diff options
Diffstat (limited to '16058-8.txt')
| -rw-r--r-- | 16058-8.txt | 4168 |
1 files changed, 4168 insertions, 0 deletions
diff --git a/16058-8.txt b/16058-8.txt new file mode 100644 index 0000000..8384273 --- /dev/null +++ b/16058-8.txt @@ -0,0 +1,4168 @@ +The Project Gutenberg eBook, Occult Chemistry, by Annie Besant and Charles +W. Leadbeater, Edited by A. P. Sinnett + + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + + + + +Title: Occult Chemistry + Clairvoyant Observations on the Chemical Elements + + +Author: Annie Besant and Charles W. Leadbeater + +Editor: A. P. Sinnett + +Release Date: June 14, 2005 [eBook #16058] + +Language: English + +Character set encoding: ISO-8859-1 + + +***START OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY*** + + +E-text prepared by Clare Boothby, Keith Edkins, and the Project Gutenberg +Online Distributed Proofreading Team + + + +Note: Project Gutenberg also has an HTML version of this + file which includes the original illustrations. + See 16058-h.htm or 16058-h.zip: + (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h/16058-h.htm) + or + (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h.zip) + + + + + +OCCULT CHEMISTRY + +Clairvoyant Observations on the Chemical Elements + +by + +ANNIE BESANT, P.T.S. + +and + +CHARLES W. LEADBEATER + +Revised Edition edited by A. P. SINNETT + +LONDON +THEOSOPHICAL PUBLISHING HOUSE +1, UPPER WOBURN PLACE, W.C. 1. + +1919 + + + + + + + +EDITOR'S PREFACE. + + + +When undertaking to prepare a new edition of this book I received +permission from the authors to "throw it into the form in which you think +it would be most useful at the present time." It was left to my discretion, +"What to use and what to omit." I have not found it necessary to avail +myself to any considerable extent of this latter permission. But as the +contents of the book were originally arranged the reader was ill-prepared +to appreciate the importance of the later research for want of introductory +matter explaining how it began, and how the early research led up to the +later investigation. I have therefore contributed an entirely new +preliminary chapter which will, I hope, help the reader to realise the +credibility of the results attained when the molecular forms and +constitution of the numerous bodies examined were definitely observed. I +have not attempted to revise the records of the later research in which I +had no personal share, so from the beginning of Chapter III to the end the +book in its present form is simply a reprint of the original edition except +for the correction of a few trifling misprints. + +I have thus endeavoured to bring into clear prominence at the outset the +scientific value of the light the book sheds on the constitution of matter. +The world owes a debt to scientific men of the ordinary type that cannot be +over-estimated, but though they have hitherto preferred to progress +gradually, from point to point, disliking leaps in the dark, the leap now +made is only in the dark for those who will not realise that the progress +to be accomplished by means of instrumental research must sooner or later +be supplemented by subtler methods. Physical science has reached the +conception that the atoms of the bodies hitherto called the chemical +elements are each composed of minor atoms. Instrumental research cannot +determine by how many, in each case. Occult research ascertained the actual +number in some cases by direct observation and then discovered the law +governing the numbers in all cases, and the relation of these numbers to +atomic weights. The law thus unveiled is a demonstration of the accuracy of +the first direct observations, and this principle once established the +credibility of accounts now given as to the arrangement of minor atoms in +the molecules of the numerous elements examined, seems to me advanced to a +degree approximating to proof. + +It remains to be seen--not how far, but rather how soon the scientific +world at large will accept the conclusions of this volume as a definite +contribution to science, blending the science of the laboratory with that +variety that has hitherto been called occult. + + + + + +CONTENTS. + + I.--A PRELIMINARY SURVEY + + II.--DETAILS OF THE EARLY RESEARCH + + THE PLATONIC SOLIDS + + III.--THE LATER RESEARCHES + + + + + + +OCCULT CHEMISTRY. + +CHAPTER I. + +A PRELIMINARY SURVEY. + +The deep interest and importance of the research which this book describes +will best be appreciated if introduced by an account of the circumstances +out of which it arose. The first edition, consisting mainly of articles +reprinted from the _Theosophist_, dealt at once with the later phases of +the research in a way which, though intelligible to the occult student, +must have been rather bewildering to the ordinary reader. These later +phases, however, endow the earlier results with a significance that in the +beginning could only be vaguely conjectured. I am the better entitled to +perform the task that has been assigned to me--that of preparing the +present edition--by reason of the fact that it was in my presence and at my +instigation that the first efforts were made to penetrate the mystery +previously enshrouding the ultimate molecule of matter. + +I remember the occasion vividly. Mr. Leadbeater was then staying at my +house, and his clairvoyant faculties were frequently exercised for the +benefit of myself, my wife and the theosophical friends around us. I had +discovered that these faculties, exercised in the appropriate direction, +were ultra-microscopic in their power. It occurred to me once to ask Mr. +Leadbeater if he thought he could actually _see_ a molecule of physical +matter. He was quite willing to try, and I suggested a molecule of gold as +one which he might try to observe. He made the appropriate effort, and +emerged from it saying the molecule in question was far too elaborate a +structure to be described. It evidently consisted of an enormous number of +some smaller atoms, quite too many to count; quite too complicated in their +arrangement to be comprehended. It struck me at once that this might be due +to the fact that gold was a heavy metal of high atomic weight, and that +observation might be more successful if directed to a body of low atomic +weight, so I suggested an atom of hydrogen as possibly more manageable. Mr. +Leadbeater accepted the suggestion and tried again. This time he found the +atom of hydrogen to be far simpler than the other, so that the minor atoms +constituting the hydrogen atom were countable. They were arranged on a +definite plan, which will be rendered intelligible by diagrams later on, +and were eighteen in number. + +We little realized at the moment the enormous significance of this +discovery, made in the year 1895, long before the discovery of radium +enabled physicists of the ordinary type to improve their acquaintance with +the "electron." Whatever name is given to that minute body it is recognised +now by ordinary science as well as by occult observation, as the +fundamental unit of physical matter. To that extent ordinary science has +overtaken the occult research I am dealing with, but that research rapidly +carried the occult student into regions of knowledge whither, it is +perfectly certain, the ordinary physicist must follow him at no distant +date. + +The research once started in the way I have described was seen to be +intensely interesting. Mrs. Besant almost immediately co-operated with Mr. +Leadbeater in its further progress. Encouraged by the success with +hydrogen, the two important gases, oxygen and nitrogen, were examined. They +proved to be rather more difficult to deal with than hydrogen but were +manageable. Oxygen was found to consist of 290 minor atoms and nitrogen of +261. Their grouping will be described later on. The interest and importance +of the whole subject will best be appreciated by a rough indication of the +results first attained. The reader will then have more patience in +following the intricacies of the later discoveries. + +The figures just quoted were soon perceived to have a possible +significance. The atomic weight of oxygen is commonly taken as 16. That is +to say, an atom of oxygen is sixteen times heavier than an atom of +hydrogen. In this way, all through the table of atomic weights, hydrogen is +taken as unity, without any attempt being made to estimate its absolute +weight. But now with the atom of hydrogen dissected, so to speak, and found +to consist of 18 somethings, while the atom of oxygen consisted of 290 of +the same things, the sixteen to one relationship reappears: 290 divided by +18 gives us 16 and a minute decimal fraction. Again the nitrogen number +divided by 18 gives us 14 and a minute fraction as the result, and that is +the accepted atomic weight of nitrogen. This gave us a glimpse of a +principle that might run all through the table of atomic weights. For +reasons having to do with other work, it was impossible for the authors of +this book to carry on the research further at the time it was begun. The +results already sketched were published as an article in the magazine then +called _Lucifer_, in November, 1895, and reprinted as a separate pamphlet +bearing the title "Occult Chemistry," a pamphlet the surviving copies of +which will one day be a recognised vindication of the method that will at +some time in the future be generally applied to the investigation of +Nature's mysteries. For the later research which this volume deals with +does establish the principle with a force that can hardly be resisted by +any fair-minded reader. With patience and industry--the authors being +assisted in the counting in a way that will be described (and the method +adopted involved a check upon the accuracy of the counting)--the minor +atoms of almost all the known chemical elements, as they are commonly +called, were counted and found to bear the same relation to their atomic +weights as had been suggested by the cases of oxygen and nitrogen. This +result throws back complete proof on the original estimate of the number of +minor atoms in hydrogen, a figure which ordinary research has so far +entirely failed to determine. The guesses have been widely various, from +unity to many hundreds, but, unacquainted with the clairvoyant method, the +ordinary physicist has no means of reaching the actual state of the facts. + +Before going on with the details of the later research some very important +discoveries arising from the early work must first be explained. As I have +already said clairvoyant faculty of the appropriate order directed to the +minute phenomena of Nature is practically infinite in its range. Not +content with estimating the number of minor atoms in physical molecules, +the authors proceeded to examine the minor atoms individually. They were +found to be themselves elaborately complicated structures which, in this +preliminary survey of the whole subject, I will not stop to explain (full +explanation will be found later on) and they are composed of atoms +belonging to an ultra-physical realm of Nature with which the occultist has +long been familiar and describes as "the Astral Plane." Some rather +pedantic critics have found fault with the term, as the "plane" in question +is of course really a sphere entirely surrounding the physical globe, but +as all occultists understand the word, "plane" simply signifies a condition +of nature. Each condition, and there are many more than the two under +consideration, blends with its neighbour, _via_ atomic structure. Thus the +atoms of the Astral plane in combination give rise to the finest variety of +physical matter, the ether of space, which is not homogeneous but really +atomic in its character, and the minute atoms of which physical molecules +are composed are atoms of ether, "etheric atoms," as we have now learned to +call them. + +Many physicists, though not all, will resent the idea of treating the ether +of space as atomic. But at all events the occultist has the satisfaction of +knowing that the great Russian chemist, Mendeleef, preferred the atomic +theory. In Sir William Tilden's recent book entitled "Chemical Discovery +and Invention in the Twentieth Century," I read that Mendeleef, +"disregarding conventional views," supposed the ether to have a molecular +or atomic structure, and in time all physicists must come to recognise that +the Electron is not, as so many suppose at present, an atom of electricity, +but an atom of ether carrying a definite unit charge of electricity. + +Long before the discovery of radium led to the recognition of the electron +as the common constituent of all the bodies previously described as +chemical elements, the minute particles of matter in question had been +identified with the cathode rays observed in Sir William Crookes' vacuum +tubes. When an electric current is passed through a tube from which the air +(or other gas it may contain) has been almost entirely exhausted, a +luminous glow pervades the tube manifestly emanating from the cathode or +negative pole of the circuit. This effect was studied by Sir William +Crookes very profoundly. Among other characteristics it was found that, if +a minute windmill was set up in the tube before it was exhausted, the +cathode ray caused the vanes to revolve, thus suggesting the idea that they +consisted of actual particles driven against the vanes; the ray being thus +evidently something more than a mere luminous effect. Here was a mechanical +energy to be explained, and at the first glance it seemed difficult to +reconcile the facts observed with the idea creeping into favour, that the +particles, already invested with the name "electron," were atoms of +electricity pure and simple. Electricity was found, or certain eminent +physicists thought they had found, that electricity _per se_ had inertia. +So the windmills in the Crookes' vacuum tubes were supposed to be moved by +the impact of electric atoms. + +Then in the progress of ordinary research the discovery of radium by Madame +Curie in the year 1902 put an entirely new face upon the subject of +electrons. The beta particles emanating from radium were soon identified +with the electrons of the cathode ray. Then followed the discovery that the +gas helium, previously treated as a separate element, evolved itself as one +consequence of the disintegration of radium. Transmutation, till then +laughed at as a superstition of the alchemist, passed quietly into the +region of accepted natural phenomena, and the chemical elements were seen +to be bodies built up of electrons in varying number and probably in +varying arrangements. So at last ordinary science had reached one important +result of the occult research carried on seven years earlier. It has not +yet reached the finer results of the occult research--the _structure_ of +the hydrogen atom with its eighteen etheric atoms and the way in which the +atomic weights of all elements are explained by the number of etheric atoms +entering into their constitution. + +The ether of space, though defying instrumental examination, comes within +scope of the clairvoyant faculty, and profoundly interesting discoveries +were made during what I have called the early research in connexion with +that branch of the inquiry. Etheric atoms combine to form molecules in many +different ways, but combinations involving fewer atoms than the eighteen +which give rise to hydrogen, make no impression on the physical senses nor +on physical instruments of research. They give rise to varieties of +molecular ether, the comprehension of which begins to illuminate realms of +natural mystery as yet entirely untrodden by the ordinary physicist. +Combinations below 18 in number give rise to three varieties of molecular +ether, the functions of which when they come to be more fully studied will +constitute a department of natural knowledge on the threshold of which we +already stand. Some day we may perhaps be presented with a volume on Occult +Physics as important in its way as the present dissertation on Occult +Chemistry. + + * * * * * + + + +CHAPTER II. + +DETAILS OF THE EARLY RESEARCH. + +The article detailing the results of the research carried on in the year +1895 (see the November issue for that year of the magazine then called +_Lucifer_), began with some general remarks about the clairvoyant faculty, +already discussed in the preceding chapter. The original record then goes +on as follows:-- + +The physical world is regarded as being composed of between sixty and +seventy chemical elements, aggregated into an infinite variety of +combinations. These combinations fall under the three main heads of solids, +liquids and gases, the recognised substates of physical matter, with the +theoretical ether scarcely admitted as material. Ether, to the scientist, +is not a substate or even a state of matter, but is a something apart by +itself. It would not be allowed that gold could be raised to the etheric +condition as it might be to the liquid and gaseous; whereas the occultist +knows that the gaseous is succeeded by the etheric, as the solid is +succeeded by the liquid, and he knows also that the word "ether" covers +four substates as distinct from each other as are the solids, liquids and +gases, and that all chemical elements have their four etheric substates, +the highest being common to all, and consisting of the ultimate physical +atoms to which all elements are finally reducible. The chemical atom is +regarded as the ultimate particle of any element, and is supposed to be +indivisible and unable to exist in a free state. Mr. Crookes' researches +have led the more advanced chemists to regard the atoms as compound, as a +more or less complex aggregation of protyle. + +To astral vision ether is a visible thing, and is seen permeating all +substances and encircling every particle. A "solid" body is a body composed +of a vast number of particles suspended in ether, each vibrating backwards +and forwards in a particular field at a high rate of velocity; the +particles are attracted towards each other more strongly than they are +attracted by external influences, and they "cohere," or maintain towards +each other a definite relation in space. Closer examination shows that the +ether is not homogeneous but consists of particles of numerous kinds, +differing in the aggregations of the minute bodies composing them; and a +careful and more detailed method of analysis reveals that it has four +distinct degrees, giving us, with the solid, liquid and gaseous, seven +instead of four substates of matter in the physical world. + +These four etheric substates will be best understood if the method be +explained by which they were studied. This method consisted of taking what +is called an atom of gas, and breaking it up time after time, until what +proved to be the ultimate physical atom was reached, the breaking up of +this last resulting in the production of astral, and no longer physical +matter. + +[Illustration] + +It is, of course, impossible to convey by words the clear conceptions that +are gained by direct vision of the objects of study, and the accompanying +diagram--cleverly drawn from the description given by the investigators--is +offered as a substitute, however poor, for the lacking vision of the +readers. The horizontal lines separate from each other the seven substates +of matter; solid, liquid, gas, ether 4, ether 3, ether 2, ether 1. On the +gas level are represented three chemical atoms, one of hydrogen (H), one of +oxygen (O), one of nitrogen (N). The successive changes undergone by each +chemical atom are shown in the compartments vertically above it, the +left-hand column showing the breaking up of the hydrogen atom, the middle +column that of the oxygen atom, the right-hand column, that of the nitrogen +atom. The ultimate physical atom is marked _a_, and is drawn only once, +although it is the same throughout. The numbers 18, 290 and 261 are the +numbers of the ultimate physical atoms found to exist in a chemical atom. + +The dots indicate the lines along which force is observed to be playing, +and the arrowheads show the direction of the force. No attempt has been +made to show this below E 2 except in the case of the hydrogen. The letters +given are intended to help the reader to trace upwards any special body; +thus _d_ in the oxygen chemical atom on the gas level may be found again on +E 4, E 3, and E 2. It must be remembered that the bodies shown +diagrammatically in no way indicate relative size; as a body is raised from +one substate to the one immediately above it, it is enormously magnified +for the purpose of investigation, and the ultimate atom on E 1 is +represented by the dot _a_ on the gaseous level. + +The first chemical atom selected for this examination was an atom of +hydrogen (H). On looking carefully at it, it was seen to consist of six +small bodies, contained in an egg-like form. It rotated with great rapidity +on its own axis, vibrating at the same time, and the internal bodies +performed similar gyrations. The whole atom spins and quivers, and has to +be steadied before exact observation is possible. The six little bodies are +arranged in two sets of three, forming two triangles that are not +interchangeable, but are related to each other as object and image. (The +lines in the diagram of it on the gaseous sub-plane are not lines of force, +but show the two triangles; on a plane surface the interpenetration of the +triangles cannot be clearly indicated.) Further, the six bodies are not all +alike; they each contain three smaller bodies--each of these being an +ultimate physical atom--but in two of them the three atoms are arranged in +a line, while in the remaining four they are arranged in a triangle. + +The wall of the limiting spheroid in which the bodies are enclosed being +composed of the matter of the third, or gaseous, kind, drops away when the +gaseous atom is raised to the next level, and the six bodies are set free. +They at once re-arrange themselves in two triangles, each enclosed by a +limiting sphere; the two marked _b_ in the diagram unite with one of those +marked _b'_ to form a body which shows a positive character, the remaining +three forming a second body negative in type. These form the hydrogen +particles of the lowest plane of ether, marked E 4--ether 4--on the +diagram. On raising these further, they undergo another disintegration, +losing their limiting walls; the positive body of E 4, on losing its wall, +becomes two bodies, one consisting of the two particles, marked _b_, +distinguishable by the linear arrangement of the contained ultimate atoms, +enclosed in a wall, and the other being the third body enclosed in E 4 and +now set free. The negative body of E 4 similarly, on losing its wall, +becomes two bodies, one consisting of the two particles marked _b'_, and +the second the remaining body, being set free. These free bodies do not +remain on E 3 but pass immediately to E 2, leaving the positive and +negative bodies, each containing two particles, as the representatives of +hydrogen on E 3. On taking these bodies a step higher their wall +disappears, and the internal bodies are set free, those containing the +atoms arranged lineally being positive, and those with the triangular +arrangement being negative. These two forms represent hydrogen on E 2, but +similar bodies of this state of matter are found entering into other +combinations, as may be seen by referring to _f_ on E 2 of nitrogen (N). On +raising these bodies yet one step further, the falling away of the walls +sets the contained atoms free, and we reach the ultimate physical atom, the +matter of E 1. The disintegration of this sets free particles of astral +matter, so that we have reached in this the limit of physical matter. The +Theosophical reader will notice with interest that we can thus observe +seven distinct substates of physical matter, and no more. + +The ultimate atom, which is the same in all the observed cases, is an +exceedingly complex body, and only its main characteristics are given in +the diagram. It is composed entirely of spirals, the spiral being in its +turn composed of 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. + +[Illustration] + +It will be seen that the tetrahedron is the fundamental form, the +three-sided pyramid on a triangular base, _i.e._, a solid figure formed +from four triangles. Two of these generate the cube and the octahedron; +five of these generate the dodecahedron and the icosahedron. + +The rhombic dodecahedron is not regular, for though the lines and surfaces +are equal, the angles are not. + +NOTES. + +Mr. C. 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. + +[Illustration: PLATE I. SODIUM.] + +In counting the number of ultimate atoms in a chemical elemental atom, we +did not count them throughout, one by one; when, for instance, we counted +up the ultimate atoms in sodium, we dictated the number in each convenient +group to Mr. Jinarâjadâsa, and he multiplied out the total, divided by 18, +and announced the result. Thus: sodium (_see_ Plate I) is composed of an +upper part, divisible into a globe and 12 funnels; a lower part, similarly +divided; and a connecting rod. We counted the number in the upper part: +globe--10; the number in two or three of the funnels--each 16; the number +of funnels--12; the same for the lower part; in the connecting rod--14. Mr. +Jinarâjadâsa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418: +divided by 18 = 23.22 recurring. By this method we guarded our counting +from any prepossession, as it was impossible for us to know how the various +numbers would result on addition, multiplication and division, and the +exciting moment came when we waited to see if our results endorsed or +approached any accepted weight. In the heavier elements, such as gold, with +3546 atoms, it would have been impossible to count each atom without quite +unnecessary waste of time, when making a preliminary investigation. Later, +it may be worth while to count each division separately, as in some we +noticed that two groups, at first sight alike, differed by 1 or 2 atoms, +and some very slight errors may, in this way, have crept into our +calculations. + +In the following table is a list of the chemical elements examined; the +first column gives the names, the asterisk affixed to some indicating that +they have not yet been discovered by orthodox chemistry. The second column +gives the number of ultimate physical atoms contained in one chemical atom +of the element concerned. The third column gives the weight as compared +with hydrogen, taken as 18, and this is obtained by dividing the calculated +number of ultimate atoms by 18. The fourth column gives the recognized +weight-number, mostly according to the latest list of atomic weights, the +"International List" of 1905, given in Erdmann's "Lehrbuch der +Unorganischen Chemie." These weights differ from those hitherto accepted, +and are generally lighter than those given in earlier text-books. It is +interesting to note that our counting endorses the earlier numbers, for the +most part, and we must wait to see if later observations will endorse the +last results of orthodox chemistry, or confirm ours. + +-------------------------------------------- +Hydrogen | 18 | 1 | 1 +*Occultum | 54 | 3 | -- +Helium | 72 | 4 | 3.94 +Lithium | 127 | 7.06 | 6.98 +Baryllium | 164 | 9.11 | 9.01 +Boron | 200 | 11.11 | 10.86 +Carbon | 216 | 12 | 11.91 +Nitrogen | 261 | 14.50 | 14.01 +Oxygen | 290 | 16.11 | 15.879 +Fluorine | 340 | 18.88 | 18.90 +Neon | 360 | 20 | 19.9 +*Meta-Neon | 402 | 22.33 | -- +Sodium | 418 | 23.22 | 22.88 +Magnesium | 432 | 24 | 24.18 +Aluminium | 486 | 27 | 26.91 +Silicon | 520 | 28.88 | 28.18 +Phosphorus | 558 | 31 | 30.77 +Sulphur | 576 | 32 | 31.82 +Chlorine | 639 | 35.50 | 35.473 +Potassium | 701 | 38.944 | 38.85 +Argon | 714 | 39.66 | 39.60 +Calcium | 720 | 40 | 39.74 +*Metargon | 756 | 42 | -- +Scandium | 792 | 44 | 43.78 +Titanium | 864 | 48 | 47.74 +Vanadium | 918 | 51 | 50.84 +Chromium | 936 | 52 | 51.74 +Manganese | 992 | 55.11 | 54.57 +Iron | 1008 | 56 | 55.47 +Cobalt | 1036 | 57.55 | 57.7 +Nickel | 1064 | 59.ll | 58.30 +Copper | 1139 | 63.277 | 63.12 +Zinc | 1170 | 65 | 64.91 +Gallium | 1260 | 70 | 69.50 +Germanium | 1300 | 72.22 | 71.93 +Arsenic | 1350 | 75 | 74.45 +Selenium | 1422 | 79 | 78.58 +Bromine | 1439 | 79.944 | 79.953 +Krypton | 1464 | 81.33 | 81.20 +*Meta-Krypton | 1506 | 83.66 | -- +Rubidium | 1530 | 85 | 84.85 +Strontium | 1568 | 87.11 | 86.95 +Yttrium | 1606 | 89.22 | 88.34 +Zirconium | 1624 | 90.22 | 89.85 +Niobium | 1719 | 95.50 | 93.25 +Molybdenum | 1746 | 97 | 95.26 +Ruthenium | 1848 | 102.66 | 100.91 +Rhodium | 1876 | 104.22 | 102.23 +Palladium | 1904 | 105.77 | 105.74 +Silver | 1945 | 108.055 | 107.93 +Cadmium | 2016 | 112 | 111.60 +Indium | 2052 | 114 | 114.05 +Tin | 2124 | 118 | 118.10 +Antimony | 2169 | 120.50 | 119.34 +Tellurium | 2223 | 123.50 | 126.64 +Iodine | 2287 | 127.055 | 126.01 +Xenon | 2298 | 127.66 | 127.10 +*Meta-Xenon | 2340 | 130 | -- +*Kalon | 3054 | 169.66 | -- +*Meta-Kalon | 3096 | 172 | -- +Osmium | 3430 | 190.55 | 189.55 +Iridium | 3458 | 192.11 | 191.56 +Platinum A | 3486 | 193.66 | 193.34 +*Platinum B | 3514 | 195.22 | -- +Gold | 3546 | 197 | 195.74 +-------------------------------------------- +[Illustration: PLATE II. MALE (left) and FEMALE (right).] + +As the words "ultimate physical atom" must frequently occur, it is +necessary to state what we mean by the phrase. Any gaseous chemical atom +may be dissociated into less complicated bodies; these, again, into still +less complicated; these, again, into yet still less complicated. These will +be dealt with presently. After the third dissociation but one more is +possible; the fourth dissociation gives the ultimate physical atom.[3] This +may vanish from the physical plane, but it can undergo no further +dissociation on it. In this ultimate state of physical matter two types of +atoms have been observed; they are alike in everything save the direction +of their whorls and of the force which pours through them. In the one case +force pours in from the "outside," from fourth-dimensional space,[4] and +passing through the atom, pours into the physical world. In the second, it +pours in from the physical world, and out through the atom into the +"outside" again,[4] _i.e._, vanishes from the physical world. The one is +like a spring, from which water bubbles out; the other is like a hole, into +which water disappears. We call the atoms from which force comes out +_positive_ or _male_; those through which it disappears, _negative_ or +_female_. All atoms, so far as observed, are of one or other of these two +forms. (Plate II.) + +It will be seen that the atom is a sphere, slightly flattened, and there is +a depression at the point where the force flows in, causing a heart-like +form. Each atom is surrounded by a field, formed of the atoms of the four +higher planes, which surround and interpenetrate it. + +The atom can scarcely be said to be a "thing," though it is the material +out of which all things physical are composed. It is formed by the flow of +the life-force[5] and vanishes with its ebb. When this force arises in +"space"[6]--the apparent void which must be filled with substance of some +kind, of inconceivable tenuity--atoms appear; if this be artificially +stopped for a single atom, the atom disappears; there is nothing left. +Presumably, were that flow checked but for an instant, the whole physical +world would vanish, as a cloud melts away in the empyrean. It is only the +persistence of that flow[7] which maintains the physical basis of the +universe.[8] + +In order to examine the construction of the atom, a space is artificially +made[9]; then, if an opening be made in the wall thus constructed, the +surrounding force flows in, and three whorls immediately appear, +surrounding the "hole" with their triple spiral of two and a half coils, +and returning to their origin by a spiral within the atom; these are at +once followed by seven finer whorls, which following the spiral of the +first three on the outer surface, and returning to their origin by a spiral +within that, flowing in the opposite direction--form a caduceus with the +first three. Each of the three coarser whorls, flattened out, makes a +closed circle; each of the seven finer ones, similarly flattened out, makes +a closed circle. The forces which flow in them, again, come from "outside," +from a fourth-dimensional space.[10] Each of the finer whorls is formed of +seven yet finer ones, set successively at right angles to each other, each +finer than its predecessor; these we call spirillæ.[11] + +It will be understood from the foregoing, that the atom cannot be said to +have a wall of its own, unless these whorls of force can be so designated; +its "wall" is the pressed back "space." As said in 1895, of the chemical +atom, the force "clears itself a space, pressing back the undifferentiated +matter of the plane, and making to itself a whirling wall of this matter." +The wall belongs to space, not to the atom. + +In the three whorls flow currents of different electricities; the seven +vibrate in response to etheric waves of all kinds--to sound, light, heat, +etc.; they show the seven colours of the spectrum; give out the seven +sounds of the natural scale; respond in a variety of ways to physical +vibration--flashing, singing, pulsing bodies, they move incessantly, +inconceivably beautiful and brilliant.[12] + +The atom has--as observed so far--three proper motions, _i.e._, motions of +its own, independent of any imposed upon it from outside. It turns +incessantly upon its own axis, spinning like a top; it describes a small +circle with its axis, as though the axis of the spinning top moved in a +small circle; it has a regular pulsation, a contraction and expansion, like +the pulsation of the heart. When a force is brought to bear upon it, it +dances up and down, flings itself wildly from side to side, performs the +most astonishing and rapid gyrations, but the three fundamental motions +incessantly persist. If it be made to vibrate, as a whole, at the rate +which gives any one of the seven colors, the whorl belonging to that color +glows out brilliantly. + +[Illustration] + +An electric current brought to bear upon the atoms checks their proper +motions, _i.e._, renders them slower; the atoms exposed to it arrange +themselves in parallel lines, and in each line the heart-shaped depression +receives the flow, which passes out through the apex into the depression of +the next, and so on. The atoms always set themselves to the current. The +well-known division of diamagnetic and paramagnetic depends generally on +this fact, or on an analogous action on molecules, as may be seen in the +accompanying diagrams.[13] + +Two atoms, positive and negative, brought near to each other, attract each +other, and then commence to revolve round each other, forming a relatively +stable duality; such a molecule is neutral. Combinations of three or more +atoms are positive, negative or neutral, according to the internal +molecular arrangement; the neutral are relatively stable, the positive and +negative are continually in search of their respective opposites, with a +view to establishing a relatively permanent union. + +Three states of matter exist between the atomic state and the gaseous--the +state in which the chemical atoms are found, the recognized chemical +elements; for our purposes we may ignore the liquid and solid states. For +the sake of clearness and brevity in description, we have been obliged to +name these states; we call the atomic state of the chemist _elemental_; the +state which results from breaking up chemical elements, _proto-elemental_; +the next higher, _meta-proto-elemental_; the next higher, +_hyper-meta-proto-elemental_; then comes the atomic state. These are +briefly marked as El., Proto., Meta., and Hyper.[14] + +The simplest unions of atoms, never, apparently consisting of more than +seven, form the first molecular state of physical matter. + +[Illustration: TYPES OF HYPER-META-PROTO-ELEMENTAL MATTER.] + +Here are some characteristic combinations of the Hyper state; the atom is +conventional, with the depression emphasised; the lines, always entering at +the depression and coming out at the apex, show the resultants of lines of +force; where no line appears entering the depression, the force wells up +from fourth-dimensional space; where no line appears leaving the apex, the +force disappears into fourth-dimensional space; where the point of entry +and departure is outside the atoms, it is indicated by a dot.[15] + +The molecules show all kinds of possible combinations; the combinations +spin, turn head over heels, and gyrate in endless ways. Each aggregation is +surrounded with an apparent cell-wall, the circle or oval, due to the +pressure on the surrounding matter caused by its whirling motion; they +strike on each other[16] and rebound, dart hither and thither, for reasons +we have not distinguished. + +[Illustration: TYPES OF META-PROTO-ELEMENTAL MATTER.] + +The Meta state, in some of its combinations, appears at first sight to +repeat those of the Hyper state; the only obvious way of distinguishing to +which some of the molecules of less complexity belong is to pull them out +of the "cell-wall"; if they are Hyper molecules they at once fly off as +separate atoms; if they are Meta molecules they break up into two or more +molecules containing a smaller number of atoms. Thus one of the Meta +molecules of iron, containing seven atoms, is identical in appearance with +a Hyper heptad, but the latter dissociates into seven atoms, the former +into two triads and a single atom. Long-continued research into the +detailed play of forces and their results is necessary; we are here only +able to give preliminary facts and details--are opening up the way. The +following may serve as characteristic Meta types:-- + +These are taken from constituents of the various elements; 1 from Gl; 2 and +3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12 +from Li; 13 and 14 from Na. Others will be seen in the course of breaking +up the elements. + +The Proto state preserves many of the forms in the elements, modified by +release from the pressure to which they are subjected in the chemical atom. +In this state various groups are thus recognizable which are characteristic +of allied metals. + +[Illustration: TYPES OF PROTO-ELEMENTAL MATTER.] + +These are taken from the products of the first disintegration of the +chemical atom, by forcibly removing it from its hole. The groups fly apart, +assuming a great variety of forms often more or less geometrical; the lines +between the constituents of the groups, where indicated, no longer +represent lines of force, but are intended to represent the impression of +form, _i.e._, of the relative position and motion of the constituents, made +on the mind of the observer. They are elusive, for there are no lines, but +the appearance of lines is caused by the rapid motion of the costituents up +and down, or along them backwards and forwards. The dots represent atoms, +or groups of atoms, within the proto-elements. 1 is found in C; 2 and 3 in +He; 4 in Fl; 5 in Li; 6 in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe; +12 in Se. We shall return to these when analysing the elements, and shall +meet many other proto-elemental groupings. + +The first thing which is noticed by the observer, when he turns his +attention to the chemical atoms, is that they show certain definite forms, +and that within these forms, modified in various ways, sub-groupings are +observable which recur in connexion with the same modified form. The main +types are not very numerous, and we found that, when we arranged the atoms +we had observed, according to their external forms, they fell into natural +classes; when these, in turn, were compared with Sir William Crookes' +classification, they proved to be singularly alike. Here is his arrangement +of the elements, as it appeared in the _Proceedings of the Royal Society_, +in a paper read on June 9th, 1898. + +[Illustration] + +This is to be read, following the lines of the "figures of eight": H, He, +Li, Gl, B, C, N, and so on, each successive element being heavier than the +one preceding it in order. The disks which fall immediately below each +other form a class; thus: H, Cl, Br, I; these resemble each other in +various ways, and, as we shall presently see, the same forms and groupings +re-appear. + +Another chart--taken from Erdmann's _Lehrbuch_--arranges the elements on a +curved line, which curiously resembles the curves within the shell of a +nautilus. The radiating lines show the classes, the whole diameter building +up a family; it will be observed that there is an empty radius between +hydrogen and helium, and we have placed occultum there; on the opposite +radius, iron, rubidium and osmium are seen. + +[Illustration] + +The external forms may be classified as follows; the internal details will +be dealt with later :-- + +[Illustration: PLATE III.] + +1. _The Dumb-bell._--The characteristics of this are a higher and lower +group, each showing 12 projecting funnels, grouped round a central body, +and a connecting rod. It appears in sodium, copper, silver, and gold,[17] +and gold is given (1 on Plate III) as the most extremely modified example +of this form. The 12 almond-like projections, above and below, are +severally contained in shadowy funnels, impossible to reproduce in the +drawing; the central globe contains three globes, and the connecting +portion has swollen out into an egg, with a very complicated central +arrangement. The dumb-bell appears also in chlorine, bromine and iodine, +but there is no trace of it in hydrogen, the head of the group. We have not +met it elsewhere. It may be remarked that, in Sir William Crookes' scheme, +in which they are all classed as monads, these two groups are the nearest +to the neutral line, on the ingoing and outgoing series, and are +respectively positive and negative. + +II and IIa. _The Tetrahedron._--The characteristics of this form are four +funnels, containing ovoid bodies, opening on the face of a tetrahedron. The +funnels generally, but not always, radiate from a central globe. We give +beryllium (glucinum) as the simplest example (2 on Plate III), and to this +group belong calcium and strontium. The tetrahedron is the form of chromium +and molybdenum, but not that of the head of their group, oxygen, which is, +like hydrogen, _sui generis_. These two groups are marked in orthodox +chemistry as respectively positive and negative, and are closely allied. +Another pair of groups show the same tetrahedral form: magnesium, zinc and +cadmium, positive; sulphur, selenium and tellurium, negative. Selenium is a +peculiarly beautiful element, with a star floating across the mouth of each +funnel; this star is extremely sensitive to light, and its rays tremble +violently and bend if a beam of light falls on it. All these are dyads. + +The tetrahedron is not confined to the external form of the above atoms; it +seems to be one of the favourite forms of nature, and repeatedly appears in +the internal arrangements. There is one tetrahedron within the unknown +element occultum; two appear in helium (3 on Plate III); yttrium has also +two within its cube, as has germanium; five, intersecting, are found in +neon, meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon, +kalon, meta-kalon, tin, titanium and zirconium. Gold contains no less than +twenty tetrahedra. + +III. _The Cube._--The cube appears to be the form of triads. It has six +funnels, containing ovoids, and opening on the faces of the cube. Boron is +chosen as an example (4 on Plate III). Its group members, scandium and +yttrium, have the same form; we have not examined the fourth; the group is +positive. Its negative complement consists of nitrogen, vanadium and +niobium, and we have again to note that nitrogen, like hydrogen and oxygen, +departs from its group type. Two other triad groups, the positive +aluminium, gallium and indium (the fourth unexamined) and the negative +phosphorus, arsenic and antimony (the fourth unexamined), have also six +funnels opening on the faces of a cube. + +IV. _The Octahedron._--The simplest example of this is carbon (5 on Plate +III). We have again the funnel with its ovoids, but now there are eight +funnels opening on the eight faces of the octahedron. In titanium (6 on +Plate III) the form is masked by the protruding arms, which give the +appearance of the old Rosicrucian Cross and Rose, but when we look into the +details later, the carbon type comes out clearly. Zirconium is exactly like +titanium in form, but contains a large number of atoms. We did not examine +the remaining two members of this group. The group is tetratomic and +positive. Its negative pendant shows the same form in silicon, germanium +and tin; again, the fourth was unexamined. + +[Illustration: PLATE IV.] + +V. _The Bars._--These characterise a set of closely allied groups, termed +"inter-periodic." Fourteen bars (or seven crossed) radiate from a centre, +as in iron (1 on Plate IV), and the members of each group--iron, nickel, +cobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum--differ +from each other by the weight of each bar, increasing in orderly +succession; the details will be given later. Manganese is often grouped +with iron, nickel, and cobalt (_see_ Crookes' lemniscates), but its +fourteen protruding bodies repeat the "lithium spike" (proto-element 5) and +are grouped round a central ovoid. This would appear to connect it with +lithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with +which it is often classed. The "lithium spike" re-appears in potassium and +rubidium. These details, again, will come out more clearly later. + +VI. _The Star._--A flat star, with five interpenetrating tetrahedra in the +centre, is the characteristic of neon and its allies (4 on Plate IV) +leaving apart helium, which, as may be seen by referring to 3, Plate IV, +has an entirely different form. + +There are thus six clearly defined forms, typical of classes, with +two--lithium and fluorine--of doubtful affinities. It is worthy of notice +that in diatomic elements _four_ funnels open on the faces of tetrahedra; +in triatomic, _six_ funnels on the faces of cubes; in tetratomic, _eight_ +funnels on the faces of octahedra. + +Thus we have a regular sequence of the platonic solids, and the question +suggests itself, will further evolution develop elements shaped to the +dodecahedron and the icosahedron? + + * * * * * + +II. + +We now pass from the consideration of the outer forms of the chemical +elements to a study of their internal structure, the arrangement within the +element of more or less complicated groups--proto-elements--capable of +separate, independent existence; these, once more, may be dissociated into +yet simpler groups--hyper-meta-proto-elements--equally capable of separate, +independent existence, and resolvable into single ultimate physical atoms, +the irreducible substratum of the physical world (see _Theosophist_, 1908, +pp. 354-356).[18] + +We shall have to study the general internal structure, and then the +breaking up of each element, and the admirable diagrams, patiently worked +out by Mr. Jinarâjadâsa, will make the study comparatively easy to carry +on. + +The diagrams, of course, can only give a very general idea of the facts +they represent; they give groupings and show relations, but much effort of +the imagination is needed to transform the two-dimensional diagram into the +three-dimensional object. The wise student will try to visualize the figure +from the diagram. Thus the two triangles of hydrogen are not in one plane; +the circles are spheres, and the atoms within them, while preserving to +each other their relative positions, are in swift movement in +three-dimensional space. Where five atoms are seen, as in bromine and +iodine, they are generally arranged with the central atom above the four, +and their motion indicates lines which erect four plane triangles--meeting +at their apices--on a square base, forming a square-based four-sided +pyramid. Each dot represents a single ultimate atom. The enclosing lines +indicate the impression of form made on the observer, and the groupings of +the atoms; the groups will divide along these lines, when the element is +broken up, so that the lines have significance, but they do not exist as +stable walls or enclosing films, but rather mark limits, not lines, of +vibrations. It should be noted that it is not possible to show five of the +prisms in the five intersecting tetrahedra of prisms, and 30 atoms must, +therefore, be added in counting. + +The diagrams are not drawn to scale, as such drawing would be impossible; +the dot representing the atom is enormously too large compared with the +enclosures, which are absurdly too small; a scale drawing would mean an +almost invisible dot on a sheet of many yards square. + +The use of the words "positive" and "negative" needs to be guarded by the +following paragraphs from the article on "Chemistry" in the _Encyclopædia +Britannica_. We use the words in their ordinary text-book meaning, and have +not, so far, detected any characteristics whereby an element can be +declared, at sight, to be either positive or negative:-- + +"When binary compounds, or compounds of two elements, are decomposed by an +electric current, the two elements make their appearance at opposite poles. +These elements which are disengaged at the negative pole are termed +electro-positive or positive or basylous elements, while those disengaged +at the positive pole are termed electro-negative or negative or chlorous +elements. But the difference between these two classes of elements is one +of degree only, and they gradually merge into each other; moreover the +electric relations of elements are not absolute, but vary according to the +state of combination in which they exist, so that it is just as impossible +to divide the elements into two classes according to this property as it is +to separate them into two distinct classes of metals and non-metals." + +We follow here the grouping according to external forms, and the student +should compare it with the groups marked in the lemniscate arrangement +shown in Article II (p. 377, properly p. 437, February), reading the group +by the disks that fall below each other; thus the first group is H, Cl, Br, +I (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered +element. The elements grow denser in descending order; thus hydrogen is an +invisible gas; chlorine a denser gas visible by its colour; bromine is a +liquid; iodine is a solid--all, of course, when temperature and pressure +are normal. By the lowering of temperature and the increase of pressure, an +element which is normally gaseous becomes a liquid, and then a solid. +Solid, liquid, gaseous, are three interchangeable states of matter, and an +element does not alter its constitution by changing its state. So far as a +chemical "atom" is concerned, it matters not whether it be drawn for +investigation from a solid, a liquid, or a gas; but the internal +arrangements of the "atoms" become much more complicated as they become +denser and denser, as is seen by the complex arrangements necessitated by +the presence of the 3546 ultimate atoms contained in the chemical "atom" of +gold, as compared with the simple arrangement of the 18 ultimate atoms of +hydrogen. + +According to the lemniscate arrangement, we should commence with hydrogen +as the head of the first negative group, but as it differs wholly from +those placed with it, it is better to take it by itself. Hydrogen is the +lightest of the known elements, and is therefore taken as 1 in ordinary +chemistry, and all atomic weights are multiples of this. We take it as 18, +because it contains eighteen ultimate atoms, the smallest number we have +found in a chemical element. So our "number-weights" are obtained by +dividing the total number of atoms in an element by 18 (see p. 349, +January). + +[Illustration: PLATE V.] + +HYDROGEN (Plate V, 1).--Hydrogen not only stands apart from its reputed +group by not having the characteristic dumb-bell shape, well shown in +sodium (Plate I, opposite p. 349, January), but it also stands apart in +being positive, serving as a base, not as a chlorous, or acid, radical, +thus "playing the part of a metal," as in hydrogen chloride (hydrochloric +acid), hydrogen sulphate (sulphuric acid), etc. + +It is most curious that hydrogen, oxygen and nitrogen, the most widely +spread gases, all differ fundamentally in form from the groups they +reputedly head.[19] Hydrogen was the first chemical element examined by us, +nearly thirteen years ago, and I reproduce here the substance of what I +wrote in November, 1895, for we have nothing to add to nor amend in it. + +Hydrogen consists of six small bodies, contained in an egg-like form (the +outer forms are not given in the diagrams). The six little bodies are +arranged in two sets of three, forming two triangles which are not +interchangeable, but are related to each other as object and image. The six +bodies are not all alike; they each contain three ultimate physical atoms, +but in four of the bodies the three atoms are arranged in a triangle, and +in the remaining two in a line. + +HYDROGEN: 6 bodies of 3 18 + Atomic weight 1 + Number weight 18/18 1 +I.--THE DUMB-BELL GROUP. + +I a.--This group consists of Cl, Br, and I (chlorine, bromine and iodine); +they are monads, diamagnetic and negative. + +CHLORINE (Plate V, 2).--As already said, the general form is that of the +dumb-bell, the lower and upper parts each consisting of twelve funnels, six +sloping upwards and six downwards, the funnels radiating outwards from a +central globe, and these two parts being united by a connecting rod (see, +again, sodium, Plate I). + +The funnel (shown flat as an isosceles triangle, standing on its apex) is a +somewhat complicated structure, of the same type as that in sodium (Plate +VI, 2), the difference consisting in the addition of one more globe, +containing nine additional atoms. The central globe is the same as in +sodium, but the connecting rod differs. We have here a regular arrangement +of five globes, containing three, four, five, four, three atoms +respectively, whereas sodium has only three bodies, containing four, six, +four. But copper and silver, its congeners, have their connecting rods of +exactly the same pattern as the chlorine rod, and the chlorine rod +reappears in both bromine and iodine. These close similarities point to +some real relation between these groups of elements, which are placed, in +the lemniscates, equi-distant from the central line, though one is on the +swing which is going towards that line and the other is on the swing away +from it. + +CHLORINE: Upper part {12 funnels of 25 atoms 300 + {Central globe 10 + Lower part same 310 + Connecting rod 19 + ---- + Total 639 + ---- + Atomic weight 35.473 + Number weight 639/18 35.50 +(The Atomic Weights are mostly from Erdmann, and the Number Weights are +those ascertained by us by counting the atoms as described on p. 349, +January, and dividing by 18. Prof. T.W. Richards, in _Nature_, July 18, +1907, gives 35.473.) + +BROMINE (Plate V, 3).--In bromine, each funnel has three additional bodies, +ovoid in shape, an addition of 33 atoms being thus made without any +disturbance of form; two pairs of atoms are added to the central globe, and +a rearrangement of the atoms is effected by drawing together and lessening +the swing of the pair of triplets, thus making symmetrical room for the +newcomers. The connecting rod remains unchanged. The total number of atoms +is thus raised from the 639 of chlorine to 1439. Over and over again, in +these investigations, were we reminded of Tyndall's fascinating description +of crystal building, and his fancy of the tiny, ingenious builders busied +therein. Truly are there such builders, and the ingenuity and effectiveness +of their devices are delightful to see.[20] + +BROMINE: Upper part {12 funnels of 58 atoms 696 + {Central globe 14 + Lower part same 710 + Connecting rod 19 + ---- + Total 1439 + ---- + Atomic weight 79.953 + Number weight 1459/18 79.944 +IODINE (Plate V, 4).--We find herein that the central globe gains 4 atoms, +the two pairs becoming 2 quartets; the connecting rod exactly reproduces +the rods of chlorine and bromine; the funnel is also that of bromine, +except that five bodies, containing 35 atoms, are added to it. The 1439 +atoms of bromine are thus raised to 2887. + +IODINE: Upper Part {12 funnels of 90 atoms 1116 + {Central globe 18 + Lower part same 1134 + Connecting rod 19 + ---- + Total 2287 + ---- + Atomic weight 126.01 + Number weight 2287/18 127.055 +The plan underlying the building up of groups is here clearly shown; a +figure is built up on a certain plan, in this case a dumb-bell; in the +succeeding members of the group additional atoms are symmetrically +introduced, modifying the appearance, but following the general idea; in +this case the connecting rod remains unaltered, while the two ends become +larger and larger, more and more overshadowing it, and causing it to become +shorter and thicker. Thus a group is gradually formed by additional +symmetrical additions. In the undiscovered remaining member of the group we +may suppose that the rod will have become still more egg-like, as in the +case of gold. + +I b.--The corresponding positive group to that which we have been +considering consists of Na, Cu, Ag, and Au (sodium, copper, silver and +gold), with an empty disk between silver and gold, showing where an element +ought to be. These four elements are monads, diamagnetic, and positive, and +they show the dumb-bell arrangement, although it is much modified in gold; +we may presume that the undiscovered element between silver and gold would +form a link between them. + +[Illustration: PLATE VI.] + +SODIUM (Plate VI, 2) has been already described (p. 349, January), as a +type of the group, so we need only refer to its internal arrangement in +order to note that it is the simplest of the dumb-bell group. Its twelve +funnels show only four enclosed bodies, the same as we see in chlorine, +bromine, iodine, copper and silver, and which is very little modified in +gold. Its central globe is the simplest of all, as is its connecting rod. +We may therefore take it that sodium is the ground-plan of the whole group. + +SODIUM: Upper part + { 12 funnels of 16 each 192 + { Central globe 10 + Lower part same 202 + Connecting rod 14 + ---- + Total 418 + ---- + Atomic weight 23.88 + Number weight 418/19 23.22 +COPPER (Plate VI, 3) introduces an addition in the funnel, that we shall +find elsewhere, _e.g._, in silver, gold, iron, platinum, zinc, tin, the +triangular arrangement near the mouth of the funnel and adds to the ten +atoms in this nineteen more in three additional enclosed bodies, thus +raising the number of atoms in a funnel from the sixteen of sodium to +forty-five. The number in the central globe is doubled, and we meet for the +first time the peculiar cigar or prism-shaped six-atomed arrangement, that +is one of the most common of atomic groups. It ought to imply some definite +quality, with its continual recurrence. The central column is the three, +four, five, four, three, arrangement already noted. + +COPPER: Upper part {12 funnels of 45 atoms 540 + {Central globe 20 + Lower part same 560 + Connecting rod 19 + ---- + Total 1139 + ---- + Atomic weight 63.12 + Number weight 1139/18 63.277 +SILVER (Plate VI, 4) follows copper in the constitution of five of the +bodies enclosed in the funnels. But the triangular group contains +twenty-one atoms as against ten, and three ovoids, each containing three +bodies with eleven atoms, raise the number of atoms in a funnel to +seventy-nine. The central globe is decreased by five, and the prisms have +disappeared. The connecting rod is unaltered. + +SILVER: Upper part {12 funnels of 79 atoms 948 + {Central globe 15 + Lower part same 963 + Connecting rod 19 + ---- + Total 1945 + ---- + Atomic weight 107.93 + Number weight 1945/18 108.055 +(This atomic weight is given by Stas, in _Nature_, August 29, 1907, but it +has been argued later that the weight should not be above 107.883.) + +[Illustration: PLATE VII.] + +GOLD (Plate VII) is so complicated that it demands a whole plate to itself. +It is difficult to recognize the familiar dumb-bell in this elongated egg, +but when we come to examine it, the characteristic groupings appear. The +egg is the enormously swollen connecting rod, and the upper and lower parts +with their central globes are the almond-like projections above and below, +with the central ovoid. Round each almond is a shadowy funnel (not drawn in +the diagram), and within the almond is the collection of bodies shown in +_e_, wherein the two lowest bodies are the same as in every other member of +the negative and positive groups; the third, ascending, is a very slight +modification of the other thirds; the fourth is a union and re-arrangement +of the fourth and fifth; the fifth, of four ovoids, adds one to the three +ovoids of bromine, iodine and silver; the triangular group is like that in +copper and silver, though with 28 atoms instead of 10 or 21, and it may be +noted that the cone in iron has also 28. The central body in the ovoid is +very complicated, and is shown in _c_, the bodies on each side, _d_, are +each made up of two tetrahedra, one with four six-atomed prisms at its +angles, and the other with four spheres, a pair with four atoms and a pair +with three. We then come to the connecting rod. One of the four similar +groups in the centre is enlarged in _a_, and one of the sixteen circling +groups is enlarged in b. These groups are arranged in two planes inclined +to one another. + +GOLD: Upper part + { 12 funnels of 97 atoms 1164 + { Central ovoid {c 101 + {2 d, 38 76 + Lower part same 1341 + Connecting rod { 4 a 84 336 + {16 b 33 528 + ---- + Total 3546 + ---- + Atomic weight 195.74 + Number weight 3546/18 197 +It may be noted that the connecting rod is made up of exactly sixteen atoms +of occultum, and that sixteen such atoms contain 864 ultimate atoms, the +exact member of atoms in titanium. + + * * * * * + +III. + +Occultum was observed by us in 1895, and, finding that it was so light, and +so simple in its composition, we thought that it might be helium, of which +we were unable, at the time, to obtain a sample. When, however, helium +itself came under observation in 1907, it proved to be quite different from +the object before observed, so we dubbed the unrecognised object Occultum, +until orthodox science shall find it and label it in proper fashion. + +OCCULTUM (Plate VI, 1). + +We here meet the tetrahedron for the first time, with each angle occupied +by a six-atomed group, the atoms arranged as on the end triangles of a +prism. This form recurs very often, and was noted, last month, as seen in +copper (Plate VI, 3); it revolves with extreme rapidity around its +longitudinal axis, and looks like a pencil sharpened at both ends, or a +cigar tapering at both ends; we habitually spoke of it as "the cigar." It +appears to be strongly coherent, for, as will be seen below, its six atoms +remain attached to each other as meta-compounds and even when divided into +two triplets as hyper-compounds, they revolve round each other. + +Above the tetrahedron is a balloon-shaped figure, apparently drawn into +shape by the attraction of the tetrahedron. The body below the tetrahedron +looks like a coil of rope, and contains fifteen atoms; they are arranged on +a slanting disk in a flat ring, and the force goes in at the top of one +atom, and out of the bottom of it into the top of the next, and so on, +making a closed circuit. The two little spheres, each containing a triplet, +are like fill-up paragraphs to a compositor--they seem to be kept standing +and popped in where wanted. The sphere marked _x_ is a proto-compound, the +balloon when set free. + +As was noted under gold (p. 41), sixteen occultum bodies, re-arranged, make +up the connecting rod in gold:-- + +OCCULTUM: Tetrahedron 24 + Balloon 9 + Triplets 6 + Rope-circle 15 + ---- + Total 54 + ---- + Atomic weight Not known + Number weight 54/18 3 +DISSOCIATION OF ATOMS. + +Before proceeding to the study of other chemical atoms, as to their general +internal arrangements, it is desirable to follow out, in those already +shown, the way in which these atoms break up into simpler forms, yielding +successively what we have called proto-, meta-, and hyper-compounds. It is +naturally easier to follow these in the simpler atoms than in the more +complex, and if the earlier dissociations are shown, the latter can be more +readily and more intelligibly described. + +The first thing that happens on removing a gaseous atom from its "hole" +(see pp. 21 to 23) or encircling "wall," is that the contained bodies are +set free, and, evidently released from tremendous pressure, assume +spherical or ovoid forms, the atoms within each re-arranging themselves, +more or less, within the new "hole" or "wall." The figures are, of course, +three-dimensional, and often remind one of crystals; tetrahedral, +octagonal, and other like forms being of constant occurrence. In the +diagrams of the proto-compounds, the constituent atoms are shown by dots. +In the diagrams of the meta-compounds the dot becomes a heart, in order to +show the resultants of the lines of force. In the diagrams of the +hyper-compounds the same plan is followed. The letters _a_, _b_, _c_, &c., +enable the student to follow the breaking up of each group through its +successive stages. + +HYDROGEN (Plate V, 1). + +[Illustration] + +The six bodies contained in the gaseous atom instantaneously re-arrange +themselves within two spheres; the two linear triplets unite with one +triangular triplet, holding to each other relative positions which, if +connected by three right lines, would form a triangle with a triplet at +each angle; the remaining three triangular triplets similarly arrange +themselves in the second sphere. These form the proto-compounds of +hydrogen. + +In the dissociation of these, each group breaks up into two, the two linear +triplets joining each other and setting free their triangular comrade, +while two of the triangular triplets similarly remain together, casting out +the third, so that hydrogen yields four meta-compounds. + +In the hyper-condition, the connexion between the double triplets is +broken, and they become four independent groups, two like ix, in the +hyper-types (p. 25), and two remaining linear, but rearranging their +internal relations; the two remaining groups break up into two pairs and a +unit. + +The final dissociation sets all the atoms free. + +OCCULTUM (Plate VI, 1). + +[Illustration] + +On the first dissociation of the component parts of occultum, the +tetrahedron separates as a whole, with its four "cigars," flattening itself +out within its hole, _a_; two "cigars" are positive and two negative, +marked respectively _a_ and _a'_. The rope becomes a ring within a sphere, +_b_, and the two bodies _d_ _d_, which are loose in the gaseous atom, come +within this ring. The balloon becomes a sphere. + +On further dissociation, the "cigars" go off independently, showing two +types, and these again each divide into triplets, as meta-compounds. _B_, +on the meta-level, casts out the two _d_ bodies, which become independent +triplets, and the "rope" breaks into two, a close ring of seven atoms and a +double cross of eight. These subdivide again to form hyper-compounds, the +ring yielding a quintet and a pair, and the double cross separating into +its two parts. + +The balloon, _c_, becomes much divided, the cohesion of its parts being +slight; it forms two triplets, a pair and a unit, and these set free, on +further dissociation, no less than five separate atoms and two duads. + +The two triplets of _d_ each cast out an atom on dissociation, and form two +pairs and two units. + +SODIUM (Plate VI, 2). + +It is convenient to consider sodium next, because it is the basic pattern +on which not only copper, silver and gold are formed, but also chlorine, +bromine and iodine. + +[Illustration] + +When sodium is set free from its gaseous condition, it divides up into +thirty-one bodies--twenty-four separate funnels, four bodies derived from +the two central globes, and three from the connecting rod. The funnels +become spheres, and each contains four enclosed spheres, with more or less +complicated contents. Each central globe yields a sextet and a quartet, and +the rod sets free two quartets and a peculiarly formed sextet. + +When the proto-compounds are dissociated, the funnel-sphere sets free: (1) +the contents of _a_, rearranged into two groups of four within a common +sphere; the sphere yields four duads as hyper-compounds; (2) the contents +of _b_, which unite themselves into a quartet, yielding two duads as +hyper-compounds; and (3) the contents of the two spheres, _c_, which +maintain their separation as meta-compounds, and become entirely +independent, the atoms within the sphere revolving round each other, but +the spheres ceasing their revolution round a common axis, and going off in +different directions. The atoms break off from each other, and gyrate in +independent solitude as hyper-"compounds." Thus each funnel yields finally +ten hyper-bodies. + +The part of the central globe, marked _d_, with its six atoms, whirling +round a common centre, becomes two triplets, at the meta-stage, preparing +for the complete separation of these as hyper-bodies. The second part of +the same globe, marked _e_, a whirling cross, with an atom at each point, +becomes a quartet in the meta-state, in which three atoms revolve round a +fourth, and in the hyper-state this central atom is set free, leaving a +triplet and a unit. + +Each of the two bodies marked _f_, liberated from the connecting rod, shows +four atoms whirling round a common centre, exactly resembling _e_ in +appearance; but there must be some difference of inner relations, for, in +the meta-state, they re-arrange themselves as two pairs, and divide into +two as hyper-bodies. + +The body marked _g_ is a four-sided pyramid, with two closely joined atoms +at its apex; these still cling to each in mutual revolution as a meta-body, +encircled by a ring of four, and this leads to a further dissociation into +three pairs on the hyper-level. + +CHLORINE (Plate V, 2). + +[Illustration] + +The description of the funnel of sodium applies to that of chlorine, until +we come to the body nearest the mouth, the sphere containing three +additional bodies; this remains within the funnel in the first +dissociation, so that again we have twenty-four separate funnels as +proto-compounds; the central globes are the same as in sodium, and yield +the same four bodies; the connecting rod sets free five bodies, of which +two are the same; we have thus thirty-three separate bodies as the result +of the dissociation of chlorine into its proto-compounds. As all the +compounds which are in sodium break up in the same way into meta- and +hyper-compounds, we need not repeat the process here. We have only to +consider the new meta- and hyper-compounds of the highest sphere within the +funnel, and the two triplets and one quintet from the connecting rod. + +The additional body within the proto-funnel is of a very simple character, +three contained triangles within the flattened sphere. On release from the +funnel, on the meta-level, the atoms rearrange themselves in a whirling set +of three triplets, and these break off from each other as hyper-compounds. +The two triplets from the connecting rod, also, are of the simplest +character and need not delay us. The five-atomed body, a four-sided pyramid +as a proto-compound, becomes a ring whirling round a centre on the meta, +and two pairs with a unit on the hyper. + +BROMINE (Plate V, 3). + +Three additional bodies appear at the top of the funnel, which otherwise +repeats that of chlorine. The connecting rod is the same and may be +disregarded. The central globes become more complex. The additions are, +however, of very easy types, and hence are readily dealt with. Each of the +three similar ovoid bodies contains two triplets--each a triangle and a +quintet--a four-sided pyramid. These are the same, as may be seen in the +connecting rod of chlorine, and we need not repeat them. Only the globe +remains. This does not break up as a proto-compound but is merely set free, +_a_ and the 2 _bs_ whirling in a plane vertical to the paper and the two +smaller bodies, _cc_, whirling on a plane at right angles to the other. +These two disengage themselves, forming a quartet as a meta-compound, while +_a_ makes a whirling cross and _bb_ a single sextet; these further +dissociate themselves into four pairs and two triplets. + +IODINE (Plate V, 4). + +[Illustration] + +Iodine has nothing new to give us, except five similar ovoid bodies at the +top of each funnel, and two quartets instead of two pairs in the central +globe. The ovoid bodies become spheres when the funnels are thrown off, and +a crystalline form is indicated within the sphere. The atoms are arranged +in two tetrahedra with a common apex, and the relationship is maintained in +the meta-body, a septet. The latter breaks up into two triplets and a unit +on the hyper-level. In the central globes, the _a_ of bromine is repeated +twice instead of the pairs in _cc_. + +COPPER (Plate VI, 3). + +We have already disposed of occultum, on this plate, and of sodium, which +lies at the root of both groups. Copper, we now find, is also very largely +off our hands, as the funnel provides us with only two new types--two +spheres--each containing five atoms in a new arrangement, and the +triangular body at the mouth with its ten atoms. This triangular body, with +an increased number of atoms, reappears in various other chemical elements. +The central globes are different from any we have had before, in their +internal arrangement, but the constituents are familiar; there are two +contained spheres with four atoms each, the _a_ in the globe of bromine +(see above) and 2 "cigars." The "cigars" may be followed under occultum +(see above). The connecting rod is as in chlorine, bromine and iodine. + +The atoms in the bodies _a_ and _b_ are curiously arranged. _A_ consists of +two square-based pyramids turned so as to meet at their apices, and breaks +up into two quartet rings and a duad. _B_ is again two four-sided pyramids, +but the bases are in contact and set at right angles to each other; the +second apex is not seen, as it is directly below the first. The pyramids +separate as meta-bodies, and the atoms assume the peculiar arrangement +indicated and then break up into four pairs and two units on the hyper +level. + + * * * * * + +IV. + +SILVER (Plate VI, 4 and Ag below). + +Silver presents us with only two new bodies, and even these are only new by +slight additions to old models. The triangular shaped body at the apex of +the funnel, containing 21 atoms, is intermediate between the similar bodies +in copper and iron. As a proto-element it becomes three triangles, joined +at their apices, in fact a tetrahedron in which no atoms are distributed on +the fourth face. The faces separate on the meta level and give three +seven-atomed figures, and each of these breaks up into two triplets and a +unit. The central globe only differs from that of bromine by the addition +of one atom, which gives the familiar four-sided pyramid with a square base +as in chlorine (see p. 46). + +GOLD (Plate VII and Au below). + +[Illustration] + +The disintegration of gold first yields forty-seven bodies on the +proto-level; the twenty-four funnels separate, and the central globes which +hold each twelve together set free their six contained globes (_c_, _d_), +thirty bodies being thus liberated. The sixteen bodies on the central +inclined planes, marked _b_, break away, their central globe, with its four +contained globes, remaining unchanged. But this condition does not last. +The motion of the funnels changes and thus the funnels cease to exist and +their contents are set free, each funnel thus liberating nine independent +bodies; the sixteen _b_ separate into two each; the four _a_ liberate five +each; the two _c_ set free thirteen each; the four _d_ finally liberate two +each: 302 proto elements in all. + +The funnel is almost that of iodine, re-arranged. Four of the first ring in +the iodine funnel are replaced by the triangular body, which becomes a +four-sided pyramid with an occupied base. The second ring of three ovoids +in iodine becomes four in gold, but the internal arrangement of each ovoid +is the same. The next two spheres in the iodine funnel coalesce into one +sphere, with similar contents, in the gold funnel. The fifth in iodine is +slightly rearranged to form the fourth in descent in gold, and the +remaining two are the same. _B_ has been broken up under occultum (p. 628) +and can be followed there. The sixteen rings set free from the four _a_, +after gyrating round the central body, now become a sphere, break up, as in +occultum (see p. 44) into a meta seven-atomed ring and an eight-atomed +double cross, and so on to the hyper level. The sphere with its two +contained bodies breaks up into eight triangles on the meta level, and each +of these, on the hyper, into a duad and a unit. The twelve septets of _c_ +assume the form of prisms as in iodine (see p. 48) and pursue the same +course, while its central body, a four-sided pyramid with its six +attendants, divides on the meta level into six duads, revolving round a +ring with a central atom as in chlorine (p. 47), the duads going off +independently on the hyper-level and the ring breaking up as in chlorine. +The "cigar" tetrahedron of _d_ follows its course as in occultum, and the +other sets free two quartets and two triplets on the meta level, yielding +six duads and two units as hyper compounds. It will be seen that, complex +as gold is, it is composed of constituents already familiar, and has iodine +and occultum as its nearest allies. + +II AND IIa.--THE TETRAHEDRAL GROUPS. + +II.--This group consists of beryllium (glucinum), calcium, strontium and +barium, all diatomic, paramagnetic and positive. The corresponding group +consists of oxygen, chromium, molybdenum, wolfram (tungsten) and uranium, +with a blank disk between wolfram and uranium: these are diatomic, +paramagnetic, and negative. We have not examined barium, wolfram, or +uranium. + +[Illustration: PLATE VIII.] + +BERYLLIUM (Plate III, 2, and Plate VIII, 1). In the tetrahedron four +funnels are found, the mouth of each funnel opening on one of its faces. +The funnels radiate from a central globe, and each funnel contains four +ovoids each with ten atoms within it arranged in three spheres. In the +accompanying diagrams one funnel with its four ovoids is shown and a single +ovoid with its three spheres, containing severally three, four, and three +atoms, is seen at the left-hand corner of the plate (7 _a_). The members of +this group are alike in arrangement, differing only in the increased +complexity of the bodies contained in the funnels. Beryllium, it will be +observed, is very simple, whereas calcium and strontium are complicated. + +BERYLLIUM: 4 funnels of 40 atoms 160 + Central globe 4 + ---- + Total 164 + ---- +Atomic weight 9.01 +Number weight 164/18 9.11 +CALCIUM (Plate VIII, 2) shows in each funnel three contained spheres, of +which the central one has within it seven ovoids identical with those of +beryllium, and the spheres above and below it contain each five ovoids (7 +_b_) in which the three contained spheres have, respectively, two, five, +and two atoms. The central globe is double, globe within globe, and is +divided into eight segments, radiating from the centre like an orange; the +internal part of the segment belonging to the inner globe has a triangular +body within it, containing four atoms (7 _c_), and the external part, +belonging to the encircling globe, shows the familiar "cigar" (7 _d_). In +this way 720 atoms are packed into the simple beryllium type. + +CALCIUM: 4 funnels of 160 atoms 640 + Central globe 80 + ---- + Total 720 + ---- + Atomic weight 39.74 + Number weight 720/18 40.00 +STRONTIUM (Plate VIII, 3) shows a still further complication within the +funnels, no less than eight spheres being found within each. Each of the +highest pair contains four subsidiary spheres, with five, seven, seven, +five atoms, respectively (7 _e_, _g_, _f_). The _g_ groups are identical +with those in gold, but difference of pressure makes the containing body +spherical instead of ovoid; similar groups are seen in the top ring of the +iodine funnel, where also the "hole" is ovoid in form. The second pair of +spheres contains ten ovoids (7 _b_) identical with those of calcium. The +third pair contains fourteen ovoids (7 _a_) identical with those of +beryllium, while the fourth pair repeats the second, with the ovoids +re-arranged. The internal divisions of the double sphere of the central +globe are the same as in calcium, but the contents differ. The "cigars" in +the external segments are replaced by seven-atomed ovoids (7 _h_)--the +iodine ovoids--and the external segments contain five-atomed triangles (7 +_i_). Thus 1,568 atoms have been packed into the beryllium type, and our +wonder is again aroused by the ingenuity with which a type is preserved +while it is adapted to new conditions. + +STRONTIUM: 4 funnels of 368 atoms 1472 + Central globe 96 + ---- + Total 1568 + ---- + Atomic weight 86.95 + Number weight 1568/18 87.11 +The corresponding group, headed by oxygen--oxygen, chromium, molybdenum, +wolfram and uranium--offers us another problem in its first member. + +OXYGEN (Plate VIII, 4). This was examined by us in 1895, and the +description may be reproduced here with a much improved diagram of its very +peculiar constitution. The gaseous atom is an ovoid body, within which a +spirally-coiled snake-like body revolves at a high velocity, five brilliant +points of light shining on the coils. The appearance given in the former +diagram will be obtained by placing the five septets on one side on the top +of those on the other, so that the ten become in appearance five, and thus +doubling the whole, the doubling point leaving eleven duads on each side. +The composition is, however, much better seen by flattening out the whole. +On the proto level the two snakes separate and are clearly seen. + +OXYGEN: Positive snake + { 55 spheres of 2 atoms } + { + 5 disks of 7 atoms } 145 + Negative snake " 145 + ---- + Total 290 + ---- + Atomic weight 15.87 + Number weight 290/18 16.11 +CHROMIUM (Plate VIII, 5) "reverts to the ancestral type," the tetrahedron; +the funnel is widened by the arrangement of its contents, three spheres +forming its first ring, as compared with the units in beryllium and +calcium, and the pairs in strontium and molybdenum. Two of these spheres +are identical in their contents--two quintets (7 _f_), a quintet (7 _j_), +and two quintets (7 _e_), _e_ and _f_ being to each other as object and +image. The remaining sphere (7 _b_) is identical with the highest in the +calcium funnel. The remaining two spheres, one below the other, are +identical with the corresponding two spheres in calcium. The central globe, +as regards its external segments, is again identical with that of calcium, +but in the internal segments a six-atomed triangle (7 _k_) is substituted +for the calcium four-atomed one (7 _e_). + +CHROMIUM: 4 funnels of 210 atoms 840 + Central globe 96 + ----- + Total 936 + ----- + Atomic weight 51.74 + Number weight 936/18 52.00 +MOLYBDENUM (Plate VIII, 6) very closely resembles strontium, differing from +it only in the composition of the highest pair of spheres in the funnels +and in the presence of a little sphere, containing two atoms only, in the +middle of the central globe. The topmost spheres contain no less than eight +subsidiary spheres within each; the highest of these (7 _e_) has four atoms +in it; the next three have four, seven and four (7 _e_ _g_ _e_), +respectively; the next three are all septets (7 _g_), and the last has +four--making in all for these two spheres 88 atoms, as against the 48 in +corresponding spheres of strontium, making a difference of 160 in the four +funnels. + +MOLYBDENUM: 4 funnels of 408 atoms 1632 + Central globe 98 + ----- + Total 1730 + ----- + Atomic weight 95.26 + Number weight 1730/18 96.11 +II a.--This group contains magnesium, zinc, cadmium, and mercury, with an +empty disk between cadmium and mercury; we did not examine mercury. All are +diatomic, diamagnetic and positive; the corresponding group consists of +sulphur, selenium and tellurium, also all diatomic and diamagnetic, but +negative. The same characteristics of four funnels opening on the faces of +a tetrahedron are found in all, but magnesium and sulphur have no central +globe, and in cadmium and tellurium the globe has become a cross. + +[Illustration: PLATE IX.] + +MAGNESIUM (Plate IX, 1) introduces us to a new arrangement: each group of +three ovoids forms a ring, and the three rings are within a funnel; at +first glance, there are three bodies in the funnel; on examination each of +these is seen to consist of three, with other bodies, spheres, again within +them. Apart from this, the composition is simple enough, all the ovoids +being alike, and composed of a triplet, a septet and a duad. + +MAGNESIUM: 4 funnels of 108 atoms 432 + Atomic weight 24.18 + Number weight 432/18 24.00 +ZINC (Plate IX, 2) also brings a new device: the funnel is of the same type +as that of magnesium, while septets are substituted for the triplets, and +36 additional atoms are thus slipped in. Then we see four spikes, +alternating with the funnels and pointing to the angles, each adding 144 +atoms to the total. The spikes show the ten-atomed triangle, already met +with in other metals, three very regular pillars, each with six spheres, +containing two, three, four, four, three, two atoms, respectively. The +supporting spheres are on the model of the central globe, but contain more +atoms. Funnels and spikes alike radiate from a simple central globe, in +which five contained spheres are arranged crosswise, preparing for the +fully developed cross of cadmium. The ends of the cross touch the bottoms +of the funnels. + +ZINC: 4 funnels of 144 atoms 576 + 4 spikes of 144 atoms 576 + Central globe 18 + ----- + Total 1170 + ----- + Atomic weight 64.91 + Number weight 1170/18 65.00 +CADMIUM (Plate IX, 3) has an increased complexity of funnels; the diagram +shows one of the three similar segments which lie within the funnels as +cylinders; each of these contains four spheres, three pillars and three +ovoids, like the spike of zinc turned upside down, and the zinc ten-atomed +triangle changed into three ten-atomed ovoids. The centre-piece is a new +form, though prefigured in the central globe of zinc. + +CADMIUM: 3 segments of 164 atoms = 492 + 4 funnels of 492 atoms 1968 + Central body 48 + ----- + Total 2016 + ----- + Atomic weight 111.60 + Number weight 2016/18 112.00 +The corresponding negative group is headed by + +[Illustration: PLATE X.] + +SULPHUR (Plate X, 1), which, like magnesium, has no central globe, and +consists simply of the zinc funnels, much less compressed than zinc but the +same in composition. + +SULPHUR: 4 funnels of 144 atoms 576 + Atomic weight 31.82 + Number weight 576/18 32.00 +SELENIUM (Plate X, 2) is distinguished by the exquisite peculiarity, +already noticed, of a quivering star, floating across the mouth of each +funnel, and dancing violently when a ray of light falls upon it. It is +known that the conductivity of selenium varies with the intensity of the +light falling upon it, and it may be that the star is in some way connected +with its conductivity. It will be seen that the star is a very complicated +body, and in each of its six points the two five-atomed spheres revolve +round the seven-atomed cone. The bodies in the funnels resemble those in +magnesium, but a reversed image of the top one is interposed between itself +and the small duad, and each pair has its own enclosure. The central globe +is the same as that of zinc. + +SELENIUM: 4 funnels of 198 atoms 792 + 4 stars of 153 atoms 612 + Central globe 18 + ----- + Total 1422 + ----- + Atomic weight 78.58 + Number weight 1422/18 79.00 +TELLURIUM (Plate X, 3), it will be seen, closely resembles cadmium, and has +three cylindrical segments--of which one is figured--making up the funnel. +The contained bodies in the pillars run three, four, five, four, three, +two, instead of starting with two; and a quartet replaces a duad in the +globes above. The central cross only differs from that of cadmium in having +a seven-atomed instead of a four-atomed centre. So close a similarity is +striking. + +TELLURIUM: 3 segments of 181 atoms = 543 + 4 funnels of 543 atoms 2172 + Central body 51 + ----- + Total 2223 + ----- + Atomic weight 126.64 + Number weight 2223/18 123.50 + * * * * * + +V. + +We must now consider the ways in which the members of the tetrahedral +groups break up, and as we proceed with this study we shall find how +continual are the repetitions, and how Nature, with a limited number of +fundamental methods, creates by varied combinations her infinite variety of +forms. + +BERYLLIUM (Plate III, 2, and VIII, 1). + +[Illustration] + +Beryllium offers us four similar funnels and a central globe, and the +proto-elements consist of these five bodies, set free. The funnel, released +from pressure, assumes a spherical form, with its four ovoids spinning +within it, and the central globe remains a sphere, containing a whirling +cross. On the meta level, the ovoids are set free, and two from each funnel +are seen to be positive, two negative--sixteen bodies in all, _plus_ the +cross, in which the resultant force-lines are changed, preparatory to its +breaking into two duads on the hyper level. On that level, the decades +disintegrate into two triplets and a quartet, the positive with the +depressions inward, the negative with the depressions outward. + +CALCIUM (Plate VIII, 2). + +The funnels, as usual, assume a spherical form on the proto level, and +show, in each case, three spheres containing ovoids. These spheres, still +on the proto level, break free from their containing funnel, as in the case +of gold (p. 49), twelve bodies being thus liberated, while the central +globe breaks up into eight segments, each of which becomes globular, and +contains within it a "cigar" and a somewhat heart-shaped body. Four +spheres, each containing seven ten-atomed ovoids, are identical with those +in beryllium, and can be followed in its diagram. Eight spheres, each +containing five nine-atomed ovoids of a different type, set free, on the +meta level, eighty duads--forty positive and forty negative--and forty +quintets, which are identical with those in chlorine. On the hyper level, +the duads become single atoms, within a sphere, and the central atom from +the quintet is also set free, one hundred and twenty in all. The remaining +four atoms of the quintet divide into two duads. + +The central globe, dividing into eight, becomes eight six-atomed spheres on +the meta, the "cigar" behaving as usual, four "cigars" being positive and +four negative, and becoming dissociated into triplets; the four atoms +within the heart-shaped body appear as a tetrahedron, remain together on +the meta level, and break up into duads on the hyper. + +STRONTIUM (PLATE VIII, 3). + +The third member of this group repeats the _a_ groups of beryllium and the +_b_ groups of calcium, and they dissociate into the bodies already +described under these respectively. The two upper globes in each funnel +repeat each other, but each globe contains four smaller spheres showing +three varieties of forms. The two marked _g_, which are repeated in the +central globe as _h_, are seven-atomed, and appear as spheres or ovoids +according to pressure. They are figured on p. 48, under iodine; _e_ and _f_ +are related as object and image, and we have already seen them in copper +(pp. 38 and 48); in each case, as in copper, they unite into a ten-atomed +figure; on the meta level the pair of fours form a ring, and the remaining +two atoms form a duad; _i_, which repeats _f_, makes a ring with the fifth +in the centre, as in the five-atomed _b_ of calcium, as shown above. There +is, thus, nothing new in strontium, but only repetitions of forms already +studied. + +OXYGEN (PLATE VIII, 4). + +[Illustration] + +The disintegration of oxygen as given in 1895 may be repeated here, and the +better presentation given on p. 54 renders it easier to follow the process. +On the proto level the two "snakes" divide; the brilliant disks are +seven-atomed, but are differently arranged, the positive snake having the +atoms arranged as in the iodine ovoids, whereas the negative snake has them +arranged as in a capital H. The snakes show the same extraordinary activity +on the proto level as on the gaseous, twisting and writhing, darting and +coiling. The body of the snake is of two-atomed beads, positive and +negative. On the meta level the snakes break into ten fragments, each +consisting of a disk, with six beads on one side and five on the other, +remaining as lively as the original snake. They shiver into their +constituent disks, and beads on the hyper level, there yielding the ten +disks, five positive and five negative, and the 110 beads, fifty-five +positive and fifty-five negative. + +CHROMIUM (PLATE VIII, 5). + +When we go on to chromium and molybdenum, we return to our familiar funnels +and central globes, and the secondary spheres within the funnels--quickly +set free, as before, on the proto level--give us no new combinations in +their contained spheres and ovoids. The _a_ of beryllium, the _b_ of +calcium and strontium, and _d_ of calcium, the _e_ and _f_ of strontium, +are all there; _j_ in chromium is the same as the central sphere in the _b_ +ovoid. In the central globe, _k_, is a pair of triangles as in hydrogen, +consisting of only six atoms, which on the meta level revolve round each +other, and break up into two duads and two units on the hyper. + +MOLYBDENUM (PLATE VIII, 6). + +Molybdenum presents us with only two new forms, and these are merely +four-atomed tetrahedra, occurring in pairs as object and image. All the +other bodies have already been analysed. + +II a.--We come now to the second great tetrahedral group, which though very +much complicated, is yet, for the most part, a repetition of familiar +forms. + +MAGNESIUM (PLATE IX, 1). + +[Illustration] + +We are still among tetrahedra, so have to do with four funnels, but each +funnel contains three rings, and each ring three ovoids; on the proto level +a triple dissociation takes place, for the funnels let free the rings as +large spheres, in each of which rotate three twelve-atomed ovoids, and then +the ovoids break loose from the spheres, and themselves become spherical, +so that we have finally thirty-six proto compounds from the tetrahedron. On +the meta level the contained bodies, a triplet, Mg _a_, a septet, Mg _b_, +and a duad, Mg _c_, are set free from each globe, thus yielding one hundred +and eight meta compounds. On the hyper level the triplet becomes a duad and +a unit; the duad becomes two units; and the septet a triplet and a quartet. + +ZINC (PLATE IX, 2). + +We can leave aside the funnel, for the only difference between it and the +magnesium funnel is the substitution of a second septet for the triplet, +and the septet is already shown in the magnesium diagram. We have, +therefore, only to consider the spikes, pointing to the angles of the +enclosing tetrahedron, and the central globe. These are set free on the +proto level and the spikes immediately release their contents, yielding +thus thirty-two separate bodies. + +The triangular arrangement at the top of the spike is the same as occurs in +copper (_b_ on p. 48), and can be there followed. One of the three similar +pillars is shown in the accompanying diagram under Zn a. The compressed +long oval becomes a globe, with six bodies revolving within it in a rather +peculiar way: the quartets turn round each other in the middle; the +triplets revolve round them in a slanting ellipse; the duads do the same on +an ellipse slanting at an angle with the first, somewhat as in gold (_a_ +and _b_, p. 40). The spheres within the globes at the base of the spikes, +Zn _b_, behave as a cross--the cross is a favourite device in the II _a_ +groups. Finally, the central globe, Zn _c_, follows the same cruciform line +of disintegration. + +CADMIUM (Plate IX, 3). + +[Illustration] + +Cadmium follows very closely on the lines of zinc; the pillars of the zinc +spike are reproduced in the rings of the cadmium funnel; the globes are +also the globes of cadmium; so neither of these needs attention. We have +only to consider the three ten-atomed ovoids, which are substituted for the +one ten-atomed triangle of zinc, and the central cross. The ovoids become +spheres (Cd _a_, _b_), the contained bodies revolving within them, _a_ +whirling on a diameter of the sphere, cutting it in halves, as it were, and +_b_ whirling round it at right angles; the cross also becomes a sphere (Cd +_c_), but the cruciform type is maintained within it by the relative +positions of the contained spheres in their revolution. The subsequent +stages are shown in the diagram. + +SULPHUR (Plate XI, 1). + +Sulphur has nothing new, but shows only the funnels already figured in +magnesium, with the substitution of a second septet for the triplet, as in +zinc. + +SELENIUM (Plate X, 2). + +[Illustration] + +The funnel of selenium is a re-arrangement of the twelve-atomed ovoids of +magnesium and the ten-atomed ovoids of cadmium. The funnels, on +disintegrating, set free twelve groups, each containing nine spheres. On +the meta level the ten-atomed bodies are set free, and the twelve-atomed +divide into duads and decads, thus yielding seventy-two decads and +thirty-six duads; the duads, however, at once recombine into hexads, thus +giving only twelve meta elements, or eighty-four in all from the funnels. +The central globe holds together on the proto level, but yields five meta +elements. The star also at first remains a unit on the proto level, and +then shoots off into seven bodies, the centre keeping together, and the six +points becoming spheres, within which the two cones, base to base, whirl in +the centre, and the globes circle round them. On the meta level all the +thirty bodies contained in the star separate from each other, and go on +their independent ways. + +Selenium offers a beautiful example of the combination of simple elements +into a most exquisite whole. + +TELLURIUM (Plate X, 3). + +Tellurium very closely resembles cadmium, and they are, therefore placed on +the same diagram. The pillars are the same as in chlorine and its +congeners, with a duad added at the base. The ten-atomed ovoid is the same +as in cadmium and follows the same course in breaking up. It would be +interesting to know why this duad remains as a duad in selenium and breaks +up into a septad and triad in the other members of the group. It may be due +to the greater pressure to which it is subjected in selenium, or there may +be some other reason. The cross in tellurium is identical with that in +cadmium, except that the centre is seven-atomed instead of four-atomed. + + * * * * * + +VI. + +III AND IIIa.--THE CUBE GROUPS. + +We have here four groups to consider, all the members of which are triads, +and have six funnels, opening on the six faces of a cube. + +III.--Boron, scandium and yttrium were examined; they are all triatomic, +paramagnetic, and positive. The corresponding group consists of nitrogen, +vanadium and niobium; they are triatomic, paramagnetic, and negative. We +have not examined the remaining members of these groups. In these two +groups nitrogen dominates, and in order to make the comparison easy the +nitrogen elements are figured on both Plate XI and Plate XII. It will be +seen that scandium and yttrium, of the positive group, differ only in +details from vanadium and niobium, of the negative group; the ground-plan +on which they are built is the same. We noted a similar close resemblance +between the positive strontium and the negative molybdenum. + +[Illustration: PLATE XI.] + +BORON (Plate III, 4, and Plate XI, 1). We have here the simplest form of +the cube; the funnels contain only five bodies--four six-atomed ovoids and +one six-atomed "cigar." The central globe has but four five-atomed spheres. +It is as simple in relation to its congeners as is beryllium to its +group-members. + +BORON: 6 funnels of 30 atoms 180 + Central globe 20 + ---- + Total 200 + ---- + Atomic weight 10.86 + Number weight 200/18 11.11 +SCANDIUM (Plate XI, 2). For the first time we meet funnels of different +types, A and B, three of each kind; A appear to be positive and B negative, +but this must be stated with reserve. + +In A the boron funnel is reproduced, the "cigar" having risen above its +companion ovoids; but the most important matter to note in respect to this +funnel is our introduction to the body marked _a_ 110. This body was +observed by us first in nitrogen, in 1895, and we gave it the name of the +"nitrogen balloon," for in nitrogen it takes the balloon form, which it +also often assumes in other gaseous elements. Here it appears as a +sphere--the form always assumed on the proto level--and it will be seen, on +reference to the detailed diagram 4 _a_, to be a complicated body, +consisting of six fourteen-atomed globes arranged round a long ovoid +containing spheres with three, four, six, six, four, three, atoms +respectively. It will be observed that this balloon appears in every member +of these two groups, except boron. + +The B funnel runs largely to triads, _c_ and _b_, _b_ (see 4 _b_) having +not only a triadic arrangement of spheres within its contained globes, but +each sphere has also a triplet of atoms. In _c_ (see 4 _c_) there is a +triadic arrangement of spheres, but each contains duads. B is completed by +a five-atomed sphere at the top of the funnel. It should be noted that _a_, +_b_ and _c_ all are constituents of nitrogen. + +The central globe repeats that of boron, with an additional four-atomed +sphere in the middle. + +SCANDIUM: 3 funnels (A) of 140 atoms 420 + 3 " (B) of 116 " 348 + Centre globe 24 + ---- + Total 792 + ---- + Atomic weight 43.78 + Number weight 792/18 44.00 +YTTRIUM (Plate XI, 3). Here we have a quite new arrangement of bodies +within the funnel--the funnel being of one type only. Two "cigars" whirl on +their own axes in the centre near the top, while four eight-atomed globes +(see 4 _e_) chase each other in a circle round them, spinning madly on +their own axes--this axial spinning seems constant in all contained +bodies--all the time. Lower down in the funnel, a similar arrangement is +seen, with a globe (see 4 _d_)--a nitrogen element--replacing the "cigars," +and six-atomed ovoids replacing the globes. + +The "nitrogen balloon" occupies the third place in the funnel, now showing +its usual shape in combination, while the _b_ globe (see 4 _b_) of scandium +takes on a lengthened form below it. + +The central globe presents us with two tetrahedra, recalling one of the +combinations in gold (see Plate VII _d_), and differing from that only by +the substitution of two quartets for the two triplets in gold. + +One funnel of yttrium contains exactly the same number of atoms as is +contained in a gaseous atom of nitrogen. Further, _a_, _b_, and _d_ are all +nitrogen elements. We put on record these facts, without trying to draw any +conclusions from them. Some day, we--or others--may find out their +significance, and trace through them obscure relations. + +YTTRIUM: 6 funnels of 261 atoms 1566 + Central globe 40 + ---- + Total 1606 + ---- + Atomic weight 88.34 + Number weight 1606/18 89.22 +The corresponding negative group, of nitrogen, vanadium and niobium, is +rendered particularly interesting by the fact that it is headed by +nitrogen, which--like the air, of which it forms so large a part--pervades +so many of the bodies we are studying. What is there in nitrogen which +renders it so inert as to conveniently dilute the fiery oxygen and make it +breathable, while it is so extraordinarily active in some of its compounds +that it enters into the most powerful explosives? Some chemist of the +future, perhaps, will find the secret in the arrangement of its constituent +parts, which we are able only to describe. + +[Illustration: PLATE XII.] + +NITROGEN (Plate XII, 1) does not assume the cubical form of its relatives, +but is in shape like an egg. Referring again to our 1895 investigations, I +quote from them. The balloon-shaped body (see 4 _a_) floats in the middle +of the egg, containing six small spheres in two horizontal rows, and a long +ovoid in the midst; this balloon-shaped body is positive, and is drawn down +towards the negative body _b_ (see 4 _b_) with its seven contained spheres, +each of which has nine atoms within it--three triads. Four spheres are +seen, in addition to the two larger bodies; two of these (see 4 _d_), each +containing five smaller globes, are positive, and two (see 4 _c_) +containing four smaller globes, are negative. + +NITROGEN: Balloon 110 + Oval 63 + 2 bodies of 20 atoms 40 + 2 " " 24 " 48 + ---- + Total 261 + ---- + Atomic weight 14.01 + Number weight 261/18 14.50 +VANADIUM (Plate XII, 2) closely follows scandium, having two types of +funnels. Funnel A only differs from that of scandium by having a globe (see +4 _d_) inserted in the ring of four ovoids; funnel B has a six-atomed, +instead of a five-atomed globe at the top, and slips a third globe +containing twenty atoms (see 4 _d_) between the two identical with those of +scandium (see 4 _c_). The central globe has seven atoms in its middle body +instead of four. In this way does vanadium succeed in overtopping scandium +by 126 atoms. + +VANADIUM: 3 funnels (A) of 160 atoms 480 + 3 " (B) " 137 " 411 + Central globe 27 + ---- + Total 918 + ---- + Atomic weight 50.84 + Number weight 918/18 51.00 +NIOBIUM (Plate XII, 3) is as closely related to yttrium as is vanadium to +scandium. The little globes that scamper round the "cigars" contain twelve +atoms instead of eight (see 4 _e_). + +The rest of the funnel is the same. In the central globe both the +tetrahedra have "cigars," and a central nine-atomed globe spins round in +the centre (see 4 _f_), seventeen atoms being thus added. + +NIOBIUM: 6 funnels of 277 atoms 1662 + Central globe 57 + ---- + Total 1719 + ---- + Atomic weight 93.25 + Number weight 1719/18 95.50 +III a.--Aluminium, gallium and indium were examined from this group. They +are triatomic, diamagnetic, and positive. The corresponding group contains +phosphorus, arsenic and antimony: bismuth also belongs to it, but was not +examined; they are triatomic, diamagnetic and negative. They have no +central globes. + +[Illustration: PLATE XIII.] + +ALUMINIUM (Plate XIII, 1), the head of the group, is, as usual, simple. +There are six similar funnels, each containing eight ovoids, below which is +a globe. + +ALUMINIUM: 6 funnels of 81 atoms 486 + Atomic weight 26.91 + Number weight 486/18 27.00 +GALLIUM (Plate XIII, 2) has two segments in every funnel; in the segment to +the left a "cigar" balances a globe, equally six-atomed, in that of the +right, and the globes to right and left are four-atomed as against +three-atomed. In the next row, the smaller contained globes have six atoms +as against four, and the cones have respectively seven and five. By these +little additions the left-hand funnel boasts one hundred and twelve atoms +as against ninety-eight. + +GALLIUM: Left segment 112 atoms } + Right segment 98 " } = 210 + 6 funnels of 210 atoms 1260 + ---- + Atomic weight 69.50 + Number weight 1260/18 70.00 +INDIUM (Plate XIII, 3) repeats the segments of gallium exactly, save in the +substitution of a sixteen-atomed body for the seven-atomed cone of the +left-hand segment, and a fourteen-atomed body for the five-atomed +corresponding one in gallium. But each funnel now has three segments +instead of two; three funnels out of the six contain two segments of type A +and one of type B; the remaining three contain two of type B, and one of +type A. + +INDIUM: Segment A 121 atoms + Segment B 107 " + 3 funnels of 2 A and 1 B ([242 + 107] 3) 1047 + 3 " " 2 B and 1 A ([214 + 121] 3) 1005 + ---- + Total 2052 + ---- + Atomic weight 114.05 + Number weight 2052/18 114.00 +The corresponding negative group, phosphorus, arsenic, and antimony, run on +very similar lines to those we have just examined. + +[Illustration: PLATE XIV.] + +PHOSPHORUS (Plate XIV, 1) offers us a very curious arrangement of atoms, +which will give some new forms in breaking up. Two segments are in each +funnel, in fact the only two of group III _a_ which do not show this +arrangement, or a modification thereof, are aluminium and arsenic. + +PHOSPHORUS: Left segment 50 atoms + Right segment 43 " + -- + 93 + 6 funnels of 93 atoms 558 + Atomic weight 30.77 + Number weight 558/18 31.00 +ARSENIC (Plate XIV, 2) resembles aluminium in having eight internal +sub-divisions in a funnel, and the ovoids which form the top ring are +identical, save for a minute difference that in aluminium the ovoids stand +the reverse way from those in arsenic. It will be noted that in the former +the top and bottom triangles of atoms have the apices upwards, and the +middle one has its apex downwards. In arsenic, the top and bottom ones +point downwards, and the middle one upwards. Arsenic inserts sixteen +spheres between the ovoids and globe shown in aluminium, and thus adds no +less than one hundred and forty-four atoms to each funnel. + +ARSENIC: 6 funnels of 225 atoms 1350 + Atomic weight 74.45 + Number weight 1350/18 75.00 +ANTIMONY (Plate XIV, 3) is a close copy of indium, and the arrangement of +types A and B in the funnels is identical. In the middle rings of both A +and B a triplet is substituted for a unit at the centre of the larger +globe. In the lowest body of type A the "cigar" has vanished, and is +represented by a seven-atomed crystalline form. + +ANTIMONY: Segment A 128 atoms + Segment B 113 atoms + 3 funnels of 2 A and 1 B ([256 + 113]3) 1107 + 3 " " 2 B and 1 A ([226 + 128]3) 1056 + ---- + Total 2163 + ---- + Atomic weight 119.34 + Number weight 120.16 + * * * * * + +VII. + +BORON (Plate III, 4, and Plate XI, 1). + +[Illustration] + +The disintegration of boron is very simple: the funnels are set free and +assume the spherical form, showing a central "cigar" and four globes each +containing two triplets. The central globe is also set free with its four +quintets, and breaks at once in two. On the meta level the "cigar" breaks +up as usual, and the triplets separate. On the hyper level, the "cigar" +follows its usual course, and the triplets become duads and units. The +globe forms two quintets on the meta level, and these are resolved into +triplets and duads. + +SCANDIUM (Plate XI, 2). + +In funnel A the "cigar" and the ovoids behave as in boron, but the +"balloon," _a_ 110 (XI, 4), escapes from the funnel as it changes to a +sphere, and holds together on the proto level; on the meta, it yields six +globes each containing seven duads, and these are all set free as duads on +the hyper level; the ovoid is also set free on the meta level becoming a +sphere, and on the hyper level liberates its contained bodies, as two +triplets, two quartets and two sextets. + +In funnel B there is a quintet, that behaves like those in the globe of +boron, on escaping from the funnel, in which the bodies remain on the proto +level, with the exception of _b_ 63, which escapes. On the meta level, _c_ +(Plate XI, 4), _c_ assumes a tetrahedral form with six atoms at each point, +and these hold together as sextets on the hyper level. At the meta stage, +_b_ (Plate XI, 4 _b_) sets free seven nine-atomed bodies, which become free +triplets on the hyper. The central globe shows a cross at its centre, with +the four quintets whirling round it, on the proto level. On the meta, the +quintets are set free, and follow the boron type, while the cross becomes a +quartet on the meta level, and two duads on the hyper. + +YTTRIUM (Plate XI, 3). + +[Illustration] + +In yttrium, on the proto level, _a_ 110 and _b_ 63 both escape from the +funnel, and behave as in scandium. The ovoids and "cigars," set free on the +meta level, behave as in boron. The central globe breaks up as in gold (pp. +49 and 50), four quartets being set free instead of two quartets and two +triplets. We have only to consider _e_ 8 and _d_ 20 (Plate XI, 4). _E_ 8 is +a tetrahedral arrangement of duads on the meta level, set free as duads on +the hyper. _D_ 20 is an arrangement of pairs of duads at the angles of a +square-based pyramid on the meta, and again free duads on the hyper. + +NITROGEN (Plate XII, 1). + +Nitrogen has nothing new to show us, all its constituents having appeared +in scandium and yttrium. + +VANADIUM (Plate XII, 2). + +The A funnel of vanadium repeats the A funnel of scandium, with the +addition of _d_ 20, already studied. In the B funnel scandium B is +repeated, with an addition of _d_ 20 and a sextet for a quintet; the sextet +is the _c_ of the "nitrogen balloon." The central globe follows boron, save +that it has a septet for its centre; this was figured in iodine (p. 48). + +NIOBIUM (Plate XII, 3). + +Niobium only differs from yttrium by the introduction of triplets for duads +in _e_; on the meta level we have therefore triplets, and on the hyper each +triplet yields a duad and a unit. The only other difference is in the +central globe. The tetrahedra separate as usual, but liberate eight +"cigars" instead of four with four quartets; the central body is simple, +becoming three triads at the angles of a triangle on the meta level, and +three duads and three units on the hyper. + +ALUMINIUM (Plate XIII, 1). + +[Illustration] + +The funnels let go the globes, but the eight ovoids remain within them, so +that seven bodies are let loose on the proto level. When the ovoids are set +free at the meta stage they become spherical and a nine-atomed body is +produced, which breaks up into triangles on the hyper level. The globe +becomes a cross at the meta stage, with one atom from the duads at each arm +in addition to its own, and these form four duads on the hyper, and a unit +from the centre. + +GALLIUM (Plate XIII, 2). + +In gallium the funnel disappears on the proto level, setting free its two +contained segments, each of which forms a cylinder, thus yielding twelve +bodies on the proto level. On the meta, the three upper globes in each +left-hand segment are set free, and soon vanish, each liberating a cigar +and two septets, the quartet and triad uniting. On the hyper the quartet +yields two duads but the triangle persists. The second set of bodies divide +on the meta level, forming a sextet and a cross with a duad at each arm; +these on the hyper level divide into two triangles, four duads and a unit. +The seven-atomed cone becomes two triangles united by a single atom, and on +the meta level these form a ring round the unit; on the hyper they form +three duads and a unit. + +In the right-hand segment, the same policy is followed, the four triads +becoming two sextets, while the central body adds a third to the number. +The second ring has a quartet instead of the sextet, but otherwise breaks +up as does that of the left; the quintet at the base follows that of boron. + +INDIUM (Plate XIII, 3). + +The complication of three segments of different types in each funnel does +not affect the process of breaking up, and indium needs little attention. A +is exactly the same as the left-hand funnel of gallium, save for the +substitution of a globe containing the familiar "cigar" and two +square-based pyramids. B is the same as the right-hand funnel of gallium, +except that its lowest body consists of two square-based pyramids and a +tetrahedron. All these are familiar. + +PHOSPHORUS (Plate XIV, 1). + +[Illustration] + +The atoms in the six similar spheres in the segments of the phosphorus +funnel are arranged on the eight angles of a cube, and the central one is +attached to all of them. On the meta level five of the nine atoms hold +together and place themselves on the angles of a square-based pyramid; the +remaining four set themselves on the angle of a tetrahedron. They yield, on +the hyper level, two triads, a duad, and a unit. The remaining bodies are +simple and familiar. + +ARSENIC (Plate XIV, 2). + +Arsenic shows the same ovoids and globe as have already been broken up in +aluminium (see _ante_); the remaining sixteen spheres form nine-atomed +bodies on the meta level, all similar to those of aluminium, thus yielding +twelve positive and twelve negative; the globe also yields a nine-atomed +body, twenty-five bodies of nine. + +ANTIMONY (Plate XIV, 3). + +Antimony follows closely in the track of gallium and indium, the upper ring +of spheres being identical. In the second ring, a triplet is substituted +for the unit, and this apparently throws the cross out of gear, and we have +a new eleven-atomed figure, which breaks up into a triplet and two quartets +on the hyper level. The lowest seven-atomed sphere of the three at the base +is the same as we met with in copper. + + * * * * * + +VIII. + +IV.--THE OCTAHEDRAL GROUPS. + +These groups are at the turns of the spiral in Sir William Crookes' +lemniscates (see p. 28). On the one side is carbon, with below it titanium +and zirconium; on the other silicon, with germanium and tin. The +characteristic form is an octahedron, rounded at the angles and a little +depressed between the faces in consequence of the rounding; in fact, we did +not, at first, recognize it as an octahedron, and we called it the "corded +bale," the nearest likeness that struck us. The members of the group are +all tetrads, and have eight funnels, opening on the eight faces of the +octahedron. The first group is paramagnetic and positive; the corresponding +one is diamagnetic and negative. The two groups are not closely allied in +composition, though both titanium and tin have in common the five +intersecting tetrahedra at their respective centres. + +[Illustration: PLATE XV.] + +CARBON (Plate III, 5, and XV, 1) gives us the fundamental octahedral form, +which becomes so masked in titanium and zirconium. As before said (p. 30), +the protrusion of the arms in these suggests the old Rosicrucian symbol of +the cross and rose, but they show at their ends the eight carbon funnels +with their characteristic contents, and thus justify their relationship. +The funnels are in pairs, one of each pair showing three "cigars," and +having as its fellow a funnel in which the middle "cigar" is truncated, +thus loosing one atom. Each "cigar" has a leaf-like body at its base, and +in the centre of the octahedron is a globe containing four atoms, each +within its own wall; these lie on the dividing lines of the faces, and each +holds a pair of the funnels together. It seems as though this atom had been +economically taken from the "cigar" to form a link. This will be more +clearly seen when we come to separate the parts from each other. It will be +noticed that the atoms in the "leaves" at the base vary in arrangement, +being alternately in a line and in a triangle. + + { left 27 +CARBON: One pair of funnels { right 22 + { centre 1 + -- + 54 + 4 pairs of funnels of 54 atoms 216 + Atomic weight 11.91 + Number weight 216/18 12.00 +TITANIUM (Plate III, 6, and XV, 2) has a complete carbon atom distributed +over the ends of its four arms, a pair of funnels with their linking atom +being seen in each. Then, in each arm, comes the elaborate body shown as 3 +_c_, with its eighty-eight atoms. A ring of twelve ovoids (3 _d_) each +holding within itself fourteen atoms, distributed among three contained +globes--two quartets and a sextet--is a new device for crowding in +material. Lastly comes the central body (4 _e_) of five intersecting +tetrahedra, with a "cigar" at each of their twenty points--of which only +fifteen can be shown in the diagram--and a ring of seven atoms round an +eighth, that forms the minute centre of the whole. Into this elaborate body +one hundred and twenty-eight atoms are built. + +TITANIUM: One carbon atom 216 + 4 _c_ of 88 atoms 352 + 12 _d_ of 14 " 168 + Central globe 128 + ---- + Total 864 + ---- + Atomic weight 47.74 + Number weight 864/18 48.00 +ZIRCONIUM (Plate XV, 3) has exactly the same outline as titanium, the +carbon atom is similarly distributed, and the central body is identical. +Only in 5 _c_ and _d_ do we find a difference on comparing them with 4 _c_ +and d. The _c_ ovoid in zirconium shows no less than fifteen secondary +globes within the five contained in the ovoid, and these, in turn, contain +altogether sixty-nine smaller spheres, with two hundred and twelve atoms +within them, arranged in pairs, triplets, quartets, quintets, a sextet and +septets. Finally, the ovoids of the ring are also made more elaborate, +showing thirty-six atoms instead of fourteen. In this way the clever +builders have piled up in zirconium no less than 1624 atoms. + +ZIRCONIUM: One Carbon atom 216 + 4 _c_ of 212 atoms 848 + 12 _d_ of 36 " 432 + Central globe 128 + ---- + Total 1624 + ---- + Atomic weight 89.85 + Number weight 90.22 +[Illustration: PLATE XVI.] + +SILICON (Plate XVI, 1) is at the head of the group which corresponds to +carbon on the opposite turn of the lemniscate. It has the usual eight +funnels, containing four ovoids in a circle, and a truncated "cigar" but no +central body of any kind. All the funnels are alike. + +SILICON: 8 funnels of 65 atoms 520 + Atomic weight 28.18 + Number weight 520/18 28.88 +GERMANIUM (Plate XVI, 2) shows the eight funnels, containing each four +segments (XVI, 4), within which are three ovoids and a "cigar." In this +case the funnels radiate from a central globe, formed of two intersecting +tetrahedra, with "cigars" at each point enclosing a four-atomed globe. + +GERMANIUM: 8 funnels of 156 atoms 1248 + Central globe 52 + ---- + Total 1300 + ---- + Atomic weight 71.93 + Number weight 1300/18 72.22 +TIN (Plate XVI, 3) repeats the funnel of germanium, and the central globe +we met with in titanium, of five intersecting tetrahedra, carrying twenty +"cigars"; the latter, however, omits the eight-atomed centre of the globe +that was found in titanium, and hence has one hundred and twenty atoms +therein instead of one hundred and twenty-eight. Tin, to make room for the +necessary increase of atoms, adopts the system of spikes, which we met with +in zinc (see Plate IX, 2); these spikes, like the funnels, radiate from the +central globe, but are only six in number. The twenty-one-atomed cone at +the head of the spike we have already seen in silver, and we shall again +find it in iridium and platinum; the pillars are new in detail though not +in principle, the contained globes yielding a series of a triplet, quintet, +sextet, septet, sextet, quintet, triplet. + +TIN: 8 funnels of 156 atoms 1248 + 6 spikes of 126 " 756 + Central globe 120 + ---- + Total 2124 + ---- + Atomic weight 118.10 + Number weight 2124/18 118.00 +V.--THE BARS GROUPS. + +[Illustration: PLATE XVII.] + +Here, for the first time, we find ourselves a little at issue with the +accepted system of chemistry. Fluorine stands at the head of a +group--called the inter-periodic--whereof the remaining members are (see +Crookes' table, p. 28), manganese, iron, cobalt, nickel; ruthenium, +rhodium, palladium; osmium, iridium, platinum. If we take all these as +group V, we find that fluorine and manganese are violently forced into +company with which they have hardly any points of relationship, and that +they intrude into an otherwise very harmonious group of closely similar +composition. Moreover, manganese reproduces the characteristic lithium +"spike" and not the bars of those into whose company it is thrust, and it +is thus allied with lithium, with which indeed it is almost identical. But +lithium is placed by Crookes at the head of a group, the other members of +which are potassium, rubidium and cæsium (the last not examined). Following +these identities of composition, I think it is better to remove manganese +and fluorine from their incongruous companions and place them with lithium +and its allies as V _a_, the Spike Groups, marking, by the identity of +number, similarities of arrangement which exist, and by the separation the +differences of composition. It is worth while noting what Sir William +Crookes, in his "Genesis of the Elements," remarks on the relations of the +interperiodic group with its neighbours. He says: "These bodies are +interperiodic because their atomic weights exclude them from the small +periods into which the other elements fall, and because their chemical +relations with some members of the neighbouring groups show that they are +probably interperiodic in the sense of being in transition stages." + +Group V in every case shows fourteen bars radiating from a centre as shown +in iron, Plate IV, 1. While the form remains unchanged throughout, the +increase of weight is gained by adding to the number of atoms contained in +a bar. The group is made up, not of single chemical elements, as in all +other cases, but of sub-groups, each containing three elements, and the +relations within each sub-group are very close; moreover the weights only +differ by two atoms per bar, making a weight difference of twenty-eight in +the whole. Thus we have per bar:-- + +Iron 72 Palladium 136 +Nickel 74 Osmium 245 +Cobalt 76 Iridium 247 +Ruthenium 132 Platinum A 249 +Rhodium 134 Platinum B 257 +It will be noticed (Plate XVII, 3, 4, 5,) that each bar has two sections, +and that the three lower sections in iron, cobalt and nickel are identical; +in the upper sections, iron has a cone of twenty-eight atoms, while cobalt +and nickel have each three ovoids, and of these the middle ones alone +differ, and that only in their upper globes, this globe being four-atomed +in cobalt and six-atomed in nickel. + +The long ovoids within each bar revolve round the central axis of the bar, +remaining parallel with it, while each spins on its own axis; the iron cone +spins round as though impaled on the axis. + + 14 bars of 72 atoms 1008 + Atomic weight 55.47 + Number weight 1008/18 56.00 +IRON (Plate IV, 1, and XVII, 3): + + 14 bars of 74 atoms 1036 + Atomic weight 57.70 + Number weight 1036/18 57.55 +COBALT (Plate XVII, 4): + + 14 bars of 76 atoms 1064 + Atomic weight 58.30 + Number weight 1064/18 59.11 +NICKEL (Plate XVII, 4): + +(The weight of cobalt, as given in Erdmann's _Lehrbuch_, is 58.55, but +Messrs. Parker and Sexton, in _Nature_, August 1, 1907, give the weight, as +the result of their experiments, as 57.7.) + +[Illustration: PLATE XVIII.] + +The next sub-group, ruthenium, rhodium, and palladium, has nothing to +detain us. It will be observed that each bar contains eight segments, +instead of the six of cobalt and nickel; that ruthenium and palladium have +the same number of atoms in their upper ovoids, although in ruthenium a +triplet and quartet represent the septet of palladium; and that in +ruthenium and rhodium the lower ovoids are identical, though one has the +order: sixteen, fourteen, sixteen, fourteen; and the other: fourteen, +sixteen, fourteen, sixteen. One constantly asks oneself: What is the +significance of these minute changes? Further investigators will probably +discover the answer. + + 14 bars of 132 atoms 1848 + Atomic weight 100.91 + Number weight 1848/18 102.66 +RUTHENIUM (Plate XVIII, 1): + + 14 bars of 134 atoms 1876 + Atomic weight 102.23 + Number weight 1876/18 104.22 +RHODIUM (Plate XVII, 2): + + 14 bars of 136 atoms 1904 + Atomic weight 105.74 + Number weight 1904/18 105.77 +PALLADIUM (XVIII, 3): + +The third sub-group, osmium, iridium and platinum, is, of course, more +complicated in its composition, but its builders succeed in preserving the +bar form, gaining the necessary increase by a multiplication of contained +spheres within the ovoids. Osmium has one peculiarity: the ovoid marked _a_ +(XVIII, 4) takes the place of axis in the upper half of the bar, and the +three ovoids, marked _b_, revolve round it. In the lower half, the four +ovoids, _c_, revolve round the central axis. In platinum, we have marked +two forms as platinum A and platinum B, the latter having two four-atomed +spheres (XVIII, 6 _b_) in the place of the two triplets marked a. It may +well be that what we have called platinum B is not a variety of platinum, +but a new element, the addition of two atoms in a bar being exactly that +which separates the other elements within each of the sub-groups. It will +be noticed that the four lower sections of the bars are identical in all +the members of this sub-group, each ovoid containing thirty atoms. The +upper ring of ovoids in iridium and platinum A are also identical, but for +the substitution, in platinum A, of a quartet for a triplet in the second +and third ovoids; their cones are identical, containing twenty-one atoms, +like those of silver and tin. + + 14 bars of 245 atoms 3430 + Atomic weight 189.55 + Number weight 3430/18 190.55 +OSMIUM (Plate XVIII, 4): + + 14 bars of 247 atoms 3458 + Atomic weight 191.11 + Number weight 3458/18 192.11 +IRIDIUM (Plate XVIII, 5): + + 14 bars of 249 atoms 3486 + Atomic weight 193.66 + Number weight 3486/18 193.34 +PLATINUM A (Plate XVIII, 6 _a_): + + 14 bars of 251 atoms 3514 + Atomic weight ------ + Number weight 3514/18 195.22 +PLATINUM B (Plate XVIII, 6 _b_): + +V a.--THE SPIKE GROUPS. + +I place within this group lithium, potassium, rubidium, fluorine, and +manganese, because of their similarity in internal composition. Manganese +has fourteen spikes, arranged as in the iron group, but radiating from a +central globe. Potassium has nine, rubidium has sixteen, in both cases +radiating from a central globe. Lithium (Plate IV, 2) and fluorine (Plate +IV, 3) are the two types which dominate the group, lithium supplying the +spike which is reproduced in all of them, and fluorine the "nitrogen +balloon" which appears in all save lithium. It will be seen that the +natural affinities are strongly marked. They are all monads and +paramagnetic; lithium, potassium and rubidium are positive, while fluorine +and manganese are negative. We seem thus to have a pair, corresponding with +each other, as in other cases, and the interperiodic group is left +interperiodic and congruous within itself. + +[Illustration: PLATE XIX.] + +LITHIUM (Plate IV, 2 and Plate XIX, 1) is a striking and beautiful form, +with its upright cone, or spike, its eight radiating petals (_x_) at the +base of the cone, and the plate-like support in the centre of which is a +globe, on which the spike rests. The spike revolves swiftly on its axis, +carrying the petals with it; the plate revolves equally swiftly in the +opposite direction. Within the spike are two globes and a long ovoid; the +spheres within the globe revolve as a cross; within the ovoid are four +spheres containing atoms arranged on tetrahedra, and a central sphere with +an axis of three atoms surrounded by a spinning wheel of six. + +LITHIUM: Spike of 63 atoms 63 + 8 petals of 6 atoms 48 + Central globe of 16 atoms 16 + ---- + Total 127 + ---- + Atomic weight 6.98 + Number weight 127/18 7.05 +POTASSIUM (Plate XIX, 2) consists of nine radiating lithium spikes, but has +not petals; its central globe contains one hundred and thirty-four atoms, +consisting of the "nitrogen balloon," encircled by six four-atomed spheres. + +POTASSIUM: 9 bars of 63 atoms 567 + Central globe 134 + ---- + Total 701 + ---- + Atomic weight 38.94 + Number weight 701/18 38.85 +(The weight, as determined by Richards [_Nature_, July 18, 1907] is +39.114.) + +RUBIDIUM: (Plate XIX, 3) adds an ovoid, containing three spheres--two +triplets and a sextet--to the lithium spike, of which it has sixteen, and +its central globe is composed of three "balloons." + +RUBIDIUM: 16 spikes of 75 atoms 1200 + Central globe 330 + ---- + Total 1530 + ---- + Atomic weight 84.85 + Number weight 1530/18 85.00 +The corresponding negative group consists only of fluorine and manganese, +so far as our investigations have gone. + +FLUORINE (Plate IV, 3, and Plate XVII, 1) is a most peculiar looking object +like a projectile, and gives one the impression of being ready to shoot off +on the smallest provocation. The eight spikes, reversed funnels, coming to +a point, are probably responsible for this warlike appearance. The +remainder of the body is occupied by two "balloons." + +FLUORINE: 8 spikes of 15 atoms 120 + 2 balloons 220 + ---- + Total 340 + ---- + Atomic weight 18.90 + Number weight 340/18 18.88 +MANGANESE (Plate XVII, 2) has fourteen spikes radiating from a central +"balloon." + +MANGANESE: 14 spikes of 63 atoms 882 + Central balloon 110 + ---- + Total 992 + ---- + Atomic weight 54.57 + Number weight 992/18 55.11 + * * * * * + +IX. + +We have now to consider the breaking up of the octahedral groups, and more +and more, as we proceed, do we find that the most complicated arrangements +are reducible to simple elements which are already familiar. + +CARBON (Plate III, 5, and XV, 1). + +[Illustration] + +Carbon is the typical octahedron, and a clear understanding of this will +enable us to follow easily the constitution and disintegration of the +various members of these groups. Its appearance as a chemical atom is shown +on Plate III, and see XV, 1. On the proto level the chemical atom breaks up +into four segments, each consisting of a pair of funnels connected by a +single atom; this is the proto element which appears at the end of each arm +of the cross in titanium and zirconium. On the meta level the five +six-atomed "cigars" show two neutral combinations, and the truncated +"cigar" of five atoms is also neutral; the "leaves" yield two forms of +triplet, five different types being thus yielded by each pair of funnels, +exclusive of the linking atom. The hyper level has triplets, duads and +units. + +TITANIUM (Plate III, 6, and XV, 2, 3). + +[Illustration] + +On the proto level, the cross breaks up completely, setting free the pairs +of funnels with the linking atom (_a_ and _b_), as in carbon, the four +bodies marked _c_, the twelve marked _d_, and the central globe marked e. +The latter breaks up again, setting free its five intersecting +cigar-bearing tetrahedra, which follow their usual course (see Occultum, p. +44). The eight-atomed body in the centre makes a ring of seven atoms round +a central one, like that in occultum (see p. 44, diagram B), from which it +only differs in having the central atom, and breaks up similarly, setting +the central atom free. The ovoid _c_ sets free its four contained globes, +and the ovoid _d_ sets free the three within it. Thus sixty-one proto +elements are yielded by titanium. On the meta level, _c_ (titanium 3) +breaks up into star-like and cruciform bodies; the component parts of these +are easily followed; on the hyper level, of the four forms of triplets one +behaves as in carbon, and the others are shown, _a_, _b_ and _f_; the +cruciform quintet yields a triplet and a duad, _c_ and _d_; the tetrahedra +yield two triplets _g_ and _h_, and two units; the septet, a triplet _k_ +and a quartet _j_. On the meta level, the bodies from _d_ behave like their +equivalents in sodium, each _d_ shows two quartets and a sextet, breaking +up, on the hyper level, into four duads and two triads. + +ZIRCONIUM (Plate XV, 2, 5). + +Zirconium reproduces in its _c_ the four forms that we have already +followed in the corresponding _c_ of titanium, and as these are set free on +the proto level, and follow the same course on the meta and hyper levels, +we need not repeat them. The central globe of zirconium _c_ sets free its +nine contained bodies; eight of these are similar and are figured in the +diagram; it will be observed that the central body is the truncated "cigar" +of carbon; their behaviour on the meta and hyper levels is easily followed +there. The central sphere is also figured; the cigar follows its usual +course, and its companions unite into a sextet and an octet. The _d_ ovoid +liberates five bodies, four of which we have already seen in titanium, as +the crosses and sextet of sodium, and which are figured under titanium; the +four quartets within the larger globe also follow a sodium model, and are +given again. + +SILICON (Plate XVI, 1). + +[Illustration] + +In silicon, the ovoids are set free from the funnels on the proto level, +and the truncated "cigar," playing the part of a leaf, is also liberated. +This, and the four "cigars," which escape from their ovoids, pass along +their usual course. The quintet and quartet remain together, and form a +nine-atomed body on the meta level, yielding a sextet and a triplet on the +hyper. + +GERMANIUM (Plate XVI, 2, 4). + +The central globe, with its two "cigar"-bearing tetrahedra, need not delay +us; the tetrahedra are set free and follow the occultum disintegration, and +the central four atoms is the sodium cross that we had in titanium. The +ovoids (XVI, 4) are liberated on the proto level, and the "cigar," as +usual, bursts its way through and goes along its accustomed path. The +others remain linked on the meta level, and break up into two triangles and +a quintet on the hyper. + +TIN (Plate XVI, 3, 4). + +Here we have only the spike to consider, as the funnels are the same as in +germanium, and the central globe is that of titanium, omitting the eight +atomed centre. The cone of the spike we have had in silver (see p. 729, +May), and it is set free on the proto level. The spike, as in zinc, becomes +a large sphere, with the single septet in the centre, the remaining six +bodies circling round it on differing planes. They break up as shown. (Tin +is Sn.) + +IRON (Plate IV, I, and XVII, 3). + +[Illustration] + +We have already dealt with the affinities of this peculiar group, and we +shall see, in the disintegration, even more clearly, the close +relationships which exist according to the classification which we here +follow. + +The fourteen bars of iron break asunder on the proto level, and each sets +free its contents--a cone and three ovoids, which as usual, become spheres. +The twenty-eight-atomed cone becomes a four-sided figure, and the ovoids +show crystalline contents. They break up, on the meta level as shown in the +diagram, and are all reduced to triplets and duads on the hyper level. + +COBALT (Plate XVII, 4). + +The ovoids in cobalt are identical with those of iron; the higher ovoids, +which replace the cone of iron, show persistently the crystalline forms so +noticeable throughout this group. + +NICKEL (Plate XVII, 5). + +The two additional atoms in a bar, which alone separate nickel from cobalt, +are seen in the upper sphere of the central ovoid. + +RUTHENIUM (Plate XVIII, 1). + +The lower ovoids in ruthenium are identical in composition, with those of +iron, cobalt and nickel and may be studied under Iron. The upper ones only +differ by the addition of a triplet. + +RHODIUM (Plate XVIII, 2). + +Rhodium has a septet, which is to be seen in the _c_ of titanium (see _k_ +in the titanium diagram) and differs only in this from its group. + +PALLADIUM (Plate XVIII, 3). + +In palladium this septet appears as the upper sphere in every ovoid of the +upper ring. + +OSMIUM (Plate XVIII, 4). + +We have here no new constituents; the ovoids are set free on the proto +level and the contained globes on the meta, all being of familiar forms. +The cigars, as usual, break free on the proto level, and leave their ovoid +with only four contained spheres, which unite into two nine-atomed bodies +as in silicon (see above). + +IRIDIUM (Plate XVIII, 5.) + +The twenty-one-atomed cone of silver here reappears, and its proceedings +may be followed under that metal (see diagram, p. 729, May). The remaining +bodies call for no remark. + +PLATINUM (Plate XVIII, 6). + +Again the silver cone is with us. The remaining bodies are set free on the +proto level, and their contained spheres on the meta. + +LITHIUM (Plate IV, 2, and XIX, 1). + +[Illustration] + +Here we have some new combinations, which recur persistently in its allies. +The bodies _a_, in Plate XIX, 1, are at the top and bottom of the ellipse; +they come to right and left of it in the proto state, and each makes a +twelve-atomed body on the meta level. + +The five bodies within the ellipse, three monads and two sextets, show two +which we have had before: _d_, which behaves like the quintet and quartet +in silicon, after their junction, and _b_, which we have had in iron. The +two bodies _c_ are a variant of the square-based pyramid, one atom at the +apex, and two at each of the other angles. The globe, _e_, is a new form, +the four tetrahedra of the proto level making a single twelve-atomed one on +the meta. The body _a_ splits up into triplets on the hyper; _b_ and _d_ +follow their iron and silicon models; _c_ yields four duads and a unit; _e_ +breaks into four quartets. + +POTASSIUM (Plate XIX, 2). + +Potassium repeats the lithium spike; the central globe shows the "nitrogen +balloon," which we already know, and which is surrounded on the proto level +with six tetrahedra, which are set free on the meta and behave as in +cobalt. Hence we have nothing new. + +RUBIDIUM (Plate XIX, 3). + +Again the lithium spike, modified slightly by the introduction of an ovoid, +in place of the top sphere; the forms here are somewhat unusual, and the +triangles of the sextet revolve round each other on the meta level; all the +triads break up on the hyper level into duads and units. + +FLUORINE (Plate IV, 3, and Plate XVII, 1). + +The reversed funnels of fluorine split asunder on the proto level, and are +set free, the "balloons" also floating off independently. The funnels, as +usual, become spheres, and on the meta level set free their contained +bodies, three quartets and a triplet from each of the eight. The balloons +disintegrate in the usual way. + +MANGANESE (Plate XVII, 2). + +Manganese offers us nothing new, being composed of "lithium spikes" and +"nitrogen balloons." + + * * * * * + +X. + +VI.--THE STAR GROUPS. + +We have now reached the last of the groups as arranged on Sir William +Crookes' lemniscates, that forming the "neutral" column; it is headed by +helium, which is _sui generis_. The remainder are in the form of a flat +star (see Plate IV, 4), with a centre formed of five intersecting and +"cigar"-bearing tetrahedra, and six radiating arms. Ten of these have been +observed, five pairs in which the second member differs but slightly from +the first; they are: Neon, Meta-neon; Argon, Metargon; Krypton, +Meta-krypton; Xenon, Meta-xenon; Kalon, Meta-kalon; the last pair and the +meta forms are not yet discovered by chemists. These all show the presence +of a periodic law; taking an arm of the star in each of the five pairs, we +find the number of atoms to be as follows :-- + +40 99 224 363 489 +47 106 231 370 496 +It will be observed that the meta form in each case shows seven more atoms +than its fellow. + +[Illustration: PLATE XX.] + +HELIUM (Plate III, 5, and Plate XX, 1) shows two "cigar"-bearing +tetrahedra, and two hydrogen triangles, the tetrahedra revolving round an +egg-shaped central body, and the triangles spinning on their own axes while +performing a similar revolution. The whole has an attractively airy +appearance, as of a fairy element. + +HELIUM: Two tetrahedra of 24 atoms 48 + Two triangles of 9 atoms 18 + Central egg 6 + ---- + Total 72 + ---- + Atomic weight 3.94 + Number weight 72/18 4.00 +NEON (Plate XX, 2 and 6) has six arms of the pattern shown in 2, radiating +from the central globe. + +NEON: Six arms of 40 atoms 240 + Central tetrahedra 120 + + ---- + Total 360 + ---- + Atomic weight 19.90 + Number weight 360/18 20.00 +META-NEON (Plate XX, 3 and 6) differs from its comrade by the insertion of +an additional atom in each of the groups included in the second body within +its arm, and substituting a seven-atomed group for one of the triplets in +neon. + +META-NEON: Six arms of 47 atoms 282 + Central tetrahedra 120 + ---- +Total 402 + ---- +Atomic weight ---- +Number weight 402/18 22.33 +ARGON (Plate XX, 4, 6 and 7) shows within its arms the _b_ 63 which we met +in nitrogen, yttrium, vanadium and niobium, but not the "balloon," which we +shall find with it in krypton and its congeners. + +ARGON: Six arms of 99 atoms 594 + Central tetrahedra 120 + ---- + Total 714 + ---- + Atomic weight 39.60 + Number weight 714/18 39.66 +METARGON (Plate XX, 5, 6 and 7) again shows only an additional seven atoms +in each arm. + +METARGON: Six arms of 106 atoms 636 + Central tetrahedra 120 + ---- + Total 756 + ---- +Atomic weight ---- +Number weight 756/18 42 +[Illustration: PLATE XXI.] + +KRYPTON (Plate XXI, 1 and 4, and Plate XX, 6 and 7) contains the nitrogen +"balloon," elongated by its juxtaposition to _b_ 63. The central tetrahedra +appear as usual. + +KRYPTON: Six arms of 224 atoms 1344 + Central tetrahedra 120 + ----- + Total 1464 + ----- + Atomic weight 81.20 + Number weight 1464/18 81.33 +META-KRYPTON differs only from krypton by the substitution of _z_ for _y_ +in each arm of the star. + +META-KRYPTON: Six arms of 231 atoms 1386 + Central tetrahedra 120 + ----- + Total 1506 + ----- + Atomic weight ----- + Number weight 1506/18 83.66 +XENON (Plate XXI, 2 and 4, and Plate XX, 6 and 7) has a peculiarity shared +only by kalon, that _x_ and _y_ are asymmetrical, the centre of one having +three atoms and the centre of the other two. Is this done in order to +preserve the difference of seven from its comrade? + +XENON: Six arms of 363 atoms 2178 + Central tetrahedra 120 + ----- + Total 2298 + ----- + Atomic weight 127.10 + Number weight 2298/18 127.66 +META-XENON differs from xenon only by the substitution of two _z_'s for _x_ +and _y_. + +META-XENON: Six arms of 370 atoms 2220 + Central tetrahedra 120 + ----- + Total 2340 + ----- + Atomic weight ----- + Number weight 2340/18 130 +KALON (Plate XXI, 3 and 4, and Plate XX, 6 and 7) has a curious cone, +possessing a kind of tail which we have not observed elsewhere; _x_ and _y_ +show the same asymmetry as in xenon. + +KALON: Six arms of 489 atoms 2934 + Central tetrahedra 120 + ---- + Total 3054 + ---- + Atomic weight ---- + Number weight 3054/18 169.66 +META-KALON again substitutes two _z_'s for _x_ and _y_. + +META-KALON: Six arms of 496 atoms 2976 + Central tetrahedra 120 + ---- + Total 3096 + ---- + Atomic weight ---- + Number weight 3096/18 172 +Only a few atoms of kalon and meta-kalon have been found in the air of a +fair-sized room. + +It does not seem worth while to break up these elements, for their +component parts are so familiar. The complicated groups--_a_ 110, _b_ 63 +and _c_ 120--have all been fully dealt with in preceding pages. + + * * * * * + +There remains now only radium, of the elements which we have, so far, +examined, and that will be now described and will bring to an end this +series of observations. A piece of close and detailed work of this kind, +although necessarily imperfect, will have its value in the future, when +science along its own lines shall have confirmed these researches. + +It will have been observed that our weights, obtained by counting, are +almost invariably slightly in excess of the orthodox ones: it is +interesting that in the latest report of the International Commission +(November 13, 1907), printed in the _Proceedings of the Chemical Society of +London_, Vol. XXIV, No. 33, and issued on January 25, 1908, the weight of +hydrogen is now taken at 1.008 instead of at 1. This would slightly raise +all the orthodox weights; thus aluminium rises from 26.91 to 27.1, antimony +from 119.34 to 120.2, and so on. + + * * * * * + +XI. + +RADIUM. + +[Illustration: PLATE XXII.] + +Radium has the form of a tetrahedron, and it is in the tetrahedral groups +(see article IV) that we shall find its nearest congeners; calcium, +strontium, chromium, molybdenum resemble it most closely in general +internal arrangements, with additions from zinc and cadmium. Radium has a +complex central sphere (Plate XXII), extraordinarily vivid and living; the +whirling motion is so rapid that continued accurate observation is very +difficult; the sphere is more closely compacted than the centre-piece in +other elements, and is much larger in proportion to the funnels and spikes +than is the case with the elements above named; reference to Plate VIII +will show that in these the funnels are much larger than the centres, +whereas in radium the diameter of the sphere and the length of the funnel +or spike are about equal. Its heart consists of a globe containing seven +atoms, which assume on the proto level the prismatic form shown in cadmium, +magnesium and selenium. This globe is the centre of two crosses, the arms +of which show respectively three-atomed and two-atomed groups. Round this +sphere are arranged, as on radii, twenty-four segments, each containing +five bodies--four quintets and a septet--and six loose atoms, which float +horizontally across the mouth of the segment; the whole sphere has thus a +kind of surface of atoms. On the proto level these six atoms in each +segment gather together and form a "cigar." In the rush of the streams +presently to be described one of these atoms is occasionally torn away, but +is generally, if not always, replaced by the capture of another which is +flung into the vacated space. + +Each of the four funnels opens, as usual, on one face of the tetrahedron, +and they resemble the funnels of strontium and molybdenum but contain three +pillars instead of four (Plate XXIII). They stand within the funnel as +though at the angles of a triangle, not side by side. The contained bodies, +though numerous, contain forms which are all familiar. + +The spikes alternate with the funnels, and point to the angles of the +tetrahedron as in zinc and cadmium; each spike contains three "lithium +spikes" (see Plate XIX) with a ten-atomed cone or cap at the top, floating +above the three (Plate XXIV). The "petals" or "cigars" of lithium exist in +the central globe in the floating atoms, and the four-atomed groups which +form the lithium "plate" may be seen in the funnels, so that the whole of +lithium appears in radium. + +So much for its composition. But a very peculiar result, so far unobserved +elsewhere, arises from the extraordinarily rapid whirling of the central +sphere. A kind of vortex is formed, and there is a constant and powerful +indraught through the funnels. By this, particles are drawn in from +without, and these are swept round with the sphere, their temperature +becoming much raised, and they are then violently shot out through the +spikes. It is these jets which occasionally sweep away an atom from the +surface of the sphere. These "particles" may be atoms, or they may be +bodies from any of the etheric levels; in some cases these bodies break up +and form new combinations. In fact lithium seems like a kind of vortex of +creative activity, drawing in, breaking up, recombining, shooting forth--a +most extraordinary element. + +RADIUM: 4 funnels of 618 atoms 2472 + 4 spikes of 199 atoms 796 + Central sphere 819 + ---- + Total 4087 + ---- + Atomic weight ---- + Number weight 4087/18 227.05 +[Illustration: PLATE XXIV.] + +[Illustration: PLATE XXIII.] + + * * * * * + +APPENDIX. + +THE ÆTHER OF SPACE. + +Much discussion has taken place, especially between physicists and +chemists, over the nature of the substances with which all space must, +according to scientific hypothesis, be filled. One side contends that it is +infinitely thinner than the thinnest gas, absolutely frictionless and +without weight; the other asserts that it is denser than the densest solid. +In this substance the ultimate atoms of matter are thought to float, like +motes in a sunbeam, and light, heat and electricity are supposed to be its +vibrations. + +Theosophical investigators, using methods not at the disposal of physical +science, have found that this hypothesis includes under one head two +entirely different and widely separated sets of phenomena. They have been +able to deal with states of matter higher than the gaseous and have +observed that it is by means of vibrations of this finer matter that light, +heat and electricity manifest themselves to us. Seeing that matter in these +higher states thus performs the functions attributed to the ether of +science, they have (perhaps unadvisedly) called these states etheric, and +have thus left themselves without a convenient name for that substance +which fulfils the other part of the scientific requirements. + +Let us for the moment name this substance _koilon_, since it fills what we +are in the habit of calling empty space. What mûlaprakrti, or +"mother-matter," is to the inconceivable totality of universes, koilon is +to our particular universe--not to our solar system merely but to the vast +unit which includes all visible suns. Between koilon and mûlaprakrti there +must be various stages, but we have at present no direct means of +estimating their number or of knowing anything whatever about them. + +In an ancient occult treatise, however, we read of a "colorless spiritual +fluid" "which exists everywhere and forms the first foundation on which our +solar system is built. Outside the latter, it is found in its pristine +purity only between the stars [suns] of the universe.... As its substance +is of a different kind from that known on earth, the inhabitants of the +latter, seeing _through it_, believe, in their illusion and ignorance, that +it is empty space. There is not one finger's breadth of void space in the +whole boundless universe."[21] "The mother-substance" is said, in this +treatise, to produce this æther of space as its seventh grade of density, +and all objective suns are said to have this for their "substance." + +To any power of sight which we can bring to bear upon it, this koilon +appears to be homogeneous, though it is probably nothing of the kind, since +homogeneity can belong to the mother-substance alone. It is out of all +proportion denser than any other substance known to us, infinitely +denser--if we may be pardoned the expression; so much denser that it seems +to belong to another type, or order, of density. But now comes the +startling part of the investigation: we might expect matter to be a +densification of this koilon; it is nothing of the kind. Matter is not +koilon, but _the absence of koilon_, and at first sight, matter and space +appear to have changed places, and emptiness has become solidity, solidity +has become emptiness. + +To help us to understand this clearly let us examine the ultimate atom of +the physical plane (see pp. 21-23). It is composed of ten rings or wires, +which lie side by side, but never touch one another. If one of these wires +be taken away from the atom, and be, as it were, untwisted from its +peculiar spiral shape and laid out on a flat surface, it will be seen that +it is a complete circle--a tightly twisted endless coil. This coil is +itself a spiral containing 1680 turns; it can be unwound, and it will then +make a much larger circle. This process of unwinding may be again +performed, and a still bigger circle obtained, and this can be repeated +till the seven sets of spirillæ are all unwound, and we have a huge circle +of the tiniest imaginable dots, like pearls threaded on an invisible +string. These dots are so inconceivably small that many millions of them +are needed to make one ultimate physical atom, and while the exact number +is not readily ascertainable, several different lines of calculation agree +in indicating it as closely approximate to the almost inconceivable total +of fourteen thousand millions. Where figures are so huge, direct counting +is obviously impossible, but fortunately the different parts of the atom +are sufficiently alike to enable us to make an estimate in which the margin +of error is not likely to be very great. The atom consists of ten wires, +which divide themselves naturally into two groups--the three which are +thicker and more prominent, and the seven thinner ones which correspond to +the colors and planets. These latter appear to be identical in constitution +though the forces flowing through them must differ, since each responds +most readily to its own special set of vibrations. By actual counting it +has been discovered that the numbers of coils or spirillæ of the first +order in each wire is 1680; and the proportion of the different orders of +spirillæ to one another is equal in all cases that have been examined, and +correspond with the number of dots in the ultimate spirillæ of the lowest +order. The ordinary sevenfold rule works quite accurately with the thinner +coils, but there is a very curious variation with regard to the set of +three. As may be seen from the drawings, these are obviously thicker and +more prominent, and this increase of size is produced by an augmentation +(so slight as to be barely perceptible) in the proportion to one another of +the different orders of spirillæ and in the number of dots in the lowest. +This augmentation, amounting at present to not more than .00571428 of the +whole of each case, suggests the unexpected possibility that this portion +of the atom may be somehow actually undergoing a change--may in fact be in +process of growth, as there is reason to suppose that these three thicker +spirals originally resembled the others. + +Since observation shows us that each physical atom is represented by +forty-nine astral atoms, each astral atom by forty-nine mental atoms, and +each mental atom by forty-nine of those on the buddhic plane, we have here +evidently several terms of a regular progressive series, and the natural +presumption is that the series continues where we are no longer able to +observe it. Further probability is lent to this assumption by the +remarkable fact that--if we assume one dot to be what corresponds to an +atom on the seventh or highest of our planes (as is suggested in _The +Ancient Wisdom_, p. 42) and then suppose the law of multiplication to begin +its operation, so that 49 dots shall form the atom of the next or sixth +plane, 2401 that of the fifth, and so on--we find that the number indicated +for the physical atom (496) corresponds almost exactly with the calculation +based upon the actual counting of the coils. Indeed, it seems probable that +but for the slight growth of the three thicker wires of the atom the +correspondence would have been perfect. + +It must be noted that a physical atom cannot be directly broken up into +astral atoms. If the unit of force which whirls those millions of dots into +the complicated shape of a physical atom be pressed back by an effort of +will over the threshold of the astral plane, the atom disappears instantly, +for the dots are released. But the same unit of force, working now upon a +higher level, expresses itself not through one astral atom, but through a +group of 49. If the process of pressing back the unit of force is repeated, +so that it energises upon the mental plane, we find the group there +enlarged to the number of 2401 of those higher atoms. Upon the buddhic +plane the number of atoms formed by the same amount of force is very much +greater still--probably the cube of 49 instead of the square, though they +have not been actually counted. Therefore one physical atom is not +_composed of_ forty-nine astral or 2401 mental atoms, but _corresponds_ to +them, in the sense that the force which manifests through it would show +itself on those higher planes by energising respectively those numbers of +atoms. + +The dots, or beads, seem to be the constituents of all matter of which we, +at present, know anything; astral, mental and buddhic atoms are built of +them, so we may fairly regard them as fundamental units, the basis of +matter. + +These units are all alike, spherical and absolutely simple in construction. +Though they are the basis of all matter, they are not themselves matter; +they are not blocks but bubbles. They do not resemble bubbles floating in +the air, which consist of a thin film of water separating the air within +them from the air outside, so that the film has both an outer and an inner +surface. Their analogy is rather with the bubbles that we see rising in +water, before they reach the surface, bubbles which may be said to have +only one surface--that of the water which is pushed back by the contained +air. Just as such bubbles are not water, but are precisely the spots from +which water is absent, so these units are not koilon, but the absence of +koilon--the only spots where it is not--specks of nothingness floating in +it, so to speak, for the interior of these space-bubbles is an absolute +void to the highest power of vision that we can turn upon them. + +That is the startling, well-nigh incredible, fact. Matter is nothingness, +the space obtained by pressing back an infinitely dense substance; Fohat +"digs holes in space" of a verity, and the holes are the airy +nothingnesses, the bubbles, of which "solid" universes are built. + +What are they, then, these bubbles, or rather, what is their content, the +force which can blow bubbles in a substance of infinite density? The +ancients called that force "the Breath," a graphic symbol, which seems to +imply that they who used it had seen the kosmic process, had seen the LOGOS +when He breathed into the "waters of space," and made the bubbles which +build universes. Scientists may call this "Force" by what names they +will--names are nothing; to us, Theosophists, it is the Breath of the +LOGOS, we know not whether of the LOGOS of this solar system or of a yet +mightier Being; the latter would seem the more likely, since in the +above-quoted occult treatise all visible suns are said to have this as +their substance. + +The Breath of the LOGOS, then, is the force which fills these spaces; His +the force which holds them open against the tremendous pressure of the +koilon; they are full of His Life, of Himself, and everything we call +matter, on however high or low a plane, is instinct with divinity; these +units of force, of life, the bricks with which He builds His universe, are +His very life scattered through space; truly is it written: "I established +this universe with a portion of myself." And when He draws in His breath, +the waters of space will close in again, and the universe will have +disappeared. It is only a breath. + +The outbreathing which makes these bubbles is quite distinct from, and long +antecedent to, the three outpourings, or Life-Waves, so familiar to the +theosophical student. The first Life-Wave catches up these bubbles, and +whirls them into the various arrangements which we call the atoms of the +several planes, and aggregates them into the molecules, and on the physical +plane into the chemical elements. The worlds are built out of these voids, +these emptinesses, which seem to us "nothing" but are divine force. It is +matter made from the privation of matter. How true were H.P.B.'s statements +in "The Secret Doctrine": "Matter is nothing but an aggregation of atomic +forces" (iii, 398); "Buddha taught that the primitive substance is eternal +and unchangeable. Its vehicle is the pure luminous æther, the boundless +infinite space, not a void, resulting from the absence of all forms, but on +the contrary, the foundation of all forms" (iii, 402). + +How vividly, how unmistakably this knowledge brings home to us the great +doctrine of Mâyâ, the transitoriness and unreality of earthly things, the +utterly deceptive nature of appearances! When the candidate for initiation +sees (not merely believes, remember, but actually _sees_) that what has +always before seemed to him empty space is in reality a solid mass of +inconceivable density, and that the matter which has appeared to be the one +tangible and certain basis of things is not only by comparison tenuous as +gossamer (the "web" spun by "Father-Mother"), but is actually composed of +emptiness and nothingness--is itself the very negation of matter--then for +the first time he thoroughly appreciates the valuelessness of the physical +senses as guides to the truth. Yet even more clearly still stands out the +glorious certainty of the immanence of the Divine; not only is everything +ensouled by the LOGOS, but even its visible manifestation is literally part +of Him, is built of His very substance, so that Matter as well as Spirit +becomes sacred to the student who really understands. + +The koilon in which all these bubbles are formed undoubtedly represents a +part, and perhaps the principal part, of what science describes as the +luminiferous æther. Whether it is actually the bearer of the vibrations of +light and heat through interplanetary space is as yet undetermined. It is +certain that these vibrations impinge upon and are perceptible to our +bodily senses only through the etheric matter of the physical plane. But +this by no means proves that they are conveyed through space in the same +manner, for we know very little of the extent to which the physical etheric +matter exists in interplanetary and interstellar space, though the +examination of meteoric matter and kosmic dust shows that at least some of +it is scattered there. + +The scientific theory is that the æther has some quality which enables it +to transmit at a certain definite velocity transverse waves of all lengths +and intensities--that velocity being what is commonly called the speed of +light, 190,000 miles per second. Quite probably this may be true of koilon, +and if so it must also be capable of communicating those waves to bubbles +or aggregations of bubbles, and before the light can reach our eyes there +must be a downward transference from plane to plane similar to that taking +place when a thought awakens emotion or causes action. + +In a recent pamphlet on "The Density of Æther," Sir Oliver Lodge remarks:-- + +"Just as the ratio of mass to volume is small in the case of a solar system +or a nebula or a cobweb, I have been driven to think that the observed +mechanical density of matter is probably an excessively small fraction of +the total density of the substance or æther contained in the space which it +thus partially occupies--the substance of which it may hypothetically be +held to be composed. + +"Thus, for instance, consider a mass of platinum, and assume that its atoms +are composed of electrons, or of some structures not wholly dissimilar: the +space which these bodies actually fill, as compared with the whole space +which in a sense they 'occupy,' is comparable to one ten-millionth of the +whole, even inside each atom; and the fraction is still smaller if it +refers to the visible mass. So that a kind of minimum estimate of ætherial +density, on this basis, would be something like ten thousand million times +that of platinum." + +And further on he adds that this density may well turn out to be fifty +thousand million times that of platinum. "The densest matter known," he +says, "is trivial and gossamer-like compared with the unmodified æther in +the same space." + +Incredible as this seems to our ordinary ideas, it is undoubtedly an +understatement rather than an exaggeration of the true proportion as +observed in the case of koilon. We shall understand how this can be so if +we remember that koilon seems absolutely homogeneous and solid even when +examined by a power of magnification which makes physical atoms appear in +size and arrangement like cottages scattered over a lonely moor, and when +we further add to this the recollection that the bubbles of which these +atoms in turn are composed are themselves what may be not inaptly called +fragments of nothingness. + +In the same pamphlet Sir Oliver Lodge makes a very striking estimate of the +intrinsic energy of the æther. He says: "The total output of a +million-kilowatt power station for thirty million years exists permanently, +and at present inaccessibly in every cubic millimetre of space." Here again +he is probably underestimating the stupendous truth. + +It may naturally be asked how, if all this be so, it is possible that we +can move about freely in a solid ten thousand million times denser, as Sir +Oliver Lodge says, than platinum. The obvious answer is that, where +densities differ sufficiently, they can move through each other with +perfect freedom; water or air can pass through cloth; air can pass through +water; an astral form passes unconsciously through a physical wall, or +through an ordinary human body; many of us have seen an astral form walk +through a physical, neither being conscious of the passage; it does not +matter whether we say that a ghost has passed through a wall, or a wall has +passed through a ghost. A gnome passes freely through a rock, and walks +about within the earth, as comfortably as we walk about in the air. A +deeper answer is that consciousness can recognize only consciousness, that +since we are of the nature of the LOGOS we can sense only those things +which are also of His nature. These bubbles are His essence, His life, and, +therefore, we, who also are part of Him, can see the matter which is built +of his substance, for all forms are but manifestations of Him. The koilon +is to us non-manifestation, because we have not unfolded powers which +enable us to cognise it, and it may be the manifestation of a loftier order +of LOGOI, utterly beyond our ken. + +As none of our investigators can raise his consciousness to the highest +plane of our universe, the âdi-tattva plane, it may be of interest to +explain how it is possible for them to see what may very probably be the +atom of that plane. That this may be understood it is essential to remember +that the power of magnification by means of which these experiments are +conducted is quite apart from the faculty of functioning upon one or other +of the planes. The latter is the result of a slow and gradual unfoldment of +the Self, while the former is merely a special development of one of the +many powers latent in man. All the planes are round us here, just as much +as any other point in space, and if a man sharpens his sight until he can +see their tiniest atoms he can make a study of them, even though he may as +yet be far from the level necessary to enable him to understand and +function upon the higher planes as a whole, or to come into touch with the +glorious Intelligences who gather those atoms into vehicles for Themselves. + +A partial analogy may be found in the position of the astronomer with +regard to the stellar universe, or let us say the Milky Way. He can observe +its constituent parts and learn a good deal about them along various lines, +but it is absolutely impossible for him to see it as a whole from outside, +or to form any certain conception of its true shape, and to know what it +really is. Suppose that the universe is, as many of the ancients thought, +some inconceivably vast Being, it is utterly impossible for us, here in the +midst of it, to know what that Being is or is doing, for that would mean +raising ourselves to a height comparable with His; but we may make +extensive and detailed examination of such particles of His body as happen +to be within our reach, for that means only the patient use of powers and +machinery already at our command. + +Let it not be supposed that, in thus unfolding a little more of the wonders +of Divine Truth by pushing our investigations to the very farthest point at +present possible to us, we in any way alter or modify all that has been +written in theosophical books of the shape and constitution of the physical +atom, and of the wonderful and orderly arrangements by which it is grouped +into the various chemical molecules; all this remains entirely unaffected. + +Nor is any change introduced as regards the three outpourings from the +LOGOS, and the marvellous facility with which the matter of the various +planes is by them moulded into forms for the service of the evolving life. +But if we wish to have a right view of the realities underlying +manifestation in this universe, we must to a considerable extent reverse +the ordinary conception as to what this matter essentially is. Instead of +thinking of its ultimate constituents as solid specks floating in a void, +we must realise that it is the apparent void itself which is solid, and +that the specks are but bubbles on it. That fact once grasped, all the rest +remains as before. The relative position of what we have hitherto called +matter and force is still for us the same as ever; it is only that, on +closer examination, both of these conceptions prove to be variants of +force, the one ensouling combinations of the other, and the real "matter," +koilon, is seen to be something which has hitherto been altogether outside +our scheme of thought. + +In view of this marvellous distribution of Himself in "space," the familiar +concept of the "sacrifice of the LOGOS" takes on a new depth and splendour; +this is His "dying in matter," His "perpetual sacrifice," and it may be the +very glory of the LOGOS that He can sacrifice Himself to the uttermost by +thus permeating and making Himself one with that portion of koilon which He +chooses as the field of His universe. + +What koilon is, what its origin, whether it is itself changed by the Divine +Breath which is poured into it--does "Dark Space" thus become "Bright +Space" at the beginning of a manifestation?--these are questions to which +we cannot at present even indicate answers. Perchance an intelligent study +of the great Scriptures of the world may yield replies. + + * * * * * + +NOTES + +[1] See footnote in next Chapter. + +[2] The drawings of the elements were done by two Theosophical artists, +Herr Hecker and Mrs. Kirby, whom we sincerely thank; the diagrams, showing +the details of the construction of each "element," we owe to the most +painstaking labour of Mr. Jinarâjadâsa, without whose aid it would have +been impossible for us to have presented clearly and definitely the +complicated arrangements by which the chemical elements are built up. We +have also to thank him for a number of most useful notes, implying much +careful research, which are incorporated in the present series, and without +which we could not have written these papers. + +[3] The atomic sub-plane. + +[4] The astral plane. + +[5] Known to Theosophists as Fohat, the force of which all the physical +plane forces--electricities--are differentiations. + +[6] When Fohat "digs holes in space." + +[7] The first life-wave, the work of the third Logos. + +[8] A mâyâ, truly. + +[9] By a certain action of the will, known to students, it is possible to +make such a space by pressing back and walling off the matter of space. + +[10] Again the astral world. + +[11] Each spirilla is animated by the life-force of a plane, and four are +at present normally active, one for each round. Their activity in an +individual may be prematurely forced by yoga practice. + +[12] "The ten numbers of the sun. These are called Dis--in reality +space--the forces spread in space, three of which are contained in the +Sun's Atman, or seventh principle, and seven are the rays shot out by the +Sun." The atom is a sun in miniature in its own universe of the +inconceivably minute. Each of the seven whorls is connected with one of the +Planetary Logoi, so that each Planetary Logos has a direct influence +playing on the very matter of which all things are constructed. It may be +supposed that the three, conveying electricity, a differentiation of Fohat, +are related to the Solar Logoi. + +[13] The action of electricity opens up ground of large extent, and cannot +be dealt with here. Does it act on the atoms themselves, or on molecules, +or sometimes on one and sometimes on the other? In soft iron, for instance, +are the internal arrangements of the chemical atom forcibly distorted, and +do they elastically return to their original relations when released? and +in steel is the distortion permanent? In all the diagrams the heart-shaped +body, exaggerated to show the depression caused by the inflow and the point +caused by the outflow, is a single atom. + +[14] These sub-planes are familiar to the Theosophist as gaseous, etheric, +super-etheric, sub-atomic, atomic; or as Gas, Ether 4, Ether 3, Ether 2, +Ether 1. + +[15] It must be remembered that the diagrams represent three-dimensional +objects, and the atoms are not all on a plane, necessarily. + +[16] That is, the surrounding magnetic fields strike on each other. + +[17] The fifth member of this group was not sought for. + +[18] This, with references which appear later (pp. 32, 33, 50, etc.), +relates to articles which appeared in the _Theosophist_, 1908. + +[19] Since writing the above I have noticed, in the _London, Edinburgh and +Dublin Philosophical Magazine and Journal of Science_, conducted by Dr. +John Joly and Mr. William Francis, in an article entitled "Evolution and +Devolution of the Elements," the statement that it is probable that in "the +nebulous state of matter there are four substances, the first two being +unknown upon earth, the third being hydrogen and the fourth ... helium. It +also seems probable that ... hydrogen, the two unknown elements, and helium +are the four original elements from which all the other elements form. To +distinguish them from the others we will term them protons." This is +suggestive as regards hydrogen, but does not help us with regard to oxygen +and nitrogen. + +[20] Theosophists call them Nature-Spirits, and often use the mediæval term +Elementals. Beings concerned with the elements truly are they, even with +chemical elements. + +[21] Quoted in "The Secret Doctrine." H.P. Blavatsky, i, 309. + + + +***END OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY*** + + +******* This file should be named 16058-8.txt or 16058-8.zip ******* + + +This and all associated files of various formats will be found in: +https://www.gutenberg.org/dirs/1/6/0/5/16058 + + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS', WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, is critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.gutenberg.org/fundraising/pglaf. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://www.gutenberg.org/about/contact + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://www.gutenberg.org/fundraising/donate + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: +https://www.gutenberg.org/fundraising/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. + |