Occult Chemistry

Clairvoyant Observations on the

Chemical Elements

by

Annie Besant and Charles W. Leadbeater

Revised Edition edited by A.P. Sinnett

London

THEOSOPHICAL PUBLISHING HOUSE

1, Upper Woburn Place

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.

OCCULT CHEMISTRY.

CHAPTER I.

A PRELIMINARY SURVEY.

The deep interest and importance of the research which this book describes will best be appreciated if introduced by an account of the circumstances out of which it arose. The first edition, consisting mainly of articles reprinted from the Theosophist, dealt at once with the later phases of the research in a way which, though intelligible to the occult student, must have been rather bewildering to the ordinary reader. These later phases, however, endow the earlier results with a significance that in the beginning could only be vaguely conjectured. I am the better entitled to perform the task that has been assigned to me—that of preparing the present edition—by reason of the fact that it was in my presence and at my instigation that the first efforts were made to penetrate the mystery previously enshrouding the ultimate molecule of matter.

I remember the occasion vividly. Mr. Leadbeater was then staying at my house, and his clairvoyant faculties were frequently exercised for the benefit of myself, my wife and the theosophical friends around us. I had discovered that these faculties, exercised in the appropriate direction, were ultra-microscopic in their power. It occurred to me once to ask Mr. Leadbeater if he thought he could actually see a molecule of physical matter. He was quite willing to try, and I suggested a molecule of gold as one which he might try to observe. He made the appropriate effort, and emerged from it saying the molecule in question was far too elaborate a structure to be described. It evidently consisted of an enormous number of some smaller atoms, quite too many to count; quite too complicated in their arrangement to be comprehended. It struck me at once that this might be due to the fact that gold was a heavy metal of high atomic weight, and that observation might be more successful if directed to a body of low atomic weight, so I suggested an atom of hydrogen as possibly more manageable. Mr. Leadbeater accepted the suggestion and tried again. This time he found the atom of hydrogen to be far simpler than the other, so that the minor atoms constituting the hydrogen atom were countable. They were arranged on a definite plan, which will be rendered intelligible by diagrams later on, and were eighteen in number.

We little realized at the moment the enormous significance of this discovery, made in the year 1895, long before the discovery of radium enabled physicists of the ordinary type to improve their acquaintance with the "electron." Whatever name is given to that minute body it is recognised now by ordinary science as well as by occult observation, as the fundamental unit of physical matter. To that extent ordinary science has overtaken the occult research I am dealing with, but that research rapidly carried the occult student into regions of knowledge whither, it is perfectly certain, the ordinary physicist must follow him at no distant date.

The research once started in the way I have described was seen to be intensely interesting. Mrs. Besant almost immediately co-operated with Mr. Leadbeater in its further progress. Encouraged by the success with hydrogen, the two important gases, oxygen and nitrogen, were examined. They proved to be rather more difficult to deal with than hydrogen but were manageable. Oxygen was found to consist of 290 minor atoms and nitrogen of 261. Their grouping will be described later on. The interest and importance of the whole subject will best be appreciated by a rough indication of the results first attained. The reader will then have more patience in following the intricacies of the later discoveries.

The figures just quoted were soon perceived to have a possible significance. The atomic weight of oxygen is commonly taken as 16. That is to say, an atom of oxygen is sixteen times heavier than an atom of hydrogen. In this way, all through the table of atomic weights, hydrogen is taken as unity, without any attempt being made to estimate its absolute weight. But now with the atom of hydrogen dissected, so to speak, and found to consist of 18 somethings, while the atom of oxygen consisted of 290 of the same things, the sixteen to one relationship reappears: 290 divided by 18 gives us 16 and a minute decimal fraction. Again the nitrogen number divided by 18 gives us 14 and a minute fraction as the result, and that is the accepted atomic weight of nitrogen. This gave us a glimpse of a principle that might run all through the table of atomic weights. For reasons having to do with other work, it was impossible for the authors of this book to carry on the research further at the time it was begun. The results already sketched were published as an article in the magazine then called Lucifer, in November, 1895, and reprinted as a separate pamphlet bearing the title "Occult Chemistry," a pamphlet the surviving copies of which will one day be a recognised vindication of the method that will at some time in the future be generally applied to the investigation of Nature's mysteries. For the later research which this volume deals with does establish the principle with a force that can hardly be resisted by any fair-minded reader. With patience and industry—the authors being assisted in the counting in a way that will be described (and the method adopted involved a check upon the accuracy of the counting)—the minor atoms of almost all the known chemical elements, as they are commonly called, were counted and found to bear the same relation to their atomic weights as had been suggested by the cases of oxygen and nitrogen. This result throws back complete proof on the original estimate of the number of minor atoms in hydrogen, a figure which ordinary research has so far entirely failed to determine. The guesses have been widely various, from unity to many hundreds, but, unacquainted with the clairvoyant method, the ordinary physicist has no means of reaching the actual state of the facts.

Before going on with the details of the later research some very important discoveries arising from the early work must first be explained. As I have already said clairvoyant faculty of the appropriate order directed to the minute phenomena of Nature is practically infinite in its range. Not content with estimating the number of minor atoms in physical molecules, the authors proceeded to examine the minor atoms individually. They were found to be themselves elaborately complicated structures which, in this preliminary survey of the whole subject, I will not stop to explain (full explanation will be found later on) and they are composed of atoms belonging to an ultra-physical realm of Nature with which the occultist has long been familiar and describes as "the Astral Plane." Some rather pedantic critics have found fault with the term, as the "plane" in question is of course really a sphere entirely surrounding the physical globe, but as all occultists understand the word, "plane" simply signifies a condition of nature. Each condition, and there are many more than the two under consideration, blends with its neighbour, via atomic structure. Thus the atoms of the Astral plane in combination give rise to the finest variety of physical matter, the ether of space, which is not homogeneous but really atomic in its character, and the minute atoms of which physical molecules are composed are atoms of ether, "etheric atoms," as we have now learned to call them.

Many physicists, though not all, will resent the idea of treating the ether of space as atomic. But at all events the occultist has the satisfaction of knowing that the great Russian chemist, Mendeleef, preferred the atomic theory. In Sir William Tilden's recent book entitled "Chemical Discovery and Invention in the Twentieth Century," I read that Mendeleef, "disregarding conventional views," supposed the ether to have a molecular or atomic structure, and in time all physicists must come to recognise that the Electron is not, as so many suppose at present, an atom of electricity, but an atom of ether carrying a definite unit charge of electricity.

Long before the discovery of radium led to the recognition of the electron as the common constituent of all the bodies previously described as chemical elements, the minute particles of matter in question had been identified with the cathode rays observed in Sir William Crookes' vacuum tubes. When an electric current is passed through a tube from which the air (or other gas it may contain) has been almost entirely exhausted, a luminous glow pervades the tube manifestly emanating from the cathode or negative pole of the circuit. This effect was studied by Sir William Crookes very profoundly. Among other characteristics it was found that, if a minute windmill was set up in the tube before it was exhausted, the cathode ray caused the vanes to revolve, thus suggesting the idea that they consisted of actual particles driven against the vanes; the ray being thus evidently something more than a mere luminous effect. Here was a mechanical energy to be explained, and at the first glance it seemed difficult to reconcile the facts observed with the idea creeping into favour, that the particles, already invested with the name "electron," were atoms of electricity pure and simple. Electricity was found, or certain eminent physicists thought they had found, that electricity per se had inertia. So the windmills in the Crookes' vacuum tubes were supposed to be moved by the impact of electric atoms.

Then in the progress of ordinary research the discovery of radium by Madame Curie in the year 1902 put an entirely new face upon the subject of electrons. The beta particles emanating from radium were soon identified with the electrons of the cathode ray. Then followed the discovery that the gas helium, previously treated as a separate element, evolved itself as one consequence of the disintegration of radium. Transmutation, till then laughed at as a superstition of the alchemist, passed quietly into the region of accepted natural phenomena, and the chemical elements were seen to be bodies built up of electrons in varying number and probably in varying arrangements. So at last ordinary science had reached one important result of the occult research carried on seven years earlier. It has not yet reached the finer results of the occult research—the structure of the hydrogen atom with its eighteen etheric atoms and the way in which the atomic weights of all elements are explained by the number of etheric atoms entering into their constitution.

The ether of space, though defying instrumental examination, comes within scope of the clairvoyant faculty, and profoundly interesting discoveries were made during what I have called the early research in connexion with that branch of the inquiry. Etheric atoms combine to form molecules in many different ways, but combinations involving fewer atoms than the eighteen which give rise to hydrogen, make no impression on the physical senses nor on physical instruments of research. They give rise to varieties of molecular ether, the comprehension of which begins to illuminate realms of natural mystery as yet entirely untrodden by the ordinary physicist. Combinations below 18 in number give rise to three varieties of molecular ether, the functions of which when they come to be more fully studied will constitute a department of natural knowledge on the threshold of which we already stand. Some day we may perhaps be presented with a volume on Occult Physics as important in its way as the present dissertation on Occult Chemistry.

CHAPTER II.

DETAILS OF THE EARLY RESEARCH.

The article detailing the results of the research carried on in the year 1895 (see the November issue for that year of the magazine then called Lucifer), began with some general remarks about the clairvoyant faculty, already discussed in the preceding chapter. The original record then goes on as follows:—

The physical world is regarded as being composed of between sixty and seventy chemical elements, aggregated into an infinite variety of combinations. These combinations fall under the three main heads of solids, liquids and gases, the recognised substates of physical matter, with the theoretical ether scarcely admitted as material. Ether, to the scientist, is not a substate or even a state of matter, but is a something apart by itself. It would not be allowed that gold could be raised to the etheric condition as it might be to the liquid and gaseous; whereas the occultist knows that the gaseous is succeeded by the etheric, as the solid is succeeded by the liquid, and he knows also that the word "ether" covers four substates as distinct from each other as are the solids, liquids and gases, and that all chemical elements have their four etheric substates, the highest being common to all, and consisting of the ultimate physical atoms to which all elements are finally reducible. The chemical atom is regarded as the ultimate particle of any element, and is supposed to be indivisible and unable to exist in a free state. Mr. Crookes' researches have led the more advanced chemists to regard the atoms as compound, as a more or less complex aggregation of protyle.

To astral vision ether is a visible thing, and is seen permeating all substances and encircling every particle. A "solid" body is a body composed of a vast number of particles suspended in ether, each vibrating backwards and forwards in a particular field at a high rate of velocity; the particles are attracted towards each other more strongly than they are attracted by external influences, and they "cohere," or maintain towards each other a definite relation in space. Closer examination shows that the ether is not homogeneous but consists of particles of numerous kinds, differing in the aggregations of the minute bodies composing them; and a careful and more detailed method of analysis reveals that it has four distinct degrees, giving us, with the solid, liquid and gaseous, seven instead of four substates of matter in the physical world.

These four etheric substates will be best understood if the method be explained by which they were studied. This method consisted of taking what is called an atom of gas, and breaking it up time after time, until what proved to be the ultimate physical atom was reached, the breaking up of this last resulting in the production of astral, and no longer physical matter.

It is, of course, impossible to convey by words the clear conceptions that are gained by direct vision of the objects of study, and the accompanying diagram—cleverly drawn from the description given by the investigators—is offered as a substitute, however poor, for the lacking vision of the readers. The horizontal lines separate from each other the seven substates of matter; solid, liquid, gas, ether 4, ether 3, ether 2, ether 1. On the gas level are represented three chemical atoms, one of hydrogen (H), one of oxygen (O), one of nitrogen (N). The successive changes undergone by each chemical atom are shown in the compartments vertically above it, the left-hand column showing the breaking up of the hydrogen atom, the middle column that of the oxygen atom, the right-hand column, that of the nitrogen atom. The ultimate physical atom is marked a, and is drawn only once, although it is the same throughout. The numbers 18, 290 and 261 are the numbers of the ultimate physical atoms found to exist in a chemical atom.

The dots indicate the lines along which force is observed to be playing, and the arrowheads show the direction of the force. No attempt has been made to show this below E 2 except in the case of the hydrogen. The letters given are intended to help the reader to trace upwards any special body; thus d in the oxygen chemical atom on the gas level may be found again on E 4, E 3, and E 2. It must be remembered that the bodies shown diagrammatically in no way indicate relative size; as a body is raised from one substate to the one immediately above it, it is enormously magnified for the purpose of investigation, and the ultimate atom on E 1 is represented by the dot a on the gaseous level.

The first chemical atom selected for this examination was an atom of hydrogen (H). On looking carefully at it, it was seen to consist of six small bodies, contained in an egg-like form. It rotated with great rapidity on its own axis, vibrating at the same time, and the internal bodies performed similar gyrations. The whole atom spins and quivers, and has to be steadied before exact observation is possible. The six little bodies are arranged in two sets of three, forming two triangles that are not interchangeable, but are related to each other as object and image. (The lines in the diagram of it on the gaseous sub-plane are not lines of force, but show the two triangles; on a plane surface the interpenetration of the triangles cannot be clearly indicated.) Further, the six bodies are not all alike; they each contain three smaller bodies—each of these being an ultimate physical atom—but in two of them the three atoms are arranged in a line, while in the remaining four they are arranged in a triangle.

The wall of the limiting spheroid in which the bodies are enclosed being composed of the matter of the third, or gaseous, kind, drops away when the gaseous atom is raised to the next level, and the six bodies are set free. They at once re-arrange themselves in two triangles, each enclosed by a limiting sphere; the two marked b in the diagram unite with one of those marked b' to form a body which shows a positive character, the remaining three forming a second body negative in type. These form the hydrogen particles of the lowest plane of ether, marked E 4—ether 4—on the diagram. On raising these further, they undergo another disintegration, losing their limiting walls; the positive body of E 4, on losing its wall, becomes two bodies, one consisting of the two particles, marked b, distinguishable by the linear arrangement of the contained ultimate atoms, enclosed in a wall, and the other being the third body enclosed in E 4 and now set free. The negative body of E 4 similarly, on losing its wall, becomes two bodies, one consisting of the two particles marked b', and the second the remaining body, being set free. These free bodies do not remain on E 3 but pass immediately to E 2, leaving the positive and negative bodies, each containing two particles, as the representatives of hydrogen on E 3. On taking these bodies a step higher their wall disappears, and the internal bodies are set free, those containing the atoms arranged lineally being positive, and those with the triangular arrangement being negative. These two forms represent hydrogen on E 2, but similar bodies of this state of matter are found entering into other combinations, as may be seen by referring to f on E 2 of nitrogen (N). On raising these bodies yet one step further, the falling away of the walls sets the contained atoms free, and we reach the ultimate physical atom, the matter of E 1. The disintegration of this sets free particles of astral matter, so that we have reached in this the limit of physical matter. The Theosophical reader will notice with interest that we can thus observe seven distinct substates of physical matter, and no more.

The ultimate atom, which is the same in all the observed cases, is an exceedingly complex body, and only its main characteristics are given in the diagram. It is composed entirely of spirals, the spiral being in its turn composed of spirillæ, and these again of minuter spirillæ. A fairly accurate drawing is given in Babbitt's "Principles of Light and Colour," p. 102. The illustrations there given of atomic combinations are entirely wrong and misleading, but if the stove-pipe run through the centre of the single atom be removed, the picture may be taken as correct, and will give some idea of the complexity of this fundamental unit of the physical universe.

Turning to the force side of the atom and its combinations, we observe that force pours in the heart-shaped depression at the top of the atom, and issues from the point, and is changed in character by its passage; further, force rushes through every spiral and every spirilla, and the changing shades of colour that flash out from the rapidly revolving and vibrating atom depend on the several activities of the spirals; sometimes one, sometimes another, is thrown into more energetic action, and with the change of activity from one spiral to another the colour changes.

The building of a gaseous atom of hydrogen may be traced downward from E 1, and, as stated above, the lines given in the diagram are intended to indicate the play of the forces which bring about the several combinations. Speaking generally, positive bodies are marked by their contained atoms setting their points towards each other and the centre of their combination, and repelling each other outwards; negative bodies are marked by the heart-shaped depressions being turned inwards, and by a tendency to move towards each other instead of away. Every combination begins by a welling up of force at a centre, which is to form the centre of the combination; in the first positive hydrogen combination, E 2, an atom revolving at right angles to the plane of the paper and also revolving on its own axis, forms the centre, and force, rushing out at its lower point, rushes in at the depressions of two other atoms, which then set themselves with their points to the centre; the lines are shown in +b, right-hand figure. (The left-hand figure indicates the revolution of the atoms each by itself.) As this atomic triad whirls round, it clears itself a space, pressing back the undifferentiated matter of the plane, and making to itself a whirling wall of this matter, thus taking the first step towards building up the chemical hydrogen atom. A negative atomic triad is similarly formed, the three atoms being symmetrically arranged round the centre of out-welling force. These atomic triads then combine, two of the linear arrangement being attracted to each other, and two of the triangular, force again welling up and forming a centre and acting on the triads as on a single atom, and a limiting wall being again formed as the combination revolves round its centre. The next stage is produced by each of these combinations on E 3 attracting to itself a third atomic triad of the triangular type from E 2, by the setting up of a new centre of up-welling force, following the lines traced in the combinations of E 4. Two of these uniting, and their triangles interpenetrating, the chemical atom is formed, and we find it to contain in all eighteen ultimate physical atoms.

The next substance investigated was oxygen, a far more complicated and puzzling body; the difficulties of observation were very much increased by the extraordinary activity shown by this element and the dazzling brilliancy of some of its constituents. The gaseous atom is an ovoid body, within which a spirally-coiled snake-like body revolves at a high velocity, five brilliant points of light shining on the coils. The snake appears to be a solid rounded body, but on raising the atom to E 4 the snake splits lengthwise into two waved bodies, and it is seen that the appearance of solidity is due to the fact that these spin round a common axis in opposite directions, and so present a continuous surface, as a ring of fire can be made by whirling a lighted stick. The brilliant bodies seen in the atom are on the crests of the waves in the positive snake, and in the hollows in the negative one; the snake itself consists of small bead-like bodies, eleven of which interpose between the larger brilliant spots. On raising these bodies to E 3 the snakes break up, each bright spot carrying with it six beads on one side and five on the other; these twist and writhe about still with the same extraordinary activity, reminding one of fire-flies stimulated to wild gyrations. It can been seen that the larger brilliant bodies each enclose seven ultimate atoms, while the beads each enclose two. (Each bright spot with its eleven beads is enclosed in a wall, accidentally omitted in the diagram.) On the next stage, E 2, the fragments of the snakes break up into their constituent parts; the positive and negative bodies, marked d and d', showing a difference of arrangement of the atoms contained in them. These again finally disintegrate, setting free the ultimate physical atoms, identical with those obtained from hydrogen. The number of ultimate atoms contained in the gaseous atom of oxygen is 290, made up as follows:—

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

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

290 / 18 = 16.11 +

The respective number of ultimate atoms contained in a chemical atom of these two bodies are thus seen to closely correspond with their accepted weight-numbers.

It may be said in passing that a chemical atom of ozone appears as an oblate spheroid, with the contained spiral much compressed and widened in the centre; the spiral consists of three snakes, one positive and two negative, formed in a single revolving body. On raising the chemical atom to the next plane, the snake divides into three, each being enclosed in its own egg.

The chemical atom of nitrogen was the third selected by the students for examination, as it seemed comparatively quiet in contrast with the ever-excited oxygen. It proved, however, to be the most complicated of all in its internal arrangements, and its quiet was therefore a little deceptive. Most prominent was the balloon-shaped body in the middle, with six smaller bodies in two horizontal rows and one large egg-shaped one in the midst, contained in it. Some chemical atoms were seen in which the internal arrangement of these contained bodies was changed and the two horizontal rows became vertical; this change seemed to be connected with a greater activity of the whole body, but the observations on this head are too incomplete to be reliable. The balloon-shaped body is positive, and is apparently drawn downwards towards the negative egg-shaped body below it, containing seven smaller particles. In addition to these large bodies, four small ones are seen, two positive and two negative, the positive containing five and the negative four minuter spots. On raising the gaseous atom to E 4, the falling away of the wall sets free the six contained bodies, and both the balloon and the egg round themselves, apparently with the removal of their propinquity, as though they had exercised over each other some attractive influence. The smaller bodies within the egg—marked q on E 4—are not on one plane, and those within n and o form respectively square-based and triangular-based pyramids. On raising all these bodies to E 3 we find the walls fall away as usual, and the contents of each "cell" are set free: p of E 4 contains six small bodies marked k, and these are shown in k of E 3, as containing each seven little bodies—marked e—each of which has within it two ultimate atoms; the long form of p E 4—marked l—appears as the long form l on E 3, and this has three pairs of smaller bodies within it, f', g and h, containing respectively three, four and six ultimate atoms; q of E 4, with its seven contained particles, m, has three particles m on E 3, each showing three ultimate atoms within them; e from n of E 4 becomes i of E 3, with contained bodies, e, showing two ultimate atoms in each; while e' from o of E 4 becomes j of E 3, each having three smaller bodies within it, e', with two ultimate atoms in each. On E 2, the arrangement of these ultimate atoms is shown, and the pairs, f', g and h are seen with the lines of force indicated; the triads in f—from m of E 3—are similarly shown, and the duads in e and e'—from i and j of E 3—are given in the same way. When all these bodies are raised to E 1, the ultimate physical atoms are set free, identical, of course, with that previously described. Reckoning up the number of ultimate physical atoms in a chemical atom of nitrogen we find they amount to 261, thus divided:—

62 + bodies with 2 ultimate atoms, 62 x 2 = 124

24 - " " 2 " " 24 x 2 = 48

21 - " " 3 " " 21 x 3 = 63

2 + " " 3 " " 2 x 3 = 6

2 + " " 4 " " 2 x 4 = 8

2 + " " 4 " " 2 x 6 = 12

----

261



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

261 / 18 =14.44 +

This is interesting as checking the observations, for weight-numbers are arrived at in so very different a fashion, and especially in the case of nitrogen the approximation is noteworthy, from the complexity of the bodies which yield the number on analysis.

Some other observations were made which went to show that as weight-numbers increased, there was a corresponding increase in the number of bodies discerned within the chemical atom; thus, gold showed forty-seven contained bodies; but these observations need repetition and checking. Investigation of a molecule of water revealed the presence of twelve bodies from hydrogen and the characteristic snake of oxygen, the encircling walls of the chemical atoms being broken away. But here again, further observations are necessary to substantiate details. The present paper is only offered as a suggestion of an inviting line of research, promising interesting results of a scientific character; the observations recorded have been repeated several times and are not the work of a single investigator, and they are believed to be correct so far as they go.

THE PLATONIC SOLIDS.

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

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

It will be seen that the tetrahedron is the fundamental form, the three-sided pyramid on a triangular base, i.e., a solid figure formed from four triangles. Two of these generate the cube and the octahedron; five of these generate the dodecahedron and the icosahedron.

The rhombic dodecahedron is not regular, for though the lines and surfaces are equal, the angles are not.

NOTES.

Mr. C. Jinarâjadâsa[1] writes:

The asterisk put before metargon in the list of elements should be omitted, for metargon had been discovered by Sir William Ramsey and Mr. Travers at the same time as neon (see Proceedings of the Royal Society, vol. lxiii, p. 411), and therefore before it was observed clairvoyantly. It is not, however, given in the latest list of elements in the Report of November 13, 1907, of the International Atomic Weights Commission, so it would seem as though it were not yet fully recognised.

Neon was discovered in 1898 by Ramsey and Travers, and the weight given to it was 22. This almost corresponds with our weight for meta-neon, 22.33; the latest weight given to neon is 20, and that corresponds within one-tenth to our weight, 19.9. From this it would seem that neon was examined in the later investigations and meta-neon in the earlier.

He says further on a probable fourth Interperiodic Group:

Thinking over the diagrams, it seemed to me likely that a fourth group exists, coming on the paramagnetic side, directly under iron, cobalt, nickel, just one complete swing of the pendulum after rhodium, ruthenium, palladium. This would make four interperiodic groups, and they would come also periodically in the table too.

I took the diagram for Osmium, and in a bar postulated only three columns for the first element of the new groups, i.e., one column less than in Osmium. This would make 183 atoms in a bar; the new group then would follow in a bar, 183, 185, 187. Here I found to my surprise that the third postulated group would have a remarkable relation to Os, Ir, Pt.

Thus

Os.--245 (in a bar); less 60 = 185

Ir. 247 less 60 = 187

Pt. 249 less 60 = 189



But strange to say also

Ruthenium (bar) 132 less 60--72

Rhodium 134 less 60--74

Palladium 136 less 60--76



But 72, 74, 76, are Iron, Cobalt and Nickel.

So there does probably exist a new group with bars (183), 185, 187, 189, with atomic weights.

X=bar 185; atoms 2590, wt. 143.3

Y= 187, 2618, wt. 145.4

Z= 189, 2646, wt. 147.0.



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

CHAPTER III.

THE LATER RESEARCHES.

The first difficulty that faced us was the identification of the forms seen on focusing the sight on gases.[2] We could only proceed tentatively. Thus, a very common form in the air had a sort of dumb-bell shape (see Plate I); we examined this, comparing our rough sketches, and counted its atoms; these, divided by 18—the number of ultimate atoms in hydrogen—gave us 23.22 as atomic weight, and this offered the presumption that it was sodium. We then took various substances—common salt, etc.—in which we knew sodium was present, and found the dumb-bell form in all. In other cases, we took small fragments of metals, as iron, tin, zinc, silver, gold; in others, again, pieces of ore, mineral waters, etc., etc., and, for the rarest substances, Mr. Leadbeater visited a mineralogical museum. In all, 57 chemical elements were examined, out of the 78 recognized by modern chemistry.

In addition to these, we found 3 chemical waifs: an unrecognized stranger between hydrogen and helium which we named occultum, for purposes of reference, and 2 varieties of one element, which we named kalon and meta-kalon, between xenon and osmium; we also found 4 varieties of 4 recognized elements and prefixed meta to the name of each, and a second form of platinum, that we named Pt. B. Thus we have tabulated in all 65 chemical elements, or chemical atoms, completing three of Sir William Crookes' lemniscates, sufficient for some amount of generalization.

Plate I. Sodium .

In counting the number of ultimate atoms in a chemical elemental atom, we did not count them throughout, one by one; when, for instance, we counted up the ultimate atoms in sodium, we dictated the number in each convenient group to Mr. Jinarâjadâsa, and he multiplied out the total, divided by 18, and announced the result. Thus: sodium (see Plate I) is composed of an upper part, divisible into a globe and 12 funnels; a lower part, similarly divided; and a connecting rod. We counted the number in the upper part: globe—10; the number in two or three of the funnels—each 16; the number of funnels—12; the same for the lower part; in the connecting rod—14. Mr. Jinarâjadâsa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418: divided by 18 = 23.22 recurring. By this method we guarded our counting from any prepossession, as it was impossible for us to know how the various numbers would result on addition, multiplication and division, and the exciting moment came when we waited to see if our results endorsed or approached any accepted weight. In the heavier elements, such as gold, with 3546 atoms, it would have been impossible to count each atom without quite unnecessary waste of time, when making a preliminary investigation. Later, it may be worth while to count each division separately, as in some we noticed that two groups, at first sight alike, differed by 1 or 2 atoms, and some very slight errors may, in this way, have crept into our calculations.

In the following table is a list of the chemical elements examined; the first column gives the names, the asterisk affixed to some indicating that they have not yet been discovered by orthodox chemistry. The second column gives the number of ultimate physical atoms contained in one chemical atom of the element concerned. The third column gives the weight as compared with hydrogen, taken as 18, and this is obtained by dividing the calculated number of ultimate atoms by 18. The fourth column gives the recognized weight-number, mostly according to the latest list of atomic weights, the "International List" of 1905, given in Erdmann's "Lehrbuch der Unorganischen Chemie." These weights differ from those hitherto accepted, and are generally lighter than those given in earlier text-books. It is interesting to note that our counting endorses the earlier numbers, for the most part, and we must wait to see if later observations will endorse the last results of orthodox chemistry, or confirm ours.

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

Hydrogen | 18 | 1 | 1

*Occultum | 54 | 3 | --

Helium | 72 | 4 | 3.94

Lithium | 127 | 7.06 | 6.98

Baryllium | 164 | 9.11 | 9.01

Boron | 200 | 11.11 | 10.86

Carbon | 216 | 12 | 11.91

Nitrogen | 261 | 14.50 | 14.01

Oxygen | 290 | 16.11 | 15.879

Fluorine | 340 | 18.88 | 18.90

Neon | 360 | 20 | 19.9

*Meta-Neon | 402 | 22.33 | --

Sodium | 418 | 23.22 | 22.88

Magnesium | 432 | 24 | 24.18

Aluminium | 486 | 27 | 26.91

Silicon | 520 | 28.88 | 28.18

Phosphorus | 558 | 31 | 30.77

Sulphur | 576 | 32 | 31.82

Chlorine | 639 | 35.50 | 35.473

Potassium | 701 | 38.944 | 38.85

Argon | 714 | 39.66 | 39.60

Calcium | 720 | 40 | 39.74

*Metargon | 756 | 42 | --

Scandium | 792 | 44 | 43.78

Titanium | 864 | 48 | 47.74

Vanadium | 918 | 51 | 50.84

Chromium | 936 | 52 | 51.74

Manganese | 992 | 55.11 | 54.57

Iron | 1008 | 56 | 55.47

Cobalt | 1036 | 57.55 | 57.7

Nickel | 1064 | 59.ll | 58.30

Copper | 1139 | 63.277 | 63.12

Zinc | 1170 | 65 | 64.91

Gallium | 1260 | 70 | 69.50

Germanium | 1300 | 72.22 | 71.93

Arsenic | 1350 | 75 | 74.45

Selenium | 1422 | 79 | 78.58

Bromine | 1439 | 79.944 | 79.953

Krypton | 1464 | 81.33 | 81.20

*Meta-Krypton | 1506 | 83.66 | --

Rubidium | 1530 | 85 | 84.85

Strontium | 1568 | 87.11 | 86.95

Yttrium | 1606 | 89.22 | 88.34

Zirconium | 1624 | 90.22 | 89.85

Niobium | 1719 | 95.50 | 93.25

Molybdenum | 1746 | 97 | 95.26

Ruthenium | 1848 | 102.66 | 100.91

Rhodium | 1876 | 104.22 | 102.23

Palladium | 1904 | 105.77 | 105.74

Silver | 1945 | 108.055 | 107.93

Cadmium | 2016 | 112 | 111.60

Indium | 2052 | 114 | 114.05

Tin | 2124 | 118 | 118.10

Antimony | 2169 | 120.50 | 119.34

Tellurium | 2223 | 123.50 | 126.64

Iodine | 2287 | 127.055 | 126.01

Xenon | 2298 | 127.66 | 127.10

*Meta-Xenon | 2340 | 130 | --

*Kalon | 3054 | 169.66 | --

*Meta-Kalon | 3096 | 172 | --

Osmium | 3430 | 190.55 | 189.55

Iridium | 3458 | 192.11 | 191.56

Platinum A | 3486 | 193.66 | 193.34

*Platinum B | 3514 | 195.22 | --

Gold | 3546 | 197 | 195.74

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



PLATE II. MALE (left) and FEMALE (right).

As the words "ultimate physical atom" must frequently occur, it is necessary to state what we mean by the phrase. Any gaseous chemical atom may be dissociated into less complicated bodies; these, again, into still less complicated; these, again, into yet still less complicated. These will be dealt with presently. After the third dissociation but one more is possible; the fourth dissociation gives the ultimate physical atom.[3] This may vanish from the physical plane, but it can undergo no further dissociation on it. In this ultimate state of physical matter two types of atoms have been observed; they are alike in everything save the direction of their whorls and of the force which pours through them. In the one case force pours in from the "outside," from fourth-dimensional space,[4] and passing through the atom, pours into the physical world. In the second, it pours in from the physical world, and out through the atom into the "outside" again,[4] i.e., vanishes from the physical world. The one is like a spring, from which water bubbles out; the other is like a hole, into which water disappears. We call the atoms from which force comes out positive or male; those through which it disappears, negative or female. All atoms, so far as observed, are of one or other of these two forms. (Plate II.)

It will be seen that the atom is a sphere, slightly flattened, and there is a depression at the point where the force flows in, causing a heart-like form. Each atom is surrounded by a field, formed of the atoms of the four higher planes, which surround and interpenetrate it.

The atom can scarcely be said to be a "thing," though it is the material out of which all things physical are composed. It is formed by the flow of the life-force[5] and vanishes with its ebb. When this force arises in "space"[6]—the apparent void which must be filled with substance of some kind, of inconceivable tenuity—atoms appear; if this be artificially stopped for a single atom, the atom disappears; there is nothing left. Presumably, were that flow checked but for an instant, the whole physical world would vanish, as a cloud melts away in the empyrean. It is only the persistence of that flow[7] which maintains the physical basis of the universe.[8]

In order to examine the construction of the atom, a space is artificially made[9]; then, if an opening be made in the wall thus constructed, the surrounding force flows in, and three whorls immediately appear, surrounding the "hole" with their triple spiral of two and a half coils, and returning to their origin by a spiral within the atom; these are at once followed by seven finer whorls, which following the spiral of the first three on the outer surface, and returning to their origin by a spiral within that, flowing in the opposite direction—form a caduceus with the first three. Each of the three coarser whorls, flattened out, makes a closed circle; each of the seven finer ones, similarly flattened out, makes a closed circle. The forces which flow in them, again, come from "outside," from a fourth-dimensional space.[10] Each of the finer whorls is formed of seven yet finer ones, set successively at right angles to each other, each finer than its predecessor; these we call spirillæ.[11]

It will be understood from the foregoing, that the atom cannot be said to have a wall of its own, unless these whorls of force can be so designated; its "wall" is the pressed back "space." As said in 1895, of the chemical atom, the force "clears itself a space, pressing back the undifferentiated matter of the plane, and making to itself a whirling wall of this matter." The wall belongs to space, not to the atom.

In the three whorls flow currents of different electricities; the seven vibrate in response to etheric waves of all kinds—to sound, light, heat, etc.; they show the seven colours of the spectrum; give out the seven sounds of the natural scale; respond in a variety of ways to physical vibration—flashing, singing, pulsing bodies, they move incessantly, inconceivably beautiful and brilliant.[12]

The atom has—as observed so far—three proper motions, i.e., motions of its own, independent of any imposed upon it from outside. It turns incessantly upon its own axis, spinning like a top; it describes a small circle with its axis, as though the axis of the spinning top moved in a small circle; it has a regular pulsation, a contraction and expansion, like the pulsation of the heart. When a force is brought to bear upon it, it dances up and down, flings itself wildly from side to side, performs the most astonishing and rapid gyrations, but the three fundamental motions incessantly persist. If it be made to vibrate, as a whole, at the rate which gives any one of the seven colors, the whorl belonging to that color glows out brilliantly.

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.

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.

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.

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.

This is to be read, following the lines of the "figures of eight": H, He, Li, Gl, B, C, N, and so on, each successive element being heavier than the one preceding it in order. The disks which fall immediately below each other form a class; thus: H, Cl, Br, I; these resemble each other in various ways, and, as we shall presently see, the same forms and groupings re-appear.

Another chart—taken from Erdmann's Lehrbuch—arranges the elements on a curved line, which curiously resembles the curves within the shell of a nautilus. The radiating lines show the classes, the whole diameter building up a family; it will be observed that there is an empty radius between hydrogen and helium, and we have placed occultum there; on the opposite radius, iron, rubidium and osmium are seen.

The external forms may be classified as follows; the internal details will be dealt with later :—

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.

Plate IV .

V. The Bars.—These characterise a set of closely allied groups, termed "inter-periodic." Fourteen bars (or seven crossed) radiate from a centre, as in iron (1 on Plate IV), and the members of each group—iron, nickel, cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum—differ from each other by the weight of each bar, increasing in orderly succession; the details will be given later. Manganese is often grouped with iron, nickel, and cobalt (see Crookes' lemniscates), but its fourteen protruding bodies repeat the "lithium spike" (proto-element 5) and are grouped round a central ovoid. This would appear to connect it with lithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with which it is often classed. The "lithium spike" re-appears in potassium and rubidium. These details, again, will come out more clearly later.

VI. The Star.—A flat star, with five interpenetrating tetrahedra in the centre, is the characteristic of neon and its allies (4 on Plate IV) leaving apart helium, which, as may be seen by referring to 3, Plate IV, has an entirely different form.

There are thus six clearly defined forms, typical of classes, with two—lithium and fluorine—of doubtful affinities. It is worthy of notice that in diatomic elements four funnels open on the faces of tetrahedra; in triatomic, six funnels on the faces of cubes; in tetratomic, eight funnels on the faces of octahedra.

Thus we have a regular sequence of the platonic solids, and the question suggests itself, will further evolution develop elements shaped to the dodecahedron and the icosahedron?

II.

We now pass from the consideration of the outer forms of the chemical elements to a study of their internal structure, the arrangement within the element of more or less complicated groups—proto-elements—capable of separate, independent existence; these, once more, may be dissociated into yet simpler groups—hyper-meta-proto-elements—equally capable of separate, independent existence, and resolvable into single ultimate physical atoms, the irreducible substratum of the physical world (see Theosophist, 1908, pp. 354-356).[18]

We shall have to study the general internal structure, and then the breaking up of each element, and the admirable diagrams, patiently worked out by Mr. Jinarâjadâsa, will make the study comparatively easy to carry on.

The diagrams, of course, can only give a very general idea of the facts they represent; they give groupings and show relations, but much effort of the imagination is needed to transform the two-dimensional diagram into the three-dimensional object. The wise student will try to visualize the figure from the diagram. Thus the two triangles of hydrogen are not in one plane; the circles are spheres, and the atoms within them, while preserving to each other their relative positions, are in swift movement in three-dimensional space. Where five atoms are seen, as in bromine and iodine, they are generally arranged with the central atom above the four, and their motion indicates lines which erect four plane triangles—meeting at their apices—on a square base, forming a square-based four-sided pyramid. Each dot represents a single ultimate atom. The enclosing lines indicate the impression of form made on the observer, and the groupings of the atoms; the groups will divide along these lines, when the element is broken up, so that the lines have significance, but they do not exist as stable walls or enclosing films, but rather mark limits, not lines, of vibrations. It should be noted that it is not possible to show five of the prisms in the five intersecting tetrahedra of prisms, and 30 atoms must, therefore, be added in counting.

The diagrams are not drawn to scale, as such drawing would be impossible; the dot representing the atom is enormously too large compared with the enclosures, which are absurdly too small; a scale drawing would mean an almost invisible dot on a sheet of many yards square.

The use of the words "positive" and "negative" needs to be guarded by the following paragraphs from the article on "Chemistry" in the Encyclopædia Britannica. We use the words in their ordinary text-book meaning, and have not, so far, detected any characteristics whereby an element can be declared, at sight, to be either positive or negative:—

"When binary compounds, or compounds of two elements, are decomposed by an electric current, the two elements make their appearance at opposite poles. These elements which are disengaged at the negative pole are termed electro-positive or positive or basylous elements, while those disengaged at the positive pole are termed electro-negative or negative or chlorous elements. But the difference between these two classes of elements is one of degree only, and they gradually merge into each other; moreover the electric relations of elements are not absolute, but vary according to the state of combination in which they exist, so that it is just as impossible to divide the elements into two classes according to this property as it is to separate them into two distinct classes of metals and non-metals."

We follow here the grouping according to external forms, and the student should compare it with the groups marked in the lemniscate arrangement shown in Article II (p. 377, properly p. 437, February), reading the group by the disks that fall below each other; thus the first group is H, Cl, Br, I (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered element. The elements grow denser in descending order; thus hydrogen is an invisible gas; chlorine a denser gas visible by its colour; bromine is a liquid; iodine is a solid—all, of course, when temperature and pressure are normal. By the lowering of temperature and the increase of pressure, an element which is normally gaseous becomes a liquid, and then a solid. Solid, liquid, gaseous, are three interchangeable states of matter, and an element does not alter its constitution by changing its state. So far as a chemical "atom" is concerned, it matters not whether it be drawn for investigation from a solid, a liquid, or a gas; but the internal arrangements of the "atoms" become much more complicated as they become denser and denser, as is seen by the complex arrangements necessitated by the presence of the 3546 ultimate atoms contained in the chemical "atom" of gold, as compared with the simple arrangement of the 18 ultimate atoms of hydrogen.

According to the lemniscate arrangement, we should commence with hydrogen as the head of the first negative group, but as it differs wholly from those placed with it, it is better to take it by itself. Hydrogen is the lightest of the known elements, and is therefore taken as 1 in ordinary chemistry, and all atomic weights are multiples of this. We take it as 18, because it contains eighteen ultimate atoms, the smallest number we have found in a chemical element. So our "number-weights" are obtained by dividing the total number of atoms in an element by 18 (see p. 349, January).

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.

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.)

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).

The six bodies contained in the gaseous atom instantaneously re-arrange themselves within two spheres; the two linear triplets unite with one triangular triplet, holding to each other relative positions which, if connected by three right lines, would form a triangle with a triplet at each angle; the remaining three triangular triplets similarly arrange themselves in the second sphere. These form the proto-compounds of hydrogen.

In the dissociation of these, each group breaks up into two, the two linear triplets joining each other and setting free their triangular comrade, while two of the triangular triplets similarly remain together, casting out the third, so that hydrogen yields four meta-compounds.

In the hyper-condition, the connexion between the double triplets is broken, and they become four independent groups, two like ix, in the hyper-types (p. 25), and two remaining linear, but rearranging their internal relations; the two remaining groups break up into two pairs and a unit.

The final dissociation sets all the atoms free.

Occultum (Plate VI, 1).

On the first dissociation of the component parts of occultum, the tetrahedron separates as a whole, with its four "cigars," flattening itself out within its hole, a; two "cigars" are positive and two negative, marked respectively a and a'. The rope becomes a ring within a sphere, b, and the two bodies d d, which are loose in the gaseous atom, come within this ring. The balloon becomes a sphere.

On further dissociation, the "cigars" go off independently, showing two types, and these again each divide into triplets, as meta-compounds. B, on the meta-level, casts out the two d bodies, which become independent triplets, and the "rope" breaks into two, a close ring of seven atoms and a double cross of eight. These subdivide again to form hyper-compounds, the ring yielding a quintet and a pair, and the double cross separating into its two parts.

The balloon, c, becomes much divided, the cohesion of its parts being slight; it forms two triplets, a pair and a unit, and these set free, on further dissociation, no less than five separate atoms and two duads.

The two triplets of d each cast out an atom on dissociation, and form two pairs and two units.

Sodium (Plate VI, 2).

It is convenient to consider sodium next, because it is the basic pattern on which not only copper, silver and gold are formed, but also chlorine, bromine and iodine.

When sodium is set free from its gaseous condition, it divides up into thirty-one bodies—twenty-four separate funnels, four bodies derived from the two central globes, and three from the connecting rod. The funnels become spheres, and each contains four enclosed spheres, with more or less complicated contents. Each central globe yields a sextet and a quartet, and the rod sets free two quartets and a peculiarly formed sextet.

When the proto-compounds are dissociated, the funnel-sphere sets free: (1) the contents of a, rearranged into two groups of four within a common sphere; the sphere yields four duads as hyper-compounds; (2) the contents of b, which unite themselves into a quartet, yielding two duads as hyper-compounds; and (3) the contents of the two spheres, c, which maintain their separation as meta-compounds, and become entirely independent, the atoms within the sphere revolving round each other, but the spheres ceasing their revolution round a common axis, and going off in different directions. The atoms break off from each other, and gyrate in independent solitude as hyper-"compounds." Thus each funnel yields finally ten hyper-bodies.

The part of the central globe, marked d, with its six atoms, whirling round a common centre, becomes two triplets, at the meta-stage, preparing for the complete separation of these as hyper-bodies. The second part of the same globe, marked e, a whirling cross, with an atom at each point, becomes a quartet in the meta-state, in which three atoms revolve round a fourth, and in the hyper-state this central atom is set free, leaving a triplet and a unit.

Each of the two bodies marked f, liberated from the connecting rod, shows four atoms whirling round a common centre, exactly resembling e in appearance; but there must be some difference of inner relations, for, in the meta-state, they re-arrange themselves as two pairs, and divide into two as hyper-bodies.

The body marked g is a four-sided pyramid, with two closely joined atoms at its apex; these still cling to each in mutual revolution as a meta-body, encircled by a ring of four, and this leads to a further dissociation into three pairs on the hyper-level.

Chlorine (Plate V, 2).

The description of the funnel of sodium applies to that of chlorine, until we come to the body nearest the mouth, the sphere containing three additional bodies; this remains within the funnel in the first dissociation, so that again we have twenty-four separate funnels as proto-compounds; the central globes are the same as in sodium, and yield the same four bodies; the connecting rod sets free five bodies, of which two are the same; we have thus thirty-three separate bodies as the result of the dissociation of chlorine into its proto-compounds. As all the compounds which are in sodium break up in the same way into meta- and hyper-compounds, we need not repeat the process here. We have only to consider the new meta- and hyper-compounds of the highest sphere within the funnel, and the two triplets and one quintet from the connecting rod.

The additional body within the proto-funnel is of a very simple character, three contained triangles within the flattened sphere. On release from the funnel, on the meta-level, the atoms rearrange themselves in a whirling set of three triplets, and these break off from each other as hyper-compounds. The two triplets from the connecting rod, also, are of the simplest character and need not delay us. The five-atomed body, a four-sided pyramid as a proto-compound, becomes a ring whirling round a centre on the meta, and two pairs with a unit on the hyper.

Bromine (Plate V, 3).

Three additional bodies appear at the top of the funnel, which otherwise repeats that of chlorine. The connecting rod is the same and may be disregarded. The central globes become more complex. The additions are, however, of very easy types, and hence are readily dealt with. Each of the three similar ovoid bodies contains two triplets—each a triangle and a quintet—a four-sided pyramid. These are the same, as may be seen in the connecting rod of chlorine, and we need not repeat them. Only the globe remains. This does not break up as a proto-compound but is merely set free, a and the 2 bs whirling in a plane vertical to the paper and the two smaller bodies, cc, whirling on a plane at right angles to the other. These two disengage themselves, forming a quartet as a meta-compound, while a makes a whirling cross and bb a single sextet; these further dissociate themselves into four pairs and two triplets.

Iodine (Plate V, 4).

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

Copper (Plate VI, 3).

We have already disposed of occultum, on this plate, and of sodium, which lies at the root of both groups. Copper, we now find, is also very largely off our hands, as the funnel provides us with only two new types—two spheres—each containing five atoms in a new arrangement, and the triangular body at the mouth with its ten atoms. This triangular body, with an increased number of atoms, reappears in various other chemical elements. The central globes are different from any we have had before, in their internal arrangement, but the constituents are familiar; there are two contained spheres with four atoms each, the a in the globe of bromine (see above) and 2 "cigars." The "cigars" may be followed under occultum (see above). The connecting rod is as in chlorine, bromine and iodine.

The atoms in the bodies a and b are curiously arranged. A consists of two square-based pyramids turned so as to meet at their apices, and breaks up into two quartet rings and a duad. B is again two four-sided pyramids, but the bases are in contact and set at right angles to each other; the second apex is not seen, as it is directly below the first. The pyramids separate as meta-bodies, and the atoms assume the peculiar arrangement indicated and then break up into four pairs and two units on the hyper level.

IV.

Silver (Plate VI, 4 and Ag below).

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

Gold (Plate VII and Au below).

The disintegration of gold first yields forty-seven bodies on the proto-level; the twenty-four funnels separate, and the central globes which hold each twelve together set free their six contained globes (c, d), thirty bodies being thus liberated. The sixteen bodies on the central inclined planes, marked b, break away, their central globe, with its four contained globes, remaining unchanged. But this condition does not last. The motion of the funnels changes and thus the funnels cease to exist and their contents are set free, each funnel thus liberating nine independent bodies; the sixteen b separate into two each; the four a liberate five each; the two c set free thirteen each; the four d finally liberate two each: 302 proto elements in all.

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

II and IIa.— The Tetrahedral Groups .

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

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.

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

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.

TELLU