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| author | Roger Frank <rfrank@pglaf.org> | 2025-10-15 04:48:05 -0700 |
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| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-15 04:48:05 -0700 |
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diff --git a/16058-h/16058-h.htm b/16058-h/16058-h.htm new file mode 100644 index 0000000..88eaccb --- /dev/null +++ b/16058-h/16058-h.htm @@ -0,0 +1,4925 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1" /> +<title>The Project Gutenberg eBook of Occult Chemistry, by Annie Besant and Charles W. Leadbeater</title> + <style type="text/css"> + +<!-- + p { margin-top: .75em; + text-align: justify; + margin-bottom: .75em; + } + H1,H2,H3,H4,H5,H6 { + text-align: center; /* all headings centered */ + } + hr {text-align: center; width: 50%;} + hr.full {width: 100%;} + hr.short {text-align: center; width: 20%;} + body { margin-left: 10%; + margin-right: 10%; + } + + td.tbar { border-left : thin solid black; vertical-align: top; } + td.tc { padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top; } + td.mbar { border-left : thin solid black; vertical-align: middle; } + table.allb { border : thin solid black; border-collapse: collapse } + td.allb { border : thin solid black; padding-left: 1em; padding-right: 1em; } + .single p {margin: 0;} + + .contents + {margin-left:30%; margin-right:10%; margin-bottom: 1em; text-align: left;} + .contents .stanza {margin: 1em 0em 1em 0em;} + .contents p {margin: 0; padding-left: 3em; text-indent: -3em;} + + .poem + {margin-left:10%; margin-right:10%; margin-bottom: 1em; text-align: left;} + .poem .stanza {margin: 1em 0em 1em 0em;} + .poem p {margin: 0; padding-left: 3em; text-indent: -3em;} + p.i2 {margin-left: 1em;} + p.i4 {margin-left: 2em;} + p.i6 {margin-left: 3em;} + p.i8 {margin-left: 4em;} + p.z8 {margin-left: 4em; font-style: italic;} + p.i10 {margin-left: 5em;} + p.z10 {margin-left: 5em; font-style: italic;} + p.i12 {margin-left: 6em;} + p.i16 {margin-left: 8em;} + p.i20 {margin-left: 10em;} + + a:link {color:blue; text-decoration:none} + a:visited {color:blue; text-decoration:none} + a:hover {color:red} + link {color:blue; text-decoration:none} + + .noflo + {margin-bottom: 1em; text-align: left;} + .noflo .stanza {margin: 1em 0em 1em 0em;} + .noflo p {margin: 0; padding-left: 3em; text-indent: -3em;} + .noflo p.i2 {margin-left: 1em;} + .noflo p.i16 {margin-left: 8em;} + + .author {text-align: right; margin-top: -1em; margin-right: 5%;} + .center {text-align: center; } + .right {text-align: right; } + .t {vertical-align: top; } + .tr {vertical-align: top;} + .tc {vertical-align: top;} + .tr p {text-align: right;} + .tc p {text-align: center;} + .m {vertical-align: middle; } + .mr {vertical-align: middle;} + .mc {vertical-align: middle;} + .mr p {text-align: right;} + .mc p {text-align: center;} + .b {vertical-align: bottom; } + .vol {/*font-weight: bold;*/ font-size: small;} + /* .grk {font-weight: bold; font-style: italic; } */ + .grk {font-style: normal; } + pre {font-family: "Courier New", Courier, monospace; margin-left: 1em; } + .sc {font-variant: small-caps; } + .linenum {position: absolute; top: auto; left: 60%;} /* poetry number */ + blockquote {margin-left: 2em; margin-right: 2em; } + blockquote.small {font-size: small; } + .pagenum {position: absolute; left: 92%; font-size: smaller; text-align: right;} /* page numbers */ + .sidenote {position: absolute; left: 92%; font-size: smaller; text-align: left;} /* sidenotes */ + .note {margin-left: 2em; margin-right: 2em; + font-size: small; } /* footnote */ + + .nobo {border: thin;} + .red {color: red;} + .figure, .figcenter, .figright, .figleft + {padding: 1em; margin: 0; text-align: center; font-size: 0.8em;} + .figure img, .figcenter img, .figright img, .figleft img + {border: none;} + .figure p, .figcenter p, .figright p, .figleft p + {margin: 0; text-indent: 1em;} + .figure p.in, .figcenter p.in, .figright p.in, .figleft p.in + {margin: 0; text-indent: 8em;} + .figcenter {margin: auto;} + .figright {float: right;} + .figleft {float: left;} + pre.pg {font-size: 8pt;} + // --> + </style> +</head> +<body> +<h1>The Project Gutenberg eBook, Occult Chemistry, by Annie Besant and Charles +W. Leadbeater, Edited by A. P. Sinnett</h1> +<pre class="pg"> +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at <a href = "https://www.gutenberg.org">www.gutenberg.org</a></pre> +<p>Title: Occult Chemistry</p> +<p> Clairvoyant Observations on the Chemical Elements</p> +<p>Author: Annie Besant and Charles W. Leadbeater</p> +<p>Editor: A. P. Sinnett</p> +<p>Release Date: June 14, 2005 [eBook #16058]</p> +<p>Language: English</p> +<p>Character set encoding: ISO-8859-1</p> +<p>***START OF THE PROJECT GUTENBERG EBOOK OCCULT CHEMISTRY***</p> +<p> </p> +<h3>E-text prepared by Clare Boothby, Keith Edkins,<br /> + and the Project Gutenberg Online Distributed Proofreading Team</h3> +<p> </p> +<hr class="full" /> +<p> </p> +<p> </p> +<h2>OCCULT CHEMISTRY</h2> + +<p class="center" style="margin-top: 2em;">Clairvoyant Observations on the<br /> +Chemical Elements</p> + +<p class="center" style="margin-top: 2em;">BY</p> + +<h3>ANNIE BESANT, <font class="sc">p.t.s.</font></h3> + +<p class="center" style="margin-top: 2em;">AND</p> + +<h3>CHARLES W. LEADBEATER</h3> + + <br clear="all" /> +<hr class="short" /> + +<p class="center" style="margin-top: 2em;"><i>Revised Edition edited by</i> A.P. <font class="sc">Sinnett</font></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">London</font></p> + +<h3>THEOSOPHICAL PUBLISHING HOUSE</h3> + +<p class="center" style="margin-top: 2em;">1, <font class="sc">Upper Woburn Place</font>, W.C. 1.</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>1919</h3> + + <br clear="all" /> +<hr /> + +<h3>EDITOR'S PREFACE.</h3> + + <br clear="all" /> +<hr class="short" /> + + <p>When undertaking to prepare a new edition of this book I received + permission from the authors to "throw it into the form in which you think + it would be most useful at the present time." It was left to my + discretion, "What to use and what to omit." I have not found it necessary + to avail myself to any considerable extent of this latter permission. But + as the contents of the book were originally arranged the reader was + ill-prepared to appreciate the importance of the later research for want + of introductory matter explaining how it began, and how the early + research led up to the later investigation. I have therefore contributed + an entirely new preliminary chapter which will, I hope, help the reader + to realise the credibility of the results attained when the molecular + forms and constitution of the numerous bodies examined were definitely + observed. I have not attempted to revise the records of the later + research in which I had no personal share, so from the beginning of + Chapter III to the end the book in its present form is simply a reprint + of the original edition except for the correction of a few trifling + misprints.</p> + + <p>I have thus endeavoured to bring into clear prominence at the outset + the scientific value of the light the book sheds on the constitution of + matter. The world owes a debt to scientific men of the ordinary type that + cannot be over-estimated, but though they have hitherto preferred to + progress gradually, from point to point, disliking leaps in the dark, the + leap now made is only in the dark for those who will not realise that the + progress to be accomplished by means of instrumental research must sooner + or later be supplemented by subtler methods. Physical science has reached + the conception that the atoms of the bodies hitherto called the chemical + elements are each composed of minor atoms. Instrumental research cannot + determine by how many, in each case. Occult research ascertained the + actual number in some cases by direct observation and then discovered the + law governing the numbers in all cases, and the relation of these numbers + to atomic weights. The law thus unveiled is a demonstration of the + accuracy of the first direct observations, and this principle once + established the credibility of accounts now given as to the arrangement + of minor atoms in the molecules of the numerous elements examined, seems + to me advanced to a degree approximating to proof.</p> + + <p>It remains to be seen—not how far, but rather how soon the + scientific world at large will accept the conclusions of this volume as a + definite contribution to science, blending the science of the laboratory + with that variety that has hitherto been called occult.</p> + + <br clear="all" /> +<hr /> + +<h3>CONTENTS.</h3> + + <div class="contents"> + <div class="stanza"> + <p>I.—<a href="#chap1"><font class="sc">A Preliminary Survey</font></a></p> + </div> + + <div class="stanza"> + <p>II.—<a href="#chap2"><font class="sc">Details of the Early Research</font></a></p> + </div> + + <div class="stanza"> + <p class="i4"><a href="#chap2b"><font class="sc">The Platonic Solids</font></a></p> + </div> + + <div class="stanza"> + <p>III.—<a href="#chap3"><font class="sc">The Later Researches</font></a></p> + </div> + </div> + <br clear="all" /> +<hr /> + + <p><a name="chap1"></a></p> + +<h2>OCCULT CHEMISTRY.</h2> + +<h3>CHAPTER I.</h3> + +<h3>A PRELIMINARY SURVEY.</h3> + + <p>The deep interest and importance of the research which this book + describes will best be appreciated if introduced by an account of the + circumstances out of which it arose. The first edition, consisting mainly + of articles reprinted from the <i>Theosophist</i>, dealt at once with the + later phases of the research in a way which, though intelligible to the + occult student, must have been rather bewildering to the ordinary reader. + These later phases, however, endow the earlier results with a + significance that in the beginning could only be vaguely conjectured. I + am the better entitled to perform the task that has been assigned to + me—that of preparing the present edition—by reason of the + fact that it was in my presence and at my instigation that the first + efforts were made to penetrate the mystery previously enshrouding the + ultimate molecule of matter.</p> + + <p>I remember the occasion vividly. Mr. Leadbeater was then staying at my + house, and his clairvoyant faculties were frequently exercised for the + benefit of myself, my wife and the theosophical friends around us. I had + discovered that these faculties, exercised in the appropriate direction, + were ultra-microscopic in their power. It occurred to me once to ask Mr. + Leadbeater if he thought he could actually <i>see</i> a molecule of + physical matter. He was quite willing to try, and I suggested a molecule + of gold as one which he might try to observe. He made the appropriate + effort, and emerged from it saying the molecule in question was far too + elaborate a structure to be described. It evidently consisted of an + enormous number of some smaller atoms, quite too many to count; quite too + complicated in their arrangement to be comprehended. It struck me at once + that this might be due to the fact that gold was a heavy metal of high + atomic weight, and that observation might be more successful if directed + to a body of low atomic weight, so I suggested an atom of hydrogen as + possibly more manageable. Mr. Leadbeater accepted the suggestion and + tried again. This time he found the atom of hydrogen to be far simpler + than the other, so that the minor atoms constituting the hydrogen atom + were countable. They were arranged on a definite plan, which will be + rendered intelligible by diagrams later on, and were eighteen in + number.</p> + + <p>We little realized at the moment the enormous significance of this + discovery, made in the year 1895, long before the discovery of radium + enabled physicists of the ordinary type to improve their acquaintance + with the "electron." Whatever name is given to that minute body it is + recognised now by ordinary science as well as by occult observation, as + the fundamental unit of physical matter. To that extent ordinary science + has overtaken the occult research I am dealing with, but that research + rapidly carried the occult student into regions of knowledge whither, it + is perfectly certain, the ordinary physicist must follow him at no + distant date.</p> + + <p>The research once started in the way I have described was seen to be + intensely interesting. Mrs. Besant almost immediately co-operated with + Mr. Leadbeater in its further progress. Encouraged by the success with + hydrogen, the two important gases, oxygen and nitrogen, were examined. + They proved to be rather more difficult to deal with than hydrogen but + were manageable. Oxygen was found to consist of 290 minor atoms and + nitrogen of 261. Their grouping will be described later on. The interest + and importance of the whole subject will best be appreciated by a rough + indication of the results first attained. The reader will then have more + patience in following the intricacies of the later discoveries.</p> + + <p>The figures just quoted were soon perceived to have a possible + significance. The atomic weight of oxygen is commonly taken as 16. That + is to say, an atom of oxygen is sixteen times heavier than an atom of + hydrogen. In this way, all through the table of atomic weights, hydrogen + is taken as unity, without any attempt being made to estimate its + absolute weight. But now with the atom of hydrogen dissected, so to + speak, and found to consist of 18 somethings, while the atom of oxygen + consisted of 290 of the same things, the sixteen to one relationship + reappears: 290 divided by 18 gives us 16 and a minute decimal fraction. + Again the nitrogen number divided by 18 gives us 14 and a minute fraction + as the result, and that is the accepted atomic weight of nitrogen. This + gave us a glimpse of a principle that might run all through the table of + atomic weights. For reasons having to do with other work, it was + impossible for the authors of this book to carry on the research further + at the time it was begun. The results already sketched were published as + an article in the magazine then called <i>Lucifer</i>, in November, 1895, + and reprinted as a separate pamphlet bearing the title "Occult + Chemistry," a pamphlet the surviving copies of which will one day be a + recognised vindication of the method that will at some time in the future + be generally applied to the investigation of Nature's mysteries. For the + later research which this volume deals with does establish the principle + with a force that can hardly be resisted by any fair-minded reader. With + patience and industry—the authors being assisted in the counting in + a way that will be described (and the method adopted involved a check + upon the accuracy of the counting)—the minor atoms of almost all + the known chemical elements, as they are commonly called, were counted + and found to bear the same relation to their atomic weights as had been + suggested by the cases of oxygen and nitrogen. This result throws back + complete proof on the original estimate of the number of minor atoms in + hydrogen, a figure which ordinary research has so far entirely failed to + determine. The guesses have been widely various, from unity to many + hundreds, but, unacquainted with the clairvoyant method, the ordinary + physicist has no means of reaching the actual state of the facts.</p> + + <p>Before going on with the details of the later research some very + important discoveries arising from the early work must first be + explained. As I have already said clairvoyant faculty of the appropriate + order directed to the minute phenomena of Nature is practically infinite + in its range. Not content with estimating the number of minor atoms in + physical molecules, the authors proceeded to examine the minor atoms + individually. They were found to be themselves elaborately complicated + structures which, in this preliminary survey of the whole subject, I will + not stop to explain (full explanation will be found later on) and they + are composed of atoms belonging to an ultra-physical realm of Nature with + which the occultist has long been familiar and describes as "the Astral + Plane." Some rather pedantic critics have found fault with the term, as + the "plane" in question is of course really a sphere entirely surrounding + the physical globe, but as all occultists understand the word, "plane" + simply signifies a condition of nature. Each condition, and there are + many more than the two under consideration, blends with its neighbour, + <i>via</i> atomic structure. Thus the atoms of the Astral plane in + combination give rise to the finest variety of physical matter, the ether + of space, which is not homogeneous but really atomic in its character, + and the minute atoms of which physical molecules are composed are atoms + of ether, "etheric atoms," as we have now learned to call them.</p> + + <p>Many physicists, though not all, will resent the idea of treating the + ether of space as atomic. But at all events the occultist has the + satisfaction of knowing that the great Russian chemist, Mendeleef, + preferred the atomic theory. In Sir William Tilden's recent book entitled + "Chemical Discovery and Invention in the Twentieth Century," I read that + Mendeleef, "disregarding conventional views," supposed the ether to have + a molecular or atomic structure, and in time all physicists must come to + recognise that the Electron is not, as so many suppose at present, an + atom of electricity, but an atom of ether carrying a definite unit charge + of electricity.</p> + + <p>Long before the discovery of radium led to the recognition of the + electron as the common constituent of all the bodies previously described + as chemical elements, the minute particles of matter in question had been + identified with the cathode rays observed in Sir William Crookes' vacuum + tubes. When an electric current is passed through a tube from which the + air (or other gas it may contain) has been almost entirely exhausted, a + luminous glow pervades the tube manifestly emanating from the cathode or + negative pole of the circuit. This effect was studied by Sir William + Crookes very profoundly. Among other characteristics it was found that, + if a minute windmill was set up in the tube before it was exhausted, the + cathode ray caused the vanes to revolve, thus suggesting the idea that + they consisted of actual particles driven against the vanes; the ray + being thus evidently something more than a mere luminous effect. Here was + a mechanical energy to be explained, and at the first glance it seemed + difficult to reconcile the facts observed with the idea creeping into + favour, that the particles, already invested with the name "electron," + were atoms of electricity pure and simple. Electricity was found, or + certain eminent physicists thought they had found, that electricity + <i>per se</i> had inertia. So the windmills in the Crookes' vacuum tubes + were supposed to be moved by the impact of electric atoms.</p> + + <p>Then in the progress of ordinary research the discovery of radium by + Madame Curie in the year 1902 put an entirely new face upon the subject + of electrons. The beta particles emanating from radium were soon + identified with the electrons of the cathode ray. Then followed the + discovery that the gas helium, previously treated as a separate element, + evolved itself as one consequence of the disintegration of radium. + Transmutation, till then laughed at as a superstition of the alchemist, + passed quietly into the region of accepted natural phenomena, and the + chemical elements were seen to be bodies built up of electrons in varying + number and probably in varying arrangements. So at last ordinary science + had reached one important result of the occult research carried on seven + years earlier. It has not yet reached the finer results of the occult + research—the <i>structure</i> of the hydrogen atom with its + eighteen etheric atoms and the way in which the atomic weights of all + elements are explained by the number of etheric atoms entering into their + constitution.</p> + + <p>The ether of space, though defying instrumental examination, comes + within scope of the clairvoyant faculty, and profoundly interesting + discoveries were made during what I have called the early research in + connexion with that branch of the inquiry. Etheric atoms combine to form + molecules in many different ways, but combinations involving fewer atoms + than the eighteen which give rise to hydrogen, make no impression on the + physical senses nor on physical instruments of research. They give rise + to varieties of molecular ether, the comprehension of which begins to + illuminate realms of natural mystery as yet entirely untrodden by the + ordinary physicist. Combinations below 18 in number give rise to three + varieties of molecular ether, the functions of which when they come to be + more fully studied will constitute a department of natural knowledge on + the threshold of which we already stand. Some day we may perhaps be + presented with a volume on Occult Physics as important in its way as the + present dissertation on Occult Chemistry.</p> + + <br clear="all" /> +<hr /> + + <p><a name="chap2"></a></p> + +<h3>CHAPTER II.</h3> + +<h3>DETAILS OF THE EARLY RESEARCH.</h3> + + <p>The article detailing the results of the research carried on in the + year 1895 (see the November issue for that year of the magazine then + called <i>Lucifer</i>), began with some general remarks about the + clairvoyant faculty, already discussed in the preceding chapter. The + original record then goes on as follows:—</p> + + <p>The physical world is regarded as being composed of between sixty and + seventy chemical elements, aggregated into an infinite variety of + combinations. These combinations fall under the three main heads of + solids, liquids and gases, the recognised substates of physical matter, + with the theoretical ether scarcely admitted as material. Ether, to the + scientist, is not a substate or even a state of matter, but is a + something apart by itself. It would not be allowed that gold could be + raised to the etheric condition as it might be to the liquid and gaseous; + whereas the occultist knows that the gaseous is succeeded by the etheric, + as the solid is succeeded by the liquid, and he knows also that the word + "ether" covers four substates as distinct from each other as are the + solids, liquids and gases, and that all chemical elements have their four + etheric substates, the highest being common to all, and consisting of the + ultimate physical atoms to which all elements are finally reducible. The + chemical atom is regarded as the ultimate particle of any element, and is + supposed to be indivisible and unable to exist in a free state. Mr. + Crookes' researches have led the more advanced chemists to regard the + atoms as compound, as a more or less complex aggregation of protyle.</p> + + <p>To astral vision ether is a visible thing, and is seen permeating all + substances and encircling every particle. A "solid" body is a body + composed of a vast number of particles suspended in ether, each vibrating + backwards and forwards in a particular field at a high rate of velocity; + the particles are attracted towards each other more strongly than they + are attracted by external influences, and they "cohere," or maintain + towards each other a definite relation in space. Closer examination shows + that the ether is not homogeneous but consists of particles of numerous + kinds, differing in the aggregations of the minute bodies composing them; + and a careful and more detailed method of analysis reveals that it has + four distinct degrees, giving us, with the solid, liquid and gaseous, + seven instead of four substates of matter in the physical world.</p> + + <p>These four etheric substates will be best understood if the method be + explained by which they were studied. This method consisted of taking + what is called an atom of gas, and breaking it up time after time, until + what proved to be the ultimate physical atom was reached, the breaking up + of this last resulting in the production of astral, and no longer + physical matter.</p> + + <p><a name="UltAtom"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-001.png" target="_blank"><img width="100%" src="images/oc-001.png" + alt="Substates of matter for hydrogen, oxygen and nitrogen." /></a> + </div> + <p>It is, of course, impossible to convey by words the clear conceptions + that are gained by direct vision of the objects of study, and the + accompanying diagram—cleverly drawn from the description given by + the investigators—is offered as a substitute, however poor, for the + lacking vision of the readers. The horizontal lines separate from each + other the seven substates of matter; solid, liquid, gas, ether 4, ether + 3, ether 2, ether 1. On the gas level are represented three chemical + atoms, one of hydrogen (H), one of oxygen (O), one of nitrogen (N). The + successive changes undergone by each chemical atom are shown in the + compartments vertically above it, the left-hand column showing the + breaking up of the hydrogen atom, the middle column that of the oxygen + atom, the right-hand column, that of the nitrogen atom. The ultimate + physical atom is marked <i>a</i>, and is drawn only once, although it is + the same throughout. The numbers 18, 290 and 261 are the numbers of the + ultimate physical atoms found to exist in a chemical atom.</p> + + <p>The dots indicate the lines along which force is observed to be + playing, and the arrowheads show the direction of the force. No attempt + has been made to show this below E 2 except in the case of the hydrogen. + The letters given are intended to help the reader to trace upwards any + special body; thus <i>d</i> in the oxygen chemical atom on the gas level + may be found again on E 4, E 3, and E 2. It must be remembered that the + bodies shown diagrammatically in no way indicate relative size; as a body + is raised from one substate to the one immediately above it, it is + enormously magnified for the purpose of investigation, and the ultimate + atom on E 1 is represented by the dot <i>a</i> on the gaseous level.</p> + + <p>The first chemical atom selected for this examination was an atom of + hydrogen (H). On looking carefully at it, it was seen to consist of six + small bodies, contained in an egg-like form. It rotated with great + rapidity on its own axis, vibrating at the same time, and the internal + bodies performed similar gyrations. The whole atom spins and quivers, and + has to be steadied before exact observation is possible. The six little + bodies are arranged in two sets of three, forming two triangles that are + not interchangeable, but are related to each other as object and image. + (The lines in the diagram of it on the gaseous sub-plane are not lines of + force, but show the two triangles; on a plane surface the + interpenetration of the triangles cannot be clearly indicated.) Further, + the six bodies are not all alike; they each contain three smaller + bodies—each of these being an ultimate physical atom—but in + two of them the three atoms are arranged in a line, while in the + remaining four they are arranged in a triangle.</p> + + <p>The wall of the limiting spheroid in which the bodies are enclosed + being composed of the matter of the third, or gaseous, kind, drops away + when the gaseous atom is raised to the next level, and the six bodies are + set free. They at once re-arrange themselves in two triangles, each + enclosed by a limiting sphere; the two marked <i>b</i> in the diagram + unite with one of those marked <i>b'</i> to form a body which shows a + positive character, the remaining three forming a second body negative in + type. These form the hydrogen particles of the lowest plane of ether, + marked E 4—ether 4—on the diagram. On raising these further, + they undergo another disintegration, losing their limiting walls; the + positive body of E 4, on losing its wall, becomes two bodies, one + consisting of the two particles, marked <i>b</i>, distinguishable by the + linear arrangement of the contained ultimate atoms, enclosed in a wall, + and the other being the third body enclosed in E 4 and now set free. The + negative body of E 4 similarly, on losing its wall, becomes two bodies, + one consisting of the two particles marked <i>b'</i>, and the second the + remaining body, being set free. These free bodies do not remain on E 3 + but pass immediately to E 2, leaving the positive and negative bodies, + each containing two particles, as the representatives of hydrogen on E 3. + On taking these bodies a step higher their wall disappears, and the + internal bodies are set free, those containing the atoms arranged + lineally being positive, and those with the triangular arrangement being + negative. These two forms represent hydrogen on E 2, but similar bodies + of this state of matter are found entering into other combinations, as + may be seen by referring to <i>f</i> on E 2 of nitrogen (N). On raising + these bodies yet one step further, the falling away of the walls sets the + contained atoms free, and we reach the ultimate physical atom, the matter + of E 1. The disintegration of this sets free particles of astral matter, + so that we have reached in this the limit of physical matter. The + Theosophical reader will notice with interest that we can thus observe + seven distinct substates of physical matter, and no more.</p> + + <p>The ultimate atom, which is the same in all the observed cases, is an + exceedingly complex body, and only its main characteristics are given in + the diagram. It is composed entirely of spirals, the spiral being in its + turn composed of spirillæ, and these again of minuter spirillæ. A fairly + accurate drawing is given in Babbitt's "Principles of Light and Colour," + p. 102. The illustrations there given of atomic combinations are entirely + wrong and misleading, but if the stove-pipe run through the centre of the + single atom be removed, the picture may be taken as correct, and will + give some idea of the complexity of this fundamental unit of the physical + universe.</p> + + <p>Turning to the force side of the atom and its combinations, we observe + that force pours in the heart-shaped depression at the top of the atom, + and issues from the point, and is changed in character by its passage; + further, force rushes through every spiral and every spirilla, and the + changing shades of colour that flash out from the rapidly revolving and + vibrating atom depend on the several activities of the spirals; sometimes + one, sometimes another, is thrown into more energetic action, and with + the change of activity from one spiral to another the colour changes.</p> + + <p>The building of a gaseous atom of hydrogen may be traced downward from + E 1, and, as stated above, the lines given in the diagram are intended to + indicate the play of the forces which bring about the several + combinations. Speaking generally, positive bodies are marked by their + contained atoms setting their points towards each other and the centre of + their combination, and repelling each other outwards; negative bodies are + marked by the heart-shaped depressions being turned inwards, and by a + tendency to move towards each other instead of away. Every combination + begins by a welling up of force at a centre, which is to form the centre + of the combination; in the first positive hydrogen combination, E 2, an + atom revolving at right angles to the plane of the paper and also + revolving on its own axis, forms the centre, and force, rushing out at + its lower point, rushes in at the depressions of two other atoms, which + then set themselves with their points to the centre; the lines are shown + in +b, right-hand figure. (The left-hand figure indicates the revolution + of the atoms each by itself.) As this atomic triad whirls round, it + clears itself a space, pressing back the undifferentiated matter of the + plane, and making to itself a whirling wall of this matter, thus taking + the first step towards building up the chemical hydrogen atom. A negative + atomic triad is similarly formed, the three atoms being symmetrically + arranged round the centre of out-welling force. These atomic triads then + combine, two of the linear arrangement being attracted to each other, and + two of the triangular, force again welling up and forming a centre and + acting on the triads as on a single atom, and a limiting wall being again + formed as the combination revolves round its centre. The next stage is + produced by each of these combinations on E 3 attracting to itself a + third atomic triad of the triangular type from E 2, by the setting up of + a new centre of up-welling force, following the lines traced in the + combinations of E 4. Two of these uniting, and their triangles + interpenetrating, the chemical atom is formed, and we find it to contain + in all eighteen ultimate physical atoms.</p> + + <p>The next substance investigated was oxygen, a far more complicated and + puzzling body; the difficulties of observation were very much increased + by the extraordinary activity shown by this element and the dazzling + brilliancy of some of its constituents. The gaseous atom is an ovoid + body, within which a spirally-coiled snake-like body revolves at a high + velocity, five brilliant points of light shining on the coils. The snake + appears to be a solid rounded body, but on raising the atom to E 4 the + snake splits lengthwise into two waved bodies, and it is seen that the + appearance of solidity is due to the fact that these spin round a common + axis in opposite directions, and so present a continuous surface, as a + ring of fire can be made by whirling a lighted stick. The brilliant + bodies seen in the atom are on the crests of the waves in the positive + snake, and in the hollows in the negative one; the snake itself consists + of small bead-like bodies, eleven of which interpose between the larger + brilliant spots. On raising these bodies to E 3 the snakes break up, each + bright spot carrying with it six beads on one side and five on the other; + these twist and writhe about still with the same extraordinary activity, + reminding one of fire-flies stimulated to wild gyrations. It can been + seen that the larger brilliant bodies each enclose seven ultimate atoms, + while the beads each enclose two. (Each bright spot with its eleven beads + is enclosed in a wall, accidentally omitted in the diagram.) On the next + stage, E 2, the fragments of the snakes break up into their constituent + parts; the positive and negative bodies, marked <i>d</i> and <i>d'</i>, + showing a difference of arrangement of the atoms contained in them. These + again finally disintegrate, setting free the ultimate physical atoms, + identical with those obtained from hydrogen. The number of ultimate atoms + contained in the gaseous atom of oxygen is 290, made up as + follows:—</p> + + <div class="poem"> + <div class="stanza"> + <p>2 in each bead, of which there are 110:</p> + <p>7 in each bright spot, of which there are 10;</p> + <p>2 x 110 + 70 = 290.</p> + </div> + </div> + <p>When the observers had worked out this, they compared it with the + number of ultimate atoms in hydrogen:—</p> + + <div class="poem"> + <div class="stanza"> + <p>290 / 18 = 16.11 +</p> + </div> + </div> + <p>The respective number of ultimate atoms contained in a chemical atom + of these two bodies are thus seen to closely correspond with their + accepted weight-numbers.</p> + + <p>It may be said in passing that a chemical atom of ozone appears as an + oblate spheroid, with the contained spiral much compressed and widened in + the centre; the spiral consists of three snakes, one positive and two + negative, formed in a single revolving body. On raising the chemical atom + to the next plane, the snake divides into three, each being enclosed in + its own egg.</p> + + <p>The chemical atom of nitrogen was the third selected by the students + for examination, as it seemed comparatively quiet in contrast with the + ever-excited oxygen. It proved, however, to be the most complicated of + all in its internal arrangements, and its quiet was therefore a little + deceptive. Most prominent was the balloon-shaped body in the middle, with + six smaller bodies in two horizontal rows and one large egg-shaped one in + the midst, contained in it. Some chemical atoms were seen in which the + internal arrangement of these contained bodies was changed and the two + horizontal rows became vertical; this change seemed to be connected with + a greater activity of the whole body, but the observations on this head + are too incomplete to be reliable. The balloon-shaped body is positive, + and is apparently drawn downwards towards the negative egg-shaped body + below it, containing seven smaller particles. In addition to these large + bodies, four small ones are seen, two positive and two negative, the + positive containing five and the negative four minuter spots. On raising + the gaseous atom to E 4, the falling away of the wall sets free the six + contained bodies, and both the balloon and the egg round themselves, + apparently with the removal of their propinquity, as though they had + exercised over each other some attractive influence. The smaller bodies + within the egg—marked <i>q</i> on E 4—are not on one plane, + and those within <i>n</i> and <i>o</i> form respectively square-based and + triangular-based pyramids. On raising all these bodies to E 3 we find the + walls fall away as usual, and the contents of each "cell" are set free: + <i>p</i> of E 4 contains six small bodies marked <i>k</i>, and these are + shown in <i>k</i> of E 3, as containing each seven little + bodies—marked <i>e</i>—each of which has within it two + ultimate atoms; the long form of <i>p</i> E 4—marked + <i>l</i>—appears as the long form <i>l</i> on E 3, and this has + three pairs of smaller bodies within it, <i>f'</i>, <i>g</i> and + <i>h</i>, containing respectively three, four and six ultimate atoms; + <i>q</i> of E 4, with its seven contained particles, <i>m</i>, has three + particles <i>m</i> on E 3, each showing three ultimate atoms within them; + <i>e</i> from <i>n</i> of E 4 becomes <i>i</i> of E 3, with contained + bodies, <i>e</i>, showing two ultimate atoms in each; while <i>e'</i> + from <i>o</i> of E 4 becomes <i>j</i> of E 3, each having three smaller + bodies within it, <i>e'</i>, with two ultimate atoms in each. On E 2, the + arrangement of these ultimate atoms is shown, and the pairs, <i>f'</i>, + <i>g</i> and <i>h</i> are seen with the lines of force indicated; the + triads in <i>f</i>—from <i>m</i> of E 3—are similarly shown, + and the duads in <i>e</i> and <i>e'</i>—from <i>i</i> and <i>j</i> + of E 3—are given in the same way. When all these bodies are raised + to E 1, the ultimate physical atoms are set free, identical, of course, + with that previously described. Reckoning up the number of ultimate + physical atoms in a chemical atom of nitrogen we find they amount to 261, + thus divided:—</p> + +<pre> + 62 + bodies with 2 ultimate atoms, 62 x 2 = 124 + 24 - " " 2 " " 24 x 2 = 48 + 21 - " " 3 " " 21 x 3 = 63 + 2 + " " 3 " " 2 x 3 = 6 + 2 + " " 4 " " 2 x 4 = 8 + 2 + " " 4 " " 2 x 6 = 12 + ---- + 261 +</pre> + <p>This again approaches closely the weight-number assigned to + nitrogen:—</p> + + <div class="poem"> + <div class="stanza"> + <p>261 / 18 =14.44 +</p> + </div> + </div> + <p>This is interesting as checking the observations, for weight-numbers + are arrived at in so very different a fashion, and especially in the case + of nitrogen the approximation is noteworthy, from the complexity of the + bodies which yield the number on analysis.</p> + + <p>Some other observations were made which went to show that as + weight-numbers increased, there was a corresponding increase in the + number of bodies discerned within the chemical atom; thus, gold showed + forty-seven contained bodies; but these observations need repetition and + checking. Investigation of a molecule of water revealed the presence of + twelve bodies from hydrogen and the characteristic snake of oxygen, the + encircling walls of the chemical atoms being broken away. But here again, + further observations are necessary to substantiate details. The present + paper is only offered as a suggestion of an inviting line of research, + promising interesting results of a scientific character; the observations + recorded have been repeated several times and are not the work of a + single investigator, and they are believed to be correct so far as they + go.</p> + + <p><a name="chap2b"></a></p> + +<h3>THE PLATONIC SOLIDS.</h3> + + <p>Some of our readers may be glad to have a drawing of the Platonic + solids, since they play so large a part in the building up of elements. + The regular solids are five, and five only; in each:</p> + + <div class="poem"> + <div class="stanza"> + <p>(1) The lines are equal.</p> + <p>(2) The angles are equal.</p> + <p>(3) The surfaces are equal.</p> + </div> + </div> + <div class="figright" style="width:50%;"> + <a href="images/oc-002.png" target="_blank"><img width="100%" src="images/oc-002.png" + alt="The five Platonic solids." /></a> + </div> + <p>It will be seen that the tetrahedron is the fundamental form, the + three-sided pyramid on a triangular base, <i>i.e.</i>, a solid figure + formed from four triangles. Two of these generate the cube and the + octahedron; five of these generate the dodecahedron and the + icosahedron.</p> + + <p>The rhombic dodecahedron is not regular, for though the lines and + surfaces are equal, the angles are not.</p> + +<h3>NOTES.</h3> + + <p>Mr. C. Jinarâjadâsa<a name="NtA_1" href="#Nt_1"><sup>[1]</sup></a> + writes:</p> + + <p>The asterisk put before metargon in the list of elements should be + omitted, for metargon had been discovered by Sir William Ramsey and Mr. + Travers at the same time as neon (see <i>Proceedings of the Royal + Society</i>, vol. lxiii, p. 411), and therefore before it was observed + clairvoyantly. It is not, however, given in the latest list of elements + in the Report of November 13, 1907, of the International Atomic Weights + Commission, so it would seem as though it were not yet fully + recognised.</p> + + <p>Neon was discovered in 1898 by Ramsey and Travers, and the weight + given to it was 22. This almost corresponds with our weight for + meta-neon, 22.33; the latest weight given to neon is 20, and that + corresponds within one-tenth to our weight, 19.9. From this it would seem + that neon was examined in the later investigations and meta-neon in the + earlier.</p> + + <p>He says further on a probable <i>fourth</i> Interperiodic Group:</p> + + <p>Thinking over the diagrams, it seemed to me likely that a fourth group + exists, coming on the paramagnetic side, directly under iron, cobalt, + nickel, just one complete swing of the pendulum after rhodium, ruthenium, + palladium. This would make four interperiodic groups, and they would come + also <i>periodically</i> in the table too.</p> + + <p>I took the diagram for Osmium, and in a bar postulated only three + columns for the first element of the new groups, <i>i.e.</i>, one column + less than in Osmium. This would make 183 atoms in a bar; the new group + then would follow in a bar, 183, 185, 187. Here I found to my surprise + that the third postulated group would have a remarkable relation to Os, + Ir, Pt.</p> + + <p>Thus</p> + +<pre> + Os.--245 (in a bar); less 60 = 185 + Ir. 247 less 60 = 187 + Pt. 249 less 60 = 189 +</pre> + <p>But strange to say <i>also</i></p> + +<pre> + Ruthenium (bar) 132 less 60--72 + Rhodium 134 less 60--74 + Palladium 136 less 60--76 +</pre> + <p>But 72, 74, 76, are Iron, Cobalt and Nickel.</p> + + <p>So there does probably exist a new group with bars (183), 185, 187, + 189, with atomic weights.</p> + +<pre> + X=bar 185; atoms 2590, wt. 143.3 + Y= 187, 2618, wt. 145.4 + Z= 189, 2646, wt. 147.0. +</pre> + <p>They come probably among the rare earths. Probably also Neodymium and + Praseodymium are two of them, for their weights are 143.6, 140.5.</p> + + <br clear="all" /> +<hr /> + + <p><a name="chap3"></a></p> + +<h3>CHAPTER III.</h3> + +<h3>THE LATER RESEARCHES.</h3> + + <p>The first difficulty that faced us was the identification of the forms + seen on focusing the sight on gases.<a name="NtA_2" + href="#Nt_2"><sup>[2]</sup></a> We could only proceed tentatively. Thus, + a very common form in the air had a sort of dumb-bell shape (see <a + href="#PlateI">Plate I</a>); we examined this, comparing our rough + sketches, and counted its atoms; these, divided by 18—the number of + ultimate atoms in hydrogen—gave us 23.22 as atomic weight, and this + offered the presumption that it was sodium. We then took various + substances—common salt, etc.—in which we knew sodium was + present, and found the dumb-bell form in all. In other cases, we took + small fragments of metals, as iron, tin, zinc, silver, gold; in others, + again, pieces of ore, mineral waters, etc., etc., and, for the rarest + substances, Mr. Leadbeater visited a mineralogical museum. In all, 57 + chemical elements were examined, out of the 78 recognized by modern + chemistry.</p> + + <p>In addition to these, we found 3 chemical waifs: an unrecognized + stranger between hydrogen and helium which we named occultum, for + purposes of reference, and 2 varieties of one element, which we named + kalon and meta-kalon, between xenon and osmium; we also found 4 varieties + of 4 recognized elements and prefixed meta to the name of each, and a + second form of platinum, that we named Pt. B. Thus we have tabulated in + all 65 chemical elements, or chemical atoms, completing three of Sir + William Crookes' lemniscates, sufficient for some amount of + generalization.</p> + + <p><a name="PlateI"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-003.png" target="_blank"><img width="100%" src="images/oc-003.png" + alt="Plate I. Sodium." /></a> + <font class="sc">Plate I. Sodium</font>. + </div> + <p>In counting the number of ultimate atoms in a chemical elemental atom, + we did not count them throughout, one by one; when, for instance, we + counted up the ultimate atoms in sodium, we dictated the number in each + convenient group to Mr. Jinarâjadâsa, and he multiplied out the total, + divided by 18, and announced the result. Thus: sodium (<i>see</i> Plate + I) is composed of an upper part, divisible into a globe and 12 funnels; a + lower part, similarly divided; and a connecting rod. We counted the + number in the upper part: globe—10; the number in two or three of + the funnels—each 16; the number of funnels—12; the same for + the lower part; in the connecting rod—14. Mr. Jinarâjadâsa + reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418: divided by + 18 = 23.22 recurring. By this method we guarded our counting from any + prepossession, as it was impossible for us to know how the various + numbers would result on addition, multiplication and division, and the + exciting moment came when we waited to see if our results endorsed or + approached any accepted weight. In the heavier elements, such as gold, + with 3546 atoms, it would have been impossible to count each atom without + quite unnecessary waste of time, when making a preliminary investigation. + Later, it may be worth while to count each division separately, as in + some we noticed that two groups, at first sight alike, differed by 1 or 2 + atoms, and some very slight errors may, in this way, have crept into our + calculations.</p> + + <p>In the following table is a list of the chemical elements examined; + the first column gives the names, the asterisk affixed to some indicating + that they have not yet been discovered by orthodox chemistry. The second + column gives the number of ultimate physical atoms contained in one + chemical atom of the element concerned. The third column gives the weight + as compared with hydrogen, taken as 18, and this is obtained by dividing + the calculated number of ultimate atoms by 18. The fourth column gives + the recognized weight-number, mostly according to the latest list of + atomic weights, the "International List" of 1905, given in Erdmann's + "Lehrbuch der Unorganischen Chemie." These weights differ from those + hitherto accepted, and are generally lighter than those given in earlier + text-books. It is interesting to note that our counting endorses the + earlier numbers, for the most part, and we must wait to see if later + observations will endorse the last results of orthodox chemistry, or + confirm ours.</p> + +<pre> +-------------------------------------------- +Hydrogen | 18 | 1 | 1 +*Occultum | 54 | 3 | -- +Helium | 72 | 4 | 3.94 +Lithium | 127 | 7.06 | 6.98 +Baryllium | 164 | 9.11 | 9.01 +Boron | 200 | 11.11 | 10.86 +Carbon | 216 | 12 | 11.91 +Nitrogen | 261 | 14.50 | 14.01 +Oxygen | 290 | 16.11 | 15.879 +Fluorine | 340 | 18.88 | 18.90 +Neon | 360 | 20 | 19.9 +*Meta-Neon | 402 | 22.33 | -- +Sodium | 418 | 23.22 | 22.88 +Magnesium | 432 | 24 | 24.18 +Aluminium | 486 | 27 | 26.91 +Silicon | 520 | 28.88 | 28.18 +Phosphorus | 558 | 31 | 30.77 +Sulphur | 576 | 32 | 31.82 +Chlorine | 639 | 35.50 | 35.473 +Potassium | 701 | 38.944 | 38.85 +Argon | 714 | 39.66 | 39.60 +Calcium | 720 | 40 | 39.74 +*Metargon | 756 | 42 | -- +Scandium | 792 | 44 | 43.78 +Titanium | 864 | 48 | 47.74 +Vanadium | 918 | 51 | 50.84 +Chromium | 936 | 52 | 51.74 +Manganese | 992 | 55.11 | 54.57 +Iron | 1008 | 56 | 55.47 +Cobalt | 1036 | 57.55 | 57.7 +Nickel | 1064 | 59.ll | 58.30 +Copper | 1139 | 63.277 | 63.12 +Zinc | 1170 | 65 | 64.91 +Gallium | 1260 | 70 | 69.50 +Germanium | 1300 | 72.22 | 71.93 +Arsenic | 1350 | 75 | 74.45 +Selenium | 1422 | 79 | 78.58 +Bromine | 1439 | 79.944 | 79.953 +Krypton | 1464 | 81.33 | 81.20 +*Meta-Krypton | 1506 | 83.66 | -- +Rubidium | 1530 | 85 | 84.85 +Strontium | 1568 | 87.11 | 86.95 +Yttrium | 1606 | 89.22 | 88.34 +Zirconium | 1624 | 90.22 | 89.85 +Niobium | 1719 | 95.50 | 93.25 +Molybdenum | 1746 | 97 | 95.26 +Ruthenium | 1848 | 102.66 | 100.91 +Rhodium | 1876 | 104.22 | 102.23 +Palladium | 1904 | 105.77 | 105.74 +Silver | 1945 | 108.055 | 107.93 +Cadmium | 2016 | 112 | 111.60 +Indium | 2052 | 114 | 114.05 +Tin | 2124 | 118 | 118.10 +Antimony | 2169 | 120.50 | 119.34 +Tellurium | 2223 | 123.50 | 126.64 +Iodine | 2287 | 127.055 | 126.01 +Xenon | 2298 | 127.66 | 127.10 +*Meta-Xenon | 2340 | 130 | -- +*Kalon | 3054 | 169.66 | -- +*Meta-Kalon | 3096 | 172 | -- +Osmium | 3430 | 190.55 | 189.55 +Iridium | 3458 | 192.11 | 191.56 +Platinum A | 3486 | 193.66 | 193.34 +*Platinum B | 3514 | 195.22 | -- +Gold | 3546 | 197 | 195.74 +-------------------------------------------- +</pre> + <p><a name="PlateII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-004.png" target="_blank"><img width="100%" src="images/oc-004.png" + alt="Plate II - Ultimate physical atoms." /></a> + PLATE II. MALE (left) and FEMALE (right). + </div> + <p>As the words "ultimate physical atom" must frequently occur, it is + necessary to state what we mean by the phrase. Any gaseous chemical atom + may be dissociated into less complicated bodies; these, again, into still + less complicated; these, again, into yet still less complicated. These + will be dealt with presently. After the third dissociation but one more + is possible; the fourth dissociation gives the ultimate physical atom.<a + name="NtA_3" href="#Nt_3"><sup>[3]</sup></a> This may vanish from the + physical plane, but it can undergo no further dissociation on it. In this + ultimate state of physical matter two types of atoms have been observed; + they are alike in everything save the direction of their whorls and of + the force which pours through them. In the one case force pours in from + the "outside," from fourth-dimensional space,<a name="NtA_4" + href="#Nt_4"><sup>[4]</sup></a> and passing through the atom, pours into + the physical world. In the second, it pours in from the physical world, + and out through the atom into the "outside" again,<a + href="#Nt_4"><sup>[4]</sup></a> <i>i.e.</i>, vanishes from the physical + world. The one is like a spring, from which water bubbles out; the other + is like a hole, into which water disappears. We call the atoms from which + force comes out <i>positive</i> or <i>male</i>; those through which it + disappears, <i>negative</i> or <i>female</i>. All atoms, so far as + observed, are of one or other of these two forms. (Plate II.)</p> + + <p>It will be seen that the atom is a sphere, slightly flattened, and + there is a depression at the point where the force flows in, causing a + heart-like form. Each atom is surrounded by a field, formed of the atoms + of the four higher planes, which surround and interpenetrate it.</p> + + <p>The atom can scarcely be said to be a "thing," though it is the + material out of which all things physical are composed. It is formed by + the flow of the life-force<a name="NtA_5" href="#Nt_5"><sup>[5]</sup></a> + and vanishes with its ebb. When this force arises in "space"<a + name="NtA_6" href="#Nt_6"><sup>[6]</sup></a>—the apparent void + which must be filled with substance of some kind, of inconceivable + tenuity—atoms appear; if this be artificially stopped for a single + atom, the atom disappears; there is nothing left. Presumably, were that + flow checked but for an instant, the whole physical world would vanish, + as a cloud melts away in the empyrean. It is only the persistence of that + flow<a name="NtA_7" href="#Nt_7"><sup>[7]</sup></a> which maintains the + physical basis of the universe.<a name="NtA_8" + href="#Nt_8"><sup>[8]</sup></a></p> + + <p>In order to examine the construction of the atom, a space is + artificially made<a name="NtA_9" href="#Nt_9"><sup>[9]</sup></a>; then, + if an opening be made in the wall thus constructed, the surrounding force + flows in, and three whorls immediately appear, surrounding the "hole" + with their triple spiral of two and a half coils, and returning to their + origin by a spiral within the atom; these are at once followed by seven + finer whorls, which following the spiral of the first three on the outer + surface, and returning to their origin by a spiral within that, flowing + in the opposite direction—form a caduceus with the first three. + Each of the three coarser whorls, flattened out, makes a closed circle; + each of the seven finer ones, similarly flattened out, makes a closed + circle. The forces which flow in them, again, come from "outside," from a + fourth-dimensional space.<a name="NtA_10" + href="#Nt_10"><sup>[10]</sup></a> Each of the finer whorls is formed of + seven yet finer ones, set successively at right angles to each other, + each finer than its predecessor; these we call spirillæ.<a name="NtA_11" + href="#Nt_11"><sup>[11]</sup></a></p> + + <p>It will be understood from the foregoing, that the atom cannot be said + to have a wall of its own, unless these whorls of force can be so + designated; its "wall" is the pressed back "space." As said in 1895, of + the chemical atom, the force "clears itself a space, pressing back the + undifferentiated matter of the plane, and making to itself a whirling + wall of this matter." The wall belongs to space, not to the atom.</p> + + <p>In the three whorls flow currents of different electricities; the + seven vibrate in response to etheric waves of all kinds—to sound, + light, heat, etc.; they show the seven colours of the spectrum; give out + the seven sounds of the natural scale; respond in a variety of ways to + physical vibration—flashing, singing, pulsing bodies, they move + incessantly, inconceivably beautiful and brilliant.<a name="NtA_12" + href="#Nt_12"><sup>[12]</sup></a></p> + + <p>The atom has—as observed so far—three proper motions, + <i>i.e.</i>, motions of its own, independent of any imposed upon it from + outside. It turns incessantly upon its own axis, spinning like a top; it + describes a small circle with its axis, as though the axis of the + spinning top moved in a small circle; it has a regular pulsation, a + contraction and expansion, like the pulsation of the heart. When a force + is brought to bear upon it, it dances up and down, flings itself wildly + from side to side, performs the most astonishing and rapid gyrations, but + the three fundamental motions incessantly persist. If it be made to + vibrate, as a whole, at the rate which gives any one of the seven colors, + the whorl belonging to that color glows out brilliantly.</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-005.png" target="_blank"><img width="100%" src="images/oc-005.png" + alt="Arrangement of atoms in an electric current." /></a> + </div> + <p>An electric current brought to bear upon the atoms checks their proper + motions, <i>i.e.</i>, renders them slower; the atoms exposed to it + arrange themselves in parallel lines, and in each line the heart-shaped + depression receives the flow, which passes out through the apex into the + depression of the next, and so on. The atoms always set themselves to the + current. The well-known division of diamagnetic and paramagnetic depends + generally on this fact, or on an analogous action on molecules, as may be + seen in the accompanying diagrams.<a name="NtA_13" + href="#Nt_13"><sup>[13]</sup></a></p> + + <p>Two atoms, positive and negative, brought near to each other, attract + each other, and then commence to revolve round each other, forming a + relatively stable duality; such a molecule is neutral. Combinations of + three or more atoms are positive, negative or neutral, according to the + internal molecular arrangement; the neutral are relatively stable, the + positive and negative are continually in search of their respective + opposites, with a view to establishing a relatively permanent union.</p> + + <p>Three states of matter exist between the atomic state and the + gaseous—the state in which the chemical atoms are found, the + recognized chemical elements; for our purposes we may ignore the liquid + and solid states. For the sake of clearness and brevity in description, + we have been obliged to name these states; we call the atomic state of + the chemist <i>elemental</i>; the state which results from breaking up + chemical elements, <i>proto-elemental</i>; the next higher, + <i>meta-proto-elemental</i>; the next higher, + <i>hyper-meta-proto-elemental</i>; then comes the atomic state. These are + briefly marked as El., Proto., Meta., and Hyper.<a name="NtA_14" + href="#Nt_14"><sup>[14]</sup></a></p> + + <p>The simplest unions of atoms, never, apparently consisting of more + than seven, form the first molecular state of physical matter.</p> + + <p><a name="Hyper"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-006.png" target="_blank"><img width="100%" src="images/oc-006.png" + alt="Types of Hyper-Meta-Proto-Elemental Matter." /></a> + <font class="sc">Types of Hyper-Meta-Proto-Elemental Matter</font>. + </div> + <p>Here are some characteristic combinations of the Hyper state; the atom + is conventional, with the depression emphasised; the lines, always + entering at the depression and coming out at the apex, show the + resultants of lines of force; where no line appears entering the + depression, the force wells up from fourth-dimensional space; where no + line appears leaving the apex, the force disappears into + fourth-dimensional space; where the point of entry and departure is + outside the atoms, it is indicated by a dot.<a name="NtA_15" + href="#Nt_15"><sup>[15]</sup></a></p> + + <p>The molecules show all kinds of possible combinations; the + combinations spin, turn head over heels, and gyrate in endless ways. Each + aggregation is surrounded with an apparent cell-wall, the circle or oval, + due to the pressure on the surrounding matter caused by its whirling + motion; they strike on each other<a name="NtA_16" + href="#Nt_16"><sup>[16]</sup></a> and rebound, dart hither and thither, + for reasons we have not distinguished.</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-007.png" target="_blank"><img width="100%" src="images/oc-007.png" + alt="Types of Meta-Proto-Elemental Matter" /></a> + <font class="sc">Types of Meta-Proto-Elemental Matter</font>. + </div> + <p>The Meta state, in some of its combinations, appears at first sight to + repeat those of the Hyper state; the only obvious way of distinguishing + to which some of the molecules of less complexity belong is to pull them + out of the "cell-wall"; if they are Hyper molecules they at once fly off + as separate atoms; if they are Meta molecules they break up into two or + more molecules containing a smaller number of atoms. Thus one of the Meta + molecules of iron, containing seven atoms, is identical in appearance + with a Hyper heptad, but the latter dissociates into seven atoms, the + former into two triads and a single atom. Long-continued research into + the detailed play of forces and their results is necessary; we are here + only able to give preliminary facts and details—are opening up the + way. The following may serve as characteristic Meta types:—</p> + + <p>These are taken from constituents of the various elements; 1 from Gl; + 2 and 3 from Fe; 4 from Bo; 5, 6 and 7 from C; 8 from He; 9 from Fl; 10, + 11, 12 from Li; 13 and 14 from Na. Others will be seen in the course of + breaking up the elements.</p> + + <p>The Proto state preserves many of the forms in the elements, modified + by release from the pressure to which they are subjected in the chemical + atom. In this state various groups are thus recognizable which are + characteristic of allied metals.</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-008.png" target="_blank"><img width="100%" src="images/oc-008.png" + alt="Types of Proto-Elemental Matter" /></a> + <font class="sc">Types of Proto-Elemental Matter</font>. + </div> + <p>These are taken from the products of the first disintegration of the + chemical atom, by forcibly removing it from its hole. The groups fly + apart, assuming a great variety of forms often more or less geometrical; + the lines between the constituents of the groups, where indicated, no + longer represent lines of force, but are intended to represent the + impression of form, <i>i.e.</i>, of the relative position and motion of + the constituents, made on the mind of the observer. They are elusive, for + there are no lines, but the appearance of lines is caused by the rapid + motion of the costituents up and down, or along them backwards and + forwards. The dots represent atoms, or groups of atoms, within the + proto-elements. 1 is found in C; 2 and 3 in He; 4 in Fl; 5 in Li; 6 in N; + 7 in Ru; 8 in Na; 9 and 10 in Co; 11 in Fe; 12 in Se. We shall return to + these when analysing the elements, and shall meet many other + proto-elemental groupings.</p> + + <p>The first thing which is noticed by the observer, when he turns his + attention to the chemical atoms, is that they show certain definite + forms, and that within these forms, modified in various ways, + sub-groupings are observable which recur in connexion with the same + modified form. The main types are not very numerous, and we found that, + when we arranged the atoms we had observed, according to their external + forms, they fell into natural classes; when these, in turn, were compared + with Sir William Crookes' classification, they proved to be singularly + alike. Here is his arrangement of the elements, as it appeared in the + <i>Proceedings of the Royal Society</i>, in a paper read on June 9th, + 1898.</p> + + <p><a name="Crookes"></a></p> + + <div class="figcenter" style="width:50%;"> + <a href="images/oc-009.png" target="_blank"><img width="100%" src="images/oc-009.png" + alt="Sir William Crookes' classification." /></a> + </div> + <p>This is to be read, following the lines of the "figures of eight": H, + He, Li, Gl, B, C, N, and so on, each successive element being heavier + than the one preceding it in order. The disks which fall immediately + below each other form a class; thus: H, Cl, Br, I; these resemble each + other in various ways, and, as we shall presently see, the same forms and + groupings re-appear.</p> + + <p>Another chart—taken from Erdmann's + <i>Lehrbuch</i>—arranges the elements on a curved line, which + curiously resembles the curves within the shell of a nautilus. The + radiating lines show the classes, the whole diameter building up a + family; it will be observed that there is an empty radius between + hydrogen and helium, and we have placed occultum there; on the opposite + radius, iron, rubidium and osmium are seen.</p> + + <div class="figcenter" style="width:50%;"> + <a href="images/oc-010.png" target="_blank"><img width="100%" src="images/oc-010.png" + alt="Chart taken from Erdmann's Lehrbuch." /></a> + </div> + <p>The external forms may be classified as follows; the internal details + will be dealt with later :—</p> + + <p><a name="PlateIII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-011.png" target="_blank"><img width="100%" src="images/oc-011.png" + alt="Plate III." /></a> + <font class="sc">Plate III</font>. + </div> + <p>1. <i>The Dumb-bell.</i>—The characteristics of this are a + higher and lower group, each showing 12 projecting funnels, grouped round + a central body, and a connecting rod. It appears in sodium, copper, + silver, and gold,<a name="NtA_17" href="#Nt_17"><sup>[17]</sup></a> and + gold is given (1 on <a href="#PlateIII">Plate III</a>) as the most + extremely modified example of this form. The 12 almond-like projections, + above and below, are severally contained in shadowy funnels, impossible + to reproduce in the drawing; the central globe contains three globes, and + the connecting portion has swollen out into an egg, with a very + complicated central arrangement. The dumb-bell appears also in chlorine, + bromine and iodine, but there is no trace of it in hydrogen, the head of + the group. We have not met it elsewhere. It may be remarked that, in Sir + William Crookes' scheme, in which they are all classed as monads, these + two groups are the nearest to the neutral line, on the ingoing and + outgoing series, and are respectively positive and negative.</p> + + <p>II and II<i>a.</i> <i>The Tetrahedron.</i>—The characteristics + of this form are four funnels, containing ovoid bodies, opening on the + face of a tetrahedron. The funnels generally, but not always, radiate + from a central globe. We give beryllium (glucinum) as the simplest + example (2 on <a href="#PlateIII">Plate III</a>), and to this group + belong calcium and strontium. The tetrahedron is the form of chromium and + molybdenum, but not that of the head of their group, oxygen, which is, + like hydrogen, <i>sui generis</i>. These two groups are marked in + orthodox chemistry as respectively positive and negative, and are closely + allied. Another pair of groups show the same tetrahedral form: magnesium, + zinc and cadmium, positive; sulphur, selenium and tellurium, negative. + Selenium is a peculiarly beautiful element, with a star floating across + the mouth of each funnel; this star is extremely sensitive to light, and + its rays tremble violently and bend if a beam of light falls on it. All + these are dyads.</p> + + <p>The tetrahedron is not confined to the external form of the above + atoms; it seems to be one of the favourite forms of nature, and + repeatedly appears in the internal arrangements. There is one tetrahedron + within the unknown element occultum; two appear in helium (3 on <a + href="#PlateIII">Plate III</a>); yttrium has also two within its cube, as + has germanium; five, intersecting, are found in neon, meta-neon, argon, + metargon, krypton, meta-krypton, xenon, meta-xenon, kalon, meta-kalon, + tin, titanium and zirconium. Gold contains no less than twenty + tetrahedra.</p> + + <p>III. <i>The Cube.</i>—The cube appears to be the form of triads. + It has six funnels, containing ovoids, and opening on the faces of the + cube. Boron is chosen as an example (4 on <a href="#PlateIII">Plate + III</a>). Its group members, scandium and yttrium, have the same form; we + have not examined the fourth; the group is positive. Its negative + complement consists of nitrogen, vanadium and niobium, and we have again + to note that nitrogen, like hydrogen and oxygen, departs from its group + type. Two other triad groups, the positive aluminium, gallium and indium + (the fourth unexamined) and the negative phosphorus, arsenic and antimony + (the fourth unexamined), have also six funnels opening on the faces of a + cube.</p> + + <p><a name="Octahedron"></a></p> + + <p>IV. <i>The Octahedron.</i>—The simplest example of this is + carbon (5 on <a href="#PlateIII">Plate III</a>). We have again the funnel + with its ovoids, but now there are eight funnels opening on the eight + faces of the octahedron. In titanium (6 on <a href="#PlateIII">Plate + III</a>) the form is masked by the protruding arms, which give the + appearance of the old Rosicrucian Cross and Rose, but when we look into + the details later, the carbon type comes out clearly. Zirconium is + exactly like titanium in form, but contains a large number of atoms. We + did not examine the remaining two members of this group. The group is + tetratomic and positive. Its negative pendant shows the same form in + silicon, germanium and tin; again, the fourth was unexamined.</p> + + <p><a name="PlateIV"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-012.png" target="_blank"><img width="100%" src="images/oc-012.png" + alt="Plate IV." /></a> + <font class="sc">Plate IV</font>. + </div> + <p>V. <i>The Bars.</i>—These characterise a set of closely allied + groups, termed "inter-periodic." Fourteen bars (or seven crossed) radiate + from a centre, as in iron (1 on Plate IV), and the members of each + group—iron, nickel, cobalt; ruthenium, rhodium, palladium; osmium, + iridium, platinum—differ from each other by the weight of each bar, + increasing in orderly succession; the details will be given later. + Manganese is often grouped with iron, nickel, and cobalt (<i>see</i> + Crookes' lemniscates), but its fourteen protruding bodies repeat the + "lithium spike" (proto-element 5) and are grouped round a central ovoid. + This would appear to connect it with lithium (2 on Plate IV) rather than + with fluorine (3 in Plate IV), with which it is often classed. The + "lithium spike" re-appears in potassium and rubidium. These details, + again, will come out more clearly later.</p> + + <p>VI. <i>The Star.</i>—A flat star, with five interpenetrating + tetrahedra in the centre, is the characteristic of neon and its allies (4 + on Plate IV) leaving apart helium, which, as may be seen by referring to + 3, Plate IV, has an entirely different form.</p> + + <p>There are thus six clearly defined forms, typical of classes, with + two—lithium and fluorine—of doubtful affinities. It is worthy + of notice that in diatomic elements <i>four</i> funnels open on the faces + of tetrahedra; in triatomic, <i>six</i> funnels on the faces of cubes; in + tetratomic, <i>eight</i> funnels on the faces of octahedra.</p> + + <p>Thus we have a regular sequence of the platonic solids, and the + question suggests itself, will further evolution develop elements shaped + to the dodecahedron and the icosahedron?</p> + + <br clear="all" /> +<hr class="short" /> + + <br clear="all" /> +<h3>II.</h3> + + <p>We now pass from the consideration of the outer forms of the chemical + elements to a study of their internal structure, the arrangement within + the element of more or less complicated + groups—proto-elements—capable of separate, independent + existence; these, once more, may be dissociated into yet simpler + groups—hyper-meta-proto-elements—equally capable of separate, + independent existence, and resolvable into single ultimate physical + atoms, the irreducible substratum of the physical world (see + <i>Theosophist</i>, 1908, pp. 354-356).<a name="NtA_18" + href="#Nt_18"><sup>[18]</sup></a></p> + + <p>We shall have to study the general internal structure, and then the + breaking up of each element, and the admirable diagrams, patiently worked + out by Mr. Jinarâjadâsa, will make the study comparatively easy to carry + on.</p> + + <p>The diagrams, of course, can only give a very general idea of the + facts they represent; they give groupings and show relations, but much + effort of the imagination is needed to transform the two-dimensional + diagram into the three-dimensional object. The wise student will try to + visualize the figure from the diagram. Thus the two triangles of hydrogen + are not in one plane; the circles are spheres, and the atoms within them, + while preserving to each other their relative positions, are in swift + movement in three-dimensional space. Where five atoms are seen, as in + bromine and iodine, they are generally arranged with the central atom + above the four, and their motion indicates lines which erect four plane + triangles—meeting at their apices—on a square base, forming a + square-based four-sided pyramid. Each dot represents a single ultimate + atom. The enclosing lines indicate the impression of form made on the + observer, and the groupings of the atoms; the groups will divide along + these lines, when the element is broken up, so that the lines have + significance, but they do not exist as stable walls or enclosing films, + but rather mark limits, not lines, of vibrations. It should be noted that + it is not possible to show five of the prisms in the five intersecting + tetrahedra of prisms, and 30 atoms must, therefore, be added in + counting.</p> + + <p>The diagrams are not drawn to scale, as such drawing would be + impossible; the dot representing the atom is enormously too large + compared with the enclosures, which are absurdly too small; a scale + drawing would mean an almost invisible dot on a sheet of many yards + square.</p> + + <p>The use of the words "positive" and "negative" needs to be guarded by + the following paragraphs from the article on "Chemistry" in the + <i>Encyclopædia Britannica</i>. We use the words in their ordinary + text-book meaning, and have not, so far, detected any characteristics + whereby an element can be declared, at sight, to be either positive or + negative:—</p> + + <p>"When binary compounds, or compounds of two elements, are decomposed + by an electric current, the two elements make their appearance at + opposite poles. These elements which are disengaged at the negative pole + are termed electro-positive or positive or basylous elements, while those + disengaged at the positive pole are termed electro-negative or negative + or chlorous elements. But the difference between these two classes of + elements is one of degree only, and they gradually merge into each other; + moreover the electric relations of elements are not absolute, but vary + according to the state of combination in which they exist, so that it is + just as impossible to divide the elements into two classes according to + this property as it is to separate them into two distinct classes of + metals and non-metals."</p> + + <p>We follow here the grouping according to external forms, and the + student should compare it with the groups marked in the lemniscate + arrangement shown in Article II (p. 377, properly p. 437, February), + reading the group by the disks that fall below each other; thus the first + group is H, Cl, Br, I (hydrogen, chlorine, bromine, iodine) and a blank + for an undiscovered element. The elements grow denser in descending + order; thus hydrogen is an invisible gas; chlorine a denser gas visible + by its colour; bromine is a liquid; iodine is a solid—all, of + course, when temperature and pressure are normal. By the lowering of + temperature and the increase of pressure, an element which is normally + gaseous becomes a liquid, and then a solid. Solid, liquid, gaseous, are + three interchangeable states of matter, and an element does not alter its + constitution by changing its state. So far as a chemical "atom" is + concerned, it matters not whether it be drawn for investigation from a + solid, a liquid, or a gas; but the internal arrangements of the "atoms" + become much more complicated as they become denser and denser, as is seen + by the complex arrangements necessitated by the presence of the 3546 + ultimate atoms contained in the chemical "atom" of gold, as compared with + the simple arrangement of the 18 ultimate atoms of hydrogen.</p> + + <p>According to the lemniscate arrangement, we should commence with + hydrogen as the head of the first negative group, but as it differs + wholly from those placed with it, it is better to take it by itself. + Hydrogen is the lightest of the known elements, and is therefore taken as + 1 in ordinary chemistry, and all atomic weights are multiples of this. We + take it as 18, because it contains eighteen ultimate atoms, the smallest + number we have found in a chemical element. So our "number-weights" are + obtained by dividing the total number of atoms in an element by 18 (see + p. 349, January).</p> + + <p><a name="PlateV"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-013.png" target="_blank"><img width="100%" src="images/oc-013.png" + alt="Plate V." /></a> + <font class="sc">Plate</font> V. + </div> +<font class="sc">Hydrogen</font> (Plate V, 1).—Hydrogen not only stands apart +from its reputed group by not having the characteristic dumb-bell +shape, well shown in sodium (<a href="#PlateI">Plate I</a>, opposite p. 349, +January), but it also stands apart in being positive, serving as a +base, not as a chlorous, or acid, radical, thus "playing the part +of a metal," as in hydrogen chloride (hydrochloric acid), hydrogen +sulphate (sulphuric acid), etc. + + <p>It is most curious that hydrogen, oxygen and nitrogen, the most widely + spread gases, all differ fundamentally in form from the groups they + reputedly head.<a name="NtA_19" href="#Nt_19"><sup>[19]</sup></a> + Hydrogen was the first chemical element examined by us, nearly thirteen + years ago, and I reproduce here the substance of what I wrote in + November, 1895, for we have nothing to add to nor amend in it.</p> + + <p>Hydrogen consists of six small bodies, contained in an egg-like form + (the outer forms are not given in the diagrams). The six little bodies + are arranged in two sets of three, forming two triangles which are not + interchangeable, but are related to each other as object and image. The + six bodies are not all alike; they each contain three ultimate physical + atoms, but in four of the bodies the three atoms are arranged in a + triangle, and in the remaining two in a line.</p> + +<pre> +HYDROGEN: 6 bodies of 3 18 + Atomic weight 1 + Number weight 18/18 1 +</pre> + <br clear="all" /> +<p class="center" style="margin-top: 2em;">I.—<font class="sc">The Dumb-bell Group</font>.</p> + + <p>I <i>a</i>.—This group consists of Cl, Br, and I (chlorine, + bromine and iodine); they are monads, diamagnetic and negative.</p> + +<font class="sc">Chlorine</font> (<a href="#PlateV">Plate V</a>, 2).—As already said, the general form is +that of the dumb-bell, the lower and upper parts each consisting +of twelve funnels, six sloping upwards and six downwards, the +funnels radiating outwards from a central globe, and these two +parts being united by a connecting rod (see, again, sodium, +<a href="#PlateI">Plate I</a>). + + <p>The funnel (shown flat as an isosceles triangle, standing on its apex) + is a somewhat complicated structure, of the same type as that in sodium + (<a href="#PlateVI">Plate VI, 2</a>), the difference consisting in the + addition of one more globe, containing nine additional atoms. The central + globe is the same as in sodium, but the connecting rod differs. We have + here a regular arrangement of five globes, containing three, four, five, + four, three atoms respectively, whereas sodium has only three bodies, + containing four, six, four. But copper and silver, its congeners, have + their connecting rods of exactly the same pattern as the chlorine rod, + and the chlorine rod reappears in both bromine and iodine. These close + similarities point to some real relation between these groups of + elements, which are placed, in the lemniscates, equi-distant from the + central line, though one is on the swing which is going towards that line + and the other is on the swing away from it.</p> + +<pre> +CHLORINE: Upper part {12 funnels of 25 atoms 300 + {Central globe 10 + Lower part same 310 + Connecting rod 19 + ---- + Total 639 + ---- + Atomic weight 35.473 + Number weight 639/18 35.50 +</pre> + <p>(The Atomic Weights are mostly from Erdmann, and the Number Weights + are those ascertained by us by counting the atoms as described on p. 349, + January, and dividing by 18. Prof. T.W. Richards, in <i>Nature</i>, July + 18, 1907, gives 35.473.)</p> + +<font class="sc">Bromine</font> (<a href="#PlateV">Plate V</a>, 3).—In bromine, each funnel has three +additional bodies, ovoid in shape, an addition of 33 atoms being +thus made without any disturbance of form; two pairs of atoms +are added to the central globe, and a rearrangement of the atoms +is effected by drawing together and lessening the swing of the +pair of triplets, thus making symmetrical room for the newcomers. +The connecting rod remains unchanged. The total +number of atoms is thus raised from the 639 of chlorine to 1439. +Over and over again, in these investigations, were we reminded +of Tyndall's fascinating description of crystal building, and his +fancy of the tiny, ingenious builders busied therein. Truly are +there such builders, and the ingenuity and effectiveness of their +devices are delightful to see.<a name="NtA_20" href="#Nt_20"><sup>[20]</sup></a> + +<pre> +BROMINE: Upper part {12 funnels of 58 atoms 696 + {Central globe 14 + Lower part same 710 + Connecting rod 19 + ---- + Total 1439 + ---- + Atomic weight 79.953 + Number weight 1459/18 79.944 +</pre> +<font class="sc">Iodine</font> (<a href="#PlateV">Plate V</a>, 4).—We find herein that the central globe +gains 4 atoms, the two pairs becoming 2 quartets; the connecting +rod exactly reproduces the rods of chlorine and bromine; +the funnel is also that of bromine, except that five bodies, containing +35 atoms, are added to it. The 1439 atoms of bromine +are thus raised to 2887. + +<pre> +IODINE: Upper Part {12 funnels of 90 atoms 1116 + {Central globe 18 + Lower part same 1134 + Connecting rod 19 + ---- + Total 2287 + ---- + Atomic weight 126.01 + Number weight 2287/18 127.055 +</pre> + <p>The plan underlying the building up of groups is here clearly shown; a + figure is built up on a certain plan, in this case a dumb-bell; in the + succeeding members of the group additional atoms are symmetrically + introduced, modifying the appearance, but following the general idea; in + this case the connecting rod remains unaltered, while the two ends become + larger and larger, more and more overshadowing it, and causing it to + become shorter and thicker. Thus a group is gradually formed by + additional symmetrical additions. In the undiscovered remaining member of + the group we may suppose that the rod will have become still more + egg-like, as in the case of gold.</p> + + <p>I <i>b</i>.—The corresponding positive group to that which we + have been considering consists of Na, Cu, Ag, and Au (sodium, copper, + silver and gold), with an empty disk between silver and gold, showing + where an element ought to be. These four elements are monads, + diamagnetic, and positive, and they show the dumb-bell arrangement, + although it is much modified in gold; we may presume that the + undiscovered element between silver and gold would form a link between + them.</p> + + <p><a name="PlateVI"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-014.png" target="_blank"><img width="100%" src="images/oc-014.png" + alt="Plate VI." /></a> + <font class="sc">Plate</font> VI. + </div> +<font class="sc">Sodium</font> (Plate VI, 2) has been already described (p. 349, +January), as a type of the group, so we need only refer to its +internal arrangement in order to note that it is the simplest of +the dumb-bell group. Its twelve funnels show only four enclosed +bodies, the same as we see in chlorine, bromine, iodine, +copper and silver, and which is very little modified in gold. Its +central globe is the simplest of all, as is its connecting rod. +We may therefore take it that sodium is the ground-plan of the +whole group. + +<pre> +SODIUM: Upper part + { 12 funnels of 16 each 192 + { Central globe 10 + Lower part same 202 + Connecting rod 14 + ---- + Total 418 + ---- + Atomic weight 23.88 + Number weight 418/19 23.22 +</pre> + <p><a name="CompCu"></a></p> + +<font class="sc">Copper</font> (<a href="#PlateVI">Plate VI</a>, 3) introduces an addition in the funnel, +that we shall find elsewhere, <i>e.g.</i>, in silver, gold, iron, platinum, +zinc, tin, the triangular arrangement near the mouth of the +funnel and adds to the ten atoms in this nineteen more in three +additional enclosed bodies, thus raising the number of atoms in +a funnel from the sixteen of sodium to forty-five. The number +in the central globe is doubled, and we meet for the first time +the peculiar cigar or prism-shaped six-atomed arrangement, that +is one of the most common of atomic groups. It ought to +imply some definite quality, with its continual recurrence. The +central column is the three, four, five, four, three, arrangement +already noted. + +<pre> +COPPER: Upper part {12 funnels of 45 atoms 540 + {Central globe 20 + Lower part same 560 + Connecting rod 19 + ---- + Total 1139 + ---- + Atomic weight 63.12 + Number weight 1139/18 63.277 +</pre> +<font class="sc">Silver</font> (<a href="#PlateVI">Plate VI</a>, 4) follows copper in the constitution of +five of the bodies enclosed in the funnels. But the triangular +group contains twenty-one atoms as against ten, and three +ovoids, each containing three bodies with eleven atoms, raise +the number of atoms in a funnel to seventy-nine. The central +globe is decreased by five, and the prisms have disappeared. +The connecting rod is unaltered. + +<pre> +SILVER: Upper part {12 funnels of 79 atoms 948 + {Central globe 15 + Lower part same 963 + Connecting rod 19 + ---- + Total 1945 + ---- + Atomic weight 107.93 + Number weight 1945/18 108.055 +</pre> + <p>(This atomic weight is given by Stas, in <i>Nature</i>, August 29, + 1907, but it has been argued later that the weight should not be above + 107.883.)</p> + + <p><a name="PlateVII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-015.png" target="_blank"><img width="100%" src="images/oc-015.png" + alt="Plate VII." /></a> + <font class="sc">Plate</font> VII. + </div> + <p><a name="CompAu"></a></p> + +<font class="sc">Gold</font> (Plate VII) is so complicated that it demands a whole +plate to itself. It is difficult to recognize the familiar dumb-bell +in this elongated egg, but when we come to examine it, the +characteristic groupings appear. The egg is the enormously +swollen connecting rod, and the upper and lower parts with +their central globes are the almond-like projections above and +below, with the central ovoid. Round each almond is a shadowy +funnel (not drawn in the diagram), and within the almond is the +collection of bodies shown in <i>e</i>, wherein the two lowest bodies +are the same as in every other member of the negative and +positive groups; the third, ascending, is a very slight modification +of the other thirds; the fourth is a union and re-arrangement +of the fourth and fifth; the fifth, of four ovoids, adds one to the +three ovoids of bromine, iodine and silver; the triangular group +is like that in copper and silver, though with 28 atoms instead of +10 or 21, and it may be noted that the cone in iron has also 28. +The central body in the ovoid is very complicated, and is shown +in <i>c</i>, the bodies on each side, <i>d</i>, are each made up of two tetrahedra, +one with four six-atomed prisms at its angles, and the +other with four spheres, a pair with four atoms and a pair with +three. We then come to the connecting rod. One of the four +similar groups in the centre is enlarged in <i>a</i>, and one of the +sixteen circling groups is enlarged in <i>b</i>. These groups are +arranged in two planes inclined to one another. + +<pre> +GOLD: Upper part + { 12 funnels of 97 atoms 1164 + { Central ovoid {<i>c</i> 101 + {2 <i>d</i>, 38 76 + Lower part same 1341 + Connecting rod { 4 <i>a</i> 84 336 + {16 <i>b</i> 33 528 + ---- + Total 3546 + ---- + Atomic weight 195.74 + Number weight 3546/18 197 +</pre> + <p>It may be noted that the connecting rod is made up of exactly sixteen + atoms of occultum, and that sixteen such atoms contain 864 ultimate + atoms, the exact member of atoms in titanium.</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>III.</h3> + + <p>Occultum was observed by us in 1895, and, finding that it was so + light, and so simple in its composition, we thought that it might be + helium, of which we were unable, at the time, to obtain a sample. When, + however, helium itself came under observation in 1907, it proved to be + quite different from the object before observed, so we dubbed the + unrecognised object Occultum, until orthodox science shall find it and + label it in proper fashion.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Occultum</font> (<a href="#PlateVI">Plate VI</a>, 1).</p> + + <p>We here meet the tetrahedron for the first time, with each angle + occupied by a six-atomed group, the atoms arranged as on the end + triangles of a prism. This form recurs very often, and was noted, last + month, as seen in copper (<a href="#PlateVI">Plate VI</a>, 3); it + revolves with extreme rapidity around its longitudinal axis, and looks + like a pencil sharpened at both ends, or a cigar tapering at both ends; + we habitually spoke of it as "the cigar." It appears to be strongly + coherent, for, as will be seen below, its six atoms remain attached to + each other as meta-compounds and even when divided into two triplets as + hyper-compounds, they revolve round each other.</p> + + <p>Above the tetrahedron is a balloon-shaped figure, apparently drawn + into shape by the attraction of the tetrahedron. The body below the + tetrahedron looks like a coil of rope, and contains fifteen atoms; they + are arranged on a slanting disk in a flat ring, and the force goes in at + the top of one atom, and out of the bottom of it into the top of the + next, and so on, making a closed circuit. The two little spheres, each + containing a triplet, are like fill-up paragraphs to a + compositor—they seem to be kept standing and popped in where + wanted. The sphere marked <i>x</i> is a proto-compound, the balloon when + set free.</p> + + <p>As was noted under gold (<a href="#CompAu">p. 41</a>), sixteen + occultum bodies, re-arranged, make up the connecting rod in + gold:—</p> + +<pre> +OCCULTUM: Tetrahedron 24 + Balloon 9 + Triplets 6 + Rope-circle 15 + ---- + Total 54 + ---- + Atomic weight Not known + Number weight 54/18 3 +</pre> +<p class="center" style="margin-top: 2em;"><font class="sc">Dissociation of Atoms</font>.</p> + + <p>Before proceeding to the study of other chemical atoms, as to their + general internal arrangements, it is desirable to follow out, in those + already shown, the way in which these atoms break up into simpler forms, + yielding successively what we have called proto-, meta-, and + hyper-compounds. It is naturally easier to follow these in the simpler + atoms than in the more complex, and if the earlier dissociations are + shown, the latter can be more readily and more intelligibly + described.</p> + + <p>The first thing that happens on removing a gaseous atom from its + "hole" (see pp. 21 to 23) or encircling "wall," is that the contained + bodies are set free, and, evidently released from tremendous pressure, + assume spherical or ovoid forms, the atoms within each re-arranging + themselves, more or less, within the new "hole" or "wall." The figures + are, of course, three-dimensional, and often remind one of crystals; + tetrahedral, octagonal, and other like forms being of constant + occurrence. In the diagrams of the proto-compounds, the constituent atoms + are shown by dots. In the diagrams of the meta-compounds the dot becomes + a heart, in order to show the resultants of the lines of force. In the + diagrams of the hyper-compounds the same plan is followed. The letters + <i>a</i>, <i>b</i>, <i>c</i>, &c., enable the student to follow the + breaking up of each group through its successive stages.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Hydrogen</font> (<a href="#PlateV">Plate V</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-016.png" target="_blank"><img width="100%" src="images/oc-016.png" + alt="Dissociation of Hydrogren." /></a> + </div> + <p>The six bodies contained in the gaseous atom instantaneously + re-arrange themselves within two spheres; the two linear triplets unite + with one triangular triplet, holding to each other relative positions + which, if connected by three right lines, would form a triangle with a + triplet at each angle; the remaining three triangular triplets similarly + arrange themselves in the second sphere. These form the proto-compounds + of hydrogen.</p> + + <p>In the dissociation of these, each group breaks up into two, the two + linear triplets joining each other and setting free their triangular + comrade, while two of the triangular triplets similarly remain together, + casting out the third, so that hydrogen yields four meta-compounds.</p> + + <p>In the hyper-condition, the connexion between the double triplets is + broken, and they become four independent groups, two like ix, in the + hyper-types (<a href="#Hyper">p. 25</a>), and two remaining linear, but + rearranging their internal relations; the two remaining groups break up + into two pairs and a unit.</p> + + <p>The final dissociation sets all the atoms free.</p> + + <br clear="all" /> + <p><a name="DisOc"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Occultum</font> (<a href="#PlateV">Plate VI</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-017.png" target="_blank"><img width="100%" src="images/oc-017.png" + alt="Dissociation of Occultum." /></a> + </div> + <p>On the first dissociation of the component parts of occultum, the + tetrahedron separates as a whole, with its four "cigars," flattening + itself out within its hole, <i>a</i>; two "cigars" are positive and two + negative, marked respectively <i>a</i> and <i>a'</i>. The rope becomes a + ring within a sphere, <i>b</i>, and the two bodies <i>d</i> <i>d</i>, + which are loose in the gaseous atom, come within this ring. The balloon + becomes a sphere.</p> + + <p>On further dissociation, the "cigars" go off independently, showing + two types, and these again each divide into triplets, as meta-compounds. + <i>B</i>, on the meta-level, casts out the two <i>d</i> bodies, which + become independent triplets, and the "rope" breaks into two, a close ring + of seven atoms and a double cross of eight. These subdivide again to form + hyper-compounds, the ring yielding a quintet and a pair, and the double + cross separating into its two parts.</p> + + <p>The balloon, <i>c</i>, becomes much divided, the cohesion of its parts + being slight; it forms two triplets, a pair and a unit, and these set + free, on further dissociation, no less than five separate atoms and two + duads.</p> + + <p>The two triplets of <i>d</i> each cast out an atom on dissociation, + and form two pairs and two units.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Sodium</font> (<a href="#PlateVI">Plate VI</a>, 2).</p> + + <p>It is convenient to consider sodium next, because it is the basic + pattern on which not only copper, silver and gold are formed, but also + chlorine, bromine and iodine.</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-018.png" target="_blank"><img width="100%" src="images/oc-018.png" + alt="Dissociation of Sodium." /></a> + </div> + <p>When sodium is set free from its gaseous condition, it divides up into + thirty-one bodies—twenty-four separate funnels, four bodies derived + from the two central globes, and three from the connecting rod. The + funnels become spheres, and each contains four enclosed spheres, with + more or less complicated contents. Each central globe yields a sextet and + a quartet, and the rod sets free two quartets and a peculiarly formed + sextet.</p> + + <p>When the proto-compounds are dissociated, the funnel-sphere sets free: + (1) the contents of <i>a</i>, rearranged into two groups of four within a + common sphere; the sphere yields four duads as hyper-compounds; (2) the + contents of <i>b</i>, which unite themselves into a quartet, yielding two + duads as hyper-compounds; and (3) the contents of the two spheres, + <i>c</i>, which maintain their separation as meta-compounds, and become + entirely independent, the atoms within the sphere revolving round each + other, but the spheres ceasing their revolution round a common axis, and + going off in different directions. The atoms break off from each other, + and gyrate in independent solitude as hyper-"compounds." Thus each funnel + yields finally ten hyper-bodies.</p> + + <p>The part of the central globe, marked <i>d</i>, with its six atoms, + whirling round a common centre, becomes two triplets, at the meta-stage, + preparing for the complete separation of these as hyper-bodies. The + second part of the same globe, marked <i>e</i>, a whirling cross, with an + atom at each point, becomes a quartet in the meta-state, in which three + atoms revolve round a fourth, and in the hyper-state this central atom is + set free, leaving a triplet and a unit.</p> + + <p>Each of the two bodies marked <i>f</i>, liberated from the connecting + rod, shows four atoms whirling round a common centre, exactly resembling + <i>e</i> in appearance; but there must be some difference of inner + relations, for, in the meta-state, they re-arrange themselves as two + pairs, and divide into two as hyper-bodies.</p> + + <p>The body marked <i>g</i> is a four-sided pyramid, with two closely + joined atoms at its apex; these still cling to each in mutual revolution + as a meta-body, encircled by a ring of four, and this leads to a further + dissociation into three pairs on the hyper-level.</p> + + <p><a name="DisCl"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Chlorine</font> (<a href="#PlateV">Plate V</a>, 2).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-019.png" target="_blank"><img width="100%" src="images/oc-019.png" + alt="Dissociation of Chlorine and Bromine." /></a> + </div> + <p>The description of the funnel of sodium applies to that of chlorine, + until we come to the body nearest the mouth, the sphere containing three + additional bodies; this remains within the funnel in the first + dissociation, so that again we have twenty-four separate funnels as + proto-compounds; the central globes are the same as in sodium, and yield + the same four bodies; the connecting rod sets free five bodies, of which + two are the same; we have thus thirty-three separate bodies as the result + of the dissociation of chlorine into its proto-compounds. As all the + compounds which are in sodium break up in the same way into meta- and + hyper-compounds, we need not repeat the process here. We have only to + consider the new meta- and hyper-compounds of the highest sphere within + the funnel, and the two triplets and one quintet from the connecting + rod.</p> + + <p>The additional body within the proto-funnel is of a very simple + character, three contained triangles within the flattened sphere. On + release from the funnel, on the meta-level, the atoms rearrange + themselves in a whirling set of three triplets, and these break off from + each other as hyper-compounds. The two triplets from the connecting rod, + also, are of the simplest character and need not delay us. The + five-atomed body, a four-sided pyramid as a proto-compound, becomes a + ring whirling round a centre on the meta, and two pairs with a unit on + the hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Bromine</font> (<a href="#PlateV">Plate V</a>, 3).</p> + + <p>Three additional bodies appear at the top of the funnel, which + otherwise repeats that of chlorine. The connecting rod is the same and + may be disregarded. The central globes become more complex. The additions + are, however, of very easy types, and hence are readily dealt with. Each + of the three similar ovoid bodies contains two triplets—each a + triangle and a quintet—a four-sided pyramid. These are the same, as + may be seen in the connecting rod of chlorine, and we need not repeat + them. Only the globe remains. This does not break up as a proto-compound + but is merely set free, <i>a</i> and the 2 <i>bs</i> whirling in a plane + vertical to the paper and the two smaller bodies, <i>cc</i>, whirling on + a plane at right angles to the other. These two disengage themselves, + forming a quartet as a meta-compound, while <i>a</i> makes a whirling + cross and <i>bb</i> a single sextet; these further dissociate themselves + into four pairs and two triplets.</p> + + <p><a name="DisI"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Iodine</font> (<a href="#PlateV">Plate V</a>, 4).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-020.png" target="_blank"><img width="100%" src="images/oc-020.png" + alt="Dissociation of Iodine and Copper." /></a> + </div> + <p>Iodine has nothing new to give us, except five similar ovoid bodies at + the top of each funnel, and two quartets instead of two pairs in the + central globe. The ovoid bodies become spheres when the funnels are + thrown off, and a crystalline form is indicated within the sphere. The + atoms are arranged in two tetrahedra with a common apex, and the + relationship is maintained in the meta-body, a septet. The latter breaks + up into two triplets and a unit on the hyper-level. In the central + globes, the <i>a</i> of bromine is repeated twice instead of the pairs in + <i>cc</i>.</p> + + <p><a name="DisCu"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Copper</font> (<a href="#PlateVI">Plate VI</a>, 3).</p> + + <p>We have already disposed of occultum, on this plate, and of sodium, + which lies at the root of both groups. Copper, we now find, is also very + largely off our hands, as the funnel provides us with only two new + types—two spheres—each containing five atoms in a new + arrangement, and the triangular body at the mouth with its ten atoms. + This triangular body, with an increased number of atoms, reappears in + various other chemical elements. The central globes are different from + any we have had before, in their internal arrangement, but the + constituents are familiar; there are two contained spheres with four + atoms each, the <i>a</i> in the globe of bromine (see above) and 2 + "cigars." The "cigars" may be followed under occultum (see above). The + connecting rod is as in chlorine, bromine and iodine.</p> + + <p>The atoms in the bodies <i>a</i> and <i>b</i> are curiously arranged. + <i>A</i> consists of two square-based pyramids turned so as to meet at + their apices, and breaks up into two quartet rings and a duad. <i>B</i> + is again two four-sided pyramids, but the bases are in contact and set at + right angles to each other; the second apex is not seen, as it is + directly below the first. The pyramids separate as meta-bodies, and the + atoms assume the peculiar arrangement indicated and then break up into + four pairs and two units on the hyper level.</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>IV.</h3> + + <p><a name="DisAg"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Silver</font> (<a href="#PlateVI">Plate VI</a>, 4 and Ag below).</p> + + <p>Silver presents us with only two new bodies, and even these are only + new by slight additions to old models. The triangular shaped body at the + apex of the funnel, containing 21 atoms, is intermediate between the + similar bodies in copper and iron. As a proto-element it becomes three + triangles, joined at their apices, in fact a tetrahedron in which no + atoms are distributed on the fourth face. The faces separate on the meta + level and give three seven-atomed figures, and each of these breaks up + into two triplets and a unit. The central globe only differs from that of + bromine by the addition of one atom, which gives the familiar four-sided + pyramid with a square base as in chlorine (see <a href="#DisCl">p. + 46</a>).</p> + + <p><a name="DisAu"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Gold</font> (<a href="#PlateVII">Plate VII</a> and Au below).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-021.png" target="_blank"><img width="100%" src="images/oc-021.png" + alt="Dissociation of Silver and Gold." /></a> + </div> + <p>The disintegration of gold first yields forty-seven bodies on the + proto-level; the twenty-four funnels separate, and the central globes + which hold each twelve together set free their six contained globes + (<i>c</i>, <i>d</i>), thirty bodies being thus liberated. The sixteen + bodies on the central inclined planes, marked <i>b</i>, break away, their + central globe, with its four contained globes, remaining unchanged. But + this condition does not last. The motion of the funnels changes and thus + the funnels cease to exist and their contents are set free, each funnel + thus liberating nine independent bodies; the sixteen <i>b</i> separate + into two each; the four <i>a</i> liberate five each; the two <i>c</i> set + free thirteen each; the four <i>d</i> finally liberate two each: 302 + proto elements in all.</p> + + <p>The funnel is almost that of iodine, re-arranged. Four of the first + ring in the iodine funnel are replaced by the triangular body, which + becomes a four-sided pyramid with an occupied base. The second ring of + three ovoids in iodine becomes four in gold, but the internal arrangement + of each ovoid is the same. The next two spheres in the iodine funnel + coalesce into one sphere, with similar contents, in the gold funnel. The + fifth in iodine is slightly rearranged to form the fourth in descent in + gold, and the remaining two are the same. <i>B</i> has been broken up + under occultum (<a href="#DisOc">p. 628</a>) and can be followed there. + The sixteen rings set free from the four <i>a</i>, after gyrating round + the central body, now become a sphere, break up, as in occultum (see <a + href="#DisOc">p. 44</a>) into a meta seven-atomed ring and an + eight-atomed double cross, and so on to the hyper level. The sphere with + its two contained bodies breaks up into eight triangles on the meta + level, and each of these, on the hyper, into a duad and a unit. The + twelve septets of <i>c</i> assume the form of prisms as in iodine (see <a + href="#DisI">p. 48</a>) and pursue the same course, while its central + body, a four-sided pyramid with its six attendants, divides on the meta + level into six duads, revolving round a ring with a central atom as in + chlorine (<a href="#DisCl">p. 47</a>), the duads going off independently + on the hyper-level and the ring breaking up as in chlorine. The "cigar" + tetrahedron of <i>d</i> follows its course as in occultum, and the other + sets free two quartets and two triplets on the meta level, yielding six + duads and two units as hyper compounds. It will be seen that, complex as + gold is, it is composed of constituents already familiar, and has iodine + and occultum as its nearest allies.</p> + + <p><a name="CompBe"></a></p> + +<p class="center" style="margin-top: 2em;">II <font class="sc">and</font> II<i>a</i>.—<font class="sc">The Tetrahedral Groups</font>.</p> + + <p>II.—This group consists of beryllium (glucinum), calcium, + strontium and barium, all diatomic, paramagnetic and positive. The + corresponding group consists of oxygen, chromium, molybdenum, wolfram + (tungsten) and uranium, with a blank disk between wolfram and uranium: + these are diatomic, paramagnetic, and negative. We have not examined + barium, wolfram, or uranium.</p> + + <p><a name="PlateVIII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-022.png" target="_blank"><img width="100%" src="images/oc-022.png" + alt="Plate VIII - Group II." /></a> + <font class="sc">Plate</font> VIII. + </div> +<font class="sc">Beryllium</font> (<a href="#PlateIII">Plate III</a>, 2, and +<a href="#PlateVIII">Plate VIII</a>, 1). In the tetrahedron +four funnels are found, the mouth of each funnel opening +on one of its faces. The funnels radiate from a central globe, +and each funnel contains four ovoids each with ten atoms within +it arranged in three spheres. In the accompanying diagrams +one funnel with its four ovoids is shown and a single ovoid with +its three spheres, containing severally three, four, and three +atoms, is seen at the left-hand corner of the plate (7 <i>a</i>). The +members of this group are alike in arrangement, differing only +in the increased complexity of the bodies contained in the +funnels. Beryllium, it will be observed, is very simple, whereas +calcium and strontium are complicated. + +<pre> +BERYLLIUM: 4 funnels of 40 atoms 160 + Central globe 4 + ---- + Total 164 + ---- +Atomic weight 9.01 +Number weight 164/18 9.11 +</pre> +<font class="sc">Calcium</font> (<a href="#PlateVIII">Plate VIII</a>, 2) shows in each funnel three contained +spheres, of which the central one has within it seven ovoids +identical with those of beryllium, and the spheres above and +below it contain each five ovoids (7 <i>b</i>) in which the three +contained spheres have, respectively, two, five, and two atoms. The +central globe is double, globe within globe, and is divided into +eight segments, radiating from the centre like an orange; the +internal part of the segment belonging to the inner globe has a +triangular body within it, containing four atoms (7 <i>c</i>), and the +external part, belonging to the encircling globe, shows the +familiar "cigar" (7 <i>d</i>). In this way 720 atoms are packed into +the simple beryllium type. + +<pre> +CALCIUM: 4 funnels of 160 atoms 640 + Central globe 80 + ---- + Total 720 + ---- + Atomic weight 39.74 + Number weight 720/18 40.00 +</pre> +<font class="sc">Strontium</font> (<a href="#PlateVIII">Plate VIII</a>, 3) shows a still further complication +within the funnels, no less than eight spheres being found within +each. Each of the highest pair contains four subsidiary spheres, +with five, seven, seven, five atoms, respectively (7 <i>e</i>, <i>g</i>, <i>f</i>). The +<i>g</i> groups are identical with those in gold, but difference of pressure +makes the containing body spherical instead of ovoid; similar +groups are seen in the top ring of the iodine funnel, where also +the "hole" is ovoid in form. The second pair of spheres +contains ten ovoids (7 <i>b</i>) identical with those of calcium. The +third pair contains fourteen ovoids (7 <i>a</i>) identical with those of +beryllium, while the fourth pair repeats the second, with the +ovoids re-arranged. The internal divisions of the double sphere +of the central globe are the same as in calcium, but the contents +differ. The "cigars" in the external segments are replaced by +seven-atomed ovoids (7 <i>h</i>)—the iodine ovoids—and the external +segments contain five-atomed triangles (7 <i>i</i>). Thus 1,568 atoms +have been packed into the beryllium type, and our wonder is +again aroused by the ingenuity with which a type is preserved +while it is adapted to new conditions. + +<pre> +STRONTIUM: 4 funnels of 368 atoms 1472 + Central globe 96 + ---- + Total 1568 + ---- + Atomic weight 86.95 + Number weight 1568/18 87.11 +</pre> + <p>The corresponding group, headed by oxygen—oxygen, chromium, + molybdenum, wolfram and uranium—offers us another problem in its + first member.</p> + + <p><a name="CompO"></a></p> + +<font class="sc">Oxygen</font> (<a href="#PlateVIII">Plate VIII</a>, 4). +This was examined by us in 1895, +and the description may be reproduced here with a much +improved diagram of its very peculiar constitution. The gaseous +atom is an ovoid body, within which a spirally-coiled snake-like +body revolves at a high velocity, five brilliant points of light +shining on the coils. The appearance given in the former +diagram will be obtained by placing the five septets on one side +on the top of those on the other, so that the ten become in +appearance five, and thus doubling the whole, the doubling point +leaving eleven duads on each side. The composition is, however, +much better seen by flattening out the whole. On the +proto level the two snakes separate and are clearly seen. + +<pre> +OXYGEN: Positive snake + { 55 spheres of 2 atoms } + { + 5 disks of 7 atoms } 145 + Negative snake " 145 + ---- + Total 290 + ---- + Atomic weight 15.87 + Number weight 290/18 16.11 +</pre> +<font class="sc">Chromium</font> (<a href="#PlateVIII">Plate VIII</a>, 5) +"reverts to the ancestral type," +the tetrahedron; the funnel is widened by the arrangement of +its contents, three spheres forming its first ring, as compared +with the units in beryllium and calcium, and the pairs in strontium +and molybdenum. Two of these spheres are identical in their +contents—two quintets (7 <i>f</i>), a quintet (7 <i>j</i>), and two quintets +(7 <i>e</i>), <i>e</i> and <i>f</i> being to each other as object and image. The +remaining sphere (7 <i>b</i>) is identical with the highest in the +calcium funnel. The remaining two spheres, one below the +other, are identical with the corresponding two spheres in +calcium. The central globe, as regards its external segments, +is again identical with that of calcium, but in the internal +segments a six-atomed triangle (7 <i>k</i>) is substituted for the calcium +four-atomed one (7 <i>e</i>). + +<pre> +CHROMIUM: 4 funnels of 210 atoms 840 + Central globe 96 + ----- + Total 936 + ----- + Atomic weight 51.74 + Number weight 936/18 52.00 +</pre> +<font class="sc">Molybdenum</font> (<a href="#PlateVIII">Plate VIII</a>, 6) very closely resembles strontium, +differing from it only in the composition of the highest pair of +spheres in the funnels and in the presence of a little sphere, +containing two atoms only, in the middle of the central globe. +The topmost spheres contain no less than eight subsidiary spheres +within each; the highest of these (7 <i>e</i>) has four atoms in it; the +next three have four, seven and four (7 <i>e</i> <i>g</i> <i>e</i>), respectively; the +next three are all septets (7 <i>g</i>), and the last has four—making in +all for these two spheres 88 atoms, as against the 48 in corresponding +spheres of strontium, making a difference of 160 in the +four funnels. + +<pre> +MOLYBDENUM: 4 funnels of 408 atoms 1632 + Central globe 98 + ----- + Total 1730 + ----- + Atomic weight 95.26 + Number weight 1730/18 96.11 +</pre> + <p>II <i>a</i>.—This group contains magnesium, zinc, cadmium, and + mercury, with an empty disk between cadmium and mercury; we did not + examine mercury. All are diatomic, diamagnetic and positive; the + corresponding group consists of sulphur, selenium and tellurium, also all + diatomic and diamagnetic, but negative. The same characteristics of four + funnels opening on the faces of a tetrahedron are found in all, but + magnesium and sulphur have no central globe, and in cadmium and tellurium + the globe has become a cross.</p> + + <p><a name="PlateIX"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-023.png" target="_blank"><img width="100%" src="images/oc-023.png" + alt="Plate IX." /></a> + <font class="sc">Plate</font> IX. + </div> +<font class="sc">Magnesium</font> (<a href="#PlateIX">Plate IX</a>, 1) introduces us to a new arrangement: +each group of three ovoids forms a ring, and the three rings are +within a funnel; at first glance, there are three bodies in the +funnel; on examination each of these is seen to consist of three, +with other bodies, spheres, again within them. Apart from this, +the composition is simple enough, all the ovoids being alike, and +composed of a triplet, a septet and a duad. + +<pre> +MAGNESIUM: 4 funnels of 108 atoms 432 + Atomic weight 24.18 + Number weight 432/18 24.00 +</pre> +<font class="sc">Zinc</font> (<a href="#PlateIX">Plate IX</a>, 2) also brings a new device: the funnel is of +the same type as that of magnesium, while septets are substituted +for the triplets, and 36 additional atoms are thus slipped in. +Then we see four spikes, alternating with the funnels and +pointing to the angles, each adding 144 atoms to the total. The +spikes show the ten-atomed triangle, already met with in other +metals, three very regular pillars, each with six spheres, containing +two, three, four, four, three, two atoms, respectively. The +supporting spheres are on the model of the central globe, but +contain more atoms. Funnels and spikes alike radiate from a +simple central globe, in which five contained spheres are arranged +crosswise, preparing for the fully developed cross of cadmium. +The ends of the cross touch the bottoms of the funnels. + +<pre> +ZINC: 4 funnels of 144 atoms 576 + 4 spikes of 144 atoms 576 + Central globe 18 + ----- + Total 1170 + ----- + Atomic weight 64.91 + Number weight 1170/18 65.00 +</pre> +<font class="sc">Cadmium</font> (<a href="#PlateIX">Plate IX</a>, 3) has an increased complexity of funnels; +the diagram shows one of the three similar segments which lie +within the funnels as cylinders; each of these contains four +spheres, three pillars and three ovoids, like the spike of zinc +turned upside down, and the zinc ten-atomed triangle changed +into three ten-atomed ovoids. The centre-piece is a new form, +though prefigured in the central globe of zinc. + +<pre> +CADMIUM: 3 segments of 164 atoms = 492 + 4 funnels of 492 atoms 1968 + Central body 48 + ----- + Total 2016 + ----- + Atomic weight 111.60 + Number weight 2016/18 112.00 +</pre> + <p>The corresponding negative group is headed by</p> + + <p><a name="PlateX"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-024.png" target="_blank"><img width="100%" src="images/oc-024.png" + alt="Plate X." /></a> + <font class="sc">Plate</font> X. + </div> +<font class="sc">Sulphur</font> (<a href="#PlateX">Plate X</a>, 1), which, like magnesium, has no central +globe, and consists simply of the zinc funnels, much less +compressed than zinc but the same in composition. + +<pre> +SULPHUR: 4 funnels of 144 atoms 576 + Atomic weight 31.82 + Number weight 576/18 32.00 +</pre> +<font class="sc">Selenium</font> (<a href="#PlateX">Plate X</a>, 2) +is distinguished by the exquisite +peculiarity, already noticed, of a quivering star, floating across +the mouth of each funnel, and dancing violently when a ray of +light falls upon it. It is known that the conductivity of selenium +varies with the intensity of the light falling upon it, and it may +be that the star is in some way connected with its conductivity. +It will be seen that the star is a very complicated body, and in +each of its six points the two five-atomed spheres revolve round +the seven-atomed cone. The bodies in the funnels resemble +those in magnesium, but a reversed image of the top one is +interposed between itself and the small duad, and each pair has +its own enclosure. The central globe is the same as that of zinc. + +<pre> +SELENIUM: 4 funnels of 198 atoms 792 + 4 stars of 153 atoms 612 + Central globe 18 + ----- + Total 1422 + ----- + Atomic weight 78.58 + Number weight 1422/18 79.00 +</pre> +<font class="sc">Tellurium</font> (<a href="#PlateX">Plate X</a>, 3), +it will be seen, closely resembles +cadmium, and has three cylindrical segments—of which one is +figured—making up the funnel. The contained bodies in the +pillars run three, four, five, four, three, two, instead of starting +with two; and a quartet replaces a duad in the globes above. +The central cross only differs from that of cadmium in having a +seven-atomed instead of a four-atomed centre. So close a +similarity is striking. + +<pre> +TELLURIUM: 3 segments of 181 atoms = 543 + 4 funnels of 543 atoms 2172 + Central body 51 + ----- + Total 2223 + ----- + Atomic weight 126.64 + Number weight 2223/18 123.50 +</pre> + <br clear="all" /> +<hr class="short" /> + +<h3>V.</h3> + + <p>We must now consider the ways in which the members of the tetrahedral + groups break up, and as we proceed with this study we shall find how + continual are the repetitions, and how Nature, with a limited number of + fundamental methods, creates by varied combinations her infinite variety + of forms.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Beryllium</font> (<a href="#PlateIII">Plate III</a>, 2, and +<a href="#PlateVIII">VIII</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-025.png" target="_blank"><img width="100%" src="images/oc-025.png" + alt="Dissociation of Beryllium and Calcium." /></a> + </div> + <p>Beryllium offers us four similar funnels and a central globe, and the + proto-elements consist of these five bodies, set free. The funnel, + released from pressure, assumes a spherical form, with its four ovoids + spinning within it, and the central globe remains a sphere, containing a + whirling cross. On the meta level, the ovoids are set free, and two from + each funnel are seen to be positive, two negative—sixteen bodies in + all, <i>plus</i> the cross, in which the resultant force-lines are + changed, preparatory to its breaking into two duads on the hyper level. + On that level, the decades disintegrate into two triplets and a quartet, + the positive with the depressions inward, the negative with the + depressions outward.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Calcium</font> (<a href="#PlateVIII">Plate VIII</a>, 2).</p> + + <p>The funnels, as usual, assume a spherical form on the proto level, and + show, in each case, three spheres containing ovoids. These spheres, still + on the proto level, break free from their containing funnel, as in the + case of gold (<a href="#DisAu">p. 49</a>), twelve bodies being thus + liberated, while the central globe breaks up into eight segments, each of + which becomes globular, and contains within it a "cigar" and a somewhat + heart-shaped body. Four spheres, each containing seven ten-atomed ovoids, + are identical with those in beryllium, and can be followed in its + diagram. Eight spheres, each containing five nine-atomed ovoids of a + different type, set free, on the meta level, eighty duads—forty + positive and forty negative—and forty quintets, which are identical + with those in chlorine. On the hyper level, the duads become single + atoms, within a sphere, and the central atom from the quintet is also set + free, one hundred and twenty in all. The remaining four atoms of the + quintet divide into two duads.</p> + + <p>The central globe, dividing into eight, becomes eight six-atomed + spheres on the meta, the "cigar" behaving as usual, four "cigars" being + positive and four negative, and becoming dissociated into triplets; the + four atoms within the heart-shaped body appear as a tetrahedron, remain + together on the meta level, and break up into duads on the hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Strontium</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 3).</p> + + <p>The third member of this group repeats the <i>a</i> groups of + beryllium and the <i>b</i> groups of calcium, and they dissociate into + the bodies already described under these respectively. The two upper + globes in each funnel repeat each other, but each globe contains four + smaller spheres showing three varieties of forms. The two marked + <i>g</i>, which are repeated in the central globe as <i>h</i>, are + seven-atomed, and appear as spheres or ovoids according to pressure. They + are figured on <a href="#DisI">p. 48</a>, under iodine; <i>e</i> and + <i>f</i> are related as object and image, and we have already seen them + in copper (<a href="#CompCu">pp. 38</a> and <a href="#DisCu">48</a>); in + each case, as in copper, they unite into a ten-atomed figure; on the meta + level the pair of fours form a ring, and the remaining two atoms form a + duad; <i>i</i>, which repeats <i>f</i>, makes a ring with the fifth in + the centre, as in the five-atomed <i>b</i> of calcium, as shown above. + There is, thus, nothing new in strontium, but only repetitions of forms + already studied.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Oxygen</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 4).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-026.png" target="_blank"><img width="100%" src="images/oc-026.png" + alt="Dissociation of Oxygen, Chromium and Molybdenum." /></a> + </div> + <p>The disintegration of oxygen as given in 1895 may be repeated here, + and the better presentation given on <a href="#CompO">p. 54</a> renders + it easier to follow the process. On the proto level the two "snakes" + divide; the brilliant disks are seven-atomed, but are differently + arranged, the positive snake having the atoms arranged as in the iodine + ovoids, whereas the negative snake has them arranged as in a capital H. + The snakes show the same extraordinary activity on the proto level as on + the gaseous, twisting and writhing, darting and coiling. The body of the + snake is of two-atomed beads, positive and negative. On the meta level + the snakes break into ten fragments, each consisting of a disk, with six + beads on one side and five on the other, remaining as lively as the + original snake. They shiver into their constituent disks, and beads on + the hyper level, there yielding the ten disks, five positive and five + negative, and the 110 beads, fifty-five positive and fifty-five + negative.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Chromium</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 5).</p> + + <p>When we go on to chromium and molybdenum, we return to our familiar + funnels and central globes, and the secondary spheres within the + funnels—quickly set free, as before, on the proto level—give + us no new combinations in their contained spheres and ovoids. The + <i>a</i> of beryllium, the <i>b</i> of calcium and strontium, and + <i>d</i> of calcium, the <i>e</i> and <i>f</i> of strontium, are all + there; <i>j</i> in chromium is the same as the central sphere in the + <i>b</i> ovoid. In the central globe, <i>k</i>, is a pair of triangles as + in hydrogen, consisting of only six atoms, which on the meta level + revolve round each other, and break up into two duads and two units on + the hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Molybdenum</font> (<a href="#PlateVIII"><font class="sc">Plate VIII</font></a>, 6).</p> + + <p>Molybdenum presents us with only two new forms, and these are merely + four-atomed tetrahedra, occurring in pairs as object and image. All the + other bodies have already been analysed.</p> + + <p>II <i>a</i>.—We come now to the second great tetrahedral group, + which though very much complicated, is yet, for the most part, a + repetition of familiar forms.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Magnesium</font> (<a href="#PlateIX"><font class="sc">Plate IX</font></a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-027.png" target="_blank"><img width="100%" src="images/oc-027.png" + alt="Dissociation of Magnesium and Zinc." /></a> + </div> + <p>We are still among tetrahedra, so have to do with four funnels, but + each funnel contains three rings, and each ring three ovoids; on the + proto level a triple dissociation takes place, for the funnels let free + the rings as large spheres, in each of which rotate three twelve-atomed + ovoids, and then the ovoids break loose from the spheres, and themselves + become spherical, so that we have finally thirty-six proto compounds from + the tetrahedron. On the meta level the contained bodies, a triplet, Mg + <i>a</i>, a septet, Mg <i>b</i>, and a duad, Mg <i>c</i>, are set free + from each globe, thus yielding one hundred and eight meta compounds. On + the hyper level the triplet becomes a duad and a unit; the duad becomes + two units; and the septet a triplet and a quartet.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Zinc</font> (<a href="#PlateIX"><font class="sc">Plate IX</font></a>, 2).</p> + + <p>We can leave aside the funnel, for the only difference between it and + the magnesium funnel is the substitution of a second septet for the + triplet, and the septet is already shown in the magnesium diagram. We + have, therefore, only to consider the spikes, pointing to the angles of + the enclosing tetrahedron, and the central globe. These are set free on + the proto level and the spikes immediately release their contents, + yielding thus thirty-two separate bodies.</p> + + <p>The triangular arrangement at the top of the spike is the same as + occurs in copper (<i>b</i> on <a href="#DisCu">p. 48</a>), and can be + there followed. One of the three similar pillars is shown in the + accompanying diagram under Zn <i>a</i>. The compressed long oval becomes + a globe, with six bodies revolving within it in a rather peculiar way: + the quartets turn round each other in the middle; the triplets revolve + round them in a slanting ellipse; the duads do the same on an ellipse + slanting at an angle with the first, somewhat as in gold (<i>a</i> and + <i>b</i>, <a href="#CompAu">p. 40</a>). The spheres within the globes at + the base of the spikes, Zn <i>b</i>, behave as a cross—the cross is + a favourite device in the II <i>a</i> groups. Finally, the central globe, + Zn <i>c</i>, follows the same cruciform line of disintegration.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Cadmium</font> (<a href="#PlateIX">Plate IX</a>, 3).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-028.png" target="_blank"><img width="100%" src="images/oc-028.png" + alt="Dissociation of Cadmium and Tellurium." /></a> + </div> + <p>Cadmium follows very closely on the lines of zinc; the pillars of the + zinc spike are reproduced in the rings of the cadmium funnel; the globes + are also the globes of cadmium; so neither of these needs attention. We + have only to consider the three ten-atomed ovoids, which are substituted + for the one ten-atomed triangle of zinc, and the central cross. The + ovoids become spheres (Cd <i>a</i>, <i>b</i>), the contained bodies + revolving within them, <i>a</i> whirling on a diameter of the sphere, + cutting it in halves, as it were, and <i>b</i> whirling round it at right + angles; the cross also becomes a sphere (Cd <i>c</i>), but the cruciform + type is maintained within it by the relative positions of the contained + spheres in their revolution. The subsequent stages are shown in the + diagram.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Sulphur</font> (<a href="#PlateXI">Plate XI</a>, 1).</p> + + <p>Sulphur has nothing new, but shows only the funnels already figured in + magnesium, with the substitution of a second septet for the triplet, as + in zinc.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Selenium</font> (<a href="#PlateX">Plate X</a>, 2).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-029.png" target="_blank"><img width="100%" src="images/oc-029.png" + alt="Dissociation of Selenium." /></a> + </div> + <p>The funnel of selenium is a re-arrangement of the twelve-atomed ovoids + of magnesium and the ten-atomed ovoids of cadmium. The funnels, on + disintegrating, set free twelve groups, each containing nine spheres. On + the meta level the ten-atomed bodies are set free, and the twelve-atomed + divide into duads and decads, thus yielding seventy-two decads and + thirty-six duads; the duads, however, at once recombine into hexads, thus + giving only twelve meta elements, or eighty-four in all from the funnels. + The central globe holds together on the proto level, but yields five meta + elements. The star also at first remains a unit on the proto level, and + then shoots off into seven bodies, the centre keeping together, and the + six points becoming spheres, within which the two cones, base to base, + whirl in the centre, and the globes circle round them. On the meta level + all the thirty bodies contained in the star separate from each other, and + go on their independent ways.</p> + + <p>Selenium offers a beautiful example of the combination of simple + elements into a most exquisite whole.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Tellurium</font> (<a href="#PlateX">Plate X</a>, 3).</p> + + <p>Tellurium very closely resembles cadmium, and they are, therefore + placed on the same diagram. The pillars are the same as in chlorine and + its congeners, with a duad added at the base. The ten-atomed ovoid is the + same as in cadmium and follows the same course in breaking up. It would + be interesting to know why this duad remains as a duad in selenium and + breaks up into a septad and triad in the other members of the group. It + may be due to the greater pressure to which it is subjected in selenium, + or there may be some other reason. The cross in tellurium is identical + with that in cadmium, except that the centre is seven-atomed instead of + four-atomed.</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>VI.</h3> + +<p class="center" style="margin-top: 2em;">III <font class="sc">and</font> III<i>a</i>.—<font class="sc">The Cube Groups</font>.</p> + + <p>We have here four groups to consider, all the members of which are + triads, and have six funnels, opening on the six faces of a cube.</p> + + <p>III.—Boron, scandium and yttrium were examined; they are all + triatomic, paramagnetic, and positive. The corresponding group consists + of nitrogen, vanadium and niobium; they are triatomic, paramagnetic, and + negative. We have not examined the remaining members of these groups. In + these two groups nitrogen dominates, and in order to make the comparison + easy the nitrogen elements are figured on both <a href="#PlateXI">Plate + XI</a> and <a href="#PlateXII">Plate XII</a>. It will be seen that + scandium and yttrium, of the positive group, differ only in details from + vanadium and niobium, of the negative group; the ground-plan on which + they are built is the same. We noted a similar close resemblance between + the positive strontium and the negative molybdenum.</p> + + <p><a name="PlateXI"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-030.png" target="_blank"><img width="100%" src="images/oc-030.png" + alt="Plate XI." /></a> + <font class="sc">Plate</font> XI. + </div> +<font class="sc">Boron</font> (<a href="#PlateIII">Plate III</a>, 4, and Plate <a href="#PlateXI">XI</a>, 1). +We have here the +simplest form of the cube; the funnels contain only five bodies—four +six-atomed ovoids and one six-atomed "cigar." The +central globe has but four five-atomed spheres. It is as simple +in relation to its congeners as is beryllium to its group-members. + +<pre> +BORON: 6 funnels of 30 atoms 180 + Central globe 20 + ---- + Total 200 + ---- + Atomic weight 10.86 + Number weight 200/18 11.11 +</pre> +<font class="sc">Scandium</font> (<a href="#PlateXI">Plate XI</a>, 2). For the first time we meet funnels +of different types, A and B, three of each kind; A appear +to be positive and B negative, but this must be stated with +reserve. + + <p>In A the boron funnel is reproduced, the "cigar" having risen above + its companion ovoids; but the most important matter to note in respect to + this funnel is our introduction to the body marked <i>a</i> 110. This + body was observed by us first in nitrogen, in 1895, and we gave it the + name of the "nitrogen balloon," for in nitrogen it takes the balloon + form, which it also often assumes in other gaseous elements. Here it + appears as a sphere—the form always assumed on the proto + level—and it will be seen, on reference to the detailed diagram 4 + <i>a</i>, to be a complicated body, consisting of six fourteen-atomed + globes arranged round a long ovoid containing spheres with three, four, + six, six, four, three, atoms respectively. It will be observed that this + balloon appears in every member of these two groups, except boron.</p> + + <p>The B funnel runs largely to triads, <i>c</i> and <i>b</i>, <i>b</i> + (see 4 <i>b</i>) having not only a triadic arrangement of spheres within + its contained globes, but each sphere has also a triplet of atoms. In + <i>c</i> (see 4 <i>c</i>) there is a triadic arrangement of spheres, but + each contains duads. B is completed by a five-atomed sphere at the top of + the funnel. It should be noted that <i>a</i>, <i>b</i> and <i>c</i> all + are constituents of nitrogen.</p> + + <p>The central globe repeats that of boron, with an additional + four-atomed sphere in the middle.</p> + +<pre> +SCANDIUM: 3 funnels (A) of 140 atoms 420 + 3 " (B) of 116 " 348 + Centre globe 24 + ---- + Total 792 + ---- + Atomic weight 43.78 + Number weight 792/18 44.00 +</pre> +<font class="sc">Yttrium</font> (<a href="#PlateXI">Plate XI</a>, 3). Here we have a quite new arrangement +of bodies within the funnel—the funnel being of one type +only. Two "cigars" whirl on their own axes in the centre near +the top, while four eight-atomed globes (see 4 <i>e</i>) chase each +other in a circle round them, spinning madly on their own axes—this +axial spinning seems constant in all contained bodies—all +the time. Lower down in the funnel, a similar arrangement is +seen, with a globe (see 4 <i>d</i>)—a nitrogen element—replacing the +"cigars," and six-atomed ovoids replacing the globes. + + <p>The "nitrogen balloon" occupies the third place in the funnel, now + showing its usual shape in combination, while the <i>b</i> globe (see 4 + <i>b</i>) of scandium takes on a lengthened form below it.</p> + + <p>The central globe presents us with two tetrahedra, recalling one of + the combinations in gold (see <a href="#PlateVII">Plate VII</a> + <i>d</i>), and differing from that only by the substitution of two + quartets for the two triplets in gold.</p> + + <p>One funnel of yttrium contains exactly the same number of atoms as is + contained in a gaseous atom of nitrogen. Further, <i>a</i>, <i>b</i>, and + <i>d</i> are all nitrogen elements. We put on record these facts, without + trying to draw any conclusions from them. Some day, we—or + others—may find out their significance, and trace through them + obscure relations.</p> + +<pre> +YTTRIUM: 6 funnels of 261 atoms 1566 + Central globe 40 + ---- + Total 1606 + ---- + Atomic weight 88.34 + Number weight 1606/18 89.22 +</pre> + <p>The corresponding negative group, of nitrogen, vanadium and niobium, + is rendered particularly interesting by the fact that it is headed by + nitrogen, which—like the air, of which it forms so large a + part—pervades so many of the bodies we are studying. What is there + in nitrogen which renders it so inert as to conveniently dilute the fiery + oxygen and make it breathable, while it is so extraordinarily active in + some of its compounds that it enters into the most powerful explosives? + Some chemist of the future, perhaps, will find the secret in the + arrangement of its constituent parts, which we are able only to + describe.</p> + + <p><a name="PlateXII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-031.png" target="_blank"><img width="100%" src="images/oc-031.png" + alt="Plate XII." /></a> + <font class="sc">Plate</font> XII. + </div> +<font class="sc">Nitrogen</font> (<a href="#PlateXII">Plate XII</a>, 1) does not assume the cubical form +of its relatives, but is in shape like an egg. Referring again to +our 1895 investigations, I quote from them. The balloon-shaped +body (see 4 <i>a</i>) floats in the middle of the egg, containing six +small spheres in two horizontal rows, and a long ovoid in the +midst; this balloon-shaped body is positive, and is drawn down +towards the negative body <i>b</i> (see 4 <i>b</i>) with its seven contained +spheres, each of which has nine atoms within it—three triads. +Four spheres are seen, in addition to the two larger bodies; two +of these (see 4 <i>d</i>), each containing five smaller globes, are +positive, and two (see 4 <i>c</i>) containing four smaller globes, are +negative. + +<pre> +NITROGEN: Balloon 110 + Oval 63 + 2 bodies of 20 atoms 40 + 2 " " 24 " 48 + ---- + Total 261 + ---- + Atomic weight 14.01 + Number weight 261/18 14.50 +</pre> +<font class="sc">Vanadium</font> (<a href="#PlateXII">Plate XII</a>, 2) closely follows scandium, having two +types of funnels. Funnel A only differs from that of scandium by +having a globe (see 4 <i>d</i>) inserted in the ring of four ovoids; funnel +B has a six-atomed, instead of a five-atomed globe at the top, and +slips a third globe containing twenty atoms (see 4 <i>d</i>) between the +two identical with those of scandium (see 4 <i>c</i>). The central +globe has seven atoms in its middle body instead of four. +In this way does vanadium succeed in overtopping scandium +by 126 atoms. + +<pre> +VANADIUM: 3 funnels (A) of 160 atoms 480 + 3 " (B) " 137 " 411 + Central globe 27 + ---- + Total 918 + ---- + Atomic weight 50.84 + Number weight 918/18 51.00 +</pre> +<font class="sc">Niobium</font> (<a href="#PlateXII">Plate XII</a>, 3) +is as closely related to yttrium as is +vanadium to scandium. The little globes that scamper round +the "cigars" contain twelve atoms instead of eight (see 4 <i>e</i>). + + <p>The rest of the funnel is the same. In the central globe both the + tetrahedra have "cigars," and a central nine-atomed globe spins round in + the centre (see 4 <i>f</i>), seventeen atoms being thus added.</p> + +<pre> +NIOBIUM: 6 funnels of 277 atoms 1662 + Central globe 57 + ---- + Total 1719 + ---- + Atomic weight 93.25 + Number weight 1719/18 95.50 +</pre> + <p>III <i>a</i>.—Aluminium, gallium and indium were examined from + this group. They are triatomic, diamagnetic, and positive. The + corresponding group contains phosphorus, arsenic and antimony: bismuth + also belongs to it, but was not examined; they are triatomic, diamagnetic + and negative. They have no central globes.</p> + + <p><a name="PlateXIII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-032.png" target="_blank"><img width="100%" src="images/oc-032.png" + alt="Plate XIII." /></a> + <font class="sc">Plate</font> XIII. + </div> +<font class="sc">Aluminium</font> (<a href="#PlateXIII">Plate XIII</a>, 1), the head of the group, is, as usual, +simple. There are six similar funnels, each containing eight +ovoids, below which is a globe. + +<pre> +ALUMINIUM: 6 funnels of 81 atoms 486 + Atomic weight 26.91 + Number weight 486/18 27.00 +</pre> +<font class="sc">Gallium</font> (<a href="#PlateXIII">Plate XIII</a>, 2) has two segments in every funnel; +in the segment to the left a "cigar" balances a globe, equally +six-atomed, in that of the right, and the globes to right and left +are four-atomed as against three-atomed. In the next row, the +smaller contained globes have six atoms as against four, and +the cones have respectively seven and five. By these little +additions the left-hand funnel boasts one hundred and twelve +atoms as against ninety-eight. + +<pre> +GALLIUM: Left segment 112 atoms } + Right segment 98 " } = 210 + 6 funnels of 210 atoms 1260 + ---- + Atomic weight 69.50 + Number weight 1260/18 70.00 +</pre> +<font class="sc">Indium</font> (<a href="#PlateXIII">Plate XIII</a>, 3) repeats the segments of gallium +exactly, save in the substitution of a sixteen-atomed body for +the seven-atomed cone of the left-hand segment, and a fourteen-atomed +body for the five-atomed corresponding one in gallium. +But each funnel now has three segments instead of two; three +funnels out of the six contain two segments of type A and one of +type B; the remaining three contain two of type B, and one +of type A. + +<pre> +INDIUM: Segment A 121 atoms + Segment B 107 " + 3 funnels of 2 A and 1 B ([242 + 107] 3) 1047 + 3 " " 2 B and 1 A ([214 + 121] 3) 1005 + ---- + Total 2052 + ---- + Atomic weight 114.05 + Number weight 2052/18 114.00 +</pre> + <p>The corresponding negative group, phosphorus, arsenic, and antimony, + run on very similar lines to those we have just examined.</p> + + <p><a name="PlateXIV"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-033.png" target="_blank"><img width="100%" src="images/oc-033.png" + alt="Plate XIV." /></a> + <font class="sc">Plate</font> XIV. + </div> +<font class="sc">Phosphorus</font> (<a href="#PlateXIV">Plate XIV</a>, 1) offers us a very curious arrangement +of atoms, which will give some new forms in breaking up. +Two segments are in each funnel, in fact the only two of +group III <i>a</i> which do not show this arrangement, or a modification +thereof, are aluminium and arsenic. + +<pre> +PHOSPHORUS: Left segment 50 atoms + Right segment 43 " + -- + 93 + 6 funnels of 93 atoms 558 + Atomic weight 30.77 + Number weight 558/18 31.00 +</pre> +<font class="sc">Arsenic</font> (<a href="#PlateXIV">Plate XIV</a>, 2) resembles aluminium in having eight +internal sub-divisions in a funnel, and the ovoids which form +the top ring are identical, save for a minute difference that in +aluminium the ovoids stand the reverse way from those in +arsenic. It will be noted that in the former the top and bottom +triangles of atoms have the apices upwards, and the middle +one has its apex downwards. In arsenic, the top and bottom +ones point downwards, and the middle one upwards. Arsenic +inserts sixteen spheres between the ovoids and globe shown +in aluminium, and thus adds no less than one hundred and +forty-four atoms to each funnel. + +<pre> +ARSENIC: 6 funnels of 225 atoms 1350 + Atomic weight 74.45 + Number weight 1350/18 75.00 +</pre> +<font class="sc">Antimony</font> (<a href="#PlateXIV">Plate XIV</a>, 3) is a close copy of indium, and the +arrangement of types A and B in the funnels is identical. In the +middle rings of both A and B a triplet is substituted for a unit at +the centre of the larger globe. In the lowest body of type A the +"cigar" has vanished, and is represented by a seven-atomed +crystalline form. + +<pre> +ANTIMONY: Segment A 128 atoms + Segment B 113 atoms + 3 funnels of 2 A and 1 B ([256 + 113]3) 1107 + 3 " " 2 B and 1 A ([226 + 128]3) 1056 + ---- + Total 2163 + ---- + Atomic weight 119.34 + Number weight 120.16 +</pre> + <br clear="all" /> +<hr class="short" /> + +<h3>VII.</h3> + +<p class="center" style="margin-top: 2em;"><font class="sc">Boron</font> (<a href="#PlateIII">Plate III</a>, 4, and Plate <a href="#PlateXI">XI</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-034.png" target="_blank"><img width="100%" src="images/oc-034.png" + alt="Dissociation of Boron and Scandium." /></a> + </div> + <p>The disintegration of boron is very simple: the funnels are set free + and assume the spherical form, showing a central "cigar" and four globes + each containing two triplets. The central globe is also set free with its + four quintets, and breaks at once in two. On the meta level the "cigar" + breaks up as usual, and the triplets separate. On the hyper level, the + "cigar" follows its usual course, and the triplets become duads and + units. The globe forms two quintets on the meta level, and these are + resolved into triplets and duads.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Scandium</font> (<a href="#PlateXI">Plate XI</a>, 2).</p> + + <p>In funnel A the "cigar" and the ovoids behave as in boron, but the + "balloon," <i>a</i> 110 (<a href="#PlateXI">XI</a>, 4), escapes from the + funnel as it changes to a sphere, and holds together on the proto level; + on the meta, it yields six globes each containing seven duads, and these + are all set free as duads on the hyper level; the ovoid is also set free + on the meta level becoming a sphere, and on the hyper level liberates its + contained bodies, as two triplets, two quartets and two sextets.</p> + + <p>In funnel B there is a quintet, that behaves like those in the globe + of boron, on escaping from the funnel, in which the bodies remain on the + proto level, with the exception of <i>b</i> 63, which escapes. On the + meta level, <i>c</i> (<a href="#PlateXI">Plate XI</a>, 4), <i>c</i> + assumes a tetrahedral form with six atoms at each point, and these hold + together as sextets on the hyper level. At the meta stage, <i>b</i> (<a + href="#PlateXI">Plate XI</a>, 4 <i>b</i>) sets free seven nine-atomed + bodies, which become free triplets on the hyper. The central globe shows + a cross at its centre, with the four quintets whirling round it, on the + proto level. On the meta, the quintets are set free, and follow the boron + type, while the cross becomes a quartet on the meta level, and two duads + on the hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Yttrium</font> (<a href="#PlateXI">Plate XI</a>, 3).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-035.png" target="_blank"><img width="100%" src="images/oc-035.png" + alt="Dissociation of Scandium (continued) and Yttrium." /></a> + </div> + <p>In yttrium, on the proto level, <i>a</i> 110 and <i>b</i> 63 both + escape from the funnel, and behave as in scandium. The ovoids and + "cigars," set free on the meta level, behave as in boron. The central + globe breaks up as in gold (<a href="#DisAu">pp. 49</a> and 50), four + quartets being set free instead of two quartets and two triplets. We have + only to consider <i>e</i> 8 and <i>d</i> 20 (<a href="#PlateXI">Plate + XI</a>, 4). <i>E</i> 8 is a tetrahedral arrangement of duads on the meta + level, set free as duads on the hyper. <i>D</i> 20 is an arrangement of + pairs of duads at the angles of a square-based pyramid on the meta, and + again free duads on the hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Nitrogen</font> (<a href="#PlateXII">Plate XII</a>, 1).</p> + + <p>Nitrogen has nothing new to show us, all its constituents having + appeared in scandium and yttrium.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Vanadium</font> (<a href="#PlateXII">Plate XII</a>, 2).</p> + + <p>The A funnel of vanadium repeats the A funnel of scandium, with the + addition of <i>d</i> 20, already studied. In the B funnel scandium B is + repeated, with an addition of <i>d</i> 20 and a sextet for a quintet; the + sextet is the <i>c</i> of the "nitrogen balloon." The central globe + follows boron, save that it has a septet for its centre; this was figured + in iodine (<a href="#DisI">p. 48</a>).</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Niobium</font> (<a href="#PlateXII">Plate XII</a>, 3).</p> + + <p>Niobium only differs from yttrium by the introduction of triplets for + duads in <i>e</i>; on the meta level we have therefore triplets, and on + the hyper each triplet yields a duad and a unit. The only other + difference is in the central globe. The tetrahedra separate as usual, but + liberate eight "cigars" instead of four with four quartets; the central + body is simple, becoming three triads at the angles of a triangle on the + meta level, and three duads and three units on the hyper.</p> + + <p><a name="DisAl"></a></p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Aluminium</font> (<a href="#PlateXIII">Plate XIII</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-036.png" target="_blank"><img width="100%" src="images/oc-036.png" + alt="Dissociation of Aluminium and Gallium." /></a> + </div> + <p>The funnels let go the globes, but the eight ovoids remain within + them, so that seven bodies are let loose on the proto level. When the + ovoids are set free at the meta stage they become spherical and a + nine-atomed body is produced, which breaks up into triangles on the hyper + level. The globe becomes a cross at the meta stage, with one atom from + the duads at each arm in addition to its own, and these form four duads + on the hyper, and a unit from the centre.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Gallium</font> (<a href="#PlateXIII">Plate XIII</a>, 2).</p> + + <p>In gallium the funnel disappears on the proto level, setting free its + two contained segments, each of which forms a cylinder, thus yielding + twelve bodies on the proto level. On the meta, the three upper globes in + each left-hand segment are set free, and soon vanish, each liberating a + cigar and two septets, the quartet and triad uniting. On the hyper the + quartet yields two duads but the triangle persists. The second set of + bodies divide on the meta level, forming a sextet and a cross with a duad + at each arm; these on the hyper level divide into two triangles, four + duads and a unit. The seven-atomed cone becomes two triangles united by a + single atom, and on the meta level these form a ring round the unit; on + the hyper they form three duads and a unit.</p> + + <p>In the right-hand segment, the same policy is followed, the four + triads becoming two sextets, while the central body adds a third to the + number. The second ring has a quartet instead of the sextet, but + otherwise breaks up as does that of the left; the quintet at the base + follows that of boron.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Indium</font> (<a href="#PlateXIII">Plate XIII</a>, 3).</p> + + <p>The complication of three segments of different types in each funnel + does not affect the process of breaking up, and indium needs little + attention. A is exactly the same as the left-hand funnel of gallium, save + for the substitution of a globe containing the familiar "cigar" and two + square-based pyramids. B is the same as the right-hand funnel of gallium, + except that its lowest body consists of two square-based pyramids and a + tetrahedron. All these are familiar.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Phosphorus</font> (<a href="#PlateXIV">Plate XIV</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-037.png" target="_blank"><img width="100%" src="images/oc-037.png" + alt="Dissociation of Phosphorus and Antimony." /></a> + </div> + <p>The atoms in the six similar spheres in the segments of the phosphorus + funnel are arranged on the eight angles of a cube, and the central one is + attached to all of them. On the meta level five of the nine atoms hold + together and place themselves on the angles of a square-based pyramid; + the remaining four set themselves on the angle of a tetrahedron. They + yield, on the hyper level, two triads, a duad, and a unit. The remaining + bodies are simple and familiar.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Arsenic</font> (<a href="#PlateXIV">Plate XIV</a>, 2).</p> + + <p>Arsenic shows the same ovoids and globe as have already been broken up + in aluminium (see <a href="#DisAl"><i>ante</i></a>); the remaining + sixteen spheres form nine-atomed bodies on the meta level, all similar to + those of aluminium, thus yielding twelve positive and twelve negative; + the globe also yields a nine-atomed body, twenty-five bodies of nine.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Antimony</font> (<a href="#PlateXIV">Plate XIV</a>, 3).</p> + + <p>Antimony follows closely in the track of gallium and indium, the upper + ring of spheres being identical. In the second ring, a triplet is + substituted for the unit, and this apparently throws the cross out of + gear, and we have a new eleven-atomed figure, which breaks up into a + triplet and two quartets on the hyper level. The lowest seven-atomed + sphere of the three at the base is the same as we met with in copper.</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>VIII.</h3> + +<p class="center" style="margin-top: 2em;">IV.—<font class="sc">The Octahedral Groups.</font></p> + + <p>These groups are at the turns of the spiral in Sir William Crookes' + lemniscates (see <a href="#Crookes">p. 28</a>). On the one side is + carbon, with below it titanium and zirconium; on the other silicon, with + germanium and tin. The characteristic form is an octahedron, rounded at + the angles and a little depressed between the faces in consequence of the + rounding; in fact, we did not, at first, recognize it as an octahedron, + and we called it the "corded bale," the nearest likeness that struck us. + The members of the group are all tetrads, and have eight funnels, opening + on the eight faces of the octahedron. The first group is paramagnetic and + positive; the corresponding one is diamagnetic and negative. The two + groups are not closely allied in composition, though both titanium and + tin have in common the five intersecting tetrahedra at their respective + centres.</p> + + <p><a name="PlateXV"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-038.png" target="_blank"><img width="100%" src="images/oc-038.png" + alt="Plate XV." /></a> + <font class="sc">Plate</font> XV. + </div> +<font class="sc">Carbon</font> (<a href="#PlateIII">Plate III</a>, 5, and +<a href="#PlateXV">XV</a>, 1) gives us the fundamental +octahedral form, which becomes so masked in titanium and +zirconium. As before said (<a href="#Octahedron">p. 30</a>), +the protrusion of the arms in +these suggests the old Rosicrucian symbol of the cross and rose, +but they show at their ends the eight carbon funnels with their +characteristic contents, and thus justify their relationship. The +funnels are in pairs, one of each pair showing three "cigars," +and having as its fellow a funnel in which the middle "cigar" +is truncated, thus loosing one atom. Each "cigar" has a leaf-like +body at its base, and in the centre of the octahedron is a +globe containing four atoms, each within its own wall; these lie +on the dividing lines of the faces, and each holds a pair of the +funnels together. It seems as though this atom had been +economically taken from the "cigar" to form a link. This will +be more clearly seen when we come to separate the parts from +each other. It will be noticed that the atoms in the "leaves" at +the base vary in arrangement, being alternately in a line and in a +triangle. + +<pre> + { left 27 +CARBON: One pair of funnels { right 22 + { centre 1 + -- + 54 + 4 pairs of funnels of 54 atoms 216 + Atomic weight 11.91 + Number weight 216/18 12.00 +</pre> +<font class="sc">Titanium</font> (<a href="#PlateIII">Plate III</a>, 6, and <a href="#PlateXV">XV</a>, 2) +has a complete carbon +atom distributed over the ends of its four arms, a pair of funnels +with their linking atom being seen in each. Then, in each arm, +comes the elaborate body shown as 3 <i>c</i>, with its eighty-eight atoms. +A ring of twelve ovoids (3 <i>d</i>) each holding within itself fourteen +atoms, distributed among three contained globes—two quartets +and a sextet—is a new device for crowding in material. Lastly +comes the central body (4 <i>e</i>) of five intersecting tetrahedra, with a +"cigar" at each of their twenty points—of which only fifteen +can be shown in the diagram—and a ring of seven atoms round +an eighth, that forms the minute centre of the whole. Into this +elaborate body one hundred and twenty-eight atoms are built. + +<pre> +TITANIUM: One carbon atom 216 + 4 <i>c</i> of 88 atoms 352 + 12 <i>d</i> of 14 " 168 + Central globe 128 + ---- + Total 864 + ---- + Atomic weight 47.74 + Number weight 864/18 48.00 +</pre> +<font class="sc">Zirconium</font> (<a href="#PlateXV">Plate XV</a>, 3) has exactly the same outline as +titanium, the carbon atom is similarly distributed, and the central +body is identical. Only in 5 <i>c</i> and <i>d</i> do we find a difference on +comparing them with 4 <i>c</i> and <i>d</i>. The <i>c</i> ovoid in zirconium shows +no less than fifteen secondary globes within the five contained in +the ovoid, and these, in turn, contain altogether sixty-nine smaller +spheres, with two hundred and twelve atoms within them, +arranged in pairs, triplets, quartets, quintets, a sextet and septets. +Finally, the ovoids of the ring are also made more elaborate, +showing thirty-six atoms instead of fourteen. In this way the +clever builders have piled up in zirconium no less than 1624 atoms. + +<pre> +ZIRCONIUM: One Carbon atom 216 + 4 <i>c</i> of 212 atoms 848 + 12 <i>d</i> of 36 " 432 + Central globe 128 + ---- + Total 1624 + ---- + Atomic weight 89.85 + Number weight 90.22 +</pre> + <p><a name="PlateXVI"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-039.png" target="_blank"><img width="100%" src="images/oc-039.png" + alt="Plate XVI." /></a> + <font class="sc">Plate</font> XVI. + </div> +<font class="sc">Silicon</font> (<a href="#PlateXVI">Plate XVI</a>, 1) is at the head of the group which +corresponds to carbon on the opposite turn of the lemniscate. +It has the usual eight funnels, containing four ovoids in a circle, +and a truncated "cigar" but no central body of any kind. All +the funnels are alike. + +<pre> +SILICON: 8 funnels of 65 atoms 520 + Atomic weight 28.18 + Number weight 520/18 28.88 +</pre> +<font class="sc">Germanium</font> (<a href="#PlateXVI">Plate XVI</a>, 2) shows the eight funnels, containing +each four segments (<a href="#PlateXVI">XVI</a>, 4), within which are three ovoids +and a "cigar." In this case the funnels radiate from a central +globe, formed of two intersecting tetrahedra, with "cigars" at +each point enclosing a four-atomed globe. + +<pre> +GERMANIUM: 8 funnels of 156 atoms 1248 + Central globe 52 + ---- + Total 1300 + ---- + Atomic weight 71.93 + Number weight 1300/18 72.22 +</pre> +<font class="sc">Tin</font> (<a href="#PlateXVI">Plate XVI</a>, 3) repeats the funnel of germanium, and the +central globe we met with in titanium, of five intersecting tetrahedra, +carrying twenty "cigars"; the latter, however, omits the +eight-atomed centre of the globe that was found in titanium, and +hence has one hundred and twenty atoms therein instead of one +hundred and twenty-eight. Tin, to make room for the necessary +increase of atoms, adopts the system of spikes, which we met +with in zinc (see <a href="#PlateIX">Plate IX</a>, 2); these spikes, like the +funnels, radiate from the central globe, but are only six in number. +The twenty-one-atomed cone at the head of the spike we have +already seen in silver, and we shall again find it in iridium and +platinum; the pillars are new in detail though not in principle, +the contained globes yielding a series of a triplet, quintet, sextet, +septet, sextet, quintet, triplet. + +<pre> +TIN: 8 funnels of 156 atoms 1248 + 6 spikes of 126 " 756 + Central globe 120 + ---- + Total 2124 + ---- + Atomic weight 118.10 + Number weight 2124/18 118.00 +</pre> +<p class="center" style="margin-top: 2em;">V.—<font class="sc">The Bars Groups.</font></p> + + <p><a name="PlateXVII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-040.png" target="_blank"><img width="100%" src="images/oc-040.png" + alt="Plate XVII." /></a> + <font class="sc">Plate</font> XVII. + </div> + <p>Here, for the first time, we find ourselves a little at issue with the + accepted system of chemistry. Fluorine stands at the head of a + group—called the inter-periodic—whereof the remaining members + are (see Crookes' table, <a href="#Crookes">p. 28</a>), manganese, iron, + cobalt, nickel; ruthenium, rhodium, palladium; osmium, iridium, platinum. + If we take all these as group V, we find that fluorine and manganese are + violently forced into company with which they have hardly any points of + relationship, and that they intrude into an otherwise very harmonious + group of closely similar composition. Moreover, manganese reproduces the + characteristic lithium "spike" and not the bars of those into whose + company it is thrust, and it is thus allied with lithium, with which + indeed it is almost identical. But lithium is placed by Crookes at the + head of a group, the other members of which are potassium, rubidium and + cæsium (the last not examined). Following these identities of + composition, I think it is better to remove manganese and fluorine from + their incongruous companions and place them with lithium and its allies + as V <i>a</i>, the Spike Groups, marking, by the identity of number, + similarities of arrangement which exist, and by the separation the + differences of composition. It is worth while noting what Sir William + Crookes, in his "Genesis of the Elements," remarks on the relations of + the interperiodic group with its neighbours. He says: "These bodies are + interperiodic because their atomic weights exclude them from the small + periods into which the other elements fall, and because their chemical + relations with some members of the neighbouring groups show that they are + probably interperiodic in the sense of being in transition stages."</p> + + <p>Group V in every case shows fourteen bars radiating from a centre as + shown in iron, <a href="#PlateIV">Plate IV</a>, 1. While the form remains + unchanged throughout, the increase of weight is gained by adding to the + number of atoms contained in a bar. The group is made up, not of single + chemical elements, as in all other cases, but of sub-groups, each + containing three elements, and the relations within each sub-group are + very close; moreover the weights only differ by two atoms per bar, making + a weight difference of twenty-eight in the whole. Thus we have per + bar:—</p> + +<pre> +Iron 72 Palladium 136 +Nickel 74 Osmium 245 +Cobalt 76 Iridium 247 +Ruthenium 132 Platinum A 249 +Rhodium 134 Platinum B 257 +</pre> + <p>It will be noticed (<a href="#PlateXVII">Plate XVII</a>, 3, 4, 5,) + that each bar has two sections, and that the three lower sections in + iron, cobalt and nickel are identical; in the upper sections, iron has a + cone of twenty-eight atoms, while cobalt and nickel have each three + ovoids, and of these the middle ones alone differ, and that only in their + upper globes, this globe being four-atomed in cobalt and six-atomed in + nickel.</p> + + <p>The long ovoids within each bar revolve round the central axis of the + bar, remaining parallel with it, while each spins on its own axis; the + iron cone spins round as though impaled on the axis.</p> + +<font class="sc">Iron</font> (Plate <a href="#PlateIV">IV</a>, 1, and <a href="#PlateXVII">XVII</a>, 3): +<pre> + 14 bars of 72 atoms 1008 + Atomic weight 55.47 + Number weight 1008/18 56.00 +</pre> + +<font class="sc">Cobalt</font> (<a href="#PlateXVII">Plate XVII</a>, 4): +<pre> + 14 bars of 74 atoms 1036 + Atomic weight 57.70 + Number weight 1036/18 57.55 +</pre> + +<font class="sc">Nickel</font> (<a href="#PlateXVII">Plate XVII</a>, 4): +<pre> + 14 bars of 76 atoms 1064 + Atomic weight 58.30 + Number weight 1064/18 59.11 +</pre> + + <p>(The weight of cobalt, as given in Erdmann's <i>Lehrbuch</i>, is + 58.55, but Messrs. Parker and Sexton, in <i>Nature</i>, August 1, 1907, + give the weight, as the result of their experiments, as 57.7.)</p> + + <p><a name="PlateXVIII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-041.png" target="_blank"><img width="100%" src="images/oc-041.png" + alt="Plate XVIII." /></a> + <font class="sc">Plate</font> XVIII. + </div> + <p>The next sub-group, ruthenium, rhodium, and palladium, has nothing to + detain us. It will be observed that each bar contains eight segments, + instead of the six of cobalt and nickel; that ruthenium and palladium + have the same number of atoms in their upper ovoids, although in + ruthenium a triplet and quartet represent the septet of palladium; and + that in ruthenium and rhodium the lower ovoids are identical, though one + has the order: sixteen, fourteen, sixteen, fourteen; and the other: + fourteen, sixteen, fourteen, sixteen. One constantly asks oneself: What + is the significance of these minute changes? Further investigators will + probably discover the answer.</p> + +<font class="sc">Ruthenium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 1): +<pre> + 14 bars of 132 atoms 1848 + Atomic weight 100.91 + Number weight 1848/18 102.66 +</pre> + +<font class="sc">Rhodium</font> (<a href="#PlateXVII">Plate XVII</a>, 2): +<pre> + 14 bars of 134 atoms 1876 + Atomic weight 102.23 + Number weight 1876/18 104.22 +</pre> + +<font class="sc">Palladium</font> (<a href="#PlateXVIII">XVIII</a>, 3): +<pre> + 14 bars of 136 atoms 1904 + Atomic weight 105.74 + Number weight 1904/18 105.77 +</pre> + + <p>The third sub-group, osmium, iridium and platinum, is, of course, more + complicated in its composition, but its builders succeed in preserving + the bar form, gaining the necessary increase by a multiplication of + contained spheres within the ovoids. Osmium has one peculiarity: the + ovoid marked <i>a</i> (<a href="#PlateXVIII">XVIII</a>, 4) takes the + place of axis in the upper half of the bar, and the three ovoids, marked + <i>b</i>, revolve round it. In the lower half, the four ovoids, <i>c</i>, + revolve round the central axis. In platinum, we have marked two forms as + platinum A and platinum B, the latter having two four-atomed spheres (<a + href="#PlateXVIII">XVIII</a>, 6 <i>b</i>) in the place of the two + triplets marked <i>a</i>. It may well be that what we have called + platinum B is not a variety of platinum, but a new element, the addition + of two atoms in a bar being exactly that which separates the other + elements within each of the sub-groups. It will be noticed that the four + lower sections of the bars are identical in all the members of this + sub-group, each ovoid containing thirty atoms. The upper ring of ovoids + in iridium and platinum A are also identical, but for the substitution, + in platinum A, of a quartet for a triplet in the second and third ovoids; + their cones are identical, containing twenty-one atoms, like those of + silver and tin.</p> + +<font class="sc">Osmium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 4): +<pre> + 14 bars of 245 atoms 3430 + Atomic weight 189.55 + Number weight 3430/18 190.55 +</pre> + +<font class="sc">Iridium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 5): +<pre> + 14 bars of 247 atoms 3458 + Atomic weight 191.11 + Number weight 3458/18 192.11 +</pre> + +<font class="sc">Platinum A</font> (<a href="#PlateXVIII">Plate XVIII</a>, 6 <i>a</i>): +<pre> + 14 bars of 249 atoms 3486 + Atomic weight 193.66 + Number weight 3486/18 193.34 +</pre> + +<font class="sc">Platinum B</font> (<a href="#PlateXVIII">Plate XVIII</a>, 6 <i>b</i>): +<pre> + 14 bars of 251 atoms 3514 + Atomic weight ------ + Number weight 3514/18 195.22 +</pre> + +<p class="center" style="margin-top: 2em;">V <i>a</i>.—<font class="sc">The Spike Groups</font>.</p> + + <p>I place within this group lithium, potassium, rubidium, fluorine, and + manganese, because of their similarity in internal composition. Manganese + has fourteen spikes, arranged as in the iron group, but radiating from a + central globe. Potassium has nine, rubidium has sixteen, in both cases + radiating from a central globe. Lithium (<a href="#PlateIV">Plate IV</a>, + 2) and fluorine (<a href="#PlateIV">Plate IV</a>, 3) are the two types + which dominate the group, lithium supplying the spike which is reproduced + in all of them, and fluorine the "nitrogen balloon" which appears in all + save lithium. It will be seen that the natural affinities are strongly + marked. They are all monads and paramagnetic; lithium, potassium and + rubidium are positive, while fluorine and manganese are negative. We seem + thus to have a pair, corresponding with each other, as in other cases, + and the interperiodic group is left interperiodic and congruous within + itself.</p> + + <p><a name="PlateXIX"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-042.png" target="_blank"><img width="100%" src="images/oc-042.png" + alt="Plate XIX." /></a> + <font class="sc">Plate</font> XIX. + </div> +<font class="sc">Lithium</font> (<a href="#PlateIV">Plate IV</a>, 2 and <a href="#PlateXIX">Plate XIX</a>, 1) +is a striking and +beautiful form, with its upright cone, or spike, its eight radiating +petals (<i>x</i>) at the base of the cone, and the plate-like support in +the centre of which is a globe, on which the spike rests. The +spike revolves swiftly on its axis, carrying the petals with it; the +plate revolves equally swiftly in the opposite direction. Within +the spike are two globes and a long ovoid; the spheres within +the globe revolve as a cross; within the ovoid are four spheres +containing atoms arranged on tetrahedra, and a central sphere +with an axis of three atoms surrounded by a spinning wheel of six. + +<pre> +LITHIUM: Spike of 63 atoms 63 + 8 petals of 6 atoms 48 + Central globe of 16 atoms 16 + ---- + Total 127 + ---- + Atomic weight 6.98 + Number weight 127/18 7.05 +</pre> +<font class="sc">Potassium</font> (<a href="#PlateXIX">Plate XIX</a>, 2) consists of nine radiating lithium +spikes, but has not petals; its central globe contains one hundred +and thirty-four atoms, consisting of the "nitrogen balloon," +encircled by six four-atomed spheres. + +<pre> +POTASSIUM: 9 bars of 63 atoms 567 + Central globe 134 + ---- + Total 701 + ---- + Atomic weight 38.94 + Number weight 701/18 38.85 +</pre> + <p>(The weight, as determined by Richards [<i>Nature</i>, July 18, 1907] + is 39.114.)</p> + +<font class="sc">Rubidium</font>: (<a href="#PlateXIX">Plate XIX</a>, 3) adds an ovoid, containing three +spheres—two triplets and a sextet—to the lithium spike, of which +it has sixteen, and its central globe is composed of three +"balloons." + +<pre> +RUBIDIUM: 16 spikes of 75 atoms 1200 + Central globe 330 + ---- + Total 1530 + ---- + Atomic weight 84.85 + Number weight 1530/18 85.00 +</pre> + <p>The corresponding negative group consists only of fluorine and + manganese, so far as our investigations have gone.</p> + +<font class="sc">Fluorine</font> (<a href="#PlateIV">Plate IV</a>, 3, and +<a href="#PlateXVII">Plate XVII</a>, 1) is a most peculiar +looking object like a projectile, and gives one the impression +of being ready to shoot off on the smallest provocation. The +eight spikes, reversed funnels, coming to a point, are probably +responsible for this warlike appearance. The remainder of the +body is occupied by two "balloons." + +<pre> +FLUORINE: 8 spikes of 15 atoms 120 + 2 balloons 220 + ---- + Total 340 + ---- + Atomic weight 18.90 + Number weight 340/18 18.88 +</pre> +<font class="sc">Manganese</font> (<a href="#PlateXVII">Plate XVII</a>, 2) has fourteen spikes radiating +from a central "balloon." + +<pre> +MANGANESE: 14 spikes of 63 atoms 882 + Central balloon 110 + ---- + Total 992 + ---- + Atomic weight 54.57 + Number weight 992/18 55.11 +</pre> + <br clear="all" /> +<hr class="short" /> + +<h3>IX.</h3> + + <p>We have now to consider the breaking up of the octahedral groups, and + more and more, as we proceed, do we find that the most complicated + arrangements are reducible to simple elements which are already + familiar.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Carbon</font> (<a href="#PlateIII">Plate III</a>, 5, and <a href="#PlateXV">XV</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-043.png" target="_blank"><img width="100%" src="images/oc-043.png" + alt="Dissociation of Carbon." /></a> + </div> + <p>Carbon is the typical octahedron, and a clear understanding of this + will enable us to follow easily the constitution and disintegration of + the various members of these groups. Its appearance as a chemical atom is + shown on <a href="#PlateIII">Plate III</a>, and see <a + href="#PlateXV">XV</a>, 1. On the proto level the chemical atom breaks up + into four segments, each consisting of a pair of funnels connected by a + single atom; this is the proto element which appears at the end of each + arm of the cross in titanium and zirconium. On the meta level the five + six-atomed "cigars" show two neutral combinations, and the truncated + "cigar" of five atoms is also neutral; the "leaves" yield two forms of + triplet, five different types being thus yielded by each pair of funnels, + exclusive of the linking atom. The hyper level has triplets, duads and + units.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Titanium</font> (<a href="#PlateIII">Plate III</a>, 6, and <a href="#PlateXV">XV</a>, 2, 3).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-044.png" target="_blank"><img width="100%" src="images/oc-044.png" + alt="Dissociation of Titanium and Zirconium." /></a> + </div> + <p>On the proto level, the cross breaks up completely, setting free the + pairs of funnels with the linking atom (<i>a</i> and <i>b</i>), as in + carbon, the four bodies marked <i>c</i>, the twelve marked <i>d</i>, and + the central globe marked <i>e</i>. The latter breaks up again, setting + free its five intersecting cigar-bearing tetrahedra, which follow their + usual course (see Occultum, <a href="#DisOc">p. 44</a>). The eight-atomed + body in the centre makes a ring of seven atoms round a central one, like + that in occultum (see p. 44, diagram B), from which it only differs in + having the central atom, and breaks up similarly, setting the central + atom free. The ovoid <i>c</i> sets free its four contained globes, and + the ovoid <i>d</i> sets free the three within it. Thus sixty-one proto + elements are yielded by titanium. On the meta level, <i>c</i> (titanium + 3) breaks up into star-like and cruciform bodies; the component parts of + these are easily followed; on the hyper level, of the four forms of + triplets one behaves as in carbon, and the others are shown, <i>a</i>, + <i>b</i> and <i>f</i>; the cruciform quintet yields a triplet and a duad, + <i>c</i> and <i>d</i>; the tetrahedra yield two triplets <i>g</i> and + <i>h</i>, and two units; the septet, a triplet <i>k</i> and a quartet + <i>j</i>. On the meta level, the bodies from <i>d</i> behave like their + equivalents in sodium, each <i>d</i> shows two quartets and a sextet, + breaking up, on the hyper level, into four duads and two triads.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Zirconium</font> (<a href="#PlateXV">Plate XV</a>, 2, 5).</p> + + <p>Zirconium reproduces in its <i>c</i> the four forms that we have + already followed in the corresponding <i>c</i> of titanium, and as these + are set free on the proto level, and follow the same course on the meta + and hyper levels, we need not repeat them. The central globe of zirconium + <i>c</i> sets free its nine contained bodies; eight of these are similar + and are figured in the diagram; it will be observed that the central body + is the truncated "cigar" of carbon; their behaviour on the meta and hyper + levels is easily followed there. The central sphere is also figured; the + cigar follows its usual course, and its companions unite into a sextet + and an octet. The <i>d</i> ovoid liberates five bodies, four of which we + have already seen in titanium, as the crosses and sextet of sodium, and + which are figured under titanium; the four quartets within the larger + globe also follow a sodium model, and are given again.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Silicon</font> (<a href="#PlateXVI">Plate XVI</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-045.png" target="_blank"><img width="100%" src="images/oc-045.png" + alt="Dissociation of Silicon and Tin." /></a> + </div> + <p>In silicon, the ovoids are set free from the funnels on the proto + level, and the truncated "cigar," playing the part of a leaf, is also + liberated. This, and the four "cigars," which escape from their ovoids, + pass along their usual course. The quintet and quartet remain together, + and form a nine-atomed body on the meta level, yielding a sextet and a + triplet on the hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Germanium</font> (<a href="#PlateXVI">Plate XVI</a>, 2, 4).</p> + + <p>The central globe, with its two "cigar"-bearing tetrahedra, need not + delay us; the tetrahedra are set free and follow the occultum + disintegration, and the central four atoms is the sodium cross that we + had in titanium. The ovoids (<a href="#PlateXVI">XVI</a>, 4) are + liberated on the proto level, and the "cigar," as usual, bursts its way + through and goes along its accustomed path. The others remain linked on + the meta level, and break up into two triangles and a quintet on the + hyper.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Tin</font> (<a href="#PlateXVI">Plate XVI</a>, 3, 4).</p> + + <p>Here we have only the spike to consider, as the funnels are the same + as in germanium, and the central globe is that of titanium, omitting the + eight atomed centre. The cone of the spike we have had in silver (see <a + href="#DisAg">p. 729</a>, May), and it is set free on the proto level. + The spike, as in zinc, becomes a large sphere, with the single septet in + the centre, the remaining six bodies circling round it on differing + planes. They break up as shown. (Tin is Sn.)</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Iron</font> (<a href="#PlateIV">Plate IV</a>, I, and <a href="#PlateXVII">XVII</a>, 3).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-046.png" target="_blank"><img width="100%" src="images/oc-046.png" + alt="Dissociation of Iron, Cobalt and Nickel." /></a> + </div> + <p>We have already dealt with the affinities of this peculiar group, and + we shall see, in the disintegration, even more clearly, the close + relationships which exist according to the classification which we here + follow.</p> + + <p>The fourteen bars of iron break asunder on the proto level, and each + sets free its contents—a cone and three ovoids, which as usual, + become spheres. The twenty-eight-atomed cone becomes a four-sided figure, + and the ovoids show crystalline contents. They break up, on the meta + level as shown in the diagram, and are all reduced to triplets and duads + on the hyper level.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Cobalt</font> (<a href="#PlateXVII">Plate XVII</a>, 4).</p> + + <p>The ovoids in cobalt are identical with those of iron; the higher + ovoids, which replace the cone of iron, show persistently the crystalline + forms so noticeable throughout this group.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Nickel</font> (<a href="#PlateXVII">Plate XVII</a>, 5).</p> + + <p>The two additional atoms in a bar, which alone separate nickel from + cobalt, are seen in the upper sphere of the central ovoid.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Ruthenium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 1).</p> + + <p>The lower ovoids in ruthenium are identical in composition, with those + of iron, cobalt and nickel and may be studied under Iron. The upper ones + only differ by the addition of a triplet.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Rhodium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 2).</p> + + <p>Rhodium has a septet, which is to be seen in the <i>c</i> of titanium + (see <i>k</i> in the titanium diagram) and differs only in this from its + group.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Palladium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 3).</p> + + <p>In palladium this septet appears as the upper sphere in every ovoid of + the upper ring.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Osmium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 4).</p> + + <p>We have here no new constituents; the ovoids are set free on the proto + level and the contained globes on the meta, all being of familiar forms. + The cigars, as usual, break free on the proto level, and leave their + ovoid with only four contained spheres, which unite into two nine-atomed + bodies as in silicon (see above).</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Iridium</font> (<a href="#PlateXVIII">Plate XVIII</a>, 5.)</p> + + <p>The twenty-one-atomed cone of silver here reappears, and its + proceedings may be followed under that metal (see diagram, <a + href="#DisAg">p. 729</a>, May). The remaining bodies call for no + remark.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Platinum</font> (<a href="#PlateXVIII">Plate XVIII</a>, 6).</p> + + <p>Again the silver cone is with us. The remaining bodies are set free on + the proto level, and their contained spheres on the meta.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Lithium</font> (<a href="#PlateIV">Plate IV</a>, 2, and <a href="#PlateXIX">XIX</a>, 1).</p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-047.png" target="_blank"><img width="100%" src="images/oc-047.png" + alt="Dissociation of Lithium." /></a> + </div> + <p>Here we have some new combinations, which recur persistently in its + allies. The bodies <i>a</i>, in Plate XIX, 1, are at the top and bottom + of the ellipse; they come to right and left of it in the proto state, and + each makes a twelve-atomed body on the meta level.</p> + + <p>The five bodies within the ellipse, three monads and two sextets, show + two which we have had before: <i>d</i>, which behaves like the quintet + and quartet in silicon, after their junction, and <i>b</i>, which we have + had in iron. The two bodies <i>c</i> are a variant of the square-based + pyramid, one atom at the apex, and two at each of the other angles. The + globe, <i>e</i>, is a new form, the four tetrahedra of the proto level + making a single twelve-atomed one on the meta. The body <i>a</i> splits + up into triplets on the hyper; <i>b</i> and <i>d</i> follow their iron + and silicon models; <i>c</i> yields four duads and a unit; <i>e</i> + breaks into four quartets.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Potassium</font> (<a href="#PlateXIX">Plate XIX</a>, 2).</p> + + <p>Potassium repeats the lithium spike; the central globe shows the + "nitrogen balloon," which we already know, and which is surrounded on the + proto level with six tetrahedra, which are set free on the meta and + behave as in cobalt. Hence we have nothing new.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Rubidium</font> (<a href="#PlateXIX">Plate XIX</a>, 3).</p> + + <p>Again the lithium spike, modified slightly by the introduction of an + ovoid, in place of the top sphere; the forms here are somewhat unusual, + and the triangles of the sextet revolve round each other on the meta + level; all the triads break up on the hyper level into duads and + units.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Fluorine</font> (<a href="#PlateIV">Plate IV</a>, 3, and Plate <a href="#PlateXVII">XVII</a>, 1).</p> + + <p>The reversed funnels of fluorine split asunder on the proto level, and + are set free, the "balloons" also floating off independently. The + funnels, as usual, become spheres, and on the meta level set free their + contained bodies, three quartets and a triplet from each of the eight. + The balloons disintegrate in the usual way.</p> + +<p class="center" style="margin-top: 2em;"><font class="sc">Manganese</font> (<a href="#PlateXVII">Plate XVII</a>, 2).</p> + + <p>Manganese offers us nothing new, being composed of "lithium spikes" + and "nitrogen balloons."</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>X.</h3> + +<p class="center" style="margin-top: 2em;">VI.—<font class="sc">The Star Groups</font>.</p> + + <p>We have now reached the last of the groups as arranged on Sir William + Crookes' lemniscates, that forming the "neutral" column; it is headed by + helium, which is <i>sui generis</i>. The remainder are in the form of a + flat star (see <a href="#PlateIV">Plate IV</a>, 4), with a centre formed + of five intersecting and "cigar"-bearing tetrahedra, and six radiating + arms. Ten of these have been observed, five pairs in which the second + member differs but slightly from the first; they are: Neon, Meta-neon; + Argon, Metargon; Krypton, Meta-krypton; Xenon, Meta-xenon; Kalon, + Meta-kalon; the last pair and the meta forms are not yet discovered by + chemists. These all show the presence of a periodic law; taking an arm of + the star in each of the five pairs, we find the number of atoms to be as + follows :—</p> + +<pre> +40 99 224 363 489 +47 106 231 370 496 +</pre> + <p>It will be observed that the meta form in each case shows seven more + atoms than its fellow.</p> + + <p><a name="PlateXX"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-048.png" target="_blank"><img width="100%" src="images/oc-048.png" + alt="Plate XX." /></a> + <font class="sc">Plate</font> XX. + </div> +<font class="sc">Helium</font> (<a href="#PlateIII">Plate III</a>, 5, and +<a href="#PlateXX">Plate XX</a>, 1) shows two "cigar"-bearing +tetrahedra, and two hydrogen triangles, the tetrahedra +revolving round an egg-shaped central body, and the triangles +spinning on their own axes while performing a similar revolution. +The whole has an attractively airy appearance, as of a fairy +element. + +<pre> +HELIUM: Two tetrahedra of 24 atoms 48 + Two triangles of 9 atoms 18 + Central egg 6 + ---- + Total 72 + ---- + Atomic weight 3.94 + Number weight 72/18 4.00 +</pre> +<font class="sc">Neon</font> (<a href="#PlateXX">Plate XX</a>, 2 and 6) has six arms of the pattern shown +in 2, radiating from the central globe. + +<pre> +NEON: Six arms of 40 atoms 240 + Central tetrahedra 120 + + ---- + Total 360 + ---- + Atomic weight 19.90 + Number weight 360/18 20.00 +</pre> +<font class="sc">Meta-neon</font> (<a href="#PlateXX">Plate XX</a>, 3 and 6) differs from its comrade by +the insertion of an additional atom in each of the groups included +in the second body within its arm, and substituting a seven-atomed +group for one of the triplets in neon. + +<pre> +META-NEON: Six arms of 47 atoms 282 + Central tetrahedra 120 + ---- +Total 402 + ---- +Atomic weight ---- +Number weight 402/18 22.33 +</pre> +<font class="sc">Argon</font> (<a href="#PlateXX">Plate XX</a>, 4, 6 and 7) shows within its arms the <i>b</i> 63 +which we met in nitrogen, yttrium, vanadium and niobium, but +not the "balloon," which we shall find with it in krypton and its +congeners. + +<pre> +ARGON: Six arms of 99 atoms 594 + Central tetrahedra 120 + ---- + Total 714 + ---- + Atomic weight 39.60 + Number weight 714/18 39.66 +</pre> +<font class="sc">Metargon</font> (<a href="#PlateXX">Plate XX</a>, 5, 6 and 7) again shows only an +additional seven atoms in each arm. + +<pre> +METARGON: Six arms of 106 atoms 636 + Central tetrahedra 120 + ---- + Total 756 + ---- +Atomic weight ---- +Number weight 756/18 42 +</pre> + <p><a name="PlateXXI"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-049.png" target="_blank"><img width="100%" src="images/oc-049.png" + alt="Plate XXI." /></a> + <font class="sc">Plate</font> XXI. + </div> +<font class="sc">Krypton</font> (<a href="#PlateXXI">Plate XXI</a>, 1 and 4, +and <a href="#PlateXX">Plate XX</a>, 6 and 7) +contains the nitrogen "balloon," elongated by its juxtaposition +to <i>b</i> 63. The central tetrahedra appear as usual. + +<pre> +KRYPTON: Six arms of 224 atoms 1344 + Central tetrahedra 120 + ----- + Total 1464 + ----- + Atomic weight 81.20 + Number weight 1464/18 81.33 +</pre> +<font class="sc">Meta-Krypton</font> differs only from krypton by the substitution +of <i>z</i> for <i>y</i> in each arm of the star. + +<pre> +META-KRYPTON: Six arms of 231 atoms 1386 + Central tetrahedra 120 + ----- + Total 1506 + ----- + Atomic weight ----- + Number weight 1506/18 83.66 +</pre> +<font class="sc">Xenon</font> (<a href="#PlateXXI">Plate XXI</a>, 2 and 4, +and <a href="#PlateXX">Plate XX</a>, 6 and 7) has a +peculiarity shared only by kalon, that <i>x</i> and <i>y</i> are asymmetrical, +the centre of one having three atoms and the centre of the other +two. Is this done in order to preserve the difference of seven +from its comrade? + +<pre> +XENON: Six arms of 363 atoms 2178 + Central tetrahedra 120 + ----- + Total 2298 + ----- + Atomic weight 127.10 + Number weight 2298/18 127.66 +</pre> +<font class="sc">Meta-Xenon</font> differs from xenon only by the substitution of +two <i>z</i>'s for <i>x</i> and <i>y</i>. + +<pre> +META-XENON: Six arms of 370 atoms 2220 + Central tetrahedra 120 + ----- + Total 2340 + ----- + Atomic weight ----- + Number weight 2340/18 130 +</pre> +<font class="sc">Kalon</font> (<a href="#PlateXXI">Plate XXI</a>, 3 and 4, +and <a href="#PlateXX">Plate XX</a>, 6 and 7) has a +curious cone, possessing a kind of tail which we have not +observed elsewhere; <i>x</i> and <i>y</i> show the same asymmetry as in +xenon. + +<pre> +KALON: Six arms of 489 atoms 2934 + Central tetrahedra 120 + ---- + Total 3054 + ---- + Atomic weight ---- + Number weight 3054/18 169.66 +</pre> +<font class="sc">Meta-Kalon</font> again substitutes two <i>z</i>'s for <i>x</i> and <i>y</i>. + +<pre> +META-KALON: Six arms of 496 atoms 2976 + Central tetrahedra 120 + ---- + Total 3096 + ---- + Atomic weight ---- + Number weight 3096/18 172 +</pre> + <p>Only a few atoms of kalon and meta-kalon have been found in the air of + a fair-sized room.</p> + + <p>It does not seem worth while to break up these elements, for their + component parts are so familiar. The complicated groups—<i>a</i> + 110, <i>b</i> 63 and <i>c</i> 120—have all been fully dealt with in + preceding pages.</p> + + <br clear="all" /> +<hr class="short" /> + + <p>There remains now only radium, of the elements which we have, so far, + examined, and that will be now described and will bring to an end this + series of observations. A piece of close and detailed work of this kind, + although necessarily imperfect, will have its value in the future, when + science along its own lines shall have confirmed these researches.</p> + + <p>It will have been observed that our weights, obtained by counting, are + almost invariably slightly in excess of the orthodox ones: it is + interesting that in the latest report of the International Commission + (November 13, 1907), printed in the <i>Proceedings of the Chemical + Society of London</i>, Vol. XXIV, No. 33, and issued on January 25, 1908, + the weight of hydrogen is now taken at 1.008 instead of at 1. This would + slightly raise all the orthodox weights; thus aluminium rises from 26.91 + to 27.1, antimony from 119.34 to 120.2, and so on.</p> + + <br clear="all" /> +<hr class="short" /> + +<h3>XI.</h3> + +<p class="center" style="margin-top: 2em;"><font class="sc">Radium</font>.</p> + + <p><a name="PlateXXII"></a></p> + + <div class="figright" style="width:50%;"> + <a href="images/oc-050.png" target="_blank"><img width="100%" src="images/oc-050.png" + alt="Plate XXII." /></a> + <font class="sc">Plate</font> XXII. + </div> + <p>Radium has the form of a tetrahedron, and it is in the tetrahedral + groups (see article <a href="#CompBe">IV</a>) that we shall find its + nearest congeners; calcium, strontium, chromium, molybdenum resemble it + most closely in general internal arrangements, with additions from zinc + and cadmium. Radium has a complex central sphere (<a + href="#PlateXXII">Plate XXII</a>), extraordinarily vivid and living; the + whirling motion is so rapid that continued accurate observation is very + difficult; the sphere is more closely compacted than the centre-piece in + other elements, and is much larger in proportion to the funnels and + spikes than is the case with the elements above named; reference to <a + href="#PlateVIII">Plate VIII</a> will show that in these the funnels are + much larger than the centres, whereas in radium the diameter of the + sphere and the length of the funnel or spike are about equal. Its heart + consists of a globe containing seven atoms, which assume on the proto + level the prismatic form shown in cadmium, magnesium and selenium. This + globe is the centre of two crosses, the arms of which show respectively + three-atomed and two-atomed groups. Round this sphere are arranged, as on + radii, twenty-four segments, each containing five bodies—four + quintets and a septet—and six loose atoms, which float horizontally + across the mouth of the segment; the whole sphere has thus a kind of + surface of atoms. On the proto level these six atoms in each segment + gather together and form a "cigar." In the rush of the streams presently + to be described one of these atoms is occasionally torn away, but is + generally, if not always, replaced by the capture of another which is + flung into the vacated space.</p> + + <p>Each of the four funnels opens, as usual, on one face of the + tetrahedron, and they resemble the funnels of strontium and molybdenum + but contain three pillars instead of four (<a href="#PlateXXIII">Plate + XXIII</a>). They stand within the funnel as though at the angles of a + triangle, not side by side. The contained bodies, though numerous, + contain forms which are all familiar.</p> + + <p>The spikes alternate with the funnels, and point to the angles of the + tetrahedron as in zinc and cadmium; each spike contains three "lithium + spikes" (see <a href="#PlateXIX">Plate XIX</a>) with a ten-atomed cone or + cap at the top, floating above the three (<a href="#PlateXXIV">Plate + XXIV</a>). The "petals" or "cigars" of lithium exist in the central globe + in the floating atoms, and the four-atomed groups which form the lithium + "plate" may be seen in the funnels, so that the whole of lithium appears + in radium.</p> + + <p>So much for its composition. But a very peculiar result, so far + unobserved elsewhere, arises from the extraordinarily rapid whirling of + the central sphere. A kind of vortex is formed, and there is a constant + and powerful indraught through the funnels. By this, particles are drawn + in from without, and these are swept round with the sphere, their + temperature becoming much raised, and they are then violently shot out + through the spikes. It is these jets which occasionally sweep away an + atom from the surface of the sphere. These "particles" may be atoms, or + they may be bodies from any of the etheric levels; in some cases these + bodies break up and form new combinations. In fact lithium seems like a + kind of vortex of creative activity, drawing in, breaking up, + recombining, shooting forth—a most extraordinary element.</p> + +<pre> +RADIUM: 4 funnels of 618 atoms 2472 + 4 spikes of 199 atoms 796 + Central sphere 819 + ---- + Total 4087 + ---- + Atomic weight ---- + Number weight 4087/18 227.05 +</pre> + <p><a name="PlateXXIII"></a></p> + + <p><a name="PlateXXIV"></a></p> + + <div class="figright" style="width:45%;"> + <a href="images/oc-052.png" target="_blank"><img width="100%" src="images/oc-052.png" + alt="Plate XXIV." /></a> + <font class="sc">Plate</font> XXIV. + </div> + <div class="figleft" style="width:45%;"> + <a href="images/oc-051.png" target="_blank"><img width="100%" src="images/oc-051.png" + alt="Plate XXIII." /></a> + <font class="sc">Plate</font> XXIII. + </div> + <br clear="all" /> + <br clear="all" /> +<hr /> + +<h3>APPENDIX.</h3> + +<p class="center" style="margin-top: 2em;">THE ÆTHER OF SPACE.</p> + + <p>Much discussion has taken place, especially between physicists and + chemists, over the nature of the substances with which all space must, + according to scientific hypothesis, be filled. One side contends that it + is infinitely thinner than the thinnest gas, absolutely frictionless and + without weight; the other asserts that it is denser than the densest + solid. In this substance the ultimate atoms of matter are thought to + float, like motes in a sunbeam, and light, heat and electricity are + supposed to be its vibrations.</p> + + <p>Theosophical investigators, using methods not at the disposal of + physical science, have found that this hypothesis includes under one head + two entirely different and widely separated sets of phenomena. They have + been able to deal with states of matter higher than the gaseous and have + observed that it is by means of vibrations of this finer matter that + light, heat and electricity manifest themselves to us. Seeing that matter + in these higher states thus performs the functions attributed to the + ether of science, they have (perhaps unadvisedly) called these states + etheric, and have thus left themselves without a convenient name for that + substance which fulfils the other part of the scientific + requirements.</p> + + <p>Let us for the moment name this substance <i>koilon</i>, since it + fills what we are in the habit of calling empty space. What mûlaprakrti, + or "mother-matter," is to the inconceivable totality of universes, koilon + is to our particular universe—not to our solar system merely but to + the vast unit which includes all visible suns. Between koilon and + mûlaprakrti there must be various stages, but we have at present no + direct means of estimating their number or of knowing anything whatever + about them.</p> + + <p>In an ancient occult treatise, however, we read of a "colorless + spiritual fluid" "which exists everywhere and forms the first foundation + on which our solar system is built. Outside the latter, it is found in + its pristine purity only between the stars [suns] of the universe.... As + its substance is of a different kind from that known on earth, the + inhabitants of the latter, seeing <i>through it</i>, believe, in their + illusion and ignorance, that it is empty space. There is not one finger's + breadth of void space in the whole boundless universe."<a name="NtA_21" + href="#Nt_21"><sup>[21]</sup></a> "The mother-substance" is said, in this + treatise, to produce this æther of space as its seventh grade of density, + and all objective suns are said to have this for their "substance."</p> + + <p>To any power of sight which we can bring to bear upon it, this koilon + appears to be homogeneous, though it is probably nothing of the kind, + since homogeneity can belong to the mother-substance alone. It is out of + all proportion denser than any other substance known to us, infinitely + denser—if we may be pardoned the expression; so much denser that it + seems to belong to another type, or order, of density. But now comes the + startling part of the investigation: we might expect matter to be a + densification of this koilon; it is nothing of the kind. Matter is not + koilon, but <i>the absence of koilon</i>, and at first sight, matter and + space appear to have changed places, and emptiness has become solidity, + solidity has become emptiness.</p> + + <p>To help us to understand this clearly let us examine the ultimate atom + of the physical plane (see <a href="#UltAtom">pp. 21</a>-23). It is + composed of ten rings or wires, which lie side by side, but never touch + one another. If one of these wires be taken away from the atom, and be, + as it were, untwisted from its peculiar spiral shape and laid out on a + flat surface, it will be seen that it is a complete circle—a + tightly twisted endless coil. This coil is itself a spiral containing + 1680 turns; it can be unwound, and it will then make a much larger + circle. This process of unwinding may be again performed, and a still + bigger circle obtained, and this can be repeated till the seven sets of + spirillæ are all unwound, and we have a huge circle of the tiniest + imaginable dots, like pearls threaded on an invisible string. These dots + are so inconceivably small that many millions of them are needed to make + one ultimate physical atom, and while the exact number is not readily + ascertainable, several different lines of calculation agree in indicating + it as closely approximate to the almost inconceivable total of fourteen + thousand millions. Where figures are so huge, direct counting is + obviously impossible, but fortunately the different parts of the atom are + sufficiently alike to enable us to make an estimate in which the margin + of error is not likely to be very great. The atom consists of ten wires, + which divide themselves naturally into two groups—the three which + are thicker and more prominent, and the seven thinner ones which + correspond to the colors and planets. These latter appear to be identical + in constitution though the forces flowing through them must differ, since + each responds most readily to its own special set of vibrations. By + actual counting it has been discovered that the numbers of coils or + spirillæ of the first order in each wire is 1680; and the proportion of + the different orders of spirillæ to one another is equal in all cases + that have been examined, and correspond with the number of dots in the + ultimate spirillæ of the lowest order. The ordinary sevenfold rule works + quite accurately with the thinner coils, but there is a very curious + variation with regard to the set of three. As may be seen from the + drawings, these are obviously thicker and more prominent, and this + increase of size is produced by an augmentation (so slight as to be + barely perceptible) in the proportion to one another of the different + orders of spirillæ and in the number of dots in the lowest. This + augmentation, amounting at present to not more than .00571428 of the + whole of each case, suggests the unexpected possibility that this portion + of the atom may be somehow actually undergoing a change—may in fact + be in process of growth, as there is reason to suppose that these three + thicker spirals originally resembled the others.</p> + + <p>Since observation shows us that each physical atom is represented by + forty-nine astral atoms, each astral atom by forty-nine mental atoms, and + each mental atom by forty-nine of those on the buddhic plane, we have + here evidently several terms of a regular progressive series, and the + natural presumption is that the series continues where we are no longer + able to observe it. Further probability is lent to this assumption by the + remarkable fact that—if we assume one dot to be what corresponds to + an atom on the seventh or highest of our planes (as is suggested in + <i>The Ancient Wisdom</i>, p. 42) and then suppose the law of + multiplication to begin its operation, so that 49 dots shall form the + atom of the next or sixth plane, 2401 that of the fifth, and so + on—we find that the number indicated for the physical atom + (49<sup>6</sup>) corresponds almost exactly with the calculation based + upon the actual counting of the coils. Indeed, it seems probable that but + for the slight growth of the three thicker wires of the atom the + correspondence would have been perfect.</p> + + <p>It must be noted that a physical atom cannot be directly broken up + into astral atoms. If the unit of force which whirls those millions of + dots into the complicated shape of a physical atom be pressed back by an + effort of will over the threshold of the astral plane, the atom + disappears instantly, for the dots are released. But the same unit of + force, working now upon a higher level, expresses itself not through one + astral atom, but through a group of 49. If the process of pressing back + the unit of force is repeated, so that it energises upon the mental + plane, we find the group there enlarged to the number of 2401 of those + higher atoms. Upon the buddhic plane the number of atoms formed by the + same amount of force is very much greater still—probably the cube + of 49 instead of the square, though they have not been actually counted. + Therefore one physical atom is not <i>composed of</i> forty-nine astral + or 2401 mental atoms, but <i>corresponds</i> to them, in the sense that + the force which manifests through it would show itself on those higher + planes by energising respectively those numbers of atoms.</p> + + <p>The dots, or beads, seem to be the constituents of all matter of which + we, at present, know anything; astral, mental and buddhic atoms are built + of them, so we may fairly regard them as fundamental units, the basis of + matter.</p> + + <p>These units are all alike, spherical and absolutely simple in + construction. Though they are the basis of all matter, they are not + themselves matter; they are not blocks but bubbles. They do not resemble + bubbles floating in the air, which consist of a thin film of water + separating the air within them from the air outside, so that the film has + both an outer and an inner surface. Their analogy is rather with the + bubbles that we see rising in water, before they reach the surface, + bubbles which may be said to have only one surface—that of the + water which is pushed back by the contained air. Just as such bubbles are + not water, but are precisely the spots from which water is absent, so + these units are not koilon, but the absence of koilon—the only + spots where it is not—specks of nothingness floating in it, so to + speak, for the interior of these space-bubbles is an absolute void to the + highest power of vision that we can turn upon them.</p> + + <p>That is the startling, well-nigh incredible, fact. Matter is + nothingness, the space obtained by pressing back an infinitely dense + substance; Fohat "digs holes in space" of a verity, and the holes are the + airy nothingnesses, the bubbles, of which "solid" universes are + built.</p> + + <p>What are they, then, these bubbles, or rather, what is their content, + the force which can blow bubbles in a substance of infinite density? The + ancients called that force "the Breath," a graphic symbol, which seems to + imply that they who used it had seen the kosmic process, had seen the + <font class="sc">Logos</font> when He breathed into the "waters of + space," and made the bubbles which build universes. Scientists may call + this "Force" by what names they will—names are nothing; to us, + Theosophists, it is the Breath of the <font class="sc">Logos</font>, we + know not whether of the <font class="sc">Logos</font> of this solar + system or of a yet mightier Being; the latter would seem the more likely, + since in the above-quoted occult treatise all visible suns are said to + have this as their substance.</p> + + <p>The Breath of the <font class="sc">Logos</font>, then, is the force + which fills these spaces; His the force which holds them open against the + tremendous pressure of the koilon; they are full of His Life, of Himself, + and everything we call matter, on however high or low a plane, is + instinct with divinity; these units of force, of life, the bricks with + which He builds His universe, are His very life scattered through space; + truly is it written: "I established this universe with a portion of + myself." And when He draws in His breath, the waters of space will close + in again, and the universe will have disappeared. It is only a + breath.</p> + + <p>The outbreathing which makes these bubbles is quite distinct from, and + long antecedent to, the three outpourings, or Life-Waves, so familiar to + the theosophical student. The first Life-Wave catches up these bubbles, + and whirls them into the various arrangements which we call the atoms of + the several planes, and aggregates them into the molecules, and on the + physical plane into the chemical elements. The worlds are built out of + these voids, these emptinesses, which seem to us "nothing" but are divine + force. It is matter made from the privation of matter. How true were + H.P.B.'s statements in "The Secret Doctrine": "Matter is nothing but an + aggregation of atomic forces" (iii, 398); "Buddha taught that the + primitive substance is eternal and unchangeable. Its vehicle is the pure + luminous æther, the boundless infinite space, not a void, resulting from + the absence of all forms, but on the contrary, the foundation of all + forms" (iii, 402).</p> + + <p>How vividly, how unmistakably this knowledge brings home to us the + great doctrine of Mâyâ, the transitoriness and unreality of earthly + things, the utterly deceptive nature of appearances! When the candidate + for initiation sees (not merely believes, remember, but actually + <i>sees</i>) that what has always before seemed to him empty space is in + reality a solid mass of inconceivable density, and that the matter which + has appeared to be the one tangible and certain basis of things is not + only by comparison tenuous as gossamer (the "web" spun by + "Father-Mother"), but is actually composed of emptiness and + nothingness—is itself the very negation of matter—then for + the first time he thoroughly appreciates the valuelessness of the + physical senses as guides to the truth. Yet even more clearly still + stands out the glorious certainty of the immanence of the Divine; not + only is everything ensouled by the <font class="sc">Logos</font>, but + even its visible manifestation is literally part of Him, is built of His + very substance, so that Matter as well as Spirit becomes sacred to the + student who really understands.</p> + + <p>The koilon in which all these bubbles are formed undoubtedly + represents a part, and perhaps the principal part, of what science + describes as the luminiferous æther. Whether it is actually the bearer of + the vibrations of light and heat through interplanetary space is as yet + undetermined. It is certain that these vibrations impinge upon and are + perceptible to our bodily senses only through the etheric matter of the + physical plane. But this by no means proves that they are conveyed + through space in the same manner, for we know very little of the extent + to which the physical etheric matter exists in interplanetary and + interstellar space, though the examination of meteoric matter and kosmic + dust shows that at least some of it is scattered there.</p> + + <p>The scientific theory is that the æther has some quality which enables + it to transmit at a certain definite velocity transverse waves of all + lengths and intensities—that velocity being what is commonly called + the speed of light, 190,000 miles per second. Quite probably this may be + true of koilon, and if so it must also be capable of communicating those + waves to bubbles or aggregations of bubbles, and before the light can + reach our eyes there must be a downward transference from plane to plane + similar to that taking place when a thought awakens emotion or causes + action.</p> + + <p>In a recent pamphlet on "The Density of Æther," Sir Oliver Lodge + remarks:—</p> + + <p>"Just as the ratio of mass to volume is small in the case of a solar + system or a nebula or a cobweb, I have been driven to think that the + observed mechanical density of matter is probably an excessively small + fraction of the total density of the substance or æther contained in the + space which it thus partially occupies—the substance of which it + may hypothetically be held to be composed.</p> + + <p>"Thus, for instance, consider a mass of platinum, and assume that its + atoms are composed of electrons, or of some structures not wholly + dissimilar: the space which these bodies actually fill, as compared with + the whole space which in a sense they 'occupy,' is comparable to one + ten-millionth of the whole, even inside each atom; and the fraction is + still smaller if it refers to the visible mass. So that a kind of minimum + estimate of ætherial density, on this basis, would be something like ten + thousand million times that of platinum."</p> + + <p>And further on he adds that this density may well turn out to be fifty + thousand million times that of platinum. "The densest matter known," he + says, "is trivial and gossamer-like compared with the unmodified æther in + the same space."</p> + + <p>Incredible as this seems to our ordinary ideas, it is undoubtedly an + understatement rather than an exaggeration of the true proportion as + observed in the case of koilon. We shall understand how this can be so if + we remember that koilon seems absolutely homogeneous and solid even when + examined by a power of magnification which makes physical atoms appear in + size and arrangement like cottages scattered over a lonely moor, and when + we further add to this the recollection that the bubbles of which these + atoms in turn are composed are themselves what may be not inaptly called + fragments of nothingness.</p> + + <p>In the same pamphlet Sir Oliver Lodge makes a very striking estimate + of the intrinsic energy of the æther. He says: "The total output of a + million-kilowatt power station for thirty million years exists + permanently, and at present inaccessibly in every cubic millimetre of + space." Here again he is probably underestimating the stupendous + truth.</p> + + <p>It may naturally be asked how, if all this be so, it is possible that + we can move about freely in a solid ten thousand million times denser, as + Sir Oliver Lodge says, than platinum. The obvious answer is that, where + densities differ sufficiently, they can move through each other with + perfect freedom; water or air can pass through cloth; air can pass + through water; an astral form passes unconsciously through a physical + wall, or through an ordinary human body; many of us have seen an astral + form walk through a physical, neither being conscious of the passage; it + does not matter whether we say that a ghost has passed through a wall, or + a wall has passed through a ghost. A gnome passes freely through a rock, + and walks about within the earth, as comfortably as we walk about in the + air. A deeper answer is that consciousness can recognize only + consciousness, that since we are of the nature of the <font + class="sc">Logos</font> we can sense only those things which are also of + His nature. These bubbles are His essence, His life, and, therefore, we, + who also are part of Him, can see the matter which is built of his + substance, for all forms are but manifestations of Him. The koilon is to + us non-manifestation, because we have not unfolded powers which enable us + to cognise it, and it may be the manifestation of a loftier order of + <font class="sc">Logoi</font>, utterly beyond our ken.</p> + + <p>As none of our investigators can raise his consciousness to the + highest plane of our universe, the âdi-tattva plane, it may be of + interest to explain how it is possible for them to see what may very + probably be the atom of that plane. That this may be understood it is + essential to remember that the power of magnification by means of which + these experiments are conducted is quite apart from the faculty of + functioning upon one or other of the planes. The latter is the result of + a slow and gradual unfoldment of the Self, while the former is merely a + special development of one of the many powers latent in man. All the + planes are round us here, just as much as any other point in space, and + if a man sharpens his sight until he can see their tiniest atoms he can + make a study of them, even though he may as yet be far from the level + necessary to enable him to understand and function upon the higher planes + as a whole, or to come into touch with the glorious Intelligences who + gather those atoms into vehicles for Themselves.</p> + + <p>A partial analogy may be found in the position of the astronomer with + regard to the stellar universe, or let us say the Milky Way. He can + observe its constituent parts and learn a good deal about them along + various lines, but it is absolutely impossible for him to see it as a + whole from outside, or to form any certain conception of its true shape, + and to know what it really is. Suppose that the universe is, as many of + the ancients thought, some inconceivably vast Being, it is utterly + impossible for us, here in the midst of it, to know what that Being is or + is doing, for that would mean raising ourselves to a height comparable + with His; but we may make extensive and detailed examination of such + particles of His body as happen to be within our reach, for that means + only the patient use of powers and machinery already at our command.</p> + + <p>Let it not be supposed that, in thus unfolding a little more of the + wonders of Divine Truth by pushing our investigations to the very + farthest point at present possible to us, we in any way alter or modify + all that has been written in theosophical books of the shape and + constitution of the physical atom, and of the wonderful and orderly + arrangements by which it is grouped into the various chemical molecules; + all this remains entirely unaffected.</p> + + <p>Nor is any change introduced as regards the three outpourings from the + <font class="sc">Logos</font>, and the marvellous facility with which the + matter of the various planes is by them moulded into forms for the + service of the evolving life. But if we wish to have a right view of the + realities underlying manifestation in this universe, we must to a + considerable extent reverse the ordinary conception as to what this + matter essentially is. Instead of thinking of its ultimate constituents + as solid specks floating in a void, we must realise that it is the + apparent void itself which is solid, and that the specks are but bubbles + on it. That fact once grasped, all the rest remains as before. The + relative position of what we have hitherto called matter and force is + still for us the same as ever; it is only that, on closer examination, + both of these conceptions prove to be variants of force, the one + ensouling combinations of the other, and the real "matter," koilon, is + seen to be something which has hitherto been altogether outside our + scheme of thought.</p> + + <p>In view of this marvellous distribution of Himself in "space," the + familiar concept of the "sacrifice of the <font class="sc">Logos</font>" + takes on a new depth and splendour; this is His "dying in matter," His + "perpetual sacrifice," and it may be the very glory of the <font + class="sc">Logos</font> that He can sacrifice Himself to the uttermost by + thus permeating and making Himself one with that portion of koilon which + He chooses as the field of His universe.</p> + + <p>What koilon is, what its origin, whether it is itself changed by the + Divine Breath which is poured into it—does "Dark Space" thus become + "Bright Space" at the beginning of a manifestation?—these are + questions to which we cannot at present even indicate answers. Perchance + an intelligent study of the great Scriptures of the world may yield + replies.</p> + + <br clear="all" /> +<hr /> + +<h3>NOTES</h3> + +<div class="note"> + <p><a name="Nt_1" href="#NtA_1">[1]</a> See footnote in next Chapter.</p> + + <p><a name="Nt_2" href="#NtA_2">[2]</a> The drawings of the elements were + done by two Theosophical artists, Herr Hecker and Mrs. Kirby, whom we + sincerely thank; the diagrams, showing the details of the construction of + each "element," we owe to the most painstaking labour of Mr. + Jinarâjadâsa, without whose aid it would have been impossible for us to + have presented clearly and definitely the complicated arrangements by + which the chemical elements are built up. We have also to thank him for a + number of most useful notes, implying much careful research, which are + incorporated in the present series, and without which we could not have + written these papers.</p> + + <p><a name="Nt_3" href="#NtA_3">[3]</a> The atomic sub-plane.</p> + + <p><a name="Nt_4" href="#NtA_4">[4]</a> The astral plane.</p> + + <p><a name="Nt_5" href="#NtA_5">[5]</a> Known to Theosophists as Fohat, + the force of which all the physical plane + forces—electricities—are differentiations.</p> + + <p><a name="Nt_6" href="#NtA_6">[6]</a> When Fohat "digs holes in + space."</p> + + <p><a name="Nt_7" href="#NtA_7">[7]</a> The first life-wave, the work of + the third Logos.</p> + + <p><a name="Nt_8" href="#NtA_8">[8]</a> A mâyâ, truly.</p> + + <p><a name="Nt_9" href="#NtA_9">[9]</a> By a certain action of the will, + known to students, it is possible to make such a space by pressing back + and walling off the matter of space.</p> + + <p><a name="Nt_10" href="#NtA_10">[10]</a> Again the astral world.</p> + + <p><a name="Nt_11" href="#NtA_11">[11]</a> Each spirilla is animated by + the life-force of a plane, and four are at present normally active, one + for each round. Their activity in an individual may be prematurely forced + by yoga practice.</p> + + <p><a name="Nt_12" href="#NtA_12">[12]</a> "The ten numbers of the sun. + These are called Dis—in reality space—the forces spread in + space, three of which are contained in the Sun's Atman, or seventh + principle, and seven are the rays shot out by the Sun." The atom is a sun + in miniature in its own universe of the inconceivably minute. Each of the + seven whorls is connected with one of the Planetary Logoi, so that each + Planetary Logos has a direct influence playing on the very matter of + which all things are constructed. It may be supposed that the three, + conveying electricity, a differentiation of Fohat, are related to the + Solar Logoi.</p> + + <p><a name="Nt_13" href="#NtA_13">[13]</a> The action of electricity + opens up ground of large extent, and cannot be dealt with here. Does it + act on the atoms themselves, or on molecules, or sometimes on one and + sometimes on the other? In soft iron, for instance, are the internal + arrangements of the chemical atom forcibly distorted, and do they + elastically return to their original relations when released? and in + steel is the distortion permanent? In all the diagrams the heart-shaped + body, exaggerated to show the depression caused by the inflow and the + point caused by the outflow, is a single atom.</p> + + <p><a name="Nt_14" href="#NtA_14">[14]</a> These sub-planes are familiar + to the Theosophist as gaseous, etheric, super-etheric, sub-atomic, + atomic; or as Gas, Ether 4, Ether 3, Ether 2, Ether 1.</p> + + <p><a name="Nt_15" href="#NtA_15">[15]</a> It must be remembered that the + diagrams represent three-dimensional objects, and the atoms are not all + on a plane, necessarily.</p> + + <p><a name="Nt_16" href="#NtA_16">[16]</a> That is, the surrounding + magnetic fields strike on each other.</p> + + <p><a name="Nt_17" href="#NtA_17">[17]</a> The fifth member of this group + was not sought for.</p> + + <p><a name="Nt_18" href="#NtA_18">[18]</a> This, with references which + appear later (pp. 32, 33, 50, etc.), relates to articles which appeared + in the <i>Theosophist</i>, 1908.</p> + + <p><a name="Nt_19" href="#NtA_19">[19]</a> Since writing the above I have + noticed, in the <i>London, Edinburgh and Dublin Philosophical Magazine + and Journal of Science</i>, conducted by Dr. John Joly and Mr. William + Francis, in an article entitled "Evolution and Devolution of the + Elements," the statement that it is probable that in "the nebulous state + of matter there are four substances, the first two being unknown upon + earth, the third being hydrogen and the fourth ... helium. It also seems + probable that ... hydrogen, the two unknown elements, and helium are the + four original elements from which all the other elements form. To + distinguish them from the others we will term them protons." This is + suggestive as regards hydrogen, but does not help us with regard to + oxygen and nitrogen.</p> + + <p><a name="Nt_20" href="#NtA_20">[20]</a> Theosophists call them + Nature-Spirits, and often use the mediæval term Elementals. Beings + concerned with the elements truly are they, even with chemical + elements.</p> + + <p><a name="Nt_21" href="#NtA_21">[21]</a> Quoted in "The Secret + Doctrine." H.P. 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