force disappears into
+  fourth-dimensional space; where the point of entry and departure is
+  outside the atoms, it is indicated by a dot.<a name="NtA_15"
+  href="#Nt_15"><sup>[15]</sup></a></p>
+
+  <p>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<a name="NtA_16"
+  href="#Nt_16"><sup>[16]</sup></a> and rebound, dart hither and thither,
+  for reasons we have not distinguished.</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-007.png" target="_blank"><img width="100%" src="images/oc-007.png"
+      alt="Types of Meta-Proto-Elemental Matter" /></a>
+    <font class="sc">Types of Meta-Proto-Elemental Matter</font>.
+  </div>
+  <p>The Meta state, in some of its combinations, appears at first sight to
+  repeat those of the Hyper state; the only obvious way of distinguishing
+  to which some of the molecules of less complexity belong is to pull them
+  out of the "cell-wall"; if they are Hyper molecules they at once fly off
+  as separate atoms; if they are Meta molecules they break up into two or
+  more molecules containing a smaller number of atoms. Thus one of the Meta
+  molecules of iron, containing seven atoms, is identical in appearance
+  with a Hyper heptad, but the latter dissociates into seven atoms, the
+  former into two triads and a single atom. Long-continued research into
+  the detailed play of forces and their results is necessary; we are here
+  only able to give preliminary facts and details&mdash;are opening up the
+  way. The following may serve as characteristic Meta types:&mdash;</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-008.png" target="_blank"><img width="100%" src="images/oc-008.png"
+      alt="Types of Proto-Elemental Matter" /></a>
+    <font class="sc">Types of Proto-Elemental Matter</font>.
+  </div>
+  <p>These are taken from the products of the first disintegration of the
+  chemical atom, by forcibly removing it from its hole. The groups fly
+  apart, assuming a great variety of forms often more or less geometrical;
+  the lines between the constituents of the groups, where indicated, no
+  longer represent lines of force, but are intended to represent the
+  impression of form, <i>i.e.</i>, 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.</p>
+
+  <p>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
+  <i>Proceedings of the Royal Society</i>, in a paper read on June 9th,
+  1898.</p>
+
+  <p><a name="Crookes"></a></p>
+
+  <div class="figcenter" style="width:50%;">
+      <a href="images/oc-009.png" target="_blank"><img width="100%" src="images/oc-009.png"
+      alt="Sir William Crookes' classification." /></a>
+  </div>
+  <p>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.</p>
+
+  <p>Another chart&mdash;taken from Erdmann's
+  <i>Lehrbuch</i>&mdash;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.</p>
+
+  <div class="figcenter" style="width:50%;">
+      <a href="images/oc-010.png" target="_blank"><img width="100%" src="images/oc-010.png"
+      alt="Chart taken from Erdmann's Lehrbuch." /></a>
+  </div>
+  <p>The external forms may be classified as follows; the internal details
+  will be dealt with later :&mdash;</p>
+
+  <p><a name="PlateIII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-011.png" target="_blank"><img width="100%" src="images/oc-011.png"
+      alt="Plate III." /></a>
+    <font class="sc">Plate III</font>.
+  </div>
+  <p>1. <i>The Dumb-bell.</i>&mdash;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,<a name="NtA_17" href="#Nt_17"><sup>[17]</sup></a> and
+  gold is given (1 on <a href="#PlateIII">Plate III</a>) 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.</p>
+
+  <p>II and II<i>a.</i> <i>The Tetrahedron.</i>&mdash;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 <a href="#PlateIII">Plate III</a>), 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, <i>sui generis</i>. These two groups are marked in
+  orthodox chemistry as respectively positive and negative, and are closely
+  allied. Another pair of groups show the same tetrahedral form: magnesium,
+  zinc and cadmium, positive; sulphur, selenium and tellurium, negative.
+  Selenium is a peculiarly beautiful element, with a star floating across
+  the mouth of each funnel; this star is extremely sensitive to light, and
+  its rays tremble violently and bend if a beam of light falls on it. All
+  these are dyads.</p>
+
+  <p>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 <a
+  href="#PlateIII">Plate III</a>); 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.</p>
+
+  <p>III. <i>The Cube.</i>&mdash;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 <a href="#PlateIII">Plate
+  III</a>). 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.</p>
+
+  <p><a name="Octahedron"></a></p>
+
+  <p>IV. <i>The Octahedron.</i>&mdash;The simplest example of this is
+  carbon (5 on <a href="#PlateIII">Plate III</a>). 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 <a href="#PlateIII">Plate
+  III</a>) 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.</p>
+
+  <p><a name="PlateIV"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-012.png" target="_blank"><img width="100%" src="images/oc-012.png"
+      alt="Plate IV." /></a>
+    <font class="sc">Plate IV</font>.
+  </div>
+  <p>V. <i>The Bars.</i>&mdash;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&mdash;iron, nickel, cobalt; ruthenium, rhodium, palladium; osmium,
+  iridium, platinum&mdash;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 (<i>see</i>
+  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.</p>
+
+  <p>VI. <i>The Star.</i>&mdash;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.</p>
+
+  <p>There are thus six clearly defined forms, typical of classes, with
+  two&mdash;lithium and fluorine&mdash;of doubtful affinities. It is worthy
+  of notice that in diatomic elements <i>four</i> funnels open on the faces
+  of tetrahedra; in triatomic, <i>six</i> funnels on the faces of cubes; in
+  tetratomic, <i>eight</i> funnels on the faces of octahedra.</p>
+
+  <p>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?</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+  <br clear="all" />
+<h3>II.</h3>
+
+  <p>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&mdash;proto-elements&mdash;capable of separate, independent
+  existence; these, once more, may be dissociated into yet simpler
+  groups&mdash;hyper-meta-proto-elements&mdash;equally capable of separate,
+  independent existence, and resolvable into single ultimate physical
+  atoms, the irreducible substratum of the physical world (see
+  <i>Theosophist</i>, 1908, pp. 354-356).<a name="NtA_18"
+  href="#Nt_18"><sup>[18]</sup></a></p>
+
+  <p>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. Jinarājadāsa, will make the study comparatively easy to carry
+  on.</p>
+
+  <p>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&mdash;meeting at their apices&mdash;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.</p>
+
+  <p>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.</p>
+
+  <p>The use of the words "positive" and "negative" needs to be guarded by
+  the following paragraphs from the article on "Chemistry" in the
+  <i>Encyclopędia Britannica</i>. 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:&mdash;</p>
+
+  <p>"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."</p>
+
+  <p>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&mdash;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.</p>
+
+  <p>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).</p>
+
+  <p><a name="PlateV"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-013.png" target="_blank"><img width="100%" src="images/oc-013.png"
+      alt="Plate V." /></a>
+    <font class="sc">Plate</font> V.
+  </div>
+<font class="sc">Hydrogen</font> (Plate V, 1).&mdash;Hydrogen not only stands apart
+from its reputed group by not having the characteristic dumb-bell
+shape, well shown in sodium (<a href="#PlateI">Plate I</a>, 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.
+
+  <p>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.<a name="NtA_19" href="#Nt_19"><sup>[19]</sup></a>
+  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.</p>
+
+  <p>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.</p>
+
+<pre>
+HYDROGEN: 6 bodies of 3            18
+          Atomic weight             1
+          Number weight 18/18       1
+</pre>
+  <br clear="all" />
+<p class="center" style="margin-top: 2em;">I.&mdash;<font class="sc">The Dumb-bell Group</font>.</p>
+
+  <p>I <i>a</i>.&mdash;This group consists of Cl, Br, and I (chlorine,
+  bromine and iodine); they are monads, diamagnetic and negative.</p>
+
+<font class="sc">Chlorine</font> (<a href="#PlateV">Plate V</a>, 2).&mdash;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,
+<a href="#PlateI">Plate I</a>).
+
+  <p>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
+  (<a href="#PlateVI">Plate VI, 2</a>), 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.</p>
+
+<pre>
+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
+</pre>
+  <p>(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 <i>Nature</i>, July
+  18, 1907, gives 35.473.)</p>
+
+<font class="sc">Bromine</font> (<a href="#PlateV">Plate V</a>, 3).&mdash;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.<a name="NtA_20" href="#Nt_20"><sup>[20]</sup></a>
+
+<pre>
+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
+</pre>
+<font class="sc">Iodine</font> (<a href="#PlateV">Plate V</a>, 4).&mdash;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.
+
+<pre>
+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
+</pre>
+  <p>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.</p>
+
+  <p>I <i>b</i>.&mdash;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.</p>
+
+  <p><a name="PlateVI"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-014.png" target="_blank"><img width="100%" src="images/oc-014.png"
+      alt="Plate VI." /></a>
+    <font class="sc">Plate</font> VI.
+  </div>
+<font class="sc">Sodium</font> (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.
+
+<pre>
+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
+</pre>
+  <p><a name="CompCu"></a></p>
+
+<font class="sc">Copper</font> (<a href="#PlateVI">Plate VI</a>, 3) introduces an addition in the funnel,
+that we shall find elsewhere, <i>e.g.</i>, in silver, gold, iron, platinum,
+zinc, tin, the triangular arrangement near the mouth of the
+funnel and adds to the ten atoms in this nineteen more in three
+additional enclosed bodies, thus raising the number of atoms in
+a funnel from the sixteen of sodium to forty-five. The number
+in the central globe is doubled, and we meet for the first time
+the peculiar cigar or prism-shaped six-atomed arrangement, that
+is one of the most common of atomic groups. It ought to
+imply some definite quality, with its continual recurrence. The
+central column is the three, four, five, four, three, arrangement
+already noted.
+
+<pre>
+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
+</pre>
+<font class="sc">Silver</font> (<a href="#PlateVI">Plate VI</a>, 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.
+
+<pre>
+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
+</pre>
+  <p>(This atomic weight is given by Stas, in <i>Nature</i>, August 29,
+  1907, but it has been argued later that the weight should not be above
+  107.883.)</p>
+
+  <p><a name="PlateVII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-015.png" target="_blank"><img width="100%" src="images/oc-015.png"
+      alt="Plate VII." /></a>
+    <font class="sc">Plate</font> VII.
+  </div>
+  <p><a name="CompAu"></a></p>
+
+<font class="sc">Gold</font> (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 <i>e</i>, 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 <i>c</i>, the bodies on each side, <i>d</i>, 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 <i>a</i>, and one of the
+sixteen circling groups is enlarged in <i>b</i>. These groups are
+arranged in two planes inclined to one another.
+
+<pre>
+GOLD: Upper part
+          { 12 funnels of 97 atoms      1164
+          { Central ovoid {<i>c</i>             101
+                          {2 <i>d</i>, 38        76
+      Lower part same                   1341
+      Connecting rod { 4 <i>a</i> 84            336
+                     {16 <i>b</i> 33            528
+                                        ----
+                      Total             3546
+                                        ----
+      Atomic weight                   195.74
+      Number weight 3546/18           197
+</pre>
+  <p>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.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>III.</h3>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Occultum</font> (<a href="#PlateVI">Plate VI</a>, 1).</p>
+
+  <p>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 (<a href="#PlateVI">Plate VI</a>, 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.</p>
+
+  <p>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&mdash;they seem to be kept standing and popped in where
+  wanted. The sphere marked <i>x</i> is a proto-compound, the balloon when
+  set free.</p>
+
+  <p>As was noted under gold (<a href="#CompAu">p. 41</a>), sixteen
+  occultum bodies, re-arranged, make up the connecting rod in
+  gold:&mdash;</p>
+
+<pre>
+OCCULTUM: Tetrahedron                  24
+          Balloon                       9
+          Triplets                      6
+          Rope-circle                  15
+                                     ----
+                     Total             54
+                                     ----
+          Atomic weight         Not known
+          Number weight 54/18           3
+</pre>
+<p class="center" style="margin-top: 2em;"><font class="sc">Dissociation of Atoms</font>.</p>
+
+  <p>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.</p>
+
+  <p>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
+  <i>a</i>, <i>b</i>, <i>c</i>, &amp;c., enable the student to follow the
+  breaking up of each group through its successive stages.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Hydrogen</font> (<a href="#PlateV">Plate V</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-016.png" target="_blank"><img width="100%" src="images/oc-016.png"
+      alt="Dissociation of Hydrogren." /></a>
+  </div>
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>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 (<a href="#Hyper">p. 25</a>), and two remaining linear, but
+  rearranging their internal relations; the two remaining groups break up
+  into two pairs and a unit.</p>
+
+  <p>The final dissociation sets all the atoms free.</p>
+
+  <br clear="all" />
+  <p><a name="DisOc"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Occultum</font> (<a href="#PlateV">Plate VI</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-017.png" target="_blank"><img width="100%" src="images/oc-017.png"
+      alt="Dissociation of Occultum." /></a>
+  </div>
+  <p>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, <i>a</i>; two "cigars" are positive and two
+  negative, marked respectively <i>a</i> and <i>a'</i>. The rope becomes a
+  ring within a sphere, <i>b</i>, and the two bodies <i>d</i> <i>d</i>,
+  which are loose in the gaseous atom, come within this ring. The balloon
+  becomes a sphere.</p>
+
+  <p>On further dissociation, the "cigars" go off independently, showing
+  two types, and these again each divide into triplets, as meta-compounds.
+  <i>B</i>, on the meta-level, casts out the two <i>d</i> 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.</p>
+
+  <p>The balloon, <i>c</i>, 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.</p>
+
+  <p>The two triplets of <i>d</i> each cast out an atom on dissociation,
+  and form two pairs and two units.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Sodium</font> (<a href="#PlateVI">Plate VI</a>, 2).</p>
+
+  <p>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.</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-018.png" target="_blank"><img width="100%" src="images/oc-018.png"
+      alt="Dissociation of Sodium." /></a>
+  </div>
+  <p>When sodium is set free from its gaseous condition, it divides up into
+  thirty-one bodies&mdash;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.</p>
+
+  <p>When the proto-compounds are dissociated, the funnel-sphere sets free:
+  (1) the contents of <i>a</i>, rearranged into two groups of four within a
+  common sphere; the sphere yields four duads as hyper-compounds; (2) the
+  contents of <i>b</i>, which unite themselves into a quartet, yielding two
+  duads as hyper-compounds; and (3) the contents of the two spheres,
+  <i>c</i>, 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.</p>
+
+  <p>The part of the central globe, marked <i>d</i>, 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 <i>e</i>, 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.</p>
+
+  <p>Each of the two bodies marked <i>f</i>, liberated from the connecting
+  rod, shows four atoms whirling round a common centre, exactly resembling
+  <i>e</i> 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.</p>
+
+  <p>The body marked <i>g</i> 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.</p>
+
+  <p><a name="DisCl"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Chlorine</font> (<a href="#PlateV">Plate V</a>, 2).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-019.png" target="_blank"><img width="100%" src="images/oc-019.png"
+      alt="Dissociation of Chlorine and Bromine." /></a>
+  </div>
+  <p>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.</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Bromine</font> (<a href="#PlateV">Plate V</a>, 3).</p>
+
+  <p>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&mdash;each a
+  triangle and a quintet&mdash;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, <i>a</i> and the 2 <i>bs</i> whirling in a plane
+  vertical to the paper and the two smaller bodies, <i>cc</i>, whirling on
+  a plane at right angles to the other. These two disengage themselves,
+  forming a quartet as a meta-compound, while <i>a</i> makes a whirling
+  cross and <i>bb</i> a single sextet; these further dissociate themselves
+  into four pairs and two triplets.</p>
+
+  <p><a name="DisI"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Iodine</font> (<a href="#PlateV">Plate V</a>, 4).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-020.png" target="_blank"><img width="100%" src="images/oc-020.png"
+      alt="Dissociation of Iodine and Copper." /></a>
+  </div>
+  <p>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 <i>a</i> of bromine is repeated twice instead of the pairs in
+  <i>cc</i>.</p>
+
+  <p><a name="DisCu"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Copper</font> (<a href="#PlateVI">Plate VI</a>, 3).</p>
+
+  <p>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&mdash;two spheres&mdash;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 <i>a</i> 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.</p>
+
+  <p>The atoms in the bodies <i>a</i> and <i>b</i> are curiously arranged.
+  <i>A</i> consists of two square-based pyramids turned so as to meet at
+  their apices, and breaks up into two quartet rings and a duad. <i>B</i>
+  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.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>IV.</h3>
+
+  <p><a name="DisAg"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Silver</font> (<a href="#PlateVI">Plate VI</a>, 4 and Ag below).</p>
+
+  <p>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 <a href="#DisCl">p.
+  46</a>).</p>
+
+  <p><a name="DisAu"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Gold</font> (<a href="#PlateVII">Plate VII</a> and Au below).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-021.png" target="_blank"><img width="100%" src="images/oc-021.png"
+      alt="Dissociation of Silver and Gold." /></a>
+  </div>
+  <p>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
+  (<i>c</i>, <i>d</i>), thirty bodies being thus liberated. The sixteen
+  bodies on the central inclined planes, marked <i>b</i>, 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 <i>b</i> separate
+  into two each; the four <i>a</i> liberate five each; the two <i>c</i> set
+  free thirteen each; the four <i>d</i> finally liberate two each: 302
+  proto elements in all.</p>
+
+  <p>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. <i>B</i> has been broken up
+  under occultum (<a href="#DisOc">p. 628</a>) and can be followed there.
+  The sixteen rings set free from the four <i>a</i>, after gyrating round
+  the central body, now become a sphere, break up, as in occultum (see <a
+  href="#DisOc">p. 44</a>) 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 <i>c</i> assume the form of prisms as in iodine (see <a
+  href="#DisI">p. 48</a>) 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 (<a href="#DisCl">p. 47</a>), the duads going off independently
+  on the hyper-level and the ring breaking up as in chlorine. The "cigar"
+  tetrahedron of <i>d</i> 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.</p>
+
+  <p><a name="CompBe"></a></p>
+
+<p class="center" style="margin-top: 2em;">II <font class="sc">and</font> II<i>a</i>.&mdash;<font class="sc">The Tetrahedral Groups</font>.</p>
+
+  <p>II.&mdash;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.</p>
+
+  <p><a name="PlateVIII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-022.png" target="_blank"><img width="100%" src="images/oc-022.png"
+      alt="Plate VIII - Group II." /></a>
+    <font class="sc">Plate</font> VIII.
+  </div>
+<font class="sc">Beryllium</font> (<a href="#PlateIII">Plate III</a>, 2, and
+<a href="#PlateVIII">Plate VIII</a>, 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 <i>a</i>). The
+members of this group are alike in arrangement, differing only
+in the increased complexity of the bodies contained in the
+funnels. Beryllium, it will be observed, is very simple, whereas
+calcium and strontium are complicated.
+
+<pre>
+BERYLLIUM: 4 funnels of 40 atoms    160
+           Central globe              4
+                                   ----
+                           Total    164
+                                   ----
+Atomic weight                      9.01
+Number weight  164/18              9.11
+</pre>
+<font class="sc">Calcium</font> (<a href="#PlateVIII">Plate VIII</a>, 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 <i>b</i>) 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 <i>c</i>), and the
+external part, belonging to the encircling globe, shows the
+familiar "cigar" (7 <i>d</i>). In this way 720 atoms are packed into
+the simple beryllium type.
+
+<pre>
+CALCIUM: 4 funnels of 160 atoms      640
+         Central globe                80
+                                    ----
+                          Total      720
+                                    ----
+         Atomic weight             39.74
+         Number weight 720/18      40.00
+</pre>
+<font class="sc">Strontium</font> (<a href="#PlateVIII">Plate VIII</a>, 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 <i>e</i>, <i>g</i>, <i>f</i>). The
+<i>g</i> 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 <i>b</i>) identical with those of calcium. The
+third pair contains fourteen ovoids (7 <i>a</i>) 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 <i>h</i>)&mdash;the iodine ovoids&mdash;and the external
+segments contain five-atomed triangles (7 <i>i</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.
+
+<pre>
+STRONTIUM: 4 funnels of 368 atoms       1472
+           Central globe                  96
+                                        ----
+                            Total       1568
+                                        ----
+           Atomic weight               86.95
+           Number weight 1568/18       87.11
+</pre>
+  <p>The corresponding group, headed by oxygen&mdash;oxygen, chromium,
+  molybdenum, wolfram and uranium&mdash;offers us another problem in its
+  first member.</p>
+
+  <p><a name="CompO"></a></p>
+
+<font class="sc">Oxygen</font> (<a href="#PlateVIII">Plate VIII</a>, 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.
+
+<pre>
+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
+</pre>
+<font class="sc">Chromium</font> (<a href="#PlateVIII">Plate VIII</a>, 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&mdash;two quintets (7 <i>f</i>), a quintet (7 <i>j</i>), and two quintets
+(7 <i>e</i>), <i>e</i> and <i>f</i> being to each other as object and image. The
+remaining sphere (7 <i>b</i>) 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 <i>k</i>) is substituted for the calcium
+four-atomed one (7 <i>e</i>).
+
+<pre>
+CHROMIUM: 4 funnels of 210 atoms      840
+          Central globe                96
+                                    -----
+                   Total              936
+                                    -----
+          Atomic weight             51.74
+          Number weight 936/18      52.00
+</pre>
+<font class="sc">Molybdenum</font> (<a href="#PlateVIII">Plate VIII</a>, 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 <i>e</i>) has four atoms in it; the
+next three have four, seven and four (7 <i>e</i> <i>g</i> <i>e</i>), respectively; the
+next three are all septets (7 <i>g</i>), and the last has four&mdash;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.
+
+<pre>
+MOLYBDENUM: 4 funnels of 408 atoms     1632
+            Central globe                98
+                                      -----
+                          Total        1730
+                                      -----
+            Atomic weight             95.26
+            Number weight 1730/18     96.11
+</pre>
+  <p>II <i>a</i>.&mdash;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.</p>
+
+  <p><a name="PlateIX"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-023.png" target="_blank"><img width="100%" src="images/oc-023.png"
+      alt="Plate IX." /></a>
+    <font class="sc">Plate</font> IX.
+  </div>
+<font class="sc">Magnesium</font> (<a href="#PlateIX">Plate IX</a>, 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.
+
+<pre>
+MAGNESIUM: 4 funnels of 108 atoms     432
+           Atomic weight            24.18
+           Number weight 432/18     24.00
+</pre>
+<font class="sc">Zinc</font> (<a href="#PlateIX">Plate IX</a>, 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.
+
+<pre>
+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
+</pre>
+<font class="sc">Cadmium</font> (<a href="#PlateIX">Plate IX</a>, 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.
+
+<pre>
+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
+</pre>
+  <p>The corresponding negative group is headed by</p>
+
+  <p><a name="PlateX"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-024.png" target="_blank"><img width="100%" src="images/oc-024.png"
+      alt="Plate X." /></a>
+    <font class="sc">Plate</font> X.
+  </div>
+<font class="sc">Sulphur</font> (<a href="#PlateX">Plate X</a>, 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.
+
+<pre>
+SULPHUR: 4 funnels of 144 atoms       576
+         Atomic weight              31.82
+         Number weight 576/18       32.00
+</pre>
+<font class="sc">Selenium</font> (<a href="#PlateX">Plate X</a>, 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.
+
+<pre>
+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
+</pre>
+<font class="sc">Tellurium</font> (<a href="#PlateX">Plate X</a>, 3),
+it will be seen, closely resembles
+cadmium, and has three cylindrical segments&mdash;of which one is
+figured&mdash;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.
+
+<pre>
+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
+</pre>
+  <br clear="all" />
+<hr class="short" />
+
+<h3>V.</h3>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Beryllium</font> (<a href="#PlateIII">Plate III</a>, 2, and
+<a href="#PlateVIII">VIII</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-025.png" target="_blank"><img width="100%" src="images/oc-025.png"
+      alt="Dissociation of Beryllium and Calcium." /></a>
+  </div>
+  <p>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&mdash;sixteen bodies in
+  all, <i>plus</i> 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Calcium</font> (<a href="#PlateVIII">Plate VIII</a>, 2).</p>
+
+  <p>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 (<a href="#DisAu">p. 49</a>), 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&mdash;forty
+  positive and forty negative&mdash;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.</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Strontium</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 3).</p>
+
+  <p>The third member of this group repeats the <i>a</i> groups of
+  beryllium and the <i>b</i> 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
+  <i>g</i>, which are repeated in the central globe as <i>h</i>, are
+  seven-atomed, and appear as spheres or ovoids according to pressure. They
+  are figured on <a href="#DisI">p. 48</a>, under iodine; <i>e</i> and
+  <i>f</i> are related as object and image, and we have already seen them
+  in copper (<a href="#CompCu">pp. 38</a> and <a href="#DisCu">48</a>); 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>i</i>, which repeats <i>f</i>, makes a ring with the fifth in
+  the centre, as in the five-atomed <i>b</i> of calcium, as shown above.
+  There is, thus, nothing new in strontium, but only repetitions of forms
+  already studied.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Oxygen</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 4).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-026.png" target="_blank"><img width="100%" src="images/oc-026.png"
+      alt="Dissociation of Oxygen, Chromium and Molybdenum." /></a>
+  </div>
+  <p>The disintegration of oxygen as given in 1895 may be repeated here,
+  and the better presentation given on <a href="#CompO">p. 54</a> 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Chromium</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 5).</p>
+
+  <p>When we go on to chromium and molybdenum, we return to our familiar
+  funnels and central globes, and the secondary spheres within the
+  funnels&mdash;quickly set free, as before, on the proto level&mdash;give
+  us no new combinations in their contained spheres and ovoids. The
+  <i>a</i> of beryllium, the <i>b</i> of calcium and strontium, and
+  <i>d</i> of calcium, the <i>e</i> and <i>f</i> of strontium, are all
+  there; <i>j</i> in chromium is the same as the central sphere in the
+  <i>b</i> ovoid. In the central globe, <i>k</i>, 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Molybdenum</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 6).</p>
+
+  <p>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.</p>
+
+  <p>II <i>a</i>.&mdash;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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Magnesium</font> (<a href="#PlateIX"><font class="sc">Plate IX</font></a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-027.png" target="_blank"><img width="100%" src="images/oc-027.png"
+      alt="Dissociation of Magnesium and Zinc." /></a>
+  </div>
+  <p>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
+  <i>a</i>, a septet, Mg <i>b</i>, and a duad, Mg <i>c</i>, 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Zinc</font> (<a href="#PlateIX"><font class="sc">Plate IX</font></a>, 2).</p>
+
+  <p>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.</p>
+
+  <p>The triangular arrangement at the top of the spike is the same as
+  occurs in copper (<i>b</i> on <a href="#DisCu">p. 48</a>), and can be
+  there followed. One of the three similar pillars is shown in the
+  accompanying diagram under Zn <i>a</i>. 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 (<i>a</i> and
+  <i>b</i>, <a href="#CompAu">p. 40</a>). The spheres within the globes at
+  the base of the spikes, Zn <i>b</i>, behave as a cross&mdash;the cross is
+  a favourite device in the II <i>a</i> groups. Finally, the central globe,
+  Zn <i>c</i>, follows the same cruciform line of disintegration.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Cadmium</font> (<a href="#PlateIX">Plate IX</a>, 3).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-028.png" target="_blank"><img width="100%" src="images/oc-028.png"
+      alt="Dissociation of Cadmium and Tellurium." /></a>
+  </div>
+  <p>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 <i>a</i>, <i>b</i>), the contained bodies
+  revolving within them, <i>a</i> whirling on a diameter of the sphere,
+  cutting it in halves, as it were, and <i>b</i> whirling round it at right
+  angles; the cross also becomes a sphere (Cd <i>c</i>), 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Sulphur</font> (<a href="#PlateXI">Plate XI</a>, 1).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Selenium</font> (<a href="#PlateX">Plate X</a>, 2).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-029.png" target="_blank"><img width="100%" src="images/oc-029.png"
+      alt="Dissociation of Selenium." /></a>
+  </div>
+  <p>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.</p>
+
+  <p>Selenium offers a beautiful example of the combination of simple
+  elements into a most exquisite whole.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Tellurium</font> (<a href="#PlateX">Plate X</a>, 3).</p>
+
+  <p>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.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>VI.</h3>
+
+<p class="center" style="margin-top: 2em;">III <font class="sc">and</font> III<i>a</i>.&mdash;<font class="sc">The Cube Groups</font>.</p>
+
+  <p>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.</p>
+
+  <p>III.&mdash;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 <a href="#PlateXI">Plate
+  XI</a> and <a href="#PlateXII">Plate XII</a>. 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.</p>
+
+  <p><a name="PlateXI"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-030.png" target="_blank"><img width="100%" src="images/oc-030.png"
+      alt="Plate XI." /></a>
+    <font class="sc">Plate</font> XI.
+  </div>
+<font class="sc">Boron</font> (<a href="#PlateIII">Plate III</a>, 4, and Plate <a href="#PlateXI">XI</a>, 1).
+We have here the
+simplest form of the cube; the funnels contain only five bodies&mdash;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.
+
+<pre>
+BORON: 6 funnels of 30 atoms    180
+       Central globe             20
+                               ----
+                         Total  200
+                               ----
+       Atomic weight          10.86
+       Number weight 200/18   11.11
+</pre>
+<font class="sc">Scandium</font> (<a href="#PlateXI">Plate XI</a>, 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.
+
+  <p>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 <i>a</i> 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&mdash;the form always assumed on the proto
+  level&mdash;and it will be seen, on reference to the detailed diagram 4
+  <i>a</i>, 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.</p>
+
+  <p>The B funnel runs largely to triads, <i>c</i> and <i>b</i>, <i>b</i>
+  (see 4 <i>b</i>) having not only a triadic arrangement of spheres within
+  its contained globes, but each sphere has also a triplet of atoms. In
+  <i>c</i> (see 4 <i>c</i>) 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 <i>a</i>, <i>b</i> and <i>c</i> all
+  are constituents of nitrogen.</p>
+
+  <p>The central globe repeats that of boron, with an additional
+  four-atomed sphere in the middle.</p>
+
+<pre>
+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
+</pre>
+<font class="sc">Yttrium</font> (<a href="#PlateXI">Plate XI</a>, 3). Here we have a quite new arrangement
+of bodies within the funnel&mdash;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 <i>e</i>) chase each
+other in a circle round them, spinning madly on their own axes&mdash;this
+axial spinning seems constant in all contained bodies&mdash;all
+the time. Lower down in the funnel, a similar arrangement is
+seen, with a globe (see 4 <i>d</i>)&mdash;a nitrogen element&mdash;replacing the
+"cigars," and six-atomed ovoids replacing the globes.
+
+  <p>The "nitrogen balloon" occupies the third place in the funnel, now
+  showing its usual shape in combination, while the <i>b</i> globe (see 4
+  <i>b</i>) of scandium takes on a lengthened form below it.</p>
+
+  <p>The central globe presents us with two tetrahedra, recalling one of
+  the combinations in gold (see <a href="#PlateVII">Plate VII</a>
+  <i>d</i>), and differing from that only by the substitution of two
+  quartets for the two triplets in gold.</p>
+
+  <p>One funnel of yttrium contains exactly the same number of atoms as is
+  contained in a gaseous atom of nitrogen. Further, <i>a</i>, <i>b</i>, and
+  <i>d</i> are all nitrogen elements. We put on record these facts, without
+  trying to draw any conclusions from them. Some day, we&mdash;or
+  others&mdash;may find out their significance, and trace through them
+  obscure relations.</p>
+
+<pre>
+YTTRIUM: 6 funnels of 261 atoms      1566
+         Central globe                 40
+                                     ----
+                             Total   1606
+                                     ----
+         Atomic weight              88.34
+         Number weight 1606/18      89.22
+</pre>
+  <p>The corresponding negative group, of nitrogen, vanadium and niobium,
+  is rendered particularly interesting by the fact that it is headed by
+  nitrogen, which&mdash;like the air, of which it forms so large a
+  part&mdash;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.</p>
+
+  <p><a name="PlateXII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-031.png" target="_blank"><img width="100%" src="images/oc-031.png"
+      alt="Plate XII." /></a>
+    <font class="sc">Plate</font> XII.
+  </div>
+<font class="sc">Nitrogen</font> (<a href="#PlateXII">Plate XII</a>, 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 <i>a</i>) 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 <i>b</i> (see 4 <i>b</i>) with its seven contained
+spheres, each of which has nine atoms within it&mdash;three triads.
+Four spheres are seen, in addition to the two larger bodies; two
+of these (see 4 <i>d</i>), each containing five smaller globes, are
+positive, and two (see 4 <i>c</i>) containing four smaller globes, are
+negative.
+
+<pre>
+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
+</pre>
+<font class="sc">Vanadium</font> (<a href="#PlateXII">Plate XII</a>, 2) closely follows scandium, having two
+types of funnels. Funnel A only differs from that of scandium by
+having a globe (see 4 <i>d</i>) 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 <i>d</i>) between the
+two identical with those of scandium (see 4 <i>c</i>). 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.
+
+<pre>
+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
+</pre>
+<font class="sc">Niobium</font> (<a href="#PlateXII">Plate XII</a>, 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 <i>e</i>).
+
+  <p>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 <i>f</i>), seventeen atoms being thus added.</p>
+
+<pre>
+NIOBIUM: 6 funnels of 277 atoms        1662
+         Central globe                   57
+                                       ----
+                             Total     1719
+                                       ----
+         Atomic weight                93.25
+         Number weight 1719/18        95.50
+</pre>
+  <p>III <i>a</i>.&mdash;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.</p>
+
+  <p><a name="PlateXIII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-032.png" target="_blank"><img width="100%" src="images/oc-032.png"
+      alt="Plate XIII." /></a>
+    <font class="sc">Plate</font> XIII.
+  </div>
+<font class="sc">Aluminium</font> (<a href="#PlateXIII">Plate XIII</a>, 1), the head of the group, is, as usual,
+simple. There are six similar funnels, each containing eight
+ovoids, below which is a globe.
+
+<pre>
+ALUMINIUM: 6 funnels of 81 atoms        486
+           Atomic weight              26.91
+           Number weight 486/18       27.00
+</pre>
+<font class="sc">Gallium</font> (<a href="#PlateXIII">Plate XIII</a>, 2) has two segments in every funnel;
+in the segment to the left a "cigar" balances a globe, equally
+six-atomed, in that of the right, and the globes to right and left
+are four-atomed as against three-atomed. In the next row, the
+smaller contained globes have six atoms as against four, and
+the cones have respectively seven and five. By these little
+additions the left-hand funnel boasts one hundred and twelve
+atoms as against ninety-eight.
+
+<pre>
+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
+</pre>
+<font class="sc">Indium</font> (<a href="#PlateXIII">Plate XIII</a>, 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.
+
+<pre>
+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
+</pre>
+  <p>The corresponding negative group, phosphorus, arsenic, and antimony,
+  run on very similar lines to those we have just examined.</p>
+
+  <p><a name="PlateXIV"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-033.png" target="_blank"><img width="100%" src="images/oc-033.png"
+      alt="Plate XIV." /></a>
+    <font class="sc">Plate</font> XIV.
+  </div>
+<font class="sc">Phosphorus</font> (<a href="#PlateXIV">Plate XIV</a>, 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 <i>a</i> which do not show this arrangement, or a modification
+thereof, are aluminium and arsenic.
+
+<pre>
+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
+</pre>
+<font class="sc">Arsenic</font> (<a href="#PlateXIV">Plate XIV</a>, 2) resembles aluminium in having eight
+internal sub-divisions in a funnel, and the ovoids which form
+the top ring are identical, save for a minute difference that in
+aluminium the ovoids stand the reverse way from those in
+arsenic. It will be noted that in the former the top and bottom
+triangles of atoms have the apices upwards, and the middle
+one has its apex downwards. In arsenic, the top and bottom
+ones point downwards, and the middle one upwards. Arsenic
+inserts sixteen spheres between the ovoids and globe shown
+in aluminium, and thus adds no less than one hundred and
+forty-four atoms to each funnel.
+
+<pre>
+ARSENIC: 6 funnels of 225 atoms    1350
+         Atomic weight            74.45
+         Number weight 1350/18    75.00
+</pre>
+<font class="sc">Antimony</font> (<a href="#PlateXIV">Plate XIV</a>, 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.
+
+<pre>
+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
+</pre>
+  <br clear="all" />
+<hr class="short" />
+
+<h3>VII.</h3>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Boron</font> (<a href="#PlateIII">Plate III</a>, 4, and Plate <a href="#PlateXI">XI</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-034.png" target="_blank"><img width="100%" src="images/oc-034.png"
+      alt="Dissociation of Boron and Scandium." /></a>
+  </div>
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Scandium</font> (<a href="#PlateXI">Plate XI</a>, 2).</p>
+
+  <p>In funnel A the "cigar" and the ovoids behave as in boron, but the
+  "balloon," <i>a</i> 110 (<a href="#PlateXI">XI</a>, 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.</p>
+
+  <p>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 <i>b</i> 63, which escapes. On the
+  meta level, <i>c</i> (<a href="#PlateXI">Plate XI</a>, 4), <i>c</i>
+  assumes a tetrahedral form with six atoms at each point, and these hold
+  together as sextets on the hyper level. At the meta stage, <i>b</i> (<a
+  href="#PlateXI">Plate XI</a>, 4 <i>b</i>) 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Yttrium</font> (<a href="#PlateXI">Plate XI</a>, 3).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-035.png" target="_blank"><img width="100%" src="images/oc-035.png"
+      alt="Dissociation of Scandium (continued) and Yttrium." /></a>
+  </div>
+  <p>In yttrium, on the proto level, <i>a</i> 110 and <i>b</i> 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 (<a href="#DisAu">pp. 49</a> and 50), four
+  quartets being set free instead of two quartets and two triplets. We have
+  only to consider <i>e</i> 8 and <i>d</i> 20 (<a href="#PlateXI">Plate
+  XI</a>, 4). <i>E</i> 8 is a tetrahedral arrangement of duads on the meta
+  level, set free as duads on the hyper. <i>D</i> 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Nitrogen</font> (<a href="#PlateXII">Plate XII</a>, 1).</p>
+
+  <p>Nitrogen has nothing new to show us, all its constituents having
+  appeared in scandium and yttrium.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Vanadium</font> (<a href="#PlateXII">Plate XII</a>, 2).</p>
+
+  <p>The A funnel of vanadium repeats the A funnel of scandium, with the
+  addition of <i>d</i> 20, already studied. In the B funnel scandium B is
+  repeated, with an addition of <i>d</i> 20 and a sextet for a quintet; the
+  sextet is the <i>c</i> of the "nitrogen balloon." The central globe
+  follows boron, save that it has a septet for its centre; this was figured
+  in iodine (<a href="#DisI">p. 48</a>).</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Niobium</font> (<a href="#PlateXII">Plate XII</a>, 3).</p>
+
+  <p>Niobium only differs from yttrium by the introduction of triplets for
+  duads in <i>e</i>; 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.</p>
+
+  <p><a name="DisAl"></a></p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Aluminium</font> (<a href="#PlateXIII">Plate XIII</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-036.png" target="_blank"><img width="100%" src="images/oc-036.png"
+      alt="Dissociation of Aluminium and Gallium." /></a>
+  </div>
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Gallium</font> (<a href="#PlateXIII">Plate XIII</a>, 2).</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Indium</font> (<a href="#PlateXIII">Plate XIII</a>, 3).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Phosphorus</font> (<a href="#PlateXIV">Plate XIV</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-037.png" target="_blank"><img width="100%" src="images/oc-037.png"
+      alt="Dissociation of Phosphorus and Antimony." /></a>
+  </div>
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Arsenic</font> (<a href="#PlateXIV">Plate XIV</a>, 2).</p>
+
+  <p>Arsenic shows the same ovoids and globe as have already been broken up
+  in aluminium (see <a href="#DisAl"><i>ante</i></a>); 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Antimony</font> (<a href="#PlateXIV">Plate XIV</a>, 3).</p>
+
+  <p>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.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>VIII.</h3>
+
+<p class="center" style="margin-top: 2em;">IV.&mdash;<font class="sc">The Octahedral Groups.</font></p>
+
+  <p>These groups are at the turns of the spiral in Sir William Crookes'
+  lemniscates (see <a href="#Crookes">p. 28</a>). 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.</p>
+
+  <p><a name="PlateXV"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-038.png" target="_blank"><img width="100%" src="images/oc-038.png"
+      alt="Plate XV." /></a>
+    <font class="sc">Plate</font> XV.
+  </div>
+<font class="sc">Carbon</font> (<a href="#PlateIII">Plate III</a>, 5, and
+<a href="#PlateXV">XV</a>, 1) gives us the fundamental
+octahedral form, which becomes so masked in titanium and
+zirconium. As before said (<a href="#Octahedron">p. 30</a>),
+the protrusion of the arms in
+these suggests the old Rosicrucian symbol of the cross and rose,
+but they show at their ends the eight carbon funnels with their
+characteristic contents, and thus justify their relationship. The
+funnels are in pairs, one of each pair showing three "cigars,"
+and having as its fellow a funnel in which the middle "cigar"
+is truncated, thus loosing one atom. Each "cigar" has a leaf-like
+body at its base, and in the centre of the octahedron is a
+globe containing four atoms, each within its own wall; these lie
+on the dividing lines of the faces, and each holds a pair of the
+funnels together. It seems as though this atom had been
+economically taken from the "cigar" to form a link. This will
+be more clearly seen when we come to separate the parts from
+each other. It will be noticed that the atoms in the "leaves" at
+the base vary in arrangement, being alternately in a line and in a
+triangle.
+
+<pre>
+                            { 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
+</pre>
+<font class="sc">Titanium</font> (<a href="#PlateIII">Plate III</a>, 6, and <a href="#PlateXV">XV</a>, 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 <i>c</i>, with its eighty-eight atoms.
+A ring of twelve ovoids (3 <i>d</i>) each holding within itself fourteen
+atoms, distributed among three contained globes&mdash;two quartets
+and a sextet&mdash;is a new device for crowding in material. Lastly
+comes the central body (4 <i>e</i>) of five intersecting tetrahedra, with a
+"cigar" at each of their twenty points&mdash;of which only fifteen
+can be shown in the diagram&mdash;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.
+
+<pre>
+TITANIUM: One carbon atom               216
+          4 <i>c</i> of 88 atoms        352
+          12 <i>d</i> of 14  "          168
+          Central globe                 128
+                                       ----
+                            Total       864
+                                       ----
+          Atomic weight               47.74
+          Number weight 864/18        48.00
+</pre>
+<font class="sc">Zirconium</font> (<a href="#PlateXV">Plate XV</a>, 3) has exactly the same outline as
+titanium, the carbon atom is similarly distributed, and the central
+body is identical. Only in 5 <i>c</i> and <i>d</i> do we find a difference on
+comparing them with 4 <i>c</i> and <i>d</i>. The <i>c</i> 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.
+
+<pre>
+ZIRCONIUM: One Carbon atom              216
+           4 <i>c</i> of 212 atoms      848
+           12 <i>d</i> of 36   "        432
+           Central globe                128
+                                       ----
+                              Total    1624
+                                       ----
+           Atomic weight              89.85
+           Number weight              90.22
+</pre>
+  <p><a name="PlateXVI"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-039.png" target="_blank"><img width="100%" src="images/oc-039.png"
+      alt="Plate XVI." /></a>
+    <font class="sc">Plate</font> XVI.
+  </div>
+<font class="sc">Silicon</font> (<a href="#PlateXVI">Plate XVI</a>, 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.
+
+<pre>
+SILICON: 8 funnels of 65 atoms          520
+         Atomic weight                28.18
+         Number weight 520/18         28.88
+</pre>
+<font class="sc">Germanium</font> (<a href="#PlateXVI">Plate XVI</a>, 2) shows the eight funnels, containing
+each four segments (<a href="#PlateXVI">XVI</a>, 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.
+
+<pre>
+GERMANIUM: 8 funnels of 156 atoms     1248
+           Central globe                52
+                                      ----
+                   Total              1300
+                                      ----
+           Atomic weight             71.93
+           Number weight 1300/18     72.22
+</pre>
+<font class="sc">Tin</font> (<a href="#PlateXVI">Plate XVI</a>, 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 <a href="#PlateIX">Plate IX</a>, 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.
+
+<pre>
+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
+</pre>
+<p class="center" style="margin-top: 2em;">V.&mdash;<font class="sc">The Bars Groups.</font></p>
+
+  <p><a name="PlateXVII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-040.png" target="_blank"><img width="100%" src="images/oc-040.png"
+      alt="Plate XVII." /></a>
+    <font class="sc">Plate</font> XVII.
+  </div>
+  <p>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&mdash;called the inter-periodic&mdash;whereof the remaining members
+  are (see Crookes' table, <a href="#Crookes">p. 28</a>), manganese, iron,
+  cobalt, nickel; ruthenium, rhodium, palladium; osmium, iridium, platinum.
+  If we take all these as group V, we find that fluorine and manganese are
+  violently forced into company with which they have hardly any points of
+  relationship, and that they intrude into an otherwise very harmonious
+  group of closely similar composition. Moreover, manganese reproduces the
+  characteristic lithium "spike" and not the bars of those into whose
+  company it is thrust, and it is thus allied with lithium, with which
+  indeed it is almost identical. But lithium is placed by Crookes at the
+  head of a group, the other members of which are potassium, rubidium and
+  cęsium (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 <i>a</i>, 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."</p>
+
+  <p>Group V in every case shows fourteen bars radiating from a centre as
+  shown in iron, <a href="#PlateIV">Plate IV</a>, 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:&mdash;</p>
+
+<pre>
+Iron             72        Palladium       136
+Nickel           74        Osmium          245
+Cobalt           76        Iridium         247
+Ruthenium       132        Platinum A      249
+Rhodium         134        Platinum B      257
+</pre>
+  <p>It will be noticed (<a href="#PlateXVII">Plate XVII</a>, 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.</p>
+
+  <p>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.</p>
+
+<font class="sc">Iron</font> (Plate <a href="#PlateIV">IV</a>, 1, and <a href="#PlateXVII">XVII</a>, 3):
+<pre>
+        14 bars of 72 atoms            1008
+        Atomic weight                 55.47
+        Number weight 1008/18         56.00
+</pre>
+
+<font class="sc">Cobalt</font> (<a href="#PlateXVII">Plate XVII</a>, 4):
+<pre>
+        14 bars of 74 atoms            1036
+        Atomic weight                 57.70
+        Number weight 1036/18         57.55
+</pre>
+
+<font class="sc">Nickel</font> (<a href="#PlateXVII">Plate XVII</a>, 4):
+<pre>
+        14 bars of 76 atoms             1064
+        Atomic weight                  58.30
+        Number weight 1064/18          59.11
+</pre>
+
+  <p>(The weight of cobalt, as given in Erdmann's <i>Lehrbuch</i>, is
+  58.55, but Messrs. Parker and Sexton, in <i>Nature</i>, August 1, 1907,
+  give the weight, as the result of their experiments, as 57.7.)</p>
+
+  <p><a name="PlateXVIII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-041.png" target="_blank"><img width="100%" src="images/oc-041.png"
+      alt="Plate XVIII." /></a>
+    <font class="sc">Plate</font> XVIII.
+  </div>
+  <p>The next sub-group, ruthenium, rhodium, and palladium, has nothing to
+  detain us. It will be observed that each bar contains eight segments,
+  instead of the six of cobalt and nickel; that ruthenium and palladium
+  have the same number of atoms in their upper ovoids, although in
+  ruthenium a triplet and quartet represent the septet of palladium; and
+  that in ruthenium and rhodium the lower ovoids are identical, though one
+  has the order: sixteen, fourteen, sixteen, fourteen; and the other:
+  fourteen, sixteen, fourteen, sixteen. One constantly asks oneself: What
+  is the significance of these minute changes? Further investigators will
+  probably discover the answer.</p>
+
+<font class="sc">Ruthenium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 1):
+<pre>
+      14 bars of 132 atoms              1848
+      Atomic weight                   100.91
+      Number weight 1848/18           102.66
+</pre>
+
+<font class="sc">Rhodium</font> (<a href="#PlateXVII">Plate XVII</a>, 2):
+<pre>
+      14 bars of 134 atoms              1876
+      Atomic weight                   102.23
+      Number weight 1876/18           104.22
+</pre>
+
+<font class="sc">Palladium</font> (<a href="#PlateXVIII">XVIII</a>, 3):
+<pre>
+      14 bars of 136 atoms              1904
+      Atomic weight                   105.74
+      Number weight 1904/18           105.77
+</pre>
+
+  <p>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 <i>a</i> (<a href="#PlateXVIII">XVIII</a>, 4) takes the
+  place of axis in the upper half of the bar, and the three ovoids, marked
+  <i>b</i>, revolve round it. In the lower half, the four ovoids, <i>c</i>,
+  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 (<a
+  href="#PlateXVIII">XVIII</a>, 6 <i>b</i>) in the place of the two
+  triplets marked <i>a</i>. 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.</p>
+
+<font class="sc">Osmium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 4):
+<pre>
+       14 bars of 245 atoms            3430
+       Atomic weight                 189.55
+       Number weight 3430/18         190.55
+</pre>
+
+<font class="sc">Iridium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 5):
+<pre>
+       14 bars of 247 atoms            3458
+       Atomic weight                 191.11
+       Number weight 3458/18         192.11
+</pre>
+
+<font class="sc">Platinum A</font> (<a href="#PlateXVIII">Plate XVIII</a>, 6 <i>a</i>):
+<pre>
+       14 bars of 249 atoms            3486
+       Atomic weight                 193.66
+       Number weight 3486/18         193.34
+</pre>
+
+<font class="sc">Platinum B</font> (<a href="#PlateXVIII">Plate XVIII</a>, 6 <i>b</i>):
+<pre>
+       14 bars of 251 atoms            3514
+       Atomic weight                 ------
+       Number weight 3514/18         195.22
+</pre>
+
+<p class="center" style="margin-top: 2em;">V <i>a</i>.&mdash;<font class="sc">The Spike Groups</font>.</p>
+
+  <p>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 (<a href="#PlateIV">Plate IV</a>,
+  2) and fluorine (<a href="#PlateIV">Plate IV</a>, 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.</p>
+
+  <p><a name="PlateXIX"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-042.png" target="_blank"><img width="100%" src="images/oc-042.png"
+      alt="Plate XIX." /></a>
+    <font class="sc">Plate</font> XIX.
+  </div>
+<font class="sc">Lithium</font> (<a href="#PlateIV">Plate IV</a>, 2 and <a href="#PlateXIX">Plate XIX</a>, 1)
+is a striking and
+beautiful form, with its upright cone, or spike, its eight radiating
+petals (<i>x</i>) at the base of the cone, and the plate-like support in
+the centre of which is a globe, on which the spike rests. The
+spike revolves swiftly on its axis, carrying the petals with it; the
+plate revolves equally swiftly in the opposite direction. Within
+the spike are two globes and a long ovoid; the spheres within
+the globe revolve as a cross; within the ovoid are four spheres
+containing atoms arranged on tetrahedra, and a central sphere
+with an axis of three atoms surrounded by a spinning wheel of six.
+
+<pre>
+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
+</pre>
+<font class="sc">Potassium</font> (<a href="#PlateXIX">Plate XIX</a>, 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.
+
+<pre>
+POTASSIUM: 9 bars of 63 atoms             567
+           Central globe                  134
+                                         ----
+                              Total       701
+                                         ----
+           Atomic weight                38.94
+           Number weight 701/18         38.85
+</pre>
+  <p>(The weight, as determined by Richards [<i>Nature</i>, July 18, 1907]
+  is 39.114.)</p>
+
+<font class="sc">Rubidium</font>: (<a href="#PlateXIX">Plate XIX</a>, 3) adds an ovoid, containing three
+spheres&mdash;two triplets and a sextet&mdash;to the lithium spike, of which
+it has sixteen, and its central globe is composed of three
+"balloons."
+
+<pre>
+RUBIDIUM: 16 spikes of 75 atoms          1200
+          Central globe                   330
+                                         ----
+                            Total        1530
+                                         ----
+          Atomic weight                 84.85
+          Number weight 1530/18         85.00
+</pre>
+  <p>The corresponding negative group consists only of fluorine and
+  manganese, so far as our investigations have gone.</p>
+
+<font class="sc">Fluorine</font> (<a href="#PlateIV">Plate IV</a>, 3, and
+<a href="#PlateXVII">Plate XVII</a>, 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."
+
+<pre>
+FLUORINE: 8 spikes of 15 atoms            120
+          2 balloons                      220
+                                         ----
+                             Total        340
+                                         ----
+          Atomic weight                 18.90
+          Number weight 340/18          18.88
+</pre>
+<font class="sc">Manganese</font> (<a href="#PlateXVII">Plate XVII</a>, 2) has fourteen spikes radiating
+from a central "balloon."
+
+<pre>
+MANGANESE: 14 spikes of 63 atoms          882
+           Central balloon                110
+                                         ----
+                           Total          992
+                                         ----
+           Atomic weight                54.57
+           Number weight 992/18         55.11
+</pre>
+  <br clear="all" />
+<hr class="short" />
+
+<h3>IX.</h3>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Carbon</font> (<a href="#PlateIII">Plate III</a>, 5, and <a href="#PlateXV">XV</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-043.png" target="_blank"><img width="100%" src="images/oc-043.png"
+      alt="Dissociation of Carbon." /></a>
+  </div>
+  <p>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 <a href="#PlateIII">Plate III</a>, and see <a
+  href="#PlateXV">XV</a>, 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Titanium</font> (<a href="#PlateIII">Plate III</a>, 6, and <a href="#PlateXV">XV</a>, 2, 3).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-044.png" target="_blank"><img width="100%" src="images/oc-044.png"
+      alt="Dissociation of Titanium and Zirconium." /></a>
+  </div>
+  <p>On the proto level, the cross breaks up completely, setting free the
+  pairs of funnels with the linking atom (<i>a</i> and <i>b</i>), as in
+  carbon, the four bodies marked <i>c</i>, the twelve marked <i>d</i>, and
+  the central globe marked <i>e</i>. The latter breaks up again, setting
+  free its five intersecting cigar-bearing tetrahedra, which follow their
+  usual course (see Occultum, <a href="#DisOc">p. 44</a>). 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 <i>c</i> sets free its four contained globes, and
+  the ovoid <i>d</i> sets free the three within it. Thus sixty-one proto
+  elements are yielded by titanium. On the meta level, <i>c</i> (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, <i>a</i>,
+  <i>b</i> and <i>f</i>; the cruciform quintet yields a triplet and a duad,
+  <i>c</i> and <i>d</i>; the tetrahedra yield two triplets <i>g</i> and
+  <i>h</i>, and two units; the septet, a triplet <i>k</i> and a quartet
+  <i>j</i>. On the meta level, the bodies from <i>d</i> behave like their
+  equivalents in sodium, each <i>d</i> shows two quartets and a sextet,
+  breaking up, on the hyper level, into four duads and two triads.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Zirconium</font> (<a href="#PlateXV">Plate XV</a>, 2, 5).</p>
+
+  <p>Zirconium reproduces in its <i>c</i> the four forms that we have
+  already followed in the corresponding <i>c</i> 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
+  <i>c</i> 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 <i>d</i> 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Silicon</font> (<a href="#PlateXVI">Plate XVI</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-045.png" target="_blank"><img width="100%" src="images/oc-045.png"
+      alt="Dissociation of Silicon and Tin." /></a>
+  </div>
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Germanium</font> (<a href="#PlateXVI">Plate XVI</a>, 2, 4).</p>
+
+  <p>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 (<a href="#PlateXVI">XVI</a>, 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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Tin</font> (<a href="#PlateXVI">Plate XVI</a>, 3, 4).</p>
+
+  <p>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 <a
+  href="#DisAg">p. 729</a>, 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.)</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Iron</font> (<a href="#PlateIV">Plate IV</a>, I, and <a href="#PlateXVII">XVII</a>, 3).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-046.png" target="_blank"><img width="100%" src="images/oc-046.png"
+      alt="Dissociation of Iron, Cobalt and Nickel." /></a>
+  </div>
+  <p>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.</p>
+
+  <p>The fourteen bars of iron break asunder on the proto level, and each
+  sets free its contents&mdash;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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Cobalt</font> (<a href="#PlateXVII">Plate XVII</a>, 4).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Nickel</font> (<a href="#PlateXVII">Plate XVII</a>, 5).</p>
+
+  <p>The two additional atoms in a bar, which alone separate nickel from
+  cobalt, are seen in the upper sphere of the central ovoid.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Ruthenium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 1).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Rhodium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 2).</p>
+
+  <p>Rhodium has a septet, which is to be seen in the <i>c</i> of titanium
+  (see <i>k</i> in the titanium diagram) and differs only in this from its
+  group.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Palladium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 3).</p>
+
+  <p>In palladium this septet appears as the upper sphere in every ovoid of
+  the upper ring.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Osmium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 4).</p>
+
+  <p>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).</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Iridium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 5.)</p>
+
+  <p>The twenty-one-atomed cone of silver here reappears, and its
+  proceedings may be followed under that metal (see diagram, <a
+  href="#DisAg">p. 729</a>, May). The remaining bodies call for no
+  remark.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Platinum</font> (<a href="#PlateXVIII">Plate XVIII</a>, 6).</p>
+
+  <p>Again the silver cone is with us. The remaining bodies are set free on
+  the proto level, and their contained spheres on the meta.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Lithium</font> (<a href="#PlateIV">Plate IV</a>, 2, and <a href="#PlateXIX">XIX</a>, 1).</p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-047.png" target="_blank"><img width="100%" src="images/oc-047.png"
+      alt="Dissociation of Lithium." /></a>
+  </div>
+  <p>Here we have some new combinations, which recur persistently in its
+  allies. The bodies <i>a</i>, 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.</p>
+
+  <p>The five bodies within the ellipse, three monads and two sextets, show
+  two which we have had before: <i>d</i>, which behaves like the quintet
+  and quartet in silicon, after their junction, and <i>b</i>, which we have
+  had in iron. The two bodies <i>c</i> are a variant of the square-based
+  pyramid, one atom at the apex, and two at each of the other angles. The
+  globe, <i>e</i>, is a new form, the four tetrahedra of the proto level
+  making a single twelve-atomed one on the meta. The body <i>a</i> splits
+  up into triplets on the hyper; <i>b</i> and <i>d</i> follow their iron
+  and silicon models; <i>c</i> yields four duads and a unit; <i>e</i>
+  breaks into four quartets.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Potassium</font> (<a href="#PlateXIX">Plate XIX</a>, 2).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Rubidium</font> (<a href="#PlateXIX">Plate XIX</a>, 3).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Fluorine</font> (<a href="#PlateIV">Plate IV</a>, 3, and Plate <a href="#PlateXVII">XVII</a>, 1).</p>
+
+  <p>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.</p>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Manganese</font> (<a href="#PlateXVII">Plate XVII</a>, 2).</p>
+
+  <p>Manganese offers us nothing new, being composed of "lithium spikes"
+  and "nitrogen balloons."</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>X.</h3>
+
+<p class="center" style="margin-top: 2em;">VI.&mdash;<font class="sc">The Star Groups</font>.</p>
+
+  <p>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 <i>sui generis</i>. The remainder are in the form of a
+  flat star (see <a href="#PlateIV">Plate IV</a>, 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 :&mdash;</p>
+
+<pre>
+40       99      224      363      489
+47      106      231      370      496
+</pre>
+  <p>It will be observed that the meta form in each case shows seven more
+  atoms than its fellow.</p>
+
+  <p><a name="PlateXX"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-048.png" target="_blank"><img width="100%" src="images/oc-048.png"
+      alt="Plate XX." /></a>
+    <font class="sc">Plate</font> XX.
+  </div>
+<font class="sc">Helium</font> (<a href="#PlateIII">Plate III</a>, 5, and
+<a href="#PlateXX">Plate XX</a>, 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.
+
+<pre>
+HELIUM: Two tetrahedra of 24 atoms   48
+        Two triangles of 9 atoms     18
+        Central egg                   6
+                                   ----
+                 Total               72
+                                   ----
+        Atomic weight              3.94
+        Number weight 72/18        4.00
+</pre>
+<font class="sc">Neon</font> (<a href="#PlateXX">Plate XX</a>, 2 and 6) has six arms of the pattern shown
+in 2, radiating from the central globe.
+
+<pre>
+NEON: Six arms of 40 atoms       240
+      Central tetrahedra         120
+
+                                ----
+                   Total         360
+                                ----
+      Atomic weight            19.90
+      Number weight 360/18     20.00
+</pre>
+<font class="sc">Meta-neon</font> (<a href="#PlateXX">Plate XX</a>, 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.
+
+<pre>
+META-NEON: Six arms of 47 atoms    282
+           Central tetrahedra      120
+                                  ----
+Total                              402
+                                  ----
+Atomic weight                     ----
+Number weight 402/18             22.33
+</pre>
+<font class="sc">Argon</font> (<a href="#PlateXX">Plate XX</a>, 4, 6 and 7) shows within its arms the <i>b</i> 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.
+
+<pre>
+ARGON: Six arms of 99 atoms     594
+       Central tetrahedra       120
+                               ----
+                 Total          714
+                               ----
+       Atomic weight          39.60
+       Number weight 714/18   39.66
+</pre>
+<font class="sc">Metargon</font> (<a href="#PlateXX">Plate XX</a>, 5, 6 and 7) again shows only an
+additional seven atoms in each arm.
+
+<pre>
+METARGON: Six arms of 106 atoms   636
+          Central tetrahedra      120
+                                 ----
+                      Total       756
+                                 ----
+Atomic weight                    ----
+Number weight 756/18               42
+</pre>
+  <p><a name="PlateXXI"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-049.png" target="_blank"><img width="100%" src="images/oc-049.png"
+      alt="Plate XXI." /></a>
+    <font class="sc">Plate</font> XXI.
+  </div>
+<font class="sc">Krypton</font> (<a href="#PlateXXI">Plate XXI</a>, 1 and 4,
+and <a href="#PlateXX">Plate XX</a>, 6 and 7)
+contains the nitrogen "balloon," elongated by its juxtaposition
+to <i>b</i> 63. The central tetrahedra appear as usual.
+
+<pre>
+KRYPTON:  Six arms of 224 atoms             1344
+          Central tetrahedra                 120
+                                           -----
+                               Total        1464
+                                           -----
+          Atomic weight                    81.20
+          Number weight 1464/18            81.33
+</pre>
+<font class="sc">Meta-Krypton</font> differs only from krypton by the substitution
+of <i>z</i> for <i>y</i> in each arm of the star.
+
+<pre>
+META-KRYPTON:  Six arms of 231 atoms        1386
+               Central tetrahedra            120
+                                           -----
+                               Total        1506
+                                           -----
+               Atomic weight               -----
+               Number weight 1506/18       83.66
+</pre>
+<font class="sc">Xenon</font> (<a href="#PlateXXI">Plate XXI</a>, 2 and 4,
+and <a href="#PlateXX">Plate XX</a>, 6 and 7) has a
+peculiarity shared only by kalon, that <i>x</i> and <i>y</i> 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?
+
+<pre>
+XENON:  Six arms of 363 atoms               2178
+        Central tetrahedra                   120
+                                           -----
+                               Total        2298
+                                           -----
+        Atomic weight                     127.10
+        Number weight 2298/18             127.66
+</pre>
+<font class="sc">Meta-Xenon</font> differs from xenon only by the substitution of
+two <i>z</i>'s for <i>x</i> and <i>y</i>.
+
+<pre>
+META-XENON:  Six arms of 370 atoms          2220
+            Central tetrahedra               120
+                                           -----
+                               Total        2340
+                                           -----
+            Atomic weight                  -----
+            Number weight 2340/18            130
+</pre>
+<font class="sc">Kalon</font> (<a href="#PlateXXI">Plate XXI</a>, 3 and 4,
+and <a href="#PlateXX">Plate XX</a>, 6 and 7) has a
+curious cone, possessing a kind of tail which we have not
+observed elsewhere; <i>x</i> and <i>y</i> show the same asymmetry as in
+xenon.
+
+<pre>
+KALON: Six arms of 489 atoms          2934
+       Central tetrahedra              120
+                                      ----
+                            Total     3054
+                                      ----
+       Atomic weight                  ----
+       Number weight 3054/18        169.66
+</pre>
+<font class="sc">Meta-Kalon</font> again substitutes two <i>z</i>'s for <i>x</i> and <i>y</i>.
+
+<pre>
+META-KALON: Six arms of 496 atoms           2976
+            Central tetrahedra               120
+                                            ----
+                            Total           3096
+                                            ----
+            Atomic weight                   ----
+            Number weight 3096/18            172
+</pre>
+  <p>Only a few atoms of kalon and meta-kalon have been found in the air of
+  a fair-sized room.</p>
+
+  <p>It does not seem worth while to break up these elements, for their
+  component parts are so familiar. The complicated groups&mdash;<i>a</i>
+  110, <i>b</i> 63 and <i>c</i> 120&mdash;have all been fully dealt with in
+  preceding pages.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+  <p>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.</p>
+
+  <p>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 <i>Proceedings of the Chemical
+  Society of London</i>, 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.</p>
+
+  <br clear="all" />
+<hr class="short" />
+
+<h3>XI.</h3>
+
+<p class="center" style="margin-top: 2em;"><font class="sc">Radium</font>.</p>
+
+  <p><a name="PlateXXII"></a></p>
+
+  <div class="figright" style="width:50%;">
+      <a href="images/oc-050.png" target="_blank"><img width="100%" src="images/oc-050.png"
+      alt="Plate XXII." /></a>
+    <font class="sc">Plate</font> XXII.
+  </div>
+  <p>Radium has the form of a tetrahedron, and it is in the tetrahedral
+  groups (see article <a href="#CompBe">IV</a>) 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 (<a
+  href="#PlateXXII">Plate XXII</a>), extraordinarily vivid and living; the
+  whirling motion is so rapid that continued accurate observation is very
+  difficult; the sphere is more closely compacted than the centre-piece in
+  other elements, and is much larger in proportion to the funnels and
+  spikes than is the case with the elements above named; reference to <a
+  href="#PlateVIII">Plate VIII</a> 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&mdash;four
+  quintets and a septet&mdash;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.</p>
+
+  <p>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 (<a href="#PlateXXIII">Plate
+  XXIII</a>). 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.</p>
+
+  <p>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 <a href="#PlateXIX">Plate XIX</a>) with a ten-atomed cone or
+  cap at the top, floating above the three (<a href="#PlateXXIV">Plate
+  XXIV</a>). 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.</p>
+
+  <p>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&mdash;a most extraordinary element.</p>
+
+<pre>
+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
+</pre>
+  <p><a name="PlateXXIII"></a></p>
+
+  <p><a name="PlateXXIV"></a></p>
+
+  <div class="figright" style="width:45%;">
+      <a href="images/oc-052.png" target="_blank"><img width="100%" src="images/oc-052.png"
+      alt="Plate XXIV." /></a>
+    <font class="sc">Plate</font> XXIV.
+  </div>
+  <div class="figleft" style="width:45%;">
+      <a href="images/oc-051.png" target="_blank"><img width="100%" src="images/oc-051.png"
+      alt="Plate XXIII." /></a>
+    <font class="sc">Plate</font> XXIII.
+  </div>
+  <br clear="all" />
+  <br clear="all" />
+<hr />
+
+<h3>APPENDIX.</h3>
+
+<p class="center" style="margin-top: 2em;">THE ĘTHER OF SPACE.</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>Let us for the moment name this substance <i>koilon</i>, since it
+  fills what we are in the habit of calling empty space. What mūlaprakrti,
+  or "mother-matter," is to the inconceivable totality of universes, koilon
+  is to our particular universe&mdash;not to our solar system merely but to
+  the vast unit which includes all visible suns. Between koilon and
+  mūlaprakrti there must be various stages, but we have at present no
+  direct means of estimating their number or of knowing anything whatever
+  about them.</p>
+
+  <p>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 <i>through it</i>, 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."<a name="NtA_21"
+  href="#Nt_21"><sup>[21]</sup></a> "The mother-substance" is said, in this
+  treatise, to produce this ęther of space as its seventh grade of density,
+  and all objective suns are said to have this for their "substance."</p>
+
+  <p>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&mdash;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 <i>the absence of koilon</i>, and at first sight, matter and
+  space appear to have changed places, and emptiness has become solidity,
+  solidity has become emptiness.</p>
+
+  <p>To help us to understand this clearly let us examine the ultimate atom
+  of the physical plane (see <a href="#UltAtom">pp. 21</a>-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&mdash;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
+  spirillę 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&mdash;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
+  spirillę of the first order in each wire is 1680; and the proportion of
+  the different orders of spirillę to one another is equal in all cases
+  that have been examined, and correspond with the number of dots in the
+  ultimate spirillę 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 spirillę 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&mdash;may in fact
+  be in process of growth, as there is reason to suppose that these three
+  thicker spirals originally resembled the others.</p>
+
+  <p>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&mdash;if we assume one dot to be what corresponds to
+  an atom on the seventh or highest of our planes (as is suggested in
+  <i>The Ancient Wisdom</i>, 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&mdash;we find that the number indicated for the physical atom
+  (49<sup>6</sup>) 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.</p>
+
+  <p>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&mdash;probably the cube
+  of 49 instead of the square, though they have not been actually counted.
+  Therefore one physical atom is not <i>composed of</i> forty-nine astral
+  or 2401 mental atoms, but <i>corresponds</i> 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.</p>
+
+  <p>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.</p>
+
+  <p>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&mdash;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&mdash;the only
+  spots where it is not&mdash;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.</p>
+
+  <p>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.</p>
+
+  <p>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
+  <font class="sc">Logos</font> 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&mdash;names are nothing; to us,
+  Theosophists, it is the Breath of the <font class="sc">Logos</font>, we
+  know not whether of the <font class="sc">Logos</font> 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.</p>
+
+  <p>The Breath of the <font class="sc">Logos</font>, 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.</p>
+
+  <p>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 ęther, 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).</p>
+
+  <p>How vividly, how unmistakably this knowledge brings home to us the
+  great doctrine of Māyā, 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
+  <i>sees</i>) 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&mdash;is itself the very negation of matter&mdash;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 <font class="sc">Logos</font>, 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.</p>
+
+  <p>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 ęther. 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.</p>
+
+  <p>The scientific theory is that the ęther has some quality which enables
+  it to transmit at a certain definite velocity transverse waves of all
+  lengths and intensities&mdash;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.</p>
+
+  <p>In a recent pamphlet on "The Density of Ęther," Sir Oliver Lodge
+  remarks:&mdash;</p>
+
+  <p>"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 ęther contained in the
+  space which it thus partially occupies&mdash;the substance of which it
+  may hypothetically be held to be composed.</p>
+
+  <p>"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 ętherial density, on this basis, would be something like ten
+  thousand million times that of platinum."</p>
+
+  <p>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 ęther in
+  the same space."</p>
+
+  <p>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.</p>
+
+  <p>In the same pamphlet Sir Oliver Lodge makes a very striking estimate
+  of the intrinsic energy of the ęther. 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.</p>
+
+  <p>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 <font
+  class="sc">Logos</font> 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
+  <font class="sc">Logoi</font>, utterly beyond our ken.</p>
+
+  <p>As none of our investigators can raise his consciousness to the
+  highest plane of our universe, the ādi-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.</p>
+
+  <p>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.</p>
+
+  <p>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.</p>
+
+  <p>Nor is any change introduced as regards the three outpourings from the
+  <font class="sc">Logos</font>, 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.</p>
+
+  <p>In view of this marvellous distribution of Himself in "space," the
+  familiar concept of the "sacrifice of the <font class="sc">Logos</font>"
+  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 <font
+  class="sc">Logos</font> 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.</p>
+
+  <p>What koilon is, what its origin, whether it is itself changed by the
+  Divine Breath which is poured into it&mdash;does "Dark Space" thus become
+  "Bright Space" at the beginning of a manifestation?&mdash;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.</p>
+
+  <br clear="all" />
+<hr />
+
+<h3>NOTES</h3>
+
+<div class="note">
+  <p><a name="Nt_1" href="#NtA_1">[1]</a> See footnote in next Chapter.</p>
+
+  <p><a name="Nt_2" href="#NtA_2">[2]</a> 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.
+  Jinarājadāsa, 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.</p>
+
+  <p><a name="Nt_3" href="#NtA_3">[3]</a> The atomic sub-plane.</p>
+
+  <p><a name="Nt_4" href="#NtA_4">[4]</a> The astral plane.</p>
+
+  <p><a name="Nt_5" href="#NtA_5">[5]</a> Known to Theosophists as Fohat,
+  the force of which all the physical plane
+  forces&mdash;electricities&mdash;are differentiations.</p>
+
+  <p><a name="Nt_6" href="#NtA_6">[6]</a> When Fohat "digs holes in
+  space."</p>
+
+  <p><a name="Nt_7" href="#NtA_7">[7]</a> The first life-wave, the work of
+  the third Logos.</p>
+
+  <p><a name="Nt_8" href="#NtA_8">[8]</a> A māyā, truly.</p>
+
+  <p><a name="Nt_9" href="#NtA_9">[9]</a> 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.</p>
+
+  <p><a name="Nt_10" href="#NtA_10">[10]</a> Again the astral world.</p>
+
+  <p><a name="Nt_11" href="#NtA_11">[11]</a> 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.</p>
+
+  <p><a name="Nt_12" href="#NtA_12">[12]</a> "The ten numbers of the sun.
+  These are called Dis&mdash;in reality space&mdash;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.</p>
+
+  <p><a name="Nt_13" href="#NtA_13">[13]</a> 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.</p>
+
+  <p><a name="Nt_14" href="#NtA_14">[14]</a> 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.</p>
+
+  <p><a name="Nt_15" href="#NtA_15">[15]</a> It must be remembered that the
+  diagrams represent three-dimensional objects, and the atoms are not all
+  on a plane, necessarily.</p>
+
+  <p><a name="Nt_16" href="#NtA_16">[16]</a> That is, the surrounding
+  magnetic fields strike on each other.</p>
+
+  <p><a name="Nt_17" href="#NtA_17">[17]</a> The fifth member of this group
+  was not sought for.</p>
+
+  <p><a name="Nt_18" href="#NtA_18">[18]</a> This, with references which
+  appear later (pp. 32, 33, 50, etc.), relates to articles which appeared
+  in the <i>Theosophist</i>, 1908.</p>
+
+  <p><a name="Nt_19" href="#NtA_19">[19]</a> Since writing the above I have
+  noticed, in the <i>London, Edinburgh and Dublin Philosophical Magazine
+  and Journal of Science</i>, 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.</p>
+
+  <p><a name="Nt_20" href="#NtA_20">[20]</a> Theosophists call them
+  Nature-Spirits, and often use the medięval term Elementals. Beings
+  concerned with the elements truly are they, even with chemical
+  elements.</p>
+
+  <p><a name="Nt_21" href="#NtA_21">[21]</a> Quoted in "The Secret
+  Doctrine." H.P. Blavatsky, i, 309.</p>
+
+</div>
+<p>&nbsp;</p>
+<p>&nbsp;</p>
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+The Project Gutenberg eBook, Occult Chemistry, by Annie Besant and Charles
+W. Leadbeater, Edited by A. P. Sinnett
+
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+
+
+
+Title: Occult Chemistry
+       Clairvoyant Observations on the Chemical Elements
+
+
+Author: Annie Besant and Charles W. Leadbeater
+
+Editor: A. P. Sinnett
+
+Release Date: June 14, 2005  [eBook #16058]
+
+Language: English
+
+Character set encoding: ISO-646-US (US-ASCII)
+
+
+***START OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY***
+
+
+E-text prepared by Clare Boothby, Keith Edkins, and the Project Gutenberg
+Online Distributed Proofreading Team
+
+
+
+Note: Project Gutenberg also has an HTML version of this
+      file which includes the original illustrations.
+      See 16058-h.htm or 16058-h.zip:
+      (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h/16058-h.htm)
+      or
+      (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h.zip)
+
+
+
+
+
+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.
+
+[Illustration]
+
+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 spirillae, and these again of minuter spirillae. 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.
+
+[Illustration]
+
+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. Jinarajadasa[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.
+
+[Illustration: PLATE I. SODIUM.]
+
+In counting the number of ultimate atoms in a chemical elemental atom, we
+did not count them throughout, one by one; when, for instance, we counted
+up the ultimate atoms in sodium, we dictated the number in each convenient
+group to Mr. Jinarajadasa, and he multiplied out the total, divided by 18,
+and announced the result. Thus: sodium (_see_ Plate I) is composed of an
+upper part, divisible into a globe and 12 funnels; a lower part, similarly
+divided; and a connecting rod. We counted the number in the upper part:
+globe--10; the number in two or three of the funnels--each 16; the number
+of funnels--12; the same for the lower part; in the connecting rod--14. Mr.
+Jinarajadasa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418:
+divided by 18 = 23.22 recurring. By this method we guarded our counting
+from any prepossession, as it was impossible for us to know how the various
+numbers would result on addition, multiplication and division, and the
+exciting moment came when we waited to see if our results endorsed or
+approached any accepted weight. In the heavier elements, such as gold, with
+3546 atoms, it would have been impossible to count each atom without quite
+unnecessary waste of time, when making a preliminary investigation. Later,
+it may be worth while to count each division separately, as in some we
+noticed that two groups, at first sight alike, differed by 1 or 2 atoms,
+and some very slight errors may, in this way, have crept into our
+calculations.
+
+In the following table is a list of the chemical elements examined; the
+first column gives the names, the asterisk affixed to some indicating that
+they have not yet been discovered by orthodox chemistry. The second column
+gives the number of ultimate physical atoms contained in one chemical atom
+of the element concerned. The third column gives the weight as compared
+with hydrogen, taken as 18, and this is obtained by dividing the calculated
+number of ultimate atoms by 18. The fourth column gives the recognized
+weight-number, mostly according to the latest list of atomic weights, the
+"International List" of 1905, given in Erdmann's "Lehrbuch der
+Unorganischen Chemie." These weights differ from those hitherto accepted,
+and are generally lighter than those given in earlier text-books. It is
+interesting to note that our counting endorses the earlier numbers, for the
+most part, and we must wait to see if later observations will endorse the
+last results of orthodox chemistry, or confirm ours.
+
+--------------------------------------------
+Hydrogen       |    18   |   1     |   1
+*Occultum      |    54   |   3     |   --
+Helium         |    72   |   4     |   3.94
+Lithium        |   127   |   7.06  |   6.98
+Baryllium      |   164   |   9.11  |   9.01
+Boron          |   200   |  11.11  |  10.86
+Carbon         |   216   |  12     |  11.91
+Nitrogen       |   261   |  14.50  |  14.01
+Oxygen         |   290   |  16.11  |  15.879
+Fluorine       |   340   |  18.88  |  18.90
+Neon           |   360   |  20     |  19.9
+*Meta-Neon     |   402   |  22.33  |   --
+Sodium         |   418   |  23.22  |  22.88
+Magnesium      |   432   |  24     |  24.18
+Aluminium      |   486   |  27     |  26.91
+Silicon        |   520   |  28.88  |  28.18
+Phosphorus     |   558   |  31     |  30.77
+Sulphur        |   576   |  32     |  31.82
+Chlorine       |   639   |  35.50  |  35.473
+Potassium      |   701   |  38.944 |  38.85
+Argon          |   714   |  39.66  |  39.60
+Calcium        |   720   |  40     |  39.74
+*Metargon      |   756   |  42     |   --
+Scandium       |   792   |  44     |  43.78
+Titanium       |   864   |  48     |  47.74
+Vanadium       |   918   |  51     |  50.84
+Chromium       |   936   |  52     |  51.74
+Manganese      |   992   |  55.11  |  54.57
+Iron           |  1008   |  56     |  55.47
+Cobalt         |  1036   |  57.55  |  57.7
+Nickel         |  1064   |  59.ll  |  58.30
+Copper         |  1139   |  63.277 |  63.12
+Zinc           |  1170   |  65     |  64.91
+Gallium        |  1260   |  70     |  69.50
+Germanium      |  1300   |  72.22  |  71.93
+Arsenic        |  1350   |  75     |  74.45
+Selenium       |  1422   |  79     |  78.58
+Bromine        |  1439   |  79.944 |  79.953
+Krypton        |  1464   |  81.33  |  81.20
+*Meta-Krypton  |  1506   |  83.66  |   --
+Rubidium       |  1530   |  85     |  84.85
+Strontium      |  1568   |  87.11  |  86.95
+Yttrium        |  1606   |  89.22  |  88.34
+Zirconium      |  1624   |  90.22  |  89.85
+Niobium        |  1719   |  95.50  |  93.25
+Molybdenum     |  1746   |  97     |  95.26
+Ruthenium      |  1848   | 102.66  | 100.91
+Rhodium        |  1876   | 104.22  | 102.23
+Palladium      |  1904   | 105.77  | 105.74
+Silver         |  1945   | 108.055 | 107.93
+Cadmium        |  2016   | 112     | 111.60
+Indium         |  2052   | 114     | 114.05
+Tin            |  2124   | 118     | 118.10
+Antimony       |  2169   | 120.50  | 119.34
+Tellurium      |  2223   | 123.50  | 126.64
+Iodine         |  2287   | 127.055 | 126.01
+Xenon          |  2298   | 127.66  | 127.10
+*Meta-Xenon    |  2340   | 130     |   --
+*Kalon         |  3054   | 169.66  |   --
+*Meta-Kalon    |  3096   | 172     |   --
+Osmium         |  3430   | 190.55  | 189.55
+Iridium        |  3458   | 192.11  | 191.56
+Platinum A     |  3486   | 193.66  | 193.34
+*Platinum B    |  3514   | 195.22  |   --
+Gold           |  3546   | 197     | 195.74
+--------------------------------------------
+[Illustration: PLATE II. MALE (left) and FEMALE (right).]
+
+As the words "ultimate physical atom" must frequently occur, it is
+necessary to state what we mean by the phrase. Any gaseous chemical atom
+may be dissociated into less complicated bodies; these, again, into still
+less complicated; these, again, into yet still less complicated. These will
+be dealt with presently. After the third dissociation but one more is
+possible; the fourth dissociation gives the ultimate physical atom.[3] This
+may vanish from the physical plane, but it can undergo no further
+dissociation on it. In this ultimate state of physical matter two types of
+atoms have been observed; they are alike in everything save the direction
+of their whorls and of the force which pours through them. In the one case
+force pours in from the "outside," from fourth-dimensional space,[4] and
+passing through the atom, pours into the physical world. In the second, it
+pours in from the physical world, and out through the atom into the
+"outside" again,[4] _i.e._, vanishes from the physical world. The one is
+like a spring, from which water bubbles out; the other is like a hole, into
+which water disappears. We call the atoms from which force comes out
+_positive_ or _male_; those through which it disappears, _negative_ or
+_female_. All atoms, so far as observed, are of one or other of these two
+forms. (Plate II.)
+
+It will be seen that the atom is a sphere, slightly flattened, and there is
+a depression at the point where the force flows in, causing a heart-like
+form. Each atom is surrounded by a field, formed of the atoms of the four
+higher planes, which surround and interpenetrate it.
+
+The atom can scarcely be said to be a "thing," though it is the material
+out of which all things physical are composed. It is formed by the flow of
+the life-force[5] and vanishes with its ebb. When this force arises in
+"space"[6]--the apparent void which must be filled with substance of some
+kind, of inconceivable tenuity--atoms appear; if this be artificially
+stopped for a single atom, the atom disappears; there is nothing left.
+Presumably, were that flow checked but for an instant, the whole physical
+world would vanish, as a cloud melts away in the empyrean. It is only the
+persistence of that flow[7] which maintains the physical basis of the
+universe.[8]
+
+In order to examine the construction of the atom, a space is artificially
+made[9]; then, if an opening be made in the wall thus constructed, the
+surrounding force flows in, and three whorls immediately appear,
+surrounding the "hole" with their triple spiral of two and a half coils,
+and returning to their origin by a spiral within the atom; these are at
+once followed by seven finer whorls, which following the spiral of the
+first three on the outer surface, and returning to their origin by a spiral
+within that, flowing in the opposite direction--form a caduceus with the
+first three. Each of the three coarser whorls, flattened out, makes a
+closed circle; each of the seven finer ones, similarly flattened out, makes
+a closed circle. The forces which flow in them, again, come from "outside,"
+from a fourth-dimensional space.[10] Each of the finer whorls is formed of
+seven yet finer ones, set successively at right angles to each other, each
+finer than its predecessor; these we call spirillae.[11]
+
+It will be understood from the foregoing, that the atom cannot be said to
+have a wall of its own, unless these whorls of force can be so designated;
+its "wall" is the pressed back "space." As said in 1895, of the chemical
+atom, the force "clears itself a space, pressing back the undifferentiated
+matter of the plane, and making to itself a whirling wall of this matter."
+The wall belongs to space, not to the atom.
+
+In the three whorls flow currents of different electricities; the seven
+vibrate in response to etheric waves of all kinds--to sound, light, heat,
+etc.; they show the seven colours of the spectrum; give out the seven
+sounds of the natural scale; respond in a variety of ways to physical
+vibration--flashing, singing, pulsing bodies, they move incessantly,
+inconceivably beautiful and brilliant.[12]
+
+The atom has--as observed so far--three proper motions, _i.e._, motions of
+its own, independent of any imposed upon it from outside. It turns
+incessantly upon its own axis, spinning like a top; it describes a small
+circle with its axis, as though the axis of the spinning top moved in a
+small circle; it has a regular pulsation, a contraction and expansion, like
+the pulsation of the heart. When a force is brought to bear upon it, it
+dances up and down, flings itself wildly from side to side, performs the
+most astonishing and rapid gyrations, but the three fundamental motions
+incessantly persist. If it be made to vibrate, as a whole, at the rate
+which gives any one of the seven colors, the whorl belonging to that color
+glows out brilliantly.
+
+[Illustration]
+
+An electric current brought to bear upon the atoms checks their proper
+motions, _i.e._, renders them slower; the atoms exposed to it arrange
+themselves in parallel lines, and in each line the heart-shaped depression
+receives the flow, which passes out through the apex into the depression of
+the next, and so on. The atoms always set themselves to the current. The
+well-known division of diamagnetic and paramagnetic depends generally on
+this fact, or on an analogous action on molecules, as may be seen in the
+accompanying diagrams.[13]
+
+Two atoms, positive and negative, brought near to each other, attract each
+other, and then commence to revolve round each other, forming a relatively
+stable duality; such a molecule is neutral. Combinations of three or more
+atoms are positive, negative or neutral, according to the internal
+molecular arrangement; the neutral are relatively stable, the positive and
+negative are continually in search of their respective opposites, with a
+view to establishing a relatively permanent union.
+
+Three states of matter exist between the atomic state and the gaseous--the
+state in which the chemical atoms are found, the recognized chemical
+elements; for our purposes we may ignore the liquid and solid states. For
+the sake of clearness and brevity in description, we have been obliged to
+name these states; we call the atomic state of the chemist _elemental_; the
+state which results from breaking up chemical elements, _proto-elemental_;
+the next higher, _meta-proto-elemental_; the next higher,
+_hyper-meta-proto-elemental_; then comes the atomic state. These are
+briefly marked as El., Proto., Meta., and Hyper.[14]
+
+The simplest unions of atoms, never, apparently consisting of more than
+seven, form the first molecular state of physical matter.
+
+[Illustration: TYPES OF HYPER-META-PROTO-ELEMENTAL MATTER.]
+
+Here are some characteristic combinations of the Hyper state; the atom is
+conventional, with the depression emphasised; the lines, always entering at
+the depression and coming out at the apex, show the resultants of lines of
+force; where no line appears entering the depression, the force wells up
+from fourth-dimensional space; where no line appears leaving the apex, the
+force disappears into fourth-dimensional space; where the point of entry
+and departure is outside the atoms, it is indicated by a dot.[15]
+
+The molecules show all kinds of possible combinations; the combinations
+spin, turn head over heels, and gyrate in endless ways. Each aggregation is
+surrounded with an apparent cell-wall, the circle or oval, due to the
+pressure on the surrounding matter caused by its whirling motion; they
+strike on each other[16] and rebound, dart hither and thither, for reasons
+we have not distinguished.
+
+[Illustration: TYPES OF META-PROTO-ELEMENTAL MATTER.]
+
+The Meta state, in some of its combinations, appears at first sight to
+repeat those of the Hyper state; the only obvious way of distinguishing to
+which some of the molecules of less complexity belong is to pull them out
+of the "cell-wall"; if they are Hyper molecules they at once fly off as
+separate atoms; if they are Meta molecules they break up into two or more
+molecules containing a smaller number of atoms. Thus one of the Meta
+molecules of iron, containing seven atoms, is identical in appearance with
+a Hyper heptad, but the latter dissociates into seven atoms, the former
+into two triads and a single atom. Long-continued research into the
+detailed play of forces and their results is necessary; we are here only
+able to give preliminary facts and details--are opening up the way. The
+following may serve as characteristic Meta types:--
+
+These are taken from constituents of the various elements; 1 from Gl; 2 and
+3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12
+from Li; 13 and 14 from Na. Others will be seen in the course of breaking
+up the elements.
+
+The Proto state preserves many of the forms in the elements, modified by
+release from the pressure to which they are subjected in the chemical atom.
+In this state various groups are thus recognizable which are characteristic
+of allied metals.
+
+[Illustration: TYPES OF PROTO-ELEMENTAL MATTER.]
+
+These are taken from the products of the first disintegration of the
+chemical atom, by forcibly removing it from its hole. The groups fly apart,
+assuming a great variety of forms often more or less geometrical; the lines
+between the constituents of the groups, where indicated, no longer
+represent lines of force, but are intended to represent the impression of
+form, _i.e._, of the relative position and motion of the constituents, made
+on the mind of the observer. They are elusive, for there are no lines, but
+the appearance of lines is caused by the rapid motion of the costituents up
+and down, or along them backwards and forwards. The dots represent atoms,
+or groups of atoms, within the proto-elements. 1 is found in C; 2 and 3 in
+He; 4 in Fl; 5 in Li; 6 in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe;
+12 in Se. We shall return to these when analysing the elements, and shall
+meet many other proto-elemental groupings.
+
+The first thing which is noticed by the observer, when he turns his
+attention to the chemical atoms, is that they show certain definite forms,
+and that within these forms, modified in various ways, sub-groupings are
+observable which recur in connexion with the same modified form. The main
+types are not very numerous, and we found that, when we arranged the atoms
+we had observed, according to their external forms, they fell into natural
+classes; when these, in turn, were compared with Sir William Crookes'
+classification, they proved to be singularly alike. Here is his arrangement
+of the elements, as it appeared in the _Proceedings of the Royal Society_,
+in a paper read on June 9th, 1898.
+
+[Illustration]
+
+This is to be read, following the lines of the "figures of eight": H, He,
+Li, Gl, B, C, N, and so on, each successive element being heavier than the
+one preceding it in order. The disks which fall immediately below each
+other form a class; thus: H, Cl, Br, I; these resemble each other in
+various ways, and, as we shall presently see, the same forms and groupings
+re-appear.
+
+Another chart--taken from Erdmann's _Lehrbuch_--arranges the elements on a
+curved line, which curiously resembles the curves within the shell of a
+nautilus. The radiating lines show the classes, the whole diameter building
+up a family; it will be observed that there is an empty radius between
+hydrogen and helium, and we have placed occultum there; on the opposite
+radius, iron, rubidium and osmium are seen.
+
+[Illustration]
+
+The external forms may be classified as follows; the internal details will
+be dealt with later :--
+
+[Illustration: PLATE III.]
+
+1. _The Dumb-bell._--The characteristics of this are a higher and lower
+group, each showing 12 projecting funnels, grouped round a central body,
+and a connecting rod. It appears in sodium, copper, silver, and gold,[17]
+and gold is given (1 on Plate III) as the most extremely modified example
+of this form. The 12 almond-like projections, above and below, are
+severally contained in shadowy funnels, impossible to reproduce in the
+drawing; the central globe contains three globes, and the connecting
+portion has swollen out into an egg, with a very complicated central
+arrangement. The dumb-bell appears also in chlorine, bromine and iodine,
+but there is no trace of it in hydrogen, the head of the group. We have not
+met it elsewhere. It may be remarked that, in Sir William Crookes' scheme,
+in which they are all classed as monads, these two groups are the nearest
+to the neutral line, on the ingoing and outgoing series, and are
+respectively positive and negative.
+
+II and IIa. _The Tetrahedron._--The characteristics of this form are four
+funnels, containing ovoid bodies, opening on the face of a tetrahedron. The
+funnels generally, but not always, radiate from a central globe. We give
+beryllium (glucinum) as the simplest example (2 on Plate III), and to this
+group belong calcium and strontium. The tetrahedron is the form of chromium
+and molybdenum, but not that of the head of their group, oxygen, which is,
+like hydrogen, _sui generis_. These two groups are marked in orthodox
+chemistry as respectively positive and negative, and are closely allied.
+Another pair of groups show the same tetrahedral form: magnesium, zinc and
+cadmium, positive; sulphur, selenium and tellurium, negative. Selenium is a
+peculiarly beautiful element, with a star floating across the mouth of each
+funnel; this star is extremely sensitive to light, and its rays tremble
+violently and bend if a beam of light falls on it. All these are dyads.
+
+The tetrahedron is not confined to the external form of the above atoms; it
+seems to be one of the favourite forms of nature, and repeatedly appears in
+the internal arrangements. There is one tetrahedron within the unknown
+element occultum; two appear in helium (3 on Plate III); yttrium has also
+two within its cube, as has germanium; five, intersecting, are found in
+neon, meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon,
+kalon, meta-kalon, tin, titanium and zirconium. Gold contains no less than
+twenty tetrahedra.
+
+III. _The Cube._--The cube appears to be the form of triads. It has six
+funnels, containing ovoids, and opening on the faces of the cube. Boron is
+chosen as an example (4 on Plate III). Its group members, scandium and
+yttrium, have the same form; we have not examined the fourth; the group is
+positive. Its negative complement consists of nitrogen, vanadium and
+niobium, and we have again to note that nitrogen, like hydrogen and oxygen,
+departs from its group type. Two other triad groups, the positive
+aluminium, gallium and indium (the fourth unexamined) and the negative
+phosphorus, arsenic and antimony (the fourth unexamined), have also six
+funnels opening on the faces of a cube.
+
+IV. _The Octahedron._--The simplest example of this is carbon (5 on Plate
+III). We have again the funnel with its ovoids, but now there are eight
+funnels opening on the eight faces of the octahedron. In titanium (6 on
+Plate III) the form is masked by the protruding arms, which give the
+appearance of the old Rosicrucian Cross and Rose, but when we look into the
+details later, the carbon type comes out clearly. Zirconium is exactly like
+titanium in form, but contains a large number of atoms. We did not examine
+the remaining two members of this group. The group is tetratomic and
+positive. Its negative pendant shows the same form in silicon, germanium
+and tin; again, the fourth was unexamined.
+
+[Illustration: PLATE IV.]
+
+V. _The Bars._--These characterise a set of closely allied groups, termed
+"inter-periodic." Fourteen bars (or seven crossed) radiate from a centre,
+as in iron (1 on Plate IV), and the members of each group--iron, nickel,
+cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum--differ
+from each other by the weight of each bar, increasing in orderly
+succession; the details will be given later. Manganese is often grouped
+with iron, nickel, and cobalt (_see_ Crookes' lemniscates), but its
+fourteen protruding bodies repeat the "lithium spike" (proto-element 5) and
+are grouped round a central ovoid. This would appear to connect it with
+lithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with
+which it is often classed. The "lithium spike" re-appears in potassium and
+rubidium. These details, again, will come out more clearly later.
+
+VI. _The Star._--A flat star, with five interpenetrating tetrahedra in the
+centre, is the characteristic of neon and its allies (4 on Plate IV)
+leaving apart helium, which, as may be seen by referring to 3, Plate IV,
+has an entirely different form.
+
+There are thus six clearly defined forms, typical of classes, with
+two--lithium and fluorine--of doubtful affinities. It is worthy of notice
+that in diatomic elements _four_ funnels open on the faces of tetrahedra;
+in triatomic, _six_ funnels on the faces of cubes; in tetratomic, _eight_
+funnels on the faces of octahedra.
+
+Thus we have a regular sequence of the platonic solids, and the question
+suggests itself, will further evolution develop elements shaped to the
+dodecahedron and the icosahedron?
+
+       *       *       *       *       *
+
+II.
+
+We now pass from the consideration of the outer forms of the chemical
+elements to a study of their internal structure, the arrangement within the
+element of more or less complicated groups--proto-elements--capable of
+separate, independent existence; these, once more, may be dissociated into
+yet simpler groups--hyper-meta-proto-elements--equally capable of separate,
+independent existence, and resolvable into single ultimate physical atoms,
+the irreducible substratum of the physical world (see _Theosophist_, 1908,
+pp. 354-356).[18]
+
+We shall have to study the general internal structure, and then the
+breaking up of each element, and the admirable diagrams, patiently worked
+out by Mr. Jinarajadasa, 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 _Encyclopaedia
+Britannica_. We use the words in their ordinary text-book meaning, and have
+not, so far, detected any characteristics whereby an element can be
+declared, at sight, to be either positive or negative:--
+
+"When binary compounds, or compounds of two elements, are decomposed by an
+electric current, the two elements make their appearance at opposite poles.
+These elements which are disengaged at the negative pole are termed
+electro-positive or positive or basylous elements, while those disengaged
+at the positive pole are termed electro-negative or negative or chlorous
+elements. But the difference between these two classes of elements is one
+of degree only, and they gradually merge into each other; moreover the
+electric relations of elements are not absolute, but vary according to the
+state of combination in which they exist, so that it is just as impossible
+to divide the elements into two classes according to this property as it is
+to separate them into two distinct classes of metals and non-metals."
+
+We follow here the grouping according to external forms, and the student
+should compare it with the groups marked in the lemniscate arrangement
+shown in Article II (p. 377, properly p. 437, February), reading the group
+by the disks that fall below each other; thus the first group is H, Cl, Br,
+I (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered
+element. The elements grow denser in descending order; thus hydrogen is an
+invisible gas; chlorine a denser gas visible by its colour; bromine is a
+liquid; iodine is a solid--all, of course, when temperature and pressure
+are normal. By the lowering of temperature and the increase of pressure, an
+element which is normally gaseous becomes a liquid, and then a solid.
+Solid, liquid, gaseous, are three interchangeable states of matter, and an
+element does not alter its constitution by changing its state. So far as a
+chemical "atom" is concerned, it matters not whether it be drawn for
+investigation from a solid, a liquid, or a gas; but the internal
+arrangements of the "atoms" become much more complicated as they become
+denser and denser, as is seen by the complex arrangements necessitated by
+the presence of the 3546 ultimate atoms contained in the chemical "atom" of
+gold, as compared with the simple arrangement of the 18 ultimate atoms of
+hydrogen.
+
+According to the lemniscate arrangement, we should commence with hydrogen
+as the head of the first negative group, but as it differs wholly from
+those placed with it, it is better to take it by itself. Hydrogen is the
+lightest of the known elements, and is therefore taken as 1 in ordinary
+chemistry, and all atomic weights are multiples of this. We take it as 18,
+because it contains eighteen ultimate atoms, the smallest number we have
+found in a chemical element. So our "number-weights" are obtained by
+dividing the total number of atoms in an element by 18 (see p. 349,
+January).
+
+[Illustration: PLATE V.]
+
+HYDROGEN (Plate V, 1).--Hydrogen not only stands apart from its reputed
+group by not having the characteristic dumb-bell shape, well shown in
+sodium (Plate I, opposite p. 349, January), but it also stands apart in
+being positive, serving as a base, not as a chlorous, or acid, radical,
+thus "playing the part of a metal," as in hydrogen chloride (hydrochloric
+acid), hydrogen sulphate (sulphuric acid), etc.
+
+It is most curious that hydrogen, oxygen and nitrogen, the most widely
+spread gases, all differ fundamentally in form from the groups they
+reputedly head.[19] Hydrogen was the first chemical element examined by us,
+nearly thirteen years ago, and I reproduce here the substance of what I
+wrote in November, 1895, for we have nothing to add to nor amend in it.
+
+Hydrogen consists of six small bodies, contained in an egg-like form (the
+outer forms are not given in the diagrams). The six little bodies are
+arranged in two sets of three, forming two triangles which are not
+interchangeable, but are related to each other as object and image. The six
+bodies are not all alike; they each contain three ultimate physical atoms,
+but in four of the bodies the three atoms are arranged in a triangle, and
+in the remaining two in a line.
+
+HYDROGEN: 6 bodies of 3            18
+          Atomic weight             1
+          Number weight 18/18       1
+I.--THE DUMB-BELL GROUP.
+
+I a.--This group consists of Cl, Br, and I (chlorine, bromine and iodine);
+they are monads, diamagnetic and negative.
+
+CHLORINE (Plate V, 2).--As already said, the general form is that of the
+dumb-bell, the lower and upper parts each consisting of twelve funnels, six
+sloping upwards and six downwards, the funnels radiating outwards from a
+central globe, and these two parts being united by a connecting rod (see,
+again, sodium, Plate I).
+
+The funnel (shown flat as an isosceles triangle, standing on its apex) is a
+somewhat complicated structure, of the same type as that in sodium (Plate
+VI, 2), the difference consisting in the addition of one more globe,
+containing nine additional atoms. The central globe is the same as in
+sodium, but the connecting rod differs. We have here a regular arrangement
+of five globes, containing three, four, five, four, three atoms
+respectively, whereas sodium has only three bodies, containing four, six,
+four. But copper and silver, its congeners, have their connecting rods of
+exactly the same pattern as the chlorine rod, and the chlorine rod
+reappears in both bromine and iodine. These close similarities point to
+some real relation between these groups of elements, which are placed, in
+the lemniscates, equi-distant from the central line, though one is on the
+swing which is going towards that line and the other is on the swing away
+from it.
+
+CHLORINE: Upper part {12 funnels of 25 atoms  300
+                     {Central globe            10
+          Lower part same                     310
+          Connecting rod                       19
+                                             ----
+                           Total              639
+                                             ----
+          Atomic weight                     35.473
+          Number weight 639/18              35.50
+(The Atomic Weights are mostly from Erdmann, and the Number Weights are
+those ascertained by us by counting the atoms as described on p. 349,
+January, and dividing by 18. Prof. T.W. Richards, in _Nature_, July 18,
+1907, gives 35.473.)
+
+BROMINE (Plate V, 3).--In bromine, each funnel has three additional bodies,
+ovoid in shape, an addition of 33 atoms being thus made without any
+disturbance of form; two pairs of atoms are added to the central globe, and
+a rearrangement of the atoms is effected by drawing together and lessening
+the swing of the pair of triplets, thus making symmetrical room for the
+newcomers. The connecting rod remains unchanged. The total number of atoms
+is thus raised from the 639 of chlorine to 1439. Over and over again, in
+these investigations, were we reminded of Tyndall's fascinating description
+of crystal building, and his fancy of the tiny, ingenious builders busied
+therein. Truly are there such builders, and the ingenuity and effectiveness
+of their devices are delightful to see.[20]
+
+BROMINE:  Upper part {12 funnels of 58 atoms   696
+                     {Central globe             14
+          Lower part same                      710
+          Connecting rod                        19
+                                              ----
+                           Total              1439
+                                              ----
+          Atomic weight                      79.953
+          Number weight 1459/18              79.944
+IODINE (Plate V, 4).--We find herein that the central globe gains 4 atoms,
+the two pairs becoming 2 quartets; the connecting rod exactly reproduces
+the rods of chlorine and bromine; the funnel is also that of bromine,
+except that five bodies, containing 35 atoms, are added to it. The 1439
+atoms of bromine are thus raised to 2887.
+
+IODINE:   Upper Part {12 funnels of 90 atoms  1116
+                     {Central globe             18
+          Lower part same                     1134
+          Connecting rod                        19
+                                              ----
+                           Total              2287
+                                              ----
+          Atomic weight                     126.01
+          Number weight  2287/18            127.055
+The plan underlying the building up of groups is here clearly shown; a
+figure is built up on a certain plan, in this case a dumb-bell; in the
+succeeding members of the group additional atoms are symmetrically
+introduced, modifying the appearance, but following the general idea; in
+this case the connecting rod remains unaltered, while the two ends become
+larger and larger, more and more overshadowing it, and causing it to become
+shorter and thicker. Thus a group is gradually formed by additional
+symmetrical additions. In the undiscovered remaining member of the group we
+may suppose that the rod will have become still more egg-like, as in the
+case of gold.
+
+I b.--The corresponding positive group to that which we have been
+considering consists of Na, Cu, Ag, and Au (sodium, copper, silver and
+gold), with an empty disk between silver and gold, showing where an element
+ought to be. These four elements are monads, diamagnetic, and positive, and
+they show the dumb-bell arrangement, although it is much modified in gold;
+we may presume that the undiscovered element between silver and gold would
+form a link between them.
+
+[Illustration: PLATE VI.]
+
+SODIUM (Plate VI, 2) has been already described (p. 349, January), as a
+type of the group, so we need only refer to its internal arrangement in
+order to note that it is the simplest of the dumb-bell group. Its twelve
+funnels show only four enclosed bodies, the same as we see in chlorine,
+bromine, iodine, copper and silver, and which is very little modified in
+gold. Its central globe is the simplest of all, as is its connecting rod.
+We may therefore take it that sodium is the ground-plan of the whole group.
+
+SODIUM:   Upper part
+              { 12 funnels of 16 each    192
+              { Central globe             10
+          Lower part same                202
+          Connecting rod                  14
+                                        ----
+                      Total              418
+                                        ----
+          Atomic weight                23.88
+          Number weight 418/19         23.22
+COPPER (Plate VI, 3) introduces an addition in the funnel, that we shall
+find elsewhere, _e.g._, in silver, gold, iron, platinum, zinc, tin, the
+triangular arrangement near the mouth of the funnel and adds to the ten
+atoms in this nineteen more in three additional enclosed bodies, thus
+raising the number of atoms in a funnel from the sixteen of sodium to
+forty-five. The number in the central globe is doubled, and we meet for the
+first time the peculiar cigar or prism-shaped six-atomed arrangement, that
+is one of the most common of atomic groups. It ought to imply some definite
+quality, with its continual recurrence. The central column is the three,
+four, five, four, three, arrangement already noted.
+
+COPPER:   Upper part {12 funnels of 45 atoms  540
+                     {Central globe            20
+          Lower part same                     560
+          Connecting rod                       19
+                                             ----
+                           Total             1139
+                                             ----
+          Atomic weight                     63.12
+          Number weight 1139/18             63.277
+SILVER (Plate VI, 4) follows copper in the constitution of five of the
+bodies enclosed in the funnels. But the triangular group contains
+twenty-one atoms as against ten, and three ovoids, each containing three
+bodies with eleven atoms, raise the number of atoms in a funnel to
+seventy-nine. The central globe is decreased by five, and the prisms have
+disappeared. The connecting rod is unaltered.
+
+SILVER:   Upper part {12 funnels of 79 atoms   948
+                     {Central globe             15
+          Lower part same                      963
+          Connecting rod                        19
+                                              ----
+                           Total              1945
+                                              ----
+          Atomic weight                     107.93
+          Number weight 1945/18             108.055
+(This atomic weight is given by Stas, in _Nature_, August 29, 1907, but it
+has been argued later that the weight should not be above 107.883.)
+
+[Illustration: PLATE VII.]
+
+GOLD (Plate VII) is so complicated that it demands a whole plate to itself.
+It is difficult to recognize the familiar dumb-bell in this elongated egg,
+but when we come to examine it, the characteristic groupings appear. The
+egg is the enormously swollen connecting rod, and the upper and lower parts
+with their central globes are the almond-like projections above and below,
+with the central ovoid. Round each almond is a shadowy funnel (not drawn in
+the diagram), and within the almond is the collection of bodies shown in
+_e_, wherein the two lowest bodies are the same as in every other member of
+the negative and positive groups; the third, ascending, is a very slight
+modification of the other thirds; the fourth is a union and re-arrangement
+of the fourth and fifth; the fifth, of four ovoids, adds one to the three
+ovoids of bromine, iodine and silver; the triangular group is like that in
+copper and silver, though with 28 atoms instead of 10 or 21, and it may be
+noted that the cone in iron has also 28. The central body in the ovoid is
+very complicated, and is shown in _c_, the bodies on each side, _d_, are
+each made up of two tetrahedra, one with four six-atomed prisms at its
+angles, and the other with four spheres, a pair with four atoms and a pair
+with three. We then come to the connecting rod. One of the four similar
+groups in the centre is enlarged in _a_, and one of the sixteen circling
+groups is enlarged in b. These groups are arranged in two planes inclined
+to one another.
+
+GOLD: Upper part
+          { 12 funnels of 97 atoms      1164
+          { Central ovoid {c             101
+                          {2 d, 38        76
+      Lower part same                   1341
+      Connecting rod { 4 a 84            336
+                     {16 b 33            528
+                                        ----
+                      Total             3546
+                                        ----
+      Atomic weight                   195.74
+      Number weight 3546/18           197
+It may be noted that the connecting rod is made up of exactly sixteen atoms
+of occultum, and that sixteen such atoms contain 864 ultimate atoms, the
+exact member of atoms in titanium.
+
+       *       *       *       *       *
+
+III.
+
+Occultum was observed by us in 1895, and, finding that it was so light, and
+so simple in its composition, we thought that it might be helium, of which
+we were unable, at the time, to obtain a sample. When, however, helium
+itself came under observation in 1907, it proved to be quite different from
+the object before observed, so we dubbed the unrecognised object Occultum,
+until orthodox science shall find it and label it in proper fashion.
+
+OCCULTUM (Plate VI, 1).
+
+We here meet the tetrahedron for the first time, with each angle occupied
+by a six-atomed group, the atoms arranged as on the end triangles of a
+prism. This form recurs very often, and was noted, last month, as seen in
+copper (Plate VI, 3); it revolves with extreme rapidity around its
+longitudinal axis, and looks like a pencil sharpened at both ends, or a
+cigar tapering at both ends; we habitually spoke of it as "the cigar." It
+appears to be strongly coherent, for, as will be seen below, its six atoms
+remain attached to each other as meta-compounds and even when divided into
+two triplets as hyper-compounds, they revolve round each other.
+
+Above the tetrahedron is a balloon-shaped figure, apparently drawn into
+shape by the attraction of the tetrahedron. The body below the tetrahedron
+looks like a coil of rope, and contains fifteen atoms; they are arranged on
+a slanting disk in a flat ring, and the force goes in at the top of one
+atom, and out of the bottom of it into the top of the next, and so on,
+making a closed circuit. The two little spheres, each containing a triplet,
+are like fill-up paragraphs to a compositor--they seem to be kept standing
+and popped in where wanted. The sphere marked _x_ is a proto-compound, the
+balloon when set free.
+
+As was noted under gold (p. 41), sixteen occultum bodies, re-arranged, make
+up the connecting rod in gold:--
+
+OCCULTUM: Tetrahedron                  24
+          Balloon                       9
+          Triplets                      6
+          Rope-circle                  15
+                                     ----
+                     Total             54
+                                     ----
+          Atomic weight         Not known
+          Number weight 54/18           3
+DISSOCIATION OF ATOMS.
+
+Before proceeding to the study of other chemical atoms, as to their general
+internal arrangements, it is desirable to follow out, in those already
+shown, the way in which these atoms break up into simpler forms, yielding
+successively what we have called proto-, meta-, and hyper-compounds. It is
+naturally easier to follow these in the simpler atoms than in the more
+complex, and if the earlier dissociations are shown, the latter can be more
+readily and more intelligibly described.
+
+The first thing that happens on removing a gaseous atom from its "hole"
+(see pp. 21 to 23) or encircling "wall," is that the contained bodies are
+set free, and, evidently released from tremendous pressure, assume
+spherical or ovoid forms, the atoms within each re-arranging themselves,
+more or less, within the new "hole" or "wall." The figures are, of course,
+three-dimensional, and often remind one of crystals; tetrahedral,
+octagonal, and other like forms being of constant occurrence. In the
+diagrams of the proto-compounds, the constituent atoms are shown by dots.
+In the diagrams of the meta-compounds the dot becomes a heart, in order to
+show the resultants of the lines of force. In the diagrams of the
+hyper-compounds the same plan is followed. The letters _a_, _b_, _c_, &c.,
+enable the student to follow the breaking up of each group through its
+successive stages.
+
+HYDROGEN (Plate V, 1).
+
+[Illustration]
+
+The six bodies contained in the gaseous atom instantaneously re-arrange
+themselves within two spheres; the two linear triplets unite with one
+triangular triplet, holding to each other relative positions which, if
+connected by three right lines, would form a triangle with a triplet at
+each angle; the remaining three triangular triplets similarly arrange
+themselves in the second sphere. These form the proto-compounds of
+hydrogen.
+
+In the dissociation of these, each group breaks up into two, the two linear
+triplets joining each other and setting free their triangular comrade,
+while two of the triangular triplets similarly remain together, casting out
+the third, so that hydrogen yields four meta-compounds.
+
+In the hyper-condition, the connexion between the double triplets is
+broken, and they become four independent groups, two like ix, in the
+hyper-types (p. 25), and two remaining linear, but rearranging their
+internal relations; the two remaining groups break up into two pairs and a
+unit.
+
+The final dissociation sets all the atoms free.
+
+OCCULTUM (Plate VI, 1).
+
+[Illustration]
+
+On the first dissociation of the component parts of occultum, the
+tetrahedron separates as a whole, with its four "cigars," flattening itself
+out within its hole, _a_; two "cigars" are positive and two negative,
+marked respectively _a_ and _a'_. The rope becomes a ring within a sphere,
+_b_, and the two bodies _d_ _d_, which are loose in the gaseous atom, come
+within this ring. The balloon becomes a sphere.
+
+On further dissociation, the "cigars" go off independently, showing two
+types, and these again each divide into triplets, as meta-compounds. _B_,
+on the meta-level, casts out the two _d_ bodies, which become independent
+triplets, and the "rope" breaks into two, a close ring of seven atoms and a
+double cross of eight. These subdivide again to form hyper-compounds, the
+ring yielding a quintet and a pair, and the double cross separating into
+its two parts.
+
+The balloon, _c_, becomes much divided, the cohesion of its parts being
+slight; it forms two triplets, a pair and a unit, and these set free, on
+further dissociation, no less than five separate atoms and two duads.
+
+The two triplets of _d_ each cast out an atom on dissociation, and form two
+pairs and two units.
+
+SODIUM (Plate VI, 2).
+
+It is convenient to consider sodium next, because it is the basic pattern
+on which not only copper, silver and gold are formed, but also chlorine,
+bromine and iodine.
+
+[Illustration]
+
+When sodium is set free from its gaseous condition, it divides up into
+thirty-one bodies--twenty-four separate funnels, four bodies derived from
+the two central globes, and three from the connecting rod. The funnels
+become spheres, and each contains four enclosed spheres, with more or less
+complicated contents. Each central globe yields a sextet and a quartet, and
+the rod sets free two quartets and a peculiarly formed sextet.
+
+When the proto-compounds are dissociated, the funnel-sphere sets free: (1)
+the contents of _a_, rearranged into two groups of four within a common
+sphere; the sphere yields four duads as hyper-compounds; (2) the contents
+of _b_, which unite themselves into a quartet, yielding two duads as
+hyper-compounds; and (3) the contents of the two spheres, _c_, which
+maintain their separation as meta-compounds, and become entirely
+independent, the atoms within the sphere revolving round each other, but
+the spheres ceasing their revolution round a common axis, and going off in
+different directions. The atoms break off from each other, and gyrate in
+independent solitude as hyper-"compounds." Thus each funnel yields finally
+ten hyper-bodies.
+
+The part of the central globe, marked _d_, with its six atoms, whirling
+round a common centre, becomes two triplets, at the meta-stage, preparing
+for the complete separation of these as hyper-bodies. The second part of
+the same globe, marked _e_, a whirling cross, with an atom at each point,
+becomes a quartet in the meta-state, in which three atoms revolve round a
+fourth, and in the hyper-state this central atom is set free, leaving a
+triplet and a unit.
+
+Each of the two bodies marked _f_, liberated from the connecting rod, shows
+four atoms whirling round a common centre, exactly resembling _e_ in
+appearance; but there must be some difference of inner relations, for, in
+the meta-state, they re-arrange themselves as two pairs, and divide into
+two as hyper-bodies.
+
+The body marked _g_ is a four-sided pyramid, with two closely joined atoms
+at its apex; these still cling to each in mutual revolution as a meta-body,
+encircled by a ring of four, and this leads to a further dissociation into
+three pairs on the hyper-level.
+
+CHLORINE (Plate V, 2).
+
+[Illustration]
+
+The description of the funnel of sodium applies to that of chlorine, until
+we come to the body nearest the mouth, the sphere containing three
+additional bodies; this remains within the funnel in the first
+dissociation, so that again we have twenty-four separate funnels as
+proto-compounds; the central globes are the same as in sodium, and yield
+the same four bodies; the connecting rod sets free five bodies, of which
+two are the same; we have thus thirty-three separate bodies as the result
+of the dissociation of chlorine into its proto-compounds. As all the
+compounds which are in sodium break up in the same way into meta- and
+hyper-compounds, we need not repeat the process here. We have only to
+consider the new meta- and hyper-compounds of the highest sphere within the
+funnel, and the two triplets and one quintet from the connecting rod.
+
+The additional body within the proto-funnel is of a very simple character,
+three contained triangles within the flattened sphere. On release from the
+funnel, on the meta-level, the atoms rearrange themselves in a whirling set
+of three triplets, and these break off from each other as hyper-compounds.
+The two triplets from the connecting rod, also, are of the simplest
+character and need not delay us. The five-atomed body, a four-sided pyramid
+as a proto-compound, becomes a ring whirling round a centre on the meta,
+and two pairs with a unit on the hyper.
+
+BROMINE (Plate V, 3).
+
+Three additional bodies appear at the top of the funnel, which otherwise
+repeats that of chlorine. The connecting rod is the same and may be
+disregarded. The central globes become more complex. The additions are,
+however, of very easy types, and hence are readily dealt with. Each of the
+three similar ovoid bodies contains two triplets--each a triangle and a
+quintet--a four-sided pyramid. These are the same, as may be seen in the
+connecting rod of chlorine, and we need not repeat them. Only the globe
+remains. This does not break up as a proto-compound but is merely set free,
+_a_ and the 2 _bs_ whirling in a plane vertical to the paper and the two
+smaller bodies, _cc_, whirling on a plane at right angles to the other.
+These two disengage themselves, forming a quartet as a meta-compound, while
+_a_ makes a whirling cross and _bb_ a single sextet; these further
+dissociate themselves into four pairs and two triplets.
+
+IODINE (Plate V, 4).
+
+[Illustration]
+
+Iodine has nothing new to give us, except five similar ovoid bodies at the
+top of each funnel, and two quartets instead of two pairs in the central
+globe. The ovoid bodies become spheres when the funnels are thrown off, and
+a crystalline form is indicated within the sphere. The atoms are arranged
+in two tetrahedra with a common apex, and the relationship is maintained in
+the meta-body, a septet. The latter breaks up into two triplets and a unit
+on the hyper-level. In the central globes, the _a_ of bromine is repeated
+twice instead of the pairs in _cc_.
+
+COPPER (Plate VI, 3).
+
+We have already disposed of occultum, on this plate, and of sodium, which
+lies at the root of both groups. Copper, we now find, is also very largely
+off our hands, as the funnel provides us with only two new types--two
+spheres--each containing five atoms in a new arrangement, and the
+triangular body at the mouth with its ten atoms. This triangular body, with
+an increased number of atoms, reappears in various other chemical elements.
+The central globes are different from any we have had before, in their
+internal arrangement, but the constituents are familiar; there are two
+contained spheres with four atoms each, the _a_ in the globe of bromine
+(see above) and 2 "cigars." The "cigars" may be followed under occultum
+(see above). The connecting rod is as in chlorine, bromine and iodine.
+
+The atoms in the bodies _a_ and _b_ are curiously arranged. _A_ consists of
+two square-based pyramids turned so as to meet at their apices, and breaks
+up into two quartet rings and a duad. _B_ is again two four-sided pyramids,
+but the bases are in contact and set at right angles to each other; the
+second apex is not seen, as it is directly below the first. The pyramids
+separate as meta-bodies, and the atoms assume the peculiar arrangement
+indicated and then break up into four pairs and two units on the hyper
+level.
+
+       *       *       *       *       *
+
+IV.
+
+SILVER (Plate VI, 4 and Ag below).
+
+Silver presents us with only two new bodies, and even these are only new by
+slight additions to old models. The triangular shaped body at the apex of
+the funnel, containing 21 atoms, is intermediate between the similar bodies
+in copper and iron. As a proto-element it becomes three triangles, joined
+at their apices, in fact a tetrahedron in which no atoms are distributed on
+the fourth face. The faces separate on the meta level and give three
+seven-atomed figures, and each of these breaks up into two triplets and a
+unit. The central globe only differs from that of bromine by the addition
+of one atom, which gives the familiar four-sided pyramid with a square base
+as in chlorine (see p. 46).
+
+GOLD (Plate VII and Au below).
+
+[Illustration]
+
+The disintegration of gold first yields forty-seven bodies on the
+proto-level; the twenty-four funnels separate, and the central globes which
+hold each twelve together set free their six contained globes (_c_, _d_),
+thirty bodies being thus liberated. The sixteen bodies on the central
+inclined planes, marked _b_, break away, their central globe, with its four
+contained globes, remaining unchanged. But this condition does not last.
+The motion of the funnels changes and thus the funnels cease to exist and
+their contents are set free, each funnel thus liberating nine independent
+bodies; the sixteen _b_ separate into two each; the four _a_ liberate five
+each; the two _c_ set free thirteen each; the four _d_ finally liberate two
+each: 302 proto elements in all.
+
+The funnel is almost that of iodine, re-arranged. Four of the first ring in
+the iodine funnel are replaced by the triangular body, which becomes a
+four-sided pyramid with an occupied base. The second ring of three ovoids
+in iodine becomes four in gold, but the internal arrangement of each ovoid
+is the same. The next two spheres in the iodine funnel coalesce into one
+sphere, with similar contents, in the gold funnel. The fifth in iodine is
+slightly rearranged to form the fourth in descent in gold, and the
+remaining two are the same. _B_ has been broken up under occultum (p. 628)
+and can be followed there. The sixteen rings set free from the four _a_,
+after gyrating round the central body, now become a sphere, break up, as in
+occultum (see p. 44) into a meta seven-atomed ring and an eight-atomed
+double cross, and so on to the hyper level. The sphere with its two
+contained bodies breaks up into eight triangles on the meta level, and each
+of these, on the hyper, into a duad and a unit. The twelve septets of _c_
+assume the form of prisms as in iodine (see p. 48) and pursue the same
+course, while its central body, a four-sided pyramid with its six
+attendants, divides on the meta level into six duads, revolving round a
+ring with a central atom as in chlorine (p. 47), the duads going off
+independently on the hyper-level and the ring breaking up as in chlorine.
+The "cigar" tetrahedron of _d_ follows its course as in occultum, and the
+other sets free two quartets and two triplets on the meta level, yielding
+six duads and two units as hyper compounds. It will be seen that, complex
+as gold is, it is composed of constituents already familiar, and has iodine
+and occultum as its nearest allies.
+
+II AND IIa.--THE TETRAHEDRAL GROUPS.
+
+II.--This group consists of beryllium (glucinum), calcium, strontium and
+barium, all diatomic, paramagnetic and positive. The corresponding group
+consists of oxygen, chromium, molybdenum, wolfram (tungsten) and uranium,
+with a blank disk between wolfram and uranium: these are diatomic,
+paramagnetic, and negative. We have not examined barium, wolfram, or
+uranium.
+
+[Illustration: PLATE VIII.]
+
+BERYLLIUM (Plate III, 2, and Plate VIII, 1). In the tetrahedron four
+funnels are found, the mouth of each funnel opening on one of its faces.
+The funnels radiate from a central globe, and each funnel contains four
+ovoids each with ten atoms within it arranged in three spheres. In the
+accompanying diagrams one funnel with its four ovoids is shown and a single
+ovoid with its three spheres, containing severally three, four, and three
+atoms, is seen at the left-hand corner of the plate (7 _a_). The members of
+this group are alike in arrangement, differing only in the increased
+complexity of the bodies contained in the funnels. Beryllium, it will be
+observed, is very simple, whereas calcium and strontium are complicated.
+
+BERYLLIUM: 4 funnels of 40 atoms    160
+           Central globe              4
+                                   ----
+                           Total    164
+                                   ----
+Atomic weight                      9.01
+Number weight  164/18              9.11
+CALCIUM (Plate VIII, 2) shows in each funnel three contained spheres, of
+which the central one has within it seven ovoids identical with those of
+beryllium, and the spheres above and below it contain each five ovoids (7
+_b_) in which the three contained spheres have, respectively, two, five,
+and two atoms. The central globe is double, globe within globe, and is
+divided into eight segments, radiating from the centre like an orange; the
+internal part of the segment belonging to the inner globe has a triangular
+body within it, containing four atoms (7 _c_), and the external part,
+belonging to the encircling globe, shows the familiar "cigar" (7 _d_). In
+this way 720 atoms are packed into the simple beryllium type.
+
+CALCIUM: 4 funnels of 160 atoms      640
+         Central globe                80
+                                    ----
+                          Total      720
+                                    ----
+         Atomic weight             39.74
+         Number weight 720/18      40.00
+STRONTIUM (Plate VIII, 3) shows a still further complication within the
+funnels, no less than eight spheres being found within each. Each of the
+highest pair contains four subsidiary spheres, with five, seven, seven,
+five atoms, respectively (7 _e_, _g_, _f_). The _g_ groups are identical
+with those in gold, but difference of pressure makes the containing body
+spherical instead of ovoid; similar groups are seen in the top ring of the
+iodine funnel, where also the "hole" is ovoid in form. The second pair of
+spheres contains ten ovoids (7 _b_) identical with those of calcium. The
+third pair contains fourteen ovoids (7 _a_) identical with those of
+beryllium, while the fourth pair repeats the second, with the ovoids
+re-arranged. The internal divisions of the double sphere of the central
+globe are the same as in calcium, but the contents differ. The "cigars" in
+the external segments are replaced by seven-atomed ovoids (7 _h_)--the
+iodine ovoids--and the external segments contain five-atomed triangles (7
+_i_). Thus 1,568 atoms have been packed into the beryllium type, and our
+wonder is again aroused by the ingenuity with which a type is preserved
+while it is adapted to new conditions.
+
+STRONTIUM: 4 funnels of 368 atoms       1472
+           Central globe                  96
+                                        ----
+                            Total       1568
+                                        ----
+           Atomic weight               86.95
+           Number weight 1568/18       87.11
+The corresponding group, headed by oxygen--oxygen, chromium, molybdenum,
+wolfram and uranium--offers us another problem in its first member.
+
+OXYGEN (Plate VIII, 4). This was examined by us in 1895, and the
+description may be reproduced here with a much improved diagram of its very
+peculiar constitution. The gaseous atom is an ovoid body, within which a
+spirally-coiled snake-like body revolves at a high velocity, five brilliant
+points of light shining on the coils. The appearance given in the former
+diagram will be obtained by placing the five septets on one side on the top
+of those on the other, so that the ten become in appearance five, and thus
+doubling the whole, the doubling point leaving eleven duads on each side.
+The composition is, however, much better seen by flattening out the whole.
+On the proto level the two snakes separate and are clearly seen.
+
+OXYGEN: Positive snake
+        { 55 spheres of 2 atoms }
+        {  + 5 disks of 7 atoms }    145
+        Negative snake     "         145
+                                    ----
+                        Total        290
+                                    ----
+        Atomic weight              15.87
+        Number weight 290/18       16.11
+CHROMIUM (Plate VIII, 5) "reverts to the ancestral type," the tetrahedron;
+the funnel is widened by the arrangement of its contents, three spheres
+forming its first ring, as compared with the units in beryllium and
+calcium, and the pairs in strontium and molybdenum. Two of these spheres
+are identical in their contents--two quintets (7 _f_), a quintet (7 _j_),
+and two quintets (7 _e_), _e_ and _f_ being to each other as object and
+image. The remaining sphere (7 _b_) is identical with the highest in the
+calcium funnel. The remaining two spheres, one below the other, are
+identical with the corresponding two spheres in calcium. The central globe,
+as regards its external segments, is again identical with that of calcium,
+but in the internal segments a six-atomed triangle (7 _k_) is substituted
+for the calcium four-atomed one (7 _e_).
+
+CHROMIUM: 4 funnels of 210 atoms      840
+          Central globe                96
+                                    -----
+                   Total              936
+                                    -----
+          Atomic weight             51.74
+          Number weight 936/18      52.00
+MOLYBDENUM (Plate VIII, 6) very closely resembles strontium, differing from
+it only in the composition of the highest pair of spheres in the funnels
+and in the presence of a little sphere, containing two atoms only, in the
+middle of the central globe. The topmost spheres contain no less than eight
+subsidiary spheres within each; the highest of these (7 _e_) has four atoms
+in it; the next three have four, seven and four (7 _e_ _g_ _e_),
+respectively; the next three are all septets (7 _g_), and the last has
+four--making in all for these two spheres 88 atoms, as against the 48 in
+corresponding spheres of strontium, making a difference of 160 in the four
+funnels.
+
+MOLYBDENUM: 4 funnels of 408 atoms     1632
+            Central globe                98
+                                      -----
+                          Total        1730
+                                      -----
+            Atomic weight             95.26
+            Number weight 1730/18     96.11
+II a.--This group contains magnesium, zinc, cadmium, and mercury, with an
+empty disk between cadmium and mercury; we did not examine mercury. All are
+diatomic, diamagnetic and positive; the corresponding group consists of
+sulphur, selenium and tellurium, also all diatomic and diamagnetic, but
+negative. The same characteristics of four funnels opening on the faces of
+a tetrahedron are found in all, but magnesium and sulphur have no central
+globe, and in cadmium and tellurium the globe has become a cross.
+
+[Illustration: PLATE IX.]
+
+MAGNESIUM (Plate IX, 1) introduces us to a new arrangement: each group of
+three ovoids forms a ring, and the three rings are within a funnel; at
+first glance, there are three bodies in the funnel; on examination each of
+these is seen to consist of three, with other bodies, spheres, again within
+them. Apart from this, the composition is simple enough, all the ovoids
+being alike, and composed of a triplet, a septet and a duad.
+
+MAGNESIUM: 4 funnels of 108 atoms     432
+           Atomic weight            24.18
+           Number weight 432/18     24.00
+ZINC (Plate IX, 2) also brings a new device: the funnel is of the same type
+as that of magnesium, while septets are substituted for the triplets, and
+36 additional atoms are thus slipped in. Then we see four spikes,
+alternating with the funnels and pointing to the angles, each adding 144
+atoms to the total. The spikes show the ten-atomed triangle, already met
+with in other metals, three very regular pillars, each with six spheres,
+containing two, three, four, four, three, two atoms, respectively. The
+supporting spheres are on the model of the central globe, but contain more
+atoms. Funnels and spikes alike radiate from a simple central globe, in
+which five contained spheres are arranged crosswise, preparing for the
+fully developed cross of cadmium. The ends of the cross touch the bottoms
+of the funnels.
+
+ZINC: 4 funnels of 144 atoms        576
+      4 spikes of 144 atoms         576
+      Central globe                  18
+                                  -----
+                        Total      1170
+                                  -----
+         Atomic weight            64.91
+         Number weight 1170/18    65.00
+CADMIUM (Plate IX, 3) has an increased complexity of funnels; the diagram
+shows one of the three similar segments which lie within the funnels as
+cylinders; each of these contains four spheres, three pillars and three
+ovoids, like the spike of zinc turned upside down, and the zinc ten-atomed
+triangle changed into three ten-atomed ovoids. The centre-piece is a new
+form, though prefigured in the central globe of zinc.
+
+CADMIUM:  3 segments of 164 atoms = 492
+          4 funnels of 492 atoms          1968
+          Central body                      48
+                                         -----
+                             Total        2016
+                                         -----
+          Atomic weight                 111.60
+          Number weight 2016/18         112.00
+The corresponding negative group is headed by
+
+[Illustration: PLATE X.]
+
+SULPHUR (Plate X, 1), which, like magnesium, has no central globe, and
+consists simply of the zinc funnels, much less compressed than zinc but the
+same in composition.
+
+SULPHUR: 4 funnels of 144 atoms       576
+         Atomic weight              31.82
+         Number weight 576/18       32.00
+SELENIUM (Plate X, 2) is distinguished by the exquisite peculiarity,
+already noticed, of a quivering star, floating across the mouth of each
+funnel, and dancing violently when a ray of light falls upon it. It is
+known that the conductivity of selenium varies with the intensity of the
+light falling upon it, and it may be that the star is in some way connected
+with its conductivity. It will be seen that the star is a very complicated
+body, and in each of its six points the two five-atomed spheres revolve
+round the seven-atomed cone. The bodies in the funnels resemble those in
+magnesium, but a reversed image of the top one is interposed between itself
+and the small duad, and each pair has its own enclosure. The central globe
+is the same as that of zinc.
+
+SELENIUM: 4 funnels of 198 atoms     792
+          4 stars of 153 atoms       612
+          Central globe               18
+                                   -----
+                         Total      1422
+                                   -----
+          Atomic weight            78.58
+          Number weight 1422/18    79.00
+TELLURIUM (Plate X, 3), it will be seen, closely resembles cadmium, and has
+three cylindrical segments--of which one is figured--making up the funnel.
+The contained bodies in the pillars run three, four, five, four, three,
+two, instead of starting with two; and a quartet replaces a duad in the
+globes above. The central cross only differs from that of cadmium in having
+a seven-atomed instead of a four-atomed centre. So close a similarity is
+striking.
+
+TELLURIUM: 3 segments of 181 atoms = 543
+           4 funnels of 543 atoms          2172
+           Central body                      51
+                                          -----
+                            Total          2223
+                                          -----
+           Atomic weight                 126.64
+           Number weight 2223/18         123.50
+       *       *       *       *       *
+
+V.
+
+We must now consider the ways in which the members of the tetrahedral
+groups break up, and as we proceed with this study we shall find how
+continual are the repetitions, and how Nature, with a limited number of
+fundamental methods, creates by varied combinations her infinite variety of
+forms.
+
+BERYLLIUM (Plate III, 2, and VIII, 1).
+
+[Illustration]
+
+Beryllium offers us four similar funnels and a central globe, and the
+proto-elements consist of these five bodies, set free. The funnel, released
+from pressure, assumes a spherical form, with its four ovoids spinning
+within it, and the central globe remains a sphere, containing a whirling
+cross. On the meta level, the ovoids are set free, and two from each funnel
+are seen to be positive, two negative--sixteen bodies in all, _plus_ the
+cross, in which the resultant force-lines are changed, preparatory to its
+breaking into two duads on the hyper level. On that level, the decades
+disintegrate into two triplets and a quartet, the positive with the
+depressions inward, the negative with the depressions outward.
+
+CALCIUM (Plate VIII, 2).
+
+The funnels, as usual, assume a spherical form on the proto level, and
+show, in each case, three spheres containing ovoids. These spheres, still
+on the proto level, break free from their containing funnel, as in the case
+of gold (p. 49), twelve bodies being thus liberated, while the central
+globe breaks up into eight segments, each of which becomes globular, and
+contains within it a "cigar" and a somewhat heart-shaped body. Four
+spheres, each containing seven ten-atomed ovoids, are identical with those
+in beryllium, and can be followed in its diagram. Eight spheres, each
+containing five nine-atomed ovoids of a different type, set free, on the
+meta level, eighty duads--forty positive and forty negative--and forty
+quintets, which are identical with those in chlorine. On the hyper level,
+the duads become single atoms, within a sphere, and the central atom from
+the quintet is also set free, one hundred and twenty in all. The remaining
+four atoms of the quintet divide into two duads.
+
+The central globe, dividing into eight, becomes eight six-atomed spheres on
+the meta, the "cigar" behaving as usual, four "cigars" being positive and
+four negative, and becoming dissociated into triplets; the four atoms
+within the heart-shaped body appear as a tetrahedron, remain together on
+the meta level, and break up into duads on the hyper.
+
+STRONTIUM (PLATE VIII, 3).
+
+The third member of this group repeats the _a_ groups of beryllium and the
+_b_ groups of calcium, and they dissociate into the bodies already
+described under these respectively. The two upper globes in each funnel
+repeat each other, but each globe contains four smaller spheres showing
+three varieties of forms. The two marked _g_, which are repeated in the
+central globe as _h_, are seven-atomed, and appear as spheres or ovoids
+according to pressure. They are figured on p. 48, under iodine; _e_ and _f_
+are related as object and image, and we have already seen them in copper
+(pp. 38 and 48); in each case, as in copper, they unite into a ten-atomed
+figure; on the meta level the pair of fours form a ring, and the remaining
+two atoms form a duad; _i_, which repeats _f_, makes a ring with the fifth
+in the centre, as in the five-atomed _b_ of calcium, as shown above. There
+is, thus, nothing new in strontium, but only repetitions of forms already
+studied.
+
+OXYGEN (PLATE VIII, 4).
+
+[Illustration]
+
+The disintegration of oxygen as given in 1895 may be repeated here, and the
+better presentation given on p. 54 renders it easier to follow the process.
+On the proto level the two "snakes" divide; the brilliant disks are
+seven-atomed, but are differently arranged, the positive snake having the
+atoms arranged as in the iodine ovoids, whereas the negative snake has them
+arranged as in a capital H. The snakes show the same extraordinary activity
+on the proto level as on the gaseous, twisting and writhing, darting and
+coiling. The body of the snake is of two-atomed beads, positive and
+negative. On the meta level the snakes break into ten fragments, each
+consisting of a disk, with six beads on one side and five on the other,
+remaining as lively as the original snake. They shiver into their
+constituent disks, and beads on the hyper level, there yielding the ten
+disks, five positive and five negative, and the 110 beads, fifty-five
+positive and fifty-five negative.
+
+CHROMIUM (PLATE VIII, 5).
+
+When we go on to chromium and molybdenum, we return to our familiar funnels
+and central globes, and the secondary spheres within the funnels--quickly
+set free, as before, on the proto level--give us no new combinations in
+their contained spheres and ovoids. The _a_ of beryllium, the _b_ of
+calcium and strontium, and _d_ of calcium, the _e_ and _f_ of strontium,
+are all there; _j_ in chromium is the same as the central sphere in the _b_
+ovoid. In the central globe, _k_, is a pair of triangles as in hydrogen,
+consisting of only six atoms, which on the meta level revolve round each
+other, and break up into two duads and two units on the hyper.
+
+MOLYBDENUM (PLATE VIII, 6).
+
+Molybdenum presents us with only two new forms, and these are merely
+four-atomed tetrahedra, occurring in pairs as object and image. All the
+other bodies have already been analysed.
+
+II a.--We come now to the second great tetrahedral group, which though very
+much complicated, is yet, for the most part, a repetition of familiar
+forms.
+
+MAGNESIUM (PLATE IX, 1).
+
+[Illustration]
+
+We are still among tetrahedra, so have to do with four funnels, but each
+funnel contains three rings, and each ring three ovoids; on the proto level
+a triple dissociation takes place, for the funnels let free the rings as
+large spheres, in each of which rotate three twelve-atomed ovoids, and then
+the ovoids break loose from the spheres, and themselves become spherical,
+so that we have finally thirty-six proto compounds from the tetrahedron. On
+the meta level the contained bodies, a triplet, Mg _a_, a septet, Mg _b_,
+and a duad, Mg _c_, are set free from each globe, thus yielding one hundred
+and eight meta compounds. On the hyper level the triplet becomes a duad and
+a unit; the duad becomes two units; and the septet a triplet and a quartet.
+
+ZINC (PLATE IX, 2).
+
+We can leave aside the funnel, for the only difference between it and the
+magnesium funnel is the substitution of a second septet for the triplet,
+and the septet is already shown in the magnesium diagram. We have,
+therefore, only to consider the spikes, pointing to the angles of the
+enclosing tetrahedron, and the central globe. These are set free on the
+proto level and the spikes immediately release their contents, yielding
+thus thirty-two separate bodies.
+
+The triangular arrangement at the top of the spike is the same as occurs in
+copper (_b_ on p. 48), and can be there followed. One of the three similar
+pillars is shown in the accompanying diagram under Zn a. The compressed
+long oval becomes a globe, with six bodies revolving within it in a rather
+peculiar way: the quartets turn round each other in the middle; the
+triplets revolve round them in a slanting ellipse; the duads do the same on
+an ellipse slanting at an angle with the first, somewhat as in gold (_a_
+and _b_, p. 40). The spheres within the globes at the base of the spikes,
+Zn _b_, behave as a cross--the cross is a favourite device in the II _a_
+groups. Finally, the central globe, Zn _c_, follows the same cruciform line
+of disintegration.
+
+CADMIUM (Plate IX, 3).
+
+[Illustration]
+
+Cadmium follows very closely on the lines of zinc; the pillars of the zinc
+spike are reproduced in the rings of the cadmium funnel; the globes are
+also the globes of cadmium; so neither of these needs attention. We have
+only to consider the three ten-atomed ovoids, which are substituted for the
+one ten-atomed triangle of zinc, and the central cross. The ovoids become
+spheres (Cd _a_, _b_), the contained bodies revolving within them, _a_
+whirling on a diameter of the sphere, cutting it in halves, as it were, and
+_b_ whirling round it at right angles; the cross also becomes a sphere (Cd
+_c_), but the cruciform type is maintained within it by the relative
+positions of the contained spheres in their revolution. The subsequent
+stages are shown in the diagram.
+
+SULPHUR (Plate XI, 1).
+
+Sulphur has nothing new, but shows only the funnels already figured in
+magnesium, with the substitution of a second septet for the triplet, as in
+zinc.
+
+SELENIUM (Plate X, 2).
+
+[Illustration]
+
+The funnel of selenium is a re-arrangement of the twelve-atomed ovoids of
+magnesium and the ten-atomed ovoids of cadmium. The funnels, on
+disintegrating, set free twelve groups, each containing nine spheres. On
+the meta level the ten-atomed bodies are set free, and the twelve-atomed
+divide into duads and decads, thus yielding seventy-two decads and
+thirty-six duads; the duads, however, at once recombine into hexads, thus
+giving only twelve meta elements, or eighty-four in all from the funnels.
+The central globe holds together on the proto level, but yields five meta
+elements. The star also at first remains a unit on the proto level, and
+then shoots off into seven bodies, the centre keeping together, and the six
+points becoming spheres, within which the two cones, base to base, whirl in
+the centre, and the globes circle round them. On the meta level all the
+thirty bodies contained in the star separate from each other, and go on
+their independent ways.
+
+Selenium offers a beautiful example of the combination of simple elements
+into a most exquisite whole.
+
+TELLURIUM (Plate X, 3).
+
+Tellurium very closely resembles cadmium, and they are, therefore placed on
+the same diagram. The pillars are the same as in chlorine and its
+congeners, with a duad added at the base. The ten-atomed ovoid is the same
+as in cadmium and follows the same course in breaking up. It would be
+interesting to know why this duad remains as a duad in selenium and breaks
+up into a septad and triad in the other members of the group. It may be due
+to the greater pressure to which it is subjected in selenium, or there may
+be some other reason. The cross in tellurium is identical with that in
+cadmium, except that the centre is seven-atomed instead of four-atomed.
+
+       *       *       *       *       *
+
+VI.
+
+III AND IIIa.--THE CUBE GROUPS.
+
+We have here four groups to consider, all the members of which are triads,
+and have six funnels, opening on the six faces of a cube.
+
+III.--Boron, scandium and yttrium were examined; they are all triatomic,
+paramagnetic, and positive. The corresponding group consists of nitrogen,
+vanadium and niobium; they are triatomic, paramagnetic, and negative. We
+have not examined the remaining members of these groups. In these two
+groups nitrogen dominates, and in order to make the comparison easy the
+nitrogen elements are figured on both Plate XI and Plate XII. It will be
+seen that scandium and yttrium, of the positive group, differ only in
+details from vanadium and niobium, of the negative group; the ground-plan
+on which they are built is the same. We noted a similar close resemblance
+between the positive strontium and the negative molybdenum.
+
+[Illustration: PLATE XI.]
+
+BORON (Plate III, 4, and Plate XI, 1). We have here the simplest form of
+the cube; the funnels contain only five bodies--four six-atomed ovoids and
+one six-atomed "cigar." The central globe has but four five-atomed spheres.
+It is as simple in relation to its congeners as is beryllium to its
+group-members.
+
+BORON: 6 funnels of 30 atoms    180
+       Central globe             20
+                               ----
+                         Total  200
+                               ----
+       Atomic weight          10.86
+       Number weight 200/18   11.11
+SCANDIUM (Plate XI, 2). For the first time we meet funnels of different
+types, A and B, three of each kind; A appear to be positive and B negative,
+but this must be stated with reserve.
+
+In A the boron funnel is reproduced, the "cigar" having risen above its
+companion ovoids; but the most important matter to note in respect to this
+funnel is our introduction to the body marked _a_ 110. This body was
+observed by us first in nitrogen, in 1895, and we gave it the name of the
+"nitrogen balloon," for in nitrogen it takes the balloon form, which it
+also often assumes in other gaseous elements. Here it appears as a
+sphere--the form always assumed on the proto level--and it will be seen, on
+reference to the detailed diagram 4 _a_, to be a complicated body,
+consisting of six fourteen-atomed globes arranged round a long ovoid
+containing spheres with three, four, six, six, four, three, atoms
+respectively. It will be observed that this balloon appears in every member
+of these two groups, except boron.
+
+The B funnel runs largely to triads, _c_ and _b_, _b_ (see 4 _b_) having
+not only a triadic arrangement of spheres within its contained globes, but
+each sphere has also a triplet of atoms. In _c_ (see 4 _c_) there is a
+triadic arrangement of spheres, but each contains duads. B is completed by
+a five-atomed sphere at the top of the funnel. It should be noted that _a_,
+_b_ and _c_ all are constituents of nitrogen.
+
+The central globe repeats that of boron, with an additional four-atomed
+sphere in the middle.
+
+SCANDIUM: 3 funnels (A) of 140 atoms   420
+          3    "    (B) of 116   "     348
+          Centre globe                  24
+                                      ----
+                               Total   792
+                                      ----
+          Atomic weight              43.78
+          Number weight 792/18       44.00
+YTTRIUM (Plate XI, 3). Here we have a quite new arrangement of bodies
+within the funnel--the funnel being of one type only. Two "cigars" whirl on
+their own axes in the centre near the top, while four eight-atomed globes
+(see 4 _e_) chase each other in a circle round them, spinning madly on
+their own axes--this axial spinning seems constant in all contained
+bodies--all the time. Lower down in the funnel, a similar arrangement is
+seen, with a globe (see 4 _d_)--a nitrogen element--replacing the "cigars,"
+and six-atomed ovoids replacing the globes.
+
+The "nitrogen balloon" occupies the third place in the funnel, now showing
+its usual shape in combination, while the _b_ globe (see 4 _b_) of scandium
+takes on a lengthened form below it.
+
+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.
+
+[Illustration: PLATE XII.]
+
+NITROGEN (Plate XII, 1) does not assume the cubical form of its relatives,
+but is in shape like an egg. Referring again to our 1895 investigations, I
+quote from them. The balloon-shaped body (see 4 _a_) floats in the middle
+of the egg, containing six small spheres in two horizontal rows, and a long
+ovoid in the midst; this balloon-shaped body is positive, and is drawn down
+towards the negative body _b_ (see 4 _b_) with its seven contained spheres,
+each of which has nine atoms within it--three triads. Four spheres are
+seen, in addition to the two larger bodies; two of these (see 4 _d_), each
+containing five smaller globes, are positive, and two (see 4 _c_)
+containing four smaller globes, are negative.
+
+NITROGEN: Balloon                         110
+          Oval                             63
+          2 bodies of 20 atoms             40
+          2   "    "  24   "               48
+                                         ----
+                              Total       261
+                                         ----
+          Atomic weight                 14.01
+          Number weight 261/18          14.50
+VANADIUM (Plate XII, 2) closely follows scandium, having two types of
+funnels. Funnel A only differs from that of scandium by having a globe (see
+4 _d_) inserted in the ring of four ovoids; funnel B has a six-atomed,
+instead of a five-atomed globe at the top, and slips a third globe
+containing twenty atoms (see 4 _d_) between the two identical with those of
+scandium (see 4 _c_). The central globe has seven atoms in its middle body
+instead of four. In this way does vanadium succeed in overtopping scandium
+by 126 atoms.
+
+VANADIUM: 3 funnels (A) of 160 atoms      480
+          3    "    (B) "  137   "        411
+          Central globe                    27
+                                         ----
+                              Total       918
+                                         ----
+          Atomic weight                 50.84
+          Number weight 918/18          51.00
+NIOBIUM (Plate XII, 3) is as closely related to yttrium as is vanadium to
+scandium. The little globes that scamper round the "cigars" contain twelve
+atoms instead of eight (see 4 _e_).
+
+The rest of the funnel is the same. In the central globe both the
+tetrahedra have "cigars," and a central nine-atomed globe spins round in
+the centre (see 4 _f_), seventeen atoms being thus added.
+
+NIOBIUM: 6 funnels of 277 atoms        1662
+         Central globe                   57
+                                       ----
+                             Total     1719
+                                       ----
+         Atomic weight                93.25
+         Number weight 1719/18        95.50
+III a.--Aluminium, gallium and indium were examined from this group. They
+are triatomic, diamagnetic, and positive. The corresponding group contains
+phosphorus, arsenic and antimony: bismuth also belongs to it, but was not
+examined; they are triatomic, diamagnetic and negative. They have no
+central globes.
+
+[Illustration: PLATE XIII.]
+
+ALUMINIUM (Plate XIII, 1), the head of the group, is, as usual, simple.
+There are six similar funnels, each containing eight ovoids, below which is
+a globe.
+
+ALUMINIUM: 6 funnels of 81 atoms        486
+           Atomic weight              26.91
+           Number weight 486/18       27.00
+GALLIUM (Plate XIII, 2) has two segments in every funnel; in the segment to
+the left a "cigar" balances a globe, equally six-atomed, in that of the
+right, and the globes to right and left are four-atomed as against
+three-atomed. In the next row, the smaller contained globes have six atoms
+as against four, and the cones have respectively seven and five. By these
+little additions the left-hand funnel boasts one hundred and twelve atoms
+as against ninety-eight.
+
+GALLIUM: Left segment 112 atoms }
+         Right segment 98   "   } = 210
+         6 funnels of 210 atoms         1260
+                                        ----
+         Atomic weight                 69.50
+         Number weight 1260/18         70.00
+INDIUM (Plate XIII, 3) repeats the segments of gallium exactly, save in the
+substitution of a sixteen-atomed body for the seven-atomed cone of the
+left-hand segment, and a fourteen-atomed body for the five-atomed
+corresponding one in gallium. But each funnel now has three segments
+instead of two; three funnels out of the six contain two segments of type A
+and one of type B; the remaining three contain two of type B, and one of
+type A.
+
+INDIUM: Segment A 121 atoms
+        Segment B 107   "
+        3 funnels of 2 A and 1 B ([242 + 107] 3)    1047
+        3    "    "  2 B and 1 A ([214 + 121] 3)    1005
+                                                    ----
+                                         Total      2052
+                                                    ----
+        Atomic weight                             114.05
+        Number weight 2052/18                     114.00
+The corresponding negative group, phosphorus, arsenic, and antimony, run on
+very similar lines to those we have just examined.
+
+[Illustration: PLATE XIV.]
+
+PHOSPHORUS (Plate XIV, 1) offers us a very curious arrangement of atoms,
+which will give some new forms in breaking up. Two segments are in each
+funnel, in fact the only two of group III _a_ which do not show this
+arrangement, or a modification thereof, are aluminium and arsenic.
+
+PHOSPHORUS: Left segment  50 atoms
+            Right segment 43   "
+                          --
+                          93
+            6 funnels of 93 atoms       558
+            Atomic weight             30.77
+            Number weight 558/18      31.00
+ARSENIC (Plate XIV, 2) resembles aluminium in having eight internal
+sub-divisions in a funnel, and the ovoids which form the top ring are
+identical, save for a minute difference that in aluminium the ovoids stand
+the reverse way from those in arsenic. It will be noted that in the former
+the top and bottom triangles of atoms have the apices upwards, and the
+middle one has its apex downwards. In arsenic, the top and bottom ones
+point downwards, and the middle one upwards. Arsenic inserts sixteen
+spheres between the ovoids and globe shown in aluminium, and thus adds no
+less than one hundred and forty-four atoms to each funnel.
+
+ARSENIC: 6 funnels of 225 atoms    1350
+         Atomic weight            74.45
+         Number weight 1350/18    75.00
+ANTIMONY (Plate XIV, 3) is a close copy of indium, and the arrangement of
+types A and B in the funnels is identical. In the middle rings of both A
+and B a triplet is substituted for a unit at the centre of the larger
+globe. In the lowest body of type A the "cigar" has vanished, and is
+represented by a seven-atomed crystalline form.
+
+ANTIMONY: Segment A 128 atoms
+          Segment B 113 atoms
+      3 funnels of 2 A and 1 B ([256 + 113]3)   1107
+      3   "     "  2 B and 1 A ([226 + 128]3)   1056
+                                                ----
+                                     Total      2163
+                                                ----
+      Atomic weight                           119.34
+      Number weight                           120.16
+       *       *       *       *       *
+
+VII.
+
+BORON (Plate III, 4, and Plate XI, 1).
+
+[Illustration]
+
+The disintegration of boron is very simple: the funnels are set free and
+assume the spherical form, showing a central "cigar" and four globes each
+containing two triplets. The central globe is also set free with its four
+quintets, and breaks at once in two. On the meta level the "cigar" breaks
+up as usual, and the triplets separate. On the hyper level, the "cigar"
+follows its usual course, and the triplets become duads and units. The
+globe forms two quintets on the meta level, and these are resolved into
+triplets and duads.
+
+SCANDIUM (Plate XI, 2).
+
+In funnel A the "cigar" and the ovoids behave as in boron, but the
+"balloon," _a_ 110 (XI, 4), escapes from the funnel as it changes to a
+sphere, and holds together on the proto level; on the meta, it yields six
+globes each containing seven duads, and these are all set free as duads on
+the hyper level; the ovoid is also set free on the meta level becoming a
+sphere, and on the hyper level liberates its contained bodies, as two
+triplets, two quartets and two sextets.
+
+In funnel B there is a quintet, that behaves like those in the globe of
+boron, on escaping from the funnel, in which the bodies remain on the proto
+level, with the exception of _b_ 63, which escapes. On the meta level, _c_
+(Plate XI, 4), _c_ assumes a tetrahedral form with six atoms at each point,
+and these hold together as sextets on the hyper level. At the meta stage,
+_b_ (Plate XI, 4 _b_) sets free seven nine-atomed bodies, which become free
+triplets on the hyper. The central globe shows a cross at its centre, with
+the four quintets whirling round it, on the proto level. On the meta, the
+quintets are set free, and follow the boron type, while the cross becomes a
+quartet on the meta level, and two duads on the hyper.
+
+YTTRIUM (Plate XI, 3).
+
+[Illustration]
+
+In yttrium, on the proto level, _a_ 110 and _b_ 63 both escape from the
+funnel, and behave as in scandium. The ovoids and "cigars," set free on the
+meta level, behave as in boron. The central globe breaks up as in gold (pp.
+49 and 50), four quartets being set free instead of two quartets and two
+triplets. We have only to consider _e_ 8 and _d_ 20 (Plate XI, 4). _E_ 8 is
+a tetrahedral arrangement of duads on the meta level, set free as duads on
+the hyper. _D_ 20 is an arrangement of pairs of duads at the angles of a
+square-based pyramid on the meta, and again free duads on the hyper.
+
+NITROGEN (Plate XII, 1).
+
+Nitrogen has nothing new to show us, all its constituents having appeared
+in scandium and yttrium.
+
+VANADIUM (Plate XII, 2).
+
+The A funnel of vanadium repeats the A funnel of scandium, with the
+addition of _d_ 20, already studied. In the B funnel scandium B is
+repeated, with an addition of _d_ 20 and a sextet for a quintet; the sextet
+is the _c_ of the "nitrogen balloon." The central globe follows boron, save
+that it has a septet for its centre; this was figured in iodine (p. 48).
+
+NIOBIUM (Plate XII, 3).
+
+Niobium only differs from yttrium by the introduction of triplets for duads
+in _e_; on the meta level we have therefore triplets, and on the hyper each
+triplet yields a duad and a unit. The only other difference is in the
+central globe. The tetrahedra separate as usual, but liberate eight
+"cigars" instead of four with four quartets; the central body is simple,
+becoming three triads at the angles of a triangle on the meta level, and
+three duads and three units on the hyper.
+
+ALUMINIUM (Plate XIII, 1).
+
+[Illustration]
+
+The funnels let go the globes, but the eight ovoids remain within them, so
+that seven bodies are let loose on the proto level. When the ovoids are set
+free at the meta stage they become spherical and a nine-atomed body is
+produced, which breaks up into triangles on the hyper level. The globe
+becomes a cross at the meta stage, with one atom from the duads at each arm
+in addition to its own, and these form four duads on the hyper, and a unit
+from the centre.
+
+GALLIUM (Plate XIII, 2).
+
+In gallium the funnel disappears on the proto level, setting free its two
+contained segments, each of which forms a cylinder, thus yielding twelve
+bodies on the proto level. On the meta, the three upper globes in each
+left-hand segment are set free, and soon vanish, each liberating a cigar
+and two septets, the quartet and triad uniting. On the hyper the quartet
+yields two duads but the triangle persists. The second set of bodies divide
+on the meta level, forming a sextet and a cross with a duad at each arm;
+these on the hyper level divide into two triangles, four duads and a unit.
+The seven-atomed cone becomes two triangles united by a single atom, and on
+the meta level these form a ring round the unit; on the hyper they form
+three duads and a unit.
+
+In the right-hand segment, the same policy is followed, the four triads
+becoming two sextets, while the central body adds a third to the number.
+The second ring has a quartet instead of the sextet, but otherwise breaks
+up as does that of the left; the quintet at the base follows that of boron.
+
+INDIUM (Plate XIII, 3).
+
+The complication of three segments of different types in each funnel does
+not affect the process of breaking up, and indium needs little attention. A
+is exactly the same as the left-hand funnel of gallium, save for the
+substitution of a globe containing the familiar "cigar" and two
+square-based pyramids. B is the same as the right-hand funnel of gallium,
+except that its lowest body consists of two square-based pyramids and a
+tetrahedron. All these are familiar.
+
+PHOSPHORUS (Plate XIV, 1).
+
+[Illustration]
+
+The atoms in the six similar spheres in the segments of the phosphorus
+funnel are arranged on the eight angles of a cube, and the central one is
+attached to all of them. On the meta level five of the nine atoms hold
+together and place themselves on the angles of a square-based pyramid; the
+remaining four set themselves on the angle of a tetrahedron. They yield, on
+the hyper level, two triads, a duad, and a unit. The remaining bodies are
+simple and familiar.
+
+ARSENIC (Plate XIV, 2).
+
+Arsenic shows the same ovoids and globe as have already been broken up in
+aluminium (see _ante_); the remaining sixteen spheres form nine-atomed
+bodies on the meta level, all similar to those of aluminium, thus yielding
+twelve positive and twelve negative; the globe also yields a nine-atomed
+body, twenty-five bodies of nine.
+
+ANTIMONY (Plate XIV, 3).
+
+Antimony follows closely in the track of gallium and indium, the upper ring
+of spheres being identical. In the second ring, a triplet is substituted
+for the unit, and this apparently throws the cross out of gear, and we have
+a new eleven-atomed figure, which breaks up into a triplet and two quartets
+on the hyper level. The lowest seven-atomed sphere of the three at the base
+is the same as we met with in copper.
+
+       *       *       *       *       *
+
+VIII.
+
+IV.--THE OCTAHEDRAL GROUPS.
+
+These groups are at the turns of the spiral in Sir William Crookes'
+lemniscates (see p. 28). On the one side is carbon, with below it titanium
+and zirconium; on the other silicon, with germanium and tin. The
+characteristic form is an octahedron, rounded at the angles and a little
+depressed between the faces in consequence of the rounding; in fact, we did
+not, at first, recognize it as an octahedron, and we called it the "corded
+bale," the nearest likeness that struck us. The members of the group are
+all tetrads, and have eight funnels, opening on the eight faces of the
+octahedron. The first group is paramagnetic and positive; the corresponding
+one is diamagnetic and negative. The two groups are not closely allied in
+composition, though both titanium and tin have in common the five
+intersecting tetrahedra at their respective centres.
+
+[Illustration: PLATE XV.]
+
+CARBON (Plate III, 5, and XV, 1) gives us the fundamental octahedral form,
+which becomes so masked in titanium and zirconium. As before said (p. 30),
+the protrusion of the arms in these suggests the old Rosicrucian symbol of
+the cross and rose, but they show at their ends the eight carbon funnels
+with their characteristic contents, and thus justify their relationship.
+The funnels are in pairs, one of each pair showing three "cigars," and
+having as its fellow a funnel in which the middle "cigar" is truncated,
+thus loosing one atom. Each "cigar" has a leaf-like body at its base, and
+in the centre of the octahedron is a globe containing four atoms, each
+within its own wall; these lie on the dividing lines of the faces, and each
+holds a pair of the funnels together. It seems as though this atom had been
+economically taken from the "cigar" to form a link. This will be more
+clearly seen when we come to separate the parts from each other. It will be
+noticed that the atoms in the "leaves" at the base vary in arrangement,
+being alternately in a line and in a triangle.
+
+                            { left  27
+CARBON: One pair of funnels { right 22
+                            { centre 1
+                                    --
+                                    54
+        4 pairs of funnels of 54 atoms   216
+        Atomic weight                  11.91
+        Number weight 216/18           12.00
+TITANIUM (Plate III, 6, and XV, 2) has a complete carbon atom distributed
+over the ends of its four arms, a pair of funnels with their linking atom
+being seen in each. Then, in each arm, comes the elaborate body shown as 3
+_c_, with its eighty-eight atoms. A ring of twelve ovoids (3 _d_) each
+holding within itself fourteen atoms, distributed among three contained
+globes--two quartets and a sextet--is a new device for crowding in
+material. Lastly comes the central body (4 _e_) of five intersecting
+tetrahedra, with a "cigar" at each of their twenty points--of which only
+fifteen can be shown in the diagram--and a ring of seven atoms round an
+eighth, that forms the minute centre of the whole. Into this elaborate body
+one hundred and twenty-eight atoms are built.
+
+TITANIUM: One carbon atom               216
+          4 _c_ of 88 atoms        352
+          12 _d_ of 14  "          168
+          Central globe                 128
+                                       ----
+                            Total       864
+                                       ----
+          Atomic weight               47.74
+          Number weight 864/18        48.00
+ZIRCONIUM (Plate XV, 3) has exactly the same outline as titanium, the
+carbon atom is similarly distributed, and the central body is identical.
+Only in 5 _c_ and _d_ do we find a difference on comparing them with 4 _c_
+and d. The _c_ ovoid in zirconium shows no less than fifteen secondary
+globes within the five contained in the ovoid, and these, in turn, contain
+altogether sixty-nine smaller spheres, with two hundred and twelve atoms
+within them, arranged in pairs, triplets, quartets, quintets, a sextet and
+septets. Finally, the ovoids of the ring are also made more elaborate,
+showing thirty-six atoms instead of fourteen. In this way the clever
+builders have piled up in zirconium no less than 1624 atoms.
+
+ZIRCONIUM: One Carbon atom              216
+           4 _c_ of 212 atoms      848
+           12 _d_ of 36   "        432
+           Central globe                128
+                                       ----
+                              Total    1624
+                                       ----
+           Atomic weight              89.85
+           Number weight              90.22
+[Illustration: PLATE XVI.]
+
+SILICON (Plate XVI, 1) is at the head of the group which corresponds to
+carbon on the opposite turn of the lemniscate. It has the usual eight
+funnels, containing four ovoids in a circle, and a truncated "cigar" but no
+central body of any kind. All the funnels are alike.
+
+SILICON: 8 funnels of 65 atoms          520
+         Atomic weight                28.18
+         Number weight 520/18         28.88
+GERMANIUM (Plate XVI, 2) shows the eight funnels, containing each four
+segments (XVI, 4), within which are three ovoids and a "cigar." In this
+case the funnels radiate from a central globe, formed of two intersecting
+tetrahedra, with "cigars" at each point enclosing a four-atomed globe.
+
+GERMANIUM: 8 funnels of 156 atoms     1248
+           Central globe                52
+                                      ----
+                   Total              1300
+                                      ----
+           Atomic weight             71.93
+           Number weight 1300/18     72.22
+TIN (Plate XVI, 3) repeats the funnel of germanium, and the central globe
+we met with in titanium, of five intersecting tetrahedra, carrying twenty
+"cigars"; the latter, however, omits the eight-atomed centre of the globe
+that was found in titanium, and hence has one hundred and twenty atoms
+therein instead of one hundred and twenty-eight. Tin, to make room for the
+necessary increase of atoms, adopts the system of spikes, which we met with
+in zinc (see Plate IX, 2); these spikes, like the funnels, radiate from the
+central globe, but are only six in number. The twenty-one-atomed cone at
+the head of the spike we have already seen in silver, and we shall again
+find it in iridium and platinum; the pillars are new in detail though not
+in principle, the contained globes yielding a series of a triplet, quintet,
+sextet, septet, sextet, quintet, triplet.
+
+TIN: 8 funnels of 156 atoms           1248
+     6 spikes  of 126   "              756
+     Central globe                     120
+                                      ----
+                      Total           2124
+                                      ----
+     Atomic weight                  118.10
+     Number weight 2124/18          118.00
+V.--THE BARS GROUPS.
+
+[Illustration: PLATE XVII.]
+
+Here, for the first time, we find ourselves a little at issue with the
+accepted system of chemistry. Fluorine stands at the head of a
+group--called the inter-periodic--whereof the remaining members are (see
+Crookes' table, p. 28), manganese, iron, cobalt, nickel; ruthenium,
+rhodium, palladium; osmium, iridium, platinum. If we take all these as
+group V, we find that fluorine and manganese are violently forced into
+company with which they have hardly any points of relationship, and that
+they intrude into an otherwise very harmonious group of closely similar
+composition. Moreover, manganese reproduces the characteristic lithium
+"spike" and not the bars of those into whose company it is thrust, and it
+is thus allied with lithium, with which indeed it is almost identical. But
+lithium is placed by Crookes at the head of a group, the other members of
+which are potassium, rubidium and caesium (the last not examined). Following
+these identities of composition, I think it is better to remove manganese
+and fluorine from their incongruous companions and place them with lithium
+and its allies as V _a_, the Spike Groups, marking, by the identity of
+number, similarities of arrangement which exist, and by the separation the
+differences of composition. It is worth while noting what Sir William
+Crookes, in his "Genesis of the Elements," remarks on the relations of the
+interperiodic group with its neighbours. He says: "These bodies are
+interperiodic because their atomic weights exclude them from the small
+periods into which the other elements fall, and because their chemical
+relations with some members of the neighbouring groups show that they are
+probably interperiodic in the sense of being in transition stages."
+
+Group V in every case shows fourteen bars radiating from a centre as shown
+in iron, Plate IV, 1. While the form remains unchanged throughout, the
+increase of weight is gained by adding to the number of atoms contained in
+a bar. The group is made up, not of single chemical elements, as in all
+other cases, but of sub-groups, each containing three elements, and the
+relations within each sub-group are very close; moreover the weights only
+differ by two atoms per bar, making a weight difference of twenty-eight in
+the whole. Thus we have per bar:--
+
+Iron             72        Palladium       136
+Nickel           74        Osmium          245
+Cobalt           76        Iridium         247
+Ruthenium       132        Platinum A      249
+Rhodium         134        Platinum B      257
+It will be noticed (Plate XVII, 3, 4, 5,) that each bar has two sections,
+and that the three lower sections in iron, cobalt and nickel are identical;
+in the upper sections, iron has a cone of twenty-eight atoms, while cobalt
+and nickel have each three ovoids, and of these the middle ones alone
+differ, and that only in their upper globes, this globe being four-atomed
+in cobalt and six-atomed in nickel.
+
+The long ovoids within each bar revolve round the central axis of the bar,
+remaining parallel with it, while each spins on its own axis; the iron cone
+spins round as though impaled on the axis.
+
+        14 bars of 72 atoms            1008
+        Atomic weight                 55.47
+        Number weight 1008/18         56.00
+IRON (Plate IV, 1, and XVII, 3):
+
+        14 bars of 74 atoms            1036
+        Atomic weight                 57.70
+        Number weight 1036/18         57.55
+COBALT (Plate XVII, 4):
+
+        14 bars of 76 atoms             1064
+        Atomic weight                  58.30
+        Number weight 1064/18          59.11
+NICKEL (Plate XVII, 4):
+
+(The weight of cobalt, as given in Erdmann's _Lehrbuch_, is 58.55, but
+Messrs. Parker and Sexton, in _Nature_, August 1, 1907, give the weight, as
+the result of their experiments, as 57.7.)
+
+[Illustration: PLATE XVIII.]
+
+The next sub-group, ruthenium, rhodium, and palladium, has nothing to
+detain us. It will be observed that each bar contains eight segments,
+instead of the six of cobalt and nickel; that ruthenium and palladium have
+the same number of atoms in their upper ovoids, although in ruthenium a
+triplet and quartet represent the septet of palladium; and that in
+ruthenium and rhodium the lower ovoids are identical, though one has the
+order: sixteen, fourteen, sixteen, fourteen; and the other: fourteen,
+sixteen, fourteen, sixteen. One constantly asks oneself: What is the
+significance of these minute changes? Further investigators will probably
+discover the answer.
+
+      14 bars of 132 atoms              1848
+      Atomic weight                   100.91
+      Number weight 1848/18           102.66
+RUTHENIUM (Plate XVIII, 1):
+
+      14 bars of 134 atoms              1876
+      Atomic weight                   102.23
+      Number weight 1876/18           104.22
+RHODIUM (Plate XVII, 2):
+
+      14 bars of 136 atoms              1904
+      Atomic weight                   105.74
+      Number weight 1904/18           105.77
+PALLADIUM (XVIII, 3):
+
+The third sub-group, osmium, iridium and platinum, is, of course, more
+complicated in its composition, but its builders succeed in preserving the
+bar form, gaining the necessary increase by a multiplication of contained
+spheres within the ovoids. Osmium has one peculiarity: the ovoid marked _a_
+(XVIII, 4) takes the place of axis in the upper half of the bar, and the
+three ovoids, marked _b_, revolve round it. In the lower half, the four
+ovoids, _c_, revolve round the central axis. In platinum, we have marked
+two forms as platinum A and platinum B, the latter having two four-atomed
+spheres (XVIII, 6 _b_) in the place of the two triplets marked a. It may
+well be that what we have called platinum B is not a variety of platinum,
+but a new element, the addition of two atoms in a bar being exactly that
+which separates the other elements within each of the sub-groups. It will
+be noticed that the four lower sections of the bars are identical in all
+the members of this sub-group, each ovoid containing thirty atoms. The
+upper ring of ovoids in iridium and platinum A are also identical, but for
+the substitution, in platinum A, of a quartet for a triplet in the second
+and third ovoids; their cones are identical, containing twenty-one atoms,
+like those of silver and tin.
+
+       14 bars of 245 atoms            3430
+       Atomic weight                 189.55
+       Number weight 3430/18         190.55
+OSMIUM (Plate XVIII, 4):
+
+       14 bars of 247 atoms            3458
+       Atomic weight                 191.11
+       Number weight 3458/18         192.11
+IRIDIUM (Plate XVIII, 5):
+
+       14 bars of 249 atoms            3486
+       Atomic weight                 193.66
+       Number weight 3486/18         193.34
+PLATINUM A (Plate XVIII, 6 _a_):
+
+       14 bars of 251 atoms            3514
+       Atomic weight                 ------
+       Number weight 3514/18         195.22
+PLATINUM B (Plate XVIII, 6 _b_):
+
+V a.--THE SPIKE GROUPS.
+
+I place within this group lithium, potassium, rubidium, fluorine, and
+manganese, because of their similarity in internal composition. Manganese
+has fourteen spikes, arranged as in the iron group, but radiating from a
+central globe. Potassium has nine, rubidium has sixteen, in both cases
+radiating from a central globe. Lithium (Plate IV, 2) and fluorine (Plate
+IV, 3) are the two types which dominate the group, lithium supplying the
+spike which is reproduced in all of them, and fluorine the "nitrogen
+balloon" which appears in all save lithium. It will be seen that the
+natural affinities are strongly marked. They are all monads and
+paramagnetic; lithium, potassium and rubidium are positive, while fluorine
+and manganese are negative. We seem thus to have a pair, corresponding with
+each other, as in other cases, and the interperiodic group is left
+interperiodic and congruous within itself.
+
+[Illustration: PLATE XIX.]
+
+LITHIUM (Plate IV, 2 and Plate XIX, 1) is a striking and beautiful form,
+with its upright cone, or spike, its eight radiating petals (_x_) at the
+base of the cone, and the plate-like support in the centre of which is a
+globe, on which the spike rests. The spike revolves swiftly on its axis,
+carrying the petals with it; the plate revolves equally swiftly in the
+opposite direction. Within the spike are two globes and a long ovoid; the
+spheres within the globe revolve as a cross; within the ovoid are four
+spheres containing atoms arranged on tetrahedra, and a central sphere with
+an axis of three atoms surrounded by a spinning wheel of six.
+
+LITHIUM: Spike of 63 atoms                 63
+         8 petals of 6 atoms               48
+         Central globe of 16 atoms         16
+                                         ----
+                               Total      127
+                                         ----
+         Atomic weight                   6.98
+         Number weight 127/18            7.05
+POTASSIUM (Plate XIX, 2) consists of nine radiating lithium spikes, but has
+not petals; its central globe contains one hundred and thirty-four atoms,
+consisting of the "nitrogen balloon," encircled by six four-atomed spheres.
+
+POTASSIUM: 9 bars of 63 atoms             567
+           Central globe                  134
+                                         ----
+                              Total       701
+                                         ----
+           Atomic weight                38.94
+           Number weight 701/18         38.85
+(The weight, as determined by Richards [_Nature_, July 18, 1907] is
+39.114.)
+
+RUBIDIUM: (Plate XIX, 3) adds an ovoid, containing three spheres--two
+triplets and a sextet--to the lithium spike, of which it has sixteen, and
+its central globe is composed of three "balloons."
+
+RUBIDIUM: 16 spikes of 75 atoms          1200
+          Central globe                   330
+                                         ----
+                            Total        1530
+                                         ----
+          Atomic weight                 84.85
+          Number weight 1530/18         85.00
+The corresponding negative group consists only of fluorine and manganese,
+so far as our investigations have gone.
+
+FLUORINE (Plate IV, 3, and Plate XVII, 1) is a most peculiar looking object
+like a projectile, and gives one the impression of being ready to shoot off
+on the smallest provocation. The eight spikes, reversed funnels, coming to
+a point, are probably responsible for this warlike appearance. The
+remainder of the body is occupied by two "balloons."
+
+FLUORINE: 8 spikes of 15 atoms            120
+          2 balloons                      220
+                                         ----
+                             Total        340
+                                         ----
+          Atomic weight                 18.90
+          Number weight 340/18          18.88
+MANGANESE (Plate XVII, 2) has fourteen spikes radiating from a central
+"balloon."
+
+MANGANESE: 14 spikes of 63 atoms          882
+           Central balloon                110
+                                         ----
+                           Total          992
+                                         ----
+           Atomic weight                54.57
+           Number weight 992/18         55.11
+       *       *       *       *       *
+
+IX.
+
+We have now to consider the breaking up of the octahedral groups, and more
+and more, as we proceed, do we find that the most complicated arrangements
+are reducible to simple elements which are already familiar.
+
+CARBON (Plate III, 5, and XV, 1).
+
+[Illustration]
+
+Carbon is the typical octahedron, and a clear understanding of this will
+enable us to follow easily the constitution and disintegration of the
+various members of these groups. Its appearance as a chemical atom is shown
+on Plate III, and see XV, 1. On the proto level the chemical atom breaks up
+into four segments, each consisting of a pair of funnels connected by a
+single atom; this is the proto element which appears at the end of each arm
+of the cross in titanium and zirconium. On the meta level the five
+six-atomed "cigars" show two neutral combinations, and the truncated
+"cigar" of five atoms is also neutral; the "leaves" yield two forms of
+triplet, five different types being thus yielded by each pair of funnels,
+exclusive of the linking atom. The hyper level has triplets, duads and
+units.
+
+TITANIUM (Plate III, 6, and XV, 2, 3).
+
+[Illustration]
+
+On the proto level, the cross breaks up completely, setting free the pairs
+of funnels with the linking atom (_a_ and _b_), as in carbon, the four
+bodies marked _c_, the twelve marked _d_, and the central globe marked e.
+The latter breaks up again, setting free its five intersecting
+cigar-bearing tetrahedra, which follow their usual course (see Occultum, p.
+44). The eight-atomed body in the centre makes a ring of seven atoms round
+a central one, like that in occultum (see p. 44, diagram B), from which it
+only differs in having the central atom, and breaks up similarly, setting
+the central atom free. The ovoid _c_ sets free its four contained globes,
+and the ovoid _d_ sets free the three within it. Thus sixty-one proto
+elements are yielded by titanium. On the meta level, _c_ (titanium 3)
+breaks up into star-like and cruciform bodies; the component parts of these
+are easily followed; on the hyper level, of the four forms of triplets one
+behaves as in carbon, and the others are shown, _a_, _b_ and _f_; the
+cruciform quintet yields a triplet and a duad, _c_ and _d_; the tetrahedra
+yield two triplets _g_ and _h_, and two units; the septet, a triplet _k_
+and a quartet _j_. On the meta level, the bodies from _d_ behave like their
+equivalents in sodium, each _d_ shows two quartets and a sextet, breaking
+up, on the hyper level, into four duads and two triads.
+
+ZIRCONIUM (Plate XV, 2, 5).
+
+Zirconium reproduces in its _c_ the four forms that we have already
+followed in the corresponding _c_ of titanium, and as these are set free on
+the proto level, and follow the same course on the meta and hyper levels,
+we need not repeat them. The central globe of zirconium _c_ sets free its
+nine contained bodies; eight of these are similar and are figured in the
+diagram; it will be observed that the central body is the truncated "cigar"
+of carbon; their behaviour on the meta and hyper levels is easily followed
+there. The central sphere is also figured; the cigar follows its usual
+course, and its companions unite into a sextet and an octet. The _d_ ovoid
+liberates five bodies, four of which we have already seen in titanium, as
+the crosses and sextet of sodium, and which are figured under titanium; the
+four quartets within the larger globe also follow a sodium model, and are
+given again.
+
+SILICON (Plate XVI, 1).
+
+[Illustration]
+
+In silicon, the ovoids are set free from the funnels on the proto level,
+and the truncated "cigar," playing the part of a leaf, is also liberated.
+This, and the four "cigars," which escape from their ovoids, pass along
+their usual course. The quintet and quartet remain together, and form a
+nine-atomed body on the meta level, yielding a sextet and a triplet on the
+hyper.
+
+GERMANIUM (Plate XVI, 2, 4).
+
+The central globe, with its two "cigar"-bearing tetrahedra, need not delay
+us; the tetrahedra are set free and follow the occultum disintegration, and
+the central four atoms is the sodium cross that we had in titanium. The
+ovoids (XVI, 4) are liberated on the proto level, and the "cigar," as
+usual, bursts its way through and goes along its accustomed path. The
+others remain linked on the meta level, and break up into two triangles and
+a quintet on the hyper.
+
+TIN (Plate XVI, 3, 4).
+
+Here we have only the spike to consider, as the funnels are the same as in
+germanium, and the central globe is that of titanium, omitting the eight
+atomed centre. The cone of the spike we have had in silver (see p. 729,
+May), and it is set free on the proto level. The spike, as in zinc, becomes
+a large sphere, with the single septet in the centre, the remaining six
+bodies circling round it on differing planes. They break up as shown. (Tin
+is Sn.)
+
+IRON (Plate IV, I, and XVII, 3).
+
+[Illustration]
+
+We have already dealt with the affinities of this peculiar group, and we
+shall see, in the disintegration, even more clearly, the close
+relationships which exist according to the classification which we here
+follow.
+
+The fourteen bars of iron break asunder on the proto level, and each sets
+free its contents--a cone and three ovoids, which as usual, become spheres.
+The twenty-eight-atomed cone becomes a four-sided figure, and the ovoids
+show crystalline contents. They break up, on the meta level as shown in the
+diagram, and are all reduced to triplets and duads on the hyper level.
+
+COBALT (Plate XVII, 4).
+
+The ovoids in cobalt are identical with those of iron; the higher ovoids,
+which replace the cone of iron, show persistently the crystalline forms so
+noticeable throughout this group.
+
+NICKEL (Plate XVII, 5).
+
+The two additional atoms in a bar, which alone separate nickel from cobalt,
+are seen in the upper sphere of the central ovoid.
+
+RUTHENIUM (Plate XVIII, 1).
+
+The lower ovoids in ruthenium are identical in composition, with those of
+iron, cobalt and nickel and may be studied under Iron. The upper ones only
+differ by the addition of a triplet.
+
+RHODIUM (Plate XVIII, 2).
+
+Rhodium has a septet, which is to be seen in the _c_ of titanium (see _k_
+in the titanium diagram) and differs only in this from its group.
+
+PALLADIUM (Plate XVIII, 3).
+
+In palladium this septet appears as the upper sphere in every ovoid of the
+upper ring.
+
+OSMIUM (Plate XVIII, 4).
+
+We have here no new constituents; the ovoids are set free on the proto
+level and the contained globes on the meta, all being of familiar forms.
+The cigars, as usual, break free on the proto level, and leave their ovoid
+with only four contained spheres, which unite into two nine-atomed bodies
+as in silicon (see above).
+
+IRIDIUM (Plate XVIII, 5.)
+
+The twenty-one-atomed cone of silver here reappears, and its proceedings
+may be followed under that metal (see diagram, p. 729, May). The remaining
+bodies call for no remark.
+
+PLATINUM (Plate XVIII, 6).
+
+Again the silver cone is with us. The remaining bodies are set free on the
+proto level, and their contained spheres on the meta.
+
+LITHIUM (Plate IV, 2, and XIX, 1).
+
+[Illustration]
+
+Here we have some new combinations, which recur persistently in its allies.
+The bodies _a_, in Plate XIX, 1, are at the top and bottom of the ellipse;
+they come to right and left of it in the proto state, and each makes a
+twelve-atomed body on the meta level.
+
+The five bodies within the ellipse, three monads and two sextets, show two
+which we have had before: _d_, which behaves like the quintet and quartet
+in silicon, after their junction, and _b_, which we have had in iron. The
+two bodies _c_ are a variant of the square-based pyramid, one atom at the
+apex, and two at each of the other angles. The globe, _e_, is a new form,
+the four tetrahedra of the proto level making a single twelve-atomed one on
+the meta. The body _a_ splits up into triplets on the hyper; _b_ and _d_
+follow their iron and silicon models; _c_ yields four duads and a unit; _e_
+breaks into four quartets.
+
+POTASSIUM (Plate XIX, 2).
+
+Potassium repeats the lithium spike; the central globe shows the "nitrogen
+balloon," which we already know, and which is surrounded on the proto level
+with six tetrahedra, which are set free on the meta and behave as in
+cobalt. Hence we have nothing new.
+
+RUBIDIUM (Plate XIX, 3).
+
+Again the lithium spike, modified slightly by the introduction of an ovoid,
+in place of the top sphere; the forms here are somewhat unusual, and the
+triangles of the sextet revolve round each other on the meta level; all the
+triads break up on the hyper level into duads and units.
+
+FLUORINE (Plate IV, 3, and Plate XVII, 1).
+
+The reversed funnels of fluorine split asunder on the proto level, and are
+set free, the "balloons" also floating off independently. The funnels, as
+usual, become spheres, and on the meta level set free their contained
+bodies, three quartets and a triplet from each of the eight. The balloons
+disintegrate in the usual way.
+
+MANGANESE (Plate XVII, 2).
+
+Manganese offers us nothing new, being composed of "lithium spikes" and
+"nitrogen balloons."
+
+       *       *       *       *       *
+
+X.
+
+VI.--THE STAR GROUPS.
+
+We have now reached the last of the groups as arranged on Sir William
+Crookes' lemniscates, that forming the "neutral" column; it is headed by
+helium, which is _sui generis_. The remainder are in the form of a flat
+star (see Plate IV, 4), with a centre formed of five intersecting and
+"cigar"-bearing tetrahedra, and six radiating arms. Ten of these have been
+observed, five pairs in which the second member differs but slightly from
+the first; they are: Neon, Meta-neon; Argon, Metargon; Krypton,
+Meta-krypton; Xenon, Meta-xenon; Kalon, Meta-kalon; the last pair and the
+meta forms are not yet discovered by chemists. These all show the presence
+of a periodic law; taking an arm of the star in each of the five pairs, we
+find the number of atoms to be as follows :--
+
+40       99      224      363      489
+47      106      231      370      496
+It will be observed that the meta form in each case shows seven more atoms
+than its fellow.
+
+[Illustration: PLATE XX.]
+
+HELIUM (Plate III, 5, and Plate XX, 1) shows two "cigar"-bearing
+tetrahedra, and two hydrogen triangles, the tetrahedra revolving round an
+egg-shaped central body, and the triangles spinning on their own axes while
+performing a similar revolution. The whole has an attractively airy
+appearance, as of a fairy element.
+
+HELIUM: Two tetrahedra of 24 atoms   48
+        Two triangles of 9 atoms     18
+        Central egg                   6
+                                   ----
+                 Total               72
+                                   ----
+        Atomic weight              3.94
+        Number weight 72/18        4.00
+NEON (Plate XX, 2 and 6) has six arms of the pattern shown in 2, radiating
+from the central globe.
+
+NEON: Six arms of 40 atoms       240
+      Central tetrahedra         120
+
+                                ----
+                   Total         360
+                                ----
+      Atomic weight            19.90
+      Number weight 360/18     20.00
+META-NEON (Plate XX, 3 and 6) differs from its comrade by the insertion of
+an additional atom in each of the groups included in the second body within
+its arm, and substituting a seven-atomed group for one of the triplets in
+neon.
+
+META-NEON: Six arms of 47 atoms    282
+           Central tetrahedra      120
+                                  ----
+Total                              402
+                                  ----
+Atomic weight                     ----
+Number weight 402/18             22.33
+ARGON (Plate XX, 4, 6 and 7) shows within its arms the _b_ 63 which we met
+in nitrogen, yttrium, vanadium and niobium, but not the "balloon," which we
+shall find with it in krypton and its congeners.
+
+ARGON: Six arms of 99 atoms     594
+       Central tetrahedra       120
+                               ----
+                 Total          714
+                               ----
+       Atomic weight          39.60
+       Number weight 714/18   39.66
+METARGON (Plate XX, 5, 6 and 7) again shows only an additional seven atoms
+in each arm.
+
+METARGON: Six arms of 106 atoms   636
+          Central tetrahedra      120
+                                 ----
+                      Total       756
+                                 ----
+Atomic weight                    ----
+Number weight 756/18               42
+[Illustration: PLATE XXI.]
+
+KRYPTON (Plate XXI, 1 and 4, and Plate XX, 6 and 7) contains the nitrogen
+"balloon," elongated by its juxtaposition to _b_ 63. The central tetrahedra
+appear as usual.
+
+KRYPTON:  Six arms of 224 atoms             1344
+          Central tetrahedra                 120
+                                           -----
+                               Total        1464
+                                           -----
+          Atomic weight                    81.20
+          Number weight 1464/18            81.33
+META-KRYPTON differs only from krypton by the substitution of _z_ for _y_
+in each arm of the star.
+
+META-KRYPTON:  Six arms of 231 atoms        1386
+               Central tetrahedra            120
+                                           -----
+                               Total        1506
+                                           -----
+               Atomic weight               -----
+               Number weight 1506/18       83.66
+XENON (Plate XXI, 2 and 4, and Plate XX, 6 and 7) has a peculiarity shared
+only by kalon, that _x_ and _y_ are asymmetrical, the centre of one having
+three atoms and the centre of the other two. Is this done in order to
+preserve the difference of seven from its comrade?
+
+XENON:  Six arms of 363 atoms               2178
+        Central tetrahedra                   120
+                                           -----
+                               Total        2298
+                                           -----
+        Atomic weight                     127.10
+        Number weight 2298/18             127.66
+META-XENON differs from xenon only by the substitution of two _z_'s for _x_
+and _y_.
+
+META-XENON:  Six arms of 370 atoms          2220
+            Central tetrahedra               120
+                                           -----
+                               Total        2340
+                                           -----
+            Atomic weight                  -----
+            Number weight 2340/18            130
+KALON (Plate XXI, 3 and 4, and Plate XX, 6 and 7) has a curious cone,
+possessing a kind of tail which we have not observed elsewhere; _x_ and _y_
+show the same asymmetry as in xenon.
+
+KALON: Six arms of 489 atoms          2934
+       Central tetrahedra              120
+                                      ----
+                            Total     3054
+                                      ----
+       Atomic weight                  ----
+       Number weight 3054/18        169.66
+META-KALON again substitutes two _z_'s for _x_ and _y_.
+
+META-KALON: Six arms of 496 atoms           2976
+            Central tetrahedra               120
+                                            ----
+                            Total           3096
+                                            ----
+            Atomic weight                   ----
+            Number weight 3096/18            172
+Only a few atoms of kalon and meta-kalon have been found in the air of a
+fair-sized room.
+
+It does not seem worth while to break up these elements, for their
+component parts are so familiar. The complicated groups--_a_ 110, _b_ 63
+and _c_ 120--have all been fully dealt with in preceding pages.
+
+       *       *       *       *       *
+
+There remains now only radium, of the elements which we have, so far,
+examined, and that will be now described and will bring to an end this
+series of observations. A piece of close and detailed work of this kind,
+although necessarily imperfect, will have its value in the future, when
+science along its own lines shall have confirmed these researches.
+
+It will have been observed that our weights, obtained by counting, are
+almost invariably slightly in excess of the orthodox ones: it is
+interesting that in the latest report of the International Commission
+(November 13, 1907), printed in the _Proceedings of the Chemical Society of
+London_, Vol. XXIV, No. 33, and issued on January 25, 1908, the weight of
+hydrogen is now taken at 1.008 instead of at 1. This would slightly raise
+all the orthodox weights; thus aluminium rises from 26.91 to 27.1, antimony
+from 119.34 to 120.2, and so on.
+
+       *       *       *       *       *
+
+XI.
+
+RADIUM.
+
+[Illustration: PLATE XXII.]
+
+Radium has the form of a tetrahedron, and it is in the tetrahedral groups
+(see article IV) that we shall find its nearest congeners; calcium,
+strontium, chromium, molybdenum resemble it most closely in general
+internal arrangements, with additions from zinc and cadmium. Radium has a
+complex central sphere (Plate XXII), extraordinarily vivid and living; the
+whirling motion is so rapid that continued accurate observation is very
+difficult; the sphere is more closely compacted than the centre-piece in
+other elements, and is much larger in proportion to the funnels and spikes
+than is the case with the elements above named; reference to Plate VIII
+will show that in these the funnels are much larger than the centres,
+whereas in radium the diameter of the sphere and the length of the funnel
+or spike are about equal. Its heart consists of a globe containing seven
+atoms, which assume on the proto level the prismatic form shown in cadmium,
+magnesium and selenium. This globe is the centre of two crosses, the arms
+of which show respectively three-atomed and two-atomed groups. Round this
+sphere are arranged, as on radii, twenty-four segments, each containing
+five bodies--four quintets and a septet--and six loose atoms, which float
+horizontally across the mouth of the segment; the whole sphere has thus a
+kind of surface of atoms. On the proto level these six atoms in each
+segment gather together and form a "cigar." In the rush of the streams
+presently to be described one of these atoms is occasionally torn away, but
+is generally, if not always, replaced by the capture of another which is
+flung into the vacated space.
+
+Each of the four funnels opens, as usual, on one face of the tetrahedron,
+and they resemble the funnels of strontium and molybdenum but contain three
+pillars instead of four (Plate XXIII). They stand within the funnel as
+though at the angles of a triangle, not side by side. The contained bodies,
+though numerous, contain forms which are all familiar.
+
+The spikes alternate with the funnels, and point to the angles of the
+tetrahedron as in zinc and cadmium; each spike contains three "lithium
+spikes" (see Plate XIX) with a ten-atomed cone or cap at the top, floating
+above the three (Plate XXIV). The "petals" or "cigars" of lithium exist in
+the central globe in the floating atoms, and the four-atomed groups which
+form the lithium "plate" may be seen in the funnels, so that the whole of
+lithium appears in radium.
+
+So much for its composition. But a very peculiar result, so far unobserved
+elsewhere, arises from the extraordinarily rapid whirling of the central
+sphere. A kind of vortex is formed, and there is a constant and powerful
+indraught through the funnels. By this, particles are drawn in from
+without, and these are swept round with the sphere, their temperature
+becoming much raised, and they are then violently shot out through the
+spikes. It is these jets which occasionally sweep away an atom from the
+surface of the sphere. These "particles" may be atoms, or they may be
+bodies from any of the etheric levels; in some cases these bodies break up
+and form new combinations. In fact lithium seems like a kind of vortex of
+creative activity, drawing in, breaking up, recombining, shooting forth--a
+most extraordinary element.
+
+RADIUM: 4 funnels of 618 atoms          2472
+        4 spikes of 199 atoms            796
+        Central sphere                   819
+                                        ----
+                             Total      4087
+                                        ----
+        Atomic weight                   ----
+        Number weight 4087/18         227.05
+[Illustration: PLATE XXIV.]
+
+[Illustration: PLATE XXIII.]
+
+       *       *       *       *       *
+
+APPENDIX.
+
+THE AETHER OF SPACE.
+
+Much discussion has taken place, especially between physicists and
+chemists, over the nature of the substances with which all space must,
+according to scientific hypothesis, be filled. One side contends that it is
+infinitely thinner than the thinnest gas, absolutely frictionless and
+without weight; the other asserts that it is denser than the densest solid.
+In this substance the ultimate atoms of matter are thought to float, like
+motes in a sunbeam, and light, heat and electricity are supposed to be its
+vibrations.
+
+Theosophical investigators, using methods not at the disposal of physical
+science, have found that this hypothesis includes under one head two
+entirely different and widely separated sets of phenomena. They have been
+able to deal with states of matter higher than the gaseous and have
+observed that it is by means of vibrations of this finer matter that light,
+heat and electricity manifest themselves to us. Seeing that matter in these
+higher states thus performs the functions attributed to the ether of
+science, they have (perhaps unadvisedly) called these states etheric, and
+have thus left themselves without a convenient name for that substance
+which fulfils the other part of the scientific requirements.
+
+Let us for the moment name this substance _koilon_, since it fills what we
+are in the habit of calling empty space. What mulaprakrti, or
+"mother-matter," is to the inconceivable totality of universes, koilon is
+to our particular universe--not to our solar system merely but to the vast
+unit which includes all visible suns. Between koilon and mulaprakrti there
+must be various stages, but we have at present no direct means of
+estimating their number or of knowing anything whatever about them.
+
+In an ancient occult treatise, however, we read of a "colorless spiritual
+fluid" "which exists everywhere and forms the first foundation on which our
+solar system is built. Outside the latter, it is found in its pristine
+purity only between the stars [suns] of the universe.... As its substance
+is of a different kind from that known on earth, the inhabitants of the
+latter, seeing _through it_, believe, in their illusion and ignorance, that
+it is empty space. There is not one finger's breadth of void space in the
+whole boundless universe."[21] "The mother-substance" is said, in this
+treatise, to produce this aether of space as its seventh grade of density,
+and all objective suns are said to have this for their "substance."
+
+To any power of sight which we can bring to bear upon it, this koilon
+appears to be homogeneous, though it is probably nothing of the kind, since
+homogeneity can belong to the mother-substance alone. It is out of all
+proportion denser than any other substance known to us, infinitely
+denser--if we may be pardoned the expression; so much denser that it seems
+to belong to another type, or order, of density. But now comes the
+startling part of the investigation: we might expect matter to be a
+densification of this koilon; it is nothing of the kind. Matter is not
+koilon, but _the absence of koilon_, and at first sight, matter and space
+appear to have changed places, and emptiness has become solidity, solidity
+has become emptiness.
+
+To help us to understand this clearly let us examine the ultimate atom of
+the physical plane (see pp. 21-23). It is composed of ten rings or wires,
+which lie side by side, but never touch one another. If one of these wires
+be taken away from the atom, and be, as it were, untwisted from its
+peculiar spiral shape and laid out on a flat surface, it will be seen that
+it is a complete circle--a tightly twisted endless coil. This coil is
+itself a spiral containing 1680 turns; it can be unwound, and it will then
+make a much larger circle. This process of unwinding may be again
+performed, and a still bigger circle obtained, and this can be repeated
+till the seven sets of spirillae are all unwound, and we have a huge circle
+of the tiniest imaginable dots, like pearls threaded on an invisible
+string. These dots are so inconceivably small that many millions of them
+are needed to make one ultimate physical atom, and while the exact number
+is not readily ascertainable, several different lines of calculation agree
+in indicating it as closely approximate to the almost inconceivable total
+of fourteen thousand millions. Where figures are so huge, direct counting
+is obviously impossible, but fortunately the different parts of the atom
+are sufficiently alike to enable us to make an estimate in which the margin
+of error is not likely to be very great. The atom consists of ten wires,
+which divide themselves naturally into two groups--the three which are
+thicker and more prominent, and the seven thinner ones which correspond to
+the colors and planets. These latter appear to be identical in constitution
+though the forces flowing through them must differ, since each responds
+most readily to its own special set of vibrations. By actual counting it
+has been discovered that the numbers of coils or spirillae of the first
+order in each wire is 1680; and the proportion of the different orders of
+spirillae to one another is equal in all cases that have been examined, and
+correspond with the number of dots in the ultimate spirillae of the lowest
+order. The ordinary sevenfold rule works quite accurately with the thinner
+coils, but there is a very curious variation with regard to the set of
+three. As may be seen from the drawings, these are obviously thicker and
+more prominent, and this increase of size is produced by an augmentation
+(so slight as to be barely perceptible) in the proportion to one another of
+the different orders of spirillae and in the number of dots in the lowest.
+This augmentation, amounting at present to not more than .00571428 of the
+whole of each case, suggests the unexpected possibility that this portion
+of the atom may be somehow actually undergoing a change--may in fact be in
+process of growth, as there is reason to suppose that these three thicker
+spirals originally resembled the others.
+
+Since observation shows us that each physical atom is represented by
+forty-nine astral atoms, each astral atom by forty-nine mental atoms, and
+each mental atom by forty-nine of those on the buddhic plane, we have here
+evidently several terms of a regular progressive series, and the natural
+presumption is that the series continues where we are no longer able to
+observe it. Further probability is lent to this assumption by the
+remarkable fact that--if we assume one dot to be what corresponds to an
+atom on the seventh or highest of our planes (as is suggested in _The
+Ancient Wisdom_, p. 42) and then suppose the law of multiplication to begin
+its operation, so that 49 dots shall form the atom of the next or sixth
+plane, 2401 that of the fifth, and so on--we find that the number indicated
+for the physical atom (496) corresponds almost exactly with the calculation
+based upon the actual counting of the coils. Indeed, it seems probable that
+but for the slight growth of the three thicker wires of the atom the
+correspondence would have been perfect.
+
+It must be noted that a physical atom cannot be directly broken up into
+astral atoms. If the unit of force which whirls those millions of dots into
+the complicated shape of a physical atom be pressed back by an effort of
+will over the threshold of the astral plane, the atom disappears instantly,
+for the dots are released. But the same unit of force, working now upon a
+higher level, expresses itself not through one astral atom, but through a
+group of 49. If the process of pressing back the unit of force is repeated,
+so that it energises upon the mental plane, we find the group there
+enlarged to the number of 2401 of those higher atoms. Upon the buddhic
+plane the number of atoms formed by the same amount of force is very much
+greater still--probably the cube of 49 instead of the square, though they
+have not been actually counted. Therefore one physical atom is not
+_composed of_ forty-nine astral or 2401 mental atoms, but _corresponds_ to
+them, in the sense that the force which manifests through it would show
+itself on those higher planes by energising respectively those numbers of
+atoms.
+
+The dots, or beads, seem to be the constituents of all matter of which we,
+at present, know anything; astral, mental and buddhic atoms are built of
+them, so we may fairly regard them as fundamental units, the basis of
+matter.
+
+These units are all alike, spherical and absolutely simple in construction.
+Though they are the basis of all matter, they are not themselves matter;
+they are not blocks but bubbles. They do not resemble bubbles floating in
+the air, which consist of a thin film of water separating the air within
+them from the air outside, so that the film has both an outer and an inner
+surface. Their analogy is rather with the bubbles that we see rising in
+water, before they reach the surface, bubbles which may be said to have
+only one surface--that of the water which is pushed back by the contained
+air. Just as such bubbles are not water, but are precisely the spots from
+which water is absent, so these units are not koilon, but the absence of
+koilon--the only spots where it is not--specks of nothingness floating in
+it, so to speak, for the interior of these space-bubbles is an absolute
+void to the highest power of vision that we can turn upon them.
+
+That is the startling, well-nigh incredible, fact. Matter is nothingness,
+the space obtained by pressing back an infinitely dense substance; Fohat
+"digs holes in space" of a verity, and the holes are the airy
+nothingnesses, the bubbles, of which "solid" universes are built.
+
+What are they, then, these bubbles, or rather, what is their content, the
+force which can blow bubbles in a substance of infinite density? The
+ancients called that force "the Breath," a graphic symbol, which seems to
+imply that they who used it had seen the kosmic process, had seen the LOGOS
+when He breathed into the "waters of space," and made the bubbles which
+build universes. Scientists may call this "Force" by what names they
+will--names are nothing; to us, Theosophists, it is the Breath of the
+LOGOS, we know not whether of the LOGOS of this solar system or of a yet
+mightier Being; the latter would seem the more likely, since in the
+above-quoted occult treatise all visible suns are said to have this as
+their substance.
+
+The Breath of the LOGOS, then, is the force which fills these spaces; His
+the force which holds them open against the tremendous pressure of the
+koilon; they are full of His Life, of Himself, and everything we call
+matter, on however high or low a plane, is instinct with divinity; these
+units of force, of life, the bricks with which He builds His universe, are
+His very life scattered through space; truly is it written: "I established
+this universe with a portion of myself." And when He draws in His breath,
+the waters of space will close in again, and the universe will have
+disappeared. It is only a breath.
+
+The outbreathing which makes these bubbles is quite distinct from, and long
+antecedent to, the three outpourings, or Life-Waves, so familiar to the
+theosophical student. The first Life-Wave catches up these bubbles, and
+whirls them into the various arrangements which we call the atoms of the
+several planes, and aggregates them into the molecules, and on the physical
+plane into the chemical elements. The worlds are built out of these voids,
+these emptinesses, which seem to us "nothing" but are divine force. It is
+matter made from the privation of matter. How true were H.P.B.'s statements
+in "The Secret Doctrine": "Matter is nothing but an aggregation of atomic
+forces" (iii, 398); "Buddha taught that the primitive substance is eternal
+and unchangeable. Its vehicle is the pure luminous aether, the boundless
+infinite space, not a void, resulting from the absence of all forms, but on
+the contrary, the foundation of all forms" (iii, 402).
+
+How vividly, how unmistakably this knowledge brings home to us the great
+doctrine of Maya, the transitoriness and unreality of earthly things, the
+utterly deceptive nature of appearances! When the candidate for initiation
+sees (not merely believes, remember, but actually _sees_) that what has
+always before seemed to him empty space is in reality a solid mass of
+inconceivable density, and that the matter which has appeared to be the one
+tangible and certain basis of things is not only by comparison tenuous as
+gossamer (the "web" spun by "Father-Mother"), but is actually composed of
+emptiness and nothingness--is itself the very negation of matter--then for
+the first time he thoroughly appreciates the valuelessness of the physical
+senses as guides to the truth. Yet even more clearly still stands out the
+glorious certainty of the immanence of the Divine; not only is everything
+ensouled by the LOGOS, but even its visible manifestation is literally part
+of Him, is built of His very substance, so that Matter as well as Spirit
+becomes sacred to the student who really understands.
+
+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 aether. 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 aether 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 AEther," 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 aether 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 aetherial
+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 aether 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 aether. 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 adi-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. Jinarajadasa, 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 maya, 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 mediaeval 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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