{"collection":"scripture-revelation","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_16058/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_16058","id":"gutenberg_16058","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/16058","summary":null,"tags":["Category: Religion/Spirituality","Category: Science - Chemistry/Biochemistry","Chemical elements","Occultism"],"text":"E-text prepared by Clare Boothby, Keith Edkins, and the Project Gutenberg\nOnline Distributed Proofreading Team\n\n\n\nNote: Project Gutenberg also has an HTML version of this\n      file which includes the original illustrations.\n      See 16058-h.htm or 16058-h.zip:\n      (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h/16058-h.htm)\n      or\n      (https://www.gutenberg.org/dirs/1/6/0/5/16058/16058-h.zip)\n\n\n\n\n\nOCCULT CHEMISTRY\n\nClairvoyant Observations on the Chemical Elements\n\nby\n\nANNIE BESANT, P.T.S.\n\nand\n\nCHARLES W. LEADBEATER\n\nRevised Edition edited by A. P. SINNETT\n\nLONDON\nTHEOSOPHICAL PUBLISHING HOUSE\n1, UPPER WOBURN PLACE, W.C. 1.\n\n1919\n\n\n\n\n\n\n\nEDITOR'S PREFACE.\n\n\n\nWhen undertaking to prepare a new edition of this book I received\npermission from the authors to \"throw it into the form in which you think\nit would be most useful at the present time.\" It was left to my discretion,\n\"What to use and what to omit.\" I have not found it necessary to avail\nmyself to any considerable extent of this latter permission. But as the\ncontents of the book were originally arranged the reader was ill-prepared\nto appreciate the importance of the later research for want of introductory\nmatter explaining how it began, and how the early research led up to the\nlater investigation. I have therefore contributed an entirely new\npreliminary chapter which will, I hope, help the reader to realise the\ncredibility of the results attained when the molecular forms and\nconstitution of the numerous bodies examined were definitely observed. I\nhave not attempted to revise the records of the later research in which I\nhad no personal share, so from the beginning of Chapter III to the end the\nbook in its present form is simply a reprint of the original edition except\nfor the correction of a few trifling misprints.\n\nI have thus endeavoured to bring into clear prominence at the outset the\nscientific value of the light the book sheds on the constitution of matter.\nThe world owes a debt to scientific men of the ordinary type that cannot be\nover-estimated, but though they have hitherto preferred to progress\ngradually, from point to point, disliking leaps in the dark, the leap now\nmade is only in the dark for those who will not realise that the progress\nto be accomplished by means of instrumental research must sooner or later\nbe supplemented by subtler methods. Physical science has reached the\nconception that the atoms of the bodies hitherto called the chemical\nelements are each composed of minor atoms. Instrumental research cannot\ndetermine by how many, in each case. Occult research ascertained the actual\nnumber in some cases by direct observation and then discovered the law\ngoverning the numbers in all cases, and the relation of these numbers to\natomic weights. The law thus unveiled is a demonstration of the accuracy of\nthe first direct observations, and this principle once established the\ncredibility of accounts now given as to the arrangement of minor atoms in\nthe molecules of the numerous elements examined, seems to me advanced to a\ndegree approximating to proof.\n\nIt remains to be seen--not how far, but rather how soon the scientific\nworld at large will accept the conclusions of this volume as a definite\ncontribution to science, blending the science of the laboratory with that\nvariety that has hitherto been called occult.\n\n\n\n\n\nCONTENTS.\n\n  I.--A PRELIMINARY SURVEY\n\n  II.--DETAILS OF THE EARLY RESEARCH\n\n       THE PLATONIC SOLIDS\n\n  III.--THE LATER RESEARCHES\n\n\n\n\n\n\nOCCULT CHEMISTRY.\n\nCHAPTER I.\n\nA PRELIMINARY SURVEY.\n\nThe deep interest and importance of the research which this book describes\nwill best be appreciated if introduced by an account of the circumstances\nout of which it arose. The first edition, consisting mainly of articles\nreprinted from the _Theosophist_, dealt at once with the later phases of\nthe research in a way which, though intelligible to the occult student,\nmust have been rather bewildering to the ordinary reader. These later\nphases, however, endow the earlier results with a significance that in the\nbeginning could only be vaguely conjectured. I am the better entitled to\nperform the task that has been assigned to me--that of preparing the\npresent edition--by reason of the fact that it was in my presence and at my\ninstigation that the first efforts were made to penetrate the mystery\npreviously enshrouding the ultimate molecule of matter.\n\nI remember the occasion vividly. Mr. Leadbeater was then staying at my\nhouse, and his clairvoyant faculties were frequently exercised for the\nbenefit of myself, my wife and the theosophical friends around us. I had\ndiscovered that these faculties, exercised in the appropriate direction,\nwere ultra-microscopic in their power. It occurred to me once to ask Mr.\nLeadbeater if he thought he could actually _see_ a molecule of physical\nmatter. He was quite willing to try, and I suggested a molecule of gold as\none which he might try to observe. He made the appropriate effort, and\nemerged from it saying the molecule in question was far too elaborate a\nstructure to be described. It evidently consisted of an enormous number of\nsome smaller atoms, quite too many to count; quite too complicated in their\narrangement to be comprehended. It struck me at once that this might be due\nto the fact that gold was a heavy metal of high atomic weight, and that\nobservation might be more successful if directed to a body of low atomic\nweight, so I suggested an atom of hydrogen as possibly more manageable. Mr.\nLeadbeater accepted the suggestion and tried again. This time he found the\natom of hydrogen to be far simpler than the other, so that the minor atoms\nconstituting the hydrogen atom were countable. They were arranged on a\ndefinite plan, which will be rendered intelligible by diagrams later on,\nand were eighteen in number.\n\nWe little realized at the moment the enormous significance of this\ndiscovery, made in the year 1895, long before the discovery of radium\nenabled physicists of the ordinary type to improve their acquaintance with\nthe \"electron.\" Whatever name is given to that minute body it is recognised\nnow by ordinary science as well as by occult observation, as the\nfundamental unit of physical matter. To that extent ordinary science has\novertaken the occult research I am dealing with, but that research rapidly\ncarried the occult student into regions of knowledge whither, it is\nperfectly certain, the ordinary physicist must follow him at no distant\ndate.\n\nThe research once started in the way I have described was seen to be\nintensely interesting. Mrs. Besant almost immediately co-operated with Mr.\nLeadbeater in its further progress. Encouraged by the success with\nhydrogen, the two important gases, oxygen and nitrogen, were examined. They\nproved to be rather more difficult to deal with than hydrogen but were\nmanageable. Oxygen was found to consist of 290 minor atoms and nitrogen of\n261. Their grouping will be described later on. The interest and importance\nof the whole subject will best be appreciated by a rough indication of the\nresults first attained. The reader will then have more patience in\nfollowing the intricacies of the later discoveries.\n\nThe figures just quoted were soon perceived to have a possible\nsignificance. The atomic weight of oxygen is commonly taken as 16. That is\nto say, an atom of oxygen is sixteen times heavier than an atom of\nhydrogen. In this way, all through the table of atomic weights, hydrogen is\ntaken as unity, without any attempt being made to estimate its absolute\nweight. But now with the atom of hydrogen dissected, so to speak, and found\nto consist of 18 somethings, while the atom of oxygen consisted of 290 of\nthe same things, the sixteen to one relationship reappears: 290 divided by\n18 gives us 16 and a minute decimal fraction. Again the nitrogen number\ndivided by 18 gives us 14 and a minute fraction as the result, and that is\nthe accepted atomic weight of nitrogen. This gave us a glimpse of a\nprinciple that might run all through the table of atomic weights. For\nreasons having to do with other work, it was impossible for the authors of\nthis book to carry on the research further at the time it was begun. The\nresults already sketched were published as an article in the magazine then\ncalled _Lucifer_, in November, 1895, and reprinted as a separate pamphlet\nbearing the title \"Occult Chemistry,\" a pamphlet the surviving copies of\nwhich will one day be a recognised vindication of the method that will at\nsome time in the future be generally applied to the investigation of\nNature's mysteries. For the later research which this volume deals with\ndoes establish the principle with a force that can hardly be resisted by\nany fair-minded reader. With patience and industry--the authors being\nassisted in the counting in a way that will be described (and the method\nadopted involved a check upon the accuracy of the counting)--the minor\natoms of almost all the known chemical elements, as they are commonly\ncalled, were counted and found to bear the same relation to their atomic\nweights as had been suggested by the cases of oxygen and nitrogen. This\nresult throws back complete proof on the original estimate of the number of\nminor atoms in hydrogen, a figure which ordinary research has so far\nentirely failed to determine. The guesses have been widely various, from\nunity to many hundreds, but, unacquainted with the clairvoyant method, the\nordinary physicist has no means of reaching the actual state of the facts.\n\nBefore going on with the details of the later research some very important\ndiscoveries arising from the early work must first be explained. As I have\nalready said clairvoyant faculty of the appropriate order directed to the\nminute phenomena of Nature is practically infinite in its range. Not\ncontent with estimating the number of minor atoms in physical molecules,\nthe authors proceeded to examine the minor atoms individually. They were\nfound to be themselves elaborately complicated structures which, in this\npreliminary survey of the whole subject, I will not stop to explain (full\nexplanation will be found later on) and they are composed of atoms\nbelonging to an ultra-physical realm of Nature with which the occultist has\nlong been familiar and describes as \"the Astral Plane.\" Some rather\npedantic critics have found fault with the term, as the \"plane\" in question\nis of course really a sphere entirely surrounding the physical globe, but\nas all occultists understand the word, \"plane\" simply signifies a condition\nof nature. Each condition, and there are many more than the two under\nconsideration, blends with its neighbour, _via_ atomic structure. Thus the\natoms of the Astral plane in combination give rise to the finest variety of\nphysical matter, the ether of space, which is not homogeneous but really\natomic in its character, and the minute atoms of which physical molecules\nare composed are atoms of ether, \"etheric atoms,\" as we have now learned to\ncall them.\n\nMany physicists, though not all, will resent the idea of treating the ether\nof space as atomic. But at all events the occultist has the satisfaction of\nknowing that the great Russian chemist, Mendeleef, preferred the atomic\ntheory. In Sir William Tilden's recent book entitled \"Chemical Discovery\nand Invention in the Twentieth Century,\" I read that Mendeleef,\n\"disregarding conventional views,\" supposed the ether to have a molecular\nor atomic structure, and in time all physicists must come to recognise that\nthe Electron is not, as so many suppose at present, an atom of electricity,\nbut an atom of ether carrying a definite unit charge of electricity.\n\nLong before the discovery of radium led to the recognition of the electron\nas the common constituent of all the bodies previously described as\nchemical elements, the minute particles of matter in question had been\nidentified with the cathode rays observed in Sir William Crookes' vacuum\ntubes. When an electric current is passed through a tube from which the air\n(or other gas it may contain) has been almost entirely exhausted, a\nluminous glow pervades the tube manifestly emanating from the cathode or\nnegative pole of the circuit. This effect was studied by Sir William\nCrookes very profoundly. Among other characteristics it was found that, if\na minute windmill was set up in the tube before it was exhausted, the\ncathode ray caused the vanes to revolve, thus suggesting the idea that they\nconsisted of actual particles driven against the vanes; the ray being thus\nevidently something more than a mere luminous effect. Here was a mechanical\nenergy to be explained, and at the first glance it seemed difficult to\nreconcile the facts observed with the idea creeping into favour, that the\nparticles, already invested with the name \"electron,\" were atoms of\nelectricity pure and simple. Electricity was found, or certain eminent\nphysicists thought they had found, that electricity _per se_ had inertia.\nSo the windmills in the Crookes' vacuum tubes were supposed to be moved by\nthe impact of electric atoms.\n\nThen in the progress of ordinary research the discovery of radium by Madame\nCurie in the year 1902 put an entirely new face upon the subject of\nelectrons. The beta particles emanating from radium were soon identified\nwith the electrons of the cathode ray. Then followed the discovery that the\ngas helium, previously treated as a separate element, evolved itself as one\nconsequence of the disintegration of radium. Transmutation, till then\nlaughed at as a superstition of the alchemist, passed quietly into the\nregion of accepted natural phenomena, and the chemical elements were seen\nto be bodies built up of electrons in varying number and probably in\nvarying arrangements. So at last ordinary science had reached one important\nresult of the occult research carried on seven years earlier. It has not\nyet reached the finer results of the occult research--the _structure_ of\nthe hydrogen atom with its eighteen etheric atoms and the way in which the\natomic weights of all elements are explained by the number of etheric atoms\nentering into their constitution.\n\nThe ether of space, though defying instrumental examination, comes within\nscope of the clairvoyant faculty, and profoundly interesting discoveries\nwere made during what I have called the early research in connexion with\nthat branch of the inquiry. Etheric atoms combine to form molecules in many\ndifferent ways, but combinations involving fewer atoms than the eighteen\nwhich give rise to hydrogen, make no impression on the physical senses nor\non physical instruments of research. They give rise to varieties of\nmolecular ether, the comprehension of which begins to illuminate realms of\nnatural mystery as yet entirely untrodden by the ordinary physicist.\nCombinations below 18 in number give rise to three varieties of molecular\nether, the functions of which when they come to be more fully studied will\nconstitute a department of natural knowledge on the threshold of which we\nalready stand. Some day we may perhaps be presented with a volume on Occult\nPhysics as important in its way as the present dissertation on Occult\nChemistry.\n\n       *       *       *       *       *\n\n\n\nCHAPTER II.\n\nDETAILS OF THE EARLY RESEARCH.\n\nThe article detailing the results of the research carried on in the year\n1895 (see the November issue for that year of the magazine then called\n_Lucifer_), began with some general remarks about the clairvoyant faculty,\nalready discussed in the preceding chapter. The original record then goes\non as follows:--\n\nThe physical world is regarded as being composed of between sixty and\nseventy chemical elements, aggregated into an infinite variety of\ncombinations. These combinations fall under the three main heads of solids,\nliquids and gases, the recognised substates of physical matter, with the\ntheoretical ether scarcely admitted as material. Ether, to the scientist,\nis not a substate or even a state of matter, but is a something apart by\nitself. It would not be allowed that gold could be raised to the etheric\ncondition as it might be to the liquid and gaseous; whereas the occultist\nknows that the gaseous is succeeded by the etheric, as the solid is\nsucceeded by the liquid, and he knows also that the word \"ether\" covers\nfour substates as distinct from each other as are the solids, liquids and\ngases, and that all chemical elements have their four etheric substates,\nthe highest being common to all, and consisting of the ultimate physical\natoms to which all elements are finally reducible. The chemical atom is\nregarded as the ultimate particle of any element, and is supposed to be\nindivisible and unable to exist in a free state. Mr. Crookes' researches\nhave led the more advanced chemists to regard the atoms as compound, as a\nmore or less complex aggregation of protyle.\n\nTo astral vision ether is a visible thing, and is seen permeating all\nsubstances and encircling every particle. A \"solid\" body is a body composed\nof a vast number of particles suspended in ether, each vibrating backwards\nand forwards in a particular field at a high rate of velocity; the\nparticles are attracted towards each other more strongly than they are\nattracted by external influences, and they \"cohere,\" or maintain towards\neach other a definite relation in space. Closer examination shows that the\nether is not homogeneous but consists of particles of numerous kinds,\ndiffering in the aggregations of the minute bodies composing them; and a\ncareful and more detailed method of analysis reveals that it has four\ndistinct degrees, giving us, with the solid, liquid and gaseous, seven\ninstead of four substates of matter in the physical world.\n\nThese four etheric substates will be best understood if the method be\nexplained by which they were studied. This method consisted of taking what\nis called an atom of gas, and breaking it up time after time, until what\nproved to be the ultimate physical atom was reached, the breaking up of\nthis last resulting in the production of astral, and no longer physical\nmatter.\n\n[Illustration]\n\nIt is, of course, impossible to convey by words the clear conceptions that\nare gained by direct vision of the objects of study, and the accompanying\ndiagram--cleverly drawn from the description given by the investigators--is\noffered as a substitute, however poor, for the lacking vision of the\nreaders. The horizontal lines separate from each other the seven substates\nof matter; solid, liquid, gas, ether 4, ether 3, ether 2, ether 1. On the\ngas level are represented three chemical atoms, one of hydrogen (H), one of\noxygen (O), one of nitrogen (N). The successive changes undergone by each\nchemical atom are shown in the compartments vertically above it, the\nleft-hand column showing the breaking up of the hydrogen atom, the middle\ncolumn that of the oxygen atom, the right-hand column, that of the nitrogen\natom. The ultimate physical atom is marked _a_, and is drawn only once,\nalthough it is the same throughout. The numbers 18, 290 and 261 are the\nnumbers of the ultimate physical atoms found to exist in a chemical atom.\n\nThe dots indicate the lines along which force is observed to be playing,\nand the arrowheads show the direction of the force. No attempt has been\nmade to show this below E 2 except in the case of the hydrogen. The letters\ngiven are intended to help the reader to trace upwards any special body;\nthus _d_ in the oxygen chemical atom on the gas level may be found again on\nE 4, E 3, and E 2. It must be remembered that the bodies shown\ndiagrammatically in no way indicate relative size; as a body is raised from\none substate to the one immediately above it, it is enormously magnified\nfor the purpose of investigation, and the ultimate atom on E 1 is\nrepresented by the dot _a_ on the gaseous level.\n\nThe first chemical atom selected for this examination was an atom of\nhydrogen (H). On looking carefully at it, it was seen to consist of six\nsmall bodies, contained in an egg-like form. It rotated with great rapidity\non its own axis, vibrating at the same time, and the internal bodies\nperformed similar gyrations. The whole atom spins and quivers, and has to\nbe steadied before exact observation is possible. The six little bodies are\narranged in two sets of three, forming two triangles that are not\ninterchangeable, but are related to each other as object and image. (The\nlines in the diagram of it on the gaseous sub-plane are not lines of force,\nbut show the two triangles; on a plane surface the interpenetration of the\ntriangles cannot be clearly indicated.) Further, the six bodies are not all\nalike; they each contain three smaller bodies--each of these being an\nultimate physical atom--but in two of them the three atoms are arranged in\na line, while in the remaining four they are arranged in a triangle.\n\nThe wall of the limiting spheroid in which the bodies are enclosed being\ncomposed of the matter of the third, or gaseous, kind, drops away when the\ngaseous atom is raised to the next level, and the six bodies are set free.\nThey at once re-arrange themselves in two triangles, each enclosed by a\nlimiting sphere; the two marked _b_ in the diagram unite with one of those\nmarked _b'_ to form a body which shows a positive character, the remaining\nthree forming a second body negative in type. These form the hydrogen\nparticles of the lowest plane of ether, marked E 4--ether 4--on the\ndiagram. On raising these further, they undergo another disintegration,\nlosing their limiting walls; the positive body of E 4, on losing its wall,\nbecomes two bodies, one consisting of the two particles, marked _b_,\ndistinguishable by the linear arrangement of the contained ultimate atoms,\nenclosed in a wall, and the other being the third body enclosed in E 4 and\nnow set free. The negative body of E 4 similarly, on losing its wall,\nbecomes two bodies, one consisting of the two particles marked _b'_, and\nthe second the remaining body, being set free. These free bodies do not\nremain on E 3 but pass immediately to E 2, leaving the positive and\nnegative bodies, each containing two particles, as the representatives of\nhydrogen on E 3. On taking these bodies a step higher their wall\ndisappears, and the internal bodies are set free, those containing the\natoms arranged lineally being positive, and those with the triangular\narrangement being negative. These two forms represent hydrogen on E 2, but\nsimilar bodies of this state of matter are found entering into other\ncombinations, as may be seen by referring to _f_ on E 2 of nitrogen (N). On\nraising these bodies yet one step further, the falling away of the walls\nsets the contained atoms free, and we reach the ultimate physical atom, the\nmatter of E 1. The disintegration of this sets free particles of astral\nmatter, so that we have reached in this the limit of physical matter. The\nTheosophical reader will notice with interest that we can thus observe\nseven distinct substates of physical matter, and no more.\n\nThe ultimate atom, which is the same in all the observed cases, is an\nexceedingly complex body, and only its main characteristics are given in\nthe diagram. It is composed entirely of spirals, the spiral being in its\nturn composed of spirillae, and these again of minuter spirillae. A fairly\naccurate drawing is given in Babbitt's \"Principles of Light and Colour,\" p.\n102. The illustrations there given of atomic combinations are entirely\nwrong and misleading, but if the stove-pipe run through the centre of the\nsingle atom be removed, the picture may be taken as correct, and will give\nsome idea of the complexity of this fundamental unit of the physical\nuniverse.\n\nTurning to the force side of the atom and its combinations, we observe that\nforce pours in the heart-shaped depression at the top of the atom, and\nissues from the point, and is changed in character by its passage; further,\nforce rushes through every spiral and every spirilla, and the changing\nshades of colour that flash out from the rapidly revolving and vibrating\natom depend on the several activities of the spirals; sometimes one,\nsometimes another, is thrown into more energetic action, and with the\nchange of activity from one spiral to another the colour changes.\n\nThe building of a gaseous atom of hydrogen may be traced downward from E 1,\nand, as stated above, the lines given in the diagram are intended to\nindicate the play of the forces which bring about the several combinations.\nSpeaking generally, positive bodies are marked by their contained atoms\nsetting their points towards each other and the centre of their\ncombination, and repelling each other outwards; negative bodies are marked\nby the heart-shaped depressions being turned inwards, and by a tendency to\nmove towards each other instead of away. Every combination begins by a\nwelling up of force at a centre, which is to form the centre of the\ncombination; in the first positive hydrogen combination, E 2, an atom\nrevolving at right angles to the plane of the paper and also revolving on\nits own axis, forms the centre, and force, rushing out at its lower point,\nrushes in at the depressions of two other atoms, which then set themselves\nwith their points to the centre; the lines are shown in +b, right-hand\nfigure. (The left-hand figure indicates the revolution of the atoms each by\nitself.) As this atomic triad whirls round, it clears itself a space,\npressing back the undifferentiated matter of the plane, and making to\nitself a whirling wall of this matter, thus taking the first step towards\nbuilding up the chemical hydrogen atom. A negative atomic triad is\nsimilarly formed, the three atoms being symmetrically arranged round the\ncentre of out-welling force. These atomic triads then combine, two of the\nlinear arrangement being attracted to each other, and two of the\ntriangular, force again welling up and forming a centre and acting on the\ntriads as on a single atom, and a limiting wall being again formed as the\ncombination revolves round its centre. The next stage is produced by each\nof these combinations on E 3 attracting to itself a third atomic triad of\nthe triangular type from E 2, by the setting up of a new centre of\nup-welling force, following the lines traced in the combinations of E 4.\nTwo of these uniting, and their triangles interpenetrating, the chemical\natom is formed, and we find it to contain in all eighteen ultimate physical\natoms.\n\nThe next substance investigated was oxygen, a far more complicated and\npuzzling body; the difficulties of observation were very much increased by\nthe extraordinary activity shown by this element and the dazzling\nbrilliancy of some of its constituents. The gaseous atom is an ovoid body,\nwithin which a spirally-coiled snake-like body revolves at a high velocity,\nfive brilliant points of light shining on the coils. The snake appears to\nbe a solid rounded body, but on raising the atom to E 4 the snake splits\nlengthwise into two waved bodies, and it is seen that the appearance of\nsolidity is due to the fact that these spin round a common axis in opposite\ndirections, and so present a continuous surface, as a ring of fire can be\nmade by whirling a lighted stick. The brilliant bodies seen in the atom are\non the crests of the waves in the positive snake, and in the hollows in the\nnegative one; the snake itself consists of small bead-like bodies, eleven\nof which interpose between the larger brilliant spots. On raising these\nbodies to E 3 the snakes break up, each bright spot carrying with it six\nbeads on one side and five on the other; these twist and writhe about still\nwith the same extraordinary activity, reminding one of fire-flies\nstimulated to wild gyrations. It can been seen that the larger brilliant\nbodies each enclose seven ultimate atoms, while the beads each enclose two.\n(Each bright spot with its eleven beads is enclosed in a wall, accidentally\nomitted in the diagram.) On the next stage, E 2, the fragments of the\nsnakes break up into their constituent parts; the positive and negative\nbodies, marked _d_ and _d'_, showing a difference of arrangement of the\natoms contained in them. These again finally disintegrate, setting free the\nultimate physical atoms, identical with those obtained from hydrogen. The\nnumber of ultimate atoms contained in the gaseous atom of oxygen is 290,\nmade up as follows:--\n\n  2 in each bead, of which there are 110:\n  7 in each bright spot, of which there are 10;\n  2 x 110 + 70 = 290.\n\nWhen the observers had worked out this, they compared it with the number of\nultimate atoms in hydrogen:--\n\n  290 / 18 = 16.11 +\n\nThe respective number of ultimate atoms contained in a chemical atom of\nthese two bodies are thus seen to closely correspond with their accepted\nweight-numbers.\n\nIt may be said in passing that a chemical atom of ozone appears as an\noblate spheroid, with the contained spiral much compressed and widened in\nthe centre; the spiral consists of three snakes, one positive and two\nnegative, formed in a single revolving body. On raising the chemical atom\nto the next plane, the snake divides into three, each being enclosed in its\nown egg.\n\nThe chemical atom of nitrogen was the third selected by the students for\nexamination, as it seemed comparatively quiet in contrast with the\never-excited oxygen. It proved, however, to be the most complicated of all\nin its internal arrangements, and its quiet was therefore a little\ndeceptive. Most prominent was the balloon-shaped body in the middle, with\nsix smaller bodies in two horizontal rows and one large egg-shaped one in\nthe midst, contained in it. Some chemical atoms were seen in which the\ninternal arrangement of these contained bodies was changed and the two\nhorizontal rows became vertical; this change seemed to be connected with a\ngreater activity of the whole body, but the observations on this head are\ntoo incomplete to be reliable. The balloon-shaped body is positive, and is\napparently drawn downwards towards the negative egg-shaped body below it,\ncontaining seven smaller particles. In addition to these large bodies, four\nsmall ones are seen, two positive and two negative, the positive containing\nfive and the negative four minuter spots. On raising the gaseous atom to\nE 4, the falling away of the wall sets free the six contained bodies, and\nboth the balloon and the egg round themselves, apparently with the removal\nof their propinquity, as though they had exercised over each other some\nattractive influence. The smaller bodies within the egg--marked _q_ on\nE 4--are not on one plane, and those within _n_ and _o_ form respectively\nsquare-based and triangular-based pyramids. On raising all these bodies to\nE 3 we find the walls fall away as usual, and the contents of each \"cell\"\nare set free: _p_ of E 4 contains six small bodies marked _k_, and these\nare shown in _k_ of E 3, as containing each seven little bodies--marked\n_e_--each of which has within it two ultimate atoms; the long form of _p_\nE 4--marked _l_--appears as the long form _l_ on E 3, and this has three\npairs of smaller bodies within it, _f'_, _g_ and _h_, containing\nrespectively three, four and six ultimate atoms; _q_ of E 4, with its seven\ncontained particles, _m_, has three particles _m_ on E 3, each showing\nthree ultimate atoms within them; _e_ from _n_ of E 4 becomes _i_ of E 3,\nwith contained bodies, _e_, showing two ultimate atoms in each; while _e'_\nfrom _o_ of E 4 becomes _j_ of E 3, each having three smaller bodies within\nit, _e'_, with two ultimate atoms in each. On E 2, the arrangement of these\nultimate atoms is shown, and the pairs, _f'_, _g_ and _h_ are seen with the\nlines of force indicated; the triads in _f_--from _m_ of E 3--are similarly\nshown, and the duads in _e_ and _e'_--from _i_ and _j_ of E 3--are given in\nthe same way. When all these bodies are raised to E 1, the ultimate\nphysical atoms are set free, identical, of course, with that previously\ndescribed. Reckoning up the number of ultimate physical atoms in a chemical\natom of nitrogen we find they amount to 261, thus divided:--\n\n        62 +  bodies with 2 ultimate atoms, 62 x 2 = 124\n        24 -    \"     \"   2    \"       \"    24 x 2 =  48\n        21 -    \"     \"   3    \"       \"    21 x 3 =  63\n         2 +    \"     \"   3    \"       \"     2 x 3 =   6\n         2 +    \"     \"   4    \"       \"     2 x 4 =   8\n         2 +    \"     \"   4    \"       \"     2 x 6 =  12\n                                                    ----\n                                                     261\nThis again approaches closely the weight-number assigned to nitrogen:--\n\n  261 / 18 =14.44 +\n\nThis is interesting as checking the observations, for weight-numbers are\narrived at in so very different a fashion, and especially in the case of\nnitrogen the approximation is noteworthy, from the complexity of the bodies\nwhich yield the number on analysis.\n\nSome other observations were made which went to show that as weight-numbers\nincreased, there was a corresponding increase in the number of bodies\ndiscerned within the chemical atom; thus, gold showed forty-seven contained\nbodies; but these observations need repetition and checking. Investigation\nof a molecule of water revealed the presence of twelve bodies from hydrogen\nand the characteristic snake of oxygen, the encircling walls of the\nchemical atoms being broken away. But here again, further observations are\nnecessary to substantiate details. The present paper is only offered as a\nsuggestion of an inviting line of research, promising interesting results\nof a scientific character; the observations recorded have been repeated\nseveral times and are not the work of a single investigator, and they are\nbelieved to be correct so far as they go.\n\nTHE PLATONIC SOLIDS.\n\nSome of our readers may be glad to have a drawing of the Platonic solids,\nsince they play so large a part in the building up of elements. The regular\nsolids are five, and five only; in each:\n\n  (1) The lines are equal.\n  (2) The angles are equal.\n  (3) The surfaces are equal.\n\n[Illustration]\n\nIt will be seen that the tetrahedron is the fundamental form, the\nthree-sided pyramid on a triangular base, _i.e._, a solid figure formed\nfrom four triangles. Two of these generate the cube and the octahedron;\nfive of these generate the dodecahedron and the icosahedron.\n\nThe rhombic dodecahedron is not regular, for though the lines and surfaces\nare equal, the angles are not.\n\nNOTES.\n\nMr. C. Jinarajadasa[1] writes:\n\nThe asterisk put before metargon in the list of elements should be omitted,\nfor metargon had been discovered by Sir William Ramsey and Mr. Travers at\nthe same time as neon (see _Proceedings of the Royal Society_, vol. lxiii,\np. 411), and therefore before it was observed clairvoyantly. It is not,\nhowever, given in the latest list of elements in the Report of November 13,\n1907, of the International Atomic Weights Commission, so it would seem as\nthough it were not yet fully recognised.\n\nNeon was discovered in 1898 by Ramsey and Travers, and the weight given to\nit was 22. This almost corresponds with our weight for meta-neon, 22.33;\nthe latest weight given to neon is 20, and that corresponds within\none-tenth to our weight, 19.9. From this it would seem that neon was\nexamined in the later investigations and meta-neon in the earlier.\n\nHe says further on a probable _fourth_ Interperiodic Group:\n\nThinking over the diagrams, it seemed to me likely that a fourth group\nexists, coming on the paramagnetic side, directly under iron, cobalt,\nnickel, just one complete swing of the pendulum after rhodium, ruthenium,\npalladium. This would make four interperiodic groups, and they would come\nalso _periodically_ in the table too.\n\nI took the diagram for Osmium, and in a bar postulated only three columns\nfor the first element of the new groups, _i.e._, one column less than in\nOsmium. This would make 183 atoms in a bar; the new group then would follow\nin a bar, 183, 185, 187. Here I found to my surprise that the third\npostulated group would have a remarkable relation to Os, Ir, Pt.\n\nThus\n\n        Os.--245     (in a bar);      less 60 = 185\n        Ir.  247                      less 60 = 187\n        Pt.  249                      less 60 = 189\nBut strange to say _also_\n\n    Ruthenium (bar) 132              less 60--72\n    Rhodium         134              less 60--74\n    Palladium       136              less 60--76\nBut 72, 74, 76, are Iron, Cobalt and Nickel.\n\nSo there does probably exist a new group with bars (183), 185, 187, 189,\nwith atomic weights.\n\n    X=bar 185;      atoms      2590, wt. 143.3\n    Y=    187,                 2618, wt. 145.4\n    Z=    189,                 2646, wt. 147.0.\nThey come probably among the rare earths. Probably also Neodymium and\nPraseodymium are two of them, for their weights are 143.6, 140.5.\n\n       *       *       *       *       *\n\n\n\nCHAPTER III.\n\nTHE LATER RESEARCHES.\n\nThe first difficulty that faced us was the identification of the forms seen\non focusing the sight on gases.[2] We could only proceed tentatively. Thus,\na very common form in the air had a sort of dumb-bell shape (see Plate I);\nwe examined this, comparing our rough sketches, and counted its atoms;\nthese, divided by 18--the number of ultimate atoms in hydrogen--gave us\n23.22 as atomic weight, and this offered the presumption that it was\nsodium. We then took various substances--common salt, etc.--in which we\nknew sodium was present, and found the dumb-bell form in all. In other\ncases, we took small fragments of metals, as iron, tin, zinc, silver, gold;\nin others, again, pieces of ore, mineral waters, etc., etc., and, for the\nrarest substances, Mr. Leadbeater visited a mineralogical museum. In all,\n57 chemical elements were examined, out of the 78 recognized by modern\nchemistry.\n\nIn addition to these, we found 3 chemical waifs: an unrecognized stranger\nbetween hydrogen and helium which we named occultum, for purposes of\nreference, and 2 varieties of one element, which we named kalon and\nmeta-kalon, between xenon and osmium; we also found 4 varieties of 4\nrecognized elements and prefixed meta to the name of each, and a second\nform of platinum, that we named Pt. B. Thus we have tabulated in all 65\nchemical elements, or chemical atoms, completing three of Sir William\nCrookes' lemniscates, sufficient for some amount of generalization.\n\n[Illustration: PLATE I. SODIUM.]\n\nIn counting the number of ultimate atoms in a chemical elemental atom, we\ndid not count them throughout, one by one; when, for instance, we counted\nup the ultimate atoms in sodium, we dictated the number in each convenient\ngroup to Mr. Jinarajadasa, and he multiplied out the total, divided by 18,\nand announced the result. Thus: sodium (_see_ Plate I) is composed of an\nupper part, divisible into a globe and 12 funnels; a lower part, similarly\ndivided; and a connecting rod. We counted the number in the upper part:\nglobe--10; the number in two or three of the funnels--each 16; the number\nof funnels--12; the same for the lower part; in the connecting rod--14. Mr.\nJinarajadasa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418:\ndivided by 18 = 23.22 recurring. By this method we guarded our counting\nfrom any prepossession, as it was impossible for us to know how the various\nnumbers would result on addition, multiplication and division, and the\nexciting moment came when we waited to see if our results endorsed or\napproached any accepted weight. In the heavier elements, such as gold, with\n3546 atoms, it would have been impossible to count each atom without quite\nunnecessary waste of time, when making a preliminary investigation. Later,\nit may be worth while to count each division separately, as in some we\nnoticed that two groups, at first sight alike, differed by 1 or 2 atoms,\nand some very slight errors may, in this way, have crept into our\ncalculations.\n\nIn the following table is a list of the chemical elements examined; the\nfirst column gives the names, the asterisk affixed to some indicating that\nthey have not yet been discovered by orthodox chemistry. The second column\ngives the number of ultimate physical atoms contained in one chemical atom\nof the element concerned. The third column gives the weight as compared\nwith hydrogen, taken as 18, and this is obtained by dividing the calculated\nnumber of ultimate atoms by 18. The fourth column gives the recognized\nweight-number, mostly according to the latest list of atomic weights, the\n\"International List\" of 1905, given in Erdmann's \"Lehrbuch der\nUnorganischen Chemie.\" These weights differ from those hitherto accepted,\nand are generally lighter than those given in earlier text-books. It is\ninteresting to note that our counting endorses the earlier numbers, for the\nmost part, and we must wait to see if later observations will endorse the\nlast results of orthodox chemistry, or confirm ours.\n\n--------------------------------------------\nHydrogen       |    18   |   1     |   1\n*Occultum      |    54   |   3     |   --\nHelium         |    72   |   4     |   3.94\nLithium        |   127   |   7.06  |   6.98\nBaryllium      |   164   |   9.11  |   9.01\nBoron          |   200   |  11.11  |  10.86\nCarbon         |   216   |  12     |  11.91\nNitrogen       |   261   |  14.50  |  14.01\nOxygen         |   290   |  16.11  |  15.879\nFluorine       |   340   |  18.88  |  18.90\nNeon           |   360   |  20     |  19.9\n*Meta-Neon     |   402   |  22.33  |   --\nSodium         |   418   |  23.22  |  22.88\nMagnesium      |   432   |  24     |  24.18\nAluminium      |   486   |  27     |  26.91\nSilicon        |   520   |  28.88  |  28.18\nPhosphorus     |   558   |  31     |  30.77\nSulphur        |   576   |  32     |  31.82\nChlorine       |   639   |  35.50  |  35.473\nPotassium      |   701   |  38.944 |  38.85\nArgon          |   714   |  39.66  |  39.60\nCalcium        |   720   |  40     |  39.74\n*Metargon      |   756   |  42     |   --\nScandium       |   792   |  44     |  43.78\nTitanium       |   864   |  48     |  47.74\nVanadium       |   918   |  51     |  50.84\nChromium       |   936   |  52     |  51.74\nManganese      |   992   |  55.11  |  54.57\nIron           |  1008   |  56     |  55.47\nCobalt         |  1036   |  57.55  |  57.7\nNickel         |  1064   |  59.ll  |  58.30\nCopper         |  1139   |  63.277 |  63.12\nZinc           |  1170   |  65     |  64.91\nGallium        |  1260   |  70     |  69.50\nGermanium      |  1300   |  72.22  |  71.93\nArsenic        |  1350   |  75     |  74.45\nSelenium       |  1422   |  79     |  78.58\nBromine        |  1439   |  79.944 |  79.953\nKrypton        |  1464   |  81.33  |  81.20\n*Meta-Krypton  |  1506   |  83.66  |   --\nRubidium       |  1530   |  85     |  84.85\nStrontium      |  1568   |  87.11  |  86.95\nYttrium        |  1606   |  89.22  |  88.34\nZirconium      |  1624   |  90.22  |  89.85\nNiobium        |  1719   |  95.50  |  93.25\nMolybdenum     |  1746   |  97     |  95.26\nRuthenium      |  1848   | 102.66  | 100.91\nRhodium        |  1876   | 104.22  | 102.23\nPalladium      |  1904   | 105.77  | 105.74\nSilver         |  1945   | 108.055 | 107.93\nCadmium        |  2016   | 112     | 111.60\nIndium         |  2052   | 114     | 114.05\nTin            |  2124   | 118     | 118.10\nAntimony       |  2169   | 120.50  | 119.34\nTellurium      |  2223   | 123.50  | 126.64\nIodine         |  2287   | 127.055 | 126.01\nXenon          |  2298   | 127.66  | 127.10\n*Meta-Xenon    |  2340   | 130     |   --\n*Kalon         |  3054   | 169.66  |   --\n*Meta-Kalon    |  3096   | 172     |   --\nOsmium         |  3430   | 190.55  | 189.55\nIridium        |  3458   | 192.11  | 191.56\nPlatinum A     |  3486   | 193.66  | 193.34\n*Platinum B    |  3514   | 195.22  |   --\nGold           |  3546   | 197     | 195.74\n--------------------------------------------\n[Illustration: PLATE II. MALE (left) and FEMALE (right).]\n\nAs the words \"ultimate physical atom\" must frequently occur, it is\nnecessary to state what we mean by the phrase. Any gaseous chemical atom\nmay be dissociated into less complicated bodies; these, again, into still\nless complicated; these, again, into yet still less complicated. These will\nbe dealt with presently. After the third dissociation but one more is\npossible; the fourth dissociation gives the ultimate physical atom.[3] This\nmay vanish from the physical plane, but it can undergo no further\ndissociation on it. In this ultimate state of physical matter two types of\natoms have been observed; they are alike in everything save the direction\nof their whorls and of the force which pours through them. In the one case\nforce pours in from the \"outside,\" from fourth-dimensional space,[4] and\npassing through the atom, pours into the physical world. In the second, it\npours in from the physical world, and out through the atom into the\n\"outside\" again,[4] _i.e._, vanishes from the physical world. The one is\nlike a spring, from which water bubbles out; the other is like a hole, into\nwhich water disappears. We call the atoms from which force comes out\n_positive_ or _male_; those through which it disappears, _negative_ or\n_female_. All atoms, so far as observed, are of one or other of these two\nforms. (Plate II.)\n\nIt will be seen that the atom is a sphere, slightly flattened, and there is\na depression at the point where the force flows in, causing a heart-like\nform. Each atom is surrounded by a field, formed of the atoms of the four\nhigher planes, which surround and interpenetrate it.\n\nThe atom can scarcely be said to be a \"thing,\" though it is the material\nout of which all things physical are composed. It is formed by the flow of\nthe life-force[5] and vanishes with its ebb. When this force arises in\n\"space\"[6]--the apparent void which must be filled with substance of some\nkind, of inconceivable tenuity--atoms appear; if this be artificially\nstopped for a single atom, the atom disappears; there is nothing left.\nPresumably, were that flow checked but for an instant, the whole physical\nworld would vanish, as a cloud melts away in the empyrean. It is only the\npersistence of that flow[7] which maintains the physical basis of the\nuniverse.[8]\n\nIn order to examine the construction of the atom, a space is artificially\nmade[9]; then, if an opening be made in the wall thus constructed, the\nsurrounding force flows in, and three whorls immediately appear,\nsurrounding the \"hole\" with their triple spiral of two and a half coils,\nand returning to their origin by a spiral within the atom; these are at\nonce followed by seven finer whorls, which following the spiral of the\nfirst three on the outer surface, and returning to their origin by a spiral\nwithin that, flowing in the opposite direction--form a caduceus with the\nfirst three. Each of the three coarser whorls, flattened out, makes a\nclosed circle; each of the seven finer ones, similarly flattened out, makes\na closed circle. The forces which flow in them, again, come from \"outside,\"\nfrom a fourth-dimensional space.[10] Each of the finer whorls is formed of\nseven yet finer ones, set successively at right angles to each other, each\nfiner than its predecessor; these we call spirillae.[11]\n\nIt will be understood from the foregoing, that the atom cannot be said to\nhave a wall of its own, unless these whorls of force can be so designated;\nits \"wall\" is the pressed back \"space.\" As said in 1895, of the chemical\natom, the force \"clears itself a space, pressing back the undifferentiated\nmatter of the plane, and making to itself a whirling wall of this matter.\"\nThe wall belongs to space, not to the atom.\n\nIn the three whorls flow currents of different electricities; the seven\nvibrate in response to etheric waves of all kinds--to sound, light, heat,\netc.; they show the seven colours of the spectrum; give out the seven\nsounds of the natural scale; respond in a variety of ways to physical\nvibration--flashing, singing, pulsing bodies, they move incessantly,\ninconceivably beautiful and brilliant.[12]\n\nThe atom has--as observed so far--three proper motions, _i.e._, motions of\nits own, independent of any imposed upon it from outside. It turns\nincessantly upon its own axis, spinning like a top; it describes a small\ncircle with its axis, as though the axis of the spinning top moved in a\nsmall circle; it has a regular pulsation, a contraction and expansion, like\nthe pulsation of the heart. When a force is brought to bear upon it, it\ndances up and down, flings itself wildly from side to side, performs the\nmost astonishing and rapid gyrations, but the three fundamental motions\nincessantly persist. If it be made to vibrate, as a whole, at the rate\nwhich gives any one of the seven colors, the whorl belonging to that color\nglows out brilliantly.\n\n[Illustration]\n\nAn electric current brought to bear upon the atoms checks their proper\nmotions, _i.e._, renders them slower; the atoms exposed to it arrange\nthemselves in parallel lines, and in each line the heart-shaped depression\nreceives the flow, which passes out through the apex into the depression of\nthe next, and so on. The atoms always set themselves to the current. The\nwell-known division of diamagnetic and paramagnetic depends generally on\nthis fact, or on an analogous action on molecules, as may be seen in the\naccompanying diagrams.[13]\n\nTwo atoms, positive and negative, brought near to each other, attract each\nother, and then commence to revolve round each other, forming a relatively\nstable duality; such a molecule is neutral. Combinations of three or more\natoms are positive, negative or neutral, according to the internal\nmolecular arrangement; the neutral are relatively stable, the positive and\nnegative are continually in search of their respective opposites, with a\nview to establishing a relatively permanent union.\n\nThree states of matter exist between the atomic state and the gaseous--the\nstate in which the chemical atoms are found, the recognized chemical\nelements; for our purposes we may ignore the liquid and solid states. For\nthe sake of clearness and brevity in description, we have been obliged to\nname these states; we call the atomic state of the chemist _elemental_; the\nstate which results from breaking up chemical elements, _proto-elemental_;\nthe next higher, _meta-proto-elemental_; the next higher,\n_hyper-meta-proto-elemental_; then comes the atomic state. These are\nbriefly marked as El., Proto., Meta., and Hyper.[14]\n\nThe simplest unions of atoms, never, apparently consisting of more than\nseven, form the first molecular state of physical matter.\n\n[Illustration: TYPES OF HYPER-META-PROTO-ELEMENTAL MATTER.]\n\nHere are some characteristic combinations of the Hyper state; the atom is\nconventional, with the depression emphasised; the lines, always entering at\nthe depression and coming out at the apex, show the resultants of lines of\nforce; where no line appears entering the depression, the force wells up\nfrom fourth-dimensional space; where no line appears leaving the apex, the\nforce disappears into fourth-dimensional space; where the point of entry\nand departure is outside the atoms, it is indicated by a dot.[15]\n\nThe molecules show all kinds of possible combinations; the combinations\nspin, turn head over heels, and gyrate in endless ways. Each aggregation is\nsurrounded with an apparent cell-wall, the circle or oval, due to the\npressure on the surrounding matter caused by its whirling motion; they\nstrike on each other[16] and rebound, dart hither and thither, for reasons\nwe have not distinguished.\n\n[Illustration: TYPES OF META-PROTO-ELEMENTAL MATTER.]\n\nThe Meta state, in some of its combinations, appears at first sight to\nrepeat those of the Hyper state; the only obvious way of distinguishing to\nwhich some of the molecules of less complexity belong is to pull them out\nof the \"cell-wall\"; if they are Hyper molecules they at once fly off as\nseparate atoms; if they are Meta molecules they break up into two or more\nmolecules containing a smaller number of atoms. Thus one of the Meta\nmolecules of iron, containing seven atoms, is identical in appearance with\na Hyper heptad, but the latter dissociates into seven atoms, the former\ninto two triads and a single atom. Long-continued research into the\ndetailed play of forces and their results is necessary; we are here only\nable to give preliminary facts and details--are opening up the way. The\nfollowing may serve as characteristic Meta types:--\n\nThese are taken from constituents of the various elements; 1 from Gl; 2 and\n3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, 11, 12\nfrom Li; 13 and 14 from Na. Others will be seen in the course of breaking\nup the elements.\n\nThe Proto state preserves many of the forms in the elements, modified by\nrelease from the pressure to which they are subjected in the chemical atom.\nIn this state various groups are thus recognizable which are characteristic\nof allied metals.\n\n[Illustration: TYPES OF PROTO-ELEMENTAL MATTER.]\n\nThese are taken from the products of the first disintegration of the\nchemical atom, by forcibly removing it from its hole. The groups fly apart,\nassuming a great variety of forms often more or less geometrical; the lines\nbetween the constituents of the groups, where indicated, no longer\nrepresent lines of force, but are intended to represent the impression of\nform, _i.e._, of the relative position and motion of the constituents, made\non the mind of the observer. They are elusive, for there are no lines, but\nthe appearance of lines is caused by the rapid motion of the costituents up\nand down, or along them backwards and forwards. The dots represent atoms,\nor groups of atoms, within the proto-elements. 1 is found in C; 2 and 3 in\nHe; 4 in Fl; 5 in Li; 6 in N; 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe;\n12 in Se. We shall return to these when analysing the elements, and shall\nmeet many other proto-elemental groupings.\n\nThe first thing which is noticed by the observer, when he turns his\nattention to the chemical atoms, is that they show certain definite forms,\nand that within these forms, modified in various ways, sub-groupings are\nobservable which recur in connexion with the same modified form. The main\ntypes are not very numerous, and we found that, when we arranged the atoms\nwe had observed, according to their external forms, they fell into natural\nclasses; when these, in turn, were compared with Sir William Crookes'\nclassification, they proved to be singularly alike. Here is his arrangement\nof the elements, as it appeared in the _Proceedings of the Royal Society_,\nin a paper read on June 9th, 1898.\n\n[Illustration]\n\nThis is to be read, following the lines of the \"figures of eight\": H, He,\nLi, Gl, B, C, N, and so on, each successive element being heavier than the\none preceding it in order. The disks which fall immediately below each\nother form a class; thus: H, Cl, Br, I; these resemble each other in\nvarious ways, and, as we shall presently see, the same forms and groupings\nre-appear.\n\nAnother chart--taken from Erdmann's _Lehrbuch_--arranges the elements on a\ncurved line, which curiously resembles the curves within the shell of a\nnautilus. The radiating lines show the classes, the whole diameter building\nup a family; it will be observed that there is an empty radius between\nhydrogen and helium, and we have placed occultum there; on the opposite\nradius, iron, rubidium and osmium are seen.\n\n[Illustration]\n\nThe external forms may be classified as follows; the internal details will\nbe dealt with later :--\n\n[Illustration: PLATE III.]\n\n1. _The Dumb-bell._--The characteristics of this are a higher and lower\ngroup, each showing 12 projecting funnels, grouped round a central body,\nand a connecting rod. It appears in sodium, copper, silver, and gold,[17]\nand gold is given (1 on Plate III) as the most extremely modified example\nof this form. The 12 almond-like projections, above and below, are\nseverally contained in shadowy funnels, impossible to reproduce in the\ndrawing; the central globe contains three globes, and the connecting\nportion has swollen out into an egg, with a very complicated central\narrangement. The dumb-bell appears also in chlorine, bromine and iodine,\nbut there is no trace of it in hydrogen, the head of the group. We have not\nmet it elsewhere. It may be remarked that, in Sir William Crookes' scheme,\nin which they are all classed as monads, these two groups are the nearest\nto the neutral line, on the ingoing and outgoing series, and are\nrespectively positive and negative.\n\nII and IIa. _The Tetrahedron._--The characteristics of this form are four\nfunnels, containing ovoid bodies, opening on the face of a tetrahedron. The\nfunnels generally, but not always, radiate from a central globe. We give\nberyllium (glucinum) as the simplest example (2 on Plate III), and to this\ngroup belong calcium and strontium. The tetrahedron is the form of chromium\nand molybdenum, but not that of the head of their group, oxygen, which is,\nlike hydrogen, _sui generis_. These two groups are marked in orthodox\nchemistry as respectively positive and negative, and are closely allied.\nAnother pair of groups show the same tetrahedral form: magnesium, zinc and\ncadmium, positive; sulphur, selenium and tellurium, negative. Selenium is a\npeculiarly beautiful element, with a star floating across the mouth of each\nfunnel; this star is extremely sensitive to light, and its rays tremble\nviolently and bend if a beam of light falls on it. All these are dyads.\n\nThe tetrahedron is not confined to the external form of the above atoms; it\nseems to be one of the favourite forms of nature, and repeatedly appears in\nthe internal arrangements. There is one tetrahedron within the unknown\nelement occultum; two appear in helium (3 on Plate III); yttrium has also\ntwo within its cube, as has germanium; five, intersecting, are found in\nneon, meta-neon, argon, metargon, krypton, meta-krypton, xenon, meta-xenon,\nkalon, meta-kalon, tin, titanium and zirconium. Gold contains no less than\ntwenty tetrahedra.\n\nIII. _The Cube._--The cube appears to be the form of triads. It has six\nfunnels, containing ovoids, and opening on the faces of the cube. Boron is\nchosen as an example (4 on Plate III). Its group members, scandium and\nyttrium, have the same form; we have not examined the fourth; the group is\npositive. Its negative complement consists of nitrogen, vanadium and\nniobium, and we have again to note that nitrogen, like hydrogen and oxygen,\ndeparts from its group type. Two other triad groups, the positive\naluminium, gallium and indium (the fourth unexamined) and the negative\nphosphorus, arsenic and antimony (the fourth unexamined), have also six\nfunnels opening on the faces of a cube.\n\nIV. _The Octahedron._--The simplest example of this is carbon (5 on Plate\nIII). We have again the funnel with its ovoids, but now there are eight\nfunnels opening on the eight faces of the octahedron. In titanium (6 on\nPlate III) the form is masked by the protruding arms, which give the\nappearance of the old Rosicrucian Cross and Rose, but when we look into the\ndetails later, the carbon type comes out clearly. Zirconium is exactly like\ntitanium in form, but contains a large number of atoms. We did not examine\nthe remaining two members of this group. The group is tetratomic and\npositive. Its negative pendant shows the same form in silicon, germanium\nand tin; again, the fourth was unexamined.\n\n[Illustration: PLATE IV.]\n\nV. _The Bars._--These characterise a set of closely allied groups, termed\n\"inter-periodic.\" Fourteen bars (or seven crossed) radiate from a centre,\nas in iron (1 on Plate IV), and the members of each group--iron, nickel,\ncobalt; ruthenium, rhodium, palladium; osmium, iridium, platinum--differ\nfrom each other by the weight of each bar, increasing in orderly\nsuccession; the details will be given later. Manganese is often grouped\nwith iron, nickel, and cobalt (_see_ Crookes' lemniscates), but its\nfourteen protruding bodies repeat the \"lithium spike\" (proto-element 5) and\nare grouped round a central ovoid. This would appear to connect it with\nlithium (2 on Plate IV) rather than with fluorine (3 in Plate IV), with\nwhich it is often classed. The \"lithium spike\" re-appears in potassium and\nrubidium. These details, again, will come out more clearly later.\n\nVI. _The Star._--A flat star, with five interpenetrating tetrahedra in the\ncentre, is the characteristic of neon and its allies (4 on Plate IV)\nleaving apart helium, which, as may be seen by referring to 3, Plate IV,\nhas an entirely different form.\n\nThere are thus six clearly defined forms, typical of classes, with\ntwo--lithium and fluorine--of doubtful affinities. It is worthy of notice\nthat in diatomic elements _four_ funnels open on the faces of tetrahedra;\nin triatomic, _six_ funnels on the faces of cubes; in tetratomic, _eight_\nfunnels on the faces of octahedra.\n\nThus we have a regular sequence of the platonic solids, and the question\nsuggests itself, will further evolution develop elements shaped to the\ndodecahedron and the icosahedron?\n\n       *       *       *       *       *\n\nII.\n\nWe now pass from the consideration of the outer forms of the chemical\nelements to a study of their internal structure, the arrangement within the\nelement of more or less complicated groups--proto-elements--capable of\nseparate, independent existence; these, once more, may be dissociated into\nyet simpler groups--hyper-meta-proto-elements--equally capable of separate,\nindependent existence, and resolvable into single ultimate physical atoms,\nthe irreducible substratum of the physical world (see _Theosophist_, 1908,\npp. 354-356).[18]\n\nWe shall have to study the general internal structure, and then the\nbreaking up of each element, and the admirable diagrams, patiently worked\nout by Mr. Jinarajadasa, will make the study comparatively easy to carry\non.\n\nThe diagrams, of course, can only give a very general idea of the facts\nthey represent; they give groupings and show relations, but much effort of\nthe imagination is needed to transform the two-dimensional diagram into the\nthree-dimensional object. The wise student will try to visualize the figure\nfrom the diagram. Thus the two triangles of hydrogen are not in one plane;\nthe circles are spheres, and the atoms within them, while preserving to\neach other their relative positions, are in swift movement in\nthree-dimensional space. Where five atoms are seen, as in bromine and\niodine, they are generally arranged with the central atom above the four,\nand their motion indicates lines which erect four plane triangles--meeting\nat their apices--on a square base, forming a square-based four-sided\npyramid. Each dot represents a single ultimate atom. The enclosing lines\nindicate the impression of form made on the observer, and the groupings of\nthe atoms; the groups will divide along these lines, when the element is\nbroken up, so that the lines have significance, but they do not exist as\nstable walls or enclosing films, but rather mark limits, not lines, of\nvibrations. It should be noted that it is not possible to show five of the\nprisms in the five intersecting tetrahedra of prisms, and 30 atoms must,\ntherefore, be added in counting.\n\nThe diagrams are not drawn to scale, as such drawing would be impossible;\nthe dot representing the atom is enormously too large compared with the\nenclosures, which are absurdly too small; a scale drawing would mean an\nalmost invisible dot on a sheet of many yards square.\n\nThe use of the words \"positive\" and \"negative\" needs to be guarded by the\nfollowing paragraphs from the article on \"Chemistry\" in the _Encyclopaedia\nBritannica_. We use the words in their ordinary text-book meaning, and have\nnot, so far, detected any characteristics whereby an element can be\ndeclared, at sight, to be either positive or negative:--\n\n\"When binary compounds, or compounds of two elements, are decomposed by an\nelectric current, the two elements make their appearance at opposite poles.\nThese elements which are disengaged at the negative pole are termed\nelectro-positive or positive or basylous elements, while those disengaged\nat the positive pole are termed electro-negative or negative or chlorous\nelements. But the difference between these two classes of elements is one\nof degree only, and they gradually merge into each other; moreover the\nelectric relations of elements are not absolute, but vary according to the\nstate of combination in which they exist, so that it is just as impossible\nto divide the elements into two classes according to this property as it is\nto separate them into two distinct classes of metals and non-metals.\"\n\nWe follow here the grouping according to external forms, and the student\nshould compare it with the groups marked in the lemniscate arrangement\nshown in Article II (p. 377, properly p. 437, February), reading the group\nby the disks that fall below each other; thus the first group is H, Cl, Br,\nI (hydrogen, chlorine, bromine, iodine) and a blank for an undiscovered\nelement. The elements grow denser in descending order; thus hydrogen is an\ninvisible gas; chlorine a denser gas visible by its colour; bromine is a\nliquid; iodine is a solid--all, of course, when temperature and pressure\nare normal. By the lowering of temperature and the increase of pressure, an\nelement which is normally gaseous becomes a liquid, and then a solid.\nSolid, liquid, gaseous, are three interchangeable states of matter, and an\nelement does not alter its constitution by changing its state. So far as a\nchemical \"atom\" is concerned, it matters not whether it be drawn for\ninvestigation from a solid, a liquid, or a gas; but the internal\narrangements of the \"atoms\" become much more complicated as they become\ndenser and denser, as is seen by the complex arrangements necessitated by\nthe presence of the 3546 ultimate atoms contained in the chemical \"atom\" of\ngold, as compared with the simple arrangement of the 18 ultimate atoms of\nhydrogen.\n\nAccording to the lemniscate arrangement, we should commence with hydrogen\nas the head of the first negative group, but as it differs wholly from\nthose placed with it, it is better to take it by itself. Hydrogen is the\nlightest of the known elements, and is therefore taken as 1 in ordinary\nchemistry, and all atomic weights are multiples of this. We take it as 18,\nbecause it contains eighteen ultimate atoms, the smallest number we have\nfound in a chemical element. So our \"number-weights\" are obtained by\ndividing the total number of atoms in an element by 18 (see p. 349,\nJanuary).\n\n[Illustration: PLATE V.]\n\nHYDROGEN (Plate V, 1).--Hydrogen not only stands apart from its reputed\ngroup by not having the characteristic dumb-bell shape, well shown in\nsodium (Plate I, opposite p. 349, January), but it also stands apart in\nbeing positive, serving as a base, not as a chlorous, or acid, radical,\nthus \"playing the part of a metal,\" as in hydrogen chloride (hydrochloric\nacid), hydrogen sulphate (sulphuric acid), etc.\n\nIt is most curious that hydrogen, oxygen and nitrogen, the most widely\nspread gases, all differ fundamentally in form from the groups they\nreputedly head.[19] Hydrogen was the first chemical element examined by us,\nnearly thirteen years ago, and I reproduce here the substance of what I\nwrote in November, 1895, for we have nothing to add to nor amend in it.\n\nHydrogen consists of six small bodies, contained in an egg-like form (the\nouter forms are not given in the diagrams). The six little bodies are\narranged in two sets of three, forming two triangles which are not\ninterchangeable, but are related to each other as object and image. The six\nbodies are not all alike; they each contain three ultimate physical atoms,\nbut in four of the bodies the three atoms are arranged in a triangle, and\nin the remaining two in a line.\n\nHYDROGEN: 6 bodies of 3            18\n          Atomic weight             1\n          Number weight 18/18       1\nI.--THE DUMB-BELL GROUP.\n\nI a.--This group consists of Cl, Br, and I (chlorine, bromine and iodine);\nthey are monads, diamagnetic and negative.\n\nCHLORINE (Plate V, 2).--As already said, the general form is that of the\ndumb-bell, the lower and upper parts each consisting of twelve funnels, six\nsloping upwards and six downwards, the funnels radiating outwards from a\ncentral globe, and these two parts being united by a connecting rod (see,\nagain, sodium, Plate I).\n\nThe funnel (shown flat as an isosceles triangle, standing on its apex) is a\nsomewhat complicated structure, of the same type as that in sodium (Plate\nVI, 2), the difference consisting in the addition of one more globe,\ncontaining nine additional atoms. The central globe is the same as in\nsodium, but the connecting rod differs. We have here a regular arrangement\nof five globes, containing three, four, five, four, three atoms\nrespectively, whereas sodium has only three bodies, containing four, six,\nfour. But copper and silver, its congeners, have their connecting rods of\nexactly the same pattern as the chlorine rod, and the chlorine rod\nreappears in both bromine and iodine. These close similarities point to\nsome real relation between these groups of elements, which are placed, in\nthe lemniscates, equi-distant from the central line, though one is on the\nswing which is going towards that line and the other is on the swing away\nfrom it.\n\nCHLORINE: Upper part {12 funnels of 25 atoms  300\n                     {Central globe            10\n          Lower part same                     310\n          Connecting rod                       19\n                                             ----\n                           Total              639\n                                             ----\n          Atomic weight                     35.473\n          Number weight 639/18              35.50\n(The Atomic Weights are mostly from Erdmann, and the Number Weights are\nthose ascertained by us by counting the atoms as described on p. 349,\nJanuary, and dividing by 18. Prof. T.W. Richards, in _Nature_, July 18,\n1907, gives 35.473.)\n\nBROMINE (Plate V, 3).--In bromine, each funnel has three additional bodies,\novoid in shape, an addition of 33 atoms being thus made without any\ndisturbance of form; two pairs of atoms are added to the central globe, and\na rearrangement of the atoms is effected by drawing together and lessening\nthe swing of the pair of triplets, thus making symmetrical room for the\nnewcomers. The connecting rod remains unchanged. The total number of atoms\nis thus raised from the 639 of chlorine to 1439. Over and over again, in\nthese investigations, were we reminded of Tyndall's fascinating description\nof crystal building, and his fancy of the tiny, ingenious builders busied\ntherein. Truly are there such builders, and the ingenuity and effectiveness\nof their devices are delightful to see.[20]\n\nBROMINE:  Upper part {12 funnels of 58 atoms   696\n                     {Central globe             14\n          Lower part same                      710\n          Connecting rod                        19\n                                              ----\n                           Total              1439\n                                              ----\n          Atomic weight                      79.953\n          Number weight 1459/18              79.944\nIODINE (Plate V, 4).--We find herein that the central globe gains 4 atoms,\nthe two pairs becoming 2 quartets; the connecting rod exactly reproduces\nthe rods of chlorine and bromine; the funnel is also that of bromine,\nexcept that five bodies, containing 35 atoms, are added to it. The 1439\natoms of bromine are thus raised to 2887.\n\nIODINE:   Upper Part {12 funnels of 90 atoms  1116\n                     {Central globe             18\n          Lower part same                     1134\n          Connecting rod                        19\n                                              ----\n                           Total              2287\n                                              ----\n          Atomic weight                     126.01\n          Number weight  2287/18            127.055\nThe plan underlying the building up of groups is here clearly shown; a\nfigure is built up on a certain plan, in this case a dumb-bell; in the\nsucceeding members of the group additional atoms are symmetrically\nintroduced, modifying the appearance, but following the general idea; in\nthis case the connecting rod remains unaltered, while the two ends become\nlarger and larger, more and more overshadowing it, and causing it to become\nshorter and thicker. Thus a group is gradually formed by additional\nsymmetrical additions. In the undiscovered remaining member of the group we\nmay suppose that the rod will have become still more egg-like, as in the\ncase of gold.\n\nI b.--The corresponding positive group to that which we have been\nconsidering consists of Na, Cu, Ag, and Au (sodium, copper, silver and\ngold), with an empty disk between silver and gold, showing where an element\nought to be. These four elements are monads, diamagnetic, and positive, and\nthey show the dumb-bell arrangement, although it is much modified in gold;\nwe may presume that the undiscovered element between silver and gold would\nform a link between them.\n\n[Illustration: PLATE VI.]\n\nSODIUM (Plate VI, 2) has been already described (p. 349, January), as a\ntype of the group, so we need only refer to its internal arrangement in\norder to note that it is the simplest of the dumb-bell group. Its twelve\nfunnels show only four enclosed bodies, the same as we see in chlorine,\nbromine, iodine, copper and silver, and which is very little modified in\ngold. Its central globe is the simplest of all, as is its connecting rod.\nWe may therefore take it that sodium is the ground-plan of the whole group.\n\nSODIUM:   Upper part\n              { 12 funnels of 16 each    192\n              { Central globe             10\n          Lower part same                202\n          Connecting rod                  14\n                                        ----\n                      Total              418\n                                        ----\n          Atomic weight                23.88\n          Number weight 418/19         23.22\nCOPPER (Plate VI, 3) introduces an addition in the funnel, that we shall\nfind elsewhere, _e.g._, in silver, gold, iron, platinum, zinc, tin, the\ntriangular arrangement near the mouth of the funnel and adds to the ten\natoms in this nineteen more in three additional enclosed bodies, thus\nraising the number of atoms in a funnel from the sixteen of sodium to\nforty-five. The number in the central globe is doubled, and we meet for the\nfirst time the peculiar cigar or prism-shaped six-atomed arrangement, that\nis one of the most common of atomic groups. It ought to imply some definite\nquality, with its continual recurrence. The central column is the three,\nfour, five, four, three, arrangement already noted.\n\nCOPPER:   Upper part {12 funnels of 45 atoms  540\n                     {Central globe            20\n          Lower part same                     560\n          Connecting rod                       19\n                                             ----\n                           Total             1139\n                                             ----\n          Atomic weight                     63.12\n          Number weight 1139/18             63.277\nSILVER (Plate VI, 4) follows copper in the constitution of five of the\nbodies enclosed in the funnels. But the triangular group contains\ntwenty-one atoms as against ten, and three ovoids, each containing three\nbodies with eleven atoms, raise the number of atoms in a funnel to\nseventy-nine. The central globe is decreased by five, and the prisms have\ndisappeared. The connecting rod is unaltered.\n\nSILVER:   Upper part {12 funnels of 79 atoms   948\n                     {Central globe             15\n          Lower part same                      963\n          Connecting rod                        19\n                                              ----\n                           Total              1945\n                                              ----\n          Atomic weight                     107.93\n          Number weight 1945/18             108.055\n(This atomic weight is given by Stas, in _Nature_, August 29, 1907, but it\nhas been argued later that the weight should not be above 107.883.)\n\n[Illustration: PLATE VII.]\n\nGOLD (Plate VII) is so complicated that it demands a whole plate to itself.\nIt is difficult to recognize the familiar dumb-bell in this elongated egg,\nbut when we come to examine it, the characteristic groupings appear. The\negg is the enormously swollen connecting rod, and the upper and lower parts\nwith their central globes are the almond-like projections above and below,\nwith the central ovoid. Round each almond is a shadowy funnel (not drawn in\nthe diagram), and within the almond is the collection of bodies shown in\n_e_, wherein the two lowest bodies are the same as in every other member of\nthe negative and positive groups; the third, ascending, is a very slight\nmodification of the other thirds; the fourth is a union and re-arrangement\nof the fourth and fifth; the fifth, of four ovoids, adds one to the three\novoids of bromine, iodine and silver; the triangular group is like that in\ncopper and silver, though with 28 atoms instead of 10 or 21, and it may be\nnoted that the cone in iron has also 28. The central body in the ovoid is\nvery complicated, and is shown in _c_, the bodies on each side, _d_, are\neach made up of two tetrahedra, one with four six-atomed prisms at its\nangles, and the other with four spheres, a pair with four atoms and a pair\nwith three. We then come to the connecting rod. One of the four similar\ngroups in the centre is enlarged in _a_, and one of the sixteen circling\ngroups is enlarged in b. These groups are arranged in two planes inclined\nto one another.\n\nGOLD: Upper part\n          { 12 funnels of 97 atoms      1164\n          { Central ovoid {c             101\n                          {2 d, 38        76\n      Lower part same                   1341\n      Connecting rod { 4 a 84            336\n                     {16 b 33            528\n                                        ----\n                      Total             3546\n                                        ----\n      Atomic weight                   195.74\n      Number weight 3546/18           197\nIt may be noted that the connecting rod is made up of exactly sixteen atoms\nof occultum, and that sixteen such atoms contain 864 ultimate atoms, the\nexact member of atoms in titanium.\n\n       *       *       *       *       *\n\nIII.\n\nOccultum was observed by us in 1895, and, finding that it was so light, and\nso simple in its composition, we thought that it might be helium, of which\nwe were unable, at the time, to obtain a sample. When, however, helium\nitself came under observation in 1907, it proved to be quite different from\nthe object before observed, so we dubbed the unrecognised object Occultum,\nuntil orthodox science shall find it and label it in proper fashion.\n\nOCCULTUM (Plate VI, 1).\n\nWe here meet the tetrahedron for the first time, with each angle occupied\nby a six-atomed group, the atoms arranged as on the end triangles of a\nprism. This form recurs very often, and was noted, last month, as seen in\ncopper (Plate VI, 3); it revolves with extreme rapidity around its\nlongitudinal axis, and looks like a pencil sharpened at both ends, or a\ncigar tapering at both ends; we habitually spoke of it as \"the cigar.\" It\nappears to be strongly coherent, for, as will be seen below, its six atoms\nremain attached to each other as meta-compounds and even when divided into\ntwo triplets as hyper-compounds, they revolve round each other.\n\nAbove the tetrahedron is a balloon-shaped figure, apparently drawn into\nshape by the attraction of the tetrahedron. The body below the tetrahedron\nlooks like a coil of rope, and contains fifteen atoms; they are arranged on\na slanting disk in a flat ring, and the force goes in at the top of one\natom, and out of the bottom of it into the top of the next, and so on,\nmaking a closed circuit. The two little spheres, each containing a triplet,\nare like fill-up paragraphs to a compositor--they seem to be kept standing\nand popped in where wanted. The sphere marked _x_ is a proto-compound, the\nballoon when set free.\n\nAs was noted under gold (p. 41), sixteen occultum bodies, re-arranged, make\nup the connecting rod in gold:--\n\nOCCULTUM: Tetrahedron                  24\n          Balloon                       9\n          Triplets                      6\n          Rope-circle                  15\n                                     ----\n                     Total             54\n                                     ----\n          Atomic weight         Not known\n          Number weight 54/18           3\nDISSOCIATION OF ATOMS.\n\nBefore proceeding to the study of other chemical atoms, as to their general\ninternal arrangements, it is desirable to follow out, in those already\nshown, the way in which these atoms break up into simpler forms, yielding\nsuccessively what we have called proto-, meta-, and hyper-compounds. It is\nnaturally easier to follow these in the simpler atoms than in the more\ncomplex, and if the earlier dissociations are shown, the latter can be more\nreadily and more intelligibly described.\n\nThe first thing that happens on removing a gaseous atom from its \"hole\"\n(see pp. 21 to 23) or encircling \"wall,\" is that the contained bodies are\nset free, and, evidently released from tremendous pressure, assume\nspherical or ovoid forms, the atoms within each re-arranging themselves,\nmore or less, within the new \"hole\" or \"wall.\" The figures are, of course,\nthree-dimensional, and often remind one of crystals; tetrahedral,\noctagonal, and other like forms being of constant occurrence. In the\ndiagrams of the proto-compounds, the constituent atoms are shown by dots.\nIn the diagrams of the meta-compounds the dot becomes a heart, in order to\nshow the resultants of the lines of force. In the diagrams of the\nhyper-compounds the same plan is followed. The letters _a_, _b_, _c_, &c.,\nenable the student to follow the breaking up of each group through its\nsuccessive stages.\n\nHYDROGEN (Plate V, 1).\n\n[Illustration]\n\nThe six bodies contained in the gaseous atom instantaneously re-arrange\nthemselves within two spheres; the two linear triplets unite with one\ntriangular triplet, holding to each other relative positions which, if\nconnected by three right lines, would form a triangle with a triplet at\neach angle; the remaining three triangular triplets similarly arrange\nthemselves in the second sphere. These form the proto-compounds of\nhydrogen.\n\nIn the dissociation of these, each group breaks up into two, the two linear\ntriplets joining each other and setting free their triangular comrade,\nwhile two of the triangular triplets similarly remain together, casting out\nthe third, so that hydrogen yields four meta-compounds.\n\nIn the hyper-condition, the connexion between the double triplets is\nbroken, and they become four independent groups, two like ix, in the\nhyper-types (p. 25), and two remaining linear, but rearranging their\ninternal relations; the two remaining groups break up into two pairs and a\nunit.\n\nThe final dissociation sets all the atoms free.\n\nOCCULTUM (Plate VI, 1).\n\n[Illustration]\n\nOn the first dissociation of the component parts of occultum, the\ntetrahedron separates as a whole, with its four \"cigars,\" flattening itself\nout within its hole, _a_; two \"cigars\" are positive and two negative,\nmarked respectively _a_ and _a'_. The rope becomes a ring within a sphere,\n_b_, and the two bodies _d_ _d_, which are loose in the gaseous atom, come\nwithin this ring. The balloon becomes a sphere.\n\nOn further dissociation, the \"cigars\" go off independently, showing two\ntypes, and these again each divide into triplets, as meta-compounds. _B_,\non the meta-level, casts out the two _d_ bodies, which become independent\ntriplets, and the \"rope\" breaks into two, a close ring of seven atoms and a\ndouble cross of eight. These subdivide again to form hyper-compounds, the\nring yielding a quintet and a pair, and the double cross separating into\nits two parts.\n\nThe balloon, _c_, becomes much divided, the cohesion of its parts being\nslight; it forms two triplets, a pair and a unit, and these set free, on\nfurther dissociation, no less than five separate atoms and two duads.\n\nThe two triplets of _d_ each cast out an atom on dissociation, and form two\npairs and two units.\n\nSODIUM (Plate VI, 2).\n\nIt is convenient to consider sodium next, because it is the basic pattern\non which not only copper, silver and gold are formed, but also chlorine,\nbromine and iodine.\n\n[Illustration]\n\nWhen sodium is set free from its gaseous condition, it divides up into\nthirty-one bodies--twenty-four separate funnels, four bodies derived from\nthe two central globes, and three from the connecting rod. The funnels\nbecome spheres, and each contains four enclosed spheres, with more or less\ncomplicated contents. Each central globe yields a sextet and a quartet, and\nthe rod sets free two quartets and a peculiarly formed sextet.\n\nWhen the proto-compounds are dissociated, the funnel-sphere sets free: (1)\nthe contents of _a_, rearranged into two groups of four within a common\nsphere; the sphere yields four duads as hyper-compounds; (2) the contents\nof _b_, which unite themselves into a quartet, yielding two duads as\nhyper-compounds; and (3) the contents of the two spheres, _c_, which\nmaintain their separation as meta-compounds, and become entirely\nindependent, the atoms within the sphere revolving round each other, but\nthe spheres ceasing their revolution round a common axis, and going off in\ndifferent directions. The atoms break off from each other, and gyrate in\nindependent solitude as hyper-\"compounds.\" Thus each funnel yields finally\nten hyper-bodies.\n\nThe part of the central globe, marked _d_, with its six atoms, whirling\nround a common centre, becomes two triplets, at the meta-stage, preparing\nfor the complete separation of these as hyper-bodies. The second part of\nthe same globe, marked _e_, a whirling cross, with an atom at each point,\nbecomes a quartet in the meta-state, in which three atoms revolve round a\nfourth, and in the hyper-state this central atom is set free, leaving a\ntriplet and a unit.\n\nEach of the two bodies marked _f_, liberated from the connecting rod, shows\nfour atoms whirling round a common centre, exactly resembling _e_ in\nappearance; but there must be some difference of inner relations, for, in\nthe meta-state, they re-arrange themselves as two pairs, and divide into\ntwo as hyper-bodies.\n\nThe body marked _g_ is a four-sided pyramid, with two closely joined atoms\nat its apex; these still cling to each in mutual revolution as a meta-body,\nencircled by a ring of four, and this leads to a further dissociation into\nthree pairs on the hyper-level.\n\nCHLORINE (Plate V, 2).\n\n[Illustration]\n\nThe description of the funnel of sodium applies to that of chlorine, until\nwe come to the body nearest the mouth, the sphere containing three\nadditional bodies; this remains within the funnel in the first\ndissociation, so that again we have twenty-four separate funnels as\nproto-compounds; the central globes are the same as in sodium, and yield\nthe same four bodies; the connecting rod sets free five bodies, of which\ntwo are the same; we have thus thirty-three separate bodies as the result\nof the dissociation of chlorine into its proto-compounds. As all the\ncompounds which are in sodium break up in the same way into meta- and\nhyper-compounds, we need not repeat the process here. We have only to\nconsider the new meta- and hyper-compounds of the highest sphere within the\nfunnel, and the two triplets and one quintet from the connecting rod.\n\nThe additional body within the proto-funnel is of a very simple character,\nthree contained triangles within the flattened sphere. On release from the\nfunnel, on the meta-level, the atoms rearrange themselves in a whirling set\nof three triplets, and these break off from each other as hyper-compounds.\nThe two triplets from the connecting rod, also, are of the simplest\ncharacter and need not delay us. The five-atomed body, a four-sided pyramid\nas a proto-compound, becomes a ring whirling round a centre on the meta,\nand two pairs with a unit on the hyper.\n\nBROMINE (Plate V, 3).\n\nThree additional bodies appear at the top of the funnel, which otherwise\nrepeats that of chlorine. The connecting rod is the same and may be\ndisregarded. The central globes become more complex. The additions are,\nhowever, of very easy types, and hence are readily dealt with. Each of the\nthree similar ovoid bodies contains two triplets--each a triangle and a\nquintet--a four-sided pyramid. These are the same, as may be seen in the\nconnecting rod of chlorine, and we need not repeat them. Only the globe\nremains. This does not break up as a proto-compound but is merely set free,\n_a_ and the 2 _bs_ whirling in a plane vertical to the paper and the two\nsmaller bodies, _cc_, whirling on a plane at right angles to the other.\nThese two disengage themselves, forming a quartet as a meta-compound, while\n_a_ makes a whirling cross and _bb_ a single sextet; these further\ndissociate themselves into four pairs and two triplets.\n\nIODINE (Plate V, 4).\n\n[Illustration]\n\nIodine has nothing new to give us, except five similar ovoid bodies at the\ntop of each funnel, and two quartets instead of two pairs in the central\nglobe. The ovoid bodies become spheres when the funnels are thrown off, and\na crystalline form is indicated within the sphere. The atoms are arranged\nin two tetrahedra with a common apex, and the relationship is maintained in\nthe meta-body, a septet. The latter breaks up into two triplets and a unit\non the hyper-level. In the central globes, the _a_ of bromine is repeated\ntwice instead of the pairs in _cc_.\n\nCOPPER (Plate VI, 3).\n\nWe have already disposed of occultum, on this plate, and of sodium, which\nlies at the root of both groups. Copper, we now find, is also very largely\noff our hands, as the funnel provides us with only two new types--two\nspheres--each containing five atoms in a new arrangement, and the\ntriangular body at the mouth with its ten atoms. This triangular body, with\nan increased number of atoms, reappears in various other chemical elements.\nThe central globes are different from any we have had before, in their\ninternal arrangement, but the constituents are familiar; there are two\ncontained spheres with four atoms each, the _a_ in the globe of bromine\n(see above) and 2 \"cigars.\" The \"cigars\" may be followed under occultum\n(see above). The connecting rod is as in chlorine, bromine and iodine.\n\nThe atoms in the bodies _a_ and _b_ are curiously arranged. _A_ consists of\ntwo square-based pyramids turned so as to meet at their apices, and breaks\nup into two quartet rings and a duad. _B_ is again two four-sided pyramids,\nbut the bases are in contact and set at right angles to each other; the\nsecond apex is not seen, as it is directly below the first. The pyramids\nseparate as meta-bodies, and the atoms assume the peculiar arrangement\nindicated and then break up into four pairs and two units on the hyper\nlevel.\n\n       *       *       *       *       *\n\nIV.\n\nSILVER (Plate VI, 4 and Ag below).\n\nSilver presents us with only two new bodies, and even these are only new by\nslight additions to old models. The triangular shaped body at the apex of\nthe funnel, containing 21 atoms, is intermediate between the similar bodies\nin copper and iron. As a proto-element it becomes three triangles, joined\nat their apices, in fact a tetrahedron in which no atoms are distributed on\nthe fourth face. The faces separate on the meta level and give three\nseven-atomed figures, and each of these breaks up into two triplets and a\nunit. The central globe only differs from that of bromine by the addition\nof one atom, which gives the familiar four-sided pyramid with a square base\nas in chlorine (see p. 46).\n\nGOLD (Plate VII and Au below).\n\n[Illustration]\n\nThe disintegration of gold first yields forty-seven bodies on the\nproto-level; the twenty-four funnels separate, and the central globes which\nhold each twelve together set free their six contained globes (_c_, _d_),\nthirty bodies being thus liberated. The sixteen bodies on the central\ninclined planes, marked _b_, break away, their central globe, with its four\ncontained globes, remaining unchanged. But this condition does not last.\nThe motion of the funnels changes and thus the funnels cease to exist and\ntheir contents are set free, each funnel thus liberating nine independent\nbodies; the sixteen _b_ separate into two each; the four _a_ liberate five\neach; the two _c_ set free thirteen each; the four _d_ finally liberate two\neach: 302 proto elements in all.\n\nThe funnel is almost that of iodine, re-arranged. Four of the first ring in\nthe iodine funnel are replaced by the triangular body, which becomes a\nfour-sided pyramid with an occupied base. The second ring of three ovoids\nin iodine becomes four in gold, but the internal arrangement of each ovoid\nis the same. The next two spheres in the iodine funnel coalesce into one\nsphere, with similar contents, in the gold funnel. The fifth in iodine is\nslightly rearranged to form the fourth in descent in gold, and the\nremaining two are the same. _B_ has been broken up under occultum (p. 628)\nand can be followed there. The sixteen rings set free from the four _a_,\nafter gyrating round the central body, now become a sphere, break up, as in\noccultum (see p. 44) into a meta seven-atomed ring and an eight-atomed\ndouble cross, and so on to the hyper level. The sphere with its two\ncontained bodies breaks up into eight triangles on the meta level, and each\nof these, on the hyper, into a duad and a unit. The twelve septets of _c_\nassume the form of prisms as in iodine (see p. 48) and pursue the same\ncourse, while its central body, a four-sided pyramid with its six\nattendants, divides on the meta level into six duads, revolving round a\nring with a central atom as in chlorine (p. 47), the duads going off\nindependently on the hyper-level and the ring breaking up as in chlorine.\nThe \"cigar\" tetrahedron of _d_ follows its course as in occultum, and the\nother sets free two quartets and two triplets on the meta level, yielding\nsix duads and two units as hyper compounds. It will be seen that, complex\nas gold is, it is composed of constituents already familiar, and has iodine\nand occultum as its nearest allies.\n\nII AND IIa.--THE TETRAHEDRAL GROUPS.\n\nII.--This group consists of beryllium (glucinum), calcium, strontium and\nbarium, all diatomic, paramagnetic and positive. The corresponding group\nconsists of oxygen, chromium, molybdenum, wolfram (tungsten) and uranium,\nwith a blank disk between wolfram and uranium: these are diatomic,\nparamagnetic, and negative. We have not examined barium, wolfram, or\nuranium.\n\n[Illustration: PLATE VIII.]\n\nBERYLLIUM (Plate III, 2, and Plate VIII, 1). In the tetrahedron four\nfunnels are found, the mouth of each funnel opening on one of its faces.\nThe funnels radiate from a central globe, and each funnel contains four\novoids each with ten atoms within it arranged in three spheres. In the\naccompanying diagrams one funnel with its four ovoids is shown and a single\novoid with its three spheres, containing severally three, four, and three\natoms, is seen at the left-hand corner of the plate (7 _a_). The members of\nthis group are alike in arrangement, differing only in the increased\ncomplexity of the bodies contained in the funnels. Beryllium, it will be\nobserved, is very simple, whereas calcium and strontium are complicated.\n\nBERYLLIUM: 4 funnels of 40 atoms    160\n           Central globe              4\n                                   ----\n                           Total    164\n                                   ----\nAtomic weight                      9.01\nNumber weight  164/18              9.11\nCALCIUM (Plate VIII, 2) shows in each funnel three contained spheres, of\nwhich the central one has within it seven ovoids identical with those of\nberyllium, and the spheres above and below it contain each five ovoids (7\n_b_) in which the three contained spheres have, respectively, two, five,\nand two atoms. The central globe is double, globe within globe, and is\ndivided into eight segments, radiating from the centre like an orange; the\ninternal part of the segment belonging to the inner globe has a triangular\nbody within it, containing four atoms (7 _c_), and the external part,\nbelonging to the encircling globe, shows the familiar \"cigar\" (7 _d_). In\nthis way 720 atoms are packed into the simple beryllium type.\n\nCALCIUM: 4 funnels of 160 atoms      640\n         Central globe                80\n                                    ----\n                          Total      720\n                                    ----\n         Atomic weight             39.74\n         Number weight 720/18      40.00\nSTRONTIUM (Plate VIII, 3) shows a still further complication within the\nfunnels, no less than eight spheres being found within each. Each of the\nhighest pair contains four subsidiary spheres, with five, seven, seven,\nfive atoms, respectively (7 _e_, _g_, _f_). The _g_ groups are identical\nwith those in gold, but difference of pressure makes the containing body\nspherical instead of ovoid; similar groups are seen in the top ring of the\niodine funnel, where also the \"hole\" is ovoid in form. The second pair of\nspheres contains ten ovoids (7 _b_) identical with those of calcium. The\nthird pair contains fourteen ovoids (7 _a_) identical with those of\nberyllium, while the fourth pair repeats the second, with the ovoids\nre-arranged. The internal divisions of the double sphere of the central\nglobe are the same as in calcium, but the contents differ. The \"cigars\" in\nthe external segments are replaced by seven-atomed ovoids (7 _h_)--the\niodine ovoids--and the external segments contain five-atomed triangles (7\n_i_). Thus 1,568 atoms have been packed into the beryllium type, and our\nwonder is again aroused by the ingenuity with which a type is preserved\nwhile it is adapted to new conditions.\n\nSTRONTIUM: 4 funnels of 368 atoms       1472\n           Central globe                  96\n                                        ----\n                            Total       1568\n                                        ----\n           Atomic weight               86.95\n           Number weight 1568/18       87.11\nThe corresponding group, headed by oxygen--oxygen, chromium, molybdenum,\nwolfram and uranium--offers us another problem in its first member.\n\nOXYGEN (Plate VIII, 4). This was examined by us in 1895, and the\ndescription may be reproduced here with a much improved diagram of its very\npeculiar constitution. The gaseous atom is an ovoid body, within which a\nspirally-coiled snake-like body revolves at a high velocity, five brilliant\npoints of light shining on the coils. The appearance given in the former\ndiagram will be obtained by placing the five septets on one side on the top\nof those on the other, so that the ten become in appearance five, and thus\ndoubling the whole, the doubling point leaving eleven duads on each side.\nThe composition is, however, much better seen by flattening out the whole.\nOn the proto level the two snakes separate and are clearly seen.\n\nOXYGEN: Positive snake\n        { 55 spheres of 2 atoms }\n        {  + 5 disks of 7 atoms }    145\n        Negative snake     \"         145\n                                    ----\n                        Total        290\n                                    ----\n        Atomic weight              15.87\n        Number weight 290/18       16.11\nCHROMIUM (Plate VIII, 5) \"reverts to the ancestral type,\" the tetrahedron;\nthe funnel is widened by the arrangement of its contents, three spheres\nforming its first ring, as compared with the units in beryllium and\ncalcium, and the pairs in strontium and molybdenum. Two of these spheres\nare identical in their contents--two quintets (7 _f_), a quintet (7 _j_),\nand two quintets (7 _e_), _e_ and _f_ being to each other as object and\nimage. The remaining sphere (7 _b_) is identical with the highest in the\ncalcium funnel. The remaining two spheres, one below the other, are\nidentical with the corresponding two spheres in calcium. The central globe,\nas regards its external segments, is again identical with that of calcium,\nbut in the internal segments a six-atomed triangle (7 _k_) is substituted\nfor the calcium four-atomed one (7 _e_).\n\nCHROMIUM: 4 funnels of 210 atoms      840\n          Central globe                96\n                                    -----\n                   Total              936\n                                    -----\n          Atomic weight             51.74\n          Number weight 936/18      52.00\nMOLYBDENUM (Plate VIII, 6) very closely resembles strontium, differing from\nit only in the composition of the highest pair of spheres in the funnels\nand in the presence of a little sphere, containing two atoms only, in the\nmiddle of the central globe. The topmost spheres contain no less than eight\nsubsidiary spheres within each; the highest of these (7 _e_) has four atoms\nin it; the next three have four, seven and four (7 _e_ _g_ _e_),\nrespectively; the next three are all septets (7 _g_), and the last has\nfour--making in all for these two spheres 88 atoms, as against the 48 in\ncorresponding spheres of strontium, making a difference of 160 in the four\nfunnels.\n\nMOLYBDENUM: 4 funnels of 408 atoms     1632\n            Central globe                98\n                                      -----\n                          Total        1730\n                                      -----\n            Atomic weight             95.26\n            Number weight 1730/18     96.11\nII a.--This group contains magnesium, zinc, cadmium, and mercury, with an\nempty disk between cadmium and mercury; we did not examine mercury. All are\ndiatomic, diamagnetic and positive; the corresponding group consists of\nsulphur, selenium and tellurium, also all diatomic and diamagnetic, but\nnegative. The same characteristics of four funnels opening on the faces of\na tetrahedron are found in all, but magnesium and sulphur have no central\nglobe, and in cadmium and tellurium the globe has become a cross.\n\n[Illustration: PLATE IX.]\n\nMAGNESIUM (Plate IX, 1) introduces us to a new arrangement: each group of\nthree ovoids forms a ring, and the three rings are within a funnel; at\nfirst glance, there are three bodies in the funnel; on examination each of\nthese is seen to consist of three, with other bodies, spheres, again within\nthem. Apart from this, the composition is simple enough, all the ovoids\nbeing alike, and composed of a triplet, a septet and a duad.\n\nMAGNESIUM: 4 funnels of 108 atoms     432\n           Atomic weight            24.18\n           Number weight 432/18     24.00\nZINC (Plate IX, 2) also brings a new device: the funnel is of the same type\nas that of magnesium, while septets are substituted for the triplets, and\n36 additional atoms are thus slipped in. Then we see four spikes,\nalternating with the funnels and pointing to the angles, each adding 144\natoms to the total. The spikes show the ten-atomed triangle, already met\nwith in other metals, three very regular pillars, each with six spheres,\ncontaining two, three, four, four, three, two atoms, respectively. The\nsupporting spheres are on the model of the central globe, but contain more\natoms. Funnels and spikes alike radiate from a simple central globe, in\nwhich five contained spheres are arranged crosswise, preparing for the\nfully developed cross of cadmium. The ends of the cross touch the bottoms\nof the funnels.\n\nZINC: 4 funnels of 144 atoms        576\n      4 spikes of 144 atoms         576\n      Central globe                  18\n                                  -----\n                        Total      1170\n                                  -----\n         Atomic weight            64.91\n         Number weight 1170/18    65.00\nCADMIUM (Plate IX, 3) has an increased complexity of funnels; the diagram\nshows one of the three similar segments which lie within the funnels as\ncylinders; each of these contains four spheres, three pillars and three\novoids, like the spike of zinc turned upside down, and the zinc ten-atomed\ntriangle changed into three ten-atomed ovoids. The centre-piece is a new\nform, though prefigured in the central globe of zinc.\n\nCADMIUM:  3 segments of 164 atoms = 492\n          4 funnels of 492 atoms          1968\n          Central body                      48\n                                         -----\n                             Total        2016\n                                         -----\n          Atomic weight                 111.60\n          Number weight 2016/18         112.00\nThe corresponding negative group is headed by\n\n[Illustration: PLATE X.]\n\nSULPHUR (Plate X, 1), which, like magnesium, has no central globe, and\nconsists simply of the zinc funnels, much less compressed than zinc but the\nsame in composition.\n\nSULPHUR: 4 funnels of 144 atoms       576\n         Atomic weight              31.82\n         Number weight 576/18       32.00\nSELENIUM (Plate X, 2) is distinguished by the exquisite peculiarity,\nalready noticed, of a quivering star, floating across the mouth of each\nfunnel, and dancing violently when a ray of light falls upon it. It is\nknown that the conductivity of selenium varies with the intensity of the\nlight falling upon it, and it may be that the star is in some way connected\nwith its conductivity. It will be seen that the star is a very complicated\nbody, and in each of its six points the two five-atomed spheres revolve\nround the seven-atomed cone. The bodies in the funnels resemble those in\nmagnesium, but a reversed image of the top one is interposed between itself\nand the small duad, and each pair has its own enclosure. The central globe\nis the same as that of zinc.\n\nSELENIUM: 4 funnels of 198 atoms     792\n          4 stars of 153 atoms       612\n          Central globe               18\n                                   -----\n                         Total      1422\n                                   -----\n          Atomic weight            78.58\n          Number weight 1422/18    79.00\nTELLURIUM (Plate X, 3), it will be seen, closely resembles cadmium, and has\nthree cylindrical segments--of which one is figured--making up the funnel.\nThe contained bodies in the pillars run three, four, five, four, three,\ntwo, instead of starting with two; and a quartet replaces a duad in the\nglobes above. The central cross only differs from that of cadmium in having\na seven-atomed instead of a four-atomed centre. So close a similarity is\nstriking.\n\nTELLURIUM: 3 segments of 181 atoms = 543\n           4 funnels of 543 atoms          2172\n           Central body                      51\n                                          -----\n                            Total          2223\n                                          -----\n           Atomic weight                 126.64\n           Number weight 2223/18         123.50\n       *       *       *       *       *\n\nV.\n\nWe must now consider the ways in which the members of the tetrahedral\ngroups break up, and as we proceed with this study we shall find how\ncontinual are the repetitions, and how Nature, with a limited number of\nfundamental methods, creates by varied combinations her infinite variety of\nforms.\n\nBERYLLIUM (Plate III, 2, and VIII, 1).\n\n[Illustration]\n\nBeryllium offers us four similar funnels and a central globe, and the\nproto-elements consist of these five bodies, set free. The funnel, released\nfrom pressure, assumes a spherical form, with its four ovoids spinning\nwithin it, and the central globe remains a sphere, containing a whirling\ncross. On the meta level, the ovoids are set free, and two from each funnel\nare seen to be positive, two negative--sixteen bodies in all, _plus_ the\ncross, in which the resultant force-lines are changed, preparatory to its\nbreaking into two duads on the hyper level. On that level, the decades\ndisintegrate into two triplets and a quartet, the positive with the\ndepressions inward, the negative with the depressions outward.\n\nCALCIUM (Plate VIII, 2).\n\nThe funnels, as usual, assume a spherical form on the proto level, and\nshow, in each case, three spheres containing ovoids. These spheres, still\non the proto level, break free from their containing funnel, as in the case\nof gold (p. 49), twelve bodies being thus liberated, while the central\nglobe breaks up into eight segments, each of which becomes globular, and\ncontains within it a \"cigar\" and a somewhat heart-shaped body. Four\nspheres, each containing seven ten-atomed ovoids, are identical with those\nin beryllium, and can be followed in its diagram. Eight spheres, each\ncontaining five nine-atomed ovoids of a different type, set free, on the\nmeta level, eighty duads--forty positive and forty negative--and forty\nquintets, which are identical with those in chlorine. On the hyper level,\nthe duads become single atoms, within a sphere, and the central atom from\nthe quintet is also set free, one hundred and twenty in all. The remaining\nfour atoms of the quintet divide into two duads.\n\nThe central globe, dividing into eight, becomes eight six-atomed spheres on\nthe meta, the \"cigar\" behaving as usual, four \"cigars\" being positive and\nfour negative, and becoming dissociated into triplets; the four atoms\nwithin the heart-shaped body appear as a tetrahedron, remain together on\nthe meta level, and break up into duads on the hyper.\n\nSTRONTIUM (PLATE VIII, 3).\n\nThe third member of this group repeats the _a_ groups of beryllium and the\n_b_ groups of calcium, and they dissociate into the bodies already\ndescribed under these respectively. The two upper globes in each funnel\nrepeat each other, but each globe contains four smaller spheres showing\nthree varieties of forms. The two marked _g_, which are repeated in the\ncentral globe as _h_, are seven-atomed, and appear as spheres or ovoids\naccording to pressure. They are figured on p. 48, under iodine; _e_ and _f_\nare related as object and image, and we have already seen them in copper\n(pp. 38 and 48); in each case, as in copper, they unite into a ten-atomed\nfigure; on the meta level the pair of fours form a ring, and the remaining\ntwo atoms form a duad; _i_, which repeats _f_, makes a ring with the fifth\nin the centre, as in the five-atomed _b_ of calcium, as shown above. There\nis, thus, nothing new in strontium, but only repetitions of forms already\nstudied.\n\nOXYGEN (PLATE VIII, 4).\n\n[Illustration]\n\nThe disintegration of oxygen as given in 1895 may be repeated here, and the\nbetter presentation given on p. 54 renders it easier to follow the process.\nOn the proto level the two \"snakes\" divide; the brilliant disks are\nseven-atomed, but are differently arranged, the positive snake having the\natoms arranged as in the iodine ovoids, whereas the negative snake has them\narranged as in a capital H. The snakes show the same extraordinary activity\non the proto level as on the gaseous, twisting and writhing, darting and\ncoiling. The body of the snake is of two-atomed beads, positive and\nnegative. On the meta level the snakes break into ten fragments, each\nconsisting of a disk, with six beads on one side and five on the other,\nremaining as lively as the original snake. They shiver into their\nconstituent disks, and beads on the hyper level, there yielding the ten\ndisks, five positive and five negative, and the 110 beads, fifty-five\npositive and fifty-five negative.\n\nCHROMIUM (PLATE VIII, 5).\n\nWhen we go on to chromium and molybdenum, we return to our familiar funnels\nand central globes, and the secondary spheres within the funnels--quickly\nset free, as before, on the proto level--give us no new combinations in\ntheir contained spheres and ovoids. The _a_ of beryllium, the _b_ of\ncalcium and strontium, and _d_ of calcium, the _e_ and _f_ of strontium,\nare all there; _j_ in chromium is the same as the central sphere in the _b_\novoid. In the central globe, _k_, is a pair of triangles as in hydrogen,\nconsisting of only six atoms, which on the meta level revolve round each\nother, and break up into two duads and two units on the hyper.\n\nMOLYBDENUM (PLATE VIII, 6).\n\nMolybdenum presents us with only two new forms, and these are merely\nfour-atomed tetrahedra, occurring in pairs as object and image. All the\nother bodies have already been analysed.\n\nII a.--We come now to the second great tetrahedral group, which though very\nmuch complicated, is yet, for the most part, a repetition of familiar\nforms.\n\nMAGNESIUM (PLATE IX, 1).\n\n[Illustration]\n\nWe are still among tetrahedra, so have to do with four funnels, but each\nfunnel contains three rings, and each ring three ovoids; on the proto level\na triple dissociation takes place, for the funnels let free the rings as\nlarge spheres, in each of which rotate three twelve-atomed ovoids, and then\nthe ovoids break loose from the spheres, and themselves become spherical,\nso that we have finally thirty-six proto compounds from the tetrahedron. On\nthe meta level the contained bodies, a triplet, Mg _a_, a septet, Mg _b_,\nand a duad, Mg _c_, are set free from each globe, thus yielding one hundred\nand eight meta compounds. On the hyper level the triplet becomes a duad and\na unit; the duad becomes two units; and the septet a triplet and a quartet.\n\nZINC (PLATE IX, 2).\n\nWe can leave aside the funnel, for the only difference between it and the\nmagnesium funnel is the substitution of a second septet for the triplet,\nand the septet is already shown in the magnesium diagram. We have,\ntherefore, only to consider the spikes, pointing to the angles of the\nenclosing tetrahedron, and the central globe. These are set free on the\nproto level and the spikes immediately release their contents, yielding\nthus thirty-two separate bodies.\n\nThe triangular arrangement at the top of the spike is the same as occurs in\ncopper (_b_ on p. 48), and can be there followed. One of the three similar\npillars is shown in the accompanying diagram under Zn a. The compressed\nlong oval becomes a globe, with six bodies revolving within it in a rather\npeculiar way: the quartets turn round each other in the middle; the\ntriplets revolve round them in a slanting ellipse; the duads do the same on\nan ellipse slanting at an angle with the first, somewhat as in gold (_a_\nand _b_, p. 40). The spheres within the globes at the base of the spikes,\nZn _b_, behave as a cross--the cross is a favourite device in the II _a_\ngroups. Finally, the central globe, Zn _c_, follows the same cruciform line\nof disintegration.\n\nCADMIUM (Plate IX, 3).\n\n[Illustration]\n\nCadmium follows very closely on the lines of zinc; the pillars of the zinc\nspike are reproduced in the rings of the cadmium funnel; the globes are\nalso the globes of cadmium; so neither of these needs attention. We have\nonly to consider the three ten-atomed ovoids, which are substituted for the\none ten-atomed triangle of zinc, and the central cross. The ovoids become\nspheres (Cd _a_, _b_), the contained bodies revolving within them, _a_\nwhirling on a diameter of the sphere, cutting it in halves, as it were, and\n_b_ whirling round it at right angles; the cross also becomes a sphere (Cd\n_c_), but the cruciform type is maintained within it by the relative\npositions of the contained spheres in their revolution. The subsequent\nstages are shown in the diagram.\n\nSULPHUR (Plate XI, 1).\n\nSulphur has nothing new, but shows only the funnels already figured in\nmagnesium, with the substitution of a second septet for the triplet, as in\nzinc.\n\nSELENIUM (Plate X, 2).\n\n[Illustration]\n\nThe funnel of selenium is a re-arrangement of the twelve-atomed ovoids of\nmagnesium and the ten-atomed ovoids of cadmium. The funnels, on\ndisintegrating, set free twelve groups, each containing nine spheres. On\nthe meta level the ten-atomed bodies are set free, and the twelve-atomed\ndivide into duads and decads, thus yielding seventy-two decads and\nthirty-six duads; the duads, however, at once recombine into hexads, thus\ngiving only twelve meta elements, or eighty-four in all from the funnels.\nThe central globe holds together on the proto level, but yields five meta\nelements. The star also at first remains a unit on the proto level, and\nthen shoots off into seven bodies, the centre keeping together, and the six\npoints becoming spheres, within which the two cones, base to base, whirl in\nthe centre, and the globes circle round them. On the meta level all the\nthirty bodies contained in the star separate from each other, and go on\ntheir independent ways.\n\nSelenium offers a beautiful example of the combination of simple elements\ninto a most exquisite whole.\n\nTELLURIUM (Plate X, 3).\n\nTellurium very closely resembles cadmium, and they are, therefore placed on\nthe same diagram. The pillars are the same as in chlorine and its\ncongeners, with a duad added at the base. The ten-atomed ovoid is the same\nas in cadmium and follows the same course in breaking up. It would be\ninteresting to know why this duad remains as a duad in selenium and breaks\nup into a septad and triad in the other members of the group. It may be due\nto the greater pressure to which it is subjected in selenium, or there may\nbe some other reason. The cross in tellurium is identical with that in\ncadmium, except that the centre is seven-atomed instead of four-atomed.\n\n       *       *       *       *       *\n\nVI.\n\nIII AND IIIa.--THE CUBE GROUPS.\n\nWe have here four groups to consider, all the members of which are triads,\nand have six funnels, opening on the six faces of a cube.\n\nIII.--Boron, scandium and yttrium were examined; they are all triatomic,\nparamagnetic, and positive. The corresponding group consists of nitrogen,\nvanadium and niobium; they are triatomic, paramagnetic, and negative. We\nhave not examined the remaining members of these groups. In these two\ngroups nitrogen dominates, and in order to make the comparison easy the\nnitrogen elements are figured on both Plate XI and Plate XII. It will be\nseen that scandium and yttrium, of the positive group, differ only in\ndetails from vanadium and niobium, of the negative group; the ground-plan\non which they are built is the same. We noted a similar close resemblance\nbetween the positive strontium and the negative molybdenum.\n\n[Illustration: PLATE XI.]\n\nBORON (Plate III, 4, and Plate XI, 1). We have here the simplest form of\nthe cube; the funnels contain only five bodies--four six-atomed ovoids and\none six-atomed \"cigar.\" The central globe has but four five-atomed spheres.\nIt is as simple in relation to its congeners as is beryllium to its\ngroup-members.\n\nBORON: 6 funnels of 30 atoms    180\n       Central globe             20\n                               ----\n                         Total  200\n                               ----\n       Atomic weight          10.86\n       Number weight 200/18   11.11\nSCANDIUM (Plate XI, 2). For the first time we meet funnels of different\ntypes, A and B, three of each kind; A appear to be positive and B negative,\nbut this must be stated with reserve.\n\nIn A the boron funnel is reproduced, the \"cigar\" having risen above its\ncompanion ovoids; but the most important matter to note in respect to this\nfunnel is our introduction to the body marked _a_ 110. This body was\nobserved by us first in nitrogen, in 1895, and we gave it the name of the\n\"nitrogen balloon,\" for in nitrogen it takes the balloon form, which it\nalso often assumes in other gaseous elements. Here it appears as a\nsphere--the form always assumed on the proto level--and it will be seen, on\nreference to the detailed diagram 4 _a_, to be a complicated body,\nconsisting of six fourteen-atomed globes arranged round a long ovoid\ncontaining spheres with three, four, six, six, four, three, atoms\nrespectively. It will be observed that this balloon appears in every member\nof these two groups, except boron.\n\nThe B funnel runs largely to triads, _c_ and _b_, _b_ (see 4 _b_) having\nnot only a triadic arrangement of spheres within its contained globes, but\neach sphere has also a triplet of atoms. In _c_ (see 4 _c_) there is a\ntriadic arrangement of spheres, but each contains duads. B is completed by\na five-atomed sphere at the top of the funnel. It should be noted that _a_,\n_b_ and _c_ all are constituents of nitrogen.\n\nThe central globe repeats that of boron, with an additional four-atomed\nsphere in the middle.\n\nSCANDIUM: 3 funnels (A) of 140 atoms   420\n          3    \"    (B) of 116   \"     348\n          Centre globe                  24\n                                      ----\n                               Total   792\n                                      ----\n          Atomic weight              43.78\n          Number weight 792/18       44.00\nYTTRIUM (Plate XI, 3). Here we have a quite new arrangement of bodies\nwithin the funnel--the funnel being of one type only. Two \"cigars\" whirl on\ntheir own axes in the centre near the top, while four eight-atomed globes\n(see 4 _e_) chase each other in a circle round them, spinning madly on\ntheir own axes--this axial spinning seems constant in all contained\nbodies--all the time. Lower down in the funnel, a similar arrangement is\nseen, with a globe (see 4 _d_)--a nitrogen element--replacing the \"cigars,\"\nand six-atomed ovoids replacing the globes.\n\nThe \"nitrogen balloon\" occupies the third place in the funnel, now showing\nits usual shape in combination, while the _b_ globe (see 4 _b_) of scandium\ntakes on a lengthened form below it.\n\nThe central globe presents us with two tetrahedra, recalling one of the\ncombinations in gold (see Plate VII _d_), and differing from that only by\nthe substitution of two quartets for the two triplets in gold.\n\nOne funnel of yttrium contains exactly the same number of atoms as is\ncontained in a gaseous atom of nitrogen. Further, _a_, _b_, and _d_ are all\nnitrogen elements. We put on record these facts, without trying to draw any\nconclusions from them. Some day, we--or others--may find out their\nsignificance, and trace through them obscure relations.\n\nYTTRIUM: 6 funnels of 261 atoms      1566\n         Central globe                 40\n                                     ----\n                             Total   1606\n                                     ----\n         Atomic weight              88.34\n         Number weight 1606/18      89.22\nThe corresponding negative group, of nitrogen, vanadium and niobium, is\nrendered particularly interesting by the fact that it is headed by\nnitrogen, which--like the air, of which it forms so large a part--pervades\nso many of the bodies we are studying. What is there in nitrogen which\nrenders it so inert as to conveniently dilute the fiery oxygen and make it\nbreathable, while it is so extraordinarily active in some of its compounds\nthat it enters into the most powerful explosives? Some chemist of the\nfuture, perhaps, will find the secret in the arrangement of its constituent\nparts, which we are able only to describe.\n\n[Illustration: PLATE XII.]\n\nNITROGEN (Plate XII, 1) does not assume the cubical form of its relatives,\nbut is in shape like an egg. Referring again to our 1895 investigations, I\nquote from them. The balloon-shaped body (see 4 _a_) floats in the middle\nof the egg, containing six small spheres in two horizontal rows, and a long\novoid in the midst; this balloon-shaped body is positive, and is drawn down\ntowards the negative body _b_ (see 4 _b_) with its seven contained spheres,\neach of which has nine atoms within it--three triads. Four spheres are\nseen, in addition to the two larger bodies; two of these (see 4 _d_), each\ncontaining five smaller globes, are positive, and two (see 4 _c_)\ncontaining four smaller globes, are negative.\n\nNITROGEN: Balloon                         110\n          Oval                             63\n          2 bodies of 20 atoms             40\n          2   \"    \"  24   \"               48\n                                         ----\n                              Total       261\n                                         ----\n          Atomic weight                 14.01\n          Number weight 261/18          14.50\nVANADIUM (Plate XII, 2) closely follows scandium, having two types of\nfunnels. Funnel A only differs from that of scandium by having a globe (see\n4 _d_) inserted in the ring of four ovoids; funnel B has a six-atomed,\ninstead of a five-atomed globe at the top, and slips a third globe\ncontaining twenty atoms (see 4 _d_) between the two identical with those of\nscandium (see 4 _c_). The central globe has seven atoms in its middle body\ninstead of four. In this way does vanadium succeed in overtopping scandium\nby 126 atoms.\n\nVANADIUM: 3 funnels (A) of 160 atoms      480\n          3    \"    (B) \"  137   \"        411\n          Central globe                    27\n                                         ----\n                              Total       918\n                                         ----\n          Atomic weight                 50.84\n          Number weight 918/18          51.00\nNIOBIUM (Plate XII, 3) is as closely related to yttrium as is vanadium to\nscandium. The little globes that scamper round the \"cigars\" contain twelve\natoms instead of eight (see 4 _e_).\n\nThe rest of the funnel is the same. In the central globe both the\ntetrahedra have \"cigars,\" and a central nine-atomed globe spins round in\nthe centre (see 4 _f_), seventeen atoms being thus added.\n\nNIOBIUM: 6 funnels of 277 atoms        1662\n         Central globe                   57\n                                       ----\n                             Total     1719\n                                       ----\n         Atomic weight                93.25\n         Number weight 1719/18        95.50\nIII a.--Aluminium, gallium and indium were examined from this group. They\nare triatomic, diamagnetic, and positive. The corresponding group contains\nphosphorus, arsenic and antimony: bismuth also belongs to it, but was not\nexamined; they are triatomic, diamagnetic and negative. They have no\ncentral globes.\n\n[Illustration: PLATE XIII.]\n\nALUMINIUM (Plate XIII, 1), the head of the group, is, as usual, simple.\nThere are six similar funnels, each containing eight ovoids, below which is\na globe.\n\nALUMINIUM: 6 funnels of 81 atoms        486\n           Atomic weight              26.91\n           Number weight 486/18       27.00\nGALLIUM (Plate XIII, 2) has two segments in every funnel; in the segment to\nthe left a \"cigar\" balances a globe, equally six-atomed, in that of the\nright, and the globes to right and left are four-atomed as against\nthree-atomed. In the next row, the smaller contained globes have six atoms\nas against four, and the cones have respectively seven and five. By these\nlittle additions the left-hand funnel boasts one hundred and twelve atoms\nas against ninety-eight.\n\nGALLIUM: Left segment 112 atoms }\n         Right segment 98   \"   } = 210\n         6 funnels of 210 atoms         1260\n                                        ----\n         Atomic weight                 69.50\n         Number weight 1260/18         70.00\nINDIUM (Plate XIII, 3) repeats the segments of gallium exactly, save in the\nsubstitution of a sixteen-atomed body for the seven-atomed cone of the\nleft-hand segment, and a fourteen-atomed body for the five-atomed\ncorresponding one in gallium. But each funnel now has three segments\ninstead of two; three funnels out of the six contain two segments of type A\nand one of type B; the remaining three contain two of type B, and one of\ntype A.\n\nINDIUM: Segment A 121 atoms\n        Segment B 107   \"\n        3 funnels of 2 A and 1 B ([242 + 107] 3)    1047\n        3    \"    \"  2 B and 1 A ([214 + 121] 3)    1005\n                                                    ----\n                                         Total      2052\n                                                    ----\n        Atomic weight                             114.05\n        Number weight 2052/18                     114.00\nThe corresponding negative group, phosphorus, arsenic, and antimony, run on\nvery similar lines to those we have just examined.\n\n[Illustration: PLATE XIV.]\n\nPHOSPHORUS (Plate XIV, 1) offers us a very curious arrangement of atoms,\nwhich will give some new forms in breaking up. Two segments are in each\nfunnel, in fact the only two of group III _a_ which do not show this\narrangement, or a modification thereof, are aluminium and arsenic.\n\nPHOSPHORUS: Left segment  50 atoms\n            Right segment 43   \"\n                          --\n                          93\n            6 funnels of 93 atoms       558\n            Atomic weight             30.77\n            Number weight 558/18      31.00\nARSENIC (Plate XIV, 2) resembles aluminium in having eight internal\nsub-divisions in a funnel, and the ovoids which form the top ring are\nidentical, save for a minute difference that in aluminium the ovoids stand\nthe reverse way from those in arsenic. It will be noted that in the former\nthe top and bottom triangles of atoms have the apices upwards, and the\nmiddle one has its apex downwards. In arsenic, the top and bottom ones\npoint downwards, and the middle one upwards. Arsenic inserts sixteen\nspheres between the ovoids and globe shown in aluminium, and thus adds no\nless than one hundred and forty-four atoms to each funnel.\n\nARSENIC: 6 funnels of 225 atoms    1350\n         Atomic weight            74.45\n         Number weight 1350/18    75.00\nANTIMONY (Plate XIV, 3) is a close copy of indium, and the arrangement of\ntypes A and B in the funnels is identical. In the middle rings of both A\nand B a triplet is substituted for a unit at the centre of the larger\nglobe. In the lowest body of type A the \"cigar\" has vanished, and is\nrepresented by a seven-atomed crystalline form.\n\nANTIMONY: Segment A 128 atoms\n          Segment B 113 atoms\n      3 funnels of 2 A and 1 B ([256 + 113]3)   1107\n      3   \"     \"  2 B and 1 A ([226 + 128]3)   1056\n                                                ----\n                                     Total      2163\n                                                ----\n      Atomic weight                           119.34\n      Number weight                           120.16\n       *       *       *       *       *\n\nVII.\n\nBORON (Plate III, 4, and Plate XI, 1).\n\n[Illustration]\n\nThe disintegration of boron is very simple: the funnels are set free and\nassume the spherical form, showing a central \"cigar\" and four globes each\ncontaining two triplets. The central globe is also set free with its four\nquintets, and breaks at once in two. On the meta level the \"cigar\" breaks\nup as usual, and the triplets separate. On the hyper level, the \"cigar\"\nfollows its usual course, and the triplets become duads and units. The\nglobe forms two quintets on the meta level, and these are resolved into\ntriplets and duads.\n\nSCANDIUM (Plate XI, 2).\n\nIn funnel A the \"cigar\" and the ovoids behave as in boron, but the\n\"balloon,\" _a_ 110 (XI, 4), escapes from the funnel as it changes to a\nsphere, and holds together on the proto level; on the meta, it yields six\nglobes each containing seven duads, and these are all set free as duads on\nthe hyper level; the ovoid is also set free on the meta level becoming a\nsphere, and on the hyper level liberates its contained bodies, as two\ntriplets, two quartets and two sextets.\n\nIn funnel B there is a quintet, that behaves like those in the globe of\nboron, on escaping from the funnel, in which the bodies remain on the proto\nlevel, with the exception of _b_ 63, which escapes. On the meta level, _c_\n(Plate XI, 4), _c_ assumes a tetrahedral form with six atoms at each point,\nand these hold together as sextets on the hyper level. At the meta stage,\n_b_ (Plate XI, 4 _b_) sets free seven nine-atomed bodies, which become free\ntriplets on the hyper. The central globe shows a cross at its centre, with\nthe four quintets whirling round it, on the proto level. On the meta, the\nquintets are set free, and follow the boron type, while the cross becomes a\nquartet on the meta level, and two duads on the hyper.\n\nYTTRIUM (Plate XI, 3).\n\n[Illustration]\n\nIn yttrium, on the proto level, _a_ 110 and _b_ 63 both escape from the\nfunnel, and behave as in scandium. The ovoids and \"cigars,\" set free on the\nmeta level, behave as in boron. The central globe breaks up as in gold (pp.\n49 and 50), four quartets being set free instead of two quartets and two\ntriplets. We have only to consider _e_ 8 and _d_ 20 (Plate XI, 4). _E_ 8 is\na tetrahedral arrangement of duads on the meta level, set free as duads on\nthe hyper. _D_ 20 is an arrangement of pairs of duads at the angles of a\nsquare-based pyramid on the meta, and again free duads on the hyper.\n\nNITROGEN (Plate XII, 1).\n\nNitrogen has nothing new to show us, all its constituents having appeared\nin scandium and yttrium.\n\nVANADIUM (Plate XII, 2).\n\nThe A funnel of vanadium repeats the A funnel of scandium, with the\naddition of _d_ 20, already studied. In the B funnel scandium B is\nrepeated, with an addition of _d_ 20 and a sextet for a quintet; the sextet\nis the _c_ of the \"nitrogen balloon.\" The central globe follows boron, save\nthat it has a septet for its centre; this was figured in iodine (p. 48).\n\nNIOBIUM (Plate XII, 3).\n\nNiobium only differs from yttrium by the introduction of triplets for duads\nin _e_; on the meta level we have therefore triplets, and on the hyper each\ntriplet yields a duad and a unit. The only other difference is in the\ncentral globe. The tetrahedra separate as usual, but liberate eight\n\"cigars\" instead of four with four quartets; the central body is simple,\nbecoming three triads at the angles of a triangle on the meta level, and\nthree duads and three units on the hyper.\n\nALUMINIUM (Plate XIII, 1).\n\n[Illustration]\n\nThe funnels let go the globes, but the eight ovoids remain within them, so\nthat seven bodies are let loose on the proto level. When the ovoids are set\nfree at the meta stage they become spherical and a nine-atomed body is\nproduced, which breaks up into triangles on the hyper level. The globe\nbecomes a cross at the meta stage, with one atom from the duads at each arm\nin addition to its own, and these form four duads on the hyper, and a unit\nfrom the centre.\n\nGALLIUM (Plate XIII, 2).\n\nIn gallium the funnel disappears on the proto level, setting free its two\ncontained segments, each of which forms a cylinder, thus yielding twelve\nbodies on the proto level. On the meta, the three upper globes in each\nleft-hand segment are set free, and soon vanish, each liberating a cigar\nand two septets, the quartet and triad uniting. On the hyper the quartet\nyields two duads but the triangle persists. The second set of bodies divide\non the meta level, forming a sextet and a cross with a duad at each arm;\nthese on the hyper level divide into two triangles, four duads and a unit.\nThe seven-atomed cone becomes two triangles united by a single atom, and on\nthe meta level these form a ring round the unit; on the hyper they form\nthree duads and a unit.\n\nIn the right-hand segment, the same policy is followed, the four triads\nbecoming two sextets, while the central body adds a third to the number.\nThe second ring has a quartet instead of the sextet, but otherwise breaks\nup as does that of the left; the quintet at the base follows that of boron.\n\nINDIUM (Plate XIII, 3).\n\nThe complication of three segments of different types in each funnel does\nnot affect the process of breaking up, and indium needs little attention. A\nis exactly the same as the left-hand funnel of gallium, save for the\nsubstitution of a globe containing the familiar \"cigar\" and two\nsquare-based pyramids. B is the same as the right-hand funnel of gallium,\nexcept that its lowest body consists of two square-based pyramids and a\ntetrahedron. All these are familiar.\n\nPHOSPHORUS (Plate XIV, 1).\n\n[Illustration]\n\nThe atoms in the six similar spheres in the segments of the phosphorus\nfunnel are arranged on the eight angles of a cube, and the central one is\nattached to all of them. On the meta level five of the nine atoms hold\ntogether and place themselves on the angles of a square-based pyramid; the\nremaining four set themselves on the angle of a tetrahedron. They yield, on\nthe hyper level, two triads, a duad, and a unit. The remaining bodies are\nsimple and familiar.\n\nARSENIC (Plate XIV, 2).\n\nArsenic shows the same ovoids and globe as have already been broken up in\naluminium (see _ante_); the remaining sixteen spheres form nine-atomed\nbodies on the meta level, all similar to those of aluminium, thus yielding\ntwelve positive and twelve negative; the globe also yields a nine-atomed\nbody, twenty-five bodies of nine.\n\nANTIMONY (Plate XIV, 3).\n\nAntimony follows closely in the track of gallium and indium, the upper ring\nof spheres being identical. In the second ring, a triplet is substituted\nfor the unit, and this apparently throws the cross out of gear, and we have\na new eleven-atomed figure, which breaks up into a triplet and two quartets\non the hyper level. The lowest seven-atomed sphere of the three at the base\nis the same as we met with in copper.\n\n       *       *       *       *       *\n\nVIII.\n\nIV.--THE OCTAHEDRAL GROUPS.\n\nThese groups are at the turns of the spiral in Sir William Crookes'\nlemniscates (see p. 28). On the one side is carbon, with below it titanium\nand zirconium; on the other silicon, with germanium and tin. The\ncharacteristic form is an octahedron, rounded at the angles and a little\ndepressed between the faces in consequence of the rounding; in fact, we did\nnot, at first, recognize it as an octahedron, and we called it the \"corded\nbale,\" the nearest likeness that struck us. The members of the group are\nall tetrads, and have eight funnels, opening on the eight faces of the\noctahedron. The first group is paramagnetic and positive; the corresponding\none is diamagnetic and negative. The two groups are not closely allied in\ncomposition, though both titanium and tin have in common the five\nintersecting tetrahedra at their respective centres.\n\n[Illustration: PLATE XV.]\n\nCARBON (Plate III, 5, and XV, 1) gives us the fundamental octahedral form,\nwhich becomes so masked in titanium and zirconium. As before said (p. 30),\nthe protrusion of the arms in these suggests the old Rosicrucian symbol of\nthe cross and rose, but they show at their ends the eight carbon funnels\nwith their characteristic contents, and thus justify their relationship.\nThe funnels are in pairs, one of each pair showing three \"cigars,\" and\nhaving as its fellow a funnel in which the middle \"cigar\" is truncated,\nthus loosing one atom. Each \"cigar\" has a leaf-like body at its base, and\nin the centre of the octahedron is a globe containing four atoms, each\nwithin its own wall; these lie on the dividing lines of the faces, and each\nholds a pair of the funnels together. It seems as though this atom had been\neconomically taken from the \"cigar\" to form a link. This will be more\nclearly seen when we come to separate the parts from each other. It will be\nnoticed that the atoms in the \"leaves\" at the base vary in arrangement,\nbeing alternately in a line and in a triangle.\n\n                            { left  27\nCARBON: One pair of funnels { right 22\n                            { centre 1\n                                    --\n                                    54\n        4 pairs of funnels of 54 atoms   216\n        Atomic weight                  11.91\n        Number weight 216/18           12.00\nTITANIUM (Plate III, 6, and XV, 2) has a complete carbon atom distributed\nover the ends of its four arms, a pair of funnels with their linking atom\nbeing seen in each. Then, in each arm, comes the elaborate body shown as 3\n_c_, with its eighty-eight atoms. A ring of twelve ovoids (3 _d_) each\nholding within itself fourteen atoms, distributed among three contained\nglobes--two quartets and a sextet--is a new device for crowding in\nmaterial. Lastly comes the central body (4 _e_) of five intersecting\ntetrahedra, with a \"cigar\" at each of their twenty points--of which only\nfifteen can be shown in the diagram--and a ring of seven atoms round an\neighth, that forms the minute centre of the whole. Into this elaborate body\none hundred and twenty-eight atoms are built.\n\nTITANIUM: One carbon atom               216\n          4 _c_ of 88 atoms        352\n          12 _d_ of 14  \"          168\n          Central globe                 128\n                                       ----\n                            Total       864\n                                       ----\n          Atomic weight               47.74\n          Number weight 864/18        48.00\nZIRCONIUM (Plate XV, 3) has exactly the same outline as titanium, the\ncarbon atom is similarly distributed, and the central body is identical.\nOnly in 5 _c_ and _d_ do we find a difference on comparing them with 4 _c_\nand d. The _c_ ovoid in zirconium shows no less than fifteen secondary\nglobes within the five contained in the ovoid, and these, in turn, contain\naltogether sixty-nine smaller spheres, with two hundred and twelve atoms\nwithin them, arranged in pairs, triplets, quartets, quintets, a sextet and\nseptets. Finally, the ovoids of the ring are also made more elaborate,\nshowing thirty-six atoms instead of fourteen. In this way the clever\nbuilders have piled up in zirconium no less than 1624 atoms.\n\nZIRCONIUM: One Carbon atom              216\n           4 _c_ of 212 atoms      848\n           12 _d_ of 36   \"        432\n           Central globe                128\n                                       ----\n                              Total    1624\n                                       ----\n           Atomic weight              89.85\n           Number weight              90.22\n[Illustration: PLATE XVI.]\n\nSILICON (Plate XVI, 1) is at the head of the group which corresponds to\ncarbon on the opposite turn of the lemniscate. It has the usual eight\nfunnels, containing four ovoids in a circle, and a truncated \"cigar\" but no\ncentral body of any kind. All the funnels are alike.\n\nSILICON: 8 funnels of 65 atoms          520\n         Atomic weight                28.18\n         Number weight 520/18         28.88\nGERMANIUM (Plate XVI, 2) shows the eight funnels, containing each four\nsegments (XVI, 4), within which are three ovoids and a \"cigar.\" In this\ncase the funnels radiate from a central globe, formed of two intersecting\ntetrahedra, with \"cigars\" at each point enclosing a four-atomed globe.\n\nGERMANIUM: 8 funnels of 156 atoms     1248\n           Central globe                52\n                                      ----\n                   Total              1300\n                                      ----\n           Atomic weight             71.93\n           Number weight 1300/18     72.22\nTIN (Plate XVI, 3) repeats the funnel of germanium, and the central globe\nwe met with in titanium, of five intersecting tetrahedra, carrying twenty\n\"cigars\"; the latter, however, omits the eight-atomed centre of the globe\nthat was found in titanium, and hence has one hundred and twenty atoms\ntherein instead of one hundred and twenty-eight. Tin, to make room for the\nnecessary increase of atoms, adopts the system of spikes, which we met with\nin zinc (see Plate IX, 2); these spikes, like the funnels, radiate from the\ncentral globe, but are only six in number. The twenty-one-atomed cone at\nthe head of the spike we have already seen in silver, and we shall again\nfind it in iridium and platinum; the pillars are new in detail though not\nin principle, the contained globes yielding a series of a triplet, quintet,\nsextet, septet, sextet, quintet, triplet.\n\nTIN: 8 funnels of 156 atoms           1248\n     6 spikes  of 126   \"              756\n     Central globe                     120\n                                      ----\n                      Total           2124\n                                      ----\n     Atomic weight                  118.10\n     Number weight 2124/18          118.00\nV.--THE BARS GROUPS.\n\n[Illustration: PLATE XVII.]\n\nHere, for the first time, we find ourselves a little at issue with the\naccepted system of chemistry. Fluorine stands at the head of a\ngroup--called the inter-periodic--whereof the remaining members are (see\nCrookes' table, p. 28), manganese, iron, cobalt, nickel; ruthenium,\nrhodium, palladium; osmium, iridium, platinum. If we take all these as\ngroup V, we find that fluorine and manganese are violently forced into\ncompany with which they have hardly any points of relationship, and that\nthey intrude into an otherwise very harmonious group of closely similar\ncomposition. Moreover, manganese reproduces the characteristic lithium\n\"spike\" and not the bars of those into whose company it is thrust, and it\nis thus allied with lithium, with which indeed it is almost identical. But\nlithium is placed by Crookes at the head of a group, the other members of\nwhich are potassium, rubidium and caesium (the last not examined). Following\nthese identities of composition, I think it is better to remove manganese\nand fluorine from their incongruous companions and place them with lithium\nand its allies as V _a_, the Spike Groups, marking, by the identity of\nnumber, similarities of arrangement which exist, and by the separation the\ndifferences of composition. It is worth while noting what Sir William\nCrookes, in his \"Genesis of the Elements,\" remarks on the relations of the\ninterperiodic group with its neighbours. He says: \"These bodies are\ninterperiodic because their atomic weights exclude them from the small\nperiods into which the other elements fall, and because their chemical\nrelations with some members of the neighbouring groups show that they are\nprobably interperiodic in the sense of being in transition stages.\"\n\nGroup V in every case shows fourteen bars radiating from a centre as shown\nin iron, Plate IV, 1. While the form remains unchanged throughout, the\nincrease of weight is gained by adding to the number of atoms contained in\na bar. The group is made up, not of single chemical elements, as in all\nother cases, but of sub-groups, each containing three elements, and the\nrelations within each sub-group are very close; moreover the weights only\ndiffer by two atoms per bar, making a weight difference of twenty-eight in\nthe whole. Thus we have per bar:--\n\nIron             72        Palladium       136\nNickel           74        Osmium          245\nCobalt           76        Iridium         247\nRuthenium       132        Platinum A      249\nRhodium         134        Platinum B      257\nIt will be noticed (Plate XVII, 3, 4, 5,) that each bar has two sections,\nand that the three lower sections in iron, cobalt and nickel are identical;\nin the upper sections, iron has a cone of twenty-eight atoms, while cobalt\nand nickel have each three ovoids, and of these the middle ones alone\ndiffer, and that only in their upper globes, this globe being four-atomed\nin cobalt and six-atomed in nickel.\n\nThe long ovoids within each bar revolve round the central axis of the bar,\nremaining parallel with it, while each spins on its own axis; the iron cone\nspins round as though impaled on the axis.\n\n        14 bars of 72 atoms            1008\n        Atomic weight                 55.47\n        Number weight 1008/18         56.00\nIRON (Plate IV, 1, and XVII, 3):\n\n        14 bars of 74 atoms            1036\n        Atomic weight                 57.70\n        Number weight 1036/18         57.55\nCOBALT (Plate XVII, 4):\n\n        14 bars of 76 atoms             1064\n        Atomic weight                  58.30\n        Number weight 1064/18          59.11\nNICKEL (Plate XVII, 4):\n\n(The weight of cobalt, as given in Erdmann's _Lehrbuch_, is 58.55, but\nMessrs. Parker and Sexton, in _Nature_, August 1, 1907, give the weight, as\nthe result of their experiments, as 57.7.)\n\n[Illustration: PLATE XVIII.]\n\nThe next sub-group, ruthenium, rhodium, and palladium, has nothing to\ndetain us. It will be observed that each bar contains eight segments,\ninstead of the six of cobalt and nickel; that ruthenium and palladium have\nthe same number of atoms in their upper ovoids, although in ruthenium a\ntriplet and quartet represent the septet of palladium; and that in\nruthenium and rhodium the lower ovoids are identical, though one has the\norder: sixteen, fourteen, sixteen, fourteen; and the other: fourteen,\nsixteen, fourteen, sixteen. One constantly asks oneself: What is the\nsignificance of these minute changes? Further investigators will probably\ndiscover the answer.\n\n      14 bars of 132 atoms              1848\n      Atomic weight                   100.91\n      Number weight 1848/18           102.66\nRUTHENIUM (Plate XVIII, 1):\n\n      14 bars of 134 atoms              1876\n      Atomic weight                   102.23\n      Number weight 1876/18           104.22\nRHODIUM (Plate XVII, 2):\n\n      14 bars of 136 atoms              1904\n      Atomic weight                   105.74\n      Number weight 1904/18           105.77\nPALLADIUM (XVIII, 3):\n\nThe third sub-group, osmium, iridium and platinum, is, of course, more\ncomplicated in its composition, but its builders succeed in preserving the\nbar form, gaining the necessary increase by a multiplication of contained\nspheres within the ovoids. Osmium has one peculiarity: the ovoid marked _a_\n(XVIII, 4) takes the place of axis in the upper half of the bar, and the\nthree ovoids, marked _b_, revolve round it. In the lower half, the four\novoids, _c_, revolve round the central axis. In platinum, we have marked\ntwo forms as platinum A and platinum B, the latter having two four-atomed\nspheres (XVIII, 6 _b_) in the place of the two triplets marked a. It may\nwell be that what we have called platinum B is not a variety of platinum,\nbut a new element, the addition of two atoms in a bar being exactly that\nwhich separates the other elements within each of the sub-groups. It will\nbe noticed that the four lower sections of the bars are identical in all\nthe members of this sub-group, each ovoid containing thirty atoms. The\nupper ring of ovoids in iridium and platinum A are also identical, but for\nthe substitution, in platinum A, of a quartet for a triplet in the second\nand third ovoids; their cones are identical, containing twenty-one atoms,\nlike those of silver and tin.\n\n       14 bars of 245 atoms            3430\n       Atomic weight                 189.55\n       Number weight 3430/18         190.55\nOSMIUM (Plate XVIII, 4):\n\n       14 bars of 247 atoms            3458\n       Atomic weight                 191.11\n       Number weight 3458/18         192.11\nIRIDIUM (Plate XVIII, 5):\n\n       14 bars of 249 atoms            3486\n       Atomic weight                 193.66\n       Number weight 3486/18         193.34\nPLATINUM A (Plate XVIII, 6 _a_):\n\n       14 bars of 251 atoms            3514\n       Atomic weight                 ------\n       Number weight 3514/18         195.22\nPLATINUM B (Plate XVIII, 6 _b_):\n\nV a.--THE SPIKE GROUPS.\n\nI place within this group lithium, potassium, rubidium, fluorine, and\nmanganese, because of their similarity in internal composition. Manganese\nhas fourteen spikes, arranged as in the iron group, but radiating from a\ncentral globe. Potassium has nine, rubidium has sixteen, in both cases\nradiating from a central globe. Lithium (Plate IV, 2) and fluorine (Plate\nIV, 3) are the two types which dominate the group, lithium supplying the\nspike which is reproduced in all of them, and fluorine the \"nitrogen\nballoon\" which appears in all save lithium. It will be seen that the\nnatural affinities are strongly marked. They are all monads and\nparamagnetic; lithium, potassium and rubidium are positive, while fluorine\nand manganese are negative. We seem thus to have a pair, corresponding with\neach other, as in other cases, and the interperiodic group is left\ninterperiodic and congruous within itself.\n\n[Illustration: PLATE XIX.]\n\nLITHIUM (Plate IV, 2 and Plate XIX, 1) is a striking and beautiful form,\nwith its upright cone, or spike, its eight radiating petals (_x_) at the\nbase of the cone, and the plate-like support in the centre of which is a\nglobe, on which the spike rests. The spike revolves swiftly on its axis,\ncarrying the petals with it; the plate revolves equally swiftly in the\nopposite direction. Within the spike are two globes and a long ovoid; the\nspheres within the globe revolve as a cross; within the ovoid are four\nspheres containing atoms arranged on tetrahedra, and a central sphere with\nan axis of three atoms surrounded by a spinning wheel of six.\n\nLITHIUM: Spike of 63 atoms                 63\n         8 petals of 6 atoms               48\n         Central globe of 16 atoms         16\n                                         ----\n                               Total      127\n                                         ----\n         Atomic weight                   6.98\n         Number weight 127/18            7.05\nPOTASSIUM (Plate XIX, 2) consists of nine radiating lithium spikes, but has\nnot petals; its central globe contains one hundred and thirty-four atoms,\nconsisting of the \"nitrogen balloon,\" encircled by six four-atomed spheres.\n\nPOTASSIUM: 9 bars of 63 atoms             567\n           Central globe                  134\n                                         ----\n                              Total       701\n                                         ----\n           Atomic weight                38.94\n           Number weight 701/18         38.85\n(The weight, as determined by Richards [_Nature_, July 18, 1907] is\n39.114.)\n\nRUBIDIUM: (Plate XIX, 3) adds an ovoid, containing three spheres--two\ntriplets and a sextet--to the lithium spike, of which it has sixteen, and\nits central globe is composed of three \"balloons.\"\n\nRUBIDIUM: 16 spikes of 75 atoms          1200\n          Central globe                   330\n                                         ----\n                            Total        1530\n                                         ----\n          Atomic weight                 84.85\n          Number weight 1530/18         85.00\nThe corresponding negative group consists only of fluorine and manganese,\nso far as our investigations have gone.\n\nFLUORINE (Plate IV, 3, and Plate XVII, 1) is a most peculiar looking object\nlike a projectile, and gives one the impression of being ready to shoot off\non the smallest provocation. The eight spikes, reversed funnels, coming to\na point, are probably responsible for this warlike appearance. The\nremainder of the body is occupied by two \"balloons.\"\n\nFLUORINE: 8 spikes of 15 atoms            120\n          2 balloons                      220\n                                         ----\n                             Total        340\n                                         ----\n          Atomic weight                 18.90\n          Number weight 340/18          18.88\nMANGANESE (Plate XVII, 2) has fourteen spikes radiating from a central\n\"balloon.\"\n\nMANGANESE: 14 spikes of 63 atoms          882\n           Central balloon                110\n                                         ----\n                           Total          992\n                                         ----\n           Atomic weight                54.57\n           Number weight 992/18         55.11\n       *       *       *       *       *\n\nIX.\n\nWe have now to consider the breaking up of the octahedral groups, and more\nand more, as we proceed, do we find that the most complicated arrangements\nare reducible to simple elements which are already familiar.\n\nCARBON (Plate III, 5, and XV, 1).\n\n[Illustration]\n\nCarbon is the typical octahedron, and a clear understanding of this will\nenable us to follow easily the constitution and disintegration of the\nvarious members of these groups. Its appearance as a chemical atom is shown\non Plate III, and see XV, 1. On the proto level the chemical atom breaks up\ninto four segments, each consisting of a pair of funnels connected by a\nsingle atom; this is the proto element which appears at the end of each arm\nof the cross in titanium and zirconium. On the meta level the five\nsix-atomed \"cigars\" show two neutral combinations, and the truncated\n\"cigar\" of five atoms is also neutral; the \"leaves\" yield two forms of\ntriplet, five different types being thus yielded by each pair of funnels,\nexclusive of the linking atom. The hyper level has triplets, duads and\nunits.\n\nTITANIUM (Plate III, 6, and XV, 2, 3).\n\n[Illustration]\n\nOn the proto level, the cross breaks up completely, setting free the pairs\nof funnels with the linking atom (_a_ and _b_), as in carbon, the four\nbodies marked _c_, the twelve marked _d_, and the central globe marked e.\nThe latter breaks up again, setting free its five intersecting\ncigar-bearing tetrahedra, which follow their usual course (see Occultum, p.\n44). The eight-atomed body in the centre makes a ring of seven atoms round\na central one, like that in occultum (see p. 44, diagram B), from which it\nonly differs in having the central atom, and breaks up similarly, setting\nthe central atom free. The ovoid _c_ sets free its four contained globes,\nand the ovoid _d_ sets free the three within it. Thus sixty-one proto\nelements are yielded by titanium. On the meta level, _c_ (titanium 3)\nbreaks up into star-like and cruciform bodies; the component parts of these\nare easily followed; on the hyper level, of the four forms of triplets one\nbehaves as in carbon, and the others are shown, _a_, _b_ and _f_; the\ncruciform quintet yields a triplet and a duad, _c_ and _d_; the tetrahedra\nyield two triplets _g_ and _h_, and two units; the septet, a triplet _k_\nand a quartet _j_. On the meta level, the bodies from _d_ behave like their\nequivalents in sodium, each _d_ shows two quartets and a sextet, breaking\nup, on the hyper level, into four duads and two triads.\n\nZIRCONIUM (Plate XV, 2, 5).\n\nZirconium reproduces in its _c_ the four forms that we have already\nfollowed in the corresponding _c_ of titanium, and as these are set free on\nthe proto level, and follow the same course on the meta and hyper levels,\nwe need not repeat them. The central globe of zirconium _c_ sets free its\nnine contained bodies; eight of these are similar and are figured in the\ndiagram; it will be observed that the central body is the truncated \"cigar\"\nof carbon; their behaviour on the meta and hyper levels is easily followed\nthere. The central sphere is also figured; the cigar follows its usual\ncourse, and its companions unite into a sextet and an octet. The _d_ ovoid\nliberates five bodies, four of which we have already seen in titanium, as\nthe crosses and sextet of sodium, and which are figured under titanium; the\nfour quartets within the larger globe also follow a sodium model, and are\ngiven again.\n\nSILICON (Plate XVI, 1).\n\n[Illustration]\n\nIn silicon, the ovoids are set free from the funnels on the proto level,\nand the truncated \"cigar,\" playing the part of a leaf, is also liberated.\nThis, and the four \"cigars,\" which escape from their ovoids, pass along\ntheir usual course. The quintet and quartet remain together, and form a\nnine-atomed body on the meta level, yielding a sextet and a triplet on the\nhyper.\n\nGERMANIUM (Plate XVI, 2, 4).\n\nThe central globe, with its two \"cigar\"-bearing tetrahedra, need not delay\nus; the tetrahedra are set free and follow the occultum disintegration, and\nthe central four atoms is the sodium cross that we had in titanium. The\novoids (XVI, 4) are liberated on the proto level, and the \"cigar,\" as\nusual, bursts its way through and goes along its accustomed path. The\nothers remain linked on the meta level, and break up into two triangles and\na quintet on the hyper.\n\nTIN (Plate XVI, 3, 4).\n\nHere we have only the spike to consider, as the funnels are the same as in\ngermanium, and the central globe is that of titanium, omitting the eight\natomed centre. The cone of the spike we have had in silver (see p. 729,\nMay), and it is set free on the proto level. The spike, as in zinc, becomes\na large sphere, with the single septet in the centre, the remaining six\nbodies circling round it on differing planes. They break up as shown. (Tin\nis Sn.)\n\nIRON (Plate IV, I, and XVII, 3).\n\n[Illustration]\n\nWe have already dealt with the affinities of this peculiar group, and we\nshall see, in the disintegration, even more clearly, the close\nrelationships which exist according to the classification which we here\nfollow.\n\nThe fourteen bars of iron break asunder on the proto level, and each sets\nfree its contents--a cone and three ovoids, which as usual, become spheres.\nThe twenty-eight-atomed cone becomes a four-sided figure, and the ovoids\nshow crystalline contents. They break up, on the meta level as shown in the\ndiagram, and are all reduced to triplets and duads on the hyper level.\n\nCOBALT (Plate XVII, 4).\n\nThe ovoids in cobalt are identical with those of iron; the higher ovoids,\nwhich replace the cone of iron, show persistently the crystalline forms so\nnoticeable throughout this group.\n\nNICKEL (Plate XVII, 5).\n\nThe two additional atoms in a bar, which alone separate nickel from cobalt,\nare seen in the upper sphere of the central ovoid.\n\nRUTHENIUM (Plate XVIII, 1).\n\nThe lower ovoids in ruthenium are identical in composition, with those of\niron, cobalt and nickel and may be studied under Iron. The upper ones only\ndiffer by the addition of a triplet.\n\nRHODIUM (Plate XVIII, 2).\n\nRhodium has a septet, which is to be seen in the _c_ of titanium (see _k_\nin the titanium diagram) and differs only in this from its group.\n\nPALLADIUM (Plate XVIII, 3).\n\nIn palladium this septet appears as the upper sphere in every ovoid of the\nupper ring.\n\nOSMIUM (Plate XVIII, 4).\n\nWe have here no new constituents; the ovoids are set free on the proto\nlevel and the contained globes on the meta, all being of familiar forms.\nThe cigars, as usual, break free on the proto level, and leave their ovoid\nwith only four contained spheres, which unite into two nine-atomed bodies\nas in silicon (see above).\n\nIRIDIUM (Plate XVIII, 5.)\n\nThe twenty-one-atomed cone of silver here reappears, and its proceedings\nmay be followed under that metal (see diagram, p. 729, May). The remaining\nbodies call for no remark.\n\nPLATINUM (Plate XVIII, 6).\n\nAgain the silver cone is with us. The remaining bodies are set free on the\nproto level, and their contained spheres on the meta.\n\nLITHIUM (Plate IV, 2, and XIX, 1).\n\n[Illustration]\n\nHere we have some new combinations, which recur persistently in its allies.\nThe bodies _a_, in Plate XIX, 1, are at the top and bottom of the ellipse;\nthey come to right and left of it in the proto state, and each makes a\ntwelve-atomed body on the meta level.\n\nThe five bodies within the ellipse, three monads and two sextets, show two\nwhich we have had before: _d_, which behaves like the quintet and quartet\nin silicon, after their junction, and _b_, which we have had in iron. The\ntwo bodies _c_ are a variant of the square-based pyramid, one atom at the\napex, and two at each of the other angles. The globe, _e_, is a new form,\nthe four tetrahedra of the proto level making a single twelve-atomed one on\nthe meta. The body _a_ splits up into triplets on the hyper; _b_ and _d_\nfollow their iron and silicon models; _c_ yields four duads and a unit; _e_\nbreaks into four quartets.\n\nPOTASSIUM (Plate XIX, 2).\n\nPotassium repeats the lithium spike; the central globe shows the \"nitrogen\nballoon,\" which we already know, and which is surrounded on the proto level\nwith six tetrahedra, which are set free on the meta and behave as in\ncobalt. Hence we have nothing new.\n\nRUBIDIUM (Plate XIX, 3).\n\nAgain the lithium spike, modified slightly by the introduction of an ovoid,\nin place of the top sphere; the forms here are somewhat unusual, and the\ntriangles of the sextet revolve round each other on the meta level; all the\ntriads break up on the hyper level into duads and units.\n\nFLUORINE (Plate IV, 3, and Plate XVII, 1).\n\nThe reversed funnels of fluorine split asunder on the proto level, and are\nset free, the \"balloons\" also floating off independently. The funnels, as\nusual, become spheres, and on the meta level set free their contained\nbodies, three quartets and a triplet from each of the eight. The balloons\ndisintegrate in the usual way.\n\nMANGANESE (Plate XVII, 2).\n\nManganese offers us nothing new, being composed of \"lithium spikes\" and\n\"nitrogen balloons.\"\n\n       *       *       *       *       *\n\nX.\n\nVI.--THE STAR GROUPS.\n\nWe have now reached the last of the groups as arranged on Sir William\nCrookes' lemniscates, that forming the \"neutral\" column; it is headed by\nhelium, which is _sui generis_. The remainder are in the form of a flat\nstar (see Plate IV, 4), with a centre formed of five intersecting and\n\"cigar\"-bearing tetrahedra, and six radiating arms. Ten of these have been\nobserved, five pairs in which the second member differs but slightly from\nthe first; they are: Neon, Meta-neon; Argon, Metargon; Krypton,\nMeta-krypton; Xenon, Meta-xenon; Kalon, Meta-kalon; the last pair and the\nmeta forms are not yet discovered by chemists. These all show the presence\nof a periodic law; taking an arm of the star in each of the five pairs, we\nfind the number of atoms to be as follows :--\n\n40       99      224      363      489\n47      106      231      370      496\nIt will be observed that the meta form in each case shows seven more atoms\nthan its fellow.\n\n[Illustration: PLATE XX.]\n\nHELIUM (Plate III, 5, and Plate XX, 1) shows two \"cigar\"-bearing\ntetrahedra, and two hydrogen triangles, the tetrahedra revolving round an\negg-shaped central body, and the triangles spinning on their own axes while\nperforming a similar revolution. The whole has an attractively airy\nappearance, as of a fairy element.\n\nHELIUM: Two tetrahedra of 24 atoms   48\n        Two triangles of 9 atoms     18\n        Central egg                   6\n                                   ----\n                 Total               72\n                                   ----\n        Atomic weight              3.94\n        Number weight 72/18        4.00\nNEON (Plate XX, 2 and 6) has six arms of the pattern shown in 2, radiating\nfrom the central globe.\n\nNEON: Six arms of 40 atoms       240\n      Central tetrahedra         120\n\n                                ----\n                   Total         360\n                                ----\n      Atomic weight            19.90\n      Number weight 360/18     20.00\nMETA-NEON (Plate XX, 3 and 6) differs from its comrade by the insertion of\nan additional atom in each of the groups included in the second body within\nits arm, and substituting a seven-atomed group for one of the triplets in\nneon.\n\nMETA-NEON: Six arms of 47 atoms    282\n           Central tetrahedra      120\n                                  ----\nTotal                              402\n                                  ----\nAtomic weight                     ----\nNumber weight 402/18             22.33\nARGON (Plate XX, 4, 6 and 7) shows within its arms the _b_ 63 which we met\nin nitrogen, yttrium, vanadium and niobium, but not the \"balloon,\" which we\nshall find with it in krypton and its congeners.\n\nARGON: Six arms of 99 atoms     594\n       Central tetrahedra       120\n                               ----\n                 Total          714\n                               ----\n       Atomic weight          39.60\n       Number weight 714/18   39.66\nMETARGON (Plate XX, 5, 6 and 7) again shows only an additional seven atoms\nin each arm.\n\nMETARGON: Six arms of 106 atoms   636\n          Central tetrahedra      120\n                                 ----\n                      Total       756\n                                 ----\nAtomic weight                    ----\nNumber weight 756/18               42\n[Illustration: PLATE XXI.]\n\nKRYPTON (Plate XXI, 1 and 4, and Plate XX, 6 and 7) contains the nitrogen\n\"balloon,\" elongated by its juxtaposition to _b_ 63. The central tetrahedra\nappear as usual.\n\nKRYPTON:  Six arms of 224 atoms             1344\n          Central tetrahedra                 120\n                                           -----\n                               Total        1464\n                                           -----\n          Atomic weight                    81.20\n          Number weight 1464/18            81.33\nMETA-KRYPTON differs only from krypton by the substitution of _z_ for _y_\nin each arm of the star.\n\nMETA-KRYPTON:  Six arms of 231 atoms        1386\n               Central tetrahedra            120\n                                           -----\n                               Total        1506\n                                           -----\n               Atomic weight               -----\n               Number weight 1506/18       83.66\nXENON (Plate XXI, 2 and 4, and Plate XX, 6 and 7) has a peculiarity shared\nonly by kalon, that _x_ and _y_ are asymmetrical, the centre of one having\nthree atoms and the centre of the other two. Is this done in order to\npreserve the difference of seven from its comrade?\n\nXENON:  Six arms of 363 atoms               2178\n        Central tetrahedra                   120\n                                           -----\n                               Total        2298\n                                           -----\n        Atomic weight                     127.10\n        Number weight 2298/18             127.66\nMETA-XENON differs from xenon only by the substitution of two _z_'s for _x_\nand _y_.\n\nMETA-XENON:  Six arms of 370 atoms          2220\n            Central tetrahedra               120\n                                           -----\n                               Total        2340\n                                           -----\n            Atomic weight                  -----\n            Number weight 2340/18            130\nKALON (Plate XXI, 3 and 4, and Plate XX, 6 and 7) has a curious cone,\npossessing a kind of tail which we have not observed elsewhere; _x_ and _y_\nshow the same asymmetry as in xenon.\n\nKALON: Six arms of 489 atoms          2934\n       Central tetrahedra              120\n                                      ----\n                            Total     3054\n                                      ----\n       Atomic weight                  ----\n       Number weight 3054/18        169.66\nMETA-KALON again substitutes two _z_'s for _x_ and _y_.\n\nMETA-KALON: Six arms of 496 atoms           2976\n            Central tetrahedra               120\n                                            ----\n                            Total           3096\n                                            ----\n            Atomic weight                   ----\n            Number weight 3096/18            172\nOnly a few atoms of kalon and meta-kalon have been found in the air of a\nfair-sized room.\n\nIt does not seem worth while to break up these elements, for their\ncomponent parts are so familiar. The complicated groups--_a_ 110, _b_ 63\nand _c_ 120--have all been fully dealt with in preceding pages.\n\n       *       *       *       *       *\n\nThere remains now only radium, of the elements which we have, so far,\nexamined, and that will be now described and will bring to an end this\nseries of observations. A piece of close and detailed work of this kind,\nalthough necessarily imperfect, will have its value in the future, when\nscience along its own lines shall have confirmed these researches.\n\nIt will have been observed that our weights, obtained by counting, are\nalmost invariably slightly in excess of the orthodox ones: it is\ninteresting that in the latest report of the International Commission\n(November 13, 1907), printed in the _Proceedings of the Chemical Society of\nLondon_, Vol. XXIV, No. 33, and issued on January 25, 1908, the weight of\nhydrogen is now taken at 1.008 instead of at 1. This would slightly raise\nall the orthodox weights; thus aluminium rises from 26.91 to 27.1, antimony\nfrom 119.34 to 120.2, and so on.\n\n       *       *       *       *       *\n\nXI.\n\nRADIUM.\n\n[Illustration: PLATE XXII.]\n\nRadium has the form of a tetrahedron, and it is in the tetrahedral groups\n(see article IV) that we shall find its nearest congeners; calcium,\nstrontium, chromium, molybdenum resemble it most closely in general\ninternal arrangements, with additions from zinc and cadmium. Radium has a\ncomplex central sphere (Plate XXII), extraordinarily vivid and living; the\nwhirling motion is so rapid that continued accurate observation is very\ndifficult; the sphere is more closely compacted than the centre-piece in\nother elements, and is much larger in proportion to the funnels and spikes\nthan is the case with the elements above named; reference to Plate VIII\nwill show that in these the funnels are much larger than the centres,\nwhereas in radium the diameter of the sphere and the length of the funnel\nor spike are about equal. Its heart consists of a globe containing seven\natoms, which assume on the proto level the prismatic form shown in cadmium,\nmagnesium and selenium. This globe is the centre of two crosses, the arms\nof which show respectively three-atomed and two-atomed groups. Round this\nsphere are arranged, as on radii, twenty-four segments, each containing\nfive bodies--four quintets and a septet--and six loose atoms, which float\nhorizontally across the mouth of the segment; the whole sphere has thus a\nkind of surface of atoms. On the proto level these six atoms in each\nsegment gather together and form a \"cigar.\" In the rush of the streams\npresently to be described one of these atoms is occasionally torn away, but\nis generally, if not always, replaced by the capture of another which is\nflung into the vacated space.\n\nEach of the four funnels opens, as usual, on one face of the tetrahedron,\nand they resemble the funnels of strontium and molybdenum but contain three\npillars instead of four (Plate XXIII). They stand within the funnel as\nthough at the angles of a triangle, not side by side. The contained bodies,\nthough numerous, contain forms which are all familiar.\n\nThe spikes alternate with the funnels, and point to the angles of the\ntetrahedron as in zinc and cadmium; each spike contains three \"lithium\nspikes\" (see Plate XIX) with a ten-atomed cone or cap at the top, floating\nabove the three (Plate XXIV). The \"petals\" or \"cigars\" of lithium exist in\nthe central globe in the floating atoms, and the four-atomed groups which\nform the lithium \"plate\" may be seen in the funnels, so that the whole of\nlithium appears in radium.\n\nSo much for its composition. But a very peculiar result, so far unobserved\nelsewhere, arises from the extraordinarily rapid whirling of the central\nsphere. A kind of vortex is formed, and there is a constant and powerful\nindraught through the funnels. By this, particles are drawn in from\nwithout, and these are swept round with the sphere, their temperature\nbecoming much raised, and they are then violently shot out through the\nspikes. It is these jets which occasionally sweep away an atom from the\nsurface of the sphere. These \"particles\" may be atoms, or they may be\nbodies from any of the etheric levels; in some cases these bodies break up\nand form new combinations. In fact lithium seems like a kind of vortex of\ncreative activity, drawing in, breaking up, recombining, shooting forth--a\nmost extraordinary element.\n\nRADIUM: 4 funnels of 618 atoms          2472\n        4 spikes of 199 atoms            796\n        Central sphere                   819\n                                        ----\n                             Total      4087\n                                        ----\n        Atomic weight                   ----\n        Number weight 4087/18         227.05\n[Illustration: PLATE XXIV.]\n\n[Illustration: PLATE XXIII.]\n\n       *       *       *       *       *\n\nAPPENDIX.\n\nTHE AETHER OF SPACE.\n\nMuch discussion has taken place, especially between physicists and\nchemists, over the nature of the substances with which all space must,\naccording to scientific hypothesis, be filled. One side contends that it is\ninfinitely thinner than the thinnest gas, absolutely frictionless and\nwithout weight; the other asserts that it is denser than the densest solid.\nIn this substance the ultimate atoms of matter are thought to float, like\nmotes in a sunbeam, and light, heat and electricity are supposed to be its\nvibrations.\n\nTheosophical investigators, using methods not at the disposal of physical\nscience, have found that this hypothesis includes under one head two\nentirely different and widely separated sets of phenomena. They have been\nable to deal with states of matter higher than the gaseous and have\nobserved that it is by means of vibrations of this finer matter that light,\nheat and electricity manifest themselves to us. Seeing that matter in these\nhigher states thus performs the functions attributed to the ether of\nscience, they have (perhaps unadvisedly) called these states etheric, and\nhave thus left themselves without a convenient name for that substance\nwhich fulfils the other part of the scientific requirements.\n\nLet us for the moment name this substance _koilon_, since it fills what we\nare in the habit of calling empty space. What mulaprakrti, or\n\"mother-matter,\" is to the inconceivable totality of universes, koilon is\nto our particular universe--not to our solar system merely but to the vast\nunit which includes all visible suns. Between koilon and mulaprakrti there\nmust be various stages, but we have at present no direct means of\nestimating their number or of knowing anything whatever about them.\n\nIn an ancient occult treatise, however, we read of a \"colorless spiritual\nfluid\" \"which exists everywhere and forms the first foundation on which our\nsolar system is built. Outside the latter, it is found in its pristine\npurity only between the stars [suns] of the universe.... As its substance\nis of a different kind from that known on earth, the inhabitants of the\nlatter, seeing _through it_, believe, in their illusion and ignorance, that\nit is empty space. There is not one finger's breadth of void space in the\nwhole boundless universe.\"[21] \"The mother-substance\" is said, in this\ntreatise, to produce this aether of space as its seventh grade of density,\nand all objective suns are said to have this for their \"substance.\"\n\nTo any power of sight which we can bring to bear upon it, this koilon\nappears to be homogeneous, though it is probably nothing of the kind, since\nhomogeneity can belong to the mother-substance alone. It is out of all\nproportion denser than any other substance known to us, infinitely\ndenser--if we may be pardoned the expression; so much denser that it seems\nto belong to another type, or order, of density. But now comes the\nstartling part of the investigation: we might expect matter to be a\ndensification of this koilon; it is nothing of the kind. Matter is not\nkoilon, but _the absence of koilon_, and at first sight, matter and space\nappear to have changed places, and emptiness has become solidity, solidity\nhas become emptiness.\n\nTo help us to understand this clearly let us examine the ultimate atom of\nthe physical plane (see pp. 21-23). It is composed of ten rings or wires,\nwhich lie side by side, but never touch one another. If one of these wires\nbe taken away from the atom, and be, as it were, untwisted from its\npeculiar spiral shape and laid out on a flat surface, it will be seen that\nit is a complete circle--a tightly twisted endless coil. This coil is\nitself a spiral containing 1680 turns; it can be unwound, and it will then\nmake a much larger circle. This process of unwinding may be again\nperformed, and a still bigger circle obtained, and this can be repeated\ntill the seven sets of spirillae are all unwound, and we have a huge circle\nof the tiniest imaginable dots, like pearls threaded on an invisible\nstring. These dots are so inconceivably small that many millions of them\nare needed to make one ultimate physical atom, and while the exact number\nis not readily ascertainable, several different lines of calculation agree\nin indicating it as closely approximate to the almost inconceivable total\nof fourteen thousand millions. Where figures are so huge, direct counting\nis obviously impossible, but fortunately the different parts of the atom\nare sufficiently alike to enable us to make an estimate in which the margin\nof error is not likely to be very great. The atom consists of ten wires,\nwhich divide themselves naturally into two groups--the three which are\nthicker and more prominent, and the seven thinner ones which correspond to\nthe colors and planets. These latter appear to be identical in constitution\nthough the forces flowing through them must differ, since each responds\nmost readily to its own special set of vibrations. By actual counting it\nhas been discovered that the numbers of coils or spirillae of the first\norder in each wire is 1680; and the proportion of the different orders of\nspirillae to one another is equal in all cases that have been examined, and\ncorrespond with the number of dots in the ultimate spirillae of the lowest\norder. The ordinary sevenfold rule works quite accurately with the thinner\ncoils, but there is a very curious variation with regard to the set of\nthree. As may be seen from the drawings, these are obviously thicker and\nmore prominent, and this increase of size is produced by an augmentation\n(so slight as to be barely perceptible) in the proportion to one another of\nthe different orders of spirillae and in the number of dots in the lowest.\nThis augmentation, amounting at present to not more than .00571428 of the\nwhole of each case, suggests the unexpected possibility that this portion\nof the atom may be somehow actually undergoing a change--may in fact be in\nprocess of growth, as there is reason to suppose that these three thicker\nspirals originally resembled the others.\n\nSince observation shows us that each physical atom is represented by\nforty-nine astral atoms, each astral atom by forty-nine mental atoms, and\neach mental atom by forty-nine of those on the buddhic plane, we have here\nevidently several terms of a regular progressive series, and the natural\npresumption is that the series continues where we are no longer able to\nobserve it. Further probability is lent to this assumption by the\nremarkable fact that--if we assume one dot to be what corresponds to an\natom on the seventh or highest of our planes (as is suggested in _The\nAncient Wisdom_, p. 42) and then suppose the law of multiplication to begin\nits operation, so that 49 dots shall form the atom of the next or sixth\nplane, 2401 that of the fifth, and so on--we find that the number indicated\nfor the physical atom (496) corresponds almost exactly with the calculation\nbased upon the actual counting of the coils. Indeed, it seems probable that\nbut for the slight growth of the three thicker wires of the atom the\ncorrespondence would have been perfect.\n\nIt must be noted that a physical atom cannot be directly broken up into\nastral atoms. If the unit of force which whirls those millions of dots into\nthe complicated shape of a physical atom be pressed back by an effort of\nwill over the threshold of the astral plane, the atom disappears instantly,\nfor the dots are released. But the same unit of force, working now upon a\nhigher level, expresses itself not through one astral atom, but through a\ngroup of 49. If the process of pressing back the unit of force is repeated,\nso that it energises upon the mental plane, we find the group there\nenlarged to the number of 2401 of those higher atoms. Upon the buddhic\nplane the number of atoms formed by the same amount of force is very much\ngreater still--probably the cube of 49 instead of the square, though they\nhave not been actually counted. Therefore one physical atom is not\n_composed of_ forty-nine astral or 2401 mental atoms, but _corresponds_ to\nthem, in the sense that the force which manifests through it would show\nitself on those higher planes by energising respectively those numbers of\natoms.\n\nThe dots, or beads, seem to be the constituents of all matter of which we,\nat present, know anything; astral, mental and buddhic atoms are built of\nthem, so we may fairly regard them as fundamental units, the basis of\nmatter.\n\nThese units are all alike, spherical and absolutely simple in construction.\nThough they are the basis of all matter, they are not themselves matter;\nthey are not blocks but bubbles. They do not resemble bubbles floating in\nthe air, which consist of a thin film of water separating the air within\nthem from the air outside, so that the film has both an outer and an inner\nsurface. Their analogy is rather with the bubbles that we see rising in\nwater, before they reach the surface, bubbles which may be said to have\nonly one surface--that of the water which is pushed back by the contained\nair. Just as such bubbles are not water, but are precisely the spots from\nwhich water is absent, so these units are not koilon, but the absence of\nkoilon--the only spots where it is not--specks of nothingness floating in\nit, so to speak, for the interior of these space-bubbles is an absolute\nvoid to the highest power of vision that we can turn upon them.\n\nThat is the startling, well-nigh incredible, fact. Matter is nothingness,\nthe space obtained by pressing back an infinitely dense substance; Fohat\n\"digs holes in space\" of a verity, and the holes are the airy\nnothingnesses, the bubbles, of which \"solid\" universes are built.\n\nWhat are they, then, these bubbles, or rather, what is their content, the\nforce which can blow bubbles in a substance of infinite density? The\nancients called that force \"the Breath,\" a graphic symbol, which seems to\nimply that they who used it had seen the kosmic process, had seen the LOGOS\nwhen He breathed into the \"waters of space,\" and made the bubbles which\nbuild universes. Scientists may call this \"Force\" by what names they\nwill--names are nothing; to us, Theosophists, it is the Breath of the\nLOGOS, we know not whether of the LOGOS of this solar system or of a yet\nmightier Being; the latter would seem the more likely, since in the\nabove-quoted occult treatise all visible suns are said to have this as\ntheir substance.\n\nThe Breath of the LOGOS, then, is the force which fills these spaces; His\nthe force which holds them open against the tremendous pressure of the\nkoilon; they are full of His Life, of Himself, and everything we call\nmatter, on however high or low a plane, is instinct with divinity; these\nunits of force, of life, the bricks with which He builds His universe, are\nHis very life scattered through space; truly is it written: \"I established\nthis universe with a portion of myself.\" And when He draws in His breath,\nthe waters of space will close in again, and the universe will have\ndisappeared. It is only a breath.\n\nThe outbreathing which makes these bubbles is quite distinct from, and long\nantecedent to, the three outpourings, or Life-Waves, so familiar to the\ntheosophical student. The first Life-Wave catches up these bubbles, and\nwhirls them into the various arrangements which we call the atoms of the\nseveral planes, and aggregates them into the molecules, and on the physical\nplane into the chemical elements. The worlds are built out of these voids,\nthese emptinesses, which seem to us \"nothing\" but are divine force. It is\nmatter made from the privation of matter. How true were H.P.B.'s statements\nin \"The Secret Doctrine\": \"Matter is nothing but an aggregation of atomic\nforces\" (iii, 398); \"Buddha taught that the primitive substance is eternal\nand unchangeable. Its vehicle is the pure luminous aether, the boundless\ninfinite space, not a void, resulting from the absence of all forms, but on\nthe contrary, the foundation of all forms\" (iii, 402).\n\nHow vividly, how unmistakably this knowledge brings home to us the great\ndoctrine of Maya, the transitoriness and unreality of earthly things, the\nutterly deceptive nature of appearances! When the candidate for initiation\nsees (not merely believes, remember, but actually _sees_) that what has\nalways before seemed to him empty space is in reality a solid mass of\ninconceivable density, and that the matter which has appeared to be the one\ntangible and certain basis of things is not only by comparison tenuous as\ngossamer (the \"web\" spun by \"Father-Mother\"), but is actually composed of\nemptiness and nothingness--is itself the very negation of matter--then for\nthe first time he thoroughly appreciates the valuelessness of the physical\nsenses as guides to the truth. Yet even more clearly still stands out the\nglorious certainty of the immanence of the Divine; not only is everything\nensouled by the LOGOS, but even its visible manifestation is literally part\nof Him, is built of His very substance, so that Matter as well as Spirit\nbecomes sacred to the student who really understands.\n\nThe koilon in which all these bubbles are formed undoubtedly represents a\npart, and perhaps the principal part, of what science describes as the\nluminiferous aether. Whether it is actually the bearer of the vibrations of\nlight and heat through interplanetary space is as yet undetermined. It is\ncertain that these vibrations impinge upon and are perceptible to our\nbodily senses only through the etheric matter of the physical plane. But\nthis by no means proves that they are conveyed through space in the same\nmanner, for we know very little of the extent to which the physical etheric\nmatter exists in interplanetary and interstellar space, though the\nexamination of meteoric matter and kosmic dust shows that at least some of\nit is scattered there.\n\nThe scientific theory is that the aether has some quality which enables it\nto transmit at a certain definite velocity transverse waves of all lengths\nand intensities--that velocity being what is commonly called the speed of\nlight, 190,000 miles per second. Quite probably this may be true of koilon,\nand if so it must also be capable of communicating those waves to bubbles\nor aggregations of bubbles, and before the light can reach our eyes there\nmust be a downward transference from plane to plane similar to that taking\nplace when a thought awakens emotion or causes action.\n\nIn a recent pamphlet on \"The Density of AEther,\" Sir Oliver Lodge remarks:--\n\n\"Just as the ratio of mass to volume is small in the case of a solar system\nor a nebula or a cobweb, I have been driven to think that the observed\nmechanical density of matter is probably an excessively small fraction of\nthe total density of the substance or aether contained in the space which it\nthus partially occupies--the substance of which it may hypothetically be\nheld to be composed.\n\n\"Thus, for instance, consider a mass of platinum, and assume that its atoms\nare composed of electrons, or of some structures not wholly dissimilar: the\nspace which these bodies actually fill, as compared with the whole space\nwhich in a sense they 'occupy,' is comparable to one ten-millionth of the\nwhole, even inside each atom; and the fraction is still smaller if it\nrefers to the visible mass. So that a kind of minimum estimate of aetherial\ndensity, on this basis, would be something like ten thousand million times\nthat of platinum.\"\n\nAnd further on he adds that this density may well turn out to be fifty\nthousand million times that of platinum. \"The densest matter known,\" he\nsays, \"is trivial and gossamer-like compared with the unmodified aether in\nthe same space.\"\n\nIncredible as this seems to our ordinary ideas, it is undoubtedly an\nunderstatement rather than an exaggeration of the true proportion as\nobserved in the case of koilon. We shall understand how this can be so if\nwe remember that koilon seems absolutely homogeneous and solid even when\nexamined by a power of magnification which makes physical atoms appear in\nsize and arrangement like cottages scattered over a lonely moor, and when\nwe further add to this the recollection that the bubbles of which these\natoms in turn are composed are themselves what may be not inaptly called\nfragments of nothingness.\n\nIn the same pamphlet Sir Oliver Lodge makes a very striking estimate of the\nintrinsic energy of the aether. He says: \"The total output of a\nmillion-kilowatt power station for thirty million years exists permanently,\nand at present inaccessibly in every cubic millimetre of space.\" Here again\nhe is probably underestimating the stupendous truth.\n\nIt may naturally be asked how, if all this be so, it is possible that we\ncan move about freely in a solid ten thousand million times denser, as Sir\nOliver Lodge says, than platinum. The obvious answer is that, where\ndensities differ sufficiently, they can move through each other with\nperfect freedom; water or air can pass through cloth; air can pass through\nwater; an astral form passes unconsciously through a physical wall, or\nthrough an ordinary human body; many of us have seen an astral form walk\nthrough a physical, neither being conscious of the passage; it does not\nmatter whether we say that a ghost has passed through a wall, or a wall has\npassed through a ghost. A gnome passes freely through a rock, and walks\nabout within the earth, as comfortably as we walk about in the air. A\ndeeper answer is that consciousness can recognize only consciousness, that\nsince we are of the nature of the LOGOS we can sense only those things\nwhich are also of His nature. These bubbles are His essence, His life, and,\ntherefore, we, who also are part of Him, can see the matter which is built\nof his substance, for all forms are but manifestations of Him. The koilon\nis to us non-manifestation, because we have not unfolded powers which\nenable us to cognise it, and it may be the manifestation of a loftier order\nof LOGOI, utterly beyond our ken.\n\nAs none of our investigators can raise his consciousness to the highest\nplane of our universe, the adi-tattva plane, it may be of interest to\nexplain how it is possible for them to see what may very probably be the\natom of that plane. That this may be understood it is essential to remember\nthat the power of magnification by means of which these experiments are\nconducted is quite apart from the faculty of functioning upon one or other\nof the planes. The latter is the result of a slow and gradual unfoldment of\nthe Self, while the former is merely a special development of one of the\nmany powers latent in man. All the planes are round us here, just as much\nas any other point in space, and if a man sharpens his sight until he can\nsee their tiniest atoms he can make a study of them, even though he may as\nyet be far from the level necessary to enable him to understand and\nfunction upon the higher planes as a whole, or to come into touch with the\nglorious Intelligences who gather those atoms into vehicles for Themselves.\n\nA partial analogy may be found in the position of the astronomer with\nregard to the stellar universe, or let us say the Milky Way. He can observe\nits constituent parts and learn a good deal about them along various lines,\nbut it is absolutely impossible for him to see it as a whole from outside,\nor to form any certain conception of its true shape, and to know what it\nreally is. Suppose that the universe is, as many of the ancients thought,\nsome inconceivably vast Being, it is utterly impossible for us, here in the\nmidst of it, to know what that Being is or is doing, for that would mean\nraising ourselves to a height comparable with His; but we may make\nextensive and detailed examination of such particles of His body as happen\nto be within our reach, for that means only the patient use of powers and\nmachinery already at our command.\n\nLet it not be supposed that, in thus unfolding a little more of the wonders\nof Divine Truth by pushing our investigations to the very farthest point at\npresent possible to us, we in any way alter or modify all that has been\nwritten in theosophical books of the shape and constitution of the physical\natom, and of the wonderful and orderly arrangements by which it is grouped\ninto the various chemical molecules; all this remains entirely unaffected.\n\nNor is any change introduced as regards the three outpourings from the\nLOGOS, and the marvellous facility with which the matter of the various\nplanes is by them moulded into forms for the service of the evolving life.\nBut if we wish to have a right view of the realities underlying\nmanifestation in this universe, we must to a considerable extent reverse\nthe ordinary conception as to what this matter essentially is. Instead of\nthinking of its ultimate constituents as solid specks floating in a void,\nwe must realise that it is the apparent void itself which is solid, and\nthat the specks are but bubbles on it. That fact once grasped, all the rest\nremains as before. The relative position of what we have hitherto called\nmatter and force is still for us the same as ever; it is only that, on\ncloser examination, both of these conceptions prove to be variants of\nforce, the one ensouling combinations of the other, and the real \"matter,\"\nkoilon, is seen to be something which has hitherto been altogether outside\nour scheme of thought.\n\nIn view of this marvellous distribution of Himself in \"space,\" the familiar\nconcept of the \"sacrifice of the LOGOS\" takes on a new depth and splendour;\nthis is His \"dying in matter,\" His \"perpetual sacrifice,\" and it may be the\nvery glory of the LOGOS that He can sacrifice Himself to the uttermost by\nthus permeating and making Himself one with that portion of koilon which He\nchooses as the field of His universe.\n\nWhat koilon is, what its origin, whether it is itself changed by the Divine\nBreath which is poured into it--does \"Dark Space\" thus become \"Bright\nSpace\" at the beginning of a manifestation?--these are questions to which\nwe cannot at present even indicate answers. Perchance an intelligent study\nof the great Scriptures of the world may yield replies.\n\n       *       *       *       *       *\n\nNOTES\n\n[1] See footnote in next Chapter.\n\n[2] The drawings of the elements were done by two Theosophical artists,\nHerr Hecker and Mrs. Kirby, whom we sincerely thank; the diagrams, showing\nthe details of the construction of each \"element,\" we owe to the most\npainstaking labour of Mr. Jinarajadasa, without whose aid it would have\nbeen impossible for us to have presented clearly and definitely the\ncomplicated arrangements by which the chemical elements are built up. We\nhave also to thank him for a number of most useful notes, implying much\ncareful research, which are incorporated in the present series, and without\nwhich we could not have written these papers.\n\n[3] The atomic sub-plane.\n\n[4] The astral plane.\n\n[5] Known to Theosophists as Fohat, the force of which all the physical\nplane forces--electricities--are differentiations.\n\n[6] When Fohat \"digs holes in space.\"\n\n[7] The first life-wave, the work of the third Logos.\n\n[8] A maya, truly.\n\n[9] By a certain action of the will, known to students, it is possible to\nmake such a space by pressing back and walling off the matter of space.\n\n[10] Again the astral world.\n\n[11] Each spirilla is animated by the life-force of a plane, and four are\nat present normally active, one for each round. Their activity in an\nindividual may be prematurely forced by yoga practice.\n\n[12] \"The ten numbers of the sun. These are called Dis--in reality\nspace--the forces spread in space, three of which are contained in the\nSun's Atman, or seventh principle, and seven are the rays shot out by the\nSun.\" The atom is a sun in miniature in its own universe of the\ninconceivably minute. Each of the seven whorls is connected with one of the\nPlanetary Logoi, so that each Planetary Logos has a direct influence\nplaying on the very matter of which all things are constructed. It may be\nsupposed that the three, conveying electricity, a differentiation of Fohat,\nare related to the Solar Logoi.\n\n[13] The action of electricity opens up ground of large extent, and cannot\nbe dealt with here. Does it act on the atoms themselves, or on molecules,\nor sometimes on one and sometimes on the other? In soft iron, for instance,\nare the internal arrangements of the chemical atom forcibly distorted, and\ndo they elastically return to their original relations when released? and\nin steel is the distortion permanent? In all the diagrams the heart-shaped\nbody, exaggerated to show the depression caused by the inflow and the point\ncaused by the outflow, is a single atom.\n\n[14] These sub-planes are familiar to the Theosophist as gaseous, etheric,\nsuper-etheric, sub-atomic, atomic; or as Gas, Ether 4, Ether 3, Ether 2,\nEther 1.\n\n[15] It must be remembered that the diagrams represent three-dimensional\nobjects, and the atoms are not all on a plane, necessarily.\n\n[16] That is, the surrounding magnetic fields strike on each other.\n\n[17] The fifth member of this group was not sought for.\n\n[18] This, with references which appear later (pp. 32, 33, 50, etc.),\nrelates to articles which appeared in the _Theosophist_, 1908.\n\n[19] Since writing the above I have noticed, in the _London, Edinburgh and\nDublin Philosophical Magazine and Journal of Science_, conducted by Dr.\nJohn Joly and Mr. William Francis, in an article entitled \"Evolution and\nDevolution of the Elements,\" the statement that it is probable that in \"the\nnebulous state of matter there are four substances, the first two being\nunknown upon earth, the third being hydrogen and the fourth ... helium. It\nalso seems probable that ... hydrogen, the two unknown elements, and helium\nare the four original elements from which all the other elements form. To\ndistinguish them from the others we will term them protons.\" This is\nsuggestive as regards hydrogen, but does not help us with regard to oxygen\nand nitrogen.\n\n[20] Theosophists call them Nature-Spirits, and often use the mediaeval term\nElementals. Beings concerned with the elements truly are they, even with\nchemical elements.\n\n[21] Quoted in \"The Secret Doctrine.\" H.P. Blavatsky, i, 309.","title":"Occult Chemistry: Clairvoyant Observations on the Chemical Elements","tradition":"scripture-revelation","translated_text":null,"word_count":32275}